From d33378c2f0859d8e5827e0b93e8aee7e695533d5 Mon Sep 17 00:00:00 2001
From: "Quintino A. G. Souza" <quin@unicamp.br>
Date: Sun, 15 Mar 2026 09:19:55 -0300
Subject: [PATCH] =?UTF-8?q?Adiciona=20termos=20de=20n=C3=ADvel=203=20ao=20?=
 =?UTF-8?q?vocabul=C3=A1rio=20MSC=202020?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Expande o CSV de ~597 para ~6100 termos incorporando o terceiro nível
hierárquico (códigos de 5 caracteres, ex.: 03B05). Inclui as traduções
pt-br dos termos de nível 3 já no CSV.

Atualiza MscTermListFormatter e MscTermSelectWidget para suportar a
hierarquia de três níveis, adiciona biblioteca CSS dedicada ao formatter
e adiciona o schema de configuração do formatter.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
---
 .../schema/site_tools_msc_2020.schema.yml     |    7 +
 .../site_tools_msc_2020/css/msc-term-list.css |   12 +
 .../site_tools_msc_2020.libraries.yml         |    6 +
 .../FieldFormatter/MscTermListFormatter.php   |  160 +-
 .../Field/FieldWidget/MscTermSelectWidget.php |  331 +-
 .../migrations/data/msc_2020_terms.csv        | 6699 +++++++++++++++--
 .../migrations/msc_2020_terms_pt_br.yml       |    5 +-
 7 files changed, 6493 insertions(+), 727 deletions(-)
 create mode 100644 modules/site_tools_msc_2020/config/schema/site_tools_msc_2020.schema.yml
 create mode 100644 modules/site_tools_msc_2020/css/msc-term-list.css

diff --git a/modules/site_tools_msc_2020/config/schema/site_tools_msc_2020.schema.yml b/modules/site_tools_msc_2020/config/schema/site_tools_msc_2020.schema.yml
new file mode 100644
index 0000000..daa1c16
--- /dev/null
+++ b/modules/site_tools_msc_2020/config/schema/site_tools_msc_2020.schema.yml
@@ -0,0 +1,7 @@
+field.widget.settings.msc_term_select:
+  type: mapping
+  label: 'Configurações do widget MSC 2020 — Seleção em cascata'
+  mapping:
+    max_depth:
+      type: integer
+      label: 'Nível máximo'
diff --git a/modules/site_tools_msc_2020/css/msc-term-list.css b/modules/site_tools_msc_2020/css/msc-term-list.css
new file mode 100644
index 0000000..fcee091
--- /dev/null
+++ b/modules/site_tools_msc_2020/css/msc-term-list.css
@@ -0,0 +1,12 @@
+.msc-terms-list {
+  list-style: none;
+  padding: 0;
+  margin: 0;
+}
+
+.msc-terms-list__l1-children,
+.msc-terms-list__l2-children {
+  list-style: none;
+  padding-left: 1.5em;
+  margin: 0;
+}
diff --git a/modules/site_tools_msc_2020/site_tools_msc_2020.libraries.yml b/modules/site_tools_msc_2020/site_tools_msc_2020.libraries.yml
index 5bc43ad..c39b896 100644
--- a/modules/site_tools_msc_2020/site_tools_msc_2020.libraries.yml
+++ b/modules/site_tools_msc_2020/site_tools_msc_2020.libraries.yml
@@ -1,2 +1,8 @@
 msc_term_select_widget:
   version: VERSION
+
+msc_term_list:
+  version: VERSION
+  css:
+    component:
+      css/msc-term-list.css: {}
diff --git a/modules/site_tools_msc_2020/src/Plugin/Field/FieldFormatter/MscTermListFormatter.php b/modules/site_tools_msc_2020/src/Plugin/Field/FieldFormatter/MscTermListFormatter.php
index 3323d01..208e073 100644
--- a/modules/site_tools_msc_2020/src/Plugin/Field/FieldFormatter/MscTermListFormatter.php
+++ b/modules/site_tools_msc_2020/src/Plugin/Field/FieldFormatter/MscTermListFormatter.php
@@ -14,9 +14,9 @@ use Symfony\Component\DependencyInjection\ContainerInterface;
 /**
  * Formatter que exibe termos MSC 2020 como lista hierárquica aninhada.
  *
- * Os termos selecionados são agrupados pela categoria pai. O pai aparece
- * como item de primeiro nível e os filhos como sub-lista dentro dele.
- * Opcionalmente, os rótulos são linkados para a página do termo.
+ * Os termos selecionados são agrupados pela sua hierarquia de ancestrais.
+ * Suporta até 3 níveis (área → subcampo → tópico). Ancestrais ausentes na
+ * seleção são carregados automaticamente para garantir o agrupamento correto.
  *
  * @FieldFormatter(
  *   id = "msc_term_list",
@@ -70,8 +70,8 @@ class MscTermListFormatter extends FormatterBase {
   public function settingsForm(array $form, FormStateInterface $form_state): array {
     $elements = parent::settingsForm($form, $form_state);
     $elements['link_to_entity'] = [
-      '#type' => 'checkbox',
-      '#title' => $this->t('Link para a entidade referenciada'),
+      '#type'          => 'checkbox',
+      '#title'         => $this->t('Link para a entidade referenciada'),
       '#default_value' => $this->getSetting('link_to_entity'),
     ];
     return $elements;
@@ -97,97 +97,159 @@ class MscTermListFormatter extends FormatterBase {
       return [];
     }
 
-    $link = (bool) $this->getSetting('link_to_entity');
+    $link    = (bool) $this->getSetting('link_to_entity');
     $storage = $this->entityTypeManager->getStorage('taxonomy_term');
     $terms   = $storage->loadMultiple($tids);
 
-    // Separa pais e filhos; coleta códigos de pais ausentes.
-    $parents_by_code  = [];
-    $children_by_code = [];
-    $missing_codes    = [];
+    // Classifica os termos selecionados pelos seus níveis na hierarquia.
+    // $l1_terms[l1_code]             = term (ou NULL se não selecionado)
+    // $l2_terms[l1_code][l2_code]    = term
+    // $l3_terms[l2_code][l3_code]    = term
+    $l1_terms = [];
+    $l2_terms = [];
+    $l3_terms = [];
+
+    // Códigos de ancestrais que precisam ser carregados para agrupamento.
+    $missing_l2_codes = [];
+    $missing_l1_codes = [];
 
     foreach ($terms as $term) {
       $code = $term->get('field_msc_code')->value;
-      if (strlen($code) === 2) {
-        $parents_by_code[$code] = $term;
+      $len  = strlen($code);
+
+      if ($len === 2) {
+        $l1_terms[$code] = $term;
       }
-      else {
-        $parent_code = substr($code, 0, 2);
-        $children_by_code[$parent_code][] = $term;
-        if (!isset($parents_by_code[$parent_code])) {
-          $missing_codes[$parent_code] = $parent_code;
+      elseif ($len === 3) {
+        $l1_code = substr($code, 0, 2);
+        $l2_terms[$l1_code][$code] = $term;
+        if (!isset($l1_terms[$l1_code])) {
+          $missing_l1_codes[$l1_code] = $l1_code;
+        }
+      }
+      elseif ($len === 5) {
+        $l2_code = substr($code, 0, 3);
+        $l1_code = substr($code, 0, 2);
+        $l3_terms[$l2_code][$code] = $term;
+        if (!array_key_exists($l2_code, $l2_terms[$l1_code] ?? [])) {
+          $missing_l2_codes[$l2_code] = $l2_code;
+        }
+        if (!isset($l1_terms[$l1_code])) {
+          $missing_l1_codes[$l1_code] = $l1_code;
         }
       }
     }
 
-    // Carrega pais que não foram selecionados mas são necessários para agrupar.
-    if (!empty($missing_codes)) {
-      $parent_tids = $storage->getQuery()
+    // Carrega L2 ausentes (necessários para agrupar L3).
+    if (!empty($missing_l2_codes)) {
+      $found_tids = $storage->getQuery()
         ->condition('vid', 'msc_2020')
-        ->condition('field_msc_code', array_values($missing_codes), 'IN')
+        ->condition('field_msc_code', array_values($missing_l2_codes), 'IN')
         ->accessCheck(FALSE)
         ->execute();
-      foreach ($storage->loadMultiple($parent_tids) as $term) {
-        $code = $term->get('field_msc_code')->value;
-        $parents_by_code[$code] = $term;
+      foreach ($storage->loadMultiple($found_tids) as $term) {
+        $code    = $term->get('field_msc_code')->value;
+        $l1_code = substr($code, 0, 2);
+        $l2_terms[$l1_code][$code] = $term;
+        if (!isset($l1_terms[$l1_code])) {
+          $missing_l1_codes[$l1_code] = $l1_code;
+        }
       }
     }
 
-    // Ordena grupos por código.
-    $all_codes = array_unique(
-      array_merge(array_keys($parents_by_code), array_keys($children_by_code))
-    );
-    sort($all_codes);
+    // Carrega L1 ausentes (necessários para agrupar L2 ou L3).
+    if (!empty($missing_l1_codes)) {
+      $found_tids = $storage->getQuery()
+        ->condition('vid', 'msc_2020')
+        ->condition('field_msc_code', array_values($missing_l1_codes), 'IN')
+        ->accessCheck(FALSE)
+        ->execute();
+      foreach ($storage->loadMultiple($found_tids) as $term) {
+        $code = $term->get('field_msc_code')->value;
+        $l1_terms[$code] = $term;
+      }
+    }
 
-    // Monta o render array como lista aninhada.
+    // Coleta todos os códigos L1 que aparecem (diretamente ou como ancestral).
+    $all_l1_codes = array_unique(array_merge(
+      array_keys($l1_terms),
+      array_keys($l2_terms),
+      array_map(fn($c) => substr($c, 0, 2), array_keys($l3_terms)),
+    ));
+    sort($all_l1_codes);
+
+    // Monta o render array como lista aninhada (até 3 níveis).
     $build = [
       '#prefix' => '<ul class="msc-terms-list">',
       '#suffix' => '</ul>',
     ];
 
-    foreach ($all_codes as $i => $code) {
-      $parent   = $parents_by_code[$code] ?? NULL;
-      $children = $children_by_code[$code] ?? [];
+    foreach ($all_l1_codes as $i => $l1_code) {
+      $l1_term  = $l1_terms[$l1_code] ?? NULL;
+      $l2_group = $l2_terms[$l1_code] ?? [];
 
-      usort($children, fn($a, $b) => strcmp(
-        $a->get('field_msc_code')->value,
-        $b->get('field_msc_code')->value,
-      ));
+      // L2 codes relevantes para este L1: os selecionados + os que agrupam L3.
+      $l3_l2_codes = array_filter(
+        array_keys($l3_terms),
+        fn($l2_code) => substr($l2_code, 0, 2) === $l1_code,
+      );
+      $all_l2_codes = array_unique(array_merge(array_keys($l2_group), $l3_l2_codes));
+      sort($all_l2_codes);
 
       $build[$i] = [
-        '#prefix' => '<li class="msc-terms-list__parent">',
+        '#prefix' => '<li class="msc-terms-list__l1 msc-terms-list__parent">',
         '#suffix' => '</li>',
-        'label'   => $this->termLabel($parent, $code, $link),
+        'label'   => $this->termLabel($l1_term, $l1_code, $link),
       ];
 
-      if (!empty($children)) {
+      if (!empty($all_l2_codes)) {
         $build[$i]['children'] = [
-          '#prefix' => '<ul class="msc-terms-list__children">',
+          '#prefix' => '<ul class="msc-terms-list__l1-children msc-terms-list__children">',
           '#suffix' => '</ul>',
         ];
-        foreach ($children as $j => $child) {
-          $child_code = $child->get('field_msc_code')->value;
+
+        foreach ($all_l2_codes as $j => $l2_code) {
+          $l2_term  = $l2_group[$l2_code] ?? NULL;
+          $l3_group = $l3_terms[$l2_code] ?? [];
+          ksort($l3_group);
+
           $build[$i]['children'][$j] = [
-            '#prefix' => '<li class="msc-terms-list__child">',
+            '#prefix' => '<li class="msc-terms-list__l2 msc-terms-list__child">',
             '#suffix' => '</li>',
-          ] + $this->termLabel($child, $child_code, $link);
+            'label'   => $this->termLabel($l2_term, $l2_code, $link),
+          ];
+
+          if (!empty($l3_group)) {
+            $build[$i]['children'][$j]['l3_children'] = [
+              '#prefix' => '<ul class="msc-terms-list__l2-children">',
+              '#suffix' => '</ul>',
+            ];
+            foreach ($l3_group as $k => $l3_term) {
+              $l3_code = $l3_term->get('field_msc_code')->value;
+              $build[$i]['children'][$j]['l3_children'][$k] = [
+                '#prefix' => '<li class="msc-terms-list__l3">',
+                '#suffix' => '</li>',
+              ] + $this->termLabel($l3_term, $l3_code, $link);
+            }
+          }
         }
       }
     }
 
+    $build['#attached']['library'][] = 'site_tools_msc_2020/msc_term_list';
+
     return [$build];
   }
 
   /**
    * Retorna um render array para o rótulo do termo, com ou sem link.
    *
-   * Quando o termo pai não está na seleção (apenas agrupa filhos), é exibido
-   * sem link mesmo que a opção esteja ativa, pois o pai não foi selecionado.
+   * Quando $term é NULL (ancestral não selecionado, apenas usado para
+   * agrupamento) o código é exibido sem link, independentemente da opção.
    *
    * @param \Drupal\taxonomy\TermInterface|null $term
-   *   Termo a exibir, ou NULL se o pai não foi carregado.
    * @param string $code
-   *   Código MSC usado como fallback quando $term é NULL.
+   *   Código MSC, usado como fallback quando $term é NULL.
    * @param bool $link
    *   Se TRUE e $term não é NULL, envolve o rótulo num link.
    */
diff --git a/modules/site_tools_msc_2020/src/Plugin/Field/FieldWidget/MscTermSelectWidget.php b/modules/site_tools_msc_2020/src/Plugin/Field/FieldWidget/MscTermSelectWidget.php
index 3413bc7..8a87641 100644
--- a/modules/site_tools_msc_2020/src/Plugin/Field/FieldWidget/MscTermSelectWidget.php
+++ b/modules/site_tools_msc_2020/src/Plugin/Field/FieldWidget/MscTermSelectWidget.php
@@ -14,10 +14,16 @@ use Symfony\Component\DependencyInjection\ContainerInterface;
 /**
  * Widget de seleção em cascata para o vocabulário MSC 2020.
  *
- * O primeiro select (categorias pai) dispara um AJAX que reconstrói o segundo
- * select (subcampos) via servidor. O valor armazenado no campo é o TID
- * selecionado no segundo select: o TID do pai para "área geral", ou o TID do
- * filho para um subcampo específico.
+ * O número de níveis exibidos é configurável por instância do widget
+ * (opção "Nível máximo" na tela Gerenciar exibição de formulário):
+ *   1 — apenas áreas principais (código de 2 dígitos, ex: "03")
+ *   2 — áreas + subcampos (padrão; código de 3 caracteres, ex: "03B")
+ *   3 — áreas + subcampos + tópicos (código de 5 caracteres, ex: "03B05")
+ *
+ * O valor armazenado no campo é sempre o TID do nível mais profundo
+ * selecionado. A opção "— área geral —" em cada nível armazena o TID
+ * do nível imediatamente superior (o usuário classificou na área mais
+ * ampla, sem especificar um sub-nível).
  *
  * @FieldWidget(
  *   id = "msc_term_select",
@@ -51,6 +57,36 @@ class MscTermSelectWidget extends WidgetBase {
     );
   }
 
+  public static function defaultSettings(): array {
+    return ['max_depth' => 2] + parent::defaultSettings();
+  }
+
+  public function settingsForm(array $form, FormStateInterface $form_state): array {
+    $elements = parent::settingsForm($form, $form_state);
+    $elements['max_depth'] = [
+      '#type' => 'select',
+      '#title' => $this->t('Nível máximo'),
+      '#options' => [
+        1 => $this->t('Nível 1 — apenas áreas principais'),
+        2 => $this->t('Nível 2 — áreas + subcampos'),
+        3 => $this->t('Nível 3 — áreas + subcampos + tópicos'),
+      ],
+      '#default_value' => $this->getSetting('max_depth'),
+    ];
+    return $elements;
+  }
+
+  public function settingsSummary(): array {
+    $labels = [
+      1 => $this->t('Nível 1 — apenas áreas principais'),
+      2 => $this->t('Nível 2 — áreas + subcampos'),
+      3 => $this->t('Nível 3 — áreas + subcampos + tópicos'),
+    ];
+    $summary = parent::settingsSummary();
+    $summary[] = $labels[(int) $this->getSetting('max_depth')] ?? $labels[2];
+    return $summary;
+  }
+
   public static function isApplicable(FieldDefinitionInterface $field_definition): bool {
     $storage = $field_definition->getFieldStorageDefinition();
     if ($storage->getSetting('target_type') !== 'taxonomy_term') {
@@ -61,15 +97,15 @@ class MscTermSelectWidget extends WidgetBase {
   }
 
   public function formElement(FieldItemListInterface $items, $delta, array $element, array &$form, FormStateInterface $form_state): array {
-    $data = $this->buildTermData();
+    $max_depth = (int) $this->getSetting('max_depth');
+    $data = $this->buildTermData($max_depth);
 
-    // getUserInput() contém os dados crus submetidos e NÃO é afetado pelo
-    // #limit_validation_errors do botão "Add another item" (que descarta
-    // valores fora do caminho do campo em $form_state->getValues()).
-    $field_name  = $this->fieldDefinition->getName();
+    $field_name   = $this->fieldDefinition->getName();
     $field_parents = $element['#field_parents'] ?? $form['#parents'] ?? [];
     $base = array_merge($field_parents, [$field_name, $delta]);
 
+    // getUserInput() contém os dados crus submetidos, não afetado pelo
+    // #limit_validation_errors de botões auxiliares.
     $raw_input = $form_state->getUserInput();
     $parent_exists = FALSE;
     $submitted_parent = NestedArray::getValue(
@@ -79,143 +115,280 @@ class MscTermSelectWidget extends WidgetBase {
     );
 
     if ($parent_exists) {
-      // Rebuild pós-submissão (AJAX de parent_select, "Add another item", etc.)
-      $initial_parent = $submitted_parent !== '' ? (int) $submitted_parent : NULL;
+      // Rebuild pós-submissão (AJAX, "Add another item", etc.)
+      $l1 = $submitted_parent !== '' ? (int) $submitted_parent : NULL;
+
       $child_exists = FALSE;
       $submitted_child = NestedArray::getValue(
         $raw_input,
-        array_merge($base, ['child_select']),
+        array_merge($base, ['child_wrapper', 'child_select']),
         $child_exists,
       );
-      $initial_child = ($child_exists && $submitted_child !== '' && $submitted_child !== NULL)
-        ? (int) $submitted_child
-        : $initial_parent;
+      $l2 = ($child_exists && $submitted_child !== '' && $submitted_child !== NULL)
+        ? (int) $submitted_child : $l1;
+
+      $grand_exists = FALSE;
+      $submitted_grand = NestedArray::getValue(
+        $raw_input,
+        array_merge($base, ['child_wrapper', 'grandchild_wrapper', 'grandchild_select']),
+        $grand_exists,
+      );
+      // Quando l2 === l1 (área geral de L2), grandchild não é aplicável;
+      // o default é usar l2 como "área geral" do L3.
+      $l3 = ($grand_exists && $submitted_grand !== '' && $submitted_grand !== NULL)
+        ? (int) $submitted_grand : $l2;
     }
     else {
       // Carga inicial: deriva do valor persistido na entidade.
       $current_value = $items[$delta]->target_id ? (int) $items[$delta]->target_id : NULL;
-      [$initial_parent, $initial_child] = $this->resolveInitialValues($current_value, $data);
+      [$l1, $l2, $l3] = $this->resolveInitialValues($current_value, $data);
     }
 
-    // Opções do segundo select: pré-populadas para a categoria pai atual.
-    $child_options = ['' => $this->t('— selecione uma categoria primeiro —')];
-    if ($initial_parent !== NULL) {
-      $child_options = [];
-      $child_options[$initial_parent] = $this->t('— área geral (sem subcampo) —');
-      $child_options += $data['children'][$initial_parent] ?? [];
-    }
-
-    $field_id  = $field_name . '--' . $delta;
-    $wrapper_id = Html::getId('msc-child-' . $field_id);
-
+    // L1 select.
     $element['parent_select'] = [
       '#type' => 'select',
       '#title' => $element['#title'] ?? $this->t('Área MSC 2020'),
       '#title_display' => $element['#title_display'] ?? 'before',
-      '#options' => ['' => $this->t('— selecione uma categoria —')] + $data['parents'],
-      '#default_value' => $initial_parent ?? '',
+      '#options' => ['' => $this->t('— selecione uma categoria —')] + $data['l1'],
+      '#default_value' => $l1 ?? '',
       '#required' => !empty($element['#required']),
       '#attributes' => ['class' => ['msc-parent-select']],
-      '#ajax' => [
-        'callback' => [static::class, 'rebuildChildSelect'],
-        'wrapper' => $wrapper_id,
-        'event' => 'change',
-      ],
     ];
 
-    // O child_select é o elemento cujo valor é salvo no campo.
-    // #validated => TRUE: aceita o valor submetido sem verificar #options,
-    // necessário pois as opções podem ter mudado entre submissões.
-    $element['child_select'] = [
-      '#type' => 'select',
-      '#title' => $this->t('Subcampo'),
-      '#prefix' => '<div id="' . $wrapper_id . '">',
-      '#suffix' => '</div>',
-      '#options' => $child_options,
-      '#default_value' => $initial_child ?? '',
-      '#validated' => TRUE,
+    if ($max_depth === 1) {
+      // Apenas L1: parent_select é o valor final, sem cascata.
+      return $element;
+    }
+
+    $field_id         = $field_name . '--' . $delta;
+    $child_wrapper_id = Html::getId('msc-child-' . $field_id);
+
+    // AJAX em L1: reconstrói child_wrapper (inclui L2 e, se max_depth=3, L3).
+    $element['parent_select']['#ajax'] = [
+      'callback' => [static::class, 'rebuildChildWrapper'],
+      'wrapper'  => $child_wrapper_id,
+      'event'    => 'change',
+    ];
+
+    // Opções do L2 select.
+    $child_options = ['' => $this->t('— selecione uma categoria primeiro —')];
+    if ($l1 !== NULL) {
+      $child_options = [$l1 => $this->t('— área geral (sem subcampo) —')];
+      $child_options += $data['l2'][$l1] ?? [];
+    }
+
+    // child_wrapper: container com id para o AJAX de L1 substituir.
+    $element['child_wrapper'] = [
+      '#type'       => 'container',
+      '#attributes' => ['id' => $child_wrapper_id],
+    ];
+
+    // L2 select. #validated => TRUE: aceita o valor submetido sem verificar
+    // #options, necessário pois as opções mudam entre submissões.
+    $element['child_wrapper']['child_select'] = [
+      '#type'       => 'select',
+      '#title'      => $this->t('Subcampo'),
+      '#options'    => $child_options,
+      '#default_value' => $l2 ?? '',
+      '#validated'  => TRUE,
       '#attributes' => ['class' => ['msc-child-select']],
     ];
 
+    if ($max_depth === 2) {
+      return $element;
+    }
+
+    // max_depth === 3: AJAX em L2 + L3 select.
+    $grandchild_wrapper_id = Html::getId('msc-grand-' . $field_id);
+
+    $element['child_wrapper']['child_select']['#ajax'] = [
+      'callback' => [static::class, 'rebuildGrandchildWrapper'],
+      'wrapper'  => $grandchild_wrapper_id,
+      'event'    => 'change',
+    ];
+
+    // Opções do L3 select.
+    // Se l2 === l1 (área geral de L2), não há L3 para mostrar.
+    $effective_l2 = ($l2 !== NULL && $l2 !== $l1) ? $l2 : NULL;
+    $grandchild_options = ['' => $this->t('— selecione um subcampo primeiro —')];
+    if ($effective_l2 !== NULL) {
+      $grandchild_options = [$effective_l2 => $this->t('— área geral (sem tópico) —')];
+      $grandchild_options += $data['l3'][$effective_l2] ?? [];
+    }
+
+    // grandchild_wrapper: container com id para o AJAX de L2 substituir.
+    $element['child_wrapper']['grandchild_wrapper'] = [
+      '#type'       => 'container',
+      '#attributes' => ['id' => $grandchild_wrapper_id],
+    ];
+
+    $element['child_wrapper']['grandchild_wrapper']['grandchild_select'] = [
+      '#type'       => 'select',
+      '#title'      => $this->t('Tópico'),
+      '#options'    => $grandchild_options,
+      '#default_value' => $l3 ?? '',
+      '#validated'  => TRUE,
+      '#attributes' => ['class' => ['msc-grandchild-select']],
+    ];
+
     return $element;
   }
 
   /**
-   * Callback AJAX: reconstrói o child_select quando o parent_select muda.
+   * AJAX: reconstrói child_wrapper quando L1 (parent_select) muda.
    *
-   * Drupal faz o rebuild completo do formulário antes de chamar este método,
-   * então formElement() já calculou as opções corretas para o novo pai.
+   * Retorna o container inteiro (L2 select + L3 select se max_depth=3),
+   * resetando ambos ao mesmo tempo.
    */
-  public static function rebuildChildSelect(array &$form, FormStateInterface $form_state): array {
+  public static function rebuildChildWrapper(array &$form, FormStateInterface $form_state): array {
     $parents = $form_state->getTriggeringElement()['#array_parents'];
-    array_pop($parents);
-    $parents[] = 'child_select';
+    array_pop($parents); // remove 'parent_select'
+    $parents[] = 'child_wrapper';
     return NestedArray::getValue($form, $parents);
   }
 
   /**
-   * Carrega todos os termos msc_2020 e retorna arrays de pais e filhos.
-   *
-   * @return array{parents: array<int,string>, children: array<int,array<int,string>>}
+   * AJAX: reconstrói grandchild_wrapper quando L2 (child_select) muda.
    */
-  protected function buildTermData(): array {
+  public static function rebuildGrandchildWrapper(array &$form, FormStateInterface $form_state): array {
+    $parents = $form_state->getTriggeringElement()['#array_parents'];
+    array_pop($parents); // remove 'child_select'
+    $parents[] = 'grandchild_wrapper';
+    return NestedArray::getValue($form, $parents);
+  }
+
+  /**
+   * Carrega todos os termos msc_2020 e retorna arrays por nível.
+   *
+   * @return array{
+   *   l1: array<int,string>,
+   *   l2: array<int,array<int,string>>,
+   *   l3: array<int,array<int,string>>,
+   * }
+   */
+  protected function buildTermData(int $max_depth): array {
     $tree = $this->entityTypeManager
       ->getStorage('taxonomy_term')
       ->loadTree('msc_2020', 0, NULL, TRUE);
 
     $code_to_tid = [];
-    $parents = [];
-    $children = [];
+    $l1 = [];
+    $l2 = [];
+    $l3 = [];
 
+    // Primeira passagem: monta mapa código→TID e coleta L1.
     foreach ($tree as $term) {
       $code = $term->get('field_msc_code')->value;
-      $tid = (int) $term->id();
+      $tid  = (int) $term->id();
       $code_to_tid[$code] = $tid;
       if (strlen($code) === 2) {
-        $parents[$tid] = $code . ' — ' . $term->label();
+        $l1[$tid] = $code . ' — ' . $term->label();
       }
     }
 
-    foreach ($tree as $term) {
-      $code = $term->get('field_msc_code')->value;
-      if (strlen($code) > 2) {
-        $parent_code = substr($code, 0, 2);
-        $parent_tid = $code_to_tid[$parent_code] ?? NULL;
-        if ($parent_tid) {
-          $tid = (int) $term->id();
-          $children[$parent_tid][$tid] = $code . ' — ' . $term->label();
+    if ($max_depth >= 2) {
+      foreach ($tree as $term) {
+        $code = $term->get('field_msc_code')->value;
+        if (strlen($code) === 3) {
+          $parent_code = substr($code, 0, 2);
+          $parent_tid  = $code_to_tid[$parent_code] ?? NULL;
+          if ($parent_tid !== NULL) {
+            $tid = (int) $term->id();
+            $l2[$parent_tid][$tid] = $code . ' — ' . $term->label();
+          }
         }
       }
     }
 
-    return ['parents' => $parents, 'children' => $children];
+    if ($max_depth >= 3) {
+      foreach ($tree as $term) {
+        $code = $term->get('field_msc_code')->value;
+        if (strlen($code) === 5) {
+          $parent_code = substr($code, 0, 3);
+          $parent_tid  = $code_to_tid[$parent_code] ?? NULL;
+          if ($parent_tid !== NULL) {
+            $tid = (int) $term->id();
+            $l3[$parent_tid][$tid] = $code . ' — ' . $term->label();
+          }
+        }
+      }
+    }
+
+    return ['l1' => $l1, 'l2' => $l2, 'l3' => $l3];
   }
 
   /**
-   * Resolve o par (parent_tid, child_tid) a partir do TID persistido.
+   * Resolve o trio (l1_tid, l2_tid, l3_tid) a partir do TID persistido.
    *
-   * @return array{int|null, int|null}
+   * Os valores retornados são os defaults a preencher em cada select:
+   *   l2_initial = l1_tid  → L2 mostrará "área geral"
+   *   l3_initial = l2_tid  → L3 mostrará "área geral"
+   *
+   * @return array{int|null, int|null, int|null}
    */
   protected function resolveInitialValues(?int $current_value, array $data): array {
     if ($current_value === NULL) {
-      return [NULL, NULL];
+      return [NULL, NULL, NULL];
     }
-    if (isset($data['parents'][$current_value])) {
-      return [$current_value, $current_value];
+
+    // TID de L1 armazenado.
+    if (isset($data['l1'][$current_value])) {
+      return [$current_value, $current_value, $current_value];
     }
-    foreach ($data['children'] as $parent_tid => $kids) {
-      if (isset($kids[$current_value])) {
-        return [$parent_tid, $current_value];
+
+    // TID de L2 armazenado.
+    foreach ($data['l2'] as $l1_tid => $l2_terms) {
+      if (isset($l2_terms[$current_value])) {
+        // l3_initial = l2_tid → L3 mostrará "área geral" se existir.
+        return [$l1_tid, $current_value, $current_value];
       }
     }
-    return [NULL, NULL];
+
+    // TID de L3 armazenado.
+    foreach ($data['l3'] as $l2_tid => $l3_terms) {
+      if (isset($l3_terms[$current_value])) {
+        foreach ($data['l2'] as $l1_tid => $l2_terms) {
+          if (isset($l2_terms[$l2_tid])) {
+            return [$l1_tid, $l2_tid, $current_value];
+          }
+        }
+      }
+    }
+
+    return [NULL, NULL, NULL];
   }
 
   public function massageFormValues(array $values, array $form, FormStateInterface $form_state): array {
+    $max_depth = (int) $this->getSetting('max_depth');
+
     foreach ($values as &$value) {
-      $child = $value['child_select'] ?? '';
-      $value = ['target_id' => $child !== '' ? (int) $child : NULL];
+      if ($max_depth === 1) {
+        $stored = ($value['parent_select'] ?? '') !== ''
+          ? (int) $value['parent_select']
+          : NULL;
+      }
+      elseif ($max_depth === 2) {
+        $child  = $value['child_wrapper']['child_select'] ?? '';
+        $stored = $child !== '' ? (int) $child : NULL;
+      }
+      else {
+        // max_depth === 3: usa o valor mais profundo disponível.
+        $grand = $value['child_wrapper']['grandchild_wrapper']['grandchild_select'] ?? '';
+        $child = $value['child_wrapper']['child_select'] ?? '';
+        if ($grand !== '' && $grand !== NULL) {
+          $stored = (int) $grand;
+        }
+        elseif ($child !== '' && $child !== NULL) {
+          $stored = (int) $child;
+        }
+        else {
+          $stored = NULL;
+        }
+      }
+
+      $value = ['target_id' => $stored];
     }
+
     return $values;
   }
 
