[ { "code": "00", "originalCode": "00-XX", "name": "General and overarching topics; collections", "description": "General and overarching topics; collections", "kind": "class", "parent": null, "page": 4 }, { "code": "00-01", "originalCode": "00-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general", "kind": "subject", "parent": "00", "page": 4 }, { "code": "00-02", "originalCode": "00-02", "name": "Research exposition (monographs, survey articles) pertaining to mathematics in general", "description": "Research exposition (monographs, survey articles) pertaining to mathematics in general", "kind": "subject", "parent": "00", "page": 4 }, { "code": "00A", "originalCode": "00Axx", "name": "General and miscellaneous specific topics", "description": "General and miscellaneous specific topics", "kind": "section", "parent": "00", "page": 4 }, { "code": "00A05", "originalCode": "00A05", "name": "Mathematics in general", "description": "Mathematics in general", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A06", "originalCode": "00A06", "name": "Mathematics for nonmathematicians (engineering, social sciences, etc.)", "description": "Mathematics for nonmathematicians (engineering, social sciences, etc.)", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A07", "originalCode": "00A07", "name": "Problem books", "description": "Problem books \\{For open problems, see 00A27\\}", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A08", "originalCode": "00A08", "name": "Recreational mathematics", "description": "Recreational mathematics", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A09", "originalCode": "00A09", "name": "Popularization of mathematics", "description": "Popularization of mathematics", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A15", "originalCode": "00A15", "name": "Bibliographies for mathematics in general", "description": "Bibliographies for mathematics in general [See also 01A70 and the classification number --00 in the other sections]", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A17", "originalCode": "00A17", "name": "External book reviews", "description": "External book reviews", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A20", "originalCode": "00A20", "name": "Dictionaries and other general reference works", "description": "Dictionaries and other general reference works [See also the classification number --00 in the other sections]", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A22", "originalCode": "00A22", "name": "Formularies", "description": "Formularies", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A27", "originalCode": "00A27", "name": "Lists of open problems", "description": "Lists of open problems", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A30", "originalCode": "00A30", "name": "Philosophy of mathematics", "description": "Philosophy of mathematics [See also 03A05]", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A35", "originalCode": "00A35", "name": "Methodology of mathematics", "description": "Methodology of mathematics \\{For mathematics education, see 97-XX\\}", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A64", "originalCode": "00A64", "name": "Mathematics and literature", "description": "Mathematics and literature", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A65", "originalCode": "00A65", "name": "Mathematics and music", "description": "Mathematics and music", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A66", "originalCode": "00A66", "name": "Mathematics and visual arts", "description": "Mathematics and visual arts", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A67", "originalCode": "00A67", "name": "Mathematics and architecture", "description": "Mathematics and architecture", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A69", "originalCode": "00A69", "name": "General applied mathematics", "description": "General applied mathematics \\{For physics, see 00A79 and Sections 70-XX through 86-XX", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A71", "originalCode": "00A71", "name": "General theory of mathematical modeling", "description": "General theory of mathematical modeling", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A72", "originalCode": "00A72", "name": "General theory of simulation", "description": "General theory of simulation", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A79", "originalCode": "00A79", "name": "Physics", "description": "Physics [Use more specific entries from Sections 70-XX through 86-XX when possible]", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00A99", "originalCode": "00A99", "name": "General and miscellaneous specific topics", "description": "None of the above, but in this section", "kind": "subject", "parent": "00A", "page": 4 }, { "code": "00B", "originalCode": "00Bxx", "name": "Conference proceedings and collections of articles", "description": "Conference proceedings and collections of articles", "kind": "section", "parent": "00", "page": 4 }, { "code": "00B05", "originalCode": "00B05", "name": "Collections of abstracts of lectures", "description": "Collections of abstracts of lectures", "kind": "subject", "parent": "00B", "page": 4 }, { "code": "00B10", "originalCode": "00B10", "name": "Collections of articles of general interest", "description": "Collections of