diff --git a/modules/site_tools_msc_2020_migrate/migrations/data/msc_2020_terms.csv b/modules/site_tools_msc_2020_migrate/migrations/data/msc_2020_terms.csv
index b45c778..41ea7f6 100644
--- a/modules/site_tools_msc_2020_migrate/migrations/data/msc_2020_terms.csv
+++ b/modules/site_tools_msc_2020_migrate/migrations/data/msc_2020_terms.csv
@@ -1,598 +1,6101 @@
-code,name_en,name_pt_br,parent_code
-00,General,Geral,
-00A,General and miscellaneous specific topics,Tópicos gerais e miscelânea,00
-00B,Conference proceedings and collections of articles,Anais de conferências e coletâneas de artigos,00
-01,History and biography,História e biografia,
-01A,History of mathematics and mathematicians,História da matemática e de matemáticos,01
-03,Mathematical logic and foundations,Lógica matemática e fundamentos,
-03A,Philosophical aspects of logic and foundations,Aspectos filosóficos da lógica e dos fundamentos,03
-03B,General logic,Lógica geral,03
-03C,Model theory,Teoria de modelos,03
-03D,Computability and recursion theory,Computabilidade e teoria da recursão,03
-03E,Set theory,Teoria dos conjuntos,03
-03F,Proof theory and constructive mathematics,Teoria da prova e matemática construtiva,03
-03G,Algebraic logic,Lógica algébrica,03
-03H,Nonstandard models,Modelos não padrão,03
-05,Combinatorics,Combinatória,
-05A,Enumerative combinatorics,Combinatória enumerativa,05
-05B,Designs and configurations,Designs e configurações,05
-05C,Graph theory,Teoria dos grafos,05
-05D,Extremal combinatorics,Combinatória extremal,05
-05E,Algebraic combinatorics,Combinatória algébrica,05
-06,Order; lattices; ordered algebraic structures,Ordem; reticulados; estruturas algébricas ordenadas,
-06A,Ordered sets,Conjuntos ordenados,06
-06B,Lattices,Reticulados,06
-06C,Modular lattices; complemented lattices,Reticulados modulares; reticulados complementados,06
-06D,Distributive lattices,Reticulados distributivos,06
-06E,Boolean algebras (Boolean rings),Álgebras de Boole (anéis booleanos),06
-06F,Ordered structures,Estruturas ordenadas,06
-08,General algebraic systems,Sistemas algébricos gerais,
-08A,Algebraic structures,Estruturas algébricas,08
-08B,Varieties,Variedades algébricas,08
-08C,Other classes of algebras,Outras classes de álgebras,08
-11,Number theory,Teoria dos números,
-11A,Elementary number theory,Teoria elementar dos números,11
-11B,Sequences and sets,Sequências e conjuntos,11
-11C,Polynomials and matrices,Polinômios e matrizes,11
-11D,Diophantine equations,Equações diofantinas,11
-11E,Forms and linear algebraic groups,Formas e grupos algébricos lineares,11
-11F,Discontinuous groups and automorphic forms,Grupos descontínuos e formas automórficas,11
-11G,Arithmetic algebraic geometry (Diophantine geometry),Geometria algébrica aritmética (geometria diofantina),11
-11H,Geometry of numbers,Geometria dos números,11
-11J,Diophantine approximation; transcendental number theory,Aproximação diofantina; teoria dos números transcendentes,11
-11K,Probabilistic theory: distribution modulo \(1\); metric theory of algorithms,Teoria probabilística: distribuição módulo \(1\); teoria métrica dos algoritmos,11
-11L,Exponential sums and character sums,Somas exponenciais e somas de caracteres,11
-11M,Zeta and \(L\)-functions: analytic theory,Funções zeta e \(L\): teoria analítica,11
-11N,Multiplicative number theory,Teoria multiplicativa dos números,11
-11P,Additive number theory; partitions,Teoria aditiva dos números; partições,11
-11R,Algebraic number theory: global fields,Teoria algébrica dos números: corpos globais,11
-11S,Algebraic number theory: local fields,Teoria algébrica dos números: corpos locais,11
-11T,Finite fields and commutative rings (number-theoretic aspects),Corpos finitos e anéis comutativos (aspectos da teoria dos números),11
-11U,Connections of number theory and logic,Conexões entre teoria dos números e lógica,11
-11Y,Computational number theory,Teoria computacional dos números,11
-11Z,Miscellaneous applications of number theory,Aplicações diversas da teoria dos números,11
-12,Field theory and polynomials,Teoria dos corpos e polinômios,
-12D,Real and complex fields,Corpos reais e complexos,12
-12E,General field theory,Teoria geral dos corpos,12
-12F,Field extensions,Extensões de corpos,12
-12G,Homological methods (field theory),Métodos homológicos (teoria dos corpos),12
-12H,Differential and difference algebra,Álgebra diferencial e de diferenças,12
-12J,Topological fields,Corpos topológicos,12
-12K,Generalizations of fields,Generalizações de corpos,12
-12L,Connections between field theory and logic,Conexões entre teoria dos corpos e lógica,12
-13,Commutative algebra,Álgebra comutativa,
-13A,General commutative ring theory,Teoria geral de anéis comutativos,13
-13B,Commutative ring extensions and related topics,Extensões de anéis comutativos e tópicos relacionados,13
-13C,Theory of modules and ideals in commutative rings,Teoria de módulos e ideais em anéis comutativos,13
-13D,Homological methods in commutative ring theory,Métodos homológicos na teoria de anéis comutativos,13
-13E,Chain conditions; finiteness conditions in commutative ring theory,Condições de cadeia; condições de finitude na teoria de anéis comutativos,13
-13F,Arithmetic rings and other special commutative rings,Anéis aritméticos e outros anéis comutativos especiais,13
-13G,Integral domains,Domínios de integridade,13
-13H,Local rings and semilocal rings,Anéis locais e semilocais,13
-13J,Topological rings and modules,Anéis e módulos topológicos,13
-13L,Applications of logic to commutative algebra,Aplicações da lógica à álgebra comutativa,13
-13M,Finite commutative rings,Anéis comutativos finitos,13
-13N,Differential algebra,Álgebra diferencial,13
-13P,Computational aspects and applications of commutative rings,Aspectos computacionais e aplicações de anéis comutativos,13
-14,Algebraic geometry,Geometria algébrica,
-14A,Foundations of algebraic geometry,Fundamentos da geometria algébrica,14
-14B,Local theory in algebraic geometry,Teoria local em geometria algébrica,14
-14C,Cycles and subschemes,Ciclos e subesquemas,14
-14D,Families; fibrations in algebraic geometry,Famílias; fibrações em geometria algébrica,14
-14E,Birational geometry,Geometria birracional,14
-14F,(Co)homology theory in algebraic geometry,Teoria de (co)homologia em geometria algébrica,14
-14G,Arithmetic problems in algebraic geometry; Diophantine geometry,Problemas aritméticos em geometria algébrica; geometria diofantina,14
-14H,Curves in algebraic geometry,Curvas em geometria algébrica,14
-14J,Surfaces and higher-dimensional varieties,Superfícies e variedades de dimensão superior,14
-14K,Abelian varieties and schemes,Variedades e esquemas abelianos,14
-14L,Algebraic groups,Grupos algébricos,14
-14M,Special varieties,Variedades especiais,14
-14N,Projective and enumerative algebraic geometry,Geometria algébrica projetiva e enumerativa,14
-14P,Real algebraic and real-analytic geometry,Geometria algébrica real e geometria analítica real,14
-14Q,Computational aspects in algebraic geometry,Aspectos computacionais em geometria algébrica,14
-14R,Affine geometry,Geometria afim,14
-14T,Tropical geometry,Geometria tropical,14
-15,Linear and multilinear algebra; matrix theory,Álgebra linear e multilinear; teoria das matrizes,
-15A,Basic linear algebra,Álgebra linear básica,15
-15B,Special matrices,Matrizes especiais,15
-16,Associative rings and algebras,Anéis e álgebras associativos,
-16B,General and miscellaneous,Geral e miscelânea,16
-16D,Modules; bimodules and ideals in associative algebras,Módulos; bimódulos e ideais em álgebras associativas,16
-16E,Homological methods in associative algebras,Métodos homológicos em álgebras associativas,16
-16G,Representation theory of associative rings and algebras,Teoria da representação de anéis e álgebras associativos,16
-16H,Associative algebras and orders,Álgebras associativas e ordens,16
-16K,Division rings and semisimple Artin rings,Anéis de divisão e anéis de Artin semissimples,16
-16L,Local rings and generalizations,Anéis locais e generalizações,16
-16N,Radicals and radical properties of associative rings,Radicais e propriedades radicais de anéis associativos,16
-16P,Chain conditions; growth conditions; and other forms of finiteness for associative rings and algebras,Condições de cadeia; condições de crescimento; e outras formas de finitude para anéis e álgebras associativos,16
-16R,Rings with polynomial identity,Anéis com identidade polinomial,16
-16S,Associative rings and algebras arising under various constructions,Anéis e álgebras associativos provenientes de diversas construções,16
-16T,Hopf algebras; quantum groups and related topics,Álgebras de Hopf; grupos quânticos e tópicos relacionados,16
-16U,Conditions on elements,Condições sobre elementos,16
-16W,Associative rings and algebras with additional structure,Anéis e álgebras associativos com estrutura adicional,16
-16Y,Generalizations,Generalizações,16
-16Z,Computational aspects of associative rings,Aspectos computacionais de anéis associativos,16
-17,Nonassociative rings and algebras,Anéis e álgebras não associativos,
-17A,General nonassociative rings,Anéis não associativos gerais,17
-17B,Lie algebras and Lie superalgebras,Álgebras de Lie e super-álgebras de Lie,17
-17C,Jordan algebras (algebras; triples and pairs),Álgebras de Jordan (álgebras; triplas e pares),17
-17D,Other nonassociative rings and algebras,Outros anéis e álgebras não associativos,17
-18,Category theory; homological algebra,Teoria das categorias; álgebra homológica,
-18A,General theory of categories and functors,Teoria geral de categorias e funtores,18
-18B,Special categories,Categorias especiais,18
-18C,Categories and theories,Categorias e teorias,18
-18D,Categorical structures,Estruturas categóricas,18
-18E,Categorical algebra,Álgebra categórica,18
-18F,Categories in geometry and topology,Categorias em geometria e topologia,18
-18G,Homological algebra in category theory; derived categories and functors,Álgebra homológica em teoria das categorias; categorias derivadas e funtores,18
-18M,Monoidal categories and operads,Categorias monoidais e operadas,18
-18N,Higher categories and homotopical algebra,Categorias superiores e álgebra homotópica,18
-19,K-theory,K-teoria,
-19A,Grothendieck groups and \(K_0\),Grupos de Grothendieck e \(K_0\),19
-19B,Whitehead groups and \(K_1\),Grupos de Whitehead e \(K_1\),19
-19C,Steinberg groups and \(K_2\),Grupos de Steinberg e \(K_2\),19
-19D,Higher algebraic \(K\)-theory,K-teoria algébrica superior,19
-19E,\(K\)-theory in geometry,K-teoria em geometria,19
-19F,\(K\)-theory in number theory,K-teoria em teoria dos números,19
-19G,\(K\)-theory of forms,K-teoria de formas,19
-19J,Obstructions from topology,Obstruções provenientes da topologia,19
-19K,\(K\)-theory and operator algebras,K-teoria e álgebras de operadores,19
-19L,Topological \(K\)-theory,K-teoria topológica,19
-19M,Miscellaneous applications of \(K\)-theory,Aplicações diversas da K-teoria,19
-20,Group theory and generalizations,Teoria dos grupos e generalizações,
-20A,Foundations,Fundamentos,20
-20B,Permutation groups,Grupos de permutação,20
-20C,Representation theory of groups,Teoria da representação de grupos,20
-20D,Abstract finite groups,Grupos finitos abstratos,20
-20E,Structure and classification of infinite or finite groups,Estrutura e classificação de grupos finitos ou infinitos,20
-20F,Special aspects of infinite or finite groups,Aspectos especiais de grupos finitos ou infinitos,20
-20G,Linear algebraic groups and related topics,Grupos algébricos lineares e tópicos relacionados,20
-20H,Other groups of matrices,Outros grupos de matrizes,20
-20J,Connections of group theory with homological algebra and category theory,Conexões da teoria dos grupos com álgebra homológica e teoria das categorias,20
-20K,Abelian groups,Grupos abelianos,20
-20L,Groupoids (i.e. small categories in which all morphisms are isomorphisms),Grupoides (i.e. pequenas categorias em que todos os morfismos são isomorfismos),20
-20M,Semigroups,Semigrupos,20
-20N,Other generalizations of groups,Outras generalizações de grupos,20
-20P,Probabilistic methods in group theory,Métodos probabilísticos em teoria dos grupos,20
-22,Topological groups; Lie groups,Grupos topológicos; grupos de Lie,
-22A,Topological and differentiable algebraic systems,Sistemas algébricos topológicos e diferenciáveis,22
-22B,Locally compact abelian groups (LCA groups),Grupos abelianos localmente compactos (grupos LCA),22
-22C,Compact groups,Grupos compactos,22
-22D,Locally compact groups and their algebras,Grupos localmente compactos e suas álgebras,22
-22E,Lie groups,Grupos de Lie,22
-22F,Noncompact transformation groups,Grupos de transformações não compactos,22
-26,Real functions,Funções reais,
-26A,Functions of one variable,Funções de uma variável,26
-26B,Functions of several variables,Funções de várias variáveis,26
-26C,Polynomials; rational functions in real analysis,Polinômios; funções racionais em análise real,26
-26D,Inequalities in real analysis,Desigualdades em análise real,26
-26E,Miscellaneous topics in real functions,Tópicos diversos em funções reais,26
-28,Measure and integration,Medida e integração,
-28A,Classical measure theory,Teoria clássica da medida,28
-28B,Set functions; measures and integrals with values in abstract spaces,Funções de conjunto; medidas e integrais com valores em espaços abstratos,28
-28C,Set functions and measures on spaces with additional structure,Funções de conjunto e medidas em espaços com estrutura adicional,28
-28D,Measure-theoretic ergodic theory,Teoria ergódica baseada em medida,28
-28E,Miscellaneous topics in measure theory,Tópicos diversos em teoria da medida,28
-30,Functions of a complex variable,Funções de variável complexa,
-30A,General properties of functions of one complex variable,Propriedades gerais de funções de uma variável complexa,30
-30B,Series expansions of functions of one complex variable,Expansões em série de funções de uma variável complexa,30
-30C,Geometric function theory,Teoria geométrica das funções,30
-30D,Entire and meromorphic functions of one complex variable; and related topics,Funções inteiras e meromorfas de uma variável complexa; e tópicos relacionados,30
-30E,Miscellaneous topics of analysis in the complex plane,Tópicos diversos de análise no plano complexo,30
-30F,Riemann surfaces,Superfícies de Riemann,30
-30G,Generalized function theory,Teoria generalizada das funções,30
-30H,Spaces and algebras of analytic functions of one complex variable,Espaços e álgebras de funções analíticas de uma variável complexa,30
-30J,Function theory on the disc,Teoria das funções no disco,30
-30K,Universal holomorphic functions of one complex variable,Funções holomorfas universais de uma variável complexa,30
-30L,Analysis on metric spaces,Análise em espaços métricos,30
-31,Potential theory,Teoria do potencial,
-31A,Two-dimensional potential theory,Teoria do potencial bidimensional,31
-31B,Higher-dimensional potential theory,Teoria do potencial em dimensão superior,31
-31C,Generalizations of potential theory,Generalizações da teoria do potencial,31
-31D,Axiomatic potential theory,Teoria axiomática do potencial,31
-31E,Potential theory on fractals and metric spaces,Teoria do potencial em fractais e espaços métricos,31
-32,Several complex variables,Várias variáveis complexas,
-32A,Holomorphic functions of several complex variables,Funções holomorfas de várias variáveis complexas,32
-32B,Local analytic geometry,Geometria analítica local,32
-32C,Analytic spaces,Espaços analíticos,32
-32D,Analytic continuation,Continuação analítica,32
-32E,Holomorphic convexity,Convexidade holomorfa,32
-32F,Geometric convexity in several complex variables,Convexidade geométrica em várias variáveis complexas,32
-32G,Deformations of analytic structures,Deformações de estruturas analíticas,32
-32H,Holomorphic mappings and correspondences,Aplicações e correspondências holomorfas,32
-32J,Compact analytic spaces,Espaços analíticos compactos,32
-32K,Generalizations of analytic spaces,Generalizações de espaços analíticos,32
-32L,Holomorphic fiber spaces,Espaços fibrados holomorfos,32
-32M,Complex spaces with a group of automorphisms,Espaços complexos com grupo de automorfismos,32
-32N,Automorphic functions,Funções automórficas,32
-32P,Non-Archimedean analysis,Análise não arquimediana,32
-32Q,Complex manifolds,Variedades complexas,32
-32S,Complex singularities,Singularidades complexas,32
-32T,Pseudoconvex domains,Domínios pseudoconvexos,32
-32U,Pluripotential theory,Teoria pluripotencial,32
-32V,CR manifolds,Variedades CR,32
-32W,Differential operators in several variables,Operadores diferenciais em várias variáveis,32
-33,Special functions,Funções especiais,
-33B,Elementary classical functions,Funções clássicas elementares,33
-33C,Hypergeometric functions,Funções hipergeométricas,33
-33D,Basic hypergeometric functions,Funções hipergeométricas básicas,33
-33E,Other special functions,Outras funções especiais,33
-33F,Computational aspects of special functions,Aspectos computacionais de funções especiais,33
-34,Ordinary differential equations,Equações diferenciais ordinárias,
-34A,General theory for ordinary differential equations,Teoria geral de equações diferenciais ordinárias,34
-34B,Boundary value problems for ordinary differential equations,Problemas de valor de contorno para equações diferenciais ordinárias,34
-34C,Qualitative theory for ordinary differential equations,Teoria qualitativa de equações diferenciais ordinárias,34
-34D,Stability theory for ordinary differential equations,Teoria da estabilidade de equações diferenciais ordinárias,34
-34E,Asymptotic theory for ordinary differential equations,Teoria assintótica de equações diferenciais ordinárias,34
-34F,Ordinary differential equations and systems with randomness,Equações diferenciais ordinárias e sistemas com aleatoriedade,34
-34G,Differential equations in abstract spaces,Equações diferenciais em espaços abstratos,34
-34H,Control problems involving ordinary differential equations,Problemas de controle envolvendo equações diferenciais ordinárias,34
-34K,Functional-differential equations (including equations with delayed; advanced or state-dependent argument),Equações diferencial-funcionais (incluindo equações com argumento atrasado; avançado ou dependente do estado),34
-34L,Ordinary differential operators,Operadores diferenciais ordinários,34
-34M,Ordinary differential equations in the complex domain,Equações diferenciais ordinárias no domínio complexo,34
-34N,Dynamic equations on time scales or measure chains,Equações dinâmicas em escalas de tempo ou cadeias de medida,34
-35,Partial differential equations,Equações diferenciais parciais,
-35A,General topics in partial differential equations,Tópicos gerais em equações diferenciais parciais,35
-35B,Qualitative properties of solutions to partial differential equations,Propriedades qualitativas de soluções de equações diferenciais parciais,35
-35C,Representations of solutions to partial differential equations,Representações de soluções de equações diferenciais parciais,35
-35D,Generalized solutions to partial differential equations,Soluções generalizadas de equações diferenciais parciais,35
-35E,Partial differential equations and systems of partial differential equations with constant coefficients,Equações diferenciais parciais e sistemas com coeficientes constantes,35
-35F,General first-order partial differential equations and systems of first-order partial differential equations,Equações diferenciais parciais de primeira ordem gerais e sistemas,35
-35G,General higher-order partial differential equations and systems of higher-order partial differential equations,Equações diferenciais parciais de ordem superior gerais e sistemas,35
-35H,Close-to-elliptic equations,Equações próximas de elípticas,35
-35J,Elliptic equations and elliptic systems,Equações elípticas e sistemas elípticos,35
-35K,Parabolic equations and parabolic systems,Equações parabólicas e sistemas parabólicos,35
-35L,Hyperbolic equations and hyperbolic systems,Equações hiperbólicas e sistemas hiperbólicos,35
-35M,Partial differential equations of mixed type and mixed-type systems of partial differential equations,Equações diferenciais parciais de tipo misto e sistemas de tipo misto,35
-35N,Overdetermined problems for partial differential equations and systems of partial differential equations,Problemas superdeterminados para equações diferenciais parciais,35
-35P,Spectral theory and eigenvalue problems for partial differential equations,Teoria espectral e problemas de autovalores para equações diferenciais parciais,35
-35Q,Partial differential equations of mathematical physics and other areas of application,Equações diferenciais parciais da física matemática e outras áreas de aplicação,35
-35R,Miscellaneous topics in partial differential equations,Tópicos diversos em equações diferenciais parciais,35
-35S,Pseudodifferential operators and other generalizations of partial differential operators,Operadores pseudodiferenciais e outras generalizações de operadores diferenciais parciais,35
-37,Dynamical systems and ergodic theory,Sistemas dinâmicos e teoria ergódica,
-37A,Ergodic theory,Teoria ergódica,37
-37B,Topological dynamics,Dinâmica topológica,37
-37C,Smooth dynamical systems: general theory,Sistemas dinâmicos suaves: teoria geral,37
-37D,Dynamical systems with hyperbolic behavior,Sistemas dinâmicos com comportamento hiperbólico,37
-37E,Low-dimensional dynamical systems,Sistemas dinâmicos de baixa dimensão,37
-37F,Dynamical systems over complex numbers,Sistemas dinâmicos sobre números complexos,37
-37G,Local and nonlocal bifurcation theory for dynamical systems,Teoria de bifurcação local e não local para sistemas dinâmicos,37
-37H,Random dynamical systems,Sistemas dinâmicos aleatórios,37
-37J,Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems,Aspectos dinâmicos de sistemas hamiltonianos e lagrangianos de dimensão finita,37
-37K,Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems,Aspectos de sistemas dinâmicos em sistemas hamiltonianos e lagrangianos de dimensão infinita,37
-37L,Infinite-dimensional dissipative dynamical systems,Sistemas dinâmicos dissipativos de dimensão infinita,37
-37M,Approximation methods and numerical treatment of dynamical systems,Métodos de aproximação e tratamento numérico de sistemas dinâmicos,37
-37N,Applications of dynamical systems,Aplicações de sistemas dinâmicos,37
-37P,Arithmetic and non-Archimedean dynamical systems,Sistemas dinâmicos aritméticos e não arquimedianos,37
-39,Difference and functional equations,Equações de diferenças e equações funcionais,
-39A,Difference equations,Equações de diferenças,39
-39B,Functional equations and inequalities,Equações funcionais e desigualdades,39
-40,Sequences; series; summability,Sequências; séries; somabilidade,
-40A,Convergence and divergence of infinite limiting processes,Convergência e divergência de processos limites infinitos,40
-40B,Multiple sequences and series,Sequências e séries múltiplas,40
-40C,General summability methods,Métodos gerais de somabilidade,40
-40D,Direct theorems on summability,Teoremas diretos sobre somabilidade,40
-40E,Inversion theorems,Teoremas de inversão,40
-40F,Absolute and strong summability,Somabilidade absoluta e forte,40
-40G,Special methods of summability,Métodos especiais de somabilidade,40
-40H,Functional analytic methods in summability,Métodos de análise funcional em somabilidade,40
-40J,Summability in abstract structures,Somabilidade em estruturas abstratas,40
-41,Approximations and expansions,Aproximações e expansões,
-41A,Approximations and expansions,Aproximações e expansões,41
-42,Fourier analysis,Análise de Fourier,
-42A,Harmonic analysis in one variable,Análise harmônica em uma variável,42
-42B,Harmonic analysis in several variables,Análise harmônica em várias variáveis,42
-42C,Nontrigonometric harmonic analysis,Análise harmônica não trigonométrica,42
-43,Abstract harmonic analysis,Análise harmônica abstrata,
-43A,Abstract harmonic analysis,Análise harmônica abstrata,43
-44,Integral transforms,Transformadas integrais,
-44A,Integral transforms; operational calculus,Transformadas integrais; cálculo operacional,44
-45,Integral equations,Equações integrais,
-45A,Linear integral equations,Equações integrais lineares,45
-45B,Fredholm integral equations,Equações integrais de Fredholm,45
-45C,Eigenvalue problems for integral equations,Problemas de autovalores para equações integrais,45
-45D,Volterra integral equations,Equações integrais de Volterra,45
-45E,Singular integral equations,Equações integrais singulares,45
-45F,Systems of linear integral equations,Sistemas de equações integrais lineares,45
-45G,Nonlinear integral equations,Equações integrais não lineares,45
-45H,Integral equations with miscellaneous special kernels,Equações integrais com núcleos especiais diversos,45
-45J,Integro-ordinary differential equations,Equações integro-diferenciais ordinárias,45
-45K,Integro-partial differential equations,Equações integro-diferenciais parciais,45
-45L,Theoretical approximation of solutions to integral equations,Aproximação teórica de soluções de equações integrais,45
-45M,Qualitative behavior of solutions to integral equations,Comportamento qualitativo de soluções de equações integrais,45
-45N,Abstract integral equations; integral equations in abstract spaces,Equações integrais abstratas; equações integrais em espaços abstratos,45
-45P,Integral operators,Operadores integrais,45
-45Q,Inverse problems for integral equations,Problemas inversos para equações integrais,45
-45R,Random integral equations,Equações integrais aleatórias,45
-46,Functional analysis,Análise funcional,
-46A,Topological linear spaces and related structures,Espaços lineares topológicos e estruturas relacionadas,46
-46B,Normed linear spaces and Banach spaces; Banach lattices,Espaços lineares normados e espaços de Banach; reticulados de Banach,46
-46C,Inner product spaces and their generalizations; Hilbert spaces,Espaços com produto interno e suas generalizações; espaços de Hilbert,46
-46E,Linear function spaces and their duals,Espaços de funções lineares e seus duais,46
-46F,Distributions; generalized functions; distribution spaces,Distribuições; funções generalizadas; espaços de distribuições,46
-46G,Measures; integration; derivative; holomorphy (all involving infinite-dimensional spaces),Medidas; integração; derivada; holomorfismo (em espaços de dimensão infinita),46
-46H,Topological algebras; normed rings and algebras; Banach algebras,Álgebras topológicas; anéis e álgebras normados; álgebras de Banach,46
-46J,Commutative Banach algebras and commutative topological algebras,Álgebras de Banach comutativas e álgebras topológicas comutativas,46
-46K,Topological (rings and) algebras with an involution,Álgebras topológicas com involução,46
-46L,Selfadjoint operator algebras (\(C^*\)-algebras; von Neumann (\(W^*\)-) algebras; etc.),Álgebras de operadores autoadjuntos (\(C^*\)-álgebras; álgebras de von Neumann (\(W^*\)-); etc.),46
-46M,Methods of category theory in functional analysis,Métodos da teoria das categorias em análise funcional,46
-46N,Miscellaneous applications of functional analysis,Aplicações diversas de análise funcional,46
-46S,Other (nonclassical) types of functional analysis,Outros tipos (não clássicos) de análise funcional,46
-46T,Nonlinear functional analysis,Análise funcional não linear,46
-47,Operator theory,Teoria dos operadores,
-47A,General theory of linear operators,Teoria geral de operadores lineares,47
-47B,Special classes of linear operators,Classes especiais de operadores lineares,47
-47C,Individual linear operators as elements of algebraic systems,Operadores lineares individuais como elementos de sistemas algébricos,47
-47D,Groups and semigroups of linear operators; their generalizations and applications,Grupos e semigrupos de operadores lineares; suas generalizações e aplicações,47
-47E,Ordinary differential operators,Operadores diferenciais ordinários,47
-47F,Partial differential operators,Operadores diferenciais parciais,47
-47G,Integral; integro-differential; and pseudodifferential operators,Operadores integrais; integro-diferenciais; e pseudodiferenciais,47
-47H,Nonlinear operators and their properties,Operadores não lineares e suas propriedades,47
-47J,Equations and inequalities involving nonlinear operators,Equações e desigualdades envolvendo operadores não lineares,47
-47L,Linear spaces and algebras of operators,Espaços lineares e álgebras de operadores,47
-47N,Miscellaneous applications of operator theory,Aplicações diversas da teoria dos operadores,47
-47S,Other (nonclassical) types of operator theory,Outros tipos (não clássicos) de teoria dos operadores,47
-49,Calculus of variations and optimal control,Cálculo das variações e controle ótimo,
-49J,Existence theories in calculus of variations and optimal control,Teorias de existência no cálculo das variações e controle ótimo,49
-49K,Optimality conditions,Condições de otimalidade,49
-49L,Hamilton-Jacobi theories,Teorias de Hamilton-Jacobi,49
-49M,Numerical methods in optimal control,Métodos numéricos em controle ótimo,49
-49N,Miscellaneous topics in calculus of variations and optimal control,Tópicos diversos no cálculo das variações e controle ótimo,49
-49Q,Manifolds and measure-geometric topics,Variedades e tópicos de geometria de medida,49
-49R,Variational methods for eigenvalues of operators,Métodos variacionais para autovalores de operadores,49
-49S,Variational principles of physics,Princípios variacionais da física,49
-51,Geometry,Geometria,
-51A,Linear incidence geometry,Geometria de incidência linear,51
-51B,Nonlinear incidence geometry,Geometria de incidência não linear,51
-51C,Ring geometry (Hjelmslev; Barbilian; etc.),Geometria de anéis (Hjelmslev; Barbilian; etc.),51
-51D,Geometric closure systems,Sistemas de fechamento geométrico,51
-51E,Finite geometry and special incidence structures,Geometria finita e estruturas de incidência especiais,51
-51F,Metric geometry,Geometria métrica,51
-51G,Ordered geometries (ordered incidence structures; etc.),Geometrias ordenadas (estruturas de incidência ordenadas; etc.),51
-51H,Topological geometry,Geometria topológica,51
-51J,Incidence groups,Grupos de incidência,51
-51K,Distance geometry,Geometria das distâncias,51
-51L,Geometric order structures,Estruturas de ordem geométrica,51
-51M,Real and complex geometry,Geometria real e complexa,51
-51N,Analytic and descriptive geometry,Geometria analítica e descritiva,51
-51P,Classical or axiomatic geometry and physics,Geometria clássica ou axiomática e física,51
-52,Convex and discrete geometry,Geometria convexa e discreta,
-52A,General convexity,Convexidade geral,52
-52B,Polytopes and polyhedra,Politopos e poliedros,52
-52C,Discrete geometry,Geometria discreta,52
-53,Differential geometry,Geometria diferencial,
-53A,Classical differential geometry,Geometria diferencial clássica,53
-53B,Local differential geometry,Geometria diferencial local,53
-53C,Global differential geometry,Geometria diferencial global,53
-53D,Symplectic geometry; contact geometry,Geometria simplética; geometria de contato,53
-53E,Geometric evolution equations,Equações de evolução geométrica,53
-53Z,Applications of differential geometry to sciences and engineering,Aplicações da geometria diferencial às ciências e à engenharia,53
-54,General topology,Topologia geral,
-54A,Generalities in topology,Generalidades em topologia,54
-54B,Basic constructions in general topology,Construções básicas em topologia geral,54
-54C,Maps and general types of topological spaces defined by maps,Aplicações e tipos gerais de espaços topológicos definidos por aplicações,54
-54D,Fairly general properties of topological spaces,Propriedades bastante gerais de espaços topológicos,54
-54E,Topological spaces with richer structures,Espaços topológicos com estruturas mais ricas,54
-54F,Special properties of topological spaces,Propriedades especiais de espaços topológicos,54
-54G,Peculiar topological spaces,Espaços topológicos peculiares,54
-54H,Connections of general topology with other structures; applications,Conexões da topologia geral com outras estruturas; aplicações,54
-54J,Nonstandard topology,Topologia não padrão,54
-55,Algebraic topology,Topologia algébrica,
-55M,Classical topics in algebraic topology,Tópicos clássicos em topologia algébrica,55
-55N,Homology and cohomology theories in algebraic topology,Teorias de homologia e cohomologia em topologia algébrica,55
-55P,Homotopy theory,Teoria da homotopia,55
-55Q,Homotopy groups,Grupos de homotopia,55
-55R,Fiber spaces and bundles in algebraic topology,Espaços fibrados e fibrados em topologia algébrica,55
-55S,Operations and obstructions in algebraic topology,Operações e obstruções em topologia algébrica,55
-55T,Spectral sequences in algebraic topology,Sequências espectrais em topologia algébrica,55
-55U,Applied homological algebra and category theory in algebraic topology,Álgebra homológica aplicada e teoria das categorias em topologia algébrica,55
-57,Manifolds and cell complexes,Variedades e complexos celulares,
-57K,Low-dimensional topology in specific dimensions,Topologia de baixa dimensão em dimensões específicas,57
-57M,General low-dimensional topology,Topologia geral de baixa dimensão,57
-57N,Topological manifolds,Variedades topológicas,57
-57P,Generalized manifolds,Variedades generalizadas,57
-57Q,PL-topology,Topologia PL,57
-57R,Differential topology,Topologia diferencial,57
-57S,Topological transformation groups,Grupos de transformações topológicas,57
-57T,Homology and homotopy of topological groups and related structures,Homologia e homotopia de grupos topológicos e estruturas relacionadas,57
-57Z,Relations of manifolds and cell complexes with science and engineering,Relações de variedades e complexos celulares com ciências e engenharia,57
-58,Global analysis; analysis on manifolds,Análise global; análise em variedades,
-58A,General theory of differentiable manifolds,Teoria geral de variedades diferenciáveis,58
-58B,Infinite-dimensional manifolds,Variedades de dimensão infinita,58
-58C,Calculus on manifolds; nonlinear operators,Cálculo em variedades; operadores não lineares,58
-58D,Spaces and manifolds of mappings (including nonlinear versions of 46Exx),Espaços e variedades de aplicações (incluindo versões não lineares de 46Exx),58
-58E,Variational problems in infinite-dimensional spaces,Problemas variacionais em espaços de dimensão infinita,58
-58H,Pseudogroups; differentiable groupoids and general structures on manifolds,Pseudogrupos; grupoides diferenciáveis e estruturas gerais em variedades,58
-58J,Partial differential equations on manifolds; differential operators,Equações diferenciais parciais em variedades; operadores diferenciais,58
-58K,Theory of singularities and catastrophe theory,Teoria das singularidades e teoria das catástrofes,58
-58Z,Applications of global analysis to the sciences,Aplicações da análise global às ciências,58
-60,Probability theory and stochastic processes,Teoria da probabilidade e processos estocásticos,
-60A,Foundations of probability theory,Fundamentos da teoria da probabilidade,60
-60B,Probability theory on algebraic and topological structures,Teoria da probabilidade em estruturas algébricas e topológicas,60
-60C,Combinatorial probability,Probabilidade combinatória,60
-60D,Geometric probability and stochastic geometry,Probabilidade geométrica e geometria estocástica,60
-60E,Distribution theory,Teoria das distribuições,60
-60F,Limit theorems in probability theory,Teoremas limite em teoria da probabilidade,60
-60G,Stochastic processes,Processos estocásticos,60
-60H,Stochastic analysis,Análise estocástica,60
-60J,Markov processes,Processos de Markov,60
-60K,Special processes,Processos especiais,60
-60L,Rough analysis,Análise rough,60
-62,Statistics,Estatística,
-62A,Foundational topics in statistics,Tópicos fundamentais em estatística,62
-62B,Sufficiency and information,Suficiência e informação,62
-62C,Statistical decision theory,Teoria da decisão estatística,62
-62D,Statistical sampling theory and related topics,Teoria da amostragem estatística e tópicos relacionados,62
-62E,Statistical distribution theory,Teoria de distribuições estatísticas,62
-62F,Parametric inference,Inferência paramétrica,62
-62G,Nonparametric inference,Inferência não paramétrica,62
-62H,Multivariate analysis,Análise multivariada,62
-62J,Linear inference; regression,Inferência linear; regressão,62
-62K,Design of statistical experiments,Planejamento de experimentos estatísticos,62
-62L,Sequential statistical methods,Métodos estatísticos sequenciais,62
-62M,Inference from stochastic processes,Inferência a partir de processos estocásticos,62
-62N,Survival analysis and censored data,Análise de sobrevivência e dados censurados,62
-62P,Applications of statistics,Aplicações da estatística,62
-62Q,Statistical tables,Tabelas estatísticas,62
-62R,Statistics on algebraic and topological structures,Estatística em estruturas algébricas e topológicas,62
-65,Numerical analysis,Análise numérica,
-65A,Tables in numerical analysis,Tabelas em análise numérica,65
-65B,Acceleration of convergence in numerical analysis,Aceleração da convergência em análise numérica,65
-65C,Probabilistic methods; stochastic differential equations,Métodos probabilísticos; equações diferenciais estocásticas,65
-65D,Numerical approximation and computational geometry (primarily algorithms),Aproximação numérica e geometria computacional (principalmente algoritmos),65
-65E,Numerical methods in complex analysis (potential theory; etc.),Métodos numéricos em análise complexa (teoria do potencial; etc.),65
-65F,Numerical linear algebra,Álgebra linear numérica,65
-65G,Error analysis and interval analysis,Análise de erros e análise intervalar,65
-65H,Nonlinear algebraic or transcendental equations,Equações algébricas ou transcendentes não lineares,65
-65J,Numerical analysis in abstract spaces,Análise numérica em espaços abstratos,65
-65K,Numerical methods for mathematical programming; optimization and variational techniques,Métodos numéricos para programação matemática; otimização e técnicas variacionais,65
-65L,Numerical methods for ordinary differential equations,Métodos numéricos para equações diferenciais ordinárias,65
-65M,Numerical methods for partial differential equations; initial value and time-dependent initial-boundary value problems,Métodos numéricos para equações diferenciais parciais; problemas de valor inicial e de contorno dependentes do tempo,65
-65N,Numerical methods for partial differential equations; boundary value problems,Métodos numéricos para equações diferenciais parciais; problemas de valor de contorno,65
-65P,Numerical problems in dynamical systems,Problemas numéricos em sistemas dinâmicos,65
-65Q,Numerical methods for difference and functional equations; recurrence relations,Métodos numéricos para equações de diferenças e equações funcionais; relações de recorrência,65
-65R,Numerical methods for integral equations; integral transforms,Métodos numéricos para equações integrais; transformadas integrais,65
-65S,Graphical methods in numerical analysis,Métodos gráficos em análise numérica,65
-65T,Numerical methods in Fourier analysis,Métodos numéricos em análise de Fourier,65
-65Y,Computer aspects of numerical algorithms,Aspectos computacionais de algoritmos numéricos,65
-65Z,Applications to the sciences,Aplicações às ciências,65
-68,Computer science,Ciência da computação,
-68M,Computer system organization,Organização de sistemas computacionais,68
-68N,Theory of software,Teoria do software,68
-68P,Theory of data,Teoria dos dados,68
-68Q,Theory of computing,Teoria da computação,68
-68R,Discrete mathematics in relation to computer science,Matemática discreta em relação à ciência da computação,68
-68T,Artificial intelligence,Inteligência artificial,68
-68U,Computing methodologies and applications,Metodologias e aplicações da computação,68
-68V,Computer science support for mathematical research and practice,Suporte da ciência da computação à pesquisa e prática matemática,68
-68W,Algorithms in computer science,Algoritmos em ciência da computação,68
-70,Mechanics of particles and systems,Mecânica de partículas e sistemas,
-70A,Axiomatics; foundations,Axiomática; fundamentos,70
-70B,Kinematics,Cinemática,70
-70C,Statics,Estática,70
-70E,Dynamics of a rigid body and of multibody systems,Dinâmica de corpo rígido e de sistemas multicorpos,70
-70F,Dynamics of a system of particles; including celestial mechanics,Dinâmica de um sistema de partículas; incluindo mecânica celeste,70
-70G,General models; approaches; and methods in mechanics of particles and systems,Modelos gerais; abordagens; e métodos em mecânica de partículas e sistemas,70
-70H,Hamiltonian and Lagrangian mechanics,Mecânica hamiltoniana e lagrangiana,70
-70J,Linear vibration theory,Teoria de vibrações lineares,70
-70K,Nonlinear dynamics in mechanics,Dinâmica não linear em mecânica,70
-70L,Random and stochastic aspects of the mechanics of particles and systems,Aspectos aleatórios e estocásticos da mecânica de partículas e sistemas,70
-70M,Orbital mechanics,Mecânica orbital,70
-70P,Variable mass; rockets,Massa variável; foguetes,70
-70Q,Control of mechanical systems,Controle de sistemas mecânicos,70
-70S,Classical field theories,Teorias clássicas de campo,70
-74,Mechanics of deformable solids,Mecânica dos sólidos deformáveis,
-74A,Generalities; axiomatics; foundations of continuum mechanics of solids,Generalidades; axiomática; fundamentos da mecânica contínua dos sólidos,74
-74B,Elastic materials,Materiais elásticos,74
-74C,Plastic materials; materials of stress-rate and internal-variable type,Materiais plásticos; materiais do tipo taxa de tensão e variável interna,74
-74D,Materials of strain-rate type and history type; other materials with memory (including elastic materials with viscous damping; various viscoelastic materials),Materiais do tipo taxa de deformação e tipo histórico; outros materiais com memória (incluindo materiais elásticos com amortecimento viscoso; vários materiais viscoelásticos),74
-74E,Material properties given special treatment,Propriedades de materiais com tratamento especial,74
-74F,Coupling of solid mechanics with other effects,Acoplamento da mecânica dos sólidos com outros efeitos,74
-74G,Equilibrium (steady-state) problems in solid mechanics,Problemas de equilíbrio (estado estacionário) em mecânica dos sólidos,74
-74H,Dynamical problems in solid mechanics,Problemas dinâmicos em mecânica dos sólidos,74
-74J,Waves in solid mechanics,Ondas em mecânica dos sólidos,74
-74K,Thin bodies; structures,Corpos delgados; estruturas,74
-74L,Special subfields of solid mechanics,Subcampos especiais da mecânica dos sólidos,74
-74M,Special kinds of problems in solid mechanics,Tipos especiais de problemas em mecânica dos sólidos,74
-74N,Phase transformations in solids,Transformações de fase em sólidos,74
-74P,Optimization problems in solid mechanics,Problemas de otimização em mecânica dos sólidos,74
-74Q,Homogenization; determination of effective properties in solid mechanics,Homogeneização; determinação de propriedades efetivas em mecânica dos sólidos,74
-74R,Fracture and damage,Fratura e dano,74
-74S,Numerical and other methods in solid mechanics,Métodos numéricos e outros métodos em mecânica dos sólidos,74
-76,Fluid mechanics,Mecânica dos fluidos,
-76A,Foundations; constitutive equations; rheology; hydrodynamical models of non-fluid phenomena,Fundamentos; equações constitutivas; reologia; modelos hidrodinâmicos de fenômenos não fluidos,76
-76B,Incompressible inviscid fluids,Fluidos incompressíveis invíscidos,76
-76D,Incompressible viscous fluids,Fluidos incompressíveis viscosos,76
-76E,Hydrodynamic stability,Estabilidade hidrodinâmica,76
-76F,Turbulence,Turbulência,76
-76G,General aerodynamics and subsonic flows,Aerodinâmica geral e escoamentos subsônicos,76
-76H,Transonic flows,Escoamentos transônicos,76
-76J,Supersonic flows,Escoamentos supersônicos,76
-76K,Hypersonic flows,Escoamentos hipersônicos,76
-76L,Shock waves and blast waves in fluid mechanics,Ondas de choque e ondas de explosão em mecânica dos fluidos,76
-76M,Basic methods in fluid mechanics,Métodos básicos em mecânica dos fluidos,76
-76N,Compressible fluids and gas dynamics,Fluidos compressíveis e dinâmica dos gases,76
-76P,Rarefied gas flows; Boltzmann equation in fluid mechanics,Escoamentos de gases rarefeitos; equação de Boltzmann em mecânica dos fluidos,76
-76Q,Hydro- and aero-acoustics,Hidroacústica e aeroacústica,76
-76R,Diffusion and convection,Difusão e convecção,76
-76S,Flows in porous media; filtration; seepage,Escoamentos em meios porosos; filtração; percolação,76
-76T,Multiphase and multicomponent flows,Escoamentos multifásicos e multicomponentes,76
-76U,Rotating fluids,Fluidos em rotação,76
-76V,Reaction effects in flows,Efeitos de reação em escoamentos,76
-76W,Magnetohydrodynamics and electrohydrodynamics,Magnetohidrodinâmica e eletrohidrodinâmica,76
-76X,Ionized gas flow in electromagnetic fields; plasmic flow,Escoamento de gás ionizado em campos eletromagnéticos; escoamento plasmático,76
-76Y,Quantum hydrodynamics and relativistic hydrodynamics,Hidrodinâmica quântica e hidrodinâmica relativística,76
-76Z,Biological fluid mechanics,Mecânica dos fluidos biológicos,76
-78,Optics; electromagnetic theory,Óptica; teoria eletromagnética,
-78A,General topics in optics and electromagnetic theory,Tópicos gerais em óptica e teoria eletromagnética,78
-78M,Basic methods for problems in optics and electromagnetic theory,Métodos básicos para problemas em óptica e teoria eletromagnética,78
-80,Classical thermodynamics; heat transfer,Termodinâmica clássica; transferência de calor,
-80A,Thermodynamics and heat transfer,Termodinâmica e transferência de calor,80
-80M,Basic methods in thermodynamics and heat transfer,Métodos básicos em termodinâmica e transferência de calor,80
-81,Quantum theory,Teoria quântica,
-81P,Foundations; quantum information and its processing; quantum axioms; and philosophy,Fundamentos; informação quântica e seu processamento; axiomas quânticos; e filosofia,81
-81Q,General mathematical topics and methods in quantum theory,Tópicos matemáticos gerais e métodos em teoria quântica,81
-81R,Groups and algebras in quantum theory,Grupos e álgebras em teoria quântica,81
-81S,General quantum mechanics and problems of quantization,Mecânica quântica geral e problemas de quantização,81
-81T,Quantum field theory; related classical field theories,Teoria quântica de campos; teorias clássicas de campo relacionadas,81
-81U,Quantum scattering theory,Teoria quântica do espalhamento,81
-81V,Applications of quantum theory to specific physical systems,Aplicações da teoria quântica a sistemas físicos específicos,81
-82,Statistical mechanics; structure of matter,Mecânica estatística; estrutura da matéria,
-82B,Equilibrium statistical mechanics,Mecânica estatística de equilíbrio,82
-82C,Time-dependent statistical mechanics (dynamic and nonequilibrium),Mecânica estatística dependente do tempo (dinâmica e não equilíbrio),82
-82D,Applications of statistical mechanics to specific types of physical systems,Aplicações da mecânica estatística a tipos específicos de sistemas físicos,82
-82M,Basic methods in statistical mechanics,Métodos básicos em mecânica estatística,82
-83,Relativity and gravitational theory,Relatividade e teoria gravitacional,
-83A,Special relativity,Relatividade especial,83
-83B,Observational and experimental questions in relativity and gravitational theory,Questões observacionais e experimentais em relatividade e teoria gravitacional,83
-83C,General relativity,Relatividade geral,83
-83D,Relativistic gravitational theories other than Einstein's; including asymmetric field theories,Teorias gravitacionais relativísticas além da teoria de Einstein; incluindo teorias de campo assimétricas,83
-83E,Unified; higher-dimensional and super field theories,Teorias de campo unificadas; de dimensão superior e superteorías,83
-83F,Relativistic cosmology,Cosmologia relativística,83
-85,Astronomy and astrophysics,Astronomia e astrofísica,
-85A,Astronomy and astrophysics,Astronomia e astrofísica,85
-86,Geophysics,Geofísica,
-86A,Geophysics,Geofísica,86
-90,Operations research; mathematical programming,Pesquisa operacional; programação matemática,
-90B,Operations research and management science,Pesquisa operacional e ciência da gestão,90
-90C,Mathematical programming,Programação matemática,90
-91,Game theory; economics; social sciences,Teoria dos jogos; economia; ciências sociais,
-91A,Game theory,Teoria dos jogos,91
-91B,Mathematical economics,Economia matemática,91
-91C,Social and behavioral sciences: general topics,Ciências sociais e comportamentais: tópicos gerais,91
-91D,Mathematical sociology (including anthropology),Sociologia matemática (incluindo antropologia),91
-91E,Mathematical psychology,Psicologia matemática,91
-91F,Other social and behavioral sciences (mathematical treatment),Outras ciências sociais e comportamentais (tratamento matemático),91
-91G,Actuarial science and mathematical finance,Ciências atuariais e finanças matemáticas,91
-92,Biology and other natural sciences,Biologia e outras ciências naturais,
-92B,Mathematical biology in general,Biologia matemática em geral,92
-92C,Physiological; cellular and medical topics,Tópicos fisiológicos; celulares e médicos,92
-92D,Genetics and population dynamics,Genética e dinâmica de populações,92
-92E,Chemistry,Química,92
-92F,Other natural sciences (mathematical treatment),Outras ciências naturais (tratamento matemático),92
-93,Systems theory; control,Teoria dos sistemas; controle,
-93A,General systems theory,Teoria geral dos sistemas,93
-93B,Controllability; observability; and system structure,Controlabilidade; observabilidade; e estrutura do sistema,93
-93C,Model systems in control theory,Sistemas modelo em teoria do controle,93
-93D,Stability of control systems,Estabilidade de sistemas de controle,93
-93E,Stochastic systems and control,Sistemas estocásticos e controle,93
-94,Information and communication; circuits,Informação e comunicação; circuitos,
-94A,Communication; information,Comunicação; informação,94
-94B,Theory of error-correcting codes and error-detecting codes,Teoria de códigos corretores de erros e códigos detectores de erros,94
-94C,Circuits; networks,Circuitos; redes,94
-94D,Miscellaneous topics in information and communication theory,Tópicos diversos em teoria da informação e comunicação,94
-97,Mathematics education,Educação matemática,
-97A,History and society (aspects of mathematics education),História e sociedade (aspectos da educação matemática),97
-97B,Educational policy and systems,Política educacional e sistemas,97
-97C,Psychology of mathematics education; research in mathematics education,Psicologia da educação matemática; pesquisa em educação matemática,97
-97D,Education and instruction in mathematics,Educação e instrução em matemática,97
-97E,Education of foundations of mathematics,Educação em fundamentos da matemática,97
-97F,Education of arithmetic and number theory,Educação em aritmética e teoria dos números,97
-97G,Geometry education,Educação em geometria,97
-97H,Algebra education,Educação em álgebra,97
-97I,Analysis education,Educação em análise,97
-97K,Education of combinatorics; graph theory; probability theory; and statistics,Educação em combinatória; teoria dos grafos; teoria da probabilidade; e estatística,97
-97M,Education of mathematical modeling and applications of mathematics,Educação em modelagem matemática e aplicações da matemática,97
-97N,Education of numerical mathematics,Educação em matemática numérica,97
-97P,Computer science (educational aspects),Ciência da computação (aspectos educacionais),97
-97U,Educational material and media and educational technology in mathematics education,Material educacional; mídia e tecnologia educacional em educação matemática,97
+code,name_en,name_pt_br,parent_code
+00,General,Geral,
+00A,General and miscellaneous specific topics,Tópicos gerais e miscelânea,00
+00B,Conference proceedings and collections of articles,Anais de conferências e coletâneas de artigos,00
+01,History and biography,História e biografia,
+01A,History of mathematics and mathematicians,História da matemática e de matemáticos,01
+03,Mathematical logic and foundations,Lógica matemática e fundamentos,
+03A,Philosophical aspects of logic and foundations,Aspectos filosóficos da lógica e dos fundamentos,03
+03B,General logic,Lógica geral,03
+03C,Model theory,Teoria de modelos,03
+03D,Computability and recursion theory,Computabilidade e teoria da recursão,03
+03E,Set theory,Teoria dos conjuntos,03
+03F,Proof theory and constructive mathematics,Teoria da prova e matemática construtiva,03
+03G,Algebraic logic,Lógica algébrica,03
+03H,Nonstandard models,Modelos não padrão,03
+05,Combinatorics,Combinatória,
+05A,Enumerative combinatorics,Combinatória enumerativa,05
+05B,Designs and configurations,Designs e configurações,05
+05C,Graph theory,Teoria dos grafos,05
+05D,Extremal combinatorics,Combinatória extremal,05
+05E,Algebraic combinatorics,Combinatória algébrica,05
+06,Order; lattices; ordered algebraic structures,Ordem; reticulados; estruturas algébricas ordenadas,
+06A,Ordered sets,Conjuntos ordenados,06
+06B,Lattices,Reticulados,06
+06C,Modular lattices; complemented lattices,Reticulados modulares; reticulados complementados,06
+06D,Distributive lattices,Reticulados distributivos,06
+06E,Boolean algebras (Boolean rings),Álgebras de Boole (anéis booleanos),06
+06F,Ordered structures,Estruturas ordenadas,06
+08,General algebraic systems,Sistemas algébricos gerais,
+08A,Algebraic structures,Estruturas algébricas,08
+08B,Varieties,Variedades algébricas,08
+08C,Other classes of algebras,Outras classes de álgebras,08
+11,Number theory,Teoria dos números,
+11A,Elementary number theory,Teoria elementar dos números,11
+11B,Sequences and sets,Sequências e conjuntos,11
+11C,Polynomials and matrices,Polinômios e matrizes,11
+11D,Diophantine equations,Equações diofantinas,11
+11E,Forms and linear algebraic groups,Formas e grupos algébricos lineares,11
+11F,Discontinuous groups and automorphic forms,Grupos descontínuos e formas automórficas,11
+11G,Arithmetic algebraic geometry (Diophantine geometry),Geometria algébrica aritmética (geometria diofantina),11
+11H,Geometry of numbers,Geometria dos números,11
+11J,Diophantine approximation; transcendental number theory,Aproximação diofantina; teoria dos números transcendentes,11
+11K,Probabilistic theory: distribution modulo \(1\); metric theory of algorithms,Teoria probabilística: distribuição módulo \(1\); teoria métrica dos algoritmos,11
+11L,Exponential sums and character sums,Somas exponenciais e somas de caracteres,11
+11M,Zeta and \(L\)-functions: analytic theory,Funções zeta e \(L\): teoria analítica,11
+11N,Multiplicative number theory,Teoria multiplicativa dos números,11
+11P,Additive number theory; partitions,Teoria aditiva dos números; partições,11
+11R,Algebraic number theory: global fields,Teoria algébrica dos números: corpos globais,11
+11S,Algebraic number theory: local fields,Teoria algébrica dos números: corpos locais,11
+11T,Finite fields and commutative rings (number-theoretic aspects),Corpos finitos e anéis comutativos (aspectos da teoria dos números),11
+11U,Connections of number theory and logic,Conexões entre teoria dos números e lógica,11
+11Y,Computational number theory,Teoria computacional dos números,11
+11Z,Miscellaneous applications of number theory,Aplicações diversas da teoria dos números,11
+12,Field theory and polynomials,Teoria dos corpos e polinômios,
+12D,Real and complex fields,Corpos reais e complexos,12
+12E,General field theory,Teoria geral dos corpos,12
+12F,Field extensions,Extensões de corpos,12
+12G,Homological methods (field theory),Métodos homológicos (teoria dos corpos),12
+12H,Differential and difference algebra,Álgebra diferencial e de diferenças,12
+12J,Topological fields,Corpos topológicos,12
+12K,Generalizations of fields,Generalizações de corpos,12
+12L,Connections between field theory and logic,Conexões entre teoria dos corpos e lógica,12
+13,Commutative algebra,Álgebra comutativa,
+13A,General commutative ring theory,Teoria geral de anéis comutativos,13
+13B,Commutative ring extensions and related topics,Extensões de anéis comutativos e tópicos relacionados,13
+13C,Theory of modules and ideals in commutative rings,Teoria de módulos e ideais em anéis comutativos,13
+13D,Homological methods in commutative ring theory,Métodos homológicos na teoria de anéis comutativos,13
+13E,Chain conditions; finiteness conditions in commutative ring theory,Condições de cadeia; condições de finitude na teoria de anéis comutativos,13
+13F,Arithmetic rings and other special commutative rings,Anéis aritméticos e outros anéis comutativos especiais,13
+13G,Integral domains,Domínios de integridade,13
+13H,Local rings and semilocal rings,Anéis locais e semilocais,13
+13J,Topological rings and modules,Anéis e módulos topológicos,13
+13L,Applications of logic to commutative algebra,Aplicações da lógica à álgebra comutativa,13
+13M,Finite commutative rings,Anéis comutativos finitos,13
+13N,Differential algebra,Álgebra diferencial,13
+13P,Computational aspects and applications of commutative rings,Aspectos computacionais e aplicações de anéis comutativos,13
+14,Algebraic geometry,Geometria algébrica,
+14A,Foundations of algebraic geometry,Fundamentos da geometria algébrica,14
+14B,Local theory in algebraic geometry,Teoria local em geometria algébrica,14
+14C,Cycles and subschemes,Ciclos e subesquemas,14
+14D,Families; fibrations in algebraic geometry,Famílias; fibrações em geometria algébrica,14
+14E,Birational geometry,Geometria birracional,14
+14F,(Co)homology theory in algebraic geometry,Teoria de (co)homologia em geometria algébrica,14
+14G,Arithmetic problems in algebraic geometry; Diophantine geometry,Problemas aritméticos em geometria algébrica; geometria diofantina,14
+14H,Curves in algebraic geometry,Curvas em geometria algébrica,14
+14J,Surfaces and higher-dimensional varieties,Superfícies e variedades de dimensão superior,14
+14K,Abelian varieties and schemes,Variedades e esquemas abelianos,14
+14L,Algebraic groups,Grupos algébricos,14
+14M,Special varieties,Variedades especiais,14
+14N,Projective and enumerative algebraic geometry,Geometria algébrica projetiva e enumerativa,14
+14P,Real algebraic and real-analytic geometry,Geometria algébrica real e geometria analítica real,14
+14Q,Computational aspects in algebraic geometry,Aspectos computacionais em geometria algébrica,14
+14R,Affine geometry,Geometria afim,14
+14T,Tropical geometry,Geometria tropical,14
+15,Linear and multilinear algebra; matrix theory,Álgebra linear e multilinear; teoria das matrizes,
+15A,Basic linear algebra,Álgebra linear básica,15
+15B,Special matrices,Matrizes especiais,15
+16,Associative rings and algebras,Anéis e álgebras associativos,
+16B,General and miscellaneous,Geral e miscelânea,16
+16D,Modules; bimodules and ideals in associative algebras,Módulos; bimódulos e ideais em álgebras associativas,16
+16E,Homological methods in associative algebras,Métodos homológicos em álgebras associativas,16
+16G,Representation theory of associative rings and algebras,Teoria da representação de anéis e álgebras associativos,16
+16H,Associative algebras and orders,Álgebras associativas e ordens,16
+16K,Division rings and semisimple Artin rings,Anéis de divisão e anéis de Artin semissimples,16
+16L,Local rings and generalizations,Anéis locais e generalizações,16
+16N,Radicals and radical properties of associative rings,Radicais e propriedades radicais de anéis associativos,16
+16P,Chain conditions; growth conditions; and other forms of finiteness for associative rings and algebras,Condições de cadeia; condições de crescimento; e outras formas de finitude para anéis e álgebras associativos,16
+16R,Rings with polynomial identity,Anéis com identidade polinomial,16
+16S,Associative rings and algebras arising under various constructions,Anéis e álgebras associativos provenientes de diversas construções,16
+16T,Hopf algebras; quantum groups and related topics,Álgebras de Hopf; grupos quânticos e tópicos relacionados,16
+16U,Conditions on elements,Condições sobre elementos,16
+16W,Associative rings and algebras with additional structure,Anéis e álgebras associativos com estrutura adicional,16
+16Y,Generalizations,Generalizações,16
+16Z,Computational aspects of associative rings,Aspectos computacionais de anéis associativos,16
+17,Nonassociative rings and algebras,Anéis e álgebras não associativos,
+17A,General nonassociative rings,Anéis não associativos gerais,17
+17B,Lie algebras and Lie superalgebras,Álgebras de Lie e super-álgebras de Lie,17
+17C,Jordan algebras (algebras; triples and pairs),Álgebras de Jordan (álgebras; triplas e pares),17
+17D,Other nonassociative rings and algebras,Outros anéis e álgebras não associativos,17
+18,Category theory; homological algebra,Teoria das categorias; álgebra homológica,
+18A,General theory of categories and functors,Teoria geral de categorias e funtores,18
+18B,Special categories,Categorias especiais,18
+18C,Categories and theories,Categorias e teorias,18
+18D,Categorical structures,Estruturas categóricas,18
+18E,Categorical algebra,Álgebra categórica,18
+18F,Categories in geometry and topology,Categorias em geometria e topologia,18
+18G,Homological algebra in category theory; derived categories and functors,Álgebra homológica em teoria das categorias; categorias derivadas e funtores,18
+18M,Monoidal categories and operads,Categorias monoidais e operadas,18
+18N,Higher categories and homotopical algebra,Categorias superiores e álgebra homotópica,18
+19,K-theory,K-teoria,
+19A,Grothendieck groups and \(K_0\),Grupos de Grothendieck e \(K_0\),19
+19B,Whitehead groups and \(K_1\),Grupos de Whitehead e \(K_1\),19
+19C,Steinberg groups and \(K_2\),Grupos de Steinberg e \(K_2\),19
+19D,Higher algebraic \(K\)-theory,K-teoria algébrica superior,19
+19E,\(K\)-theory in geometry,K-teoria em geometria,19
+19F,\(K\)-theory in number theory,K-teoria em teoria dos números,19
+19G,\(K\)-theory of forms,K-teoria de formas,19
+19J,Obstructions from topology,Obstruções provenientes da topologia,19
+19K,\(K\)-theory and operator algebras,K-teoria e álgebras de operadores,19
+19L,Topological \(K\)-theory,K-teoria topológica,19
+19M,Miscellaneous applications of \(K\)-theory,Aplicações diversas da K-teoria,19
+20,Group theory and generalizations,Teoria dos grupos e generalizações,
+20A,Foundations,Fundamentos,20
+20B,Permutation groups,Grupos de permutação,20
+20C,Representation theory of groups,Teoria da representação de grupos,20
+20D,Abstract finite groups,Grupos finitos abstratos,20
+20E,Structure and classification of infinite or finite groups,Estrutura e classificação de grupos finitos ou infinitos,20
+20F,Special aspects of infinite or finite groups,Aspectos especiais de grupos finitos ou infinitos,20
+20G,Linear algebraic groups and related topics,Grupos algébricos lineares e tópicos relacionados,20
+20H,Other groups of matrices,Outros grupos de matrizes,20
+20J,Connections of group theory with homological algebra and category theory,Conexões da teoria dos grupos com álgebra homológica e teoria das categorias,20
+20K,Abelian groups,Grupos abelianos,20
+20L,Groupoids (i.e. small categories in which all morphisms are isomorphisms),Grupoides (i.e. pequenas categorias em que todos os morfismos são isomorfismos),20
+20M,Semigroups,Semigrupos,20
+20N,Other generalizations of groups,Outras generalizações de grupos,20
+20P,Probabilistic methods in group theory,Métodos probabilísticos em teoria dos grupos,20
+22,Topological groups; Lie groups,Grupos topológicos; grupos de Lie,
+22A,Topological and differentiable algebraic systems,Sistemas algébricos topológicos e diferenciáveis,22
+22B,Locally compact abelian groups (LCA groups),Grupos abelianos localmente compactos (grupos LCA),22
+22C,Compact groups,Grupos compactos,22
+22D,Locally compact groups and their algebras,Grupos localmente compactos e suas álgebras,22
+22E,Lie groups,Grupos de Lie,22
+22F,Noncompact transformation groups,Grupos de transformações não compactos,22
+26,Real functions,Funções reais,
+26A,Functions of one variable,Funções de uma variável,26
+26B,Functions of several variables,Funções de várias variáveis,26
+26C,Polynomials; rational functions in real analysis,Polinômios; funções racionais em análise real,26
+26D,Inequalities in real analysis,Desigualdades em análise real,26
+26E,Miscellaneous topics in real functions,Tópicos diversos em funções reais,26
+28,Measure and integration,Medida e integração,
+28A,Classical measure theory,Teoria clássica da medida,28
+28B,Set functions; measures and integrals with values in abstract spaces,Funções de conjunto; medidas e integrais com valores em espaços abstratos,28
+28C,Set functions and measures on spaces with additional structure,Funções de conjunto e medidas em espaços com estrutura adicional,28
+28D,Measure-theoretic ergodic theory,Teoria ergódica baseada em medida,28
+28E,Miscellaneous topics in measure theory,Tópicos diversos em teoria da medida,28
+30,Functions of a complex variable,Funções de variável complexa,
+30A,General properties of functions of one complex variable,Propriedades gerais de funções de uma variável complexa,30
+30B,Series expansions of functions of one complex variable,Expansões em série de funções de uma variável complexa,30
+30C,Geometric function theory,Teoria geométrica das funções,30
+30D,Entire and meromorphic functions of one complex variable; and related topics,Funções inteiras e meromorfas de uma variável complexa; e tópicos relacionados,30
+30E,Miscellaneous topics of analysis in the complex plane,Tópicos diversos de análise no plano complexo,30
+30F,Riemann surfaces,Superfícies de Riemann,30
+30G,Generalized function theory,Teoria generalizada das funções,30
+30H,Spaces and algebras of analytic functions of one complex variable,Espaços e álgebras de funções analíticas de uma variável complexa,30
+30J,Function theory on the disc,Teoria das funções no disco,30
+30K,Universal holomorphic functions of one complex variable,Funções holomorfas universais de uma variável complexa,30
+30L,Analysis on metric spaces,Análise em espaços métricos,30
+31,Potential theory,Teoria do potencial,
+31A,Two-dimensional potential theory,Teoria do potencial bidimensional,31
+31B,Higher-dimensional potential theory,Teoria do potencial em dimensão superior,31
+31C,Generalizations of potential theory,Generalizações da teoria do potencial,31
+31D,Axiomatic potential theory,Teoria axiomática do potencial,31
+31E,Potential theory on fractals and metric spaces,Teoria do potencial em fractais e espaços métricos,31
+32,Several complex variables,Várias variáveis complexas,
+32A,Holomorphic functions of several complex variables,Funções holomorfas de várias variáveis complexas,32
+32B,Local analytic geometry,Geometria analítica local,32
+32C,Analytic spaces,Espaços analíticos,32
+32D,Analytic continuation,Continuação analítica,32
+32E,Holomorphic convexity,Convexidade holomorfa,32
+32F,Geometric convexity in several complex variables,Convexidade geométrica em várias variáveis complexas,32
+32G,Deformations of analytic structures,Deformações de estruturas analíticas,32
+32H,Holomorphic mappings and correspondences,Aplicações e correspondências holomorfas,32
+32J,Compact analytic spaces,Espaços analíticos compactos,32
+32K,Generalizations of analytic spaces,Generalizações de espaços analíticos,32
+32L,Holomorphic fiber spaces,Espaços fibrados holomorfos,32
+32M,Complex spaces with a group of automorphisms,Espaços complexos com grupo de automorfismos,32
+32N,Automorphic functions,Funções automórficas,32
+32P,Non-Archimedean analysis,Análise não arquimediana,32
+32Q,Complex manifolds,Variedades complexas,32
+32S,Complex singularities,Singularidades complexas,32
+32T,Pseudoconvex domains,Domínios pseudoconvexos,32
+32U,Pluripotential theory,Teoria pluripotencial,32
+32V,CR manifolds,Variedades CR,32
+32W,Differential operators in several variables,Operadores diferenciais em várias variáveis,32
+33,Special functions,Funções especiais,
+33B,Elementary classical functions,Funções clássicas elementares,33
+33C,Hypergeometric functions,Funções hipergeométricas,33
+33D,Basic hypergeometric functions,Funções hipergeométricas básicas,33
+33E,Other special functions,Outras funções especiais,33
+33F,Computational aspects of special functions,Aspectos computacionais de funções especiais,33
+34,Ordinary differential equations,Equações diferenciais ordinárias,
+34A,General theory for ordinary differential equations,Teoria geral de equações diferenciais ordinárias,34
+34B,Boundary value problems for ordinary differential equations,Problemas de valor de contorno para equações diferenciais ordinárias,34
+34C,Qualitative theory for ordinary differential equations,Teoria qualitativa de equações diferenciais ordinárias,34
+34D,Stability theory for ordinary differential equations,Teoria da estabilidade de equações diferenciais ordinárias,34
+34E,Asymptotic theory for ordinary differential equations,Teoria assintótica de equações diferenciais ordinárias,34
+34F,Ordinary differential equations and systems with randomness,Equações diferenciais ordinárias e sistemas com aleatoriedade,34
+34G,Differential equations in abstract spaces,Equações diferenciais em espaços abstratos,34
+34H,Control problems involving ordinary differential equations,Problemas de controle envolvendo equações diferenciais ordinárias,34
+34K,Functional-differential equations (including equations with delayed; advanced or state-dependent argument),Equações diferencial-funcionais (incluindo equações com argumento atrasado; avançado ou dependente do estado),34
+34L,Ordinary differential operators,Operadores diferenciais ordinários,34
+34M,Ordinary differential equations in the complex domain,Equações diferenciais ordinárias no domínio complexo,34
+34N,Dynamic equations on time scales or measure chains,Equações dinâmicas em escalas de tempo ou cadeias de medida,34
+35,Partial differential equations,Equações diferenciais parciais,
+35A,General topics in partial differential equations,Tópicos gerais em equações diferenciais parciais,35
+35B,Qualitative properties of solutions to partial differential equations,Propriedades qualitativas de soluções de equações diferenciais parciais,35
+35C,Representations of solutions to partial differential equations,Representações de soluções de equações diferenciais parciais,35
+35D,Generalized solutions to partial differential equations,Soluções generalizadas de equações diferenciais parciais,35
+35E,Partial differential equations and systems of partial differential equations with constant coefficients,Equações diferenciais parciais e sistemas com coeficientes constantes,35
+35F,General first-order partial differential equations and systems of first-order partial differential equations,Equações diferenciais parciais de primeira ordem gerais e sistemas,35
+35G,General higher-order partial differential equations and systems of higher-order partial differential equations,Equações diferenciais parciais de ordem superior gerais e sistemas,35
+35H,Close-to-elliptic equations,Equações próximas de elípticas,35
+35J,Elliptic equations and elliptic systems,Equações elípticas e sistemas elípticos,35
+35K,Parabolic equations and parabolic systems,Equações parabólicas e sistemas parabólicos,35
+35L,Hyperbolic equations and hyperbolic systems,Equações hiperbólicas e sistemas hiperbólicos,35
+35M,Partial differential equations of mixed type and mixed-type systems of partial differential equations,Equações diferenciais parciais de tipo misto e sistemas de tipo misto,35
+35N,Overdetermined problems for partial differential equations and systems of partial differential equations,Problemas superdeterminados para equações diferenciais parciais,35
+35P,Spectral theory and eigenvalue problems for partial differential equations,Teoria espectral e problemas de autovalores para equações diferenciais parciais,35
+35Q,Partial differential equations of mathematical physics and other areas of application,Equações diferenciais parciais da física matemática e outras áreas de aplicação,35
+35R,Miscellaneous topics in partial differential equations,Tópicos diversos em equações diferenciais parciais,35
+35S,Pseudodifferential operators and other generalizations of partial differential operators,Operadores pseudodiferenciais e outras generalizações de operadores diferenciais parciais,35
+37,Dynamical systems and ergodic theory,Sistemas dinâmicos e teoria ergódica,
+37A,Ergodic theory,Teoria ergódica,37
+37B,Topological dynamics,Dinâmica topológica,37
+37C,Smooth dynamical systems: general theory,Sistemas dinâmicos suaves: teoria geral,37
+37D,Dynamical systems with hyperbolic behavior,Sistemas dinâmicos com comportamento hiperbólico,37
+37E,Low-dimensional dynamical systems,Sistemas dinâmicos de baixa dimensão,37
+37F,Dynamical systems over complex numbers,Sistemas dinâmicos sobre números complexos,37
+37G,Local and nonlocal bifurcation theory for dynamical systems,Teoria de bifurcação local e não local para sistemas dinâmicos,37
+37H,Random dynamical systems,Sistemas dinâmicos aleatórios,37
+37J,Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems,Aspectos dinâmicos de sistemas hamiltonianos e lagrangianos de dimensão finita,37
+37K,Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems,Aspectos de sistemas dinâmicos em sistemas hamiltonianos e lagrangianos de dimensão infinita,37
+37L,Infinite-dimensional dissipative dynamical systems,Sistemas dinâmicos dissipativos de dimensão infinita,37
+37M,Approximation methods and numerical treatment of dynamical systems,Métodos de aproximação e tratamento numérico de sistemas dinâmicos,37
+37N,Applications of dynamical systems,Aplicações de sistemas dinâmicos,37
+37P,Arithmetic and non-Archimedean dynamical systems,Sistemas dinâmicos aritméticos e não arquimedianos,37
+39,Difference and functional equations,Equações de diferenças e equações funcionais,
+39A,Difference equations,Equações de diferenças,39
+39B,Functional equations and inequalities,Equações funcionais e desigualdades,39
+40,Sequences; series; summability,Sequências; séries; somabilidade,
+40A,Convergence and divergence of infinite limiting processes,Convergência e divergência de processos limites infinitos,40
+40B,Multiple sequences and series,Sequências e séries múltiplas,40
+40C,General summability methods,Métodos gerais de somabilidade,40
+40D,Direct theorems on summability,Teoremas diretos sobre somabilidade,40
+40E,Inversion theorems,Teoremas de inversão,40
+40F,Absolute and strong summability,Somabilidade absoluta e forte,40
+40G,Special methods of summability,Métodos especiais de somabilidade,40
+40H,Functional analytic methods in summability,Métodos de análise funcional em somabilidade,40
+40J,Summability in abstract structures,Somabilidade em estruturas abstratas,40
+41,Approximations and expansions,Aproximações e expansões,
+41A,Approximations and expansions,Aproximações e expansões,41
+42,Fourier analysis,Análise de Fourier,
+42A,Harmonic analysis in one variable,Análise harmônica em uma variável,42
+42B,Harmonic analysis in several variables,Análise harmônica em várias variáveis,42
+42C,Nontrigonometric harmonic analysis,Análise harmônica não trigonométrica,42
+43,Abstract harmonic analysis,Análise harmônica abstrata,
+43A,Abstract harmonic analysis,Análise harmônica abstrata,43
+44,Integral transforms,Transformadas integrais,
+44A,Integral transforms; operational calculus,Transformadas integrais; cálculo operacional,44
+45,Integral equations,Equações integrais,
+45A,Linear integral equations,Equações integrais lineares,45
+45B,Fredholm integral equations,Equações integrais de Fredholm,45
+45C,Eigenvalue problems for integral equations,Problemas de autovalores para equações integrais,45
+45D,Volterra integral equations,Equações integrais de Volterra,45
+45E,Singular integral equations,Equações integrais singulares,45
+45F,Systems of linear integral equations,Sistemas de equações integrais lineares,45
+45G,Nonlinear integral equations,Equações integrais não lineares,45
+45H,Integral equations with miscellaneous special kernels,Equações integrais com núcleos especiais diversos,45
+45J,Integro-ordinary differential equations,Equações integro-diferenciais ordinárias,45
+45K,Integro-partial differential equations,Equações integro-diferenciais parciais,45
+45L,Theoretical approximation of solutions to integral equations,Aproximação teórica de soluções de equações integrais,45
+45M,Qualitative behavior of solutions to integral equations,Comportamento qualitativo de soluções de equações integrais,45
+45N,Abstract integral equations; integral equations in abstract spaces,Equações integrais abstratas; equações integrais em espaços abstratos,45
+45P,Integral operators,Operadores integrais,45
+45Q,Inverse problems for integral equations,Problemas inversos para equações integrais,45
+45R,Random integral equations,Equações integrais aleatórias,45
+46,Functional analysis,Análise funcional,
+46A,Topological linear spaces and related structures,Espaços lineares topológicos e estruturas relacionadas,46
+46B,Normed linear spaces and Banach spaces; Banach lattices,Espaços lineares normados e espaços de Banach; reticulados de Banach,46
+46C,Inner product spaces and their generalizations; Hilbert spaces,Espaços com produto interno e suas generalizações; espaços de Hilbert,46
+46E,Linear function spaces and their duals,Espaços de funções lineares e seus duais,46
+46F,Distributions; generalized functions; distribution spaces,Distribuições; funções generalizadas; espaços de distribuições,46
+46G,Measures; integration; derivative; holomorphy (all involving infinite-dimensional spaces),Medidas; integração; derivada; holomorfismo (em espaços de dimensão infinita),46
+46H,Topological algebras; normed rings and algebras; Banach algebras,Álgebras topológicas; anéis e álgebras normados; álgebras de Banach,46
+46J,Commutative Banach algebras and commutative topological algebras,Álgebras de Banach comutativas e álgebras topológicas comutativas,46
+46K,Topological (rings and) algebras with an involution,Álgebras topológicas com involução,46
+46L,Selfadjoint operator algebras (\(C^*\)-algebras; von Neumann (\(W^*\)-) algebras; etc.),Álgebras de operadores autoadjuntos (\(C^*\)-álgebras; álgebras de von Neumann (\(W^*\)-); etc.),46
+46M,Methods of category theory in functional analysis,Métodos da teoria das categorias em análise funcional,46
+46N,Miscellaneous applications of functional analysis,Aplicações diversas de análise funcional,46
+46S,Other (nonclassical) types of functional analysis,Outros tipos (não clássicos) de análise funcional,46
+46T,Nonlinear functional analysis,Análise funcional não linear,46
+47,Operator theory,Teoria dos operadores,
+47A,General theory of linear operators,Teoria geral de operadores lineares,47
+47B,Special classes of linear operators,Classes especiais de operadores lineares,47
+47C,Individual linear operators as elements of algebraic systems,Operadores lineares individuais como elementos de sistemas algébricos,47
+47D,Groups and semigroups of linear operators; their generalizations and applications,Grupos e semigrupos de operadores lineares; suas generalizações e aplicações,47
+47E,Ordinary differential operators,Operadores diferenciais ordinários,47
+47F,Partial differential operators,Operadores diferenciais parciais,47
+47G,Integral; integro-differential; and pseudodifferential operators,Operadores integrais; integro-diferenciais; e pseudodiferenciais,47
+47H,Nonlinear operators and their properties,Operadores não lineares e suas propriedades,47
+47J,Equations and inequalities involving nonlinear operators,Equações e desigualdades envolvendo operadores não lineares,47
+47L,Linear spaces and algebras of operators,Espaços lineares e álgebras de operadores,47
+47N,Miscellaneous applications of operator theory,Aplicações diversas da teoria dos operadores,47
+47S,Other (nonclassical) types of operator theory,Outros tipos (não clássicos) de teoria dos operadores,47
+49,Calculus of variations and optimal control,Cálculo das variações e controle ótimo,
+49J,Existence theories in calculus of variations and optimal control,Teorias de existência no cálculo das variações e controle ótimo,49
+49K,Optimality conditions,Condições de otimalidade,49
+49L,Hamilton-Jacobi theories,Teorias de Hamilton-Jacobi,49
+49M,Numerical methods in optimal control,Métodos numéricos em controle ótimo,49
+49N,Miscellaneous topics in calculus of variations and optimal control,Tópicos diversos no cálculo das variações e controle ótimo,49
+49Q,Manifolds and measure-geometric topics,Variedades e tópicos de geometria de medida,49
+49R,Variational methods for eigenvalues of operators,Métodos variacionais para autovalores de operadores,49
+49S,Variational principles of physics,Princípios variacionais da física,49
+51,Geometry,Geometria,
+51A,Linear incidence geometry,Geometria de incidência linear,51
+51B,Nonlinear incidence geometry,Geometria de incidência não linear,51
+51C,Ring geometry (Hjelmslev; Barbilian; etc.),Geometria de anéis (Hjelmslev; Barbilian; etc.),51
+51D,Geometric closure systems,Sistemas de fechamento geométrico,51
+51E,Finite geometry and special incidence structures,Geometria finita e estruturas de incidência especiais,51
+51F,Metric geometry,Geometria métrica,51
+51G,Ordered geometries (ordered incidence structures; etc.),Geometrias ordenadas (estruturas de incidência ordenadas; etc.),51
+51H,Topological geometry,Geometria topológica,51
+51J,Incidence groups,Grupos de incidência,51
+51K,Distance geometry,Geometria das distâncias,51
+51L,Geometric order structures,Estruturas de ordem geométrica,51
+51M,Real and complex geometry,Geometria real e complexa,51
+51N,Analytic and descriptive geometry,Geometria analítica e descritiva,51
+51P,Classical or axiomatic geometry and physics,Geometria clássica ou axiomática e física,51
+52,Convex and discrete geometry,Geometria convexa e discreta,
+52A,General convexity,Convexidade geral,52
+52B,Polytopes and polyhedra,Politopos e poliedros,52
+52C,Discrete geometry,Geometria discreta,52
+53,Differential geometry,Geometria diferencial,
+53A,Classical differential geometry,Geometria diferencial clássica,53
+53B,Local differential geometry,Geometria diferencial local,53
+53C,Global differential geometry,Geometria diferencial global,53
+53D,Symplectic geometry; contact geometry,Geometria simplética; geometria de contato,53
+53E,Geometric evolution equations,Equações de evolução geométrica,53
+53Z,Applications of differential geometry to sciences and engineering,Aplicações da geometria diferencial às ciências e à engenharia,53
+54,General topology,Topologia geral,
+54A,Generalities in topology,Generalidades em topologia,54
+54B,Basic constructions in general topology,Construções básicas em topologia geral,54
+54C,Maps and general types of topological spaces defined by maps,Aplicações e tipos gerais de espaços topológicos definidos por aplicações,54
+54D,Fairly general properties of topological spaces,Propriedades bastante gerais de espaços topológicos,54
+54E,Topological spaces with richer structures,Espaços topológicos com estruturas mais ricas,54
+54F,Special properties of topological spaces,Propriedades especiais de espaços topológicos,54
+54G,Peculiar topological spaces,Espaços topológicos peculiares,54
+54H,Connections of general topology with other structures; applications,Conexões da topologia geral com outras estruturas; aplicações,54
+54J,Nonstandard topology,Topologia não padrão,54
+55,Algebraic topology,Topologia algébrica,
+55M,Classical topics in algebraic topology,Tópicos clássicos em topologia algébrica,55
+55N,Homology and cohomology theories in algebraic topology,Teorias de homologia e cohomologia em topologia algébrica,55
+55P,Homotopy theory,Teoria da homotopia,55
+55Q,Homotopy groups,Grupos de homotopia,55
+55R,Fiber spaces and bundles in algebraic topology,Espaços fibrados e fibrados em topologia algébrica,55
+55S,Operations and obstructions in algebraic topology,Operações e obstruções em topologia algébrica,55
+55T,Spectral sequences in algebraic topology,Sequências espectrais em topologia algébrica,55
+55U,Applied homological algebra and category theory in algebraic topology,Álgebra homológica aplicada e teoria das categorias em topologia algébrica,55
+57,Manifolds and cell complexes,Variedades e complexos celulares,
+57K,Low-dimensional topology in specific dimensions,Topologia de baixa dimensão em dimensões específicas,57
+57M,General low-dimensional topology,Topologia geral de baixa dimensão,57
+57N,Topological manifolds,Variedades topológicas,57
+57P,Generalized manifolds,Variedades generalizadas,57
+57Q,PL-topology,Topologia PL,57
+57R,Differential topology,Topologia diferencial,57
+57S,Topological transformation groups,Grupos de transformações topológicas,57
+57T,Homology and homotopy of topological groups and related structures,Homologia e homotopia de grupos topológicos e estruturas relacionadas,57
+57Z,Relations of manifolds and cell complexes with science and engineering,Relações de variedades e complexos celulares com ciências e engenharia,57
+58,Global analysis; analysis on manifolds,Análise global; análise em variedades,
+58A,General theory of differentiable manifolds,Teoria geral de variedades diferenciáveis,58
+58B,Infinite-dimensional manifolds,Variedades de dimensão infinita,58
+58C,Calculus on manifolds; nonlinear operators,Cálculo em variedades; operadores não lineares,58
+58D,Spaces and manifolds of mappings (including nonlinear versions of 46Exx),Espaços e variedades de aplicações (incluindo versões não lineares de 46Exx),58
+58E,Variational problems in infinite-dimensional spaces,Problemas variacionais em espaços de dimensão infinita,58
+58H,Pseudogroups; differentiable groupoids and general structures on manifolds,Pseudogrupos; grupoides diferenciáveis e estruturas gerais em variedades,58
+58J,Partial differential equations on manifolds; differential operators,Equações diferenciais parciais em variedades; operadores diferenciais,58
+58K,Theory of singularities and catastrophe theory,Teoria das singularidades e teoria das catástrofes,58
+58Z,Applications of global analysis to the sciences,Aplicações da análise global às ciências,58
+60,Probability theory and stochastic processes,Teoria da probabilidade e processos estocásticos,
+60A,Foundations of probability theory,Fundamentos da teoria da probabilidade,60
+60B,Probability theory on algebraic and topological structures,Teoria da probabilidade em estruturas algébricas e topológicas,60
+60C,Combinatorial probability,Probabilidade combinatória,60
+60D,Geometric probability and stochastic geometry,Probabilidade geométrica e geometria estocástica,60
+60E,Distribution theory,Teoria das distribuições,60
+60F,Limit theorems in probability theory,Teoremas limite em teoria da probabilidade,60
+60G,Stochastic processes,Processos estocásticos,60
+60H,Stochastic analysis,Análise estocástica,60
+60J,Markov processes,Processos de Markov,60
+60K,Special processes,Processos especiais,60
+60L,Rough analysis,Análise rough,60
+62,Statistics,Estatística,
+62A,Foundational topics in statistics,Tópicos fundamentais em estatística,62
+62B,Sufficiency and information,Suficiência e informação,62
+62C,Statistical decision theory,Teoria da decisão estatística,62
+62D,Statistical sampling theory and related topics,Teoria da amostragem estatística e tópicos relacionados,62
+62E,Statistical distribution theory,Teoria de distribuições estatísticas,62
+62F,Parametric inference,Inferência paramétrica,62
+62G,Nonparametric inference,Inferência não paramétrica,62
+62H,Multivariate analysis,Análise multivariada,62
+62J,Linear inference; regression,Inferência linear; regressão,62
+62K,Design of statistical experiments,Planejamento de experimentos estatísticos,62
+62L,Sequential statistical methods,Métodos estatísticos sequenciais,62
+62M,Inference from stochastic processes,Inferência a partir de processos estocásticos,62
+62N,Survival analysis and censored data,Análise de sobrevivência e dados censurados,62
+62P,Applications of statistics,Aplicações da estatística,62
+62Q,Statistical tables,Tabelas estatísticas,62
+62R,Statistics on algebraic and topological structures,Estatística em estruturas algébricas e topológicas,62
+65,Numerical analysis,Análise numérica,
+65A,Tables in numerical analysis,Tabelas em análise numérica,65
+65B,Acceleration of convergence in numerical analysis,Aceleração da convergência em análise numérica,65
+65C,Probabilistic methods; stochastic differential equations,Métodos probabilísticos; equações diferenciais estocásticas,65
+65D,Numerical approximation and computational geometry (primarily algorithms),Aproximação numérica e geometria computacional (principalmente algoritmos),65
+65E,Numerical methods in complex analysis (potential theory; etc.),Métodos numéricos em análise complexa (teoria do potencial; etc.),65
+65F,Numerical linear algebra,Álgebra linear numérica,65
+65G,Error analysis and interval analysis,Análise de erros e análise intervalar,65
+65H,Nonlinear algebraic or transcendental equations,Equações algébricas ou transcendentes não lineares,65
+65J,Numerical analysis in abstract spaces,Análise numérica em espaços abstratos,65
+65K,Numerical methods for mathematical programming; optimization and variational techniques,Métodos numéricos para programação matemática; otimização e técnicas variacionais,65
+65L,Numerical methods for ordinary differential equations,Métodos numéricos para equações diferenciais ordinárias,65
+65M,Numerical methods for partial differential equations; initial value and time-dependent initial-boundary value problems,Métodos numéricos para equações diferenciais parciais; problemas de valor inicial e de contorno dependentes do tempo,65
+65N,Numerical methods for partial differential equations; boundary value problems,Métodos numéricos para equações diferenciais parciais; problemas de valor de contorno,65
+65P,Numerical problems in dynamical systems,Problemas numéricos em sistemas dinâmicos,65
+65Q,Numerical methods for difference and functional equations; recurrence relations,Métodos numéricos para equações de diferenças e equações funcionais; relações de recorrência,65
+65R,Numerical methods for integral equations; integral transforms,Métodos numéricos para equações integrais; transformadas integrais,65
+65S,Graphical methods in numerical analysis,Métodos gráficos em análise numérica,65
+65T,Numerical methods in Fourier analysis,Métodos numéricos em análise de Fourier,65
+65Y,Computer aspects of numerical algorithms,Aspectos computacionais de algoritmos numéricos,65
+65Z,Applications to the sciences,Aplicações às ciências,65
+68,Computer science,Ciência da computação,
+68M,Computer system organization,Organização de sistemas computacionais,68
+68N,Theory of software,Teoria do software,68
+68P,Theory of data,Teoria dos dados,68
+68Q,Theory of computing,Teoria da computação,68
+68R,Discrete mathematics in relation to computer science,Matemática discreta em relação à ciência da computação,68
+68T,Artificial intelligence,Inteligência artificial,68
+68U,Computing methodologies and applications,Metodologias e aplicações da computação,68
+68V,Computer science support for mathematical research and practice,Suporte da ciência da computação à pesquisa e prática matemática,68
+68W,Algorithms in computer science,Algoritmos em ciência da computação,68
+70,Mechanics of particles and systems,Mecânica de partículas e sistemas,
+70A,Axiomatics; foundations,Axiomática; fundamentos,70
+70B,Kinematics,Cinemática,70
+70C,Statics,Estática,70
+70E,Dynamics of a rigid body and of multibody systems,Dinâmica de corpo rígido e de sistemas multicorpos,70
+70F,Dynamics of a system of particles; including celestial mechanics,Dinâmica de um sistema de partículas; incluindo mecânica celeste,70
+70G,General models; approaches; and methods in mechanics of particles and systems,Modelos gerais; abordagens; e métodos em mecânica de partículas e sistemas,70
+70H,Hamiltonian and Lagrangian mechanics,Mecânica hamiltoniana e lagrangiana,70
+70J,Linear vibration theory,Teoria de vibrações lineares,70
+70K,Nonlinear dynamics in mechanics,Dinâmica não linear em mecânica,70
+70L,Random and stochastic aspects of the mechanics of particles and systems,Aspectos aleatórios e estocásticos da mecânica de partículas e sistemas,70
+70M,Orbital mechanics,Mecânica orbital,70
+70P,Variable mass; rockets,Massa variável; foguetes,70
+70Q,Control of mechanical systems,Controle de sistemas mecânicos,70
+70S,Classical field theories,Teorias clássicas de campo,70
+74,Mechanics of deformable solids,Mecânica dos sólidos deformáveis,
+74A,Generalities; axiomatics; foundations of continuum mechanics of solids,Generalidades; axiomática; fundamentos da mecânica contínua dos sólidos,74
+74B,Elastic materials,Materiais elásticos,74
+74C,Plastic materials; materials of stress-rate and internal-variable type,Materiais plásticos; materiais do tipo taxa de tensão e variável interna,74
+74D,Materials of strain-rate type and history type; other materials with memory (including elastic materials with viscous damping; various viscoelastic materials),Materiais do tipo taxa de deformação e tipo histórico; outros materiais com memória (incluindo materiais elásticos com amortecimento viscoso; vários materiais viscoelásticos),74
+74E,Material properties given special treatment,Propriedades de materiais com tratamento especial,74
+74F,Coupling of solid mechanics with other effects,Acoplamento da mecânica dos sólidos com outros efeitos,74
+74G,Equilibrium (steady-state) problems in solid mechanics,Problemas de equilíbrio (estado estacionário) em mecânica dos sólidos,74
+74H,Dynamical problems in solid mechanics,Problemas dinâmicos em mecânica dos sólidos,74
+74J,Waves in solid mechanics,Ondas em mecânica dos sólidos,74
+74K,Thin bodies; structures,Corpos delgados; estruturas,74
+74L,Special subfields of solid mechanics,Subcampos especiais da mecânica dos sólidos,74
+74M,Special kinds of problems in solid mechanics,Tipos especiais de problemas em mecânica dos sólidos,74
+74N,Phase transformations in solids,Transformações de fase em sólidos,74
+74P,Optimization problems in solid mechanics,Problemas de otimização em mecânica dos sólidos,74
+74Q,Homogenization; determination of effective properties in solid mechanics,Homogeneização; determinação de propriedades efetivas em mecânica dos sólidos,74
+74R,Fracture and damage,Fratura e dano,74
+74S,Numerical and other methods in solid mechanics,Métodos numéricos e outros métodos em mecânica dos sólidos,74
+76,Fluid mechanics,Mecânica dos fluidos,
+76A,Foundations; constitutive equations; rheology; hydrodynamical models of non-fluid phenomena,Fundamentos; equações constitutivas; reologia; modelos hidrodinâmicos de fenômenos não fluidos,76
+76B,Incompressible inviscid fluids,Fluidos incompressíveis invíscidos,76
+76D,Incompressible viscous fluids,Fluidos incompressíveis viscosos,76
+76E,Hydrodynamic stability,Estabilidade hidrodinâmica,76
+76F,Turbulence,Turbulência,76
+76G,General aerodynamics and subsonic flows,Aerodinâmica geral e escoamentos subsônicos,76
+76H,Transonic flows,Escoamentos transônicos,76
+76J,Supersonic flows,Escoamentos supersônicos,76
+76K,Hypersonic flows,Escoamentos hipersônicos,76
+76L,Shock waves and blast waves in fluid mechanics,Ondas de choque e ondas de explosão em mecânica dos fluidos,76
+76M,Basic methods in fluid mechanics,Métodos básicos em mecânica dos fluidos,76
+76N,Compressible fluids and gas dynamics,Fluidos compressíveis e dinâmica dos gases,76
+76P,Rarefied gas flows; Boltzmann equation in fluid mechanics,Escoamentos de gases rarefeitos; equação de Boltzmann em mecânica dos fluidos,76
+76Q,Hydro- and aero-acoustics,Hidroacústica e aeroacústica,76
+76R,Diffusion and convection,Difusão e convecção,76
+76S,Flows in porous media; filtration; seepage,Escoamentos em meios porosos; filtração; percolação,76
+76T,Multiphase and multicomponent flows,Escoamentos multifásicos e multicomponentes,76
+76U,Rotating fluids,Fluidos em rotação,76
+76V,Reaction effects in flows,Efeitos de reação em escoamentos,76
+76W,Magnetohydrodynamics and electrohydrodynamics,Magnetohidrodinâmica e eletrohidrodinâmica,76
+76X,Ionized gas flow in electromagnetic fields; plasmic flow,Escoamento de gás ionizado em campos eletromagnéticos; escoamento plasmático,76
+76Y,Quantum hydrodynamics and relativistic hydrodynamics,Hidrodinâmica quântica e hidrodinâmica relativística,76
+76Z,Biological fluid mechanics,Mecânica dos fluidos biológicos,76
+78,Optics; electromagnetic theory,Óptica; teoria eletromagnética,
+78A,General topics in optics and electromagnetic theory,Tópicos gerais em óptica e teoria eletromagnética,78
+78M,Basic methods for problems in optics and electromagnetic theory,Métodos básicos para problemas em óptica e teoria eletromagnética,78
+80,Classical thermodynamics; heat transfer,Termodinâmica clássica; transferência de calor,
+80A,Thermodynamics and heat transfer,Termodinâmica e transferência de calor,80
+80M,Basic methods in thermodynamics and heat transfer,Métodos básicos em termodinâmica e transferência de calor,80
+81,Quantum theory,Teoria quântica,
+81P,Foundations; quantum information and its processing; quantum axioms; and philosophy,Fundamentos; informação quântica e seu processamento; axiomas quânticos; e filosofia,81
+81Q,General mathematical topics and methods in quantum theory,Tópicos matemáticos gerais e métodos em teoria quântica,81
+81R,Groups and algebras in quantum theory,Grupos e álgebras em teoria quântica,81
+81S,General quantum mechanics and problems of quantization,Mecânica quântica geral e problemas de quantização,81
+81T,Quantum field theory; related classical field theories,Teoria quântica de campos; teorias clássicas de campo relacionadas,81
+81U,Quantum scattering theory,Teoria quântica do espalhamento,81
+81V,Applications of quantum theory to specific physical systems,Aplicações da teoria quântica a sistemas físicos específicos,81
+82,Statistical mechanics; structure of matter,Mecânica estatística; estrutura da matéria,
+82B,Equilibrium statistical mechanics,Mecânica estatística de equilíbrio,82
+82C,Time-dependent statistical mechanics (dynamic and nonequilibrium),Mecânica estatística dependente do tempo (dinâmica e não equilíbrio),82
+82D,Applications of statistical mechanics to specific types of physical systems,Aplicações da mecânica estatística a tipos específicos de sistemas físicos,82
+82M,Basic methods in statistical mechanics,Métodos básicos em mecânica estatística,82
+83,Relativity and gravitational theory,Relatividade e teoria gravitacional,
+83A,Special relativity,Relatividade especial,83
+83B,Observational and experimental questions in relativity and gravitational theory,Questões observacionais e experimentais em relatividade e teoria gravitacional,83
+83C,General relativity,Relatividade geral,83
+83D,Relativistic gravitational theories other than Einstein's; including asymmetric field theories,Teorias gravitacionais relativísticas além da teoria de Einstein; incluindo teorias de campo assimétricas,83
+83E,Unified; higher-dimensional and super field theories,Teorias de campo unificadas; de dimensão superior e superteorías,83
+83F,Relativistic cosmology,Cosmologia relativística,83
+85,Astronomy and astrophysics,Astronomia e astrofísica,
+85A,Astronomy and astrophysics,Astronomia e astrofísica,85
+86,Geophysics,Geofísica,
+86A,Geophysics,Geofísica,86
+90,Operations research; mathematical programming,Pesquisa operacional; programação matemática,
+90B,Operations research and management science,Pesquisa operacional e ciência da gestão,90
+90C,Mathematical programming,Programação matemática,90
+91,Game theory; economics; social sciences,Teoria dos jogos; economia; ciências sociais,
+91A,Game theory,Teoria dos jogos,91
+91B,Mathematical economics,Economia matemática,91
+91C,Social and behavioral sciences: general topics,Ciências sociais e comportamentais: tópicos gerais,91
+91D,Mathematical sociology (including anthropology),Sociologia matemática (incluindo antropologia),91
+91E,Mathematical psychology,Psicologia matemática,91
+91F,Other social and behavioral sciences (mathematical treatment),Outras ciências sociais e comportamentais (tratamento matemático),91
+91G,Actuarial science and mathematical finance,Ciências atuariais e finanças matemáticas,91
+92,Biology and other natural sciences,Biologia e outras ciências naturais,
+92B,Mathematical biology in general,Biologia matemática em geral,92
+92C,Physiological; cellular and medical topics,Tópicos fisiológicos; celulares e médicos,92
+92D,Genetics and population dynamics,Genética e dinâmica de populações,92
+92E,Chemistry,Química,92
+92F,Other natural sciences (mathematical treatment),Outras ciências naturais (tratamento matemático),92
+93,Systems theory; control,Teoria dos sistemas; controle,
+93A,General systems theory,Teoria geral dos sistemas,93
+93B,Controllability; observability; and system structure,Controlabilidade; observabilidade; e estrutura do sistema,93
+93C,Model systems in control theory,Sistemas modelo em teoria do controle,93
+93D,Stability of control systems,Estabilidade de sistemas de controle,93
+93E,Stochastic systems and control,Sistemas estocásticos e controle,93
+94,Information and communication; circuits,Informação e comunicação; circuitos,
+94A,Communication; information,Comunicação; informação,94
+94B,Theory of error-correcting codes and error-detecting codes,Teoria de códigos corretores de erros e códigos detectores de erros,94
+94C,Circuits; networks,Circuitos; redes,94
+94D,Miscellaneous topics in information and communication theory,Tópicos diversos em teoria da informação e comunicação,94
+97,Mathematics education,Educação matemática,
+97A,History and society (aspects of mathematics education),História e sociedade (aspectos da educação matemática),97
+97B,Educational policy and systems,Política educacional e sistemas,97
+97C,Psychology of mathematics education; research in mathematics education,Psicologia da educação matemática; pesquisa em educação matemática,97
+97D,Education and instruction in mathematics,Educação e instrução em matemática,97
+97E,Education of foundations of mathematics,Educação em fundamentos da matemática,97
+97F,Education of arithmetic and number theory,Educação em aritmética e teoria dos números,97
+97G,Geometry education,Educação em geometria,97
+97H,Algebra education,Educação em álgebra,97
+97I,Analysis education,Educação em análise,97
+97K,Education of combinatorics; graph theory; probability theory; and statistics,Educação em combinatória; teoria dos grafos; teoria da probabilidade; e estatística,97
+97M,Education of mathematical modeling and applications of mathematics,Educação em modelagem matemática e aplicações da matemática,97
+97N,Education of numerical mathematics,Educação em matemática numérica,97
+97P,Computer science (educational aspects),Ciência da computação (aspectos educacionais),97
+97U,Educational material and media and educational technology in mathematics education,Material educacional; mídia e tecnologia educacional em educação matemática,97
+00A05,Mathematics in general,,00A
+00A06,"Mathematics for nonmathematicians (engineering, social sciences, etc.)",,00A
+00A07,Problem books,,00A
+00A08,Recreational mathematics,,00A
+00A09,Popularization of mathematics,,00A
+00A15,Bibliographies for mathematics in general,,00A
+00A17,External book reviews,,00A
+00A20,Dictionaries and other general reference works,,00A
+00A22,Formularies,,00A
+00A27,Lists of open problems,,00A
+00A30,Philosophy of mathematics,,00A
+00A35,Methodology of mathematics,,00A
+00A64,Mathematics and literature,,00A
+00A65,Mathematics and music,,00A
+00A66,Mathematics and visual arts,,00A
+00A67,Mathematics and architecture,,00A
+00A69,General applied mathematics,,00A
+00A71,General theory of mathematical modeling,,00A
+00A72,General theory of simulation,,00A
+00A79,Physics,,00A
+00A99,General and miscellaneous specific topics,,00A
+00B05,Collections of abstracts of lectures,,00B
+00B10,Collections of articles of general interest,,00B
+00B15,Collections of articles of miscellaneous specific interest,,00B
+00B20,Proceedings of conferences of general interest,,00B
+00B25,Proceedings of conferences of miscellaneous specific interest,,00B
+00B30,Festschriften,,00B
+00B50,Collections of translated articles of general interest,,00B
+00B55,Collections of translated articles of miscellaneous specific interest,,00B
+00B60,Collections of reprinted articles,,00B
+00B99,Conference proceedings and collections of articles,,00B
+01A05,"General histories, source books",,01A
+01A07,Ethnomathematics (general),,01A
+01A10,History of mathematics in Paleolithic and Neolithic times,,01A
+01A11,"History of mathematics of the indigenous cultures of Africa, Asia, and Oceania",,01A
+01A12,History of mathematics of the indigenous cultures of the Americas,,01A
+01A15,"History of mathematics of the indigenous cultures of Europe (pre-Greek, etc.)",,01A
+01A16,History of Egyptian mathematics,,01A
+01A17,History of Babylonian mathematics,,01A
+01A20,History of Greek and Roman mathematics,,01A
+01A25,History of Chinese mathematics,,01A
+01A27,History of Japanese mathematics,,01A
+01A29,"History of East and Southeast Asian mathematics (non-Chinese, non-Japanese)",,01A
+01A30,History of mathematics in the Golden Age of Islam,,01A
+01A32,History of Indian mathematics,,01A
+01A35,History of mathematics in Late Antiquity and medieval Europe,,01A
+01A40,"History of mathematics in the 15th and 16th centuries, Renaissance",,01A
+01A45,History of mathematics in the 17th century,,01A
+01A50,History of mathematics in the 18th century,,01A
+01A55,History of mathematics in the 19th century,,01A
+01A60,History of mathematics in the 20th century,,01A
+01A61,History of mathematics in the 21st century,,01A
+01A65,Development of contemporary mathematics,,01A
+01A67,Future perspectives in mathematics,,01A
+01A70,"Biographies, obituaries, personalia, bibliographies",,01A
+01A72,Schools of mathematics,,01A
+01A73,History of mathematics at specific universities,,01A
+01A74,History of mathematics at institutions and academies (non-university),,01A
+01A75,Collected or selected works; reprintings or translations of classics,,01A
+01A80,Sociology (and profession) of mathematics,,01A
+01A85,Historiography,,01A
+01A90,Bibliographic studies,,01A
+01A99,History of mathematics and mathematicians,,01A
+03A05,Philosophical and critical aspects of logic and foundations,,03A
+03A10,Logic in the philosophy of science,,03A
+03A99,Philosophical aspects of logic and foundations,,03A
+03B05,Classical propositional logic,,03B
+03B10,Classical first-order logic,,03B
+03B16,Higher-order logic,,03B
+03B20,Subsystems of classical logic (including intuitionistic logic),,03B
+03B22,Abstract deductive systems,,03B
+03B25,Decidability of theories and sets of sentences,,03B
+03B30,Foundations of classical theories (including reverse mathematics),,03B
+03B35,Mechanization of proofs and logical operations,,03B
+03B38,Type theory,,03B
+03B40,Combinatory logic and lambda calculus,,03B
+03B42,Logics of knowledge and belief (including belief change),,03B
+03B44,Temporal logic,,03B
+03B45,Modal logic (including the logic of norms),,03B
+03B47,"Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)",,03B
+03B48,Probability and inductive logic,,03B
+03B50,Many-valued logic,,03B
+03B52,Fuzzy logic; logic of vagueness,,03B
+03B53,Paraconsistent logics,,03B
+03B55,Intermediate logics,,03B
+03B60,Other nonclassical logic,,03B
+03B62,Combined logics,,03B
+03B65,Logic of natural languages,,03B
+03B70,Logic in computer science,,03B
+03B80,Other applications of logic,,03B
+03B99,General logic,,03B
+03C05,"Equational classes, universal algebra in model theory",,03C
+03C07,Basic properties of first-order languages and structures,,03C
+03C10,"Quantifier elimination, model completeness, and related topics",,03C
+03C13,Model theory of finite structures,,03C
+03C15,Model theory of denumerable and separable structures,,03C
+03C20,Ultraproducts and related constructions,,03C
+03C25,Model-theoretic forcing,,03C
+03C30,Other model constructions,,03C
+03C35,Categoricity and completeness of theories,,03C
+03C40,"Interpolation, preservation, definability",,03C
+03C45,"Classification theory, stability, and related concepts in model theory",,03C
+03C48,Abstract elementary classes and related topics,,03C
+03C50,"Models with special properties (saturated, rigid, etc.)",,03C
+03C52,Properties of classes of models,,03C
+03C55,Set-theoretic model theory,,03C
+03C57,"Computable structure theory, computable model theory",,03C
+03C60,Model-theoretic algebra,,03C
+03C62,Models of arithmetic and set theory,,03C
+03C64,Model theory of ordered structures; o-minimality,,03C
+03C65,Models of other mathematical theories,,03C
+03C66,"Continuous model theory, model theory of metric structures",,03C
+03C68,Other classical first-order model theory,,03C
+03C70,Logic on admissible sets,,03C
+03C75,Other infinitary logic,,03C
+03C80,Logic with extra quantifiers and operators,,03C
+03C85,Second- and higher-order model theory,,03C
+03C90,"Nonclassical models (Boolean-valued, sheaf, etc.)",,03C
+03C95,Abstract model theory,,03C
+03C98,Applications of model theory,,03C
+03C99,Model theory,,03C
+03D03,"Thue and Post systems, etc.",,03D
+03D05,Automata and formal grammars in connection with logical questions,,03D
+03D10,Turing machines and related notions,,03D
+03D15,Complexity of computation (including implicit computational complexity),,03D
+03D20,"Recursive functions and relations, subrecursive hierarchies",,03D
+03D25,Recursively (computably) enumerable sets and degrees,,03D
+03D28,Other Turing degree structures,,03D
+03D30,Other degrees and reducibilities in computability and recursion theory,,03D
+03D32,Algorithmic randomness and dimension,,03D
+03D35,Undecidability and degrees of sets of sentences,,03D
+03D40,"Word problems, etc. in computability and recursion theory",,03D
+03D45,"Theory of numerations, effectively presented structures",,03D
+03D50,"Recursive equivalence types of sets and structures, isols",,03D
+03D55,Hierarchies of computability and definability,,03D
+03D60,"Computability and recursion theory on ordinals, admissible sets, etc.",,03D
+03D65,Higher-type and set recursion theory,,03D
+03D70,Inductive definability,,03D
+03D75,Abstract and axiomatic computability and recursion theory,,03D
+03D78,"Computation over the reals, computable analysis",,03D
+03D80,Applications of computability and recursion theory,,03D
+03D99,Computability and recursion theory,,03D
+03E02,Partition relations,,03E
+03E04,Ordered sets and their cofinalities; pcf theory,,03E
+03E05,Other combinatorial set theory,,03E
+03E10,Ordinal and cardinal numbers,,03E
+03E15,Descriptive set theory,,03E
+03E17,Cardinal characteristics of the continuum,,03E
+03E20,"Other classical set theory (including functions, relations, and set algebra)",,03E
+03E25,Axiom of choice and related propositions,,03E
+03E30,Axiomatics of classical set theory and its fragments,,03E
+03E35,Consistency and independence results,,03E
+03E40,Other aspects of forcing and Boolean-valued models,,03E
+03E45,"Inner models, including constructibility, ordinal definability, and core models",,03E
+03E47,Other notions of set-theoretic definability,,03E
+03E50,Continuum hypothesis and Martin's axiom,,03E
+03E55,Large cardinals,,03E
+03E57,Generic absoluteness and forcing axioms,,03E
+03E60,Determinacy principles,,03E
+03E65,Other set-theoretic hypotheses and axioms,,03E
+03E70,Nonclassical and second-order set theories,,03E
+03E72,"Theory of fuzzy sets, etc.",,03E
+03E75,Applications of set theory,,03E
+03E99,Set theory,,03E
+03F03,Proof theory in general (including proof-theoretic semantics),,03F
+03F05,Cut-elimination and normal-form theorems,,03F
+03F07,Structure of proofs,,03F
+03F10,Functionals in proof theory,,03F
+03F15,Recursive ordinals and ordinal notations,,03F
+03F20,Complexity of proofs,,03F
+03F25,Relative consistency and interpretations,,03F
+03F30,First-order arithmetic and fragments,,03F
+03F35,Second- and higher-order arithmetic and fragments,,03F
+03F40,Gödel numberings and issues of incompleteness,,03F
+03F45,"Provability logics and related algebras (e.g., diagonalizable algebras)",,03F
+03F50,Metamathematics of constructive systems,,03F
+03F52,Proof-theoretic aspects of linear logic and other substructural logics,,03F
+03F55,Intuitionistic mathematics,,03F
+03F60,Constructive and recursive analysis,,03F
+03F65,Other constructive mathematics,,03F
+03F99,Proof theory and constructive mathematics,,03F
+03G05,Logical aspects of Boolean algebras,,03G
+03G10,Logical aspects of lattices and related structures,,03G
+03G12,Quantum logic,,03G
+03G15,Cylindric and polyadic algebras; relation algebras,,03G
+03G20,Logical aspects of ?ukasiewicz and Post algebras,,03G
+03G25,Other algebras related to logic,,03G
+03G27,Abstract algebraic logic,,03G
+03G30,"Categorical logic, topoi",,03G
+03G99,Algebraic logic,,03G
+03H05,Nonstandard models in mathematics,,03H
+03H10,"Other applications of nonstandard models (economics, physics, etc.)",,03H
+03H15,Nonstandard models of arithmetic,,03H
+03H99,Nonstandard models,,03H
+05A05,"Permutations, words, matrices",,05A
+05A10,"Factorials, binomial coefficients, combinatorial functions",,05A
+05A15,"Exact enumeration problems, generating functions",,05A
+05A16,Asymptotic enumeration,,05A
+05A17,Combinatorial aspects of partitions of integers,,05A
+05A18,Partitions of sets,,05A
+05A19,"Combinatorial identities, bijective combinatorics",,05A
+05A20,Combinatorial inequalities,,05A
+05A30,\(q\)-calculus and related topics,,05A
+05A40,Umbral calculus,,05A
+05A99,Enumerative combinatorics,,05A
+05B05,Combinatorial aspects of block designs,,05B
+05B07,Triple systems,,05B
+05B10,"Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)",,05B
+05B15,"Orthogonal arrays, Latin squares, Room squares",,05B
+05B20,"Combinatorial aspects of matrices (incidence, Hadamard, etc.)",,05B
+05B25,Combinatorial aspects of finite geometries,,05B
+05B30,"Other designs, configurations",,05B
+05B35,Combinatorial aspects of matroids and geometric lattices,,05B
+05B40,Combinatorial aspects of packing and covering,,05B
+05B45,Combinatorial aspects of tessellation and tiling problems,,05B
+05B50,Polyominoes,,05B
+05B99,Designs and configurations,,05B
+05C05,Trees,,05C
+05C07,Vertex degrees,,05C
+05C09,"Graphical indices (Wiener index, Zagreb index, Randi? index, etc.)",,05C
+05C10,Planar graphs; geometric and topological aspects of graph theory,,05C
+05C12,Distance in graphs,,05C
+05C15,Coloring of graphs and hypergraphs,,05C
+05C17,Perfect graphs,,05C
+05C20,"Directed graphs (digraphs), tournaments",,05C
+05C21,Flows in graphs,,05C
+05C22,Signed and weighted graphs,,05C
+05C25,"Graphs and abstract algebra (groups, rings, fields, etc.)",,05C
+05C30,Enumeration in graph theory,,05C
+05C31,Graph polynomials,,05C
+05C35,Extremal problems in graph theory,,05C
+05C38,Paths and cycles,,05C
+05C40,Connectivity,,05C
+05C42,"Density (toughness, etc.)",,05C
+05C45,Eulerian and Hamiltonian graphs,,05C
+05C48,Expander graphs,,05C
+05C50,"Graphs and linear algebra (matrices, eigenvalues, etc.)",,05C
+05C51,Graph designs and isomorphic decomposition,,05C
+05C55,Generalized Ramsey theory,,05C
+05C57,Games on graphs (graph-theoretic aspects),,05C
+05C60,"Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)",,05C
+05C62,"Graph representations (geometric and intersection representations, etc.)",,05C
+05C63,Infinite graphs,,05C
+05C65,Hypergraphs,,05C
+05C69,"Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)",,05C
+05C70,"Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)",,05C
+05C72,"Fractional graph theory, fuzzy graph theory",,05C
+05C75,Structural characterization of families of graphs,,05C
+05C76,"Graph operations (line graphs, products, etc.)",,05C
+05C78,"Graph labelling (graceful graphs, bandwidth, etc.)",,05C
+05C80,Random graphs (graph-theoretic aspects),,05C
+05C81,Random walks on graphs,,05C
+05C82,"Small world graphs, complex networks (graph-theoretic aspects)",,05C
+05C83,Graph minors,,05C
+05C85,Graph algorithms (graph-theoretic aspects),,05C
+05C90,Applications of graph theory,,05C
+05C92,Chemical graph theory,,05C
+05C99,Graph theory,,05C
+05D05,Extremal set theory,,05D
+05D10,Ramsey theory,,05D
+05D15,Transversal (matching) theory,,05D
+05D40,"Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.)",,05D
+05D99,Extremal combinatorics,,05D
+05E05,Symmetric functions and generalizations,,05E
+05E10,Combinatorial aspects of representation theory,,05E
+05E14,Combinatorial aspects of algebraic geometry,,05E
+05E16,Combinatorial aspects of groups and algebras,,05E
+05E18,Group actions on combinatorial structures,,05E
+05E30,"Association schemes, strongly regular graphs",,05E
+05E40,Combinatorial aspects of commutative algebra,,05E
+05E45,Combinatorial aspects of simplicial complexes,,05E
+05E99,Algebraic combinatorics,,05E
+06A05,Total orders,,06A
+06A06,"Partial orders, general",,06A
+06A07,Combinatorics of partially ordered sets,,06A
+06A11,Algebraic aspects of posets,,06A
+06A12,Semilattices,,06A
+06A15,"Galois correspondences, closure operators (in relation to ordered sets)",,06A
+06A75,Generalizations of ordered sets,,06A
+06A99,Ordered sets,,06A
+06B05,Structure theory of lattices,,06B
+06B10,"Lattice ideals, congruence relations",,06B
+06B15,Representation theory of lattices,,06B
+06B20,Varieties of lattices,,06B
+06B23,"Complete lattices, completions",,06B
+06B25,"Free lattices, projective lattices, word problems",,06B
+06B30,Topological lattices,,06B
+06B35,"Continuous lattices and posets, applications",,06B
+06B75,Generalizations of lattices,,06B
+06B99,Lattices,,06B
+06C05,"Modular lattices, Desarguesian lattices",,06C
+06C10,"Semimodular lattices, geometric lattices",,06C
+06C15,"Complemented lattices, orthocomplemented lattices and posets",,06C
+06C20,"Complemented modular lattices, continuous geometries",,06C
+06C99,"Modular lattices, complemented lattices",,06C
+06D05,Structure and representation theory of distributive lattices,,06D
+06D10,Complete distributivity,,06D
+06D15,Pseudocomplemented lattices,,06D
+06D20,Heyting algebras (lattice-theoretic aspects),,06D
+06D22,"Frames, locales",,06D
+06D25,Post algebras (lattice-theoretic aspects),,06D
+06D30,"De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects)",,06D
+06D35,MV-algebras,,06D
+06D50,Lattices and duality,,06D
+06D72,Fuzzy lattices (soft algebras) and related topics,,06D
+06D75,Other generalizations of distributive lattices,,06D
+06D99,Distributive lattices,,06D
+06E05,Structure theory of Boolean algebras,,06E
+06E10,"Chain conditions, complete algebras",,06E
+06E15,Stone spaces (Boolean spaces) and related structures,,06E
+06E20,Ring-theoretic properties of Boolean algebras,,06E
+06E25,"Boolean algebras with additional operations (diagonalizable algebras, etc.)",,06E
+06E30,Boolean functions,,06E
+06E75,Generalizations of Boolean algebras,,06E
+06E99,Boolean algebras (Boolean rings),,06E
+06F05,Ordered semigroups and monoids,,06F
+06F07,Quantales,,06F
+06F10,Noether lattices,,06F
+06F15,Ordered groups,,06F
+06F20,"Ordered abelian groups, Riesz groups, ordered linear spaces",,06F
+06F25,"Ordered rings, algebras, modules",,06F
+06F30,Ordered topological structures,,06F
+06F35,"BCK-algebras, BCI-algebras",,06F
+06F99,Ordered structures,,06F
+08A02,"Relational systems, laws of composition",,08A
+08A05,Structure theory of algebraic structures,,08A
+08A30,"Subalgebras, congruence relations",,08A
+08A35,Automorphisms and endomorphisms of algebraic structures,,08A
+08A40,"Operations and polynomials in algebraic structures, primal algebras",,08A