articles of general interest", "kind": "subject", "parent": "00B", "page": 4 }, { "code": "00B15", "originalCode": "00B15", "name": "Collections of articles of miscellaneous specific interest", "description": "Collections of articles of miscellaneous specific interest", "kind": "subject", "parent": "00B", "page": 4 }, { "code": "00B20", "originalCode": "00B20", "name": "Proceedings of conferences of general interest", "description": "Proceedings of conferences of general interest", "kind": "subject", "parent": "00B", "page": 4 }, { "code": "00B25", "originalCode": "00B25", "name": "Proceedings of conferences of miscellaneous specific interest", "description": "Proceedings of conferences of miscellaneous specific interest", "kind": "subject", "parent": "00B", "page": 4 }, { "code": "00B30", "originalCode": "00B30", "name": "Festschriften", "description": "Festschriften", "kind": "subject", "parent": "00B", "page": 4 }, { "code": "00B50", "originalCode": "00B50", "name": "Collections of translated articles of general interest", "description": "Collections of translated articles of general interest", "kind": "subject", "parent": "00B", "page": 5 }, { "code": "00B55", "originalCode": "00B55", "name": "Collections of translated articles of miscellaneous specific interest", "description": "Collections of translated articles of miscellaneous specific interest", "kind": "subject", "parent": "00B", "page": 5 }, { "code": "00B60", "originalCode": "00B60", "name": "Collections of reprinted articles", "description": "Collections of reprinted articles [See also 01A75]", "kind": "subject", "parent": "00B", "page": 5 }, { "code": "00B99", "originalCode": "00B99", "name": "Conference proceedings and collections of articles", "description": "None of the above, but in this section", "kind": "subject", "parent": "00B", "page": 5 }, { "code": "01", "originalCode": "01-XX", "name": "History and biography", "description": "History and biography [See also the classification number --03 in the other sections]", "kind": "class", "parent": null, "page": 5 }, { "code": "01-00", "originalCode": "01-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography", "kind": "subject", "parent": "01", "page": 5 }, { "code": "01-01", "originalCode": "01-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography", "kind": "subject", "parent": "01", "page": 5 }, { "code": "01-02", "originalCode": "01-02", "name": "Research exposition (monographs, survey articles) pertaining to history and biography", "description": "Research exposition (monographs, survey articles) pertaining to history and biography", "kind": "subject", "parent": "01", "page": 5 }, { "code": "01-06", "originalCode": "01-06", "name": "Proceedings, conferences, collections, etc. pertaining to history and biography", "description": "Proceedings, conferences, collections, etc. pertaining to history and biography", "kind": "subject", "parent": "01", "page": 5 }, { "code": "01-11", "originalCode": "01-11", "name": "Research data for problems pertaining to history and biography", "description": "Research data for problems pertaining to history and biography", "kind": "subject", "parent": "01", "page": 5 }, { "code": "01A", "originalCode": "01Axx", "name": "History of mathematics and mathematicians", "description": "History of mathematics and mathematicians", "kind": "section", "parent": "01", "page": 5 }, { "code": "01A05", "originalCode": "01A05", "name": "General histories, source books", "description": "General histories, source books", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A07", "originalCode": "01A07", "name": "Ethnomathematics (general)", "description": "Ethnomathematics (general)", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A10", "originalCode": "01A10", "name": "History of mathematics in Paleolithic and Neolithic times", "description": "History of mathematics in Paleolithic and Neolithic times", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A11", "originalCode": "01A11", "name": "History of mathematics of the indigenous cultures of Africa, Asia, and Oceania", "description": "History of mathematics of the indigenous cultures of Africa, Asia, and Oceania", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A12", "originalCode": "01A12", "name": "History of mathematics of the indigenous cultures of the Americas", "description": "History of mathematics of the indigenous cultures of the Americas", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A15", "originalCode": "01A15", "name": "History of mathematics of the indigenous cultures of Europe (pre-Greek, etc.)", "description": "History of mathematics of the indigenous cultures of Europe (pre-Greek, etc.)", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A16", "originalCode": "01A16", "name": "History of Egyptian mathematics", "description": "History of Egyptian mathematics", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A17", "originalCode": "01A17", "name": "History of Babylonian mathematics", "description": "History of Babylonian mathematics", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A20", "originalCode": "01A20", "name": "History of Greek and Roman mathematics", "description": "History of Greek and Roman mathematics", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A25", "originalCode": "01A25", "name": "History of Chinese