+08A45,Equational compactness,,08A
+08A50,Word problems (aspects of algebraic structures),,08A
+08A55,Partial algebras,,08A
+08A60,Unary algebras,,08A
+08A62,Finitary algebras,,08A
+08A65,Infinitary algebras,,08A
+08A68,Heterogeneous algebras,,08A
+08A70,Applications of universal algebra in computer science,,08A
+08A72,Fuzzy algebraic structures,,08A
+08A99,Algebraic structures,,08A
+08B05,"Equational logic, Mal'tsev conditions",,08B
+08B10,"Congruence modularity, congruence distributivity",,08B
+08B15,Lattices of varieties,,08B
+08B20,Free algebras,,08B
+08B25,"Products, amalgamated products, and other kinds of limits and colimits",,08B
+08B26,Subdirect products and subdirect irreducibility,,08B
+08B30,"Injectives, projectives",,08B
+08B99,Varieties,,08B
+08C05,Categories of algebras,,08C
+08C10,Axiomatic model classes,,08C
+08C15,Quasivarieties,,08C
+08C20,Natural dualities for classes of algebras,,08C
+08C99,Other classes of algebras,,08C
+11A05,Multiplicative structure; Euclidean algorithm; greatest common divisors,,11A
+11A07,Congruences; primitive roots; residue systems,,11A
+11A15,"Power residues, reciprocity",,11A
+11A25,Arithmetic functions; related numbers; inversion formulas,,11A
+11A41,Primes,,11A
+11A51,Factorization; primality,,11A
+11A55,Continued fractions,,11A
+11A63,Radix representation; digital problems,,11A
+11A67,Other number representations,,11A
+11A99,Elementary number theory,,11A
+11B05,"Density, gaps, topology",,11B
+11B13,"Additive bases, including sumsets",,11B
+11B25,Arithmetic progressions,,11B
+11B30,Arithmetic combinatorics; higher degree uniformity,,11B
+11B34,Representation functions,,11B
+11B37,Recurrences,,11B
+11B39,Fibonacci and Lucas numbers and polynomials and generalizations,,11B
+11B50,Sequences (mod \(m\)),,11B
+11B57,"Farey sequences; the sequences \(1^k, 2^k, \dots\)",,11B
+11B65,Binomial coefficients; factorials; \(q\)-identities,,11B
+11B68,Bernoulli and Euler numbers and polynomials,,11B
+11B73,Bell and Stirling numbers,,11B
+11B75,Other combinatorial number theory,,11B
+11B83,Special sequences and polynomials,,11B
+11B85,Automata sequences,,11B
+11B99,Sequences and sets,,11B
+11C08,Polynomials in number theory,,11C
+11C20,"Matrices, determinants in number theory",,11C
+11C99,Polynomials and matrices,,11C
+11D04,Linear Diophantine equations,,11D
+11D07,The Frobenius problem,,11D
+11D09,Quadratic and bilinear Diophantine equations,,11D
+11D25,Cubic and quartic Diophantine equations,,11D
+11D41,Higher degree equations; Fermat's equation,,11D
+11D45,Counting solutions of Diophantine equations,,11D
+11D57,Multiplicative and norm form equations,,11D
+11D59,Thue-Mahler equations,,11D
+11D61,Exponential Diophantine equations,,11D
+11D68,Rational numbers as sums of fractions,,11D
+11D72,Diophantine equations in many variables,,11D
+11D75,Diophantine inequalities,,11D
+11D79,Congruences in many variables,,11D
+11D85,Representation problems,,11D
+11D88,\(p\)-adic and power series fields,,11D
+11D99,Diophantine equations,,11D
+11E04,Quadratic forms over general fields,,11E
+11E08,Quadratic forms over local rings and fields,,11E
+11E10,Forms over real fields,,11E
+11E12,Quadratic forms over global rings and fields,,11E
+11E16,General binary quadratic forms,,11E
+11E20,General ternary and quaternary quadratic forms; forms of more than two variables,,11E
+11E25,Sums of squares and representations by other particular quadratic forms,,11E
+11E39,Bilinear and Hermitian forms,,11E
+11E41,Class numbers of quadratic and Hermitian forms,,11E
+11E45,Analytic theory (Epstein zeta functions; relations with automorphic forms and functions),,11E
+11E57,Classical groups,,11E
+11E70,\(K\)-theory of quadratic and Hermitian forms,,11E
+11E72,Galois cohomology of linear algebraic groups,,11E
+11E76,Forms of degree higher than two,,11E
+11E81,Algebraic theory of quadratic forms; Witt groups and rings,,11E
+11E88,Quadratic spaces; Clifford algebras,,11E
+11E95,\(p\)-adic theory,,11E
+11E99,Forms and linear algebraic groups,,11E
+11F03,Modular and automorphic functions,,11F
+11F06,Structure of modular groups and generalizations; arithmetic groups,,11F
+11F11,Holomorphic modular forms of integral weight,,11F
+11F12,"Automorphic forms, one variable",,11F
+11F20,"Dedekind eta function, Dedekind sums",,11F
+11F22,Relationship to Lie algebras and finite simple groups,,11F
+11F23,Relations with algebraic geometry and topology,,11F
+11F25,"Hecke-Petersson operators, differential operators (one variable)",,11F
+11F27,Theta series; Weil representation; theta correspondences,,11F
+11F30,Fourier coefficients of automorphic forms,,11F
+11F32,"Modular correspondences, etc.",,11F
+11F33,Congruences for modular and \(p\)-adic modular forms,,11F
+11F37,Forms of half-integer weight; nonholomorphic modular forms,,11F
+11F41,Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces,,11F
+11F46,Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms,,11F
+11F50,Jacobi forms,,11F
+11F52,Modular forms associated to Drinfel'd modules,,11F
+11F55,Other groups and their modular and automorphic forms (several variables),,11F
+11F60,"Hecke-Petersson operators, differential operators (several variables)",,11F
+11F66,Langlands \(L\)-functions; one variable Dirichlet series and functional equations,,11F
+11F67,"Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols",,11F
+11F68,Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series,,11F
+11F70,Representation-theoretic methods; automorphic representations over local and global fields,,11F
+11F72,"Spectral theory; trace formulas (e.g., that of Selberg)",,11F
+11F75,Cohomology of arithmetic groups,,11F
+11F77,Automorphic forms and their relations with perfectoid spaces,,11F
+11F80,Galois representations,,11F
+11F85,"\(p\)-adic theory, local fields",,11F
+11F99,Discontinuous groups and automorphic forms,,11F
+11G05,Elliptic curves over global fields,,11G
+11G07,Elliptic curves over local fields,,11G
+11G09,"Drinfel'd modules; higher-dimensional motives, etc.",,11G
+11G10,Abelian varieties of dimension \(> 1\),,11G
+11G15,Complex multiplication and moduli of abelian varieties,,11G
+11G16,Elliptic and modular units,,11G
+11G18,Arithmetic aspects of modular and Shimura varieties,,11G
+11G20,Curves over finite and local fields,,11G
+11G25,Varieties over finite and local fields,,11G
+11G30,Curves of arbitrary genus or genus \(\ne 1\) over global fields,,11G
+11G32,"Arithmetic aspects of dessins d'enfants, Bely? theory",,11G
+11G35,Varieties over global fields,,11G
+11G40,\(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture,,11G
+11G42,Arithmetic mirror symmetry,,11G
+11G45,Geometric class field theory,,11G
+11G50,Heights,,11G
+11G55,Polylogarithms and relations with \(K\)-theory,,11G
+11G99,Arithmetic algebraic geometry (Diophantine geometry),,11G
+11H06,Lattices and convex bodies (number-theoretic aspects),,11H
+11H16,Nonconvex bodies,,11H
+11H31,Lattice packing and covering (number-theoretic aspects),,11H
+11H46,Products of linear forms,,11H
+11H50,Minima of forms,,11H
+11H55,"Quadratic forms (reduction theory, extreme forms, etc.)",,11H
+11H56,Automorphism groups of lattices,,11H
+11H60,Mean value and transfer theorems,,11H
+11H71,Relations with coding theory,,11H
+11H99,Geometry of numbers,,11H
+11J04,Homogeneous approximation to one number,,11J
+11J06,Markov and Lagrange spectra and generalizations,,11J
+11J13,"Simultaneous homogeneous approximation, linear forms",,11J
+11J17,Approximation by numbers from a fixed field,,11J
+11J20,Inhomogeneous linear forms,,11J
+11J25,Diophantine inequalities,,11J
+11J54,Small fractional parts of polynomials and generalizations,,11J
+11J61,Approximation in non-Archimedean valuations,,11J
+11J68,Approximation to algebraic numbers,,11J
+11J70,Continued fractions and generalizations,,11J
+11J71,Distribution modulo one,,11J
+11J72,Irrationality; linear independence over a field,,11J
+11J81,Transcendence (general theory),,11J
+11J82,Measures of irrationality and of transcendence,,11J
+11J83,Metric theory,,11J
+11J85,Algebraic independence; Gel'fond's method,,11J
+11J86,Linear forms in logarithms; Baker's method,,11J
+11J87,Schmidt Subspace Theorem and applications,,11J
+11J89,Transcendence theory of elliptic and abelian functions,,11J
+11J91,Transcendence theory of other special functions,,11J
+11J93,Transcendence theory of Drinfel'd and \(t\)-modules,,11J
+11J95,Results involving abelian varieties,,11J
+11J97,Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.),,11J
+11J99,"Diophantine approximation, transcendental number theory",,11J
+11K06,General theory of distribution modulo \(1\),,11K
+11K16,"Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.",,11K
+11K31,Special sequences,,11K
+11K36,Well-distributed sequences and other variations,,11K
+11K38,"Irregularities of distribution, discrepancy",,11K
+11K41,"Continuous, \(p\)-adic and abstract analogues",,11K
+11K45,Pseudo-random numbers; Monte Carlo methods,,11K
+11K50,Metric theory of continued fractions,,11K
+11K55,Metric theory of other algorithms and expansions; measure and Hausdorff dimension,,11K
+11K60,Diophantine approximation in probabilistic number theory,,11K
+11K65,Arithmetic functions in probabilistic number theory,,11K
+11K70,Harmonic analysis and almost periodicity in probabilistic number theory,,11K
+11K99,Probabilistic theory: distribution modulo \(1\); metric theory of algorithms,,11K
+11L03,Trigonometric and exponential sums (general theory),,11L
+11L05,Gauss and Kloosterman sums; generalizations,,11L
+11L07,Estimates on exponential sums,,11L
+11L10,Jacobsthal and Brewer sums; other complete character sums,,11L
+11L15,Weyl sums,,11L
+11L20,Sums over primes,,11L
+11L26,Sums over arbitrary intervals,,11L
+11L40,Estimates on character sums,,11L
+11L99,Exponential sums and character sums,,11L
+11M06,"\(\zeta (s)\) and \(L(s, \chi)\)",,11M
+11M20,"Real zeros of \(L(s, \chi)\); results on \(L(1, \chi)\)",,11M
+11M26,"Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses",,11M
+11M32,Multiple Dirichlet series and zeta functions and multizeta values,,11M
+11M35,Hurwitz and Lerch zeta functions,,11M
+11M36,"Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)",,11M
+11M38,Zeta and \(L\)-functions in characteristic \(p\),,11M
+11M41,Other Dirichlet series and zeta functions,,11M
+11M45,Tauberian theorems,,11M
+11M50,Relations with random matrices,,11M
+11M55,Relations with noncommutative geometry,,11M
+11M99,Zeta and \(L\)-functions: analytic theory,,11M
+11N05,Distribution of primes,,11N
+11N13,Primes in congruence classes,,11N
+11N25,Distribution of integers with specified multiplicative constraints,,11N
+11N30,Turán theory,,11N
+11N32,Primes represented by polynomials; other multiplicative structures of polynomial values,,11N
+11N35,Sieves,,11N
+11N36,Applications of sieve methods,,11N
+11N37,Asymptotic results on arithmetic functions,,11N
+11N45,Asymptotic results on counting functions for algebraic and topological structures,,11N
+11N56,Rate of growth of arithmetic functions,,11N
+11N60,Distribution functions associated with additive and positive multiplicative functions,,11N
+11N64,Other results on the distribution of values or the characterization of arithmetic functions,,11N
+11N69,Distribution of integers in special residue classes,,11N
+11N75,Applications of automorphic functions and forms to multiplicative problems,,11N
+11N80,Generalized primes and integers,,11N
+11N99,Multiplicative number theory,,11N
+11P05,Waring's problem and variants,,11P
+11P21,Lattice points in specified regions,,11P
+11P32,Goldbach-type theorems; other additive questions involving primes,,11P
+11P55,Applications of the Hardy-Littlewood method,,11P
+11P70,"Inverse problems of additive number theory, including sumsets",,11P
+11P81,Elementary theory of partitions,,11P
+11P82,Analytic theory of partitions,,11P
+11P83,Partitions; congruences and congruential restrictions,,11P
+11P84,Partition identities; identities of Rogers-Ramanujan type,,11P
+11P99,Additive number theory; partitions,,11P
+11R04,Algebraic numbers; rings of algebraic integers,,11R
+11R06,PV-numbers and generalizations; other special algebraic numbers; Mahler measure,,11R
+11R09,"Polynomials (irreducibility, etc.)",,11R
+11R11,Quadratic extensions,,11R
+11R16,Cubic and quartic extensions,,11R
+11R18,Cyclotomic extensions,,11R
+11R20,Other abelian and metabelian extensions,,11R
+11R21,Other number fields,,11R
+11R23,Iwasawa theory,,11R
+11R27,Units and factorization,,11R
+11R29,"Class numbers, class groups, discriminants",,11R
+11R32,Galois theory,,11R
+11R33,Integral representations related to algebraic numbers; Galois module structure of rings of integers,,11R
+11R34,Galois cohomology,,11R
+11R37,Class field theory,,11R
+11R39,"Langlands-Weil conjectures, nonabelian class field theory",,11R
+11R42,Zeta functions and \(L\)-functions of number fields,,11R
+11R44,Distribution of prime ideals,,11R
+11R45,Density theorems,,11R
+11R47,Other analytic theory,,11R
+11R52,"Quaternion and other division algebras: arithmetic, zeta functions",,11R
+11R54,"Other algebras and orders, and their zeta and \(L\)-functions",,11R
+11R56,Adèle rings and groups,,11R
+11R58,Arithmetic theory of algebraic function fields,,11R
+11R59,Zeta functions and \(L\)-functions of function fields,,11R
+11R60,"Cyclotomic function fields (class groups, Bernoulli objects, etc.)",,11R
+11R65,Class groups and Picard groups of orders,,11R
+11R70,\(K\)-theory of global fields,,11R
+11R80,Totally real fields,,11R
+11R99,Algebraic number theory: global fields,,11R
+11S05,Polynomials,,11S
+11S15,Ramification and extension theory,,11S
+11S20,Galois theory,,11S
+11S23,Integral representations,,11S
+11S25,Galois cohomology,,11S
+11S31,Class field theory; \(p\)-adic formal groups,,11S
+11S37,"Langlands-Weil conjectures, nonabelian class field theory",,11S
+11S40,Zeta functions and \(L\)-functions,,11S
+11S45,"Algebras and orders, and their zeta functions",,11S
+11S70,\(K\)-theory of local fields,,11S
+11S80,"Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)",,11S
+11S82,Non-Archimedean dynamical systems,,11S
+11S85,Other nonanalytic theory,,11S
+11S90,Prehomogeneous vector spaces,,11S
+11S99,Algebraic number theory: local fields,,11S
+11T06,Polynomials over finite fields,,11T
+11T22,Cyclotomy,,11T
+11T23,Exponential sums,,11T
+11T24,Other character sums and Gauss sums,,11T
+11T30,Structure theory for finite fields and commutative rings (number-theoretic aspects),,11T
+11T55,Arithmetic theory of polynomial rings over finite fields,,11T
+11T60,Finite upper half-planes,,11T
+11T71,Algebraic coding theory; cryptography (number-theoretic aspects),,11T
+11T99,Finite fields and commutative rings (number-theoretic aspects),,11T
+11U05,Decidability (number-theoretic aspects),,11U
+11U07,Ultraproducts (number-theoretic aspects),,11U
+11U09,Model theory (number-theoretic aspects),,11U
+11U10,Nonstandard arithmetic (number-theoretic aspects),,11U
+11U99,Connections of number theory and logic,,11U
+11Y05,Factorization,,11Y
+11Y11,Primality,,11Y
+11Y16,Number-theoretic algorithms; complexity,,11Y
+11Y35,Analytic computations,,11Y
+11Y40,Algebraic number theory computations,,11Y
+11Y50,Computer solution of Diophantine equations,,11Y
+11Y55,Calculation of integer sequences,,11Y
+11Y60,Evaluation of number-theoretic constants,,11Y
+11Y65,Continued fraction calculations (number-theoretic aspects),,11Y
+11Y70,Values of arithmetic functions; tables,,11Y
+11Y99,Computational number theory,,11Y
+11Z05,Miscellaneous applications of number theory,,11Z
+11Z99,Miscellaneous applications of number theory,,11Z
+12D05,Polynomials in real and complex fields: factorization,,12D
+12D10,Polynomials in real and complex fields: location of zeros (algebraic theorems),,12D
+12D15,"Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)",,12D
+12D99,Real and complex fields,,12D
+12E05,"Polynomials in general fields (irreducibility, etc.)",,12E
+12E10,Special polynomials in general fields,,12E
+12E12,Equations in general fields,,12E
+12E15,"Skew fields, division rings",,12E
+12E20,Finite fields (field-theoretic aspects),,12E
+12E25,Hilbertian fields; Hilbert's irreducibility theorem,,12E
+12E30,Field arithmetic,,12E
+12E99,General field theory,,12E
+12F05,Algebraic field extensions,,12F
+12F10,"Separable extensions, Galois theory",,12F
+12F12,Inverse Galois theory,,12F
+12F15,Inseparable field extensions,,12F
+12F20,Transcendental field extensions,,12F
+12F99,Field extensions,,12F
+12G05,Galois cohomology,,12G
+12G10,Cohomological dimension of fields,,12G
+12G99,Homological methods (field theory),,12G
+12H05,Differential algebra,,12H
+12H10,Difference algebra,,12H
+12H20,Abstract differential equations,,12H
+12H25,\(p\)-adic differential equations,,12H
+12H99,Differential and difference algebra,,12H
+12J05,Normed fields,,12J
+12J10,Valued fields,,12J
+12J12,Formally \(p\)-adic fields,,12J
+12J15,Ordered fields,,12J
+12J17,Topological semifields,,12J
+12J20,General valuation theory for fields,,12J
+12J25,Non-Archimedean valued fields,,12J
+12J27,Krasner-Tate algebras,,12J
+12J99,Topological fields,,12J
+12K05,Near-fields,,12K
+12K10,Semifields,,12K
+12K99,Generalizations of fields,,12K
+12L05,Decidability and field theory,,12L
+12L10,Ultraproducts and field theory,,12L
+12L12,Model theory of fields,,12L
+12L15,Nonstandard arithmetic and field theory,,12L
+12L99,Connections between field theory and logic,,12L
+13A02,Graded rings,,13A
+13A05,Divisibility and factorizations in commutative rings,,13A
+13A15,Ideals and multiplicative ideal theory in commutative rings,,13A
+13A18,Valuations and their generalizations for commutative rings,,13A
+13A30,"Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics",,13A
+13A35,Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure,,13A
+13A50,Actions of groups on commutative rings; invariant theory,,13A
+13A70,"General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.)",,13A
+13A99,General commutative ring theory,,13A
+13B02,Extension theory of commutative rings,,13B
+13B05,Galois theory and commutative ring extensions,,13B
+13B10,Morphisms of commutative rings,,13B
+13B21,"Integral dependence in commutative rings; going up, going down",,13B
+13B22,Integral closure of commutative rings and ideals,,13B
+13B25,Polynomials over commutative rings,,13B
+13B30,Rings of fractions and localization for commutative rings,,13B
+13B35,Completion of commutative rings,,13B
+13B40,Étale and flat extensions; Henselization; Artin approximation,,13B
+13B99,Commutative ring extensions and related topics,,13B
+13C05,"Structure, classification theorems for modules and ideals in commutative rings",,13C
+13C10,Projective and free modules and ideals in commutative rings,,13C
+13C11,Injective and flat modules and ideals in commutative rings,,13C
+13C12,Torsion modules and ideals in commutative rings,,13C
+13C13,Other special types of modules and ideals in commutative rings,,13C
+13C14,Cohen-Macaulay modules,,13C
+13C15,"Dimension theory, depth, related commutative rings (catenary, etc.)",,13C
+13C20,Class groups,,13C
+13C40,"Linkage, complete intersections and determinantal ideals",,13C
+13C60,Module categories and commutative rings,,13C
+13C70,Theory of modules and ideals in commutative rings described by combinatorial properties,,13C
+13C99,Theory of modules and ideals in commutative rings,,13C
+13D02,"Syzygies, resolutions, complexes and commutative rings",,13D
+13D03,"(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)",,13D
+13D05,Homological dimension and commutative rings,,13D
+13D07,"Homological functors on modules of commutative rings (Tor, Ext, etc.)",,13D
+13D09,Derived categories and commutative rings,,13D
+13D10,Deformations and infinitesimal methods in commutative ring theory,,13D
+13D15,"Grothendieck groups, \(K\)-theory and commutative rings",,13D
+13D22,Homological conjectures (intersection theorems) in commutative ring theory,,13D
+13D30,Torsion theory for commutative rings,,13D
+13D40,Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series,,13D
+13D45,Local cohomology and commutative rings,,13D
+13D99,Homological methods in commutative ring theory,,13D
+13E05,Commutative Noetherian rings and modules,,13E
+13E10,"Commutative Artinian rings and modules, finite-dimensional algebras",,13E
+13E15,Commutative rings and modules of finite generation or presentation; number of generators,,13E
+13E99,"Chain conditions, finiteness conditions in commutative ring theory",,13E
+13F05,"Dedekind, Prüfer, Krull and Mori rings and their generalizations",,13F
+13F07,Euclidean rings and generalizations,,13F
+13F10,Principal ideal rings,,13F
+13F15,"Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial)",,13F
+13F20,Polynomial rings and ideals; rings of integer-valued polynomials,,13F
+13F25,Formal power series rings,,13F
+13F30,Valuation rings,,13F
+13F35,Witt vectors and related rings,,13F
+13F40,Excellent rings,,13F
+13F45,Seminormal rings,,13F
+13F50,"Rings with straightening laws, Hodge algebras",,13F
+13F55,Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes,,13F
+13F60,Cluster algebras,,13F
+13F65,"Commutative rings defined by binomial ideals, toric rings, etc.",,13F
+13F70,Other commutative rings defined by combinatorial properties,,13F
+13F99,Arithmetic rings and other special commutative rings,,13F
+13G05,Integral domains,,13G
+13G99,Integral domains,,13G
+13H05,Regular local rings,,13H
+13H10,"Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)",,13H
+13H15,Multiplicity theory and related topics,,13H
+13H99,Local rings and semilocal rings,,13H
+13J05,Power series rings,,13J
+13J07,Analytical algebras and rings,,13J
+13J10,"Complete rings, completion",,13J
+13J15,Henselian rings,,13J
+13J20,Global topological rings,,13J
+13J25,Ordered rings,,13J
+13J30,Real algebra,,13J
+13J99,Topological rings and modules,,13J
+13L05,Applications of logic to commutative algebra,,13L
+13L99,Applications of logic to commutative algebra,,13L
+13M05,Structure of finite commutative rings,,13M
+13M10,Polynomials and finite commutative rings,,13M
+13M99,Finite commutative rings,,13M
+13N05,Modules of differentials,,13N
+13N10,Commutative rings of differential operators and their modules,,13N
+13N15,Derivations and commutative rings,,13N
+13N99,Differential algebra,,13N
+13P05,"Polynomials, factorization in commutative rings",,13P
+13P10,"Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)",,13P
+13P15,Solving polynomial systems; resultants,,13P
+13P20,Computational homological algebra,,13P
+13P25,"Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)",,13P
+13P99,Computational aspects and applications of commutative rings,,13P
+14A05,Relevant commutative algebra,,14A
+14A10,Varieties and morphisms,,14A
+14A15,Schemes and morphisms,,14A
+14A20,"Generalizations (algebraic spaces, stacks)",,14A
+14A21,"Logarithmic algebraic geometry, log schemes",,14A
+14A22,Noncommutative algebraic geometry,,14A
+14A23,Geometry over the field with one element,,14A
+14A25,Elementary questions in algebraic geometry,,14A
+14A30,"Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.)",,14A
+14A99,Foundations of algebraic geometry,,14A
+14B05,Singularities in algebraic geometry,,14B
+14B07,Deformations of singularities,,14B
+14B10,Infinitesimal methods in algebraic geometry,,14B
+14B12,"Local deformation theory, Artin approximation, etc.",,14B
+14B15,Local cohomology and algebraic geometry,,14B
+14B20,Formal neighborhoods in algebraic geometry,,14B
+14B25,"Local structure of morphisms in algebraic geometry: étale, flat, etc.",,14B
+14B99,Local theory in algebraic geometry,,14B
+14C05,Parametrization (Chow and Hilbert schemes),,14C
+14C15,(Equivariant) Chow groups and rings; motives,,14C
+14C17,"Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry",,14C
+14C20,"Divisors, linear systems, invertible sheaves",,14C
+14C21,"Pencils, nets, webs in algebraic geometry",,14C
+14C22,Picard groups,,14C
+14C25,Algebraic cycles,,14C
+14C30,"Transcendental methods, Hodge theory (algebro-geometric aspects)",,14C
+14C34,Torelli problem,,14C
+14C35,Applications of methods of algebraic \(K\)-theory in algebraic geometry,,14C
+14C40,Riemann-Roch theorems,,14C
+14C99,Cycles and subschemes,,14C
+14D05,"Structure of families (Picard-Lefschetz, monodromy, etc.)",,14D
+14D06,"Fibrations, degenerations in algebraic geometry",,14D
+14D07,Variation of Hodge structures (algebro-geometric aspects),,14D
+14D10,"Arithmetic ground fields (finite, local, global) and families or fibrations",,14D
+14D15,Formal methods and deformations in algebraic geometry,,14D
+14D20,"Algebraic moduli problems, moduli of vector bundles",,14D
+14D21,"Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)",,14D
+14D22,Fine and coarse moduli spaces,,14D
+14D23,Stacks and moduli problems,,14D
+14D24,Geometric Langlands program (algebro-geometric aspects),,14D
+14D99,"Families, fibrations in algebraic geometry",,14D
+14E05,Rational and birational maps,,14E
+14E07,"Birational automorphisms, Cremona group and generalizations",,14E
+14E08,Rationality questions in algebraic geometry,,14E
+14E15,Global theory and resolution of singularities (algebro-geometric aspects),,14E
+14E16,McKay correspondence,,14E
+14E18,Arcs and motivic integration,,14E
+14E20,Coverings in algebraic geometry,,14E
+14E22,Ramification problems in algebraic geometry,,14E
+14E25,Embeddings in algebraic geometry,,14E
+14E30,"Minimal model program (Mori theory, extremal rays)",,14E
+14E99,Birational geometry,,14E
+14F06,Sheaves in algebraic geometry,,14F
+14F08,"Derived categories of sheaves, dg categories, and related constructions in algebraic geometry",,14F
+14F10,Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials,,14F
+14F17,Vanishing theorems in algebraic geometry,,14F
+14F18,Multiplier ideals,,14F
+14F20,Étale and other Grothendieck topologies and (co)homologies,,14F
+14F22,Brauer groups of schemes,,14F
+14F25,Classical real and complex (co)homology in algebraic geometry,,14F
+14F30,"\(p\)-adic cohomology, crystalline cohomology",,14F
+14F35,Homotopy theory and fundamental groups in algebraic geometry,,14F
+14F40,de Rham cohomology and algebraic geometry,,14F
+14F42,Motivic cohomology; motivic homotopy theory,,14F
+14F43,"Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)",,14F
+14F45,Topological properties in algebraic geometry,,14F
+14F99,(Co)homology theory in algebraic geometry,,14F
+14G05,Rational points,,14G
+14G10,"Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)",,14G
+14G12,"Hasse principle, weak and strong approximation, Brauer-Manin obstruction",,14G
+14G15,Finite ground fields in algebraic geometry,,14G
+14G17,Positive characteristic ground fields in algebraic geometry,,14G
+14G20,Local ground fields in algebraic geometry,,14G
+14G22,Rigid analytic geometry,,14G
+14G25,Global ground fields in algebraic geometry,,14G
+14G27,Other nonalgebraically closed ground fields in algebraic geometry,,14G
+14G32,"Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)",,14G
+14G35,Modular and Shimura varieties,,14G
+14G40,Arithmetic varieties and schemes; Arakelov theory; heights,,14G
+14G45,Perfectoid spaces and mixed characteristic,,14G
+14G50,Applications to coding theory and cryptography of arithmetic geometry,,14G
+14G99,Arithmetic problems in algebraic geometry; Diophantine geometry,,14G
+14H05,Algebraic functions and function fields in algebraic geometry,,14H
+14H10,"Families, moduli of curves (algebraic)",,14H
+14H15,"Families, moduli of curves (analytic)",,14H
+14H20,"Singularities of curves, local rings",,14H
+14H25,Arithmetic ground fields for curves,,14H
+14H30,"Coverings of curves, fundamental group",,14H
+14H37,Automorphisms of curves,,14H
+14H40,"Jacobians, Prym varieties",,14H
+14H42,Theta functions and curves; Schottky problem,,14H
+14H45,Special algebraic curves and curves of low genus,,14H
+14H50,Plane and space curves,,14H
+14H51,"Special divisors on curves (gonality, Brill-Noether theory)",,14H
+14H52,Elliptic curves,,14H
+14H55,Riemann surfaces; Weierstrass points; gap sequences,,14H
+14H57,Dessins d'enfants theory,,14H
+14H60,Vector bundles on curves and their moduli,,14H
+14H70,Relationships between algebraic curves and integrable systems,,14H
+14H81,Relationships between algebraic curves and physics,,14H
+14H99,Curves in algebraic geometry,,14H
+14J10,"Families, moduli, classification: algebraic theory",,14J
+14J15,"Moduli, classification: analytic theory; relations with modular forms",,14J
+14J17,Singularities of surfaces or higher-dimensional varieties,,14J
+14J20,Arithmetic ground fields for surfaces or higher-dimensional varieties,,14J
+14J25,Special surfaces,,14J
+14J26,Rational and ruled surfaces,,14J
+14J27,"Elliptic surfaces, elliptic or Calabi-Yau fibrations",,14J
+14J28,\(K3\) surfaces and Enriques surfaces,,14J
+14J29,Surfaces of general type,,14J
+14J30,\(3\)-folds,,14J
+14J32,Calabi-Yau manifolds (algebro-geometric aspects),,14J
+14J33,Mirror symmetry (algebro-geometric aspects),,14J
+14J35,\(4\)-folds,,14J
+14J40,\(n\)-folds (\(n>4\)),,14J
+14J42,"Holomorphic symplectic varieties, hyper-Kähler varieties",,14J
+14J45,Fano varieties,,14J
+14J50,Automorphisms of surfaces and higher-dimensional varieties,,14J
+14J60,"Vector bundles on surfaces and higher-dimensional varieties, and their moduli",,14J
+14J70,Hypersurfaces and algebraic geometry,,14J
+14J80,"Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)",,14J
+14J81,"Relationships between surfaces, higher-dimensional varieties, and physics",,14J
+14J99,Surfaces and higher-dimensional varieties,,14J
+14K02,Isogeny,,14K
+14K05,Algebraic theory of abelian varieties,,14K
+14K10,"Algebraic moduli of abelian varieties, classification",,14K
+14K12,Subvarieties of abelian varieties,,14K
+14K15,Arithmetic ground fields for abelian varieties,,14K
+14K20,Analytic theory of abelian varieties; abelian integrals and differentials,,14K
+14K22,Complex multiplication and abelian varieties,,14K
+14K25,Theta functions and abelian varieties,,14K
+14K30,"Picard schemes, higher Jacobians",,14K
+14K99,Abelian varieties and schemes,,14K
+14L05,"Formal groups, \(p\)-divisible groups",,14L
+14L10,Group varieties,,14L
+14L15,Group schemes,,14L
+14L17,"Affine algebraic groups, hyperalgebra constructions",,14L
+14L24,Geometric invariant theory,,14L
+14L30,Group actions on varieties or schemes (quotients),,14L
+14L35,Classical groups (algebro-geometric aspects),,14L
+14L40,Other algebraic groups (geometric aspects),,14L
+14L99,Algebraic groups,,14L
+14M05,"Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)",,14M
+14M06,Linkage,,14M
+14M07,Low codimension problems in algebraic geometry,,14M
+14M10,Complete intersections,,14M
+14M12,Determinantal varieties,,14M
+14M15,"Grassmannians, Schubert varieties, flag manifolds",,14M
+14M17,Homogeneous spaces and generalizations,,14M
+14M20,Rational and unirational varieties,,14M
+14M22,Rationally connected varieties,,14M
+14M25,"Toric varieties, Newton polyhedra, Okounkov bodies",,14M
+14M27,Compactifications; symmetric and spherical varieties,,14M
+14M30,Supervarieties,,14M
+14M35,Character varieties,,14M
+14M99,Special varieties,,14M
+14N05,Projective techniques in algebraic geometry,,14N
+14N07,"Secant varieties, tensor rank, varieties of sums of powers",,14N
+14N10,Enumerative problems (combinatorial problems) in algebraic geometry,,14N
+14N15,"Classical problems, Schubert calculus",,14N
+14N20,Configurations and arrangements of linear subspaces,,14N
+14N25,Varieties of low degree,,14N
+14N30,Adjunction problems,,14N
+14N35,"Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)",,14N
+14N99,Projective and enumerative algebraic geometry,,14N
+14P05,Real algebraic sets,,14P
+14P10,Semialgebraic sets and related spaces,,14P
+14P15,Real-analytic and semi-analytic sets,,14P
+14P20,Nash functions and manifolds,,14P
+14P25,Topology of real algebraic varieties,,14P
+14P99,Real algebraic and real-analytic geometry,,14P
+14Q05,Computational aspects of algebraic curves,,14Q
+14Q10,Computational aspects of algebraic surfaces,,14Q
+14Q15,Computational aspects of higher-dimensional varieties,,14Q
+14Q20,"Effectivity, complexity and computational aspects of algebraic geometry",,14Q
+14Q25,Computational algebraic geometry over arithmetic ground fields,,14Q
+14Q30,Computational real algebraic geometry,,14Q
+14Q65,Geometric aspects of numerical algebraic geometry,,14Q
+14Q99,Computational aspects in algebraic geometry,,14Q
+14R05,Classification of affine varieties,,14R
+14R10,"Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)",,14R
+14R15,Jacobian problem,,14R
+14R20,Group actions on affine varieties,,14R
+14R25,Affine fibrations,,14R
+14R99,Affine geometry,,14R
+14T10,Foundations of tropical geometry and relations with algebra,,14T
+14T15,Combinatorial aspects of tropical varieties,,14T
+14T20,Geometric aspects of tropical varieties,,14T
+14T25,Arithmetic aspects of tropical varieties,,14T
+14T90,Applications of tropical geometry,,14T
+14T99,Tropical geometry,,14T
+15A03,"Vector spaces, linear dependence, rank, lineability",,15A
+15A04,"Linear transformations, semilinear transformations",,15A
+15A06,Linear equations (linear algebraic aspects),,15A
+15A09,Theory of matrix inversion and generalized inverses,,15A
+15A10,Applications of generalized inverses,,15A
+15A12,Conditioning of matrices,,15A
+15A15,"Determinants, permanents, traces, other special matrix functions",,15A
+15A16,Matrix exponential and similar functions of matrices,,15A
+15A18,"Eigenvalues, singular values, and eigenvectors",,15A
+15A20,"Diagonalization, Jordan forms",,15A
+15A21,"Canonical forms, reductions, classification",,15A
+15A22,Matrix pencils,,15A
+15A23,Factorization of matrices,,15A
+15A24,Matrix equations and identities,,15A
+15A27,Commutativity of matrices,,15A
+15A29,Inverse problems in linear algebra,,15A
+15A30,Algebraic systems of matrices,,15A
+15A39,Linear inequalities of matrices,,15A
+15A42,Inequalities involving eigenvalues and eigenvectors,,15A
+15A45,Miscellaneous inequalities involving matrices,,15A
+15A54,Matrices over function rings in one or more variables,,15A
+15A60,"Norms of matrices, numerical range, applications of functional analysis to matrix theory",,15A
+15A63,"Quadratic and bilinear forms, inner products",,15A
+15A66,"Clifford algebras, spinors",,15A
+15A67,"Applications of Clifford algebras to physics, etc.",,15A
+15A69,"Multilinear algebra, tensor calculus",,15A
+15A72,"Vector and tensor algebra, theory of invariants",,15A
+15A75,"Exterior algebra, Grassmann algebras",,15A
+15A78,Other algebras built from modules,,15A
+15A80,Max-plus and related algebras,,15A
+15A83,Matrix completion problems,,15A
+15A86,Linear preserver problems,,15A
+15A99,Basic linear algebra,,15A
+15B05,"Toeplitz, Cauchy, and related matrices",,15B
+15B10,Orthogonal matrices,,15B
+15B15,Fuzzy matrices,,15B
+15B30,Matrix Lie algebras,,15B
+15B33,"Matrices over special rings (quaternions, finite fields, etc.)",,15B
+15B34,Boolean and Hadamard matrices,,15B
+15B35,Sign pattern matrices,,15B
+15B36,Matrices of integers,,15B
+15B48,Positive matrices and their generalizations; cones of matrices,,15B
+15B51,Stochastic matrices,,15B
+15B52,Random matrices (algebraic aspects),,15B
+15B57,"Hermitian, skew-Hermitian, and related matrices",,15B
+15B99,Special matrices,,15B
+16B50,Category-theoretic methods and results in associative algebras (except as in 16D90),,16B
+16B70,Applications of logic in associative algebras,,16B
+16B99,General and miscellaneous,,16B
+16D10,General module theory in associative algebras,,16D
+16D20,Bimodules in associative algebras,,16D
+16D25,Ideals in associative algebras,,16D
+16D30,Infinite-dimensional simple rings (except as in 16Kxx),,16D
+16D40,"Free, projective, and flat modules and ideals in associative algebras",,16D
+16D50,"Injective modules, self-injective associative rings",,16D
+16D60,"Simple and semisimple modules, primitive rings and ideals in associative algebras",,16D
+16D70,"Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)",,16D
+16D80,Other classes of modules and ideals in associative algebras,,16D
+16D90,Module categories in associative algebras,,16D
+16D99,"Modules, bimodules and ideals in associative algebras",,16D
+16E05,"Syzygies, resolutions, complexes in associative algebras",,16E
+16E10,Homological dimension in associative algebras,,16E
+16E20,"Grothendieck groups, \(K\)-theory, etc.",,16E
+16E30,"Homological functors on modules (Tor, Ext, etc.) in associative algebras",,16E
+16E35,Derived categories and associative algebras,,16E
+16E40,"(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)",,16E
+16E45,Differential graded algebras and applications (associative algebraic aspects),,16E
+16E50,von Neumann regular rings and generalizations (associative algebraic aspects),,16E
+16E60,"Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.",,16E
+16E65,"Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)",,16E
+16E99,Homological methods in associative algebras,,16E
+16G10,Representations of associative Artinian rings,,16G
+16G20,Representations of quivers and partially ordered sets,,16G
+16G30,"Representations of orders, lattices, algebras over commutative rings",,16G
+16G50,Cohen-Macaulay modules in associative algebras,,16G
+16G60,"Representation type (finite, tame, wild, etc.) of associative algebras",,16G
+16G70,Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers,,16G
+16G99,Representation theory of associative rings and algebras,,16G
+16H05,"Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)",,16H
+16H10,Orders in separable algebras,,16H
+16H15,Commutative orders,,16H
+16H20,Lattices over orders,,16H
+16H99,Associative algebras and orders,,16H
+16K20,Finite-dimensional division rings,,16K
+16K40,Infinite-dimensional and general division rings,,16K
+16K50,Brauer groups (algebraic aspects),,16K
+16K99,Division rings and semisimple Artin rings,,16K
+16L30,"Noncommutative local and semilocal rings, perfect rings",,16L
+16L60,Quasi-Frobenius rings,,16L
+16L99,Local rings and generalizations,,16L
+16N20,"Jacobson radical, quasimultiplication",,16N
+16N40,"Nil and nilpotent radicals, sets, ideals, associative rings",,16N
+16N60,Prime and semiprime associative rings,,16N
+16N80,General radicals and associative rings,,16N
+16N99,Radicals and radical properties of associative rings,,16N
+16P10,Finite rings and finite-dimensional associative algebras,,16P
+16P20,Artinian rings and modules (associative rings and algebras),,16P
+16P40,Noetherian rings and modules (associative rings and algebras),,16P
+16P50,Localization and associative Noetherian rings,,16P
+16P60,Chain conditions on annihilators and summands: Goldie-type conditions,,16P
+16P70,"Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)",,16P
+16P90,"Growth rate, Gelfand-Kirillov dimension",,16P
+16P99,"Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras",,16P
+16R10,"\(T\)-ideals, identities, varieties of associative rings and algebras",,16R
+16R20,"Semiprime p.i. rings, rings embeddable in matrices over commutative rings",,16R
+16R30,Trace rings and invariant theory (associative rings and algebras),,16R
+16R40,Identities other than those of matrices over commutative rings,,16R
+16R50,"Other kinds of identities (generalized polynomial, rational, involution)",,16R
+16R60,Functional identities (associative rings and algebras),,16R
+16R99,Rings with polynomial identity,,16R
+16S10,"Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)",,16S
+16S15,"Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)",,16S
+16S20,Centralizing and normalizing extensions,,16S
+16S30,Universal enveloping algebras of Lie algebras,,16S
+16S32,Rings of differential operators (associative algebraic aspects),,16S
+16S34,Group rings,,16S
+16S35,"Twisted and skew group rings, crossed products",,16S
+16S36,Ordinary and skew polynomial rings and semigroup rings,,16S
+16S37,Quadratic and Koszul algebras,,16S
+16S38,Rings arising from noncommutative algebraic geometry,,16S
+16S40,Smash products of general Hopf actions,,16S
+16S50,Endomorphism rings; matrix rings,,16S
+16S60,"Associative rings of functions, subdirect products, sheaves of rings",,16S
+16S70,Extensions of associative rings by ideals,,16S
+16S80,Deformations of associative rings,,16S
+16S85,Associative rings of fractions and localizations,,16S
+16S88,Leavitt path algebras,,16S
+16S90,Torsion theories; radicals on module categories (associative algebraic aspects),,16S
+16S99,Associative rings and algebras arising under various constructions,,16S
+16T05,Hopf algebras and their applications,,16T
+16T10,Bialgebras,,16T
+16T15,Coalgebras and comodules; corings,,16T
+16T20,Ring-theoretic aspects of quantum groups,,16T
+16T25,Yang-Baxter equations,,16T
+16T30,Connections of Hopf algebras with combinatorics,,16T
+16T99,"Hopf algebras, quantum groups and related topics",,16T
+16U10,Integral domains (associative rings and algebras),,16U
+16U20,"Ore rings, multiplicative sets, Ore localization",,16U
+16U30,"Divisibility, noncommutative UFDs",,16U
+16U40,Idempotent elements (associative rings and algebras),,16U
+16U60,"Units, groups of units (associative rings and algebras)",,16U
+16U70,"Center, normalizer (invariant elements) (associative rings and algebras)",,16U
+16U80,Generalizations of commutativity (associative rings and algebras),,16U
+16U90,Generalized inverses (associative rings and algebras),,16U
+16U99,Conditions on elements,,16U
+16W10,"Rings with involution; Lie, Jordan and other nonassociative structures",,16W
+16W20,Automorphisms and endomorphisms,,16W
+16W22,Actions of groups and semigroups; invariant theory (associative rings and algebras),,16W
+16W25,"Derivations, actions of Lie algebras",,16W
+16W50,Graded rings and modules (associative rings and algebras),,16W
+16W55,``Super'' (or ``skew'') structure,,16W
+16W60,"Valuations, completions, formal power series and related constructions (associative rings and algebras)",,16W
+16W70,Filtered associative rings; filtrational and graded techniques,,16W
+16W80,Topological and ordered rings and modules,,16W
+16W99,Associative rings and algebras with additional structure,,16W
+16Y20,Hyperrings,,16Y
+16Y30,Near-rings,,16Y
+16Y60,Semirings,,16Y
+16Y80,\(\Gamma\) and fuzzy structures,,16Y
+16Y99,Generalizations,,16Y
+16Z05,Computational aspects of associative rings (general theory),,16Z
+16Z10,Gröbner-Shirshov bases,,16Z
+16Z99,Computational aspects of associative rings,,16Z
+17A01,General theory of nonassociative rings and algebras,,17A
+17A05,Power-associative rings,,17A
+17A15,Noncommutative Jordan algebras,,17A
+17A20,Flexible algebras,,17A
+17A30,Nonassociative algebras satisfying other identities,,17A
+17A32,Leibniz algebras,,17A
+17A35,Nonassociative division algebras,,17A
+17A36,"Automorphisms, derivations, other operators (nonassociative rings and algebras)",,17A
+17A40,Ternary compositions,,17A
+17A42,Other \(n\)-ary compositions \((n \ge 3)\),,17A
+17A45,Quadratic algebras (but not quadratic Jordan algebras),,17A
+17A50,Free nonassociative algebras,,17A
+17A60,Structure theory for nonassociative algebras,,17A
+17A61,Gröbner-Shirshov bases in nonassociative algebras,,17A
+17A65,Radical theory (nonassociative rings and algebras),,17A
+17A70,Superalgebras,,17A
+17A75,Composition algebras,,17A
+17A80,Valued algebras,,17A
+17A99,General nonassociative rings,,17A
+17B01,"Identities, free Lie (super)algebras",,17B
+17B05,Structure theory for Lie algebras and superalgebras,,17B
+17B08,Coadjoint orbits; nilpotent varieties,,17B
+17B10,"Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)",,17B
+17B15,"Representations of Lie algebras and Lie superalgebras, analytic theory",,17B
+17B20,"Simple, semisimple, reductive (super)algebras",,17B
+17B22,Root systems,,17B
+17B25,Exceptional (super)algebras,,17B
+17B30,"Solvable, nilpotent (super)algebras",,17B
+17B35,Universal enveloping (super)algebras,,17B
+17B37,Quantum groups (quantized enveloping algebras) and related deformations,,17B
+17B38,Yang-Baxter equations and Rota-Baxter operators,,17B
+17B40,"Automorphisms, derivations, other operators for Lie algebras and super algebras",,17B
+17B45,Lie algebras of linear algebraic groups,,17B
+17B50,Modular Lie (super)algebras,,17B
+17B55,Homological methods in Lie (super)algebras,,17B
+17B56,Cohomology of Lie (super)algebras,,17B
+17B60,"Lie (super)algebras associated with other structures (associative, Jordan, etc.)",,17B
+17B61,Hom-Lie and related algebras,,17B
+17B62,Lie bialgebras; Lie coalgebras,,17B
+17B63,Poisson algebras,,17B
+17B65,Infinite-dimensional Lie (super)algebras,,17B
+17B66,Lie algebras of vector fields and related (super) algebras,,17B
+17B67,Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras,,17B
+17B68,Virasoro and related algebras,,17B
+17B69,Vertex operators; vertex operator algebras and related structures,,17B
+17B70,Graded Lie (super)algebras,,17B
+17B75,Color Lie (super)algebras,,17B
+17B80,Applications of Lie algebras and superalgebras to integrable systems,,17B
+17B81,"Applications of Lie (super)algebras to physics, etc.",,17B
+17B99,Lie algebras and Lie superalgebras,,17B
+17C05,Identities and free Jordan structures,,17C
+17C10,Structure theory for Jordan algebras,,17C
+17C17,Radicals in Jordan algebras,,17C
+17C20,"Simple, semisimple Jordan algebras",,17C
+17C27,"Idempotents, Peirce decompositions",,17C
+17C30,"Associated groups, automorphisms of Jordan algebras",,17C
+17C36,Associated manifolds of Jordan algebras,,17C
+17C37,Associated geometries of Jordan algebras,,17C
+17C40,Exceptional Jordan structures,,17C
+17C50,Jordan structures associated with other structures,,17C
+17C55,Finite-dimensional structures of Jordan algebras,,17C
+17C60,Division algebras and Jordan algebras,,17C
+17C65,Jordan structures on Banach spaces and algebras,,17C
+17C70,Super structures,,17C
+17C90,"Applications of Jordan algebras to physics, etc.",,17C
+17C99,"Jordan algebras (algebras, triples and pairs)",,17C
+17D05,Alternative rings,,17D
+17D10,Mal'tsev rings and algebras,,17D
+17D15,Right alternative rings,,17D
+17D20,"\((\gamma, \delta)\)-rings, including \((1,-1)\)-rings",,17D
+17D25,Lie-admissible algebras,,17D
+17D30,(non-Lie) Hom algebras and topics,,17D
+17D92,Genetic algebras,,17D
+17D99,Other nonassociative rings and algebras,,17D
+18A05,Definitions and generalizations in theory of categories,,18A
+18A10,"Graphs, diagram schemes, precategories",,18A
+18A15,"Foundations, relations to logic and deductive systems",,18A
+18A20,"Epimorphisms, monomorphisms, special classes of morphisms, null morphisms",,18A
+18A22,"Special properties of functors (faithful, full, etc.)",,18A
+18A23,"Natural morphisms, dinatural morphisms",,18A
+18A25,"Functor categories, comma categories",,18A
+18A30,"Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)",,18A
+18A32,"Factorization systems, substructures, quotient structures, congruences, amalgams",,18A
+18A35,"Categories admitting limits (complete categories), functors preserving limits, completions",,18A
+18A40,"Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)",,18A
+18A50,Graded categories (general),,18A
+18A99,General theory of categories and functors,,18A
+18B05,"Categories of sets, characterizations",,18B
+18B10,"Categories of spans/cospans, relations, or partial maps",,18B
+18B15,"Embedding theorems, universal categories",,18B
+18B20,"Categories of machines, automata",,18B
+18B25,Topoi,,18B
+18B35,"Preorders, orders, domains and lattices (viewed as categories)",,18B
+18B40,"Groupoids, semigroupoids, semigroups, groups (viewed as categories)",,18B
+18B50,"Extensive, distributive, and adhesive categories",,18B
+18B99,Special categories,,18B
+18C05,Equational categories,,18C
+18C10,"Theories (e.g., algebraic theories), structure, and semantics",,18C
+18C15,"Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads",,18C
+18C20,Eilenberg-Moore and Kleisli constructions for monads,,18C
+18C30,Sketches and generalizations,,18C
+18C35,Accessible and locally presentable categories,,18C
+18C40,"Structured objects in a category (group objects, etc.)",,18C
+18C50,Categorical semantics of formal languages,,18C
+18C99,Categories and theories,,18C
+18D15,"Closed categories (closed monoidal and Cartesian closed categories, etc.)",,18D
+18D20,Enriched categories (over closed or monoidal categories),,18D
+18D25,"Actions of a monoidal category, tensorial strength",,18D
+18D30,Fibered categories,,18D
+18D40,Internal categories and groupoids,,18D
+18D60,"Profunctors (= correspondences, distributors, modules)",,18D
+18D65,"Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads)",,18D
+18D70,Formal category theory,,18D
+18D99,Categorical structures,,18D
+18E05,"Preadditive, additive categories",,18E
+18E08,"Regular categories, Barr-exact categories",,18E
+18E10,"Abelian categories, Grothendieck categories",,18E
+18E13,"Protomodular categories, semi-abelian categories, Mal'tsev categories",,18E
+18E20,Categorical embedding theorems,,18E
+18E35,"Localization of categories, calculus of fractions",,18E
+18E40,"Torsion theories, radicals",,18E
+18E45,Definable subcategories and connections with model theory,,18E
+18E50,Categorical Galois theory,,18E
+18E99,Categorical algebra,,18E
+18F05,Local categories and functors,,18F
+18F10,Grothendieck topologies and Grothendieck topoi,,18F
+18F15,Abstract manifolds and fiber bundles (category-theoretic aspects),,18F
+18F20,"Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)",,18F
+18F25,Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects),,18F
+18F30,Grothendieck groups (category-theoretic aspects),,18F
+18F40,"Synthetic differential geometry, tangent categories, differential categories",,18F
+18F50,Goodwillie calculus and functor calculus,,18F
+18F60,Categories of topological spaces and continuous mappings,,18F
+18F70,"Frames and locales, pointfree topology, Stone duality",,18F
+18F75,Quantales,,18F
+18F99,Categories in geometry and topology,,18F
+18G05,Projectives and injectives (category-theoretic aspects),,18G
+18G10,Resolutions; derived functors (category-theoretic aspects),,18G
+18G15,"Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)",,18G
+18G20,Homological dimension (category-theoretic aspects),,18G
+18G25,"Relative homological algebra, projective classes (category-theoretic aspects)",,18G
+18G31,Simplicial modules and Dold-Kan correspondence,,18G
+18G35,"Chain complexes (category-theoretic aspects), dg categories",,18G
+18G40,"Spectral sequences, hypercohomology",,18G
+18G45,"2-groups, crossed modules, crossed complexes",,18G
+18G50,Nonabelian homological algebra (category-theoretic aspects),,18G
+18G65,Stable module categories,,18G
+18G70,"\(A_{\infty}\)-categories, relations with homological mirror symmetry",,18G
+18G80,"Derived categories, triangulated categories",,18G
+18G85,Graph complexes and graph homology,,18G
+18G90,Other (co)homology theories (category-theoretic aspects),,18G
+18G99,"Homological algebra in category theory, derived categories and functors",,18G
+18M05,"Monoidal categories, symmetric monoidal categories",,18M
+18M10,"Traced monoidal categories, compact closed categories, star-autonomous categories",,18M
+18M15,Braided monoidal categories and ribbon categories,,18M
+18M20,"Fusion categories, modular tensor categories, modular functors",,18M
+18M25,Tannakian categories,,18M
+18M30,String diagrams and graphical calculi,,18M
+18M35,"Categories of networks and processes, compositionality",,18M
+18M40,"Dagger categories, categorical quantum mechanics",,18M
+18M45,Categorical aspects of linear logic,,18M
+18M50,"Bimonoidal, skew-monoidal, duoidal categories",,18M
+18M60,Operads (general),,18M
+18M65,"Non-symmetric operads, multicategories, generalized multicategories",,18M
+18M70,"Algebraic operads, cooperads, and Koszul duality",,18M
+18M75,Topological and simplicial operads,,18M
+18M80,"Species, Hopf monoids, operads in combinatorics",,18M
+18M85,"Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads",,18M
+18M90,Globular operads,,18M
+18M99,Monoidal categories and operads,,18M
+18N10,"2-categories, bicategories, double categories",,18N
+18N15,2-dimensional monad theory,,18N
+18N20,"Tricategories, weak \(n\)-categories, coherence, semi-strictification",,18N
+18N25,Categorification,,18N
+18N30,"Strict omega-categories, computads, polygraphs",,18N
+18N40,"Homotopical algebra, Quillen model categories, derivators",,18N
+18N45,"Categories of fibrations, relations to \(K\)-theory, relations to type theory",,18N
+18N50,"Simplicial sets, simplicial objects",,18N
+18N55,"Localizations (e.g., simplicial localization, Bousfield localization)",,18N
+18N60,"\((\infty,1)\)-categories (quasi-categories, Segal spaces, etc.); \(\infty\)-topoi, stable \(\infty\)-categories",,18N
+18N65,"\((\infty, n)\)-categories and \((\infty,\infty)\)-categories",,18N
+18N70,\(\infty\)-operads and higher algebra,,18N
+18N99,Higher categories and homotopical algebra,,18N
+19A13,Stability for projective modules,,19A
+19A15,Efficient generation of modules,,19A
+19A22,"Frobenius induction, Burnside and representation rings",,19A
+19A31,\(K_0\) of group rings and orders,,19A
+19A49,\(K_0\) of other rings,,19A
+19A99,Grothendieck groups and \(K_0\),,19A
+19B10,Stable range conditions,,19B
+19B14,Stability for linear groups,,19B
+19B28,\(K_1\) of group rings and orders,,19B
+19B37,Congruence subgroup problems,,19B
+19B99,Whitehead groups and \(K_1\),,19B
+19C09,Central extensions and Schur multipliers,,19C
+19C20,"Symbols, presentations and stability of \(K_2\)",,19C
+19C30,\(K_2\) and the Brauer group,,19C
+19C40,Excision for \(K_2\),,19C
+19C99,Steinberg groups and \(K_2\),,19C
+19D06,\(Q\)- and plus-constructions,,19D
+19D10,Algebraic \(K\)-theory of spaces,,19D
+19D23,Symmetric monoidal categories,,19D
+19D25,Karoubi-Villamayor-Gersten \(K\)-theory,,19D
+19D35,"Negative \(K\)-theory, NK and Nil",,19D
+19D45,"Higher symbols, Milnor \(K\)-theory",,19D
+19D50,Computations of higher \(K\)-theory of rings,,19D
+19D55,\(K\)-theory and homology; cyclic homology and cohomology,,19D
+19D99,Higher algebraic \(K\)-theory,,19D
+19E08,\(K\)-theory of schemes,,19E
+19E15,Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects),,19E
+19E20,Relations of \(K\)-theory with cohomology theories,,19E
+19E99,\(K\)-theory in geometry,,19E
+19F05,Generalized class field theory (\(K\)-theoretic aspects),,19F
+19F15,Symbols and arithmetic (\(K\)-theoretic aspects),,19F
+19F27,"Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects)",,19F
+19F99,\(K\)-theory in number theory,,19F
+19G05,Stability for quadratic modules,,19G
+19G12,Witt groups of rings,,19G
+19G24,\(L\)-theory of group rings,,19G
+19G38,"Hermitian \(K\)-theory, relations with \(K\)-theory of rings",,19G
+19G99,\(K\)-theory of forms,,19G
+19J05,Finiteness and other obstructions in \(K_0\),,19J
+19J10,Whitehead (and related) torsion,,19J
+19J25,Surgery obstructions (\(K\)-theoretic aspects),,19J
+19J35,Obstructions to group actions (\(K\)-theoretic aspects),,19J
+19J99,Obstructions from topology,,19J
+19K14,"\(K_0\) as an ordered group, traces",,19K
+19K33,Ext and \(K\)-homology,,19K
+19K35,Kasparov theory (\(KK\)-theory),,19K
+19K56,Index theory,,19K
+19K99,\(K\)-theory and operator algebras,,19K
+19L10,"Riemann-Roch theorems, Chern characters",,19L
+19L20,"\(J\)-homomorphism, Adams operations",,19L
+19L41,"Connective \(K\)-theory, cobordism",,19L
+19L47,Equivariant \(K\)-theory,,19L
+19L50,Twisted \(K\)-theory; differential \(K\)-theory,,19L
+19L64,Geometric applications of topological \(K\)-theory,,19L
+19L99,Topological \(K\)-theory,,19L
+19M05,Miscellaneous applications of \(K\)-theory,,19M
+19M99,Miscellaneous applications of \(K\)-theory,,19M
+20A05,Axiomatics and elementary properties of groups,,20A
+20A10,Metamathematical considerations in group theory,,20A
+20A15,Applications of logic to group theory,,20A
+20A99,Foundations,,20A
+20B05,General theory for finite permutation groups,,20B
+20B07,General theory for infinite permutation groups,,20B
+20B10,Characterization theorems for permutation groups,,20B
+20B15,Primitive groups,,20B
+20B20,Multiply transitive finite groups,,20B
+20B22,Multiply transitive infinite groups,,20B
+20B25,"Finite automorphism groups of algebraic, geometric, or combinatorial structures",,20B
+20B27,Infinite automorphism groups,,20B
+20B30,Symmetric groups,,20B
+20B35,Subgroups of symmetric groups,,20B
+20B99,Permutation groups,,20B
+20C05,Group rings of finite groups and their modules (group-theoretic aspects),,20C
+20C07,Group rings of infinite groups and their modules (group-theoretic aspects),,20C
+20C08,Hecke algebras and their representations,,20C
+20C10,Integral representations of finite groups,,20C
+20C11,\(p\)-adic representations of finite groups,,20C
+20C12,Integral representations of infinite groups,,20C
+20C15,Ordinary representations and characters,,20C
+20C20,Modular representations and characters,,20C
+20C25,Projective representations and multipliers,,20C
+20C30,Representations of finite symmetric groups,,20C
+20C32,Representations of infinite symmetric groups,,20C
+20C33,Representations of finite groups of Lie type,,20C
+20C34,Representations of sporadic groups,,20C
+20C35,Applications of group representations to physics and other areas of science,,20C
+20C99,Representation theory of groups,,20C
+20D05,Finite simple groups and their classification,,20D
+20D06,Simple groups: alternating groups and groups of Lie type,,20D
+20D08,Simple groups: sporadic groups,,20D
+20D10,"Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks",,20D
+20D15,"Finite nilpotent groups, \(p\)-groups",,20D
+20D20,"Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure",,20D
+20D25,"Special subgroups (Frattini, Fitting, etc.)",,20D
+20D30,Series and lattices of subgroups,,20D
+20D35,Subnormal subgroups of abstract finite groups,,20D
+20D40,Products of subgroups of abstract finite groups,,20D
+20D45,Automorphisms of abstract finite groups,,20D
+20D60,Arithmetic and combinatorial problems involving abstract finite groups,,20D
+20D99,Abstract finite groups,,20D
+20E05,Free nonabelian groups,,20E
+20E06,"Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations",,20E
+20E07,Subgroup theorems; subgroup growth,,20E
+20E08,Groups acting on trees,,20E
+20E10,Quasivarieties and varieties of groups,,20E
+20E15,"Chains and lattices of subgroups, subnormal subgroups",,20E
+20E18,"Limits, profinite groups",,20E
+20E22,"Extensions, wreath products, and other compositions of groups",,20E
+20E25,Local properties of groups,,20E
+20E26,Residual properties and generalizations; residually finite groups,,20E
+20E28,Maximal subgroups,,20E
+20E32,Simple groups,,20E
+20E34,General structure theorems for groups,,20E
+20E36,Automorphisms of infinite groups,,20E
+20E42,Groups with a \(BN\)-pair; buildings,,20E
+20E45,Conjugacy classes for groups,,20E
+20E99,Structure and classification of infinite or finite groups,,20E
+20F05,"Generators, relations, and presentations of groups",,20F
+20F06,Cancellation theory of groups; application of van Kampen diagrams,,20F
+20F10,"Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)",,20F
+20F11,Groups of finite Morley rank,,20F
+20F12,Commutator calculus,,20F
+20F14,"Derived series, central series, and generalizations for groups",,20F
+20F16,"Solvable groups, supersolvable groups",,20F
+20F17,"Formations of groups, Fitting classes",,20F
+20F18,Nilpotent groups,,20F
+20F19,Generalizations of solvable and nilpotent groups,,20F
+20F22,Other classes of groups defined by subgroup chains,,20F
+20F24,FC-groups and their generalizations,,20F
+20F28,Automorphism groups of groups,,20F
+20F29,Representations of groups as automorphism groups of algebraic systems,,20F
+20F34,Fundamental groups and their automorphisms (group-theoretic aspects),,20F
+20F36,Braid groups; Artin groups,,20F
+20F38,Other groups related to topology or analysis,,20F
+20F40,Associated Lie structures for groups,,20F
+20F45,Engel conditions,,20F
+20F50,Periodic groups; locally finite groups,,20F
+20F55,Reflection and Coxeter groups (group-theoretic aspects),,20F
+20F60,Ordered groups (group-theoretic aspects),,20F
+20F65,Geometric group theory,,20F
+20F67,Hyperbolic groups and nonpositively curved groups,,20F
+20F69,Asymptotic properties of groups,,20F
+20F70,Algebraic geometry over groups; equations over groups,,20F
+20F99,Special aspects of infinite or finite groups,,20F
+20G05,Representation theory for linear algebraic groups,,20G
+20G07,Structure theory for linear algebraic groups,,20G
+20G10,Cohomology theory for linear algebraic groups,,20G
+20G15,Linear algebraic groups over arbitrary fields,,20G
+20G20,"Linear algebraic groups over the reals, the complexes, the quaternions",,20G
+20G25,Linear algebraic groups over local fields and their integers,,20G
+20G30,Linear algebraic groups over global fields and their integers,,20G
+20G35,Linear algebraic groups over adèles and other rings and schemes,,20G
+20G40,Linear algebraic groups over finite fields,,20G
+20G41,Exceptional groups,,20G
+20G42,Quantum groups (quantized function algebras) and their representations,,20G
+20G43,Schur and \(q\)-Schur algebras,,20G
+20G44,Kac-Moody groups,,20G
+20G45,Applications of linear algebraic groups to the sciences,,20G
+20G99,Linear algebraic groups and related topics,,20G
+20H05,"Unimodular groups, congruence subgroups (group-theoretic aspects)",,20H
+20H10,Fuchsian groups and their generalizations (group-theoretic aspects),,20H
+20H15,"Other geometric groups, including crystallographic groups",,20H
+20H20,Other matrix groups over fields,,20H
+20H25,Other matrix groups over rings,,20H
+20H30,Other matrix groups over finite fields,,20H
+20H99,Other groups of matrices,,20H
+20J05,Homological methods in group theory,,20J
+20J06,Cohomology of groups,,20J
+20J15,Category of groups,,20J
+20J99,Connections of group theory with homological algebra and category theory,,20J
+20K01,Finite abelian groups,,20K
+20K10,"Torsion groups, primary groups and generalized primary groups",,20K
+20K15,"Torsion-free groups, finite rank",,20K
+20K20,"Torsion-free groups, infinite rank",,20K
+20K21,Mixed groups,,20K
+20K25,"Direct sums, direct products, etc. for abelian groups",,20K
+20K27,Subgroups of abelian groups,,20K
+20K30,"Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups",,20K
+20K35,Extensions of abelian groups,,20K
+20K40,Homological and categorical methods for abelian groups,,20K
+20K45,Topological methods for abelian groups,,20K
+20K99,Abelian groups,,20K
+20L05,Groupoids (i.e. small categories in which all morphisms are isomorphisms),,20L
+20L99,Groupoids (i.e. small categories in which all morphisms are isomorphisms),,20L
+20M05,"Free semigroups, generators and relations, word problems",,20M
+20M07,Varieties and pseudovarieties of semigroups,,20M
+20M10,General structure theory for semigroups,,20M
+20M11,Radical theory for semigroups,,20M
+20M12,Ideal theory for semigroups,,20M
+20M13,Arithmetic theory of semigroups,,20M
+20M14,Commutative semigroups,,20M
+20M15,Mappings of semigroups,,20M
+20M17,Regular semigroups,,20M
+20M18,Inverse semigroups,,20M
+20M19,Orthodox semigroups,,20M
+20M20,"Semigroups of transformations, relations, partitions, etc.",,20M
+20M25,"Semigroup rings, multiplicative semigroups of rings",,20M
+20M30,Representation of semigroups; actions of semigroups on sets,,20M
+20M32,Algebraic monoids,,20M
+20M35,"Semigroups in automata theory, linguistics, etc.",,20M
+20M50,Connections of semigroups with homological algebra and category theory,,20M
+20M75,Generalizations of semigroups,,20M
+20M99,Semigroups,,20M
+20N02,Sets with a single binary operation (groupoids),,20N
+20N05,"Loops, quasigroups",,20N
+20N10,"Ternary systems (heaps, semiheaps, heapoids, etc.)",,20N
+20N15,\(n\)-ary systems \((n\ge 3)\),,20N
+20N20,Hypergroups,,20N
+20N25,Fuzzy groups,,20N
+20N99,Other generalizations of groups,,20N
+20P05,Probabilistic methods in group theory,,20P
+20P99,Probabilistic methods in group theory,,20P
+22A05,Structure of general topological groups,,22A
+22A10,Analysis on general topological groups,,22A
+22A15,Structure of topological semigroups,,22A
+22A20,Analysis on topological semigroups,,22A
+22A22,Topological groupoids (including differentiable and Lie groupoids),,22A
+22A25,Representations of general topological groups and semigroups,,22A
+22A26,"Topological semilattices, lattices and applications",,22A
+22A30,Other topological algebraic systems and their representations,,22A
+22A99,Topological and differentiable algebraic systems,,22A
+22B05,General properties and structure of LCA groups,,22B
+22B10,Structure of group algebras of LCA groups,,22B
+22B99,Locally compact abelian groups (LCA groups),,22B
+22C05,Compact groups,,22C
+22C99,Compact groups,,22C
+22D05,General properties and structure of locally compact groups,,22D
+22D10,Unitary representations of locally compact groups,,22D
+22D12,Other representations of locally compact groups,,22D
+22D15,Group algebras of locally compact groups,,22D
+22D20,Representations of group algebras,,22D
+22D25,\(C^*\)-algebras and \(W^*\)-algebras in relation to group representations,,22D
+22D30,Induced representations for locally compact groups,,22D
+22D35,Duality theorems for locally compact groups,,22D
+22D40,Ergodic theory on groups,,22D
+22D45,Automorphism groups of locally compact groups,,22D
+22D50,Rigidity in locally compact groups,,22D
+22D55,"Kazhdan's property (T), the Haagerup property, and generalizations",,22D
+22D99,Locally compact groups and their algebras,,22D
+22E05,Local Lie groups,,22E
+22E10,General properties and structure of complex Lie groups,,22E
+22E15,General properties and structure of real Lie groups,,22E
+22E20,General properties and structure of other Lie groups,,22E
+22E25,Nilpotent and solvable Lie groups,,22E
+22E27,"Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)",,22E
+22E30,Analysis on real and complex Lie groups,,22E
+22E35,Analysis on \(p\)-adic Lie groups,,22E
+22E40,Discrete subgroups of Lie groups,,22E
+22E41,Continuous cohomology of Lie groups,,22E
+22E43,Structure and representation of the Lorentz group,,22E
+22E45,Representations of Lie and linear algebraic groups over real fields: analytic methods,,22E
+22E46,Semisimple Lie groups and their representations,,22E
+22E47,"Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)",,22E
+22E50,Representations of Lie and linear algebraic groups over local fields,,22E
+22E55,Representations of Lie and linear algebraic groups over global fields and adèle rings,,22E
+22E57,Geometric Langlands program: representation-theoretic aspects,,22E
+22E60,Lie algebras of Lie groups,,22E
+22E65,Infinite-dimensional Lie groups and their Lie algebras: general properties,,22E
+22E66,Analysis on and representations of infinite-dimensional Lie groups,,22E
+22E67,"Loop groups and related constructions, group-theoretic treatment",,22E
+22E70,Applications of Lie groups to the sciences; explicit representations,,22E
+22E99,Lie groups,,22E
+22F05,General theory of group and pseudogroup actions,,22F
+22F10,Measurable group actions,,22F
+22F30,Homogeneous spaces,,22F
+22F50,Groups as automorphisms of other structures,,22F
+22F99,Noncompact transformation groups,,22F
+26A03,"Foundations: limits and generalizations, elementary topology of the line",,26A
+26A06,One-variable calculus,,26A
+26A09,Elementary functions,,26A
+26A12,"Rate of growth of functions, orders of infinity, slowly varying functions",,26A
+26A15,"Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable",,26A
+26A16,Lipschitz (Hölder) classes,,26A
+26A18,Iteration of real functions in one variable,,26A
+26A21,Classification of real functions; Baire classification of sets and functions,,26A
+26A24,"Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems",,26A
+26A27,"Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives",,26A
+26A30,"Singular functions, Cantor functions, functions with other special properties",,26A
+26A33,Fractional derivatives and integrals,,26A
+26A36,Antidifferentiation,,26A
+26A39,"Denjoy and Perron integrals, other special integrals",,26A
+26A42,"Integrals of Riemann, Stieltjes and Lebesgue type",,26A
+26A45,"Functions of bounded variation, generalizations",,26A
+26A46,Absolutely continuous real functions in one variable,,26A
+26A48,"Monotonic functions, generalizations",,26A
+26A51,"Convexity of real functions in one variable, generalizations",,26A
+26A99,Functions of one variable,,26A
+26B05,Continuity and differentiation questions,,26B
+26B10,"Implicit function theorems, Jacobians, transformations with several variables",,26B
+26B12,Calculus of vector functions,,26B
+26B15,"Integration of real functions of several variables: length, area, volume",,26B
+26B20,"Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)",,26B
+26B25,"Convexity of real functions of several variables, generalizations",,26B
+26B30,"Absolutely continuous real functions of several variables, functions of bounded variation",,26B
+26B35,"Special properties of functions of several variables, Hölder conditions, etc.",,26B
+26B40,Representation and superposition of functions,,26B
+26B99,Functions of several variables,,26B
+26C05,"Real polynomials: analytic properties, etc.",,26C
+26C10,Real polynomials: location of zeros,,26C
+26C15,Real rational functions,,26C
+26C99,"Polynomials, rational functions in real analysis",,26C
+26D05,Inequalities for trigonometric functions and polynomials,,26D
+26D07,Inequalities involving other types of functions,,26D
+26D10,Inequalities involving derivatives and differential and integral operators,,26D
+26D15,"Inequalities for sums, series and integrals",,26D
+26D20,Other analytical inequalities,,26D
+26D99,Inequalities in real analysis,,26D
+26E05,Real-analytic functions,,26E
+26E10,"\(C^\infty\)-functions, quasi-analytic functions",,26E
+26E15,Calculus of functions on infinite-dimensional spaces,,26E
+26E20,Calculus of functions taking values in infinite-dimensional spaces,,26E
+26E25,Set-valued functions,,26E
+26E30,Non-Archimedean analysis,,26E
+26E35,Nonstandard analysis,,26E
+26E40,Constructive real analysis,,26E
+26E50,Fuzzy real analysis,,26E
+26E60,Means,,26E
+26E70,Real analysis on time scales or measure chains,,26E
+26E99,Miscellaneous topics in real functions,,26E
+28A05,"Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets",,28A
+28A10,Real- or complex-valued set functions,,28A
+28A12,"Contents, measures, outer measures, capacities",,28A
+28A15,"Abstract differentiation theory, differentiation of set functions",,28A
+28A20,"Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence",,28A
+28A25,Integration with respect to measures and other set functions,,28A
+28A33,"Spaces of measures, convergence of measures",,28A
+28A35,Measures and integrals in product spaces,,28A
+28A50,Integration and disintegration of measures,,28A
+28A51,Lifting theory,,28A
+28A60,"Measures on Boolean rings, measure algebras",,28A
+28A75,"Length, area, volume, other geometric measure theory",,28A
+28A78,Hausdorff and packing measures,,28A
+28A80,Fractals,,28A
+28A99,Classical measure theory,,28A
+28B05,"Vector-valued set functions, measures and integrals",,28B
+28B10,"Group- or semigroup-valued set functions, measures and integrals",,28B
+28B15,"Set functions, measures and integrals with values in ordered spaces",,28B
+28B20,Set-valued set functions and measures; integration of set-valued functions; measurable selections,,28B
+28B99,"Set functions, measures and integrals with values in abstract spaces",,28B
+28C05,"Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures",,28C
+28C10,"Set functions and measures on topological groups or semigroups, Haar measures, invariant measures",,28C
+28C15,"Set functions and measures on topological spaces (regularity of measures, etc.)",,28C
+28C20,"Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)",,28C
+28C99,Set functions and measures on spaces with additional structure,,28C
+28D05,Measure-preserving transformations,,28D
+28D10,One-parameter continuous families of measure-preserving transformations,,28D
+28D15,General groups of measure-preserving transformations,,28D
+28D20,Entropy and other invariants,,28D
+28D99,Measure-theoretic ergodic theory,,28D
+28E05,Nonstandard measure theory,,28E
+28E10,Fuzzy measure theory,,28E
+28E15,Other connections with logic and set theory,,28E
+28E99,Miscellaneous topics in measure theory,,28E
+30A05,Monogenic and polygenic functions of one complex variable,,30A
+30A10,Inequalities in the complex plane,,30A
+30A99,General properties of functions of one complex variable,,30A
+30B10,Power series (including lacunary series) in one complex variable,,30B
+30B20,Random power series in one complex variable,,30B
+30B30,Boundary behavior of power series in one complex variable; over-convergence,,30B
+30B40,Analytic continuation of functions of one complex variable,,30B
+30B50,"Dirichlet series, exponential series and other series in one complex variable",,30B
+30B60,"Completeness problems, closure of a system of functions of one complex variable",,30B
+30B70,Continued fractions; complex-analytic aspects,,30B
+30B99,Series expansions of functions of one complex variable,,30B
+30C10,Polynomials and rational functions of one complex variable,,30C
+30C15,"Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)",,30C
+30C20,Conformal mappings of special domains,,30C
+30C25,Covering theorems in conformal mapping theory,,30C
+30C30,Schwarz-Christoffel-type mappings,,30C
+30C35,General theory of conformal mappings,,30C
+30C40,Kernel functions in one complex variable and applications,,30C
+30C45,"Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)",,30C
+30C50,Coefficient problems for univalent and multivalent functions of one complex variable,,30C
+30C55,General theory of univalent and multivalent functions of one complex variable,,30C
+30C62,Quasiconformal mappings in the complex plane,,30C
+30C65,"Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations",,30C
+30C70,"Extremal problems for conformal and quasiconformal mappings, variational methods",,30C
+30C75,"Extremal problems for conformal and quasiconformal mappings, other methods",,30C
+30C80,"Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination",,30C
+30C85,Capacity and harmonic measure in the complex plane,,30C
+30C99,Geometric function theory,,30C
+30D05,"Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable",,30D
+30D10,Representations of entire functions of one complex variable by series and integrals,,30D
+30D15,Special classes of entire functions of one complex variable and growth estimates,,30D
+30D20,Entire functions of one complex variable (general theory),,30D
+30D30,Meromorphic functions of one complex variable (general theory),,30D
+30D35,"Value distribution of meromorphic functions of one complex variable, Nevanlinna theory",,30D
+30D40,"Cluster sets, prime ends, boundary behavior",,30D
+30D45,"Normal functions of one complex variable, normal families",,30D
+30D60,Quasi-analytic and other classes of functions of one complex variable,,30D
+30D99,"Entire and meromorphic functions of one complex variable, and related topics",,30D
+30E05,Moment problems and interpolation problems in the complex plane,,30E
+30E10,Approximation in the complex plane,,30E
+30E15,Asymptotic representations in the complex plane,,30E
+30E20,"Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane",,30E
+30E25,Boundary value problems in the complex plane,,30E
+30E99,Miscellaneous topics of analysis in the complex plane,,30E
+30F10,Compact Riemann surfaces and uniformization,,30F
+30F15,Harmonic functions on Riemann surfaces,,30F
+30F20,Classification theory of Riemann surfaces,,30F
+30F25,Ideal boundary theory for Riemann surfaces,,30F
+30F30,Differentials on Riemann surfaces,,30F
+30F35,Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization),,30F
+30F40,Kleinian groups (aspects of compact Riemann surfaces and uniformization),,30F
+30F45,"Conformal metrics (hyperbolic, Poincaré, distance functions)",,30F
+30F50,Klein surfaces,,30F
+30F60,Teichmüller theory for Riemann surfaces,,30F
+30F99,Riemann surfaces,,30F
+30G06,Non-Archimedean function theory,,30G
+30G12,Finely holomorphic functions and topological function theory,,30G
+30G20,"Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.)",,30G
+30G25,Discrete analytic functions,,30G
+30G30,Other generalizations of analytic functions (including abstract-valued functions),,30G
+30G35,Functions of hypercomplex variables and generalized variables,,30G
+30G99,Generalized function theory,,30G
+30H05,Spaces of bounded analytic functions of one complex variable,,30H
+30H10,Hardy spaces,,30H
+30H15,Nevanlinna spaces and Smirnov spaces,,30H
+30H20,Bergman spaces and Fock spaces,,30H
+30H25,Besov spaces and \(Q_p\)-spaces,,30H
+30H30,Bloch spaces,,30H
+30H35,BMO-spaces,,30H
+30H40,Zygmund spaces,,30H
+30H45,de Branges-Rovnyak spaces,,30H
+30H50,Algebras of analytic functions of one complex variable,,30H
+30H80,Corona theorems,,30H
+30H99,Spaces and algebras of analytic functions of one complex variable,,30H
+30J05,Inner functions of one complex variable,,30J
+30J10,Blaschke products,,30J
+30J15,Singular inner functions of one complex variable,,30J
+30J99,Function theory on the disc,,30J
+30K05,Universal Taylor series in one complex variable,,30K
+30K10,Universal Dirichlet series in one complex variable,,30K
+30K15,Universal functions of one complex variable,,30K
+30K20,Compositional universality,,30K
+30K99,Universal holomorphic functions of one complex variable,,30K
+30L05,Geometric embeddings of metric spaces,,30L
+30L10,Quasiconformal mappings in metric spaces,,30L
+30L15,Inequalities in metric spaces,,30L
+30L99,Analysis on metric spaces,,30L
+31A05,"Harmonic, subharmonic, superharmonic functions in two dimensions",,31A
+31A10,"Integral representations, integral operators, integral equations methods in two dimensions",,31A
+31A15,"Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions",,31A
+31A20,"Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions",,31A
+31A25,Boundary value and inverse problems for harmonic functions in two dimensions,,31A
+31A30,"Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions",,31A
+31A35,Connections of harmonic functions with differential equations in two dimensions,,31A
+31A99,Two-dimensional potential theory,,31A
+31B05,"Harmonic, subharmonic, superharmonic functions in higher dimensions",,31B
+31B10,"Integral representations, integral operators, integral equations methods in higher dimensions",,31B
+31B15,"Potentials and capacities, extremal length and related notions in higher dimensions",,31B
+31B20,Boundary value and inverse problems for harmonic functions in higher dimensions,,31B
+31B25,Boundary behavior of harmonic functions in higher dimensions,,31B
+31B30,Biharmonic and polyharmonic equations and functions in higher dimensions,,31B
+31B35,Connections of harmonic functions with differential equations in higher dimensions,,31B
+31B99,Higher-dimensional potential theory,,31B
+31C05,"Harmonic, subharmonic, superharmonic functions on other spaces",,31C
+31C10,Pluriharmonic and plurisubharmonic functions,,31C
+31C12,Potential theory on Riemannian manifolds and other spaces,,31C
+31C15,Potentials and capacities on other spaces,,31C
+31C20,Discrete potential theory,,31C
+31C25,Dirichlet forms,,31C
+31C35,Martin boundary theory,,31C
+31C40,Fine potential theory; fine properties of sets and functions,,31C
+31C45,"Other generalizations (nonlinear potential theory, etc.)",,31C
+31C99,Generalizations of potential theory,,31C
+31D05,Axiomatic potential theory,,31D
+31D99,Axiomatic potential theory,,31D
+31E05,Potential theory on fractals and metric spaces,,31E
+31E99,Potential theory on fractals and metric spaces,,31E
+32A05,"Power series, series of functions of several complex variables",,32A
+32A08,Polynomials and rational functions of several complex variables,,32A
+32A10,Holomorphic functions of several complex variables,,32A
+32A12,Multifunctions of several complex variables,,32A
+32A15,Entire functions of several complex variables,,32A
+32A17,Special families of functions of several complex variables,,32A
+32A18,"Bloch functions, normal functions of several complex variables",,32A
+32A19,"Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.)",,32A
+32A20,Meromorphic functions of several complex variables,,32A
+32A22,Nevanlinna theory; growth estimates; other inequalities of several complex variables,,32A
+32A25,"Integral representations; canonical kernels (Szeg?, Bergman, etc.)",,32A
+32A26,"Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)",,32A
+32A27,Residues for several complex variables,,32A
+32A30,Other generalizations of function theory of one complex variable,,32A
+32A35,"\(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables",,32A
+32A36,Bergman spaces of functions in several complex variables,,32A
+32A37,"Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))",,32A
+32A38,Algebras of holomorphic functions of several complex variables,,32A
+32A40,Boundary behavior of holomorphic functions of several complex variables,,32A
+32A45,Hyperfunctions,,32A
+32A50,Harmonic analysis of several complex variables,,32A
+32A55,Singular integrals of functions in several complex variables,,32A
+32A60,Zero sets of holomorphic functions of several complex variables,,32A
+32A65,Banach algebra techniques applied to functions of several complex variables,,32A
+32A70,Functional analysis techniques applied to functions of several complex variables,,32A
+32A99,Holomorphic functions of several complex variables,,32A
+32B05,"Analytic algebras and generalizations, preparation theorems",,32B
+32B10,"Germs of analytic sets, local parametrization",,32B
+32B15,Analytic subsets of affine space,,32B
+32B20,"Semi-analytic sets, subanalytic sets, and generalizations",,32B
+32B25,"Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions",,32B
+32B99,Local analytic geometry,,32B
+32C05,"Real-analytic manifolds, real-analytic spaces",,32C
+32C07,"Real-analytic sets, complex Nash functions",,32C
+32C09,Embedding of real-analytic manifolds,,32C
+32C11,Complex supergeometry,,32C
+32C15,Complex spaces,,32C
+32C18,Topology of analytic spaces,,32C
+32C20,Normal analytic spaces,,32C
+32C22,Embedding of analytic spaces,,32C
+32C25,Analytic subsets and submanifolds,,32C
+32C30,"Integration on analytic sets and spaces, currents",,32C
+32C35,Analytic sheaves and cohomology groups,,32C
+32C36,Local cohomology of analytic spaces,,32C
+32C37,Duality theorems for analytic spaces,,32C
+32C38,"Sheaves of differential operators and their modules, \(D\)-modules",,32C
+32C55,The Levi problem in complex spaces; generalizations,,32C
+32C81,Applications of analytic spaces to physics and other areas of science,,32C
+32C99,Analytic spaces,,32C
+32D05,Domains of holomorphy,,32D
+32D10,Envelopes of holomorphy,,32D
+32D15,Continuation of analytic objects in several complex variables,,32D
+32D20,Removable singularities in several complex variables,,32D
+32D26,Riemann domains,,32D
+32D99,Analytic continuation,,32D
+32E05,"Holomorphically convex complex spaces, reduction theory",,32E
+32E10,Stein spaces,,32E
+32E20,"Polynomial convexity, rational convexity, meromorphic convexity in several complex variables",,32E
+32E30,"Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs",,32E
+32E35,Global boundary behavior of holomorphic functions of several complex variables,,32E
+32E40,The Levi problem,,32E
+32E99,Holomorphic convexity,,32E
+32F10,"\(q\)-convexity, \(q\)-concavity",,32F
+32F17,Other notions of convexity in relation to several complex variables,,32F
+32F18,Finite-type conditions for the boundary of a domain,,32F
+32F27,Topological consequences of geometric convexity,,32F
+32F32,"Analytical consequences of geometric convexity (vanishing theorems, etc.)",,32F
+32F45,Invariant metrics and pseudodistances in several complex variables,,32F
+32F99,Geometric convexity in several complex variables,,32F
+32G05,Deformations of complex structures,,32G
+32G07,"Deformations of special (e.g., CR) structures",,32G
+32G08,Deformations of fiber bundles,,32G
+32G10,Deformations of submanifolds and subspaces,,32G
+32G13,Complex-analytic moduli problems,,32G
+32G15,"Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)",,32G
+32G20,"Period matrices, variation of Hodge structure; degenerations",,32G
+32G34,"Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation)",,32G
+32G81,Applications of deformations of analytic structures to the sciences,,32G
+32G99,Deformations of analytic structures,,32G
+32H02,"Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables",,32H
+32H04,Meromorphic mappings in several complex variables,,32H
+32H12,Boundary uniqueness of mappings in several complex variables,,32H
+32H25,Picard-type theorems and generalizations for several complex variables,,32H
+32H30,Value distribution theory in higher dimensions,,32H
+32H35,"Proper holomorphic mappings, finiteness theorems",,32H
+32H40,Boundary regularity of mappings in several complex variables,,32H
+32H50,"Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables",,32H
+32H99,Holomorphic mappings and correspondences,,32H
+32J05,Compactification of analytic spaces,,32J
+32J10,Algebraic dependence theorems,,32J
+32J15,Compact complex surfaces,,32J
+32J17,Compact complex \(3\)-folds,,32J
+32J18,Compact complex \(n\)-folds,,32J
+32J25,Transcendental methods of algebraic geometry (complex-analytic aspects),,32J
+32J27,"Compact Kähler manifolds: generalizations, classification",,32J
+32J81,Applications of compact analytic spaces to the sciences,,32J
+32J99,Compact analytic spaces,,32J
+32K05,Banach analytic manifolds and spaces,,32K
+32K07,Formal and graded complex spaces,,32K
+32K12,Holomorphic maps with infinite-dimensional arguments or values,,32K
+32K15,"Differentiable functions on analytic spaces, differentiable spaces",,32K
+32K99,Generalizations of analytic spaces,,32K
+32L05,Holomorphic bundles and generalizations,,32L
+32L10,"Sheaves and cohomology of sections of holomorphic vector bundles, general results",,32L
+32L15,Bundle convexity,,32L
+32L20,Vanishing theorems,,32L
+32L25,"Twistor theory, double fibrations (complex-analytic aspects)",,32L
+32L81,Applications of holomorphic fiber spaces to the sciences,,32L
+32L99,Holomorphic fiber spaces,,32L
+32M05,"Complex Lie groups, group actions on complex spaces",,32M
+32M10,Homogeneous complex manifolds,,32M
+32M12,Almost homogeneous manifolds and spaces,,32M
+32M15,"Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)",,32M
+32M17,Automorphism groups of \(\mathbb{C}^n\) and affine manifolds,,32M
+32M18,Automorphism groups of other complex spaces,,32M
+32M25,"Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions",,32M
+32M99,Complex spaces with a group of automorphisms,,32M
+32N05,General theory of automorphic functions of several complex variables,,32N
+32N10,Automorphic forms in several complex variables,,32N
+32N15,Automorphic functions in symmetric domains,,32N
+32N99,Automorphic functions,,32N
+32P05,Non-Archimedean analysis,,32P
+32P99,Non-Archimedean analysis,,32P
+32Q02,"Special domains (Reinhardt, Hartogs, circular, tube, etc.) in \(\mathbb{C}^n\) and complex manifolds",,32Q
+32Q05,Negative curvature complex manifolds,,32Q
+32Q10,Positive curvature complex manifolds,,32Q
+32Q15,Kähler manifolds,,32Q
+32Q20,Kähler-Einstein manifolds,,32Q
+32Q25,Calabi-Yau theory (complex-analytic aspects),,32Q
+32Q26,Notions of stability for complex manifolds,,32Q
+32Q28,Stein manifolds,,32Q
+32Q30,Uniformization of complex manifolds,,32Q
+32Q35,Complex manifolds as subdomains of Euclidean space,,32Q
+32Q40,Embedding theorems for complex manifolds,,32Q
+32Q45,Hyperbolic and Kobayashi hyperbolic manifolds,,32Q
+32Q55,Topological aspects of complex manifolds,,32Q
+32Q56,Oka principle and Oka manifolds,,32Q
+32Q57,Classification theorems for complex manifolds,,32Q
+32Q60,Almost complex manifolds,,32Q
+32Q65,Pseudoholomorphic curves,,32Q
+32Q99,Complex manifolds,,32Q
+32S05,Local complex singularities,,32S
+32S10,Invariants of analytic local rings,,32S
+32S15,Equisingularity (topological and analytic),,32S
+32S20,Global theory of complex singularities; cohomological properties,,32S
+32S22,Relations with arrangements of hyperplanes,,32S
+32S25,Complex surface and hypersurface singularities,,32S
+32S30,Deformations of complex singularities; vanishing cycles,,32S
+32S35,Mixed Hodge theory of singular varieties (complex-analytic aspects),,32S
+32S40,Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects),,32S
+32S45,Modifications; resolution of singularities (complex-analytic aspects),,32S
+32S50,"Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants",,32S
+32S55,Milnor fibration; relations with knot theory,,32S
+32S60,Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects),,32S
+32S65,Singularities of holomorphic vector fields and foliations,,32S
+32S70,Other operations on complex singularities,,32S
+32S99,Complex singularities,,32S
+32T05,Domains of holomorphy,,32T
+32T15,Strongly pseudoconvex domains,,32T
+32T20,Worm domains,,32T
+32T25,Finite-type domains,,32T
+32T27,Geometric and analytic invariants on weakly pseudoconvex boundaries,,32T
+32T35,Exhaustion functions,,32T
+32T40,Peak functions,,32T
+32T99,Pseudoconvex domains,,32T
+32U05,Plurisubharmonic functions and generalizations,,32U
+32U10,Plurisubharmonic exhaustion functions,,32U
+32U15,General pluripotential theory,,32U
+32U20,Capacity theory and generalizations,,32U
+32U25,Lelong numbers,,32U
+32U30,Removable sets in pluripotential theory,,32U
+32U35,"Plurisubharmonic extremal functions, pluricomplex Green functions",,32U
+32U40,Currents,,32U
+32U99,Pluripotential theory,,32U
+32V05,"CR structures, CR operators, and generalizations",,32V
+32V10,CR functions,,32V
+32V15,CR manifolds as boundaries of domains,,32V
+32V20,Analysis on CR manifolds,,32V
+32V25,Extension of functions and other analytic objects from CR manifolds,,32V
+32V30,Embeddings of CR manifolds,,32V
+32V35,Finite-type conditions on CR manifolds,,32V
+32V40,Real submanifolds in complex manifolds,,32V
+32V99,CR manifolds,,32V
+32W05,\(\overline\partial\) and \(\overline\partial\)-Neumann operators,,32W
+32W10,\(\overline\partial_b\) and \(\overline\partial_b\)-Neumann operators,,32W
+32W20,Complex Monge-Ampère operators,,32W
+32W25,Pseudodifferential operators in several complex variables,,32W
+32W30,Heat kernels in several complex variables,,32W
+32W50,Other partial differential equations of complex analysis in several variables,,32W
+32W99,Differential operators in several variables,,32W
+33B10,Exponential and trigonometric functions,,33B
+33B15,"Gamma, beta and polygamma functions",,33B
+33B20,"Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)",,33B
+33B30,Higher logarithm functions,,33B
+33B99,Elementary classical functions,,33B
+33C05,"Classical hypergeometric functions, \({}_2F_1\)",,33C
+33C10,"Bessel and Airy functions, cylinder functions, \({}_0F_1\)",,33C
+33C15,"Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)",,33C
+33C20,"Generalized hypergeometric series, \({}_pF_q\)",,33C
+33C45,"Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)",,33C
+33C47,Other special orthogonal polynomials and functions,,33C
+33C50,Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable,,33C
+33C52,Orthogonal polynomials and functions associated with root systems,,33C
+33C55,Spherical harmonics,,33C
+33C60,"Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)",,33C
+33C65,"Appell, Horn and Lauricella functions",,33C
+33C67,Hypergeometric functions associated with root systems,,33C
+33C70,Other hypergeometric functions and integrals in several variables,,33C
+33C75,Elliptic integrals as hypergeometric functions,,33C
+33C80,"Connections of hypergeometric functions with groups and algebras, and related topics",,33C
+33C90,Applications of hypergeometric functions,,33C
+33C99,Hypergeometric functions,,33C
+33D05,"\(q\)-gamma functions, \(q\)-beta functions and integrals",,33D
+33D15,"Basic hypergeometric functions in one variable, \({}_r\phi_s\)",,33D
+33D45,"Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)",,33D
+33D50,Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable,,33D
+33D52,"Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)",,33D
+33D60,Basic hypergeometric integrals and functions defined by them,,33D
+33D65,Bibasic functions and multiple bases,,33D
+33D67,Basic hypergeometric functions associated with root systems,,33D
+33D70,Other basic hypergeometric functions and integrals in several variables,,33D
+33D80,"Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics",,33D
+33D90,Applications of basic hypergeometric functions,,33D
+33D99,Basic hypergeometric functions,,33D
+33E05,Elliptic functions and integrals,,33E
+33E10,"Lamé, Mathieu, and spheroidal wave functions",,33E
+33E12,Mittag-Leffler functions and generalizations,,33E
+33E15,Other wave functions,,33E
+33E17,Painlevé-type functions,,33E
+33E20,Other functions defined by series and integrals,,33E
+33E30,"Other functions coming from differential, difference and integral equations",,33E
+33E50,"Special functions in characteristic \(p\) (gamma functions, etc.)",,33E
+33E99,Other special functions,,33E
+33F05,Numerical approximation and evaluation of special functions,,33F
+33F10,"Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)",,33F
+33F99,Computational aspects of special functions,,33F
+34A05,"Explicit solutions, first integrals of ordinary differential equations",,34A
+34A06,"Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.)",,34A
+34A07,Fuzzy ordinary differential equations,,34A
+34A08,Fractional ordinary differential equations,,34A
+34A09,"Implicit ordinary differential equations, differential-algebraic equations",,34A
+34A12,"Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations",,34A
+34A25,"Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.",,34A
+34A26,Geometric methods in ordinary differential equations,,34A
+34A30,Linear ordinary differential equations and systems,,34A
+34A33,Ordinary lattice differential equations,,34A
+34A34,Nonlinear ordinary differential equations and systems,,34A
+34A35,Ordinary differential equations of infinite order,,34A
+34A36,Discontinuous ordinary differential equations,,34A
+34A37,Ordinary differential equations with impulses,,34A
+34A38,Hybrid systems of ordinary differential equations,,34A
+34A40,Differential inequalities involving functions of a single real variable,,34A
+34A45,Theoretical approximation of solutions to ordinary differential equations,,34A
+34A55,Inverse problems involving ordinary differential equations,,34A
+34A60,Ordinary differential inclusions,,34A
+34A99,General theory for ordinary differential equations,,34A
+34B05,Linear boundary value problems for ordinary differential equations,,34B
+34B07,Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter,,34B
+34B08,Parameter dependent boundary value problems for ordinary differential equations,,34B
+34B09,Boundary eigenvalue problems for ordinary differential equations,,34B
+34B10,Nonlocal and multipoint boundary value problems for ordinary differential equations,,34B
+34B15,Nonlinear boundary value problems for ordinary differential equations,,34B
+34B16,Singular nonlinear boundary value problems for ordinary differential equations,,34B
+34B18,Positive solutions to nonlinear boundary value problems for ordinary differential equations,,34B
+34B20,Weyl theory and its generalizations for ordinary differential equations,,34B
+34B24,Sturm-Liouville theory,,34B
+34B27,Green's functions for ordinary differential equations,,34B
+34B30,"Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)",,34B
+34B37,Boundary value problems with impulses for ordinary differential equations,,34B
+34B40,Boundary value problems on infinite intervals for ordinary differential equations,,34B
+34B45,Boundary value problems on graphs and networks for ordinary differential equations,,34B
+34B60,Applications of boundary value problems involving ordinary differential equations,,34B
+34B99,Boundary value problems for ordinary differential equations,,34B
+34C05,"Topological structure of integral curves, singular points, limit cycles of ordinary differential equations",,34C
+34C07,"Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations",,34C
+34C08,"Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.)",,34C
+34C10,"Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations",,34C
+34C11,Growth and boundedness of solutions to ordinary differential equations,,34C
+34C12,Monotone systems involving ordinary differential equations,,34C
+34C14,"Symmetries, invariants of ordinary differential equations",,34C
+34C15,Nonlinear oscillations and coupled oscillators for ordinary differential equations,,34C
+34C20,"Transformation and reduction of ordinary differential equations and systems, normal forms",,34C
+34C23,Bifurcation theory for ordinary differential equations,,34C
+34C25,Periodic solutions to ordinary differential equations,,34C
+34C26,Relaxation oscillations for ordinary differential equations,,34C
+34C27,Almost and pseudo-almost periodic solutions to ordinary differential equations,,34C
+34C28,Complex behavior and chaotic systems of ordinary differential equations,,34C
+34C29,Averaging method for ordinary differential equations,,34C
+34C37,Homoclinic and heteroclinic solutions to ordinary differential equations,,34C
+34C40,Ordinary differential equations and systems on manifolds,,34C
+34C41,Equivalence and asymptotic equivalence of ordinary differential equations,,34C
+34C45,Invariant manifolds for ordinary differential equations,,34C
+34C46,Multifrequency systems of ordinary differential equations,,34C
+34C55,Hysteresis for ordinary differential equations,,34C
+34C60,Qualitative investigation and simulation of ordinary differential equation models,,34C
+34C99,Qualitative theory for ordinary differential equations,,34C
+34D05,Asymptotic properties of solutions to ordinary differential equations,,34D
+34D06,Synchronization of solutions to ordinary differential equations,,34D
+34D08,Characteristic and Lyapunov exponents of ordinary differential equations,,34D
+34D09,"Dichotomy, trichotomy of solutions to ordinary differential equations",,34D
+34D10,Perturbations of ordinary differential equations,,34D
+34D15,Singular perturbations of ordinary differential equations,,34D
+34D20,Stability of solutions to ordinary differential equations,,34D
+34D23,Global stability of solutions to ordinary differential equations,,34D
+34D30,Structural stability and analogous concepts of solutions to ordinary differential equations,,34D
+34D35,Stability of manifolds of solutions to ordinary differential equations,,34D
+34D45,Attractors of solutions to ordinary differential equations,,34D
+34D99,Stability theory for ordinary differential equations,,34D
+34E05,Asymptotic expansions of solutions to ordinary differential equations,,34E
+34E10,"Perturbations, asymptotics of solutions to ordinary differential equations",,34E
+34E13,Multiple scale methods for ordinary differential equations,,34E
+34E15,Singular perturbations for ordinary differential equations,,34E
+34E17,Canard solutions to ordinary differential equations,,34E
+34E18,Methods of nonstandard analysis for ordinary differential equations,,34E
+34E20,"Singular perturbations, turning point theory, WKB methods for ordinary differential equations",,34E
+34E99,Asymptotic theory for ordinary differential equations,,34E
+34F05,Ordinary differential equations and systems with randomness,,34F
+34F10,Bifurcation of solutions to ordinary differential equations involving randomness,,34F
+34F15,Resonance phenomena for ordinary differential equations involving randomness,,34F
+34F99,Ordinary differential equations and systems with randomness,,34F
+34G10,Linear differential equations in abstract spaces,,34G
+34G20,Nonlinear differential equations in abstract spaces,,34G
+34G25,Evolution inclusions,,34G
+34G99,Differential equations in abstract spaces,,34G
+34H05,Control problems involving ordinary differential equations,,34H
+34H10,Chaos control for problems involving ordinary differential equations,,34H
+34H15,Stabilization of solutions to ordinary differential equations,,34H
+34H20,Bifurcation control of ordinary differential equations,,34H
+34H99,Control problems involving ordinary differential equations,,34H
+34K04,"Symmetries, invariants of functional-differential equations",,34K
+34K05,General theory of functional-differential equations,,34K
+34K06,Linear functional-differential equations,,34K
+34K07,Theoretical approximation of solutions to functional-differential equations,,34K
+34K08,Spectral theory of functional-differential operators,,34K
+34K09,Functional-differential inclusions,,34K
+34K10,Boundary value problems for functional-differential equations,,34K
+34K11,Oscillation theory of functional-differential equations,,34K
+34K12,"Growth, boundedness, comparison of solutions to functional-differential equations",,34K
+34K13,Periodic solutions to functional-differential equations,,34K
+34K14,Almost and pseudo-almost periodic solutions to functional-differential equations,,34K
+34K16,Heteroclinic and homoclinic orbits of functional-differential equations,,34K
+34K17,"Transformation and reduction of functional-differential equations and systems, normal forms",,34K
+34K18,Bifurcation theory of functional-differential equations,,34K
+34K19,Invariant manifolds of functional-differential equations,,34K
+34K20,Stability theory of functional-differential equations,,34K
+34K21,Stationary solutions of functional-differential equations,,34K
+34K23,Complex (chaotic) behavior of solutions to functional-differential equations,,34K
+34K24,Synchronization of functional-differential equations,,34K
+34K25,Asymptotic theory of functional-differential equations,,34K
+34K26,Singular perturbations of functional-differential equations,,34K
+34K27,Perturbations of functional-differential equations,,34K
+34K29,Inverse problems for functional-differential equations,,34K
+34K30,Functional-differential equations in abstract spaces,,34K
+34K31,Lattice functional-differential equations,,34K
+34K32,Implicit functional-differential equations,,34K
+34K33,Averaging for functional-differential equations,,34K
+34K34,Hybrid systems of functional-differential equations,,34K
+34K35,Control problems for functional-differential equations,,34K
+34K36,Fuzzy functional-differential equations,,34K
+34K37,Functional-differential equations with fractional derivatives,,34K
+34K38,Functional-differential inequalities,,34K
+34K39,Discontinuous functional-differential equations,,34K
+34K40,Neutral functional-differential equations,,34K
+34K41,Functional-differential equations in the complex domain,,34K
+34K42,Functional-differential equations on time scales or measure chains,,34K
+34K43,Functional-differential equations with state-dependent arguments,,34K
+34K45,Functional-differential equations with impulses,,34K
+34K50,Stochastic functional-differential equations,,34K
+34K60,Qualitative investigation and simulation of models involving functional-differential equations,,34K
+34K99,"Functional-differential equations (including equations with delayed, advanced or state-dependent argument)",,34K
+34L05,General spectral theory of ordinary differential operators,,34L
+34L10,"Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators",,34L
+34L15,"Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators",,34L
+34L16,Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators,,34L
+34L20,"Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators",,34L
+34L25,"Scattering theory, inverse scattering involving ordinary differential operators",,34L
+34L30,Nonlinear ordinary differential operators,,34L
+34L40,"Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)",,34L
+34L99,Ordinary differential operators,,34L
+34M03,Linear ordinary differential equations and systems in the complex domain,,34M
+34M04,Nonlinear ordinary differential equations and systems in the complex domain,,34M
+34M05,Entire and meromorphic solutions to ordinary differential equations in the complex domain,,34M
+34M10,"Oscillation, growth of solutions to ordinary differential equations in the complex domain",,34M
+34M15,"Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain",,34M
+34M25,Formal solutions and transform techniques for ordinary differential equations in the complex domain,,34M
+34M30,Asymptotics and summation methods for ordinary differential equations in the complex domain,,34M
+34M35,"Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms",,34M
+34M40,Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain,,34M
+34M45,Ordinary differential equations on complex manifolds,,34M
+34M46,Spectral theory for ordinary differential operators in the complex domain,,34M
+34M50,"Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain",,34M
+34M55,"Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies",,34M
+34M56,Isomonodromic deformations for ordinary differential equations in the complex domain,,34M
+34M60,"Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent)",,34M
+34M65,Topological structure of trajectories of ordinary differential equations in the complex domain,,34M
+34M99,Ordinary differential equations in the complex domain,,34M
+34N05,Dynamic equations on time scales or measure chains,,34N
+34N99,Dynamic equations on time scales or measure chains,,34N
+35A01,"Existence problems for PDEs: global existence, local existence, non-existence",,35A
+35A02,"Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness",,35A
+35A08,Fundamental solutions to PDEs,,35A
+35A09,Classical solutions to PDEs,,35A
+35A10,Cauchy-Kovalevskaya theorems,,35A
+35A15,Variational methods applied to PDEs,,35A
+35A16,Topological and monotonicity methods applied to PDEs,,35A
+35A17,Parametrices in context of PDEs,,35A
+35A18,Wave front sets in context of PDEs,,35A
+35A20,Analyticity in context of PDEs,,35A
+35A21,Singularity in context of PDEs,,35A
+35A22,"Transform methods (e.g., integral transforms) applied to PDEs",,35A
+35A23,"Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals",,35A
+35A24,Methods of ordinary differential equations applied to PDEs,,35A
+35A25,Other special methods applied to PDEs,,35A
+35A27,Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs,,35A
+35A30,"Geometric theory, characteristics, transformations in context of PDEs",,35A
+35A35,Theoretical approximation in context of PDEs,,35A
+35A99,General topics in partial differential equations,,35A
+35B05,"Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs",,35B
+35B06,"Symmetries, invariants, etc. in context of PDEs",,35B
+35B07,Axially symmetric solutions to PDEs,,35B
+35B08,Entire solutions to PDEs,,35B
+35B09,Positive solutions to PDEs,,35B
+35B10,Periodic solutions to PDEs,,35B
+35B15,Almost and pseudo-almost periodic solutions to PDEs,,35B
+35B20,Perturbations in context of PDEs,,35B
+35B25,Singular perturbations in context of PDEs,,35B
+35B27,Homogenization in context of PDEs; PDEs in media with periodic structure,,35B
+35B30,Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs,,35B
+35B32,Bifurcations in context of PDEs,,35B
+35B33,Critical exponents in context of PDEs,,35B
+35B34,Resonance in context of PDEs,,35B
+35B35,Stability in context of PDEs,,35B
+35B36,Pattern formations in context of PDEs,,35B
+35B38,"Critical points of functionals in context of PDEs (e.g., energy functionals)",,35B
+35B40,Asymptotic behavior of solutions to PDEs,,35B
+35B41,Attractors,,35B
+35B42,Inertial manifolds,,35B
+35B44,Blow-up in context of PDEs,,35B
+35B45,A priori estimates in context of PDEs,,35B
+35B50,Maximum principles in context of PDEs,,35B
+35B51,Comparison principles in context of PDEs,,35B
+35B53,Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs,,35B
+35B60,Continuation and prolongation of solutions to PDEs,,35B
+35B65,Smoothness and regularity of solutions to PDEs,,35B
+35B99,Qualitative properties of solutions to partial differential equations,,35B
+35C05,Solutions to PDEs in closed form,,35C
+35C06,Self-similar solutions to PDEs,,35C
+35C07,Traveling wave solutions,,35C
+35C08,Soliton solutions,,35C
+35C09,Trigonometric solutions to PDEs,,35C
+35C10,Series solutions to PDEs,,35C
+35C11,Polynomial solutions to PDEs,,35C
+35C15,Integral representations of solutions to PDEs,,35C
+35C20,Asymptotic expansions of solutions to PDEs,,35C
+35C99,Representations of solutions to partial differential equations,,35C
+35D30,Weak solutions to PDEs,,35D
+35D35,Strong solutions to PDEs,,35D
+35D40,Viscosity solutions to PDEs,,35D
+35D99,Generalized solutions to partial differential equations,,35D
+35E05,Fundamental solutions to PDEs and systems of PDEs with constant coefficients,,35E
+35E10,Convexity properties of solutions to PDEs with constant coefficients,,35E
+35E15,Initial value problems for PDEs and systems of PDEs with constant coefficients,,35E
+35E20,General theory of PDEs and systems of PDEs with constant coefficients,,35E
+35E99,Partial differential equations and systems of partial differential equations with constant coefficients,,35E
+35F05,Linear first-order PDEs,,35F
+35F10,Initial value problems for linear first-order PDEs,,35F
+35F15,Boundary value problems for linear first-order PDEs,,35F
+35F16,Initial-boundary value problems for linear first-order PDEs,,35F
+35F20,Nonlinear first-order PDEs,,35F
+35F21,Hamilton-Jacobi equations,,35F
+35F25,Initial value problems for nonlinear first-order PDEs,,35F
+35F30,Boundary value problems for nonlinear first-order PDEs,,35F
+35F31,Initial-boundary value problems for nonlinear first-order PDEs,,35F
+35F35,Systems of linear first-order PDEs,,35F
+35F40,Initial value problems for systems of linear first-order PDEs,,35F
+35F45,Boundary value problems for systems of linear first-order PDEs,,35F
+35F46,Initial-boundary value problems for systems of linear first-order PDEs,,35F
+35F50,Systems of nonlinear first-order PDEs,,35F
+35F55,Initial value problems for systems of nonlinear first-order PDEs,,35F
+35F60,Boundary value problems for systems of nonlinear first-order PDEs,,35F
+35F61,Initial-boundary value problems for systems of nonlinear first-order PDEs,,35F
+35F99,General first-order partial differential equations and systems of first-order partial differential equations,,35F
+35G05,Linear higher-order PDEs,,35G
+35G10,Initial value problems for linear higher-order PDEs,,35G
+35G15,Boundary value problems for linear higher-order PDEs,,35G
+35G16,Initial-boundary value problems for linear higher-order PDEs,,35G
+35G20,Nonlinear higher-order PDEs,,35G
+35G25,Initial value problems for nonlinear higher-order PDEs,,35G
+35G30,Boundary value problems for nonlinear higher-order PDEs,,35G
+35G31,Initial-boundary value problems for nonlinear higher-order PDEs,,35G
+35G35,Systems of linear higher-order PDEs,,35G
+35G40,Initial value problems for systems of linear higher-order PDEs,,35G
+35G45,Boundary value problems for systems of linear higher-order PDEs,,35G
+35G46,Initial-boundary value problems for systems of linear higher-order PDEs,,35G
+35G50,Systems of nonlinear higher-order PDEs,,35G
+35G55,Initial value problems for systems of nonlinear higher-order PDEs,,35G
+35G60,Boundary value problems for systems of nonlinear higher-order PDEs,,35G
+35G61,Initial-boundary value problems for systems of nonlinear higher-order PDEs,,35G
+35G99,General higher-order partial differential equations and systems of higher-order partial differential equations,,35G
+35H10,Hypoelliptic equations,,35H
+35H20,Subelliptic equations,,35H
+35H30,Quasielliptic equations,,35H
+35H99,Close-to-elliptic equations,,35H
+35J05,"Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation",,35J
+35J08,Green's functions for elliptic equations,,35J
+35J10,"Schrödinger operator, Schrödinger equation",,35J
+35J15,Second-order elliptic equations,,35J
+35J20,Variational methods for second-order elliptic equations,,35J
+35J25,Boundary value problems for second-order elliptic equations,,35J
+35J30,Higher-order elliptic equations,,35J
+35J35,Variational methods for higher-order elliptic equations,,35J
+35J40,Boundary value problems for higher-order elliptic equations,,35J
+35J46,First-order elliptic systems,,35J
+35J47,Second-order elliptic systems,,35J
+35J48,Higher-order elliptic systems,,35J
+35J50,Variational methods for elliptic systems,,35J
+35J56,Boundary value problems for first-order elliptic systems,,35J
+35J57,Boundary value problems for second-order elliptic systems,,35J
+35J58,Boundary value problems for higher-order elliptic systems,,35J
+35J60,Nonlinear elliptic equations,,35J
+35J61,Semilinear elliptic equations,,35J
+35J62,Quasilinear elliptic equations,,35J
+35J65,Nonlinear boundary value problems for linear elliptic equations,,35J
+35J66,Nonlinear boundary value problems for nonlinear elliptic equations,,35J
+35J67,Boundary values of solutions to elliptic equations and elliptic systems,,35J
+35J70,Degenerate elliptic equations,,35J
+35J75,Singular elliptic equations,,35J
+35J86,Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators,,35J
+35J87,Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators,,35J
+35J88,Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators,,35J
+35J91,"Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian",,35J
+35J92,Quasilinear elliptic equations with \(p\)-Laplacian,,35J
+35J93,Quasilinear elliptic equations with mean curvature operator,,35J
+35J94,Elliptic equations with infinity-Laplacian,,35J
+35J96,Monge-Ampère equations,,35J
+35J99,Elliptic equations and elliptic systems,,35J
+35K05,Heat equation,,35K
+35K08,Heat kernel,,35K
+35K10,Second-order parabolic equations,,35K
+35K15,Initial value problems for second-order parabolic equations,,35K
+35K20,Initial-boundary value problems for second-order parabolic equations,,35K
+35K25,Higher-order parabolic equations,,35K
+35K30,Initial value problems for higher-order parabolic equations,,35K
+35K35,Initial-boundary value problems for higher-order parabolic equations,,35K
+35K40,Second-order parabolic systems,,35K
+35K41,Higher-order parabolic systems,,35K
+35K45,Initial value problems for second-order parabolic systems,,35K
+35K46,Initial value problems for higher-order parabolic systems,,35K
+35K51,Initial-boundary value problems for second-order parabolic systems,,35K
+35K52,Initial-boundary value problems for higher-order parabolic systems,,35K
+35K55,Nonlinear parabolic equations,,35K
+35K57,Reaction-diffusion equations,,35K
+35K58,Semilinear parabolic equations,,35K
+35K59,Quasilinear parabolic equations,,35K
+35K60,"Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations",,35K
+35K61,"Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations",,35K
+35K65,Degenerate parabolic equations,,35K
+35K67,Singular parabolic equations,,35K
+35K70,"Ultraparabolic equations, pseudoparabolic equations, etc.",,35K
+35K85,Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators,,35K
+35K86,Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators,,35K
+35K87,Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators,,35K
+35K90,Abstract parabolic equations,,35K
+35K91,"Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian",,35K
+35K92,Quasilinear parabolic equations with \(p\)-Laplacian,,35K
+35K93,Quasilinear parabolic equations with mean curvature operator,,35K
+35K96,Parabolic Monge-Ampère equations,,35K
+35K99,Parabolic equations and parabolic systems,,35K
+35L02,First-order hyperbolic equations,,35L
+35L03,Initial value problems for first-order hyperbolic equations,,35L
+35L04,Initial-boundary value problems for first-order hyperbolic equations,,35L
+35L05,Wave equation,,35L
+35L10,Second-order hyperbolic equations,,35L
+35L15,Initial value problems for second-order hyperbolic equations,,35L
+35L20,Initial-boundary value problems for second-order hyperbolic equations,,35L
+35L25,Higher-order hyperbolic equations,,35L
+35L30,Initial value problems for higher-order hyperbolic equations,,35L
+35L35,Initial-boundary value problems for higher-order hyperbolic equations,,35L
+35L40,First-order hyperbolic systems,,35L
+35L45,Initial value problems for first-order hyperbolic systems,,35L
+35L50,Initial-boundary value problems for first-order hyperbolic systems,,35L
+35L51,Second-order hyperbolic systems,,35L
+35L52,Initial value problems for second-order hyperbolic systems,,35L
+35L53,Initial-boundary value problems for second-order hyperbolic systems,,35L
+35L55,Higher-order hyperbolic systems,,35L
+35L56,Initial value problems for higher-order hyperbolic systems,,35L
+35L57,Initial-boundary value problems for higher-order hyperbolic systems,,35L
+35L60,First-order nonlinear hyperbolic equations,,35L
+35L65,Hyperbolic conservation laws,,35L
+35L67,Shocks and singularities for hyperbolic equations,,35L
+35L70,Second-order nonlinear hyperbolic equations,,35L
+35L71,Second-order semilinear hyperbolic equations,,35L
+35L72,Second-order quasilinear hyperbolic equations,,35L
+35L75,Higher-order nonlinear hyperbolic equations,,35L
+35L76,Higher-order semilinear hyperbolic equations,,35L
+35L77,Higher-order quasilinear hyperbolic equations,,35L
+35L80,Degenerate hyperbolic equations,,35L
+35L81,Singular hyperbolic equations,,35L
+35L82,Pseudohyperbolic equations,,35L
+35L85,Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators,,35L
+35L86,Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators,,35L
+35L87,Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators,,35L
+35L90,Abstract hyperbolic equations,,35L
+35L99,Hyperbolic equations and hyperbolic systems,,35L
+35M10,PDEs of mixed type,,35M
+35M11,Initial value problems for PDEs of mixed type,,35M
+35M12,Boundary value problems for PDEs of mixed type,,35M
+35M13,Initial-boundary value problems for PDEs of mixed type,,35M
+35M30,Mixed-type systems of PDEs,,35M
+35M31,Initial value problems for mixed-type systems of PDEs,,35M
+35M32,Boundary value problems for mixed-type systems of PDEs,,35M
+35M33,Initial-boundary value problems for mixed-type systems of PDEs,,35M
+35M85,Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type,,35M
+35M86,Unilateral problems for nonlinear PDEs of mixed type and variational inequalities with nonlinear partial differential operators of mixed type,,35M
+35M87,Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type,,35M
+35M99,Partial differential equations of mixed type and mixed-type systems of partial differential equations,,35M
+35N05,Overdetermined systems of PDEs with constant coefficients,,35N
+35N10,Overdetermined systems of PDEs with variable coefficients,,35N
+35N15,\(\overline\partial\)-Neumann problems and formal complexes in context of PDEs,,35N
+35N20,Overdetermined initial value problems for PDEs and systems of PDEs,,35N
+35N25,Overdetermined boundary value problems for PDEs and systems of PDEs,,35N
+35N30,Overdetermined initial-boundary value problems for PDEs and systems of PDEs,,35N
+35N99,Overdetermined problems for partial differential equations and systems of partial differential equations,,35N
+35P05,General topics in linear spectral theory for PDEs,,35P
+35P10,Completeness of eigenfunctions and eigenfunction expansions in context of PDEs,,35P
+35P15,Estimates of eigenvalues in context of PDEs,,35P
+35P20,Asymptotic distributions of eigenvalues in context of PDEs,,35P
+35P25,Scattering theory for PDEs,,35P
+35P30,Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs,,35P
+35P99,Spectral theory and eigenvalue problems for partial differential equations,,35P
+35Q05,Euler-Poisson-Darboux equations,,35Q
+35Q07,Fuchsian PDEs,,35Q
+35Q15,Riemann-Hilbert problems in context of PDEs,,35Q
+35Q20,Boltzmann equations,,35Q
+35Q30,Navier-Stokes equations,,35Q
+35Q31,Euler equations,,35Q
+35Q35,PDEs in connection with fluid mechanics,,35Q
+35Q40,PDEs in connection with quantum mechanics,,35Q