mathematics", "description": "History of Chinese mathematics", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A27", "originalCode": "01A27", "name": "History of Japanese mathematics", "description": "History of Japanese mathematics", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A29", "originalCode": "01A29", "name": "History of East and Southeast Asian mathematics (non-Chinese, non-Japanese)", "description": "History of East and Southeast Asian mathematics (non-Chinese, non-Japanese)", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A30", "originalCode": "01A30", "name": "History of mathematics in the Golden Age of Islam", "description": "History of mathematics in the Golden Age of Islam", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A32", "originalCode": "01A32", "name": "History of Indian mathematics", "description": "History of Indian mathematics", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A35", "originalCode": "01A35", "name": "History of mathematics in Late Antiquity and medieval Europe", "description": "History of mathematics in Late Antiquity and medieval Europe", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A40", "originalCode": "01A40", "name": "History of mathematics in the 15th and 16th centuries, Renaissance", "description": "History of mathematics in the 15th and 16th centuries, Renaissance", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A45", "originalCode": "01A45", "name": "History of mathematics in the 17th century", "description": "History of mathematics in the 17th century", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A50", "originalCode": "01A50", "name": "History of mathematics in the 18th century", "description": "History of mathematics in the 18th century", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A55", "originalCode": "01A55", "name": "History of mathematics in the 19th century", "description": "History of mathematics in the 19th century", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A60", "originalCode": "01A60", "name": "History of mathematics in the 20th century", "description": "History of mathematics in the 20th century", "kind": "subject", "parent": "01A", "page": 5 }, { "code": "01A61", "originalCode": "01A61", "name": "History of mathematics in the 21st century", "description": "History of mathematics in the 21st century", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A65", "originalCode": "01A65", "name": "Development of contemporary mathematics", "description": "Development of contemporary mathematics", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A67", "originalCode": "01A67", "name": "Future perspectives in mathematics", "description": "Future perspectives in mathematics", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A70", "originalCode": "01A70", "name": "Biographies, obituaries, personalia, bibliographies", "description": "Biographies, obituaries, personalia, bibliographies", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A72", "originalCode": "01A72", "name": "Schools of mathematics", "description": "Schools of mathematics", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A73", "originalCode": "01A73", "name": "History of mathematics at specific universities", "description": "History of mathematics at specific universities", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A74", "originalCode": "01A74", "name": "History of mathematics at institutions and academies (non-university)", "description": "History of mathematics at institutions and academies (non-university)", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A75", "originalCode": "01A75", "name": "Collected or selected works; reprintings or translations of classics", "description": "Collected or selected works; reprintings or translations of classics [See also 00B60]", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A80", "originalCode": "01A80", "name": "Sociology (and profession) of mathematics", "description": "Sociology (and profession) of mathematics", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A85", "originalCode": "01A85", "name": "Historiography", "description": "Historiography", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A90", "originalCode": "01A90", "name": "Bibliographic studies", "description": "Bibliographic studies", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "01A99", "originalCode": "01A99", "name": "History of mathematics and mathematicians", "description": "None of the above, but in this section", "kind": "subject", "parent": "01A", "page": 6 }, { "code": "03", "originalCode": "03-XX", "name": "Mathematical logic and foundations", "description": "Mathematical logic and foundations", "kind": "class", "parent": null, "page": 6 }, { "code": "03-00", "originalCode": "03-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations", "kind": "subject", "parent": "03", "page": 6 }, { "code": "03-01", "originalCode": "03-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations", "kind": "subject", "parent": "03", "page": 6 }, { "code": "03-02", "originalCode": "03-02", "name": "Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations", "description": "Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations", "kind": "subject", "parent": "03", "page": 6 }, { "code": "03-03", "originalCode": "03-03", "name": "History