+35Q41,Time-dependent Schrödinger equations and Dirac equations,,35Q
+35Q49,Transport equations,,35Q
+35Q51,Soliton equations,,35Q
+35Q53,KdV equations (Korteweg-de Vries equations),,35Q
+35Q55,NLS equations (nonlinear Schrödinger equations),,35Q
+35Q56,Ginzburg-Landau equations,,35Q
+35Q60,PDEs in connection with optics and electromagnetic theory,,35Q
+35Q61,Maxwell equations,,35Q
+35Q62,PDEs in connection with statistics,,35Q
+35Q68,PDEs in connection with computer science,,35Q
+35Q70,PDEs in connection with mechanics of particles and systems of particles,,35Q
+35Q74,PDEs in connection with mechanics of deformable solids,,35Q
+35Q75,PDEs in connection with relativity and gravitational theory,,35Q
+35Q76,Einstein equations,,35Q
+35Q79,PDEs in connection with classical thermodynamics and heat transfer,,35Q
+35Q81,PDEs in connection with semiconductor devices,,35Q
+35Q82,PDEs in connection with statistical mechanics,,35Q
+35Q83,Vlasov equations,,35Q
+35Q84,Fokker-Planck equations,,35Q
+35Q85,PDEs in connection with astronomy and astrophysics,,35Q
+35Q86,PDEs in connection with geophysics,,35Q
+35Q89,PDEs in connection with mean field game theory,,35Q
+35Q90,PDEs in connection with mathematical programming,,35Q
+35Q91,"PDEs in connection with game theory, economics, social and behavioral sciences",,35Q
+35Q92,"PDEs in connection with biology, chemistry and other natural sciences",,35Q
+35Q93,PDEs in connection with control and optimization,,35Q
+35Q94,PDEs in connection with information and communication,,35Q
+35Q99,Partial differential equations of mathematical physics and other areas of application,,35Q
+35R01,PDEs on manifolds,,35R
+35R02,PDEs on graphs and networks (ramified or polygonal spaces),,35R
+35R03,"PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.",,35R
+35R05,PDEs with low regular coefficients and/or low regular data,,35R
+35R06,PDEs with measure,,35R
+35R07,PDEs on time scales,,35R
+35R09,Integro-partial differential equations,,35R
+35R10,Partial functional-differential equations,,35R
+35R11,Fractional partial differential equations,,35R
+35R12,Impulsive partial differential equations,,35R
+35R13,Fuzzy partial differential equations,,35R
+35R15,"PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)",,35R
+35R20,Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions),,35R
+35R25,Ill-posed problems for PDEs,,35R
+35R30,Inverse problems for PDEs,,35R
+35R35,Free boundary problems for PDEs,,35R
+35R37,Moving boundary problems for PDEs,,35R
+35R45,Partial differential inequalities and systems of partial differential inequalities,,35R
+35R50,PDEs of infinite order,,35R
+35R60,"PDEs with randomness, stochastic partial differential equations",,35R
+35R70,PDEs with multivalued right-hand sides,,35R
+35R99,Miscellaneous topics in partial differential equations,,35R
+35S05,Pseudodifferential operators as generalizations of partial differential operators,,35S
+35S10,Initial value problems for PDEs with pseudodifferential operators,,35S
+35S15,Boundary value problems for PDEs with pseudodifferential operators,,35S
+35S16,Initial-boundary value problems for PDEs with pseudodifferential operators,,35S
+35S30,Fourier integral operators applied to PDEs,,35S
+35S35,"Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc.",,35S
+35S50,Paradifferential operators as generalizations of partial differential operators in context of PDEs,,35S
+35S99,Pseudodifferential operators and other generalizations of partial differential operators,,35S
+37A05,Dynamical aspects of measure-preserving transformations,,37A
+37A10,Dynamical systems involving one-parameter continuous families of measure-preserving transformations,,37A
+37A15,General groups of measure-preserving transformations and dynamical systems,,37A
+37A17,Homogeneous flows,,37A
+37A20,"Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations",,37A
+37A25,"Ergodicity, mixing, rates of mixing",,37A
+37A30,"Ergodic theorems, spectral theory, Markov operators",,37A
+37A35,"Entropy and other invariants, isomorphism, classification in ergodic theory",,37A
+37A40,Nonsingular (and infinite-measure preserving) transformations,,37A
+37A44,Relations between ergodic theory and number theory,,37A
+37A46,Relations between ergodic theory and harmonic analysis,,37A
+37A50,Dynamical systems and their relations with probability theory and stochastic processes,,37A
+37A55,Dynamical systems and the theory of \(C^*\)-algebras,,37A
+37A60,Dynamical aspects of statistical mechanics,,37A
+37A99,Ergodic theory,,37A
+37B02,Dynamics in general topological spaces,,37B
+37B05,"Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)",,37B
+37B10,Symbolic dynamics,,37B
+37B15,Dynamical aspects of cellular automata,,37B
+37B20,Notions of recurrence and recurrent behavior in topological dynamical systems,,37B
+37B25,Stability of topological dynamical systems,,37B
+37B30,"Index theory for dynamical systems, Morse-Conley indices",,37B
+37B35,"Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems",,37B
+37B40,Topological entropy,,37B
+37B45,Continua theory in dynamics,,37B
+37B51,Multidimensional shifts of finite type,,37B
+37B52,Tiling dynamics,,37B
+37B55,Topological dynamics of nonautonomous systems,,37B
+37B65,"Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems",,37B
+37B99,Topological dynamics,,37B
+37C05,Dynamical systems involving smooth mappings and diffeomorphisms,,37C
+37C10,Dynamics induced by flows and semiflows,,37C
+37C15,"Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems",,37C
+37C20,"Generic properties, structural stability of dynamical systems",,37C
+37C25,Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics,,37C
+37C27,Periodic orbits of vector fields and flows,,37C
+37C29,Homoclinic and heteroclinic orbits for dynamical systems,,37C
+37C30,"Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.",,37C
+37C35,Orbit growth in dynamical systems,,37C
+37C40,"Smooth ergodic theory, invariant measures for smooth dynamical systems",,37C
+37C45,Dimension theory of smooth dynamical systems,,37C
+37C50,"Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics",,37C
+37C55,Periodic and quasi-periodic flows and diffeomorphisms,,37C
+37C60,Nonautonomous smooth dynamical systems,,37C
+37C65,Monotone flows as dynamical systems,,37C
+37C70,Attractors and repellers of smooth dynamical systems and their topological structure,,37C
+37C75,Stability theory for smooth dynamical systems,,37C
+37C79,Symmetries and invariants of dynamical systems,,37C
+37C81,Equivariant dynamical systems,,37C
+37C83,"Dynamical systems with singularities (billiards, etc.)",,37C
+37C85,"Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)",,37C
+37C86,Foliations generated by dynamical systems,,37C
+37C99,Smooth dynamical systems: general theory,,37C
+37D05,Dynamical systems with hyperbolic orbits and sets,,37D
+37D10,Invariant manifold theory for dynamical systems,,37D
+37D15,Morse-Smale systems,,37D
+37D20,"Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)",,37D
+37D25,"Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)",,37D
+37D30,Partially hyperbolic systems and dominated splittings,,37D
+37D35,"Thermodynamic formalism, variational principles, equilibrium states for dynamical systems",,37D
+37D40,"Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)",,37D
+37D45,"Strange attractors, chaotic dynamics of systems with hyperbolic behavior",,37D
+37D99,Dynamical systems with hyperbolic behavior,,37D
+37E05,Dynamical systems involving maps of the interval,,37E
+37E10,Dynamical systems involving maps of the circle,,37E
+37E15,Combinatorial dynamics (types of periodic orbits),,37E
+37E20,Universality and renormalization of dynamical systems,,37E
+37E25,Dynamical systems involving maps of trees and graphs,,37E
+37E30,Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces,,37E
+37E35,Flows on surfaces,,37E
+37E40,Dynamical aspects of twist maps,,37E
+37E45,Rotation numbers and vectors,,37E
+37E99,Low-dimensional dynamical systems,,37E
+37F05,Dynamical systems involving relations and correspondences in one complex variable,,37F
+37F10,"Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets",,37F
+37F12,Critical orbits for holomorphic dynamical systems,,37F
+37F15,Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems,,37F
+37F20,Combinatorics and topology in relation with holomorphic dynamical systems,,37F
+37F25,Renormalization of holomorphic dynamical systems,,37F
+37F31,Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics,,37F
+37F32,Fuchsian and Kleinian groups as dynamical systems,,37F
+37F34,Teichmüller theory; moduli spaces of holomorphic dynamical systems,,37F
+37F35,Conformal densities and Hausdorff dimension for holomorphic dynamical systems,,37F
+37F40,Geometric limits in holomorphic dynamics,,37F
+37F44,Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps,,37F
+37F46,Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets,,37F
+37F50,"Small divisors, rotation domains and linearization in holomorphic dynamics",,37F
+37F75,Dynamical aspects of holomorphic foliations and vector fields,,37F
+37F80,Higher-dimensional holomorphic and meromorphic dynamics,,37F
+37F99,Dynamical systems over complex numbers,,37F
+37G05,Normal forms for dynamical systems,,37G
+37G10,Bifurcations of singular points in dynamical systems,,37G
+37G15,Bifurcations of limit cycles and periodic orbits in dynamical systems,,37G
+37G20,Hyperbolic singular points with homoclinic trajectories in dynamical systems,,37G
+37G25,Bifurcations connected with nontransversal intersection in dynamical systems,,37G
+37G30,Infinite nonwandering sets arising in bifurcations of dynamical systems,,37G
+37G35,Dynamical aspects of attractors and their bifurcations,,37G
+37G40,"Dynamical aspects of symmetries, equivariant bifurcation theory",,37G
+37G99,Local and nonlocal bifurcation theory for dynamical systems,,37G
+37H05,General theory of random and stochastic dynamical systems,,37H
+37H10,"Generation, random and stochastic difference and differential equations",,37H
+37H12,Random iteration,,37H
+37H15,"Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents",,37H
+37H20,Bifurcation theory for random and stochastic dynamical systems,,37H
+37H30,Stability theory for random and stochastic dynamical systems,,37H
+37H99,Random dynamical systems,,37H
+37J06,"General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants",,37J
+37J11,Symplectic and canonical mappings,,37J
+37J12,Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems,,37J
+37J20,Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems,,37J
+37J25,Stability problems for finite-dimensional Hamiltonian and Lagrangian systems,,37J
+37J30,Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria),,37J
+37J35,"Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests",,37J
+37J37,Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures,,37J
+37J38,"Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions",,37J
+37J39,"Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.)",,37J
+37J40,"Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion",,37J
+37J46,"Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems",,37J
+37J51,Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods,,37J
+37J55,Contact systems,,37J
+37J60,Nonholonomic dynamical systems,,37J
+37J65,"Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.)",,37J
+37J70,Completely integrable discrete dynamical systems,,37J
+37J99,Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems,,37J
+37K06,"General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws",,37K
+37K10,"Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)",,37K
+37K15,Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems,,37K
+37K20,"Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions",,37K
+37K25,"Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry",,37K
+37K30,Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures,,37K
+37K35,Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems,,37K
+37K40,"Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems",,37K
+37K45,Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems,,37K
+37K50,Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems,,37K
+37K55,"Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems",,37K
+37K58,Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems,,37K
+37K60,Lattice dynamics; integrable lattice equations,,37K
+37K65,Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics,,37K
+37K99,Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems,,37K
+37L05,"General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations",,37L
+37L10,"Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems",,37L
+37L15,Stability problems for infinite-dimensional dissipative dynamical systems,,37L
+37L20,Symmetries of infinite-dimensional dissipative dynamical systems,,37L
+37L25,Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems,,37L
+37L30,"Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems",,37L
+37L40,Invariant measures for infinite-dimensional dissipative dynamical systems,,37L
+37L45,"Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems",,37L
+37L50,"Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems",,37L
+37L55,Infinite-dimensional random dynamical systems; stochastic equations,,37L
+37L60,Lattice dynamics and infinite-dimensional dissipative dynamical systems,,37L
+37L65,"Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems",,37L
+37L99,Infinite-dimensional dissipative dynamical systems,,37L
+37M05,Simulation of dynamical systems,,37M
+37M10,Time series analysis of dynamical systems,,37M
+37M15,"Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems",,37M
+37M20,Computational methods for bifurcation problems in dynamical systems,,37M
+37M21,Computational methods for invariant manifolds of dynamical systems,,37M
+37M22,Computational methods for attractors of dynamical systems,,37M
+37M25,"Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)",,37M
+37M99,Approximation methods and numerical treatment of dynamical systems,,37M
+37N05,Dynamical systems in classical and celestial mechanics,,37N
+37N10,"Dynamical systems in fluid mechanics, oceanography and meteorology",,37N
+37N15,Dynamical systems in solid mechanics,,37N
+37N20,"Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)",,37N
+37N25,Dynamical systems in biology,,37N
+37N30,Dynamical systems in numerical analysis,,37N
+37N35,Dynamical systems in control,,37N
+37N40,Dynamical systems in optimization and economics,,37N
+37N99,Applications of dynamical systems,,37N
+37P05,Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps,,37P
+37P10,Arithmetic and non-Archimedean dynamical systems involving analytic and meromorphic maps,,37P
+37P15,Dynamical systems over global ground fields,,37P
+37P20,Dynamical systems over non-Archimedean local ground fields,,37P
+37P25,Dynamical systems over finite ground fields,,37P
+37P30,Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems,,37P
+37P35,Arithmetic properties of periodic points,,37P
+37P40,Non-Archimedean Fatou and Julia sets,,37P
+37P45,Families and moduli spaces in arithmetic and non-Archimedean dynamical systems,,37P
+37P50,Dynamical systems on Berkovich spaces,,37P
+37P55,Arithmetic dynamics on general algebraic varieties,,37P
+37P99,Arithmetic and non-Archimedean dynamical systems,,37P
+39A05,General theory of difference equations,,39A
+39A06,Linear difference equations,,39A
+39A10,Additive difference equations,,39A
+39A12,Discrete version of topics in analysis,,39A
+39A13,"Difference equations, scaling (\(q\)-differences)",,39A
+39A14,Partial difference equations,,39A
+39A20,Multiplicative and other generalized difference equations,,39A
+39A21,Oscillation theory for difference equations,,39A
+39A22,"Growth, boundedness, comparison of solutions to difference equations",,39A
+39A23,Periodic solutions of difference equations,,39A
+39A24,Almost periodic solutions of difference equations,,39A
+39A26,Fuzzy difference equations,,39A
+39A27,Boundary value problems for difference equations,,39A
+39A28,Bifurcation theory for difference equations,,39A
+39A30,Stability theory for difference equations,,39A
+39A33,Chaotic behavior of solutions of difference equations,,39A
+39A36,Integrable difference and lattice equations; integrability tests,,39A
+39A45,Difference equations in the complex domain,,39A
+39A50,Stochastic difference equations,,39A
+39A60,Applications of difference equations,,39A
+39A70,Difference operators,,39A
+39A99,Difference equations,,39A
+39B05,General theory of functional equations and inequalities,,39B
+39B12,"Iteration theory, iterative and composite equations",,39B
+39B22,Functional equations for real functions,,39B
+39B32,Functional equations for complex functions,,39B
+39B42,Matrix and operator functional equations,,39B
+39B52,Functional equations for functions with more general domains and/or ranges,,39B
+39B55,Orthogonal additivity and other conditional functional equations,,39B
+39B62,"Functional inequalities, including subadditivity, convexity, etc.",,39B
+39B72,Systems of functional equations and inequalities,,39B
+39B82,"Stability, separation, extension, and related topics for functional equations",,39B
+39B99,Functional equations and inequalities,,39B
+40A05,Convergence and divergence of series and sequences,,40A
+40A10,Convergence and divergence of integrals,,40A
+40A15,Convergence and divergence of continued fractions,,40A
+40A20,Convergence and divergence of infinite products,,40A
+40A25,"Approximation to limiting values (summation of series, etc.)",,40A
+40A30,Convergence and divergence of series and sequences of functions,,40A
+40A35,Ideal and statistical convergence,,40A
+40A99,Convergence and divergence of infinite limiting processes,,40A
+40B05,Multiple sequences and series,,40B
+40B99,Multiple sequences and series,,40B
+40C05,Matrix methods for summability,,40C
+40C10,Integral methods for summability,,40C
+40C15,Function-theoretic methods (including power series methods and semicontinuous methods) for summability,,40C
+40C99,General summability methods,,40C
+40D05,General theorems on summability,,40D
+40D09,Structure of summability fields,,40D
+40D10,Tauberian constants and oscillation limits in summability theory,,40D
+40D15,Convergence factors and summability factors,,40D
+40D20,Summability and bounded fields of methods,,40D
+40D25,Inclusion and equivalence theorems in summability theory,,40D
+40D99,Direct theorems on summability,,40D
+40E05,Tauberian theorems,,40E
+40E10,Growth estimates,,40E
+40E15,Lacunary inversion theorems,,40E
+40E20,Tauberian constants,,40E
+40E99,Inversion theorems,,40E
+40F05,Absolute and strong summability,,40F
+40F99,Absolute and strong summability,,40F
+40G05,"Cesàro, Euler, Nörlund and Hausdorff methods",,40G
+40G10,"Abel, Borel and power series methods",,40G
+40G15,Summability methods using statistical convergence,,40G
+40G99,Special methods of summability,,40G
+40H05,Functional analytic methods in summability,,40H
+40H99,Functional analytic methods in summability,,40H
+40J05,Summability in abstract structures,,40J
+40J99,Summability in abstract structures,,40J
+41A05,Interpolation in approximation theory,,41A
+41A10,Approximation by polynomials,,41A
+41A15,Spline approximation,,41A
+41A17,"Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities)",,41A
+41A20,Approximation by rational functions,,41A
+41A21,Padé approximation,,41A
+41A25,"Rate of convergence, degree of approximation",,41A
+41A27,Inverse theorems in approximation theory,,41A
+41A28,Simultaneous approximation,,41A
+41A29,Approximation with constraints,,41A
+41A30,Approximation by other special function classes,,41A
+41A35,"Approximation by operators (in particular, by integral operators)",,41A
+41A36,Approximation by positive operators,,41A
+41A40,Saturation in approximation theory,,41A
+41A44,Best constants in approximation theory,,41A
+41A45,Approximation by arbitrary linear expressions,,41A
+41A46,Approximation by arbitrary nonlinear expressions; widths and entropy,,41A
+41A50,"Best approximation, Chebyshev systems",,41A
+41A52,Uniqueness of best approximation,,41A
+41A55,Approximate quadratures,,41A
+41A58,"Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)",,41A
+41A60,"Asymptotic approximations, asymptotic expansions (steepest descent, etc.)",,41A
+41A63,Multidimensional problems,,41A
+41A65,Abstract approximation theory (approximation in normed linear spaces and other abstract spaces),,41A
+41A80,Remainders in approximation formulas,,41A
+41A81,Weighted approximation,,41A
+41A99,Approximations and expansions,,41A
+42A05,"Trigonometric polynomials, inequalities, extremal problems",,42A
+42A10,Trigonometric approximation,,42A
+42A15,Trigonometric interpolation,,42A
+42A16,"Fourier coefficients, Fourier series of functions with special properties, special Fourier series",,42A
+42A20,Convergence and absolute convergence of Fourier and trigonometric series,,42A
+42A24,Summability and absolute summability of Fourier and trigonometric series,,42A
+42A32,"Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)",,42A
+42A38,Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type,,42A
+42A45,Multipliers in one variable harmonic analysis,,42A
+42A50,"Conjugate functions, conjugate series, singular integrals",,42A
+42A55,Lacunary series of trigonometric and other functions; Riesz products,,42A
+42A61,Probabilistic methods for one variable harmonic analysis,,42A
+42A63,"Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization",,42A
+42A65,Completeness of sets of functions in one variable harmonic analysis,,42A
+42A70,Trigonometric moment problems in one variable harmonic analysis,,42A
+42A75,"Classical almost periodic functions, mean periodic functions",,42A
+42A82,Positive definite functions in one variable harmonic analysis,,42A
+42A85,"Convolution, factorization for one variable harmonic analysis",,42A
+42A99,Harmonic analysis in one variable,,42A
+42B05,Fourier series and coefficients in several variables,,42B
+42B08,Summability in several variables,,42B
+42B10,Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type,,42B
+42B15,Multipliers for harmonic analysis in several variables,,42B
+42B20,"Singular and oscillatory integrals (Calderón-Zygmund, etc.)",,42B
+42B25,"Maximal functions, Littlewood-Paley theory",,42B
+42B30,\(H^p\)-spaces,,42B
+42B35,Function spaces arising in harmonic analysis,,42B
+42B37,Harmonic analysis and PDEs,,42B
+42B99,Harmonic analysis in several variables,,42B
+42C05,"Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis",,42C
+42C10,"Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)",,42C
+42C15,"General harmonic expansions, frames",,42C
+42C20,Other transformations of harmonic type,,42C
+42C25,Uniqueness and localization for orthogonal series,,42C
+42C30,Completeness of sets of functions in nontrigonometric harmonic analysis,,42C
+42C40,Nontrigonometric harmonic analysis involving wavelets and other special systems,,42C
+42C99,Nontrigonometric harmonic analysis,,42C
+43A05,"Measures on groups and semigroups, etc.",,43A
+43A07,"Means on groups, semigroups, etc.; amenable groups",,43A
+43A10,"Measure algebras on groups, semigroups, etc.",,43A
+43A15,"\(L^p\)-spaces and other function spaces on groups, semigroups, etc.",,43A
+43A17,"Analysis on ordered groups, \(H^p\)-theory",,43A
+43A20,"\(L^1\)-algebras on groups, semigroups, etc.",,43A
+43A22,"Homomorphisms and multipliers of function spaces on groups, semigroups, etc.",,43A
+43A25,Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups,,43A
+43A30,"Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.",,43A
+43A32,Other transforms and operators of Fourier type,,43A
+43A35,"Positive definite functions on groups, semigroups, etc.",,43A
+43A40,Character groups and dual objects,,43A
+43A45,"Spectral synthesis on groups, semigroups, etc.",,43A
+43A46,"Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)",,43A
+43A50,Convergence of Fourier series and of inverse transforms,,43A
+43A55,"Summability methods on groups, semigroups, etc.",,43A
+43A60,"Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions",,43A
+43A62,Harmonic analysis on hypergroups,,43A
+43A65,"Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)",,43A
+43A70,Analysis on specific locally compact and other abelian groups,,43A
+43A75,Harmonic analysis on specific compact groups,,43A
+43A77,Harmonic analysis on general compact groups,,43A
+43A80,Analysis on other specific Lie groups,,43A
+43A85,Harmonic analysis on homogeneous spaces,,43A
+43A90,Harmonic analysis and spherical functions,,43A
+43A95,Categorical methods for abstract harmonic analysis,,43A
+43A99,Abstract harmonic analysis,,43A
+44A05,General integral transforms,,44A
+44A10,Laplace transform,,44A
+44A12,Radon transform,,44A
+44A15,"Special integral transforms (Legendre, Hilbert, etc.)",,44A
+44A20,Integral transforms of special functions,,44A
+44A30,Multiple integral transforms,,44A
+44A35,Convolution as an integral transform,,44A
+44A40,Calculus of Mikusi?ski and other operational calculi,,44A
+44A45,Classical operational calculus,,44A
+44A55,Discrete operational calculus,,44A
+44A60,Moment problems,,44A
+44A99,"Integral transforms, operational calculus",,44A
+45A05,Linear integral equations,,45A
+45A99,Linear integral equations,,45A
+45B05,Fredholm integral equations,,45B
+45B99,Fredholm integral equations,,45B
+45C05,Eigenvalue problems for integral equations,,45C
+45C99,Eigenvalue problems for integral equations,,45C
+45D05,Volterra integral equations,,45D
+45D99,Volterra integral equations,,45D
+45E05,Integral equations with kernels of Cauchy type,,45E
+45E10,"Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)",,45E
+45E99,Singular integral equations,,45E
+45F05,Systems of nonsingular linear integral equations,,45F
+45F10,"Dual, triple, etc., integral and series equations",,45F
+45F15,Systems of singular linear integral equations,,45F
+45F99,Systems of linear integral equations,,45F
+45G05,Singular nonlinear integral equations,,45G
+45G10,Other nonlinear integral equations,,45G
+45G15,Systems of nonlinear integral equations,,45G
+45G99,Nonlinear integral equations,,45G
+45H05,Integral equations with miscellaneous special kernels,,45H
+45H99,Integral equations with miscellaneous special kernels,,45H
+45J05,Integro-ordinary differential equations,,45J
+45J99,Integro-ordinary differential equations,,45J
+45K05,Integro-partial differential equations,,45K
+45K99,Integro-partial differential equations,,45K
+45L05,Theoretical approximation of solutions to integral equations,,45L
+45L99,Theoretical approximation of solutions to integral equations,,45L
+45M05,Asymptotics of solutions to integral equations,,45M
+45M10,Stability theory for integral equations,,45M
+45M15,Periodic solutions of integral equations,,45M
+45M20,Positive solutions of integral equations,,45M
+45M99,Qualitative behavior of solutions to integral equations,,45M
+45N05,"Abstract integral equations, integral equations in abstract spaces",,45N
+45N99,"Abstract integral equations, integral equations in abstract spaces",,45N
+45P05,Integral operators,,45P
+45P99,Integral operators,,45P
+45Q05,Inverse problems for integral equations,,45Q
+45Q99,Inverse problems for integral equations,,45Q
+45R05,Random integral equations,,45R
+45R99,Random integral equations,,45R
+46A03,General theory of locally convex spaces,,46A
+46A04,Locally convex Fréchet spaces and (DF)-spaces,,46A
+46A08,"Barrelled spaces, bornological spaces",,46A
+46A11,"Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)",,46A
+46A13,"Spaces defined by inductive or projective limits (LB, LF, etc.)",,46A
+46A16,"Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)",,46A
+46A17,"Bornologies and related structures; Mackey convergence, etc.",,46A
+46A19,"Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.)",,46A
+46A20,Duality theory for topological vector spaces,,46A
+46A22,Theorems of Hahn-Banach type; extension and lifting of functionals and operators,,46A
+46A25,Reflexivity and semi-reflexivity,,46A
+46A30,"Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)",,46A
+46A32,Spaces of linear operators; topological tensor products; approximation properties,,46A
+46A35,Summability and bases in topological vector spaces,,46A
+46A40,"Ordered topological linear spaces, vector lattices",,46A
+46A45,Sequence spaces (including Köthe sequence spaces),,46A
+46A50,"Compactness in topological linear spaces; angelic spaces, etc.",,46A
+46A55,Convex sets in topological linear spaces; Choquet theory,,46A
+46A61,Graded Fréchet spaces and tame operators,,46A
+46A63,"Topological invariants ((DN), (\(\Omega\)), etc.) for locally convex spaces",,46A
+46A70,"Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)",,46A
+46A80,Modular spaces,,46A
+46A99,Topological linear spaces and related structures,,46A
+46B03,Isomorphic theory (including renorming) of Banach spaces,,46B
+46B04,Isometric theory of Banach spaces,,46B
+46B06,Asymptotic theory of Banach spaces,,46B
+46B07,Local theory of Banach spaces,,46B
+46B08,Ultraproduct techniques in Banach space theory,,46B
+46B09,Probabilistic methods in Banach space theory,,46B
+46B10,Duality and reflexivity in normed linear and Banach spaces,,46B
+46B15,Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces,,46B
+46B20,Geometry and structure of normed linear spaces,,46B
+46B22,"Radon-Nikodým, Kre?n-Milman and related properties",,46B
+46B25,Classical Banach spaces in the general theory,,46B
+46B26,Nonseparable Banach spaces,,46B
+46B28,Spaces of operators; tensor products; approximation properties,,46B
+46B40,Ordered normed spaces,,46B
+46B42,Banach lattices,,46B
+46B45,Banach sequence spaces,,46B
+46B50,Compactness in Banach (or normed) spaces,,46B
+46B70,Interpolation between normed linear spaces,,46B
+46B80,Nonlinear classification of Banach spaces; nonlinear quotients,,46B
+46B85,Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science,,46B
+46B87,Lineability in functional analysis,,46B
+46B99,Normed linear spaces and Banach spaces; Banach lattices,,46B
+46C05,Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product),,46C
+46C07,"Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)",,46C
+46C15,Characterizations of Hilbert spaces,,46C
+46C20,"Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.)",,46C
+46C50,"Generalizations of inner products (semi-inner products, partial inner products, etc.)",,46C
+46C99,"Inner product spaces and their generalizations, Hilbert spaces",,46C
+46E05,"Lattices of continuous, differentiable or analytic functions",,46E
+46E10,"Topological linear spaces of continuous, differentiable or analytic functions",,46E
+46E15,"Banach spaces of continuous, differentiable or analytic functions",,46E
+46E20,"Hilbert spaces of continuous, differentiable or analytic functions",,46E
+46E22,"Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)",,46E
+46E25,"Rings and algebras of continuous, differentiable or analytic functions",,46E
+46E27,Spaces of measures,,46E
+46E30,"Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)",,46E
+46E35,"Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems",,46E
+46E36,Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces,,46E
+46E39,Sobolev (and similar kinds of) spaces of functions of discrete variables,,46E
+46E40,Spaces of vector- and operator-valued functions,,46E
+46E50,Spaces of differentiable or holomorphic functions on infinite-dimensional spaces,,46E
+46E99,Linear function spaces and their duals,,46E
+46F05,"Topological linear spaces of test functions, distributions and ultradistributions",,46F
+46F10,Operations with distributions and generalized functions,,46F
+46F12,Integral transforms in distribution spaces,,46F
+46F15,"Hyperfunctions, analytic functionals",,46F
+46F20,Distributions and ultradistributions as boundary values of analytic functions,,46F
+46F25,Distributions on infinite-dimensional spaces,,46F
+46F30,"Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)",,46F
+46F99,"Distributions, generalized functions, distribution spaces",,46F
+46G05,Derivatives of functions in infinite-dimensional spaces,,46G
+46G10,Vector-valued measures and integration,,46G
+46G12,Measures and integration on abstract linear spaces,,46G
+46G15,Functional analytic lifting theory,,46G
+46G20,Infinite-dimensional holomorphy,,46G
+46G25,"(Spaces of) multilinear mappings, polynomials",,46G
+46G99,"Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)",,46G
+46H05,General theory of topological algebras,,46H
+46H10,Ideals and subalgebras,,46H
+46H15,Representations of topological algebras,,46H
+46H20,"Structure, classification of topological algebras",,46H
+46H25,"Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)",,46H
+46H30,Functional calculus in topological algebras,,46H
+46H35,Topological algebras of operators,,46H
+46H40,Automatic continuity,,46H
+46H70,Nonassociative topological algebras,,46H
+46H99,"Topological algebras, normed rings and algebras, Banach algebras",,46H
+46J05,General theory of commutative topological algebras,,46J
+46J10,"Banach algebras of continuous functions, function algebras",,46J
+46J15,"Banach algebras of differentiable or analytic functions, \(H^p\)-spaces",,46J
+46J20,"Ideals, maximal ideals, boundaries",,46J
+46J25,Representations of commutative topological algebras,,46J
+46J30,Subalgebras of commutative topological algebras,,46J
+46J40,Structure and classification of commutative topological algebras,,46J
+46J45,Radical Banach algebras,,46J
+46J99,Commutative Banach algebras and commutative topological algebras,,46J
+46K05,General theory of topological algebras with involution,,46K
+46K10,Representations of topological algebras with involution,,46K
+46K15,Hilbert algebras,,46K
+46K50,Nonselfadjoint (sub)algebras in algebras with involution,,46K
+46K70,Nonassociative topological algebras with an involution,,46K
+46K99,Topological (rings and) algebras with an involution,,46K
+46L05,General theory of \(C^*\)-algebras,,46L
+46L06,Tensor products of \(C^*\)-algebras,,46L
+46L07,Operator spaces and completely bounded maps,,46L
+46L08,\(C^*\)-modules,,46L
+46L09,Free products of \(C^*\)-algebras,,46L
+46L10,General theory of von Neumann algebras,,46L
+46L30,States of selfadjoint operator algebras,,46L
+46L35,Classifications of \(C^*\)-algebras,,46L
+46L36,Classification of factors,,46L
+46L37,Subfactors and their classification,,46L
+46L40,Automorphisms of selfadjoint operator algebras,,46L
+46L45,Decomposition theory for \(C^*\)-algebras,,46L
+46L51,Noncommutative measure and integration,,46L
+46L52,Noncommutative function spaces,,46L
+46L53,Noncommutative probability and statistics,,46L
+46L54,Free probability and free operator algebras,,46L
+46L55,Noncommutative dynamical systems,,46L
+46L57,"Derivations, dissipations and positive semigroups in \(C^*\)-algebras",,46L
+46L60,Applications of selfadjoint operator algebras to physics,,46L
+46L65,"Quantizations, deformations for selfadjoint operator algebras",,46L
+46L67,Quantum groups (operator algebraic aspects),,46L
+46L70,Nonassociative selfadjoint operator algebras,,46L
+46L80,\(K\)-theory and operator algebras (including cyclic theory),,46L
+46L85,Noncommutative topology,,46L
+46L87,Noncommutative differential geometry,,46L
+46L89,Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory,,46L
+46L99,"Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)",,46L
+46M05,Tensor products in functional analysis,,46M
+46M07,Ultraproducts in functional analysis,,46M
+46M10,Projective and injective objects in functional analysis,,46M
+46M15,"Categories, functors in functional analysis",,46M
+46M18,"Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.)",,46M
+46M20,"Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)",,46M
+46M35,Abstract interpolation of topological vector spaces,,46M
+46M40,Inductive and projective limits in functional analysis,,46M
+46M99,Methods of category theory in functional analysis,,46M
+46N10,"Applications of functional analysis in optimization, convex analysis, mathematical programming, economics",,46N
+46N20,Applications of functional analysis to differential and integral equations,,46N
+46N30,Applications of functional analysis in probability theory and statistics,,46N
+46N40,Applications of functional analysis in numerical analysis,,46N
+46N50,Applications of functional analysis in quantum physics,,46N
+46N55,Applications of functional analysis in statistical physics,,46N
+46N60,Applications of functional analysis in biology and other sciences,,46N
+46N99,Miscellaneous applications of functional analysis,,46N
+46S05,Quaternionic functional analysis,,46S
+46S10,Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis,,46S
+46S20,Nonstandard functional analysis,,46S
+46S30,Constructive functional analysis,,46S
+46S40,Fuzzy functional analysis,,46S
+46S50,Functional analysis in probabilistic metric linear spaces,,46S
+46S60,Functional analysis on superspaces (supermanifolds) or graded spaces,,46S
+46S99,Other (nonclassical) types of functional analysis,,46S
+46T05,Infinite-dimensional manifolds,,46T
+46T10,Manifolds of mappings,,46T
+46T12,"Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds",,46T
+46T20,Continuous and differentiable maps in nonlinear functional analysis,,46T
+46T25,Holomorphic maps in nonlinear functional analysis,,46T
+46T30,Distributions and generalized functions on nonlinear spaces,,46T
+46T99,Nonlinear functional analysis,,46T
+47A05,"General (adjoints, conjugates, products, inverses, domains, ranges, etc.)",,47A
+47A06,Linear relations (multivalued linear operators),,47A
+47A07,"Forms (bilinear, sesquilinear, multilinear)",,47A
+47A08,Operator matrices,,47A
+47A10,"Spectrum, resolvent",,47A
+47A11,Local spectral properties of linear operators,,47A
+47A12,"Numerical range, numerical radius",,47A
+47A13,"Several-variable operator theory (spectral, Fredholm, etc.)",,47A
+47A15,Invariant subspaces of linear operators,,47A
+47A16,"Cyclic vectors, hypercyclic and chaotic operators",,47A
+47A20,"Dilations, extensions, compressions of linear operators",,47A
+47A25,Spectral sets of linear operators,,47A
+47A30,"Norms (inequalities, more than one norm, etc.) of linear operators",,47A
+47A35,Ergodic theory of linear operators,,47A
+47A40,Scattering theory of linear operators,,47A
+47A45,Canonical models for contractions and nonselfadjoint linear operators,,47A
+47A46,"Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.",,47A
+47A48,"Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.",,47A
+47A50,"Equations and inequalities involving linear operators, with vector unknowns",,47A
+47A52,"Linear operators and ill-posed problems, regularization",,47A
+47A53,(Semi-) Fredholm operators; index theories,,47A
+47A55,Perturbation theory of linear operators,,47A
+47A56,"Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)",,47A
+47A57,"Linear operator methods in interpolation, moment and extension problems",,47A
+47A58,Linear operator approximation theory,,47A
+47A60,Functional calculus for linear operators,,47A
+47A62,"Equations involving linear operators, with operator unknowns",,47A
+47A63,Linear operator inequalities,,47A
+47A64,"Operator means involving linear operators, shorted linear operators, etc.",,47A
+47A65,Structure theory of linear operators,,47A
+47A66,"Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators",,47A
+47A67,Representation theory of linear operators,,47A
+47A68,Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators,,47A
+47A70,(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces,,47A
+47A75,Eigenvalue problems for linear operators,,47A
+47A80,Tensor products of linear operators,,47A
+47A99,General theory of linear operators,,47A
+47B01,Operators on Banach spaces,,47B
+47B02,Operators on Hilbert spaces (general),,47B
+47B06,"Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators",,47B
+47B07,Linear operators defined by compactness properties,,47B
+47B10,"Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)",,47B
+47B12,Sectorial operators,,47B
+47B13,Cowen-Douglas operators,,47B
+47B15,"Hermitian and normal operators (spectral measures, functional calculus, etc.)",,47B
+47B20,"Subnormal operators, hyponormal operators, etc.",,47B
+47B25,Linear symmetric and selfadjoint operators (unbounded),,47B
+47B28,Nonselfadjoint operators,,47B
+47B32,"Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)",,47B
+47B33,Linear composition operators,,47B
+47B34,Kernel operators,,47B
+47B35,"Toeplitz operators, Hankel operators, Wiener-Hopf operators",,47B
+47B36,Jacobi (tridiagonal) operators (matrices) and generalizations,,47B
+47B37,"Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)",,47B
+47B38,Linear operators on function spaces (general),,47B
+47B39,Linear difference operators,,47B
+47B40,"Spectral operators, decomposable operators, well-bounded operators, etc.",,47B
+47B44,"Linear accretive operators, dissipative operators, etc.",,47B
+47B47,"Commutators, derivations, elementary operators, etc.",,47B
+47B48,Linear operators on Banach algebras,,47B
+47B49,"Transformers, preservers (linear operators on spaces of linear operators)",,47B
+47B50,Linear operators on spaces with an indefinite metric,,47B
+47B60,Linear operators on ordered spaces,,47B
+47B65,Positive linear operators and order-bounded operators,,47B
+47B80,Random linear operators,,47B
+47B90,Operator theory and harmonic analysis,,47B
+47B91,Operators on complex function spaces,,47B
+47B92,Operators on real function spaces,,47B
+47B93,Operators arising in mathematical physics,,47B
+47B99,Special classes of linear operators,,47B
+47C05,Linear operators in algebras,,47C
+47C10,Linear operators in \({}^*\)-algebras,,47C
+47C15,Linear operators in \(C^*\)- or von Neumann algebras,,47C
+47C99,Individual linear operators as elements of algebraic systems,,47C
+47D03,Groups and semigroups of linear operators,,47D
+47D06,One-parameter semigroups and linear evolution equations,,47D
+47D07,Markov semigroups and applications to diffusion processes,,47D
+47D08,Schrödinger and Feynman-Kac semigroups,,47D
+47D09,Operator sine and cosine functions and higher-order Cauchy problems,,47D
+47D60,"\(C\)-semigroups, regularized semigroups",,47D
+47D62,Integrated semigroups,,47D
+47D99,"Groups and semigroups of linear operators, their generalizations and applications",,47D
+47E05,General theory of ordinary differential operators,,47E
+47E07,Functional-differential and differential-difference operators,,47E
+47E99,Ordinary differential operators,,47E
+47F05,General theory of partial differential operators,,47F
+47F10,Elliptic operators and their generalizations,,47F
+47F99,Partial differential operators,,47F
+47G10,Integral operators,,47G
+47G20,Integro-differential operators,,47G
+47G30,Pseudodifferential operators,,47G
+47G40,Potential operators,,47G
+47G99,"Integral, integro-differential, and pseudodifferential operators",,47G
+47H04,Set-valued operators,,47H
+47H05,Monotone operators and generalizations,,47H
+47H06,"Nonlinear accretive operators, dissipative operators, etc.",,47H
+47H07,Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces,,47H
+47H08,"Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.",,47H
+47H09,"Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.",,47H
+47H10,Fixed-point theorems,,47H
+47H11,Degree theory for nonlinear operators,,47H
+47H14,Perturbations of nonlinear operators,,47H
+47H20,Semigroups of nonlinear operators,,47H
+47H25,Nonlinear ergodic theorems,,47H
+47H30,"Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.)",,47H
+47H40,Random nonlinear operators,,47H
+47H60,Multilinear and polynomial operators,,47H
+47H99,Nonlinear operators and their properties,,47H
+47J05,Equations involving nonlinear operators (general),,47J
+47J06,Nonlinear ill-posed problems,,47J
+47J07,Abstract inverse mapping and implicit function theorems involving nonlinear operators,,47J
+47J10,"Nonlinear spectral theory, nonlinear eigenvalue problems",,47J
+47J15,Abstract bifurcation theory involving nonlinear operators,,47J
+47J20,Variational and other types of inequalities involving nonlinear operators (general),,47J
+47J22,Variational and other types of inclusions,,47J
+47J25,Iterative procedures involving nonlinear operators,,47J
+47J26,Fixed-point iterations,,47J
+47J30,Variational methods involving nonlinear operators,,47J
+47J35,Nonlinear evolution equations,,47J
+47J40,Equations with nonlinear hysteresis operators,,47J
+47J99,Equations and inequalities involving nonlinear operators,,47J
+47L05,Linear spaces of operators,,47L
+47L07,Convex sets and cones of operators,,47L
+47L10,Algebras of operators on Banach spaces and other topological linear spaces,,47L
+47L15,Operator algebras with symbol structure,,47L
+47L20,Operator ideals,,47L
+47L22,Ideals of polynomials and of multilinear mappings in operator theory,,47L
+47L25,Operator spaces (= matricially normed spaces),,47L
+47L30,Abstract operator algebras on Hilbert spaces,,47L
+47L35,"Nest algebras, CSL algebras",,47L
+47L40,"Limit algebras, subalgebras of \(C^*\)-algebras",,47L
+47L45,Dual algebras; weakly closed singly generated operator algebras,,47L
+47L50,Dual spaces of operator algebras,,47L
+47L55,Representations of (nonselfadjoint) operator algebras,,47L
+47L60,Algebras of unbounded operators; partial algebras of operators,,47L
+47L65,Crossed product algebras (analytic crossed products),,47L
+47L70,Nonassociative nonselfadjoint operator algebras,,47L
+47L75,Other nonselfadjoint operator algebras,,47L
+47L80,"Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)",,47L
+47L90,Applications of operator algebras to the sciences,,47L
+47L99,Linear spaces and algebras of operators,,47L
+47N10,"Applications of operator theory in optimization, convex analysis, mathematical programming, economics",,47N
+47N20,Applications of operator theory to differential and integral equations,,47N
+47N30,Applications of operator theory in probability theory and statistics,,47N
+47N40,Applications of operator theory in numerical analysis,,47N
+47N50,Applications of operator theory in the physical sciences,,47N
+47N60,Applications of operator theory in chemistry and life sciences,,47N
+47N70,"Applications of operator theory in systems, signals, circuits, and control theory",,47N
+47N99,Miscellaneous applications of operator theory,,47N
+47S05,Quaternionic operator theory,,47S
+47S10,"Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory",,47S
+47S20,Nonstandard operator theory,,47S
+47S30,Constructive operator theory,,47S
+47S40,Fuzzy operator theory,,47S
+47S50,Operator theory in probabilistic metric linear spaces,,47S
+47S99,Other (nonclassical) types of operator theory,,47S
+49J05,Existence theories for free problems in one independent variable,,49J
+49J10,Existence theories for free problems in two or more independent variables,,49J
+49J15,Existence theories for optimal control problems involving ordinary differential equations,,49J
+49J20,Existence theories for optimal control problems involving partial differential equations,,49J
+49J21,Existence theories for optimal control problems involving relations other than differential equations,,49J
+49J27,Existence theories for problems in abstract spaces,,49J
+49J30,"Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)",,49J
+49J35,Existence of solutions for minimax problems,,49J
+49J40,Variational inequalities,,49J
+49J45,Methods involving semicontinuity and convergence; relaxation,,49J
+49J50,Fréchet and Gateaux differentiability in optimization,,49J
+49J52,Nonsmooth analysis,,49J
+49J53,Set-valued and variational analysis,,49J
+49J55,Existence of optimal solutions to problems involving randomness,,49J
+49J99,Existence theories in calculus of variations and optimal control,,49J
+49K05,Optimality conditions for free problems in one independent variable,,49K
+49K10,Optimality conditions for free problems in two or more independent variables,,49K
+49K15,Optimality conditions for problems involving ordinary differential equations,,49K
+49K20,Optimality conditions for problems involving partial differential equations,,49K
+49K21,Optimality conditions for problems involving relations other than differential equations,,49K
+49K27,Optimality conditions for problems in abstract spaces,,49K
+49K30,"Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)",,49K
+49K35,Optimality conditions for minimax problems,,49K
+49K40,"Sensitivity, stability, well-posedness",,49K
+49K45,Optimality conditions for problems involving randomness,,49K
+49K99,Optimality conditions,,49K
+49L12,Hamilton-Jacobi equations in optimal control and differential games,,49L
+49L20,Dynamic programming in optimal control and differential games,,49L
+49L25,Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games,,49L
+49L99,Hamilton-Jacobi theories,,49L
+49M05,Numerical methods based on necessary conditions,,49M
+49M15,Newton-type methods,,49M
+49M20,Numerical methods of relaxation type,,49M
+49M25,Discrete approximations in optimal control,,49M
+49M27,Decomposition methods,,49M
+49M29,Numerical methods involving duality,,49M
+49M37,Numerical methods based on nonlinear programming,,49M
+49M41,PDE constrained optimization (numerical aspects),,49M
+49M99,Numerical methods in optimal control,,49M
+49N05,Linear optimal control problems,,49N
+49N10,Linear-quadratic optimal control problems,,49N
+49N15,Duality theory (optimization),,49N
+49N20,Periodic optimal control problems,,49N
+49N25,Impulsive optimal control problems,,49N
+49N30,Problems with incomplete information (optimization),,49N
+49N35,Optimal feedback synthesis,,49N
+49N45,Inverse problems in optimal control,,49N
+49N60,Regularity of solutions in optimal control,,49N
+49N70,Differential games and control,,49N
+49N75,Pursuit and evasion games,,49N
+49N80,Mean field games and control,,49N
+49N90,Applications of optimal control and differential games,,49N
+49N99,Miscellaneous topics in calculus of variations and optimal control,,49N
+49Q05,Minimal surfaces and optimization,,49Q
+49Q10,Optimization of shapes other than minimal surfaces,,49Q
+49Q12,Sensitivity analysis for optimization problems on manifolds,,49Q
+49Q15,"Geometric measure and integration theory, integral and normal currents in optimization",,49Q
+49Q20,Variational problems in a geometric measure-theoretic setting,,49Q
+49Q22,Optimal transportation,,49Q
+49Q99,Manifolds and measure-geometric topics,,49Q
+49R05,Variational methods for eigenvalues of operators,,49R
+49R99,Variational methods for eigenvalues of operators,,49R
+49S05,Variational principles of physics,,49S
+49S99,Variational principles of physics,,49S
+51A05,General theory of linear incidence geometry and projective geometries,,51A
+51A10,"Homomorphism, automorphism and dualities in linear incidence geometry",,51A
+51A15,Linear incidence geometric structures with parallelism,,51A
+51A20,Configuration theorems in linear incidence geometry,,51A
+51A25,Algebraization in linear incidence geometry,,51A
+51A30,Desarguesian and Pappian geometries,,51A
+51A35,Non-Desarguesian affine and projective planes,,51A
+51A40,Translation planes and spreads in linear incidence geometry,,51A
+51A45,Incidence structures embeddable into projective geometries,,51A
+51A50,"Polar geometry, symplectic spaces, orthogonal spaces",,51A
+51A99,Linear incidence geometry,,51A
+51B05,General theory of nonlinear incidence geometry,,51B
+51B10,Möbius geometries,,51B
+51B15,Laguerre geometries,,51B
+51B20,Minkowski geometries in nonlinear incidence geometry,,51B
+51B25,Lie geometries in nonlinear incidence geometry,,51B
+51B99,Nonlinear incidence geometry,,51B
+51C05,"Ring geometry (Hjelmslev, Barbilian, etc.)",,51C
+51C99,"Ring geometry (Hjelmslev, Barbilian, etc.)",,51C
+51D05,Abstract (Maeda) geometries,,51D
+51D10,Abstract geometries with exchange axiom,,51D
+51D15,Abstract geometries with parallelism,,51D
+51D20,Combinatorial geometries and geometric closure systems,,51D
+51D25,Lattices of subspaces and geometric closure systems,,51D
+51D30,"Continuous geometries, geometric closure systems and related topics",,51D
+51D99,Geometric closure systems,,51D
+51E05,General block designs in finite geometry,,51E
+51E10,Steiner systems in finite geometry,,51E
+51E12,Generalized quadrangles and generalized polygons in finite geometry,,51E
+51E14,"Finite partial geometries (general), nets, partial spreads",,51E
+51E15,Finite affine and projective planes (geometric aspects),,51E
+51E20,Combinatorial structures in finite projective spaces,,51E
+51E21,"Blocking sets, ovals, \(k\)-arcs",,51E
+51E22,Linear codes and caps in Galois spaces,,51E
+51E23,Spreads and packing problems in finite geometry,,51E
+51E24,Buildings and the geometry of diagrams,,51E
+51E25,Other finite nonlinear geometries,,51E
+51E26,Other finite linear geometries,,51E
+51E30,Other finite incidence structures (geometric aspects),,51E
+51E99,Finite geometry and special incidence structures,,51E
+51F05,Absolute planes in metric geometry,,51F
+51F10,Absolute spaces in metric geometry,,51F
+51F15,"Reflection groups, reflection geometries",,51F
+51F20,Congruence and orthogonality in metric geometry,,51F
+51F25,Orthogonal and unitary groups in metric geometry,,51F
+51F30,Lipschitz and coarse geometry of metric spaces,,51F
+51F99,Metric geometry,,51F
+51G05,"Ordered geometries (ordered incidence structures, etc.)",,51G
+51G99,"Ordered geometries (ordered incidence structures, etc.)",,51G
+51H05,General theory of topological geometry,,51H
+51H10,Topological linear incidence structures,,51H
+51H15,Topological nonlinear incidence structures,,51H
+51H20,Topological geometries on manifolds,,51H
+51H25,Geometries with differentiable structure,,51H
+51H30,Geometries with algebraic manifold structure,,51H
+51H99,Topological geometry,,51H
+51J05,General theory of incidence groups,,51J
+51J10,Projective incidence groups,,51J
+51J15,Kinematic spaces,,51J
+51J20,Representation by near-fields and near-algebras,,51J
+51J99,Incidence groups,,51J
+51K05,General theory of distance geometry,,51K
+51K10,Synthetic differential geometry,,51K
+51K99,Distance geometry,,51K
+51L05,Geometry of orders of nondifferentiable curves,,51L
+51L10,Directly differentiable curves in geometric order structures,,51L
+51L15,\(n\)-vertex theorems via direct methods,,51L
+51L20,Geometry of orders of surfaces,,51L
+51L99,Geometric order structures,,51L
+51M04,Elementary problems in Euclidean geometries,,51M
+51M05,Euclidean geometries (general) and generalizations,,51M
+51M09,Elementary problems in hyperbolic and elliptic geometries,,51M
+51M10,Hyperbolic and elliptic geometries (general) and generalizations,,51M
+51M15,Geometric constructions in real or complex geometry,,51M
+51M16,Inequalities and extremum problems in real or complex geometry,,51M
+51M20,"Polyhedra and polytopes; regular figures, division of spaces",,51M
+51M25,"Length, area and volume in real or complex geometry",,51M
+51M30,Line geometries and their generalizations,,51M
+51M35,"Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)",,51M
+51M99,Real and complex geometry,,51M
+51N05,Descriptive geometry,,51N
+51N10,Affine analytic geometry,,51N
+51N15,Projective analytic geometry,,51N
+51N20,Euclidean analytic geometry,,51N
+51N25,Analytic geometry with other transformation groups,,51N
+51N30,Geometry of classical groups,,51N
+51N35,Questions of classical algebraic geometry,,51N
+51N99,Analytic and descriptive geometry,,51N
+51P05,Classical or axiomatic geometry and physics,,51P
+51P99,Classical or axiomatic geometry and physics,,51P
+52A01,Axiomatic and generalized convexity,,52A
+52A05,Convex sets without dimension restrictions (aspects of convex geometry),,52A
+52A07,Convex sets in topological vector spaces (aspects of convex geometry),,52A
+52A10,Convex sets in \(2\) dimensions (including convex curves),,52A
+52A15,Convex sets in \(3\) dimensions (including convex surfaces),,52A
+52A20,Convex sets in \(n\) dimensions (including convex hypersurfaces),,52A
+52A21,"Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)",,52A
+52A22,Random convex sets and integral geometry (aspects of convex geometry),,52A
+52A23,Asymptotic theory of convex bodies,,52A
+52A27,Approximation by convex sets,,52A
+52A30,"Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.)",,52A
+52A35,Helly-type theorems and geometric transversal theory,,52A
+52A37,Other problems of combinatorial convexity,,52A
+52A38,"Length, area, volume and convex sets (aspects of convex geometry)",,52A
+52A39,Mixed volumes and related topics in convex geometry,,52A
+52A40,Inequalities and extremum problems involving convexity in convex geometry,,52A
+52A41,Convex functions and convex programs in convex geometry,,52A
+52A55,Spherical and hyperbolic convexity,,52A
+52A99,General convexity,,52A
+52B05,"Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)",,52B
+52B10,Three-dimensional polytopes,,52B
+52B11,\(n\)-dimensional polytopes,,52B
+52B12,"Special polytopes (linear programming, centrally symmetric, etc.)",,52B
+52B15,Symmetry properties of polytopes,,52B
+52B20,Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry),,52B
+52B22,Shellability for polytopes and polyhedra,,52B
+52B35,Gale and other diagrams,,52B
+52B40,"Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)",,52B
+52B45,"Dissections and valuations (Hilbert's third problem, etc.)",,52B
+52B55,Computational aspects related to convexity,,52B
+52B60,Isoperimetric problems for polytopes,,52B
+52B70,Polyhedral manifolds,,52B
+52B99,Polytopes and polyhedra,,52B
+52C05,Lattices and convex bodies in \(2\) dimensions (aspects of discrete geometry),,52C
+52C07,Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry),,52C
+52C10,Erd?s problems and related topics of discrete geometry,,52C
+52C15,Packing and covering in \(2\) dimensions (aspects of discrete geometry),,52C
+52C17,Packing and covering in \(n\) dimensions (aspects of discrete geometry),,52C
+52C20,Tilings in \(2\) dimensions (aspects of discrete geometry),,52C
+52C22,Tilings in \(n\) dimensions (aspects of discrete geometry),,52C
+52C23,Quasicrystals and aperiodic tilings in discrete geometry,,52C
+52C25,Rigidity and flexibility of structures (aspects of discrete geometry),,52C
+52C26,Circle packings and discrete conformal geometry,,52C
+52C30,Planar arrangements of lines and pseudolines (aspects of discrete geometry),,52C
+52C35,"Arrangements of points, flats, hyperplanes (aspects of discrete geometry)",,52C
+52C40,Oriented matroids in discrete geometry,,52C
+52C45,Combinatorial complexity of geometric structures,,52C
+52C99,Discrete geometry,,52C
+53A04,Curves in Euclidean and related spaces,,53A
+53A05,Surfaces in Euclidean and related spaces,,53A
+53A07,Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces,,53A
+53A10,"Minimal surfaces in differential geometry, surfaces with prescribed mean curvature",,53A
+53A15,Affine differential geometry,,53A
+53A17,Differential geometric aspects in kinematics,,53A
+53A20,Projective differential geometry,,53A
+53A25,Differential line geometry,,53A
+53A31,Differential geometry of submanifolds of Möbius space,,53A
+53A35,Non-Euclidean differential geometry,,53A
+53A40,Other special differential geometries,,53A
+53A45,Differential geometric aspects in vector and tensor analysis,,53A
+53A55,"Differential invariants (local theory), geometric objects",,53A
+53A60,Differential geometry of webs,,53A
+53A70,Discrete differential geometry,,53A
+53A99,Classical differential geometry,,53A
+53B05,Linear and affine connections,,53B
+53B10,Projective connections,,53B
+53B12,Differential geometric aspects of statistical manifolds and information geometry,,53B
+53B15,Other connections,,53B
+53B20,Local Riemannian geometry,,53B
+53B21,Methods of local Riemannian geometry,,53B
+53B25,Local submanifolds,,53B
+53B30,"Local differential geometry of Lorentz metrics, indefinite metrics",,53B
+53B35,Local differential geometry of Hermitian and Kählerian structures,,53B
+53B40,Local differential geometry of Finsler spaces and generalizations (areal metrics),,53B
+53B50,Applications of local differential geometry to the sciences,,53B
+53B99,Local differential geometry,,53B
+53C05,Connections (general theory),,53C
+53C07,"Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)",,53C
+53C08,Differential geometric aspects of gerbes and differential characters,,53C
+53C10,\(G\)-structures,,53C
+53C12,Foliations (differential geometric aspects),,53C
+53C15,"General geometric structures on manifolds (almost complex, almost product structures, etc.)",,53C
+53C17,Sub-Riemannian geometry,,53C
+53C18,Conformal structures on manifolds,,53C
+53C20,"Global Riemannian geometry, including pinching",,53C
+53C21,"Methods of global Riemannian geometry, including PDE methods; curvature restrictions",,53C
+53C22,Geodesics in global differential geometry,,53C
+53C23,Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces,,53C
+53C24,Rigidity results,,53C
+53C25,"Special Riemannian manifolds (Einstein, Sasakian, etc.)",,53C
+53C26,"Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry",,53C
+53C27,Spin and Spin\({}^c\) geometry,,53C
+53C28,Twistor methods in differential geometry,,53C
+53C29,Issues of holonomy in differential geometry,,53C
+53C30,Differential geometry of homogeneous manifolds,,53C
+53C35,Differential geometry of symmetric spaces,,53C
+53C38,Calibrations and calibrated geometries,,53C
+53C40,Global submanifolds,,53C
+53C42,"Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)",,53C
+53C43,Differential geometric aspects of harmonic maps,,53C
+53C45,Global surface theory (convex surfaces à la A. D. Aleksandrov),,53C
+53C50,"Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics",,53C
+53C55,Global differential geometry of Hermitian and Kählerian manifolds,,53C
+53C56,Other complex differential geometry,,53C
+53C60,Global differential geometry of Finsler spaces and generalizations (areal metrics),,53C
+53C65,Integral geometry,,53C
+53C70,"Direct methods (\(G\)-spaces of Busemann, etc.)",,53C
+53C75,"Geometric orders, order geometry",,53C
+53C80,Applications of global differential geometry to the sciences,,53C
+53C99,Global differential geometry,,53C
+53D05,Symplectic manifolds (general theory),,53D
+53D10,Contact manifolds (general theory),,53D
+53D12,Lagrangian submanifolds; Maslov index,,53D
+53D15,Almost contact and almost symplectic manifolds,,53D
+53D17,Poisson manifolds; Poisson groupoids and algebroids,,53D
+53D18,Generalized geometries (à la Hitchin),,53D
+53D20,Momentum maps; symplectic reduction,,53D
+53D22,Canonical transformations in symplectic and contact geometry,,53D
+53D25,Geodesic flows in symplectic geometry and contact geometry,,53D
+53D30,Symplectic structures of moduli spaces,,53D
+53D35,Global theory of symplectic and contact manifolds,,53D
+53D37,"Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category",,53D
+53D40,Symplectic aspects of Floer homology and cohomology,,53D
+53D42,Symplectic field theory; contact homology,,53D
+53D45,"Gromov-Witten invariants, quantum cohomology, Frobenius manifolds",,53D
+53D50,Geometric quantization,,53D
+53D55,"Deformation quantization, star products",,53D
+53D99,"Symplectic geometry, contact geometry",,53D
+53E10,Flows related to mean curvature,,53E
+53E20,Ricci flows,,53E
+53E30,"Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows)",,53E
+53E40,Higher-order geometric flows,,53E
+53E50,Flows related to symplectic and contact structures,,53E
+53E99,Geometric evolution equations,,53E
+53Z05,Applications of differential geometry to physics,,53Z
+53Z10,Applications of differential geometry to biology,,53Z
+53Z15,Applications of differential geometry to chemistry,,53Z
+53Z30,Applications of differential geometry to engineering,,53Z
+53Z50,Applications of differential geometry to data and computer science,,53Z
+53Z99,Applications of differential geometry to sciences and engineering,,53Z
+54A05,"Topological spaces and generalizations (closure spaces, etc.)",,54A
+54A10,"Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)",,54A
+54A15,Syntopogeneous structures,,54A
+54A20,"Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)",,54A
+54A25,"Cardinality properties (cardinal functions and inequalities, discrete subsets)",,54A
+54A35,Consistency and independence results in general topology,,54A
+54A40,Fuzzy topology,,54A
+54A99,Generalities in topology,,54A
+54B05,Subspaces in general topology,,54B
+54B10,Product spaces in general topology,,54B
+54B15,"Quotient spaces, decompositions in general topology",,54B
+54B17,Adjunction spaces and similar constructions in general topology,,54B
+54B20,Hyperspaces in general topology,,54B
+54B30,Categorical methods in general topology,,54B
+54B35,Spectra in general topology,,54B
+54B40,Presheaves and sheaves in general topology,,54B
+54B99,Basic constructions in general topology,,54B
+54C05,Continuous maps,,54C
+54C08,Weak and generalized continuity,,54C
+54C10,"Special maps on topological spaces (open, closed, perfect, etc.)",,54C
+54C15,Retraction,,54C
+54C20,Extension of maps,,54C
+54C25,Embedding,,54C
+54C30,Real-valued functions in general topology,,54C
+54C35,Function spaces in general topology,,54C
+54C40,Algebraic properties of function spaces in general topology,,54C
+54C45,\(C\)- and \(C^*\)-embedding,,54C
+54C50,Topology of special sets defined by functions,,54C
+54C55,"Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)",,54C
+54C56,Shape theory in general topology,,54C
+54C60,Set-valued maps in general topology,,54C
+54C65,Selections in general topology,,54C
+54C70,Entropy in general topology,,54C
+54C99,Maps and general types of topological spaces defined by maps,,54C
+54D05,Connected and locally connected spaces (general aspects),,54D
+54D10,"Lower separation axioms (\(T_0\)--\(T_3\), etc.)",,54D
+54D15,"Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)",,54D
+54D20,"Noncompact covering properties (paracompact, Lindelöf, etc.)",,54D
+54D25,``\(P\)-minimal'' and ``\(P\)-closed'' spaces,,54D
+54D30,Compactness,,54D
+54D35,"Extensions of spaces (compactifications, supercompactifications, completions, etc.)",,54D
+54D40,Remainders in general topology,,54D
+54D45,"Local compactness, \(\sigma\)-compactness",,54D
+54D50,\(k\)-spaces,,54D
+54D55,Sequential spaces,,54D
+54D60,Realcompactness and realcompactification,,54D
+54D65,Separability of topological spaces,,54D
+54D70,Base properties of topological spaces,,54D
+54D80,"Special constructions of topological spaces (spaces of ultrafilters, etc.)",,54D
+54D99,Fairly general properties of topological spaces,,54D
+54E05,Proximity structures and generalizations,,54E
+54E15,Uniform structures and generalizations,,54E
+54E17,Nearness spaces,,54E
+54E18,"\(p\)-spaces, \(M\)-spaces, \(\sigma\)-spaces, etc.",,54E
+54E20,"Stratifiable spaces, cosmic spaces, etc.",,54E
+54E25,Semimetric spaces,,54E
+54E30,Moore spaces,,54E
+54E35,"Metric spaces, metrizability",,54E
+54E40,Special maps on metric spaces,,54E
+54E45,Compact (locally compact) metric spaces,,54E
+54E50,Complete metric spaces,,54E
+54E52,"Baire category, Baire spaces",,54E
+54E55,Bitopologies,,54E
+54E70,Probabilistic metric spaces,,54E
+54E99,Topological spaces with richer structures,,54E
+54F05,"Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces",,54F
+54F15,Continua and generalizations,,54F
+54F16,Hyperspaces of continua,,54F
+54F17,Inverse limits of set-valued functions,,54F
+54F35,Higher-dimensional local connectedness,,54F
+54F45,Dimension theory in general topology,,54F
+54F50,"Topological spaces of dimension \(\leq 1\); curves, dendrites",,54F
+54F55,"Unicoherence, multicoherence",,54F
+54F65,Topological characterizations of particular spaces,,54F
+54F99,Special properties of topological spaces,,54F
+54G05,"Extremally disconnected spaces, \(F\)-spaces, etc.",,54G
+54G10,\(P\)-spaces,,54G
+54G12,Scattered spaces,,54G
+54G15,Pathological topological spaces,,54G
+54G20,Counterexamples in general topology,,54G
+54G99,Peculiar topological spaces,,54G
+54H05,"Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)",,54H
+54H10,Topological representations of algebraic systems,,54H
+54H11,Topological groups (topological aspects),,54H
+54H12,"Topological lattices, etc. (topological aspects)",,54H
+54H13,"Topological fields, rings, etc. (topological aspects)",,54H
+54H15,Transformation groups and semigroups (topological aspects),,54H
+54H25,Fixed-point and coincidence theorems (topological aspects),,54H
+54H30,"Applications of general topology to computer science (e.g., digital topology, image processing)",,54H
+54H99,"Connections of general topology with other structures, applications",,54H
+54J05,Nonstandard topology,,54J
+54J99,Nonstandard topology,,54J
+55M05,Duality in algebraic topology,,55M
+55M10,Dimension theory in algebraic topology,,55M
+55M15,Absolute neighborhood retracts,,55M
+55M20,Fixed points and coincidences in algebraic topology,,55M
+55M25,"Degree, winding number",,55M
+55M30,"Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects)",,55M
+55M35,Finite groups of transformations in algebraic topology (including Smith theory),,55M
+55M99,Classical topics in algebraic topology,,55M
+55N05,?ech types,,55N
+55N07,Steenrod-Sitnikov homologies,,55N
+55N10,Singular homology and cohomology theory,,55N
+55N15,Topological \(K\)-theory,,55N
+55N20,Generalized (extraordinary) homology and cohomology theories in algebraic topology,,55N
+55N22,Bordism and cobordism theories and formal group laws in algebraic topology,,55N
+55N25,"Homology with local coefficients, equivariant cohomology",,55N
+55N30,Sheaf cohomology in algebraic topology,,55N
+55N31,"Persistent homology and applications, topological data analysis",,55N
+55N32,Orbifold cohomology,,55N
+55N33,Intersection homology and cohomology in algebraic topology,,55N
+55N34,Elliptic cohomology,,55N
+55N35,Other homology theories in algebraic topology,,55N
+55N40,Axioms for homology theory and uniqueness theorems in algebraic topology,,55N
+55N45,Products and intersections in homology and cohomology,,55N
+55N91,Equivariant homology and cohomology in algebraic topology,,55N
+55N99,Homology and cohomology theories in algebraic topology,,55N
+55P05,"Homotopy extension properties, cofibrations in algebraic topology",,55P
+55P10,Homotopy equivalences in algebraic topology,,55P
+55P15,Classification of homotopy type,,55P
+55P20,Eilenberg-Mac Lane spaces,,55P
+55P25,Spanier-Whitehead duality,,55P
+55P30,Eckmann-Hilton duality,,55P
+55P35,Loop spaces,,55P
+55P40,Suspensions,,55P
+55P42,"Stable homotopy theory, spectra",,55P
+55P43,"Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.)",,55P
+55P45,\(H\)-spaces and duals,,55P
+55P47,Infinite loop spaces,,55P
+55P48,Loop space machines and operads in algebraic topology,,55P
+55P50,String topology,,55P
+55P55,Shape theory,,55P
+55P57,Proper homotopy theory,,55P
+55P60,Localization and completion in homotopy theory,,55P
+55P62,Rational homotopy theory,,55P
+55P65,Homotopy functors in algebraic topology,,55P
+55P91,Equivariant homotopy theory in algebraic topology,,55P
+55P92,Relations between equivariant and nonequivariant homotopy theory in algebraic topology,,55P
+55P99,Homotopy theory,,55P
+55Q05,"Homotopy groups, general; sets of homotopy classes",,55Q
+55Q07,Shape groups,,55Q
+55Q10,Stable homotopy groups,,55Q
+55Q15,Whitehead products and generalizations,,55Q
+55Q20,"Homotopy groups of wedges, joins, and simple spaces",,55Q
+55Q25,Hopf invariants,,55Q
+55Q35,Operations in homotopy groups,,55Q
+55Q40,Homotopy groups of spheres,,55Q
+55Q45,Stable homotopy of spheres,,55Q
+55Q50,\(J\)-morphism,,55Q
+55Q51,\(v_n\)-periodicity,,55Q
+55Q52,Homotopy groups of special spaces,,55Q
+55Q55,Cohomotopy groups,,55Q
+55Q70,Homotopy groups of special types,,55Q
+55Q91,Equivariant homotopy groups,,55Q
+55Q99,Homotopy groups,,55Q
+55R05,Fiber spaces in algebraic topology,,55R
+55R10,Fiber bundles in algebraic topology,,55R
+55R12,Transfer for fiber spaces and bundles in algebraic topology,,55R
+55R15,Classification of fiber spaces or bundles in algebraic topology,,55R
+55R20,Spectral sequences and homology of fiber spaces in algebraic topology,,55R
+55R25,Sphere bundles and vector bundles in algebraic topology,,55R
+55R35,Classifying spaces of groups and \(H\)-spaces in algebraic topology,,55R
+55R37,Maps between classifying spaces in algebraic topology,,55R
+55R40,Homology of classifying spaces and characteristic classes in algebraic topology,,55R
+55R45,Homology and homotopy of \(B\mathrm{O}\) and \(B\mathrm{U}\); Bott periodicity,,55R
+55R50,Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory,,55R
+55R55,Fiberings with singularities in algebraic topology,,55R
+55R60,Microbundles and block bundles in algebraic topology,,55R
+55R65,Generalizations of fiber spaces and bundles in algebraic topology,,55R
+55R70,Fibrewise topology,,55R
+55R80,Discriminantal varieties and configuration spaces in algebraic topology,,55R
+55R91,Equivariant fiber spaces and bundles in algebraic topology,,55R
+55R99,Fiber spaces and bundles in algebraic topology,,55R
+55S05,Primary cohomology operations in algebraic topology,,55S
+55S10,Steenrod algebra,,55S
+55S12,Dyer-Lashof operations,,55S
+55S15,Symmetric products and cyclic products in algebraic topology,,55S
+55S20,Secondary and higher cohomology operations in algebraic topology,,55S
+55S25,\(K\)-theory operations and generalized cohomology operations in algebraic topology,,55S
+55S30,Massey products,,55S
+55S35,Obstruction theory in algebraic topology,,55S
+55S36,Extension and compression of mappings in algebraic topology,,55S
+55S37,Classification of mappings in algebraic topology,,55S
+55S40,Sectioning fiber spaces and bundles in algebraic topology,,55S
+55S45,"Postnikov systems, \(k\)-invariants",,55S
+55S91,Equivariant operations and obstructions in algebraic topology,,55S
+55S99,Operations and obstructions in algebraic topology,,55S
+55T05,General theory of spectral sequences in algebraic topology,,55T
+55T10,Serre spectral sequences,,55T
+55T15,Adams spectral sequences,,55T
+55T20,Eilenberg-Moore spectral sequences,,55T
+55T25,Generalized cohomology and spectral sequences in algebraic topology,,55T
+55T99,Spectral sequences in algebraic topology,,55T
+55U05,Abstract complexes in algebraic topology,,55U
+55U10,Simplicial sets and complexes in algebraic topology,,55U
+55U15,Chain complexes in algebraic topology,,55U
+55U20,"Universal coefficient theorems, Bockstein operator",,55U
+55U25,"Homology of a product, Künneth formula",,55U
+55U30,Duality in applied homological algebra and category theory (aspects of algebraic topology),,55U
+55U35,Abstract and axiomatic homotopy theory in algebraic topology,,55U
+55U40,"Topological categories, foundations of homotopy theory",,55U
+55U99,Applied homological algebra and category theory in algebraic topology,,55U
+57K10,Knot theory,,57K
+57K12,"Generalized knots (virtual knots, welded knots, quandles, etc.)",,57K
+57K14,Knot polynomials,,57K
+57K16,"Finite-type and quantum invariants, topological quantum field theories (TQFT)",,57K
+57K18,"Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.)",,57K
+57K20,"2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.)",,57K
+57K30,General topology of 3-manifolds,,57K
+57K31,"Invariants of 3-manifolds (including skein modules, character varieties)",,57K
+57K32,Hyperbolic 3-manifolds,,57K
+57K33,Contact structures in 3 dimensions,,57K
+57K35,Other geometric structures on 3-manifolds,,57K
+57K40,General topology of 4-manifolds,,57K
+57K41,Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants),,57K
+57K43,Symplectic structures in 4 dimensions,,57K
+57K45,Higher-dimensional knots and links,,57K
+57K50,Low-dimensional manifolds of specific dimension 5 or higher,,57K
+57K99,Low-dimensional topology in specific dimensions,,57K
+57M05,"Fundamental group, presentations, free differential calculus",,57M
+57M07,Topological methods in group theory,,57M
+57M10,Covering spaces and low-dimensional topology,,57M
+57M12,"Low-dimensional topology of special (e.g., branched) coverings",,57M
+57M15,Relations of low-dimensional topology with graph theory,,57M
+57M30,Wild embeddings,,57M
+57M50,General geometric structures on low-dimensional manifolds,,57M
+57M60,Group actions on manifolds and cell complexes in low dimensions,,57M
+57M99,General low-dimensional topology,,57M
+57N16,Geometric structures on manifolds of high or arbitrary dimension,,57N
+57N17,Topology of topological vector spaces,,57N
+57N20,Topology of infinite-dimensional manifolds,,57N
+57N25,Shapes (aspects of topological manifolds),,57N
+57N30,Engulfing in topological manifolds,,57N
+57N35,Embeddings and immersions in topological manifolds,,57N
+57N37,Isotopy and pseudo-isotopy,,57N
+57N40,Neighborhoods of submanifolds,,57N
+57N45,Flatness and tameness of topological manifolds,,57N
+57N50,"\(S^{n-1}\subset E^n\), Schoenflies problem",,57N
+57N55,Microbundles and block bundles,,57N
+57N60,Cellularity in topological manifolds,,57N
+57N65,Algebraic topology of manifolds,,57N
+57N70,Cobordism and concordance in topological manifolds,,57N
+57N75,General position and transversality,,57N
+57N80,Stratifications in topological manifolds,,57N
+57N99,Topological manifolds,,57N
+57P05,Local properties of generalized manifolds,,57P
+57P10,Poincaré duality spaces,,57P
+57P99,Generalized manifolds,,57P
+57Q05,General topology of complexes,,57Q
+57Q10,"Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.",,57Q
+57Q12,Wall finiteness obstruction for CW-complexes,,57Q
+57Q15,Triangulating manifolds,,57Q
+57Q20,Cobordism in PL-topology,,57Q
+57Q25,"Comparison of PL-structures: classification, Hauptvermutung",,57Q
+57Q30,Engulfing,,57Q
+57Q35,Embeddings and immersions in PL-topology,,57Q
+57Q37,Isotopy in PL-topology,,57Q
+57Q40,Regular neighborhoods in PL-topology,,57Q
+57Q50,Microbundles and block bundles,,57Q
+57Q55,Approximations in PL-topology,,57Q
+57Q60,Cobordism and concordance in PL-topology,,57Q
+57Q65,General position and transversality,,57Q
+57Q70,Discrete Morse theory and related ideas in manifold topology,,57Q
+57Q91,Equivariant PL-topology,,57Q
+57Q99,PL-topology,,57Q
+57R05,Triangulating,,57R
+57R10,Smoothing in differential topology,,57R
+57R12,Smooth approximations in differential topology,,57R
+57R15,"Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)",,57R
+57R17,Symplectic and contact topology in high or arbitrary dimension,,57R
+57R18,Topology and geometry of orbifolds,,57R
+57R19,Algebraic topology on manifolds and differential topology,,57R
+57R20,Characteristic classes and numbers in differential topology,,57R
+57R22,Topology of vector bundles and fiber bundles,,57R
+57R25,"Vector fields, frame fields in differential topology",,57R
+57R27,Controllability of vector fields on \(C^\infty\) and real-analytic manifolds,,57R
+57R30,Foliations in differential topology; geometric theory,,57R
+57R32,Classifying spaces for foliations; Gelfand-Fuks cohomology,,57R
+57R35,Differentiable mappings in differential topology,,57R
+57R40,Embeddings in differential topology,,57R
+57R42,Immersions in differential topology,,57R
+57R45,Singularities of differentiable mappings in differential topology,,57R
+57R50,Differential topological aspects of diffeomorphisms,,57R
+57R52,Isotopy in differential topology,,57R
+57R55,Differentiable structures in differential topology,,57R
+57R56,Topological quantum field theories (aspects of differential topology),,57R
+57R57,Applications of global analysis to structures on manifolds,,57R
+57R58,Floer homology,,57R
+57R60,"Homotopy spheres, Poincaré conjecture",,57R
+57R65,Surgery and handlebodies,,57R
+57R67,"Surgery obstructions, Wall groups",,57R
+57R70,Critical points and critical submanifolds in differential topology,,57R
+57R75,\(\mathrm{O}\)- and \(\mathrm{SO}\)-cobordism,,57R
+57R77,Complex cobordism (\(\mathrm{U}\)- and \(\mathrm{SU}\)-cobordism),,57R
+57R80,\(h\)- and \(s\)-cobordism,,57R
+57R85,Equivariant cobordism,,57R
+57R90,Other types of cobordism,,57R
+57R91,Equivariant algebraic topology of manifolds,,57R
+57R95,Realizing cycles by submanifolds,,57R
+57R99,Differential topology,,57R
+57S05,Topological properties of groups of homeomorphisms or diffeomorphisms,,57S
+57S10,Compact groups of homeomorphisms,,57S
+57S12,Toric topology,,57S
+57S15,Compact Lie groups of differentiable transformations,,57S
+57S17,Finite transformation groups,,57S
+57S20,Noncompact Lie groups of transformations,,57S
+57S25,Groups acting on specific manifolds,,57S
+57S30,Discontinuous groups of transformations,,57S
+57S99,Topological transformation groups,,57S
+57T05,Hopf algebras (aspects of homology and homotopy of topological groups),,57T
+57T10,Homology and cohomology of Lie groups,,57T
+57T15,Homology and cohomology of homogeneous spaces of Lie groups,,57T
+57T20,Homotopy groups of topological groups and homogeneous spaces,,57T
+57T25,Homology and cohomology of \(H\)-spaces,,57T
+57T30,Bar and cobar constructions,,57T
+57T35,Applications of Eilenberg-Moore spectral sequences,,57T
+57T99,Homology and homotopy of topological groups and related structures,,57T
+57Z05,Relations of manifolds and cell complexes with physics,,57Z
+57Z10,Relations of manifolds and cell complexes with biology,,57Z
+57Z15,Relations of manifolds and cell complexes with chemistry,,57Z
+57Z20,Relations of manifolds and cell complexes with engineering,,57Z
+57Z25,Relations of manifolds and cell complexes with computer and data science,,57Z
+57Z99,Relations of manifolds and cell complexes with science and engineering,,57Z
+58A03,Topos-theoretic approach to differentiable manifolds,,58A
+58A05,"Differentiable manifolds, foundations",,58A
+58A07,Real-analytic and Nash manifolds,,58A
+58A10,Differential forms in global analysis,,58A
+58A12,de Rham theory in global analysis,,58A
+58A14,Hodge theory in global analysis,,58A
+58A15,Exterior differential systems (Cartan theory),,58A
+58A17,Pfaffian systems,,58A
+58A20,Jets in global analysis,,58A
+58A25,Currents in global analysis,,58A
+58A30,Vector distributions (subbundles of the tangent bundles),,58A
+58A32,Natural bundles,,58A
+58A35,Stratified sets,,58A
+58A40,Differential spaces,,58A
+58A50,Supermanifolds and graded manifolds,,58A
+58A99,General theory of differentiable manifolds,,58A
+58B05,Homotopy and topological questions for infinite-dimensional manifolds,,58B
+58B10,Differentiability questions for infinite-dimensional manifolds,,58B
+58B12,Questions of holomorphy and infinite-dimensional manifolds,,58B
+58B15,Fredholm structures on infinite-dimensional manifolds,,58B
+58B20,"Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds",,58B
+58B25,Group structures and generalizations on infinite-dimensional manifolds,,58B
+58B32,Geometry of quantum groups,,58B
+58B34,Noncommutative geometry (à la Connes),,58B
+58B99,Infinite-dimensional manifolds,,58B
+58C05,Real-valued functions on manifolds,,58C
+58C06,Set-valued and function-space-valued mappings on manifolds,,58C
+58C07,Continuity properties of mappings on manifolds,,58C
+58C10,Holomorphic maps on manifolds,,58C
+58C15,Implicit function theorems; global Newton methods on manifolds,,58C
+58C20,"Differentiation theory (Gateaux, Fréchet, etc.) on manifolds",,58C
+58C25,Differentiable maps on manifolds,,58C
+58C30,Fixed-point theorems on manifolds,,58C
+58C35,Integration on manifolds; measures on manifolds,,58C
+58C40,Spectral theory; eigenvalue problems on manifolds,,58C
+58C50,Analysis on supermanifolds or graded manifolds,,58C
+58C99,Calculus on manifolds; nonlinear operators,,58C
+58D05,Groups of diffeomorphisms and homeomorphisms as manifolds,,58D
+58D07,Groups and semigroups of nonlinear operators,,58D
+58D10,Spaces of embeddings and immersions,,58D
+58D15,Manifolds of mappings,,58D
+58D17,Manifolds of metrics (especially Riemannian),,58D
+58D19,Group actions and symmetry properties,,58D
+58D20,"Measures (Gaussian, cylindrical, etc.) on manifolds of maps",,58D
+58D25,Equations in function spaces; evolution equations,,58D
+58D27,Moduli problems for differential geometric structures,,58D
+58D29,Moduli problems for topological structures,,58D
+58D30,Applications of manifolds of mappings to the sciences,,58D
+58D99,Spaces and manifolds of mappings (including nonlinear versions of 46Exx),,58D
+58E05,"Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces",,58E
+58E07,Variational problems in abstract bifurcation theory in infinite-dimensional spaces,,58E
+58E09,Group-invariant bifurcation theory in infinite-dimensional spaces,,58E
+58E10,Variational problems in applications to the theory of geodesics (problems in one independent variable),,58E
+58E11,Critical metrics,,58E
+58E12,Variational problems concerning minimal surfaces (problems in two independent variables),,58E
+58E15,Variational problems concerning extremal problems in several variables; Yang-Mills functionals,,58E
+58E17,"Multiobjective variational problems, Pareto optimality, applications to economics, etc.",,58E
+58E20,"Harmonic maps, etc.",,58E
+58E25,Applications of variational problems to control theory,,58E
+58E30,Variational principles in infinite-dimensional spaces,,58E
+58E35,Variational inequalities (global problems) in infinite-dimensional spaces,,58E
+58E40,Variational aspects of group actions in infinite-dimensional spaces,,58E
+58E50,Applications of variational problems in infinite-dimensional spaces to the sciences,,58E
+58E99,Variational problems in infinite-dimensional spaces,,58E
+58H05,Pseudogroups and differentiable groupoids,,58H
+58H10,"Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)",,58H
+58H15,Deformations of general structures on manifolds,,58H
+58H99,"Pseudogroups, differentiable groupoids and general structures on manifolds",,58H
+58J05,"Elliptic equations on manifolds, general theory",,58J
+58J10,Differential complexes,,58J
+58J15,Relations of PDEs on manifolds with hyperfunctions,,58J
+58J20,Index theory and related fixed-point theorems on manifolds,,58J
+58J22,Exotic index theories on manifolds,,58J
+58J26,Elliptic genera,,58J
+58J28,"Eta-invariants, Chern-Simons invariants",,58J
+58J30,Spectral flows,,58J
+58J32,Boundary value problems on manifolds,,58J
+58J35,Heat and other parabolic equation methods for PDEs on manifolds,,58J
+58J37,Perturbations of PDEs on manifolds; asymptotics,,58J
+58J40,Pseudodifferential and Fourier integral operators on manifolds,,58J
+58J42,"Noncommutative global analysis, noncommutative residues",,58J
+58J45,Hyperbolic equations on manifolds,,58J
+58J47,Propagation of singularities; initial value problems on manifolds,,58J
+58J50,Spectral problems; spectral geometry; scattering theory on manifolds,,58J
+58J51,"Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity",,58J
+58J52,"Determinants and determinant bundles, analytic torsion",,58J
+58J53,Isospectrality,,58J
+58J55,Bifurcation theory for PDEs on manifolds,,58J
+58J60,"Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)",,58J
+58J65,Diffusion processes and stochastic analysis on manifolds,,58J
+58J70,Invariance and symmetry properties for PDEs on manifolds,,58J
+58J72,"Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds",,58J
+58J90,Applications of PDEs on manifolds,,58J
+58J99,Partial differential equations on manifolds; differential operators,,58J
+58K05,Critical points of functions and mappings on manifolds,,58K
+58K10,Monodromy on manifolds,,58K
+58K15,Topological properties of mappings on manifolds,,58K
+58K20,Algebraic and analytic properties of mappings on manifolds,,58K
+58K25,Stability theory for manifolds,,58K
+58K30,Global theory of singularities,,58K
+58K35,Catastrophe theory,,58K
+58K40,Classification; finite determinacy of map germs,,58K
+58K45,"Singularities of vector fields, topological aspects",,58K
+58K50,Normal forms on manifolds,,58K
+58K55,Asymptotic behavior of solutions to equations on manifolds,,58K
+58K60,Deformation of singularities,,58K
+58K65,Topological invariants on manifolds,,58K
+58K70,"Symmetries, equivariance on manifolds",,58K
+58K99,Theory of singularities and catastrophe theory,,58K
+58Z05,Applications of global analysis to the sciences,,58Z
+58Z99,Applications of global analysis to the sciences,,58Z
+60A05,Axioms; other general questions in probability,,60A
+60A10,Probabilistic measure theory,,60A
+60A86,Fuzzy probability,,60A
+60A99,Foundations of probability theory,,60A
+60B05,Probability measures on topological spaces,,60B
+60B10,Convergence of probability measures,,60B
+60B11,Probability theory on linear topological spaces,,60B
+60B12,Limit theorems for vector-valued random variables (infinite-dimensional case),,60B
+60B15,"Probability measures on groups or semigroups, Fourier transforms, factorization",,60B
+60B20,Random matrices (probabilistic aspects),,60B
+60B99,Probability theory on algebraic and topological structures,,60B
+60C05,Combinatorial probability,,60C
+60C99,Combinatorial probability,,60C
+60D05,Geometric probability and stochastic geometry,,60D
+60D99,Geometric probability and stochastic geometry,,60D
+60E05,Probability distributions: general theory,,60E
+60E07,Infinitely divisible distributions; stable distributions,,60E
+60E10,Characteristic functions; other transforms,,60E
+60E15,Inequalities; stochastic orderings,,60E
+60E99,Distribution theory,,60E
+60F05,Central limit and other weak theorems,,60F
+60F10,Large deviations,,60F
+60F15,Strong limit theorems,,60F
+60F17,Functional limit theorems; invariance principles,,60F
+60F20,Zero-one laws,,60F
+60F25,\(L^p\)-limit theorems,,60F
+60F99,Limit theorems in probability theory,,60F
+60G05,Foundations of stochastic processes,,60G
+60G07,General theory of stochastic processes,,60G
+60G09,Exchangeability for stochastic processes,,60G
+60G10,Stationary stochastic processes,,60G
+60G12,General second-order stochastic processes,,60G
+60G15,Gaussian processes,,60G
+60G17,Sample path properties,,60G
+60G18,Self-similar stochastic processes,,60G
+60G20,Generalized stochastic processes,,60G
+60G22,"Fractional processes, including fractional Brownian motion",,60G
+60G25,Prediction theory (aspects of stochastic processes),,60G
+60G30,Continuity and singularity of induced measures,,60G
+60G35,Signal detection and filtering (aspects of stochastic processes),,60G
+60G40,Stopping times; optimal stopping problems; gambling theory,,60G
+60G42,Martingales with discrete parameter,,60G
+60G44,Martingales with continuous parameter,,60G
+60G46,Martingales and classical analysis,,60G
+60G48,Generalizations of martingales,,60G
+60G50,Sums of independent random variables; random walks,,60G
+60G51,Processes with independent increments; Lévy processes,,60G
+60G52,Stable stochastic processes,,60G
+60G53,Feller processes,,60G
+60G55,"Point processes (e.g., Poisson, Cox, Hawkes processes)",,60G
+60G57,Random measures,,60G
+60G60,Random fields,,60G
+60G65,"Nonlinear processes (e.g., \(G\)-Brownian motion, \(G\)-Lévy processes)",,60G
+60G70,Extreme value theory; extremal stochastic processes,,60G
+60G99,Stochastic processes,,60G
+60H05,Stochastic integrals,,60H
+60H07,Stochastic calculus of variations and the Malliavin calculus,,60H
+60H10,Stochastic ordinary differential equations (aspects of stochastic analysis),,60H
+60H15,Stochastic partial differential equations (aspects of stochastic analysis),,60H
+60H17,Singular stochastic partial differential equations,,60H
+60H20,Stochastic integral equations,,60H
+60H25,Random operators and equations (aspects of stochastic analysis),,60H
+60H30,"Applications of stochastic analysis (to PDEs, etc.)",,60H
+60H35,Computational methods for stochastic equations (aspects of stochastic analysis),,60H
+60H40,White noise theory,,60H
+60H50,Regularization by noise,,60H
+60H99,Stochastic analysis,,60H
+60J05,Discrete-time Markov processes on general state spaces,,60J
+60J10,Markov chains (discrete-time Markov processes on discrete state spaces),,60J
+60J20,"Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)",,60J
+60J22,Computational methods in Markov chains,,60J
+60J25,Continuous-time Markov processes on general state spaces,,60J
+60J27,Continuous-time Markov processes on discrete state spaces,,60J
+60J28,Applications of continuous-time Markov processes on discrete state spaces,,60J
+60J35,"Transition functions, generators and resolvents",,60J
+60J40,Right processes,,60J
+60J45,Probabilistic potential theory,,60J
+60J46,Dirichlet form methods in Markov processes,,60J
+60J50,Boundary theory for Markov processes,,60J
+60J55,Local time and additive functionals,,60J
+60J57,Multiplicative functionals and Markov processes,,60J
+60J60,Diffusion processes,,60J
+60J65,Brownian motion,,60J
+60J67,Stochastic (Schramm-)Loewner evolution (SLE),,60J
+60J68,Superprocesses,,60J
+60J70,"Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)",,60J
+60J74,Jump processes on discrete state spaces,,60J
+60J76,Jump processes on general state spaces,,60J
+60J80,"Branching processes (Galton-Watson, birth-and-death, etc.)",,60J
+60J85,Applications of branching processes,,60J
+60J90,Coalescent processes,,60J
+60J95,Applications of coalescent processes,,60J
+60J99,Markov processes,,60J
+60K05,Renewal theory,,60K
+60K10,"Applications of renewal theory (reliability, demand theory, etc.)",,60K
+60K15,"Markov renewal processes, semi-Markov processes",,60K
+60K20,"Applications of Markov renewal processes (reliability, queueing networks, etc.)",,60K
+60K25,Queueing theory (aspects of probability theory),,60K
+60K30,"Applications of queueing theory (congestion, allocation, storage, traffic, etc.)",,60K
+60K35,Interacting random processes; statistical mechanics type models; percolation theory,,60K
+60K37,Processes in random environments,,60K
+60K40,Other physical applications of random processes,,60K
+60K50,"Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.)",,60K
+60K99,Special processes,,60K
+60L10,Signatures and data streams,,60L
+60L20,Rough paths,,60L
+60L30,Regularity structures,,60L
+60L40,Paracontrolled distributions and alternative approaches,,60L
+60L50,Rough partial differential equations,,60L
+60L70,Algebraic structures and computation,,60L
+60L90,Applications of rough analysis,,60L
+60L99,Rough analysis,,60L
+62A01,Foundations and philosophical topics in statistics,,62A
+62A09,Graphical methods in statistics,,62A
+62A86,Fuzzy analysis in statistics,,62A
+62A99,Foundational topics in statistics,,62A
+62B05,Sufficient statistics and fields,,62B
+62B10,Statistical aspects of information-theoretic topics,,62B
+62B11,Information geometry (statistical aspects),,62B
+62B15,Theory of statistical experiments,,62B
+62B86,"Statistical aspects of fuzziness, sufficiency, and information",,62B
+62B99,Sufficiency and information,,62B
+62C05,General considerations in statistical decision theory,,62C
+62C07,Complete class results in statistical decision theory,,62C
+62C10,Bayesian problems; characterization of Bayes procedures,,62C
+62C12,Empirical decision procedures; empirical Bayes procedures,,62C
+62C15,Admissibility in statistical decision theory,,62C
+62C20,Minimax procedures in statistical decision theory,,62C
+62C25,Compound decision problems in statistical decision theory,,62C
+62C86,Statistical decision theory and fuzziness,,62C
+62C99,Statistical decision theory,,62C
+62D05,"Sampling theory, sample surveys",,62D
+62D10,Missing data,,62D
+62D20,Causal inference from observational studies,,62D
+62D99,Statistical sampling theory and related topics,,62D
+62E10,Characterization and structure theory of statistical distributions,,62E
+62E15,Exact distribution theory in statistics,,62E
+62E17,Approximations to statistical distributions (nonasymptotic),,62E
+62E20,Asymptotic distribution theory in statistics,,62E
+62E86,Fuzziness in connection with statistical distributions,,62E
+62E99,Statistical distribution theory,,62E
+62F03,Parametric hypothesis testing,,62F
+62F05,Asymptotic properties of parametric tests,,62F
+62F07,Statistical ranking and selection procedures,,62F
+62F10,Point estimation,,62F
+62F12,Asymptotic properties of parametric estimators,,62F
+62F15,Bayesian inference,,62F
+62F25,Parametric tolerance and confidence regions,,62F
+62F30,Parametric inference under constraints,,62F
+62F35,Robustness and adaptive procedures (parametric inference),,62F
+62F40,"Bootstrap, jackknife and other resampling methods",,62F
+62F86,Parametric inference and fuzziness,,62F
+62F99,Parametric inference,,62F
+62G05,Nonparametric estimation,,62G
+62G07,Density estimation,,62G
+62G08,Nonparametric regression and quantile regression,,62G
+62G09,Nonparametric statistical resampling methods,,62G
+62G10,Nonparametric hypothesis testing,,62G
+62G15,Nonparametric tolerance and confidence regions,,62G
+62G20,Asymptotic properties of nonparametric inference,,62G
+62G30,Order statistics; empirical distribution functions,,62G
+62G32,Statistics of extreme values; tail inference,,62G
+62G35,Nonparametric robustness,,62G
+62G86,Nonparametric inference and fuzziness,,62G
+62G99,Nonparametric inference,,62G
+62H05,Characterization and structure theory for multivariate probability distributions; copulas,,62H
+62H10,Multivariate distribution of statistics,,62H
+62H11,Directional data; spatial statistics,,62H
+62H12,Estimation in multivariate analysis,,62H
+62H15,Hypothesis testing in multivariate analysis,,62H
+62H17,Contingency tables,,62H
+62H20,"Measures of association (correlation, canonical correlation, etc.)",,62H
+62H22,Probabilistic graphical models,,62H
+62H25,Factor analysis and principal components; correspondence analysis,,62H
+62H30,Classification and discrimination; cluster analysis (statistical aspects),,62H
+62H35,Image analysis in multivariate analysis,,62H
+62H86,Multivariate analysis and fuzziness,,62H
+62H99,Multivariate analysis,,62H
+62J02,General nonlinear regression,,62J
+62J05,Linear regression; mixed models,,62J
+62J07,Ridge regression; shrinkage estimators (Lasso),,62J
+62J10,Analysis of variance and covariance (ANOVA),,62J
+62J12,Generalized linear models (logistic models),,62J
+62J15,Paired and multiple comparisons; multiple testing,,62J
+62J20,"Diagnostics, and linear inference and regression",,62J
+62J86,"Fuzziness, and linear inference and regression",,62J
+62J99,"Linear inference, regression",,62J
+62K05,Optimal statistical designs,,62K
+62K10,Statistical block designs,,62K
+62K15,Factorial statistical designs,,62K
+62K20,Response surface designs,,62K
+62K25,Robust parameter designs,,62K
+62K86,Fuzziness and design of statistical experiments,,62K
+62K99,Design of statistical experiments,,62K
+62L05,Sequential statistical design,,62L
+62L10,Sequential statistical analysis,,62L
+62L12,Sequential estimation,,62L
+62L15,Optimal stopping in statistics,,62L
+62L20,Stochastic approximation,,62L
+62L86,Fuzziness and sequential statistical methods,,62L
+62L99,Sequential statistical methods,,62L
+62M02,Markov processes: hypothesis testing,,62M
+62M05,Markov processes: estimation; hidden Markov models,,62M
+62M07,Non-Markovian processes: hypothesis testing,,62M
+62M09,Non-Markovian processes: estimation,,62M
+62M10,"Time series, auto-correlation, regression, etc. in statistics (GARCH)",,62M
+62M15,Inference from stochastic processes and spectral analysis,,62M
+62M20,Inference from stochastic processes and prediction,,62M
+62M30,Inference from spatial processes,,62M
+62M40,Random fields; image analysis,,62M
+62M45,Neural nets and related approaches to inference from stochastic processes,,62M
+62M86,Inference from stochastic processes and fuzziness,,62M
+62M99,Inference from stochastic processes,,62M
+62N01,Censored data models,,62N
+62N02,Estimation in survival analysis and censored data,,62N
+62N03,Testing in survival analysis and censored data,,62N
+62N05,Reliability and life testing,,62N
+62N86,"Fuzziness, and survival analysis and censored data",,62N
+62N99,Survival analysis and censored data,,62N
+62P05,Applications of statistics to actuarial sciences and financial mathematics,,62P
+62P10,Applications of statistics to biology and medical sciences; meta analysis,,62P
+62P12,Applications of statistics to environmental and related topics,,62P
+62P15,Applications of statistics to psychology,,62P
+62P20,Applications of statistics to economics,,62P
+62P25,Applications of statistics to social sciences,,62P
+62P30,Applications of statistics in engineering and industry; control charts,,62P
+62P35,Applications of statistics to physics,,62P
+62P99,Applications of statistics,,62P
+62Q05,Statistical tables,,62Q
+62Q99,Statistical tables,,62Q
+62R01,Algebraic statistics,,62R
+62R07,Statistical aspects of big data and data science,,62R
+62R10,Functional data analysis,,62R
+62R20,Statistics on metric spaces,,62R
+62R30,Statistics on manifolds,,62R
+62R40,Topological data analysis,,62R
+62R99,Statistics on algebraic and topological structures,,62R
+65A05,Tables in numerical analysis,,65A
+65A99,Tables in numerical analysis,,65A
+65B05,"Extrapolation to the limit, deferred corrections",,65B
+65B10,Numerical summation of series,,65B
+65B15,Euler-Maclaurin formula in numerical analysis,,65B
+65B99,Acceleration of convergence in numerical analysis,,65B
+65C05,Monte Carlo methods,,65C
+65C10,Random number generation in numerical analysis,,65C
+65C20,"Probabilistic models, generic numerical methods in probability and statistics",,65C
+65C30,Numerical solutions to stochastic differential and integral equations,,65C
+65C35,Stochastic particle methods,,65C
+65C40,Numerical analysis or methods applied to Markov chains,,65C
+65C99,"Probabilistic methods, stochastic differential equations",,65C
+65D05,Numerical interpolation,,65D
+65D07,Numerical computation using splines,,65D
+65D10,"Numerical smoothing, curve fitting",,65D
+65D12,Numerical radial basis function approximation,,65D
+65D15,Algorithms for approximation of functions,,65D
+65D17,Computer-aided design (modeling of curves and surfaces),,65D
+65D18,"Numerical aspects of computer graphics, image analysis, and computational geometry",,65D
+65D19,Computational issues in computer and robotic vision,,65D
+65D20,"Computation of special functions and constants, construction of tables",,65D
+65D25,Numerical differentiation,,65D
+65D30,Numerical integration,,65D
+65D32,Numerical quadrature and cubature formulas,,65D
+65D40,Numerical approximation of high-dimensional functions; sparse grids,,65D
+65D99,Numerical approximation and computational geometry (primarily algorithms),,65D
+65E05,"General theory of numerical methods in complex analysis (potential theory, etc.)",,65E
+65E10,Numerical methods in conformal mappings,,65E
+65E99,"Numerical methods in complex analysis (potential theory, etc.)",,65E
+65F05,Direct numerical methods for linear systems and matrix inversion,,65F
+65F08,Preconditioners for iterative methods,,65F
+65F10,Iterative numerical methods for linear systems,,65F
+65F15,Numerical computation of eigenvalues and eigenvectors of matrices,,65F
+65F18,Numerical solutions to inverse eigenvalue problems,,65F
+65F20,"Numerical solutions to overdetermined systems, pseudoinverses",,65F
+65F22,Ill-posedness and regularization problems in numerical linear algebra,,65F
+65F25,Orthogonalization in numerical linear algebra,,65F
+65F35,"Numerical computation of matrix norms, conditioning, scaling",,65F
+65F40,Numerical computation of determinants,,65F
+65F45,Numerical methods for matrix equations,,65F
+65F50,Computational methods for sparse matrices,,65F
+65F55,Numerical methods for low-rank matrix approximation; matrix compression,,65F
+65F60,Numerical computation of matrix exponential and similar matrix functions,,65F
+65F99,Numerical linear algebra,,65F
+65G20,Algorithms with automatic result verification,,65G
+65G30,Interval and finite arithmetic,,65G
+65G40,General methods in interval analysis,,65G
+65G50,Roundoff error,,65G
+65G99,Error analysis and interval analysis,,65G
+65H04,Numerical computation of roots of polynomial equations,,65H
+65H05,Numerical computation of solutions to single equations,,65H
+65H10,Numerical computation of solutions to systems of equations,,65H
+65H14,Numerical algebraic geometry,,65H
+65H17,Numerical solution of nonlinear eigenvalue and eigenvector problems,,65H
+65H20,"Global methods, including homotopy approaches to the numerical solution of nonlinear equations",,65H
+65H99,Nonlinear algebraic or transcendental equations,,65H
+65J05,General theory of numerical analysis in abstract spaces,,65J
+65J08,Numerical solutions to abstract evolution equations,,65J
+65J10,Numerical solutions to equations with linear operators,,65J
+65J15,Numerical solutions to equations with nonlinear operators,,65J
+65J20,Numerical solutions of ill-posed problems in abstract spaces; regularization,,65J
+65J22,Numerical solution to inverse problems in abstract spaces,,65J
+65J99,Numerical analysis in abstract spaces,,65J
+65K05,Numerical mathematical programming methods,,65K
+65K10,Numerical optimization and variational techniques,,65K
+65K15,Numerical methods for variational inequalities and related problems,,65K
+65K99,"Numerical methods for mathematical programming, optimization and variational techniques",,65K
+65L03,Numerical methods for functional-differential equations,,65L
+65L04,Numerical methods for stiff equations,,65L
+65L05,Numerical methods for initial value problems involving ordinary differential equations,,65L
+65L06,"Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations",,65L
+65L07,Numerical investigation of stability of solutions to ordinary differential equations,,65L
+65L08,Numerical solution of ill-posed problems involving ordinary differential equations,,65L
+65L09,Numerical solution of inverse problems involving ordinary differential equations,,65L
+65L10,Numerical solution of boundary value problems involving ordinary differential equations,,65L
+65L11,Numerical solution of singularly perturbed problems involving ordinary differential equations,,65L
+65L12,Finite difference and finite volume methods for ordinary differential equations,,65L
+65L15,Numerical solution of eigenvalue problems involving ordinary differential equations,,65L
+65L20,Stability and convergence of numerical methods for ordinary differential equations,,65L
+65L50,"Mesh generation, refinement, and adaptive methods for ordinary differential equations",,65L
+65L60,"Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations",,65L
+65L70,Error bounds for numerical methods for ordinary differential equations,,65L
+65L80,Numerical methods for differential-algebraic equations,,65L
+65L99,Numerical methods for ordinary differential equations,,65L
+65M06,Finite difference methods for initial value and initial-boundary value problems involving PDEs,,65M
+65M08,Finite volume methods for initial value and initial-boundary value problems involving PDEs,,65M
+65M12,Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs,,65M
+65M15,Error bounds for initial value and initial-boundary value problems involving PDEs,,65M
+65M20,Method of lines for initial value and initial-boundary value problems involving PDEs,,65M
+65M22,Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs,,65M
+65M25,Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs,,65M
+65M30,Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs,,65M
+65M32,Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs,,65M
+65M38,Boundary element methods for initial value and initial-boundary value problems involving PDEs,,65M
+65M50,"Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs",,65M
+65M55,Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs,,65M
+65M60,"Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs",,65M
+65M70,"Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs",,65M
+65M75,"Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs",,65M
+65M80,"Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs",,65M
+65M85,Fictitious domain methods for initial value and initial-boundary value problems involving PDEs,,65M
+65M99,"Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems",,65M
+65N06,Finite difference methods for boundary value problems involving PDEs,,65N
+65N08,Finite volume methods for boundary value problems involving PDEs,,65N
+65N12,Stability and convergence of numerical methods for boundary value problems involving PDEs,,65N
+65N15,Error bounds for boundary value problems involving PDEs,,65N
+65N20,Numerical methods for ill-posed problems for boundary value problems involving PDEs,,65N
+65N21,Numerical methods for inverse problems for boundary value problems involving PDEs,,65N
+65N22,Numerical solution of discretized equations for boundary value problems involving PDEs,,65N
+65N25,Numerical methods for eigenvalue problems for boundary value problems involving PDEs,,65N
+65N30,"Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs",,65N
+65N35,"Spectral, collocation and related methods for boundary value problems involving PDEs",,65N
+65N38,Boundary element methods for boundary value problems involving PDEs,,65N
+65N40,Method of lines for boundary value problems involving PDEs,,65N
+65N45,Method of contraction of the boundary for boundary value problems involving PDEs,,65N
+65N50,"Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs",,65N
+65N55,Multigrid methods; domain decomposition for boundary value problems involving PDEs,,65N
+65N75,"Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs",,65N
+65N80,"Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs",,65N
+65N85,Fictitious domain methods for boundary value problems involving PDEs,,65N
+65N99,"Numerical methods for partial differential equations, boundary value problems",,65N
+65P10,Numerical methods for Hamiltonian systems including symplectic integrators,,65P
+65P20,Numerical chaos,,65P
+65P30,Numerical bifurcation problems,,65P
+65P40,Numerical nonlinear stabilities in dynamical systems,,65P
+65P99,Numerical problems in dynamical systems,,65P
+65Q10,Numerical methods for difference equations,,65Q
+65Q20,Numerical methods for functional equations,,65Q
+65Q30,Numerical aspects of recurrence relations,,65Q
+65Q99,"Numerical methods for difference and functional equations, recurrence relations",,65Q
+65R10,Numerical methods for integral transforms,,65R
+65R15,Numerical methods for eigenvalue problems in integral equations,,65R
+65R20,Numerical methods for integral equations,,65R
+65R30,Numerical methods for ill-posed problems for integral equations,,65R
+65R32,Numerical methods for inverse problems for integral equations,,65R
+65R99,"Numerical methods for integral equations, integral transforms",,65R
+65S05,Graphical methods in numerical analysis,,65S
+65S99,Graphical methods in numerical analysis,,65S
+65T40,Numerical methods for trigonometric approximation and interpolation,,65T
+65T50,Numerical methods for discrete and fast Fourier transforms,,65T
+65T60,Numerical methods for wavelets,,65T
+65T99,Numerical methods in Fourier analysis,,65T
+65Y04,"Numerical algorithms for computer arithmetic, etc.",,65Y
+65Y05,Parallel numerical computation,,65Y
+65Y10,Numerical algorithms for specific classes of architectures,,65Y
+65Y15,Packaged methods for numerical algorithms,,65Y
+65Y20,Complexity and performance of numerical algorithms,,65Y
+65Y99,Computer aspects of numerical algorithms,,65Y
+65Z05,Applications to the sciences,,65Z
+65Z99,Applications to the sciences,,65Z
+68M01,General theory of computer systems,,68M
+68M07,Mathematical problems of computer architecture,,68M
+68M10,Network design and communication in computer systems,,68M
+68M11,Internet topics,,68M
+68M12,Network protocols,,68M
+68M14,Distributed systems,,68M
+68M15,"Reliability, testing and fault tolerance of networks and computer systems",,68M
+68M18,Wireless sensor networks as related to computer science,,68M
+68M20,"Performance evaluation, queueing, and scheduling in the context of computer systems",,68M
+68M25,Computer security,,68M
+68M99,Computer system organization,,68M
+68N01,General topics in the theory of software,,68N
+68N15,Theory of programming languages,,68N
+68N17,Logic programming,,68N
+68N18,Functional programming and lambda calculus,,68N
+68N19,"Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.)",,68N
+68N20,Theory of compilers and interpreters,,68N
+68N25,Theory of operating systems,,68N
+68N30,"Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)",,68N
+68N99,Theory of software,,68N
+68P01,General topics in the theory of data,,68P
+68P05,Data structures,,68P
+68P10,Searching and sorting,,68P
+68P15,Database theory,,68P
+68P20,Information storage and retrieval of data,,68P
+68P25,Data encryption (aspects in computer science),,68P
+68P27,Privacy of data,,68P
+68P30,"Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)",,68P
+68P99,Theory of data,,68P
+68Q01,General topics in the theory of computing,,68Q
+68Q04,"Classical models of computation (Turing machines, etc.)",,68Q
+68Q06,Networks and circuits as models of computation; circuit complexity,,68Q
+68Q07,"Biologically inspired models of computation (DNA computing, membrane computing, etc.)",,68Q
+68Q09,Other nonclassical models of computation,,68Q
+68Q10,"Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)",,68Q
+68Q11,"Communication complexity, information complexity",,68Q
+68Q12,Quantum algorithms and complexity in the theory of computing,,68Q
+68Q15,"Complexity classes (hierarchies, relations among complexity classes, etc.)",,68Q
+68Q17,"Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)",,68Q
+68Q19,Descriptive complexity and finite models,,68Q
+68Q25,Analysis of algorithms and problem complexity,,68Q
+68Q27,"Parameterized complexity, tractability and kernelization",,68Q
+68Q30,"Algorithmic information theory (Kolmogorov complexity, etc.)",,68Q
+68Q32,Computational learning theory,,68Q
+68Q42,Grammars and rewriting systems,,68Q
+68Q45,Formal languages and automata,,68Q
+68Q55,Semantics in the theory of computing,,68Q
+68Q60,"Specification and verification (program logics, model checking, etc.)",,68Q
+68Q65,Abstract data types; algebraic specification,,68Q
+68Q70,Algebraic theory of languages and automata,,68Q
+68Q80,Cellular automata (computational aspects),,68Q
+68Q85,"Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)",,68Q
+68Q87,"Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)",,68Q
+68Q99,Theory of computing,,68Q
+68R01,General topics of discrete mathematics in relation to computer science,,68R
+68R05,Combinatorics in computer science,,68R
+68R07,Computational aspects of satisfiability,,68R
+68R10,Graph theory (including graph drawing) in computer science,,68R
+68R12,Metric embeddings as related to computational problems and algorithms,,68R
+68R15,Combinatorics on words,,68R
+68R99,Discrete mathematics in relation to computer science,,68R
+68T01,General topics in artificial intelligence,,68T
+68T05,Learning and adaptive systems in artificial intelligence,,68T
+68T07,Artificial neural networks and deep learning,,68T
+68T09,Computational aspects of data analysis and big data,,68T
+68T10,"Pattern recognition, speech recognition",,68T
+68T20,"Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)",,68T
+68T27,Logic in artificial intelligence,,68T
+68T30,Knowledge representation,,68T
+68T35,"Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence",,68T
+68T37,Reasoning under uncertainty in the context of artificial intelligence,,68T
+68T40,Artificial intelligence for robotics,,68T
+68T42,Agent technology and artificial intelligence,,68T
+68T45,Machine vision and scene understanding,,68T
+68T50,Natural language processing,,68T
+68T99,Artificial intelligence,,68T
+68U01,General topics in computing methodologies,,68U
+68U03,Computational aspects of digital topology,,68U
+68U05,Computer graphics; computational geometry (digital and algorithmic aspects),,68U
+68U07,Computer science aspects of computer-aided design,,68U
+68U10,Computing methodologies for image processing,,68U
+68U15,Computing methodologies for text processing; mathematical typography,,68U
+68U35,"Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)",,68U
+68U99,Computing methodologies and applications,,68U
+68V05,Computer assisted proofs of proofs-by-exhaustion type,,68V
+68V15,"Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)",,68V
+68V20,Formalization of mathematics in connection with theorem provers,,68V
+68V25,Presentation and content markup for mathematics,,68V
+68V30,Mathematical knowledge management,,68V
+68V35,Digital mathematics libraries and repositories,,68V
+68V99,Computer science support for mathematical research and practice,,68V
+68W01,General topics in the theory of algorithms,,68W
+68W05,Nonnumerical algorithms,,68W
+68W10,Parallel algorithms in computer science,,68W
+68W15,Distributed algorithms,,68W
+68W20,Randomized algorithms,,68W
+68W25,Approximation algorithms,,68W
+68W27,Online algorithms; streaming algorithms,,68W
+68W30,Symbolic computation and algebraic computation,,68W
+68W32,Algorithms on strings,,68W
+68W35,"Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.)",,68W
+68W40,Analysis of algorithms,,68W
+68W50,"Evolutionary algorithms, genetic algorithms (computational aspects)",,68W
+68W99,Algorithms in computer science,,68W
+70A05,"Axiomatics, foundations",,70A
+70A99,"Axiomatics, foundations",,70A
+70B05,Kinematics of a particle,,70B
+70B10,Kinematics of a rigid body,,70B
+70B15,Kinematics of mechanisms and robots,,70B
+70B99,Kinematics,,70B
+70C20,Statics,,70C
+70C99,Statics,,70C
+70E05,Motion of the gyroscope,,70E
+70E15,Free motion of a rigid body,,70E
+70E17,Motion of a rigid body with a fixed point,,70E
+70E18,Motion of a rigid body in contact with a solid surface,,70E
+70E20,Perturbation methods for rigid body dynamics,,70E
+70E40,Integrable cases of motion in rigid body dynamics,,70E
+70E45,Higher-dimensional generalizations in rigid body dynamics,,70E
+70E50,Stability problems in rigid body dynamics,,70E
+70E55,Dynamics of multibody systems,,70E
+70E60,Robot dynamics and control of rigid bodies,,70E
+70E99,Dynamics of a rigid body and of multibody systems,,70E
+70F05,Two-body problems,,70F
+70F07,Three-body problems,,70F
+70F10,\(n\)-body problems,,70F
+70F15,Celestial mechanics,,70F
+70F16,"Collisions in celestial mechanics, regularization",,70F
+70F17,Inverse problems for systems of particles,,70F
+70F20,Holonomic systems related to the dynamics of a system of particles,,70F
+70F25,Nonholonomic systems related to the dynamics of a system of particles,,70F
+70F35,Collision of rigid or pseudo-rigid bodies,,70F
+70F40,Problems involving a system of particles with friction,,70F
+70F45,The dynamics of infinite particle systems,,70F
+70F99,"Dynamics of a system of particles, including celestial mechanics",,70F
+70G10,"Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics",,70G
+70G40,Topological and differential topological methods for problems in mechanics,,70G
+70G45,"Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics",,70G
+70G55,Algebraic geometry methods for problems in mechanics,,70G
+70G60,Dynamical systems methods for problems in mechanics,,70G
+70G65,"Symmetries, Lie group and Lie algebra methods for problems in mechanics",,70G
+70G70,Functional analytic methods for problems in mechanics,,70G
+70G75,Variational methods for problems in mechanics,,70G
+70G99,"General models, approaches, and methods in mechanics of particles and systems",,70G
+70H03,Lagrange's equations,,70H
+70H05,Hamilton's equations,,70H
+70H06,Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H07,Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H08,"Nearly integrable Hamiltonian systems, KAM theory",,70H
+70H09,Perturbation theories for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H11,Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H12,Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H14,Stability problems for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H15,Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H20,Hamilton-Jacobi equations in mechanics,,70H
+70H25,Hamilton's principle,,70H
+70H30,Other variational principles in mechanics,,70H