of mathematical logic and foundations", "description": "History of mathematical logic and foundations [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "03", "page": 6 }, { "code": "03-04", "originalCode": "03-04", "name": "Software, source code, etc. for problems pertaining to mathematical logic and foundations", "description": "Software, source code, etc. for problems pertaining to mathematical logic and foundations", "kind": "subject", "parent": "03", "page": 6 }, { "code": "03-06", "originalCode": "03-06", "name": "Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations", "description": "Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations", "kind": "subject", "parent": "03", "page": 6 }, { "code": "03-08", "originalCode": "03-08", "name": "Computational methods for problems pertaining to mathematical logic and foundations", "description": "Computational methods for problems pertaining to mathematical logic and foundations", "kind": "subject", "parent": "03", "page": 6 }, { "code": "03-11", "originalCode": "03-11", "name": "Research data for problems pertaining to mathematical logic and foundations", "description": "Research data for problems pertaining to mathematical logic and foundations", "kind": "subject", "parent": "03", "page": 6 }, { "code": "03A", "originalCode": "03Axx", "name": "Philosophical aspects of logic and foundations", "description": "Philosophical aspects of logic and foundations", "kind": "section", "parent": "03", "page": 6 }, { "code": "03A05", "originalCode": "03A05", "name": "Philosophical and critical aspects of logic and foundations", "description": "Philosophical and critical aspects of logic and foundations \\{For philosophy of mathematics, see also 00A30\\}", "kind": "subject", "parent": "03A", "page": 6 }, { "code": "03A10", "originalCode": "03A10", "name": "Logic in the philosophy of science", "description": "Logic in the philosophy of science", "kind": "subject", "parent": "03A", "page": 6 }, { "code": "03A99", "originalCode": "03A99", "name": "Philosophical aspects of logic and foundations", "description": "None of the above, but in this section", "kind": "subject", "parent": "03A", "page": 6 }, { "code": "03B", "originalCode": "03Bxx", "name": "General logic", "description": "General logic", "kind": "section", "parent": "03", "page": 7 }, { "code": "03B05", "originalCode": "03B05", "name": "Classical propositional logic", "description": "Classical propositional logic", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B10", "originalCode": "03B10", "name": "Classical first-order logic", "description": "Classical first-order logic", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B16", "originalCode": "03B16", "name": "Higher-order logic", "description": "Higher-order logic", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B20", "originalCode": "03B20", "name": "Subsystems of classical logic (including intuitionistic logic)", "description": "Subsystems of classical logic (including intuitionistic logic)", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B22", "originalCode": "03B22", "name": "Abstract deductive systems", "description": "Abstract deductive systems", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B25", "originalCode": "03B25", "name": "Decidability of theories and sets of sentences", "description": "Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B30", "originalCode": "03B30", "name": "Foundations of classical theories (including reverse mathematics)", "description": "Foundations of classical theories (including reverse mathematics) [See also 03F35]", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B35", "originalCode": "03B35", "name": "Mechanization of proofs and logical operations", "description": "Mechanization of proofs and logical operations [See also 68V15]", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B38", "originalCode": "03B38", "name": "Type theory", "description": "Type theory", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B40", "originalCode": "03B40", "name": "Combinatory logic and lambda calculus", "description": "Combinatory logic and lambda calculus [See also 68N18]", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B42", "originalCode": "03B42", "name": "Logics of knowledge and belief (including belief change)", "description": "Logics of knowledge and belief (including belief change)", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B44", "originalCode": "03B44", "name": "Temporal logic", "description": "Temporal logic", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B45", "originalCode": "03B45", "name": "Modal logic (including the logic of norms)", "description": "Modal logic (including the logic of norms) \\{For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45\\}", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B47", "originalCode": "03B47", "name": "Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)", "description": "Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) \\{For proof-theoretic aspects, see 03F52\\}", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B48", "originalCode": "03B48", "name": "Probability and inductive logic", "description": "Probability and inductive logic [See also 60A05]", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B50", "originalCode": "03B50", "name": "Many-valued logic", "description": "Many-valued logic", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B52", "originalCode": "03B52", "name": "Fuzzy logic; logic of vagueness", "description": "Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B53", "originalCode": "03B53", "name": "Paraconsistent logics", "description": "Paraconsistent logics", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B55", "originalCode": "03B55", "name": "Intermediate logics", "description": "Intermediate logics", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B60", "originalCode": "03B60", "name": "Other nonclassical logic", "description": "Other nonclassical logic", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B62", "originalCode": "03B62", "name": "Combined logics", "description": "Combined logics", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B65", "originalCode": "03B65", "name": "Logic of natural languages", "description": "Logic of natural languages [See also 68T50, 91F20]", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B70", "originalCode": "03B70", "name": "Logic in computer science", "description": "Logic in computer science [See also 68-XX]", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B80", "originalCode": "03B80", "name": "Other applications of logic", "description": "Other applications of logic", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03B99", "originalCode": "03B99", "name": "General logic", "description": "None of the above, but in this section", "kind": "subject", "parent": "03B", "page": 7 }, { "code": "03C", "originalCode": "03Cxx", "name": "Model theory", "description": "Model theory", "kind": "section", "parent": "03", "page": 8 }, { "code": "03C05", "originalCode": "03C05", "name": "Equational classes, universal algebra in model theory", "description": "Equational classes, universal algebra in model theory [See also 08Axx, 08Bxx, 18C05]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C07", "originalCode": "03C07", "name": "Basic properties of first-order languages and structures", "description": "Basic properties of first-order languages and structures", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C10", "originalCode": "03C10", "name": "Quantifier elimination, model completeness, and related topics", "description": "Quantifier elimination, model completeness, and related topics", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C13", "originalCode": "03C13", "name": "Model theory of finite structures", "description": "Model theory of finite structures [See also 68Q15, 68Q19]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C15", "originalCode": "03C15", "name": "Model theory of denumerable and separable structures", "description": "Model theory of denumerable and separable structures", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C20", "originalCode": "03C20", "name": "Ultraproducts and related constructions", "description": "Ultraproducts and related constructions", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C25", "originalCode": "03C25", "name": "Model-theoretic forcing", "description": "Model-theoretic forcing", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C30", "originalCode": "03C30", "name": "Other model constructions", "description": "Other model constructions", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C35", "originalCode": "03C35", "name": "Categoricity and completeness of theories", "description": "Categoricity and completeness of theories", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C40", "originalCode": "03C40", "name": "Interpolation, preservation, definability", "description": "Interpolation, preservation, definability", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C45", "originalCode": "03C45", "name": "Classification theory, stability, and related concepts in model theory", "description": "Classification theory, stability, and related concepts in model theory [See also 03C48]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C48", "originalCode": "03C48", "name": "Abstract elementary classes and related topics", "description": "Abstract elementary classes and related topics [See also 03C45]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C50", "originalCode": "03C50", "name": "Models with special properties (saturated, rigid, etc.)", "description": "Models with special properties (saturated, rigid, etc.)", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C52", "originalCode": "03C52", "name": "Properties of classes of models", "description": "Properties of classes of models", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C55", "originalCode": "03C55", "name": "Set-theoretic model theory", "description": "Set-theoretic model theory", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C57", "originalCode": "03C57", "name": "Computable structure theory, computable model theory", "description": "Computable structure theory, computable model theory [See also 03D45]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C60", "originalCode": "03C60", "name": "Model-theoretic algebra", "description": "Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C62", "originalCode": "03C62", "name": "Models of arithmetic and set theory", "description": "Models of arithmetic and set theory [See also 03Hxx]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C64", "originalCode": "03C64", "name": "Model theory of ordered structures; o-minimality", "description": "Model theory of ordered structures; o-minimality", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C65", "originalCode": "03C65", "name": "Models of other mathematical theories", "description": "Models of other mathematical theories", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C66", "originalCode": "03C66", "name": "Continuous model theory, model theory of metric structures", "description": "Continuous model theory, model theory of metric structures", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C68", "originalCode": "03C68", "name": "Other classical first-order model theory", "description": "Other classical first-order model theory", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C70", "originalCode": "03C70", "name": "Logic on admissible sets", "description": "Logic on admissible sets", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C75", "originalCode": "03C75", "name": "Other infinitary logic", "description": "Other infinitary logic", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C80", "originalCode": "03C80", "name": "Logic with extra quantifiers and operators", "description": "Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C85", "originalCode": "03C85", "name": "Second- and higher-order model theory", "description": "Second- and higher-order model theory", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C90", "originalCode": "03C90", "name": "Nonclassical models (Boolean-valued, sheaf, etc.)", "description": "Nonclassical models (Boolean-valued, sheaf, etc.)", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C95", "originalCode": "03C95", "name": "Abstract model theory", "description": "Abstract model theory", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C98", "originalCode": "03C98", "name": "Applications of model theory", "description": "Applications of model theory [See also 03C60]", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03C99", "originalCode": "03C99", "name": "Model theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "03C", "page": 8 }, { "code": "03D", "originalCode": "03Dxx", "name": "Computability and recursion theory", "description": "Computability and recursion theory", "kind": "section", "parent": "03", "page": 9 }, { "code": "03D03", "originalCode": "03D03", "name": "Thue and Post systems, etc.", "description": "Thue and Post systems, etc.", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D05", "originalCode": "03D05", "name": "Automata and formal grammars in connection with logical questions", "description": "Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D10", "originalCode": "03D10", "name": "Turing machines and related notions", "description": "Turing machines and related notions [See also 68Q04]", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D15", "originalCode": "03D15", "name": "Complexity of computation (including implicit computational complexity)", "description": "Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17]", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D20", "originalCode": "03D20", "name": "Recursive functions and relations, subrecursive hierarchies", "description": "Recursive functions and relations, subrecursive hierarchies", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D25", "originalCode": "03D25", "name": "Recursively (computably) enumerable sets and degrees", "description": "Recursively (computably) enumerable sets and degrees", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D28", "originalCode": "03D28", "name": "Other Turing degree structures", "description": "Other Turing degree structures", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D30", "originalCode": "03D30", "name": "Other degrees and reducibilities in computability and recursion theory", "description": "Other degrees and reducibilities in computability and recursion theory", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D32", "originalCode": "03D32", "name": "Algorithmic randomness and dimension", "description": "Algorithmic randomness and dimension [See also 68Q30]", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D35", "originalCode": "03D35", "name": "Undecidability and degrees of sets of sentences", "description": "Undecidability and degrees of sets of sentences", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D40", "originalCode": "03D40", "name": "Word problems, etc. in computability and recursion theory", "description": "Word problems, etc. in computability and recursion theory [See also 06B25, 08A50, 20F10, 68R15]", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D45", "originalCode": "03D45", "name": "Theory of numerations, effectively presented structures", "description": "Theory of numerations, effectively presented structures [See also 03C57] \\{For intuitionistic and similar approaches, see 03F55\\}", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D50", "originalCode": "03D50", "name": "Recursive equivalence types of sets and structures, isols", "description": "Recursive equivalence types of sets and structures, isols", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D55", "originalCode": "03D55", "name": "Hierarchies of computability and definability", "description": "Hierarchies of computability and definability", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D60", "originalCode": "03D60", "name": "Computability and recursion theory on ordinals, admissible sets, etc.", "description": "Computability and recursion theory on ordinals, admissible sets, etc.", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D65", "originalCode": "03D65", "name": "Higher-type and set recursion theory", "description": "Higher-type and set recursion theory", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D70", "originalCode": "03D70", "name": "Inductive definability", "description": "Inductive definability", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D75", "originalCode": "03D75", "name": "Abstract and axiomatic computability and recursion theory", "description": "Abstract and axiomatic computability and recursion theory", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D78", "originalCode": "03D78", "name": "Computation over the reals, computable analysis", "description": "Computation over the reals, computable analysis \\{For constructive aspects, see 03F60\\}", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D80", "originalCode": "03D80", "name": "Applications of computability and recursion theory", "description": "Applications of computability and recursion theory", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03D99", "originalCode": "03D99", "name": "Computability and recursion theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "03D", "page": 9 }, { "code": "03E", "originalCode": "03Exx", "name": "Set theory", "description": "Set theory", "kind": "section", "parent": "03", "page": 9 }, { "code": "03E02", "originalCode": "03E02", "name": "Partition relations", "description": "Partition relations", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E04", "originalCode": "03E04", "name": "Ordered sets and their cofinalities; pcf theory", "description": "Ordered sets and their cofinalities; pcf theory", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E05", "originalCode": "03E05", "name": "Other combinatorial set theory", "description": "Other combinatorial set theory", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E10", "originalCode": "03E10", "name": "Ordinal and cardinal numbers", "description": "Ordinal and cardinal numbers", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E15", "originalCode": "03E15", "name": "Descriptive set theory", "description": "Descriptive set theory [See also 28A05, 54H05]", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E17", "originalCode": "03E17", "name": "Cardinal characteristics of the continuum", "description": "Cardinal characteristics of the continuum", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E20", "originalCode": "03E20", "name": "Other classical set theory (including functions, relations, and set algebra)", "description": "Other classical set theory (including functions, relations, and set algebra)", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E25", "originalCode": "03E25", "name": "Axiom of choice and related propositions", "description": "Axiom of choice and related propositions", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E30", "originalCode": "03E30", "name": "Axiomatics of classical set theory and its fragments", "description": "Axiomatics of classical set theory and its fragments", "kind": "subject", "parent": "03E", "page": 9 }, { "code": "03E35", "originalCode": "03E35", "name": "Consistency and independence results", "description": "Consistency and independence results", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E40", "originalCode": "03E40", "name": "Other aspects of forcing and Boolean-valued models", "description": "Other aspects of forcing and Boolean-valued models", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E45", "originalCode": "03E45", "name": "Inner models, including constructibility, ordinal definability, and core models", "description": "Inner models, including constructibility, ordinal definability, and core models", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E47", "originalCode": "03E47", "name": "Other notions of set-theoretic definability", "description": "Other notions of set-theoretic definability", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E50", "originalCode": "03E50", "name": "Continuum hypothesis and Martin's axiom", "description": "Continuum hypothesis and Martin's axiom [See also 03E57]", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E55", "originalCode": "03E55", "name": "Large cardinals", "description": "Large cardinals", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E57", "originalCode": "03E57", "name": "Generic absoluteness and forcing axioms", "description": "Generic absoluteness and forcing axioms [See also 03E50]", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E60", "originalCode": "03E60", "name": "Determinacy principles", "description": "Determinacy principles", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E65", "originalCode": "03E65", "name": "Other set-theoretic hypotheses and axioms", "description": "Other set-theoretic hypotheses and axioms", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E70", "originalCode": "03E70", "name": "Nonclassical and second-order set theories", "description": "Nonclassical and second-