+70H33,"Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics",,70H
+70H40,Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H45,"Constrained dynamics, Dirac's theory of constraints",,70H
+70H50,Higher-order theories for problems in Hamiltonian and Lagrangian mechanics,,70H
+70H99,Hamiltonian and Lagrangian mechanics,,70H
+70J10,Modal analysis in linear vibration theory,,70J
+70J25,Stability for problems in linear vibration theory,,70J
+70J30,Free motions in linear vibration theory,,70J
+70J35,Forced motions in linear vibration theory,,70J
+70J40,Parametric resonances in linear vibration theory,,70J
+70J50,Systems arising from the discretization of structural vibration problems,,70J
+70J99,Linear vibration theory,,70J
+70K05,"Phase plane analysis, limit cycles for nonlinear problems in mechanics",,70K
+70K20,Stability for nonlinear problems in mechanics,,70K
+70K25,Free motions for nonlinear problems in mechanics,,70K
+70K28,Parametric resonances for nonlinear problems in mechanics,,70K
+70K30,Nonlinear resonances for nonlinear problems in mechanics,,70K
+70K40,Forced motions for nonlinear problems in mechanics,,70K
+70K42,Equilibria and periodic trajectories for nonlinear problems in mechanics,,70K
+70K43,Quasi-periodic motions and invariant tori for nonlinear problems in mechanics,,70K
+70K44,Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics,,70K
+70K45,Normal forms for nonlinear problems in mechanics,,70K
+70K50,Bifurcations and instability for nonlinear problems in mechanics,,70K
+70K55,Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics,,70K
+70K60,General perturbation schemes for nonlinear problems in mechanics,,70K
+70K65,Averaging of perturbations for nonlinear problems in mechanics,,70K
+70K70,Systems with slow and fast motions for nonlinear problems in mechanics,,70K
+70K75,Nonlinear modes,,70K
+70K99,Nonlinear dynamics in mechanics,,70K
+70L05,Random vibrations in mechanics of particles and systems,,70L
+70L10,Stochastic geometric mechanics,,70L
+70L99,Random and stochastic aspects of the mechanics of particles and systems,,70L
+70M20,Orbital mechanics,,70M
+70M99,Orbital mechanics,,70M
+70P05,"Variable mass, rockets",,70P
+70P99,"Variable mass, rockets",,70P
+70Q05,Control of mechanical systems,,70Q
+70Q99,Control of mechanical systems,,70Q
+70S05,Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems,,70S
+70S10,Symmetries and conservation laws in mechanics of particles and systems,,70S
+70S15,Yang-Mills and other gauge theories in mechanics of particles and systems,,70S
+70S20,More general nonquantum field theories in mechanics of particles and systems,,70S
+70S99,Classical field theories,,70S
+74A05,Kinematics of deformation,,74A
+74A10,Stress,,74A
+74A15,Thermodynamics in solid mechanics,,74A
+74A20,Theory of constitutive functions in solid mechanics,,74A
+74A25,"Molecular, statistical, and kinetic theories in solid mechanics",,74A
+74A30,Nonsimple materials,,74A
+74A35,Polar materials,,74A
+74A40,Random materials and composite materials,,74A
+74A45,Theories of fracture and damage,,74A
+74A50,"Structured surfaces and interfaces, coexistent phases",,74A
+74A55,Theories of friction (tribology),,74A
+74A60,Micromechanical theories,,74A
+74A65,Reactive materials,,74A
+74A70,Peridynamics,,74A
+74A99,"Generalities, axiomatics, foundations of continuum mechanics of solids",,74A
+74B05,Classical linear elasticity,,74B
+74B10,Linear elasticity with initial stresses,,74B
+74B15,Equations linearized about a deformed state (small deformations superposed on large),,74B
+74B20,Nonlinear elasticity,,74B
+74B99,Elastic materials,,74B
+74C05,"Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)",,74C
+74C10,"Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)",,74C
+74C15,"Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)",,74C
+74C20,"Large-strain, rate-dependent theories of plasticity",,74C
+74C99,"Plastic materials, materials of stress-rate and internal-variable type",,74C
+74D05,Linear constitutive equations for materials with memory,,74D
+74D10,Nonlinear constitutive equations for materials with memory,,74D
+74D99,"Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)",,74D
+74E05,Inhomogeneity in solid mechanics,,74E
+74E10,Anisotropy in solid mechanics,,74E
+74E15,Crystalline structure,,74E
+74E20,Granularity,,74E
+74E25,Texture in solid mechanics,,74E
+74E30,Composite and mixture properties,,74E
+74E35,Random structure in solid mechanics,,74E
+74E40,Chemical structure in solid mechanics,,74E
+74E99,Material properties given special treatment,,74E
+74F05,Thermal effects in solid mechanics,,74F
+74F10,"Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)",,74F
+74F15,Electromagnetic effects in solid mechanics,,74F
+74F20,Mixture effects in solid mechanics,,74F
+74F25,Chemical and reactive effects in solid mechanics,,74F
+74F99,Coupling of solid mechanics with other effects,,74F
+74G05,Explicit solutions of equilibrium problems in solid mechanics,,74G
+74G10,"Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics",,74G
+74G15,Numerical approximation of solutions of equilibrium problems in solid mechanics,,74G
+74G22,Existence of solutions of equilibrium problems in solid mechanics,,74G
+74G30,Uniqueness of solutions of equilibrium problems in solid mechanics,,74G
+74G35,Multiplicity of solutions of equilibrium problems in solid mechanics,,74G
+74G40,Regularity of solutions of equilibrium problems in solid mechanics,,74G
+74G45,Bounds for solutions of equilibrium problems in solid mechanics,,74G
+74G50,Saint-Venant's principle,,74G
+74G55,Qualitative behavior of solutions of equilibrium problems in solid mechanics,,74G
+74G60,Bifurcation and buckling,,74G
+74G65,Energy minimization in equilibrium problems in solid mechanics,,74G
+74G70,"Stress concentrations, singularities in solid mechanics",,74G
+74G75,Inverse problems in equilibrium solid mechanics,,74G
+74G99,Equilibrium (steady-state) problems in solid mechanics,,74G
+74H05,Explicit solutions of dynamical problems in solid mechanics,,74H
+74H10,"Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics",,74H
+74H15,Numerical approximation of solutions of dynamical problems in solid mechanics,,74H
+74H20,Existence of solutions of dynamical problems in solid mechanics,,74H
+74H25,Uniqueness of solutions of dynamical problems in solid mechanics,,74H
+74H30,Regularity of solutions of dynamical problems in solid mechanics,,74H
+74H35,"Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics",,74H
+74H40,Long-time behavior of solutions for dynamical problems in solid mechanics,,74H
+74H45,Vibrations in dynamical problems in solid mechanics,,74H
+74H50,Random vibrations in dynamical problems in solid mechanics,,74H
+74H55,Stability of dynamical problems in solid mechanics,,74H
+74H60,Dynamical bifurcation of solutions to dynamical problems in solid mechanics,,74H
+74H65,Chaotic behavior of solutions to dynamical problems in solid mechanics,,74H
+74H75,Inverse problems in dynamical solid mechanics,,74H
+74H80,Energy minimization in dynamical problems in solid mechanics,,74H
+74H99,Dynamical problems in solid mechanics,,74H
+74J05,Linear waves in solid mechanics,,74J
+74J10,Bulk waves in solid mechanics,,74J
+74J15,Surface waves in solid mechanics,,74J
+74J20,Wave scattering in solid mechanics,,74J
+74J25,Inverse problems for waves in solid mechanics,,74J
+74J30,Nonlinear waves in solid mechanics,,74J
+74J35,Solitary waves in solid mechanics,,74J
+74J40,Shocks and related discontinuities in solid mechanics,,74J
+74J99,Waves in solid mechanics,,74J
+74K05,Strings,,74K
+74K10,"Rods (beams, columns, shafts, arches, rings, etc.)",,74K
+74K15,Membranes,,74K
+74K20,Plates,,74K
+74K25,Shells,,74K
+74K30,Junctions,,74K
+74K35,Thin films,,74K
+74K99,"Thin bodies, structures",,74K
+74L05,Geophysical solid mechanics,,74L
+74L10,Soil and rock mechanics,,74L
+74L15,Biomechanical solid mechanics,,74L
+74L99,Special subfields of solid mechanics,,74L
+74M05,"Control, switches and devices (``smart materials'') in solid mechanics",,74M
+74M10,Friction in solid mechanics,,74M
+74M15,Contact in solid mechanics,,74M
+74M20,Impact in solid mechanics,,74M
+74M25,Micromechanics of solids,,74M
+74M99,Special kinds of problems in solid mechanics,,74M
+74N05,Crystals in solids,,74N
+74N10,Displacive transformations in solids,,74N
+74N15,Analysis of microstructure in solids,,74N
+74N20,Dynamics of phase boundaries in solids,,74N
+74N25,Transformations involving diffusion in solids,,74N
+74N30,Problems involving hysteresis in solids,,74N
+74N99,Phase transformations in solids,,74N
+74P05,Compliance or weight optimization in solid mechanics,,74P
+74P10,Optimization of other properties in solid mechanics,,74P
+74P15,Topological methods for optimization problems in solid mechanics,,74P
+74P20,Geometrical methods for optimization problems in solid mechanics,,74P
+74P99,Optimization problems in solid mechanics,,74P
+74Q05,Homogenization in equilibrium problems of solid mechanics,,74Q
+74Q10,Homogenization and oscillations in dynamical problems of solid mechanics,,74Q
+74Q15,Effective constitutive equations in solid mechanics,,74Q
+74Q20,Bounds on effective properties in solid mechanics,,74Q
+74Q99,"Homogenization, determination of effective properties in solid mechanics",,74Q
+74R05,Brittle damage,,74R
+74R10,Brittle fracture,,74R
+74R15,High-velocity fracture,,74R
+74R20,Anelastic fracture and damage,,74R
+74R99,Fracture and damage,,74R
+74S05,Finite element methods applied to problems in solid mechanics,,74S
+74S10,Finite volume methods applied to problems in solid mechanics,,74S
+74S15,Boundary element methods applied to problems in solid mechanics,,74S
+74S20,Finite difference methods applied to problems in solid mechanics,,74S
+74S22,Isogeometric methods applied to problems in solid mechanics,,74S
+74S25,Spectral and related methods applied to problems in solid mechanics,,74S
+74S40,Applications of fractional calculus in solid mechanics,,74S
+74S50,Applications of graph theory in solid mechanics,,74S
+74S60,Stochastic and other probabilistic methods applied to problems in solid mechanics,,74S
+74S70,Complex-variable methods applied to problems in solid mechanics,,74S
+74S99,Numerical and other methods in solid mechanics,,74S
+76A02,Foundations of fluid mechanics,,76A
+76A05,Non-Newtonian fluids,,76A
+76A10,Viscoelastic fluids,,76A
+76A15,Liquid crystals,,76A
+76A20,Thin fluid films,,76A
+76A25,Superfluids (classical aspects),,76A
+76A30,Traffic and pedestrian flow models,,76A
+76A99,"Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena",,76A
+76B03,"Existence, uniqueness, and regularity theory for incompressible inviscid fluids",,76B
+76B07,Free-surface potential flows for incompressible inviscid fluids,,76B
+76B10,"Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing",,76B
+76B15,"Water waves, gravity waves; dispersion and scattering, nonlinear interaction",,76B
+76B20,Ship waves,,76B
+76B25,Solitary waves for incompressible inviscid fluids,,76B
+76B45,Capillarity (surface tension) for incompressible inviscid fluids,,76B
+76B47,Vortex flows for incompressible inviscid fluids,,76B
+76B55,Internal waves for incompressible inviscid fluids,,76B
+76B70,Stratification effects in inviscid fluids,,76B
+76B75,Flow control and optimization for incompressible inviscid fluids,,76B
+76B99,Incompressible inviscid fluids,,76B
+76D03,"Existence, uniqueness, and regularity theory for incompressible viscous fluids",,76D
+76D05,Navier-Stokes equations for incompressible viscous fluids,,76D
+76D06,Statistical solutions of Navier-Stokes and related equations,,76D
+76D07,"Stokes and related (Oseen, etc.) flows",,76D
+76D08,Lubrication theory,,76D
+76D09,Viscous-inviscid interaction,,76D
+76D10,"Boundary-layer theory, separation and reattachment, higher-order effects",,76D
+76D17,Viscous vortex flows,,76D
+76D25,Wakes and jets,,76D
+76D27,Other free boundary flows; Hele-Shaw flows,,76D
+76D33,Waves for incompressible viscous fluids,,76D
+76D45,Capillarity (surface tension) for incompressible viscous fluids,,76D
+76D50,Stratification effects in viscous fluids,,76D
+76D55,Flow control and optimization for incompressible viscous fluids,,76D
+76D99,Incompressible viscous fluids,,76D
+76E05,Parallel shear flows in hydrodynamic stability,,76E
+76E06,Convection in hydrodynamic stability,,76E
+76E07,Rotation in hydrodynamic stability,,76E
+76E09,Stability and instability of nonparallel flows in hydrodynamic stability,,76E
+76E15,Absolute and convective instability and stability in hydrodynamic stability,,76E
+76E17,Interfacial stability and instability in hydrodynamic stability,,76E
+76E19,Compressibility effects in hydrodynamic stability,,76E
+76E20,Stability and instability of geophysical and astrophysical flows,,76E
+76E25,Stability and instability of magnetohydrodynamic and electrohydrodynamic flows,,76E
+76E30,Nonlinear effects in hydrodynamic stability,,76E
+76E99,Hydrodynamic stability,,76E
+76F02,Fundamentals of turbulence,,76F
+76F05,Isotropic turbulence; homogeneous turbulence,,76F
+76F06,Transition to turbulence,,76F
+76F10,Shear flows and turbulence,,76F
+76F20,Dynamical systems approach to turbulence,,76F
+76F25,"Turbulent transport, mixing",,76F
+76F30,Renormalization and other field-theoretical methods for turbulence,,76F
+76F35,Convective turbulence,,76F
+76F40,Turbulent boundary layers,,76F
+76F45,Stratification effects in turbulence,,76F
+76F50,Compressibility effects in turbulence,,76F
+76F55,Statistical turbulence modeling,,76F
+76F60,\(k\)-\(\varepsilon\) modeling in turbulence,,76F
+76F65,Direct numerical and large eddy simulation of turbulence,,76F
+76F70,Control of turbulent flows,,76F
+76F80,Turbulent combustion; reactive turbulence,,76F
+76F99,Turbulence,,76F
+76G25,General aerodynamics and subsonic flows,,76G
+76G99,General aerodynamics and subsonic flows,,76G
+76H05,Transonic flows,,76H
+76H99,Transonic flows,,76H
+76J20,Supersonic flows,,76J
+76J99,Supersonic flows,,76J
+76K05,Hypersonic flows,,76K
+76K99,Hypersonic flows,,76K
+76L05,Shock waves and blast waves in fluid mechanics,,76L
+76L99,Shock waves and blast waves in fluid mechanics,,76L
+76M10,Finite element methods applied to problems in fluid mechanics,,76M
+76M12,Finite volume methods applied to problems in fluid mechanics,,76M
+76M15,Boundary element methods applied to problems in fluid mechanics,,76M
+76M20,Finite difference methods applied to problems in fluid mechanics,,76M
+76M21,Inverse problems in fluid mechanics,,76M
+76M22,Spectral methods applied to problems in fluid mechanics,,76M
+76M23,Vortex methods applied to problems in fluid mechanics,,76M
+76M27,Visualization algorithms applied to problems in fluid mechanics,,76M
+76M28,Particle methods and lattice-gas methods,,76M
+76M30,Variational methods applied to problems in fluid mechanics,,76M
+76M35,Stochastic analysis applied to problems in fluid mechanics,,76M
+76M40,Complex variables methods applied to problems in fluid mechanics,,76M
+76M45,"Asymptotic methods, singular perturbations applied to problems in fluid mechanics",,76M
+76M50,Homogenization applied to problems in fluid mechanics,,76M
+76M55,Dimensional analysis and similarity applied to problems in fluid mechanics,,76M
+76M60,"Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics",,76M
+76M99,Basic methods in fluid mechanics,,76M
+76N06,Compressible Navier-Stokes equations,,76N
+76N10,"Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics",,76N
+76N15,Gas dynamics (general theory),,76N
+76N17,Viscous-inviscid interaction for compressible fluids and gas dynamics,,76N
+76N20,Boundary-layer theory for compressible fluids and gas dynamics,,76N
+76N25,Flow control and optimization for compressible fluids and gas dynamics,,76N
+76N30,Waves in compressible fluids,,76N
+76N99,Compressible fluids and gas dynamics,,76N
+76P05,"Rarefied gas flows, Boltzmann equation in fluid mechanics",,76P
+76P99,"Rarefied gas flows, Boltzmann equation in fluid mechanics",,76P
+76Q05,Hydro- and aero-acoustics,,76Q
+76Q99,Hydro- and aero-acoustics,,76Q
+76R05,Forced convection,,76R
+76R10,Free convection,,76R
+76R50,Diffusion,,76R
+76R99,Diffusion and convection,,76R
+76S05,Flows in porous media; filtration; seepage,,76S
+76S99,Flows in porous media; filtration; seepage,,76S
+76T06,Liquid-liquid two component flows,,76T
+76T10,"Liquid-gas two-phase flows, bubbly flows",,76T
+76T15,Dusty-gas two-phase flows,,76T
+76T17,Two gas multicomponent flows,,76T
+76T20,Suspensions,,76T
+76T25,Granular flows,,76T
+76T30,Three or more component flows,,76T
+76T99,Multiphase and multicomponent flows,,76T
+76U05,General theory of rotating fluids,,76U
+76U60,Geophysical flows,,76U
+76U65,Rossby waves,,76U
+76U99,Rotating fluids,,76U
+76V05,Reaction effects in flows,,76V
+76V99,Reaction effects in flows,,76V
+76W05,Magnetohydrodynamics and electrohydrodynamics,,76W
+76W99,Magnetohydrodynamics and electrohydrodynamics,,76W
+76X05,Ionized gas flow in electromagnetic fields; plasmic flow,,76X
+76X99,Ionized gas flow in electromagnetic fields; plasmic flow,,76X
+76Y05,Quantum hydrodynamics and relativistic hydrodynamics,,76Y
+76Y99,Quantum hydrodynamics and relativistic hydrodynamics,,76Y
+76Z05,Physiological flows,,76Z
+76Z10,Biopropulsion in water and in air,,76Z
+76Z99,Biological fluid mechanics,,76Z
+78A02,Foundations in optics and electromagnetic theory,,78A
+78A05,Geometric optics,,78A
+78A10,Physical optics,,78A
+78A15,Electron optics,,78A
+78A20,Space charge waves,,78A
+78A25,Electromagnetic theory (general),,78A
+78A30,Electro- and magnetostatics,,78A
+78A35,Motion of charged particles,,78A
+78A37,Ion traps,,78A
+78A40,Waves and radiation in optics and electromagnetic theory,,78A
+78A45,"Diffraction, scattering",,78A
+78A46,Inverse problems (including inverse scattering) in optics and electromagnetic theory,,78A
+78A48,Composite media; random media in optics and electromagnetic theory,,78A
+78A50,"Antennas, waveguides in optics and electromagnetic theory",,78A
+78A55,Technical applications of optics and electromagnetic theory,,78A
+78A57,Electrochemistry,,78A
+78A60,"Lasers, masers, optical bistability, nonlinear optics",,78A
+78A70,Biological applications of optics and electromagnetic theory,,78A
+78A97,Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in Section 78-XX),,78A
+78A99,General topics in optics and electromagnetic theory,,78A
+78M05,Method of moments applied to problems in optics and electromagnetic theory,,78M
+78M10,"Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory",,78M
+78M12,"Finite volume methods, finite integration techniques applied to problems in optics and electromagnetic theory",,78M
+78M15,Boundary element methods applied to problems in optics and electromagnetic theory,,78M
+78M16,Multipole methods applied to problems in optics and electromagnetic theory,,78M
+78M20,Finite difference methods applied to problems in optics and electromagnetic theory,,78M
+78M22,"Spectral, collocation and related methods applied to problems in optics and electromagnetic theory",,78M
+78M30,Variational methods applied to problems in optics and electromagnetic theory,,78M
+78M31,Monte Carlo methods applied to problems in optics and electromagnetic theory,,78M
+78M32,Neural and heuristic methods applied to problems in optics and electromagnetic theory,,78M
+78M34,Model reduction in optics and electromagnetic theory,,78M
+78M35,Asymptotic analysis in optics and electromagnetic theory,,78M
+78M40,Homogenization in optics and electromagnetic theory,,78M
+78M50,Optimization problems in optics and electromagnetic theory,,78M
+78M99,Basic methods for problems in optics and electromagnetic theory,,78M
+80A05,Foundations of thermodynamics and heat transfer,,80A
+80A10,Classical and relativistic thermodynamics,,80A
+80A17,Thermodynamics of continua,,80A
+80A19,"Diffusive and convective heat and mass transfer, heat flow",,80A
+80A21,Radiative heat transfer,,80A
+80A22,"Stefan problems, phase changes, etc.",,80A
+80A23,Inverse problems in thermodynamics and heat transfer,,80A
+80A25,Combustion,,80A
+80A30,Chemical kinetics in thermodynamics and heat transfer,,80A
+80A32,Chemically reacting flows,,80A
+80A50,Chemistry (general) in thermodynamics and heat transfer,,80A
+80A99,Thermodynamics and heat transfer,,80A
+80M10,"Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer",,80M
+80M12,Finite volume methods applied to problems in thermodynamics and heat transfer,,80M
+80M15,Boundary element methods applied to problems in thermodynamics and heat transfer,,80M
+80M20,Finite difference methods applied to problems in thermodynamics and heat transfer,,80M
+80M22,"Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer",,80M
+80M30,Variational methods applied to problems in thermodynamics and heat transfer,,80M
+80M31,Monte Carlo methods applied to problems in thermodynamics and heat transfer,,80M
+80M35,Asymptotic analysis for problems in thermodynamics and heat transfer,,80M
+80M40,Homogenization for problems in thermodynamics and heat transfer,,80M
+80M50,Optimization problems in thermodynamics and heat transfer,,80M
+80M60,Stochastic analysis in thermodynamics and heat transfer,,80M
+80M99,Basic methods in thermodynamics and heat transfer,,80M
+81P05,General and philosophical questions in quantum theory,,81P
+81P10,Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects),,81P
+81P13,Contextuality in quantum theory,,81P
+81P15,"Quantum measurement theory, state operations, state preparations",,81P
+81P16,"Quantum state spaces, operational and probabilistic concepts",,81P
+81P17,Quantum entropies,,81P
+81P18,"Quantum state tomography, quantum state discrimination",,81P
+81P20,Stochastic mechanics (including stochastic electrodynamics),,81P
+81P40,"Quantum coherence, entanglement, quantum correlations",,81P
+81P42,"Entanglement measures, concurrencies, separability criteria",,81P
+81P43,Quantum discord,,81P
+81P45,"Quantum information, communication, networks (quantum-theoretic aspects)",,81P
+81P47,"Quantum channels, fidelity",,81P
+81P48,"LOCC, teleportation, dense coding, remote state operations, distillation",,81P
+81P50,"Quantum state estimation, approximate cloning",,81P
+81P55,"Special bases (entangled, mutual unbiased, etc.)",,81P
+81P65,Quantum gates,,81P
+81P68,Quantum computation,,81P
+81P70,Quantum coding (general),,81P
+81P73,Computational stability and error-correcting codes for quantum computation and communication processing,,81P
+81P94,Quantum cryptography (quantum-theoretic aspects),,81P
+81P99,"Foundations, quantum information and its processing, quantum axioms, and philosophy",,81P
+81Q05,"Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics",,81Q
+81Q10,"Selfadjoint operator theory in quantum theory, including spectral analysis",,81Q
+81Q12,Nonselfadjoint operator theory in quantum theory including creation and destruction operators,,81Q
+81Q15,Perturbation theories for operators and differential equations in quantum theory,,81Q
+81Q20,"Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory",,81Q
+81Q30,Feynman integrals and graphs; applications of algebraic topology and algebraic geometry,,81Q
+81Q35,"Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices",,81Q
+81Q37,"Quantum dots, waveguides, ratchets, etc.",,81Q
+81Q40,Bethe-Salpeter and other integral equations arising in quantum theory,,81Q
+81Q50,Quantum chaos,,81Q
+81Q60,Supersymmetry and quantum mechanics,,81Q
+81Q65,"Alternative quantum mechanics (including hidden variables, etc.)",,81Q
+81Q70,"Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory",,81Q
+81Q80,"Special quantum systems, such as solvable systems",,81Q
+81Q93,Quantum control,,81Q
+81Q99,General mathematical topics and methods in quantum theory,,81Q
+81R05,Finite-dimensional groups and algebras motivated by physics and their representations,,81R
+81R10,"Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations",,81R
+81R12,Groups and algebras in quantum theory and relations with integrable systems,,81R
+81R15,Operator algebra methods applied to problems in quantum theory,,81R
+81R20,"Covariant wave equations in quantum theory, relativistic quantum mechanics",,81R
+81R25,Spinor and twistor methods applied to problems in quantum theory,,81R
+81R30,Coherent states,,81R
+81R40,Symmetry breaking in quantum theory,,81R
+81R50,Quantum groups and related algebraic methods applied to problems in quantum theory,,81R
+81R60,Noncommutative geometry in quantum theory,,81R
+81R99,Groups and algebras in quantum theory,,81R
+81S05,Commutation relations and statistics as related to quantum mechanics (general),,81S
+81S07,"Uncertainty relations, also entropic",,81S
+81S08,Canonical quantization,,81S
+81S10,"Geometry and quantization, symplectic methods",,81S
+81S20,Stochastic quantization,,81S
+81S22,"Open systems, reduced dynamics, master equations, decoherence",,81S
+81S25,Quantum stochastic calculus,,81S
+81S30,"Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics",,81S
+81S40,Path integrals in quantum mechanics,,81S
+81S99,General quantum mechanics and problems of quantization,,81S
+81T05,Axiomatic quantum field theory; operator algebras,,81T
+81T08,Constructive quantum field theory,,81T
+81T10,Model quantum field theories,,81T
+81T11,Higher spin theories,,81T
+81T12,Effective quantum field theories,,81T
+81T13,Yang-Mills and other gauge theories in quantum field theory,,81T
+81T15,Perturbative methods of renormalization applied to problems in quantum field theory,,81T
+81T16,Nonperturbative methods of renormalization applied to problems in quantum field theory,,81T
+81T17,Renormalization group methods applied to problems in quantum field theory,,81T
+81T18,Feynman diagrams,,81T
+81T20,Quantum field theory on curved space or space-time backgrounds,,81T
+81T25,Quantum field theory on lattices,,81T
+81T27,Continuum limits in quantum field theory,,81T
+81T28,Thermal quantum field theory,,81T
+81T30,"String and superstring theories; other extended objects (e.g., branes) in quantum field theory",,81T
+81T32,Matrix models and tensor models for quantum field theory,,81T
+81T33,Dimensional compactification in quantum field theory,,81T
+81T35,"Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.)",,81T
+81T40,"Two-dimensional field theories, conformal field theories, etc. in quantum mechanics",,81T
+81T45,Topological field theories in quantum mechanics,,81T
+81T50,Anomalies in quantum field theory,,81T
+81T55,Casimir effect in quantum field theory,,81T
+81T60,Supersymmetric field theories in quantum mechanics,,81T
+81T70,Quantization in field theory; cohomological methods,,81T
+81T75,Noncommutative geometry methods in quantum field theory,,81T
+81T99,Quantum field theory; related classical field theories,,81T
+81U05,\(2\)-body potential quantum scattering theory,,81U
+81U10,\(n\)-body potential quantum scattering theory,,81U
+81U15,Exactly and quasi-solvable systems arising in quantum theory,,81U
+81U20,"\(S\)-matrix theory, etc. in quantum theory",,81U
+81U24,Resonances in quantum scattering theory,,81U
+81U26,Tunneling in quantum theory,,81U
+81U30,"Dispersion theory, dispersion relations arising in quantum theory",,81U
+81U35,Inelastic and multichannel quantum scattering,,81U
+81U40,Inverse scattering problems in quantum theory,,81U
+81U90,Particle decays,,81U
+81U99,Quantum scattering theory,,81U
+81V05,"Strong interaction, including quantum chromodynamics",,81V
+81V10,Electromagnetic interaction; quantum electrodynamics,,81V
+81V15,Weak interaction in quantum theory,,81V
+81V17,Gravitational interaction in quantum theory,,81V
+81V19,Other fundamental interactions in quantum theory,,81V
+81V22,Unified quantum theories,,81V
+81V25,Other elementary particle theory in quantum theory,,81V
+81V27,Anyons,,81V
+81V35,Nuclear physics,,81V
+81V45,Atomic physics,,81V
+81V55,Molecular physics,,81V
+81V60,"Mono-, di- and multipole moments (EM and other), gyromagnetic relations",,81V
+81V65,Quantum dots as quasi particles,,81V
+81V70,Many-body theory; quantum Hall effect,,81V
+81V72,Particle exchange symmetries in quantum theory (general),,81V
+81V73,Bosonic systems in quantum theory,,81V
+81V74,Fermionic systems in quantum theory,,81V
+81V80,Quantum optics,,81V
+81V99,Applications of quantum theory to specific physical systems,,81V
+82B03,Foundations of equilibrium statistical mechanics,,82B
+82B05,Classical equilibrium statistical mechanics (general),,82B
+82B10,Quantum equilibrium statistical mechanics (general),,82B
+82B20,"Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics",,82B
+82B21,"Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics",,82B
+82B23,Exactly solvable models; Bethe ansatz,,82B
+82B24,Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics,,82B
+82B26,Phase transitions (general) in equilibrium statistical mechanics,,82B
+82B27,Critical phenomena in equilibrium statistical mechanics,,82B
+82B28,Renormalization group methods in equilibrium statistical mechanics,,82B
+82B30,Statistical thermodynamics,,82B
+82B31,Stochastic methods applied to problems in equilibrium statistical mechanics,,82B
+82B35,"Irreversible thermodynamics, including Onsager-Machlup theory",,82B
+82B40,Kinetic theory of gases in equilibrium statistical mechanics,,82B
+82B41,"Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics",,82B
+82B43,Percolation,,82B
+82B44,"Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics",,82B
+82B99,Equilibrium statistical mechanics,,82B
+82C03,Foundations of time-dependent statistical mechanics,,82C
+82C05,Classical dynamic and nonequilibrium statistical mechanics (general),,82C
+82C10,Quantum dynamics and nonequilibrium statistical mechanics (general),,82C
+82C20,"Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics",,82C
+82C21,"Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics",,82C
+82C22,Interacting particle systems in time-dependent statistical mechanics,,82C
+82C23,Exactly solvable dynamic models in time-dependent statistical mechanics,,82C
+82C24,Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics,,82C
+82C26,Dynamic and nonequilibrium phase transitions (general) in statistical mechanics,,82C
+82C27,Dynamic critical phenomena in statistical mechanics,,82C
+82C28,Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics,,82C
+82C31,"Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics",,82C
+82C32,Neural nets applied to problems in time-dependent statistical mechanics,,82C
+82C35,"Irreversible thermodynamics, including Onsager-Machlup theory",,82C
+82C40,Kinetic theory of gases in time-dependent statistical mechanics,,82C
+82C41,"Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics",,82C
+82C43,Time-dependent percolation in statistical mechanics,,82C
+82C44,"Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics",,82C
+82C70,Transport processes in time-dependent statistical mechanics,,82C
+82C99,Time-dependent statistical mechanics (dynamic and nonequilibrium),,82C
+82D03,Statistical mechanics in condensed matter (general),,82D
+82D05,Statistical mechanics of gases,,82D
+82D10,Statistical mechanics of plasmas,,82D
+82D15,Statistical mechanics of liquids,,82D
+82D20,Statistical mechanics of solids,,82D
+82D25,Statistical mechanics of crystals,,82D
+82D30,"Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)",,82D
+82D35,Statistical mechanics of metals,,82D
+82D37,Statistical mechanics of semiconductors,,82D
+82D40,Statistical mechanics of magnetic materials,,82D
+82D45,Statistical mechanics of ferroelectrics,,82D
+82D50,Statistical mechanics of superfluids,,82D
+82D55,Statistical mechanics of superconductors,,82D
+82D60,Statistical mechanics of polymers,,82D
+82D75,Nuclear reactor theory; neutron transport,,82D
+82D77,"Quantum waveguides, quantum wires",,82D
+82D80,Statistical mechanics of nanostructures and nanoparticles,,82D
+82D99,Applications of statistical mechanics to specific types of physical systems,,82D
+82M10,"Finite element, Galerkin and related methods applied to problems in statistical mechanics",,82M
+82M12,Finite volume methods applied to problems in statistical mechanics,,82M
+82M15,Boundary element methods applied to problems in statistical mechanics,,82M
+82M20,Finite difference methods applied to problems in statistical mechanics,,82M
+82M22,"Spectral, collocation and related (meshless) methods applied to problems in statistical mechanics",,82M
+82M30,Variational methods applied to problems in statistical mechanics,,82M
+82M31,Monte Carlo methods applied to problems in statistical mechanics,,82M
+82M36,Computational density functional analysis in statistical mechanics,,82M
+82M37,Computational molecular dynamics in statistical mechanics,,82M
+82M60,Stochastic analysis in statistical mechanics,,82M
+82M99,Basic methods in statistical mechanics,,82M
+83A05,Special relativity,,83A
+83A99,Special relativity,,83A
+83B05,Observational and experimental questions in relativity and gravitational theory,,83B
+83B99,Observational and experimental questions in relativity and gravitational theory,,83B
+83C05,"Einstein's equations (general structure, canonical formalism, Cauchy problems)",,83C
+83C10,Equations of motion in general relativity and gravitational theory,,83C
+83C15,Exact solutions to problems in general relativity and gravitational theory,,83C
+83C20,"Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory",,83C
+83C22,Einstein-Maxwell equations,,83C
+83C25,"Approximation procedures, weak fields in general relativity and gravitational theory",,83C
+83C27,"Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory",,83C
+83C30,"Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory",,83C
+83C35,Gravitational waves,,83C
+83C40,Gravitational energy and conservation laws; groups of motions,,83C
+83C45,Quantization of the gravitational field,,83C
+83C47,Methods of quantum field theory in general relativity and gravitational theory,,83C
+83C50,Electromagnetic fields in general relativity and gravitational theory,,83C
+83C55,"Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)",,83C
+83C56,Dark matter and dark energy,,83C
+83C57,Black holes,,83C
+83C60,Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism,,83C
+83C65,Methods of noncommutative geometry in general relativity,,83C
+83C75,"Space-time singularities, cosmic censorship, etc.",,83C
+83C80,Analogues of general relativity in lower dimensions,,83C
+83C99,General relativity,,83C
+83D05,"Relativistic gravitational theories other than Einstein's, including asymmetric field theories",,83D
+83D99,"Relativistic gravitational theories other than Einstein's, including asymmetric field theories",,83D
+83E05,Geometrodynamics and the holographic principle,,83E
+83E15,Kaluza-Klein and other higher-dimensional theories,,83E
+83E30,String and superstring theories in gravitational theory,,83E
+83E50,Supergravity,,83E
+83E99,"Unified, higher-dimensional and super field theories",,83E
+83F05,Relativistic cosmology,,83F
+83F99,Relativistic cosmology,,83F
+85A04,General questions in astronomy and astrophysics,,85A
+85A05,Galactic and stellar dynamics,,85A
+85A15,Galactic and stellar structure,,85A
+85A20,Planetary atmospheres,,85A
+85A25,Radiative transfer in astronomy and astrophysics,,85A
+85A30,Hydrodynamic and hydromagnetic problems in astronomy and astrophysics,,85A
+85A35,Statistical astronomy,,85A
+85A40,Astrophysical cosmology,,85A
+85A99,Astronomy and astrophysics,,85A
+86A04,General questions in geophysics,,86A
+86A05,"Hydrology, hydrography, oceanography",,86A
+86A08,Climate science and climate modeling,,86A
+86A10,Meteorology and atmospheric physics,,86A
+86A15,"Seismology (including tsunami modeling), earthquakes",,86A
+86A20,"Potentials, prospecting",,86A
+86A22,Inverse problems in geophysics,,86A
+86A25,Geo-electricity and geomagnetism,,86A
+86A30,"Geodesy, mapping problems",,86A
+86A32,Geostatistics,,86A
+86A40,Glaciology,,86A
+86A60,Geological problems,,86A
+86A70,Vulcanology; magma and lava flow,,86A
+86A99,Geophysics,,86A
+90B05,"Inventory, storage, reservoirs",,90B
+90B06,"Transportation, logistics and supply chain management",,90B
+90B10,Deterministic network models in operations research,,90B
+90B15,Stochastic network models in operations research,,90B
+90B18,Communication networks in operations research,,90B
+90B20,Traffic problems in operations research,,90B
+90B22,Queues and service in operations research,,90B
+90B25,"Reliability, availability, maintenance, inspection in operations research",,90B
+90B30,Production models,,90B
+90B35,Deterministic scheduling theory in operations research,,90B
+90B36,Stochastic scheduling theory in operations research,,90B
+90B40,Search theory,,90B
+90B50,"Management decision making, including multiple objectives",,90B
+90B60,"Marketing, advertising",,90B
+90B70,"Theory of organizations, manpower planning in operations research",,90B
+90B80,Discrete location and assignment,,90B
+90B85,Continuous location,,90B
+90B90,Case-oriented studies in operations research,,90B
+90B99,Operations research and management science,,90B
+90C05,Linear programming,,90C
+90C06,Large-scale problems in mathematical programming,,90C
+90C08,"Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)",,90C
+90C09,Boolean programming,,90C
+90C10,Integer programming,,90C
+90C11,Mixed integer programming,,90C
+90C15,Stochastic programming,,90C
+90C17,Robustness in mathematical programming,,90C
+90C20,Quadratic programming,,90C
+90C22,Semidefinite programming,,90C
+90C23,Polynomial optimization,,90C
+90C24,"Tropical optimization (e.g., max-plus optimization)",,90C
+90C25,Convex programming,,90C
+90C26,"Nonconvex programming, global optimization",,90C
+90C27,Combinatorial optimization,,90C
+90C29,Multi-objective and goal programming,,90C
+90C30,Nonlinear programming,,90C
+90C31,"Sensitivity, stability, parametric optimization",,90C
+90C32,Fractional programming,,90C
+90C33,Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming),,90C
+90C34,Semi-infinite programming,,90C
+90C35,Programming involving graphs or networks,,90C
+90C39,Dynamic programming,,90C
+90C40,Markov and semi-Markov decision processes,,90C
+90C46,Optimality conditions and duality in mathematical programming,,90C
+90C47,Minimax problems in mathematical programming,,90C
+90C48,Programming in abstract spaces,,90C
+90C49,Extreme-point and pivoting methods,,90C
+90C51,Interior-point methods,,90C
+90C52,Methods of reduced gradient type,,90C
+90C53,Methods of quasi-Newton type,,90C
+90C55,Methods of successive quadratic programming type,,90C
+90C56,Derivative-free methods and methods using generalized derivatives,,90C
+90C57,"Polyhedral combinatorics, branch-and-bound, branch-and-cut",,90C
+90C59,Approximation methods and heuristics in mathematical programming,,90C
+90C60,Abstract computational complexity for mathematical programming problems,,90C
+90C70,Fuzzy and other nonstochastic uncertainty mathematical programming,,90C
+90C90,Applications of mathematical programming,,90C
+90C99,Mathematical programming,,90C
+91A05,2-person games,,91A
+91A06,"\(n\)-person games, \(n>2\)",,91A
+91A07,Games with infinitely many players,,91A
+91A10,Noncooperative games,,91A
+91A11,Equilibrium refinements,,91A
+91A12,Cooperative games,,91A
+91A14,Potential and congestion games,,91A
+91A15,"Stochastic games, stochastic differential games",,91A
+91A16,Mean field games (aspects of game theory),,91A
+91A18,Games in extensive form,,91A
+91A20,Multistage and repeated games,,91A
+91A22,Evolutionary games,,91A
+91A23,Differential games (aspects of game theory),,91A
+91A24,"Positional games (pursuit and evasion, etc.)",,91A
+91A25,Dynamic games,,91A
+91A26,Rationality and learning in game theory,,91A
+91A27,"Games with incomplete information, Bayesian games",,91A
+91A28,Signaling and communication in game theory,,91A
+91A30,Utility theory for games,,91A
+91A35,Decision theory for games,,91A
+91A40,Other game-theoretic models,,91A
+91A43,Games involving graphs,,91A
+91A44,"Games involving topology, set theory, or logic",,91A
+91A46,Combinatorial games,,91A
+91A50,Discrete-time games,,91A
+91A55,Games of timing,,91A
+91A60,Probabilistic games; gambling,,91A
+91A65,Hierarchical games (including Stackelberg games),,91A
+91A68,Algorithmic game theory and complexity,,91A
+91A70,Spaces of games,,91A
+91A80,Applications of game theory,,91A
+91A81,Quantum games,,91A
+91A86,Game theory and fuzziness,,91A
+91A90,Experimental studies,,91A
+91A99,Game theory,,91A
+91B02,"Fundamental topics (basic mathematics, methodology; applicable to economics in general)",,91B
+91B03,Mechanism design theory,,91B
+91B05,Risk models (general),,91B
+91B06,Decision theory,,91B
+91B08,Individual preferences,,91B
+91B10,Group preferences,,91B
+91B12,Voting theory,,91B
+91B14,Social choice,,91B
+91B15,Welfare economics,,91B
+91B16,Utility theory,,91B
+91B18,Public goods,,91B
+91B24,Microeconomic theory (price theory and economic markets),,91B
+91B26,"Auctions, bargaining, bidding and selling, and other market models",,91B
+91B32,"Resource and cost allocation (including fair division, apportionment, etc.)",,91B
+91B38,"Production theory, theory of the firm",,91B
+91B39,Labor markets,,91B
+91B41,"Contract theory (moral hazard, adverse selection)",,91B
+91B42,"Consumer behavior, demand theory",,91B
+91B43,Principal-agent models,,91B
+91B44,Economics of information,,91B
+91B50,General equilibrium theory,,91B
+91B51,Dynamic stochastic general equilibrium theory,,91B
+91B52,Special types of economic equilibria,,91B
+91B54,"Special types of economic markets (including Cournot, Bertrand)",,91B
+91B55,Economic dynamics,,91B
+91B60,Trade models,,91B
+91B62,Economic growth models,,91B
+91B64,"Macroeconomic theory (monetary models, models of taxation)",,91B
+91B66,Multisectoral models in economics,,91B
+91B68,Matching models,,91B
+91B69,Heterogeneous agent models,,91B
+91B70,Stochastic models in economics,,91B
+91B72,Spatial models in economics,,91B
+91B74,"Economic models of real-world systems (e.g., electricity markets, etc.)",,91B
+91B76,"Environmental economics (natural resource models, harvesting, pollution, etc.)",,91B
+91B80,Applications of statistical and quantum mechanics to economics (econophysics),,91B
+91B82,Statistical methods; economic indices and measures,,91B
+91B84,Economic time series analysis,,91B
+91B86,Mathematical economics and fuzziness,,91B
+91B99,Mathematical economics,,91B
+91C05,Measurement theory in the social and behavioral sciences,,91C
+91C15,One- and multidimensional scaling in the social and behavioral sciences,,91C
+91C20,Clustering in the social and behavioral sciences,,91C
+91C99,Social and behavioral sciences: general topics,,91C
+91D10,"Models of societies, social and urban evolution",,91D
+91D15,Social learning,,91D
+91D20,Mathematical geography and demography,,91D
+91D25,Spatial models in sociology,,91D
+91D30,Social networks; opinion dynamics,,91D
+91D35,Manpower systems in sociology,,91D
+91D99,Mathematical sociology (including anthropology),,91D
+91E10,Cognitive psychology,,91E
+91E30,Psychophysics and psychophysiology; perception,,91E
+91E40,Memory and learning in psychology,,91E
+91E45,Measurement and performance in psychology,,91E
+91E99,Mathematical psychology,,91E
+91F10,"History, political science",,91F
+91F20,Linguistics,,91F
+91F99,Other social and behavioral sciences (mathematical treatment),,91F
+91G05,Actuarial mathematics,,91G
+91G10,Portfolio theory,,91G
+91G15,Financial markets,,91G
+91G20,"Derivative securities (option pricing, hedging, etc.)",,91G
+91G30,"Interest rates, asset pricing, etc. (stochastic models)",,91G
+91G40,Credit risk,,91G
+91G45,"Financial networks (including contagion, systemic risk, regulation)",,91G
+91G50,"Corporate finance (dividends, real options, etc.)",,91G
+91G60,Numerical methods (including Monte Carlo methods),,91G
+91G70,Statistical methods; risk measures,,91G
+91G80,Financial applications of other theories,,91G
+91G99,Actuarial science and mathematical finance,,91G
+92B05,General biology and biomathematics,,92B
+92B10,"Taxonomy, cladistics, statistics in mathematical biology",,92B
+92B15,General biostatistics,,92B
+92B20,"Neural networks for/in biological studies, artificial life and related topics",,92B
+92B25,Biological rhythms and synchronization,,92B
+92B99,Mathematical biology in general,,92B
+92C05,Biophysics,,92C
+92C10,Biomechanics,,92C
+92C15,"Developmental biology, pattern formation",,92C
+92C17,"Cell movement (chemotaxis, etc.)",,92C
+92C20,Neural biology,,92C
+92C30,Physiology (general),,92C
+92C32,"Pathology, pathophysiology",,92C
+92C35,Physiological flow,,92C
+92C37,Cell biology,,92C
+92C40,"Biochemistry, molecular biology",,92C
+92C42,"Systems biology, networks",,92C
+92C45,"Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)",,92C
+92C47,Biosensors (not for medical applications),,92C
+92C50,Medical applications (general),,92C
+92C55,Biomedical imaging and signal processing,,92C
+92C60,Medical epidemiology,,92C
+92C70,Microbiology,,92C
+92C75,Biotechnology,,92C
+92C80,Plant biology,,92C
+92C99,"Physiological, cellular and medical topics",,92C
+92D10,Genetics and epigenetics,,92D
+92D15,Problems related to evolution,,92D
+92D20,"Protein sequences, DNA sequences",,92D
+92D25,Population dynamics (general),,92D
+92D30,Epidemiology,,92D
+92D40,Ecology,,92D
+92D45,Pest management,,92D
+92D50,Animal behavior,,92D
+92D99,Genetics and population dynamics,,92D
+92E10,"Molecular structure (graph-theoretic methods, methods of differential topology, etc.)",,92E
+92E20,"Classical flows, reactions, etc. in chemistry",,92E
+92E99,Chemistry,,92E
+92F05,Other natural sciences (mathematical treatment),,92F
+92F99,Other natural sciences (mathematical treatment),,92F
+93A05,Axiomatic systems theory,,93A
+93A10,General systems,,93A
+93A13,Hierarchical systems,,93A
+93A14,Decentralized systems,,93A
+93A15,Large-scale systems,,93A
+93A16,Multi-agent systems,,93A
+93A99,General systems theory,,93A
+93B03,"Attainable sets, reachability",,93B
+93B05,Controllability,,93B
+93B07,Observability,,93B
+93B10,Canonical structure,,93B
+93B11,System structure simplification,,93B
+93B12,Variable structure systems,,93B
+93B15,Realizations from input-output data,,93B
+93B17,Transformations,,93B
+93B18,Linearizations,,93B
+93B20,Minimal systems representations,,93B
+93B24,Topological methods,,93B
+93B25,Algebraic methods,,93B
+93B27,Geometric methods,,93B
+93B28,Operator-theoretic methods,,93B
+93B30,System identification,,93B
+93B35,Sensitivity (robustness),,93B
+93B36,\(H^\infty\)-control,,93B
+93B45,Model predictive control,,93B
+93B47,Iterative learning control,,93B
+93B50,Synthesis problems,,93B
+93B51,"Design techniques (robust design, computer-aided design, etc.)",,93B
+93B52,Feedback control,,93B
+93B53,Observers,,93B
+93B55,Pole and zero placement problems,,93B
+93B60,Eigenvalue problems,,93B
+93B70,Networked control,,93B
+93B99,"Controllability, observability, and system structure",,93B
+93C05,Linear systems in control theory,,93C
+93C10,Nonlinear systems in control theory,,93C
+93C15,Control/observation systems governed by ordinary differential equations,,93C
+93C20,Control/observation systems governed by partial differential equations,,93C
+93C23,Control/observation systems governed by functional-differential equations,,93C
+93C25,Control/observation systems in abstract spaces,,93C
+93C27,Impulsive control/observation systems,,93C
+93C28,Positive control/observation systems,,93C
+93C29,Boolean control/observation systems,,93C
+93C30,Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems),,93C
+93C35,"Multivariable systems, multidimensional control systems",,93C
+93C40,Adaptive control/observation systems,,93C
+93C41,Control/observation systems with incomplete information,,93C
+93C42,Fuzzy control/observation systems,,93C
+93C43,Delay control/observation systems,,93C
+93C55,Discrete-time control/observation systems,,93C
+93C57,Sampled-data control/observation systems,,93C
+93C62,Digital control/observation systems,,93C
+93C65,Discrete event control/observation systems,,93C
+93C70,Time-scale analysis and singular perturbations in control/observation systems,,93C
+93C73,Perturbations in control/observation systems,,93C
+93C80,Frequency-response methods in control theory,,93C
+93C83,"Control/observation systems involving computers (process control, etc.)",,93C
+93C85,"Automated systems (robots, etc.) in control theory",,93C
+93C95,Application models in control theory,,93C
+93C99,Model systems in control theory,,93C
+93D05,"Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory",,93D
+93D09,Robust stability,,93D
+93D10,Popov-type stability of feedback systems,,93D
+93D15,Stabilization of systems by feedback,,93D
+93D20,Asymptotic stability in control theory,,93D
+93D21,Adaptive or robust stabilization,,93D
+93D23,Exponential stability,,93D
+93D25,Input-output approaches in control theory,,93D
+93D30,Lyapunov and storage functions,,93D
+93D40,Finite-time stability,,93D
+93D50,Consensus,,93D
+93D99,Stability of control systems,,93D
+93E03,Stochastic systems in control theory (general),,93E
+93E10,Estimation and detection in stochastic control theory,,93E
+93E11,Filtering in stochastic control theory,,93E
+93E12,Identification in stochastic control theory,,93E
+93E14,Data smoothing in stochastic control theory,,93E
+93E15,Stochastic stability in control theory,,93E
+93E20,Optimal stochastic control,,93E
+93E24,Least squares and related methods for stochastic control systems,,93E
+93E35,Stochastic learning and adaptive control,,93E
+93E99,Stochastic systems and control,,93E
+94A05,Communication theory,,94A
+94A08,"Image processing (compression, reconstruction, etc.) in information and communication theory",,94A
+94A11,Application of orthogonal and other special functions,,94A
+94A12,"Signal theory (characterization, reconstruction, filtering, etc.)",,94A
+94A13,Detection theory in information and communication theory,,94A
+94A14,Modulation and demodulation in information and communication theory,,94A
+94A15,Information theory (general),,94A
+94A16,Informational aspects of data analysis and big data,,94A
+94A17,"Measures of information, entropy",,94A
+94A20,Sampling theory in information and communication theory,,94A
+94A24,Coding theorems (Shannon theory),,94A
+94A29,Source coding,,94A
+94A34,Rate-distortion theory in information and communication theory,,94A
+94A40,Channel models (including quantum) in information and communication theory,,94A
+94A45,"Prefix, length-variable, comma-free codes",,94A
+94A50,Theory of questionnaires,,94A
+94A55,Shift register sequences and sequences over finite alphabets in information and communication theory,,94A
+94A60,Cryptography,,94A
+94A62,"Authentication, digital signatures and secret sharing",,94A
+94A99,"Communication, information",,94A
+94B05,Linear codes (general theory),,94B
+94B10,Convolutional codes,,94B
+94B12,Combined modulation schemes (including trellis codes) in coding theory,,94B
+94B15,Cyclic codes,,94B
+94B20,Burst-correcting codes,,94B
+94B25,Combinatorial codes,,94B
+94B27,Geometric methods (including applications of algebraic geometry) applied to coding theory,,94B
+94B30,Majority codes,,94B
+94B35,Decoding,,94B
+94B40,Arithmetic codes,,94B
+94B50,Synchronization error-correcting codes,,94B
+94B60,Other types of codes,,94B
+94B65,Bounds on codes,,94B
+94B70,Error probability in coding theory,,94B
+94B75,"Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory",,94B
+94B99,Theory of error-correcting codes and error-detecting codes,,94B
+94C05,Analytic circuit theory,,94C
+94C11,"Switching theory, applications of Boolean algebras to circuits and networks",,94C
+94C12,Fault detection; testing in circuits and networks,,94C
+94C15,Applications of graph theory to circuits and networks,,94C
+94C30,Applications of design theory to circuits and networks,,94C
+94C60,Circuits in qualitative investigation and simulation of models,,94C
+94C99,"Circuits, networks",,94C
+94D05,"Fuzzy sets and logic (in connection with information, communication, or circuits theory)",,94D
+94D10,Boolean functions,,94D
+94D99,Miscellaneous topics in information and communication theory,,94D
+97A30,History in mathematics education,,97A
+97A40,Mathematics education and society,,97A
+97A99,History and society (aspects of mathematics education),,97A
+97B10,Mathematics educational research and planning,,97B
+97B20,Educational policy for general education,,97B
+97B30,Educational policy for vocational education,,97B
+97B40,Educational policy for higher education,,97B
+97B50,Mathematics teacher education,,97B
+97B60,Educational policy for adult and further education,,97B
+97B70,"Syllabuses, educational standards",,97B
+97B99,Educational policy and systems,,97B
+97C10,Comprehensive works on psychology of mathematics education,,97C
+97C20,Affective behavior and mathematics education,,97C
+97C30,"Cognitive processes, learning theories (aspects of mathematics education)",,97C
+97C40,Intelligence and aptitudes (aspects of mathematics education),,97C
+97C50,Language and verbal communities (aspects of mathematics education),,97C
+97C60,Sociological aspects of learning (aspects of mathematics education),,97C
+97C70,Teaching-learning processes in mathematics education,,97C
+97C99,"Psychology of mathematics education, research in mathematics education",,97C
+97D10,Comprehensive works and comparative studies on education and instruction in mathematics,,97D
+97D20,Philosophical and theoretical contributions (didactics of mathematics),,97D
+97D30,Objectives and goals of mathematics teaching,,97D
+97D40,Mathematics teaching methods and classroom techniques,,97D
+97D50,Teaching mathematical problem solving and heuristic strategies,,97D
+97D60,"Student assessment, achievement control, and rating (aspects of mathematics education)",,97D
+97D70,Learning difficulties and student errors (aspects of mathematics education),,97D
+97D80,Mathematics teaching units and draft lessons,,97D
+97D99,Education and instruction in mathematics,,97D
+97E10,Comprehensive works on education of foundations of mathematics,,97E
+97E20,Philosophy and mathematics (educational aspects),,97E
+97E30,Logic (educational aspects),,97E
+97E40,Language of mathematics (educational aspects),,97E
+97E50,Reasoning and proving in the mathematics classroom,,97E
+97E60,"Sets, relations, set theory (educational aspects)",,97E
+97E99,Education of foundations of mathematics,,97E
+97F10,Comprehensive works on education of arithmetic and number theory,,97F
+97F20,"Pre-numerical stage, concept of numbers",,97F
+97F30,Natural numbers (educational aspects),,97F
+97F40,"Integers, rational numbers (educational aspects)",,97F
+97F50,"Real numbers, complex numbers (educational aspects)",,97F
+97F60,Number theory (educational aspects),,97F
+97F70,Measures and units (educational aspects),,97F
+97F80,"Ratio and proportion, percentages (educational aspects)",,97F
+97F90,"Real-life mathematics, practical arithmetic (educational aspects)",,97F
+97F99,Education of arithmetic and number theory,,97F
+97G10,Comprehensive works on geometry education,,97G
+97G20,Informal geometry (educational aspects),,97G
+97G30,Area and volume (educational aspects),,97G
+97G40,Plane and solid geometry (educational aspects),,97G
+97G50,Transformation geometry (educational aspects),,97G
+97G60,Plane and spherical trigonometry (educational aspects),,97G
+97G70,"Analytic geometry, vector algebra (educational aspects)",,97G
+97G80,Descriptive geometry (educational aspects),,97G
+97G99,Geometry education,,97G
+97H10,Comprehensive works on algebra education,,97H
+97H20,Elementary algebra (educational aspects),,97H
+97H30,Equations and inequalities (educational aspects),,97H
+97H40,"Groups, rings, fields (educational aspects)",,97H
+97H50,Ordered algebraic structures (educational aspects),,97H
+97H60,Linear algebra (educational aspects),,97H
+97H99,Algebra education,,97H
+97I10,Comprehensive works on analysis education,,97I
+97I20,Mappings and functions (educational aspects),,97I
+97I30,Sequences and series (educational aspects),,97I
+97I40,Differential calculus (educational aspects),,97I
+97I50,Integral calculus (educational aspects),,97I
+97I60,Functions of several variables (educational aspects),,97I
+97I70,Functional equations (educational aspects),,97I
+97I80,Complex analysis (educational aspects),,97I
+97I99,Analysis education,,97I
+97K10,"Comprehensive works on combinatorics, graph theory, and probability (educational aspects)",,97K
+97K20,Combinatorics (educational aspects),,97K
+97K30,Graph theory (educational aspects),,97K
+97K40,Descriptive statistics (educational aspects),,97K
+97K50,Probability theory (educational aspects),,97K
+97K60,Distributions and stochastic processes (educational aspects),,97K
+97K70,Foundations and methodology of statistics (educational aspects),,97K
+97K80,Applied statistics (educational aspects),,97K
+97K99,"Education of combinatorics, graph theory, probability theory, and statistics",,97K
+97M10,Modeling and interdisciplinarity (aspects of mathematics education),,97M
+97M20,Mathematics in vocational training and career education,,97M
+97M30,Financial and insurance mathematics (aspects of mathematics education),,97M
+97M40,"Operations research, economics (aspects of mathematics education)",,97M
+97M50,"Physics, astronomy, technology, engineering (aspects of mathematics education)",,97M
+97M60,"Biology, chemistry, medicine (aspects of mathematics education)",,97M
+97M70,Behavioral and social sciences (aspects of mathematics education),,97M
+97M80,"Arts, music, language, architecture (aspects of mathematics education)",,97M
+97M99,Education of mathematical modeling and applications of mathematics,,97M
+97N10,Comprehensive works on education of numerical mathematics,,97N
+97N20,"Rounding, estimation, theory of errors (educational aspects)",,97N
+97N30,Numerical algebra (educational aspects),,97N
+97N40,Numerical analysis (educational aspects),,97N
+97N50,Interpolation and approximation (educational aspects),,97N
+97N60,Mathematical programming (educational aspects),,97N
+97N70,Discrete mathematics (educational aspects),,97N
+97N80,"Mathematical software, computer programs (educational aspects)",,97N
+97N99,Education of numerical mathematics,,97N
+97P10,Comprehensive works on computer science (educational aspects),,97P
+97P20,Theoretical computer science (educational aspects),,97P
+97P30,"Systems, databases (educational aspects)",,97P
+97P40,Programming languages (educational aspects),,97P
+97P50,Programming techniques (educational aspects),,97P
+97P80,Artificial intelligence (educational aspects),,97P
+97P99,Computer science (educational aspects),,97P
+97U10,Comprehensive works on educational material and media and educational technology in mathematics education,,97U
+97U20,"Textbooks, textbook research (aspects of mathematics education)",,97U
+97U30,Teachers' manuals and planning aids (aspects of mathematics education),,97U
+97U40,"Problem books, competitions, examinations (aspects of mathematics education)",,97U
+97U50,"Computer-assisted instruction, e-learning (aspects of mathematics education)",,97U
+97U60,Manipulative materials (aspects of mathematics education),,97U
+97U70,"Technological tools, calculators (aspects of mathematics education)",,97U
+97U80,Audiovisual media (aspects of mathematics education),,97U
+97U99,Educational material and media and educational technology in mathematics education,,97U
diff --git a/modules/site_tools_msc_2020_migrate/migrations/msc_2020_terms_pt_br.yml b/modules/site_tools_msc_2020_migrate/migrations/msc_2020_terms_pt_br.yml
index b937314..646d40f 100644
--- a/modules/site_tools_msc_2020_migrate/migrations/msc_2020_terms_pt_br.yml
+++ b/modules/site_tools_msc_2020_migrate/migrations/msc_2020_terms_pt_br.yml
@@ -21,7 +21,10 @@ process:
   langcode:
     plugin: default_value
     default_value: pt-br
-  name: name_pt_br
+  name:
+    - plugin: skip_on_empty
+      method: row
+      source: name_pt_br
   content_translation_source:
     plugin: default_value
     default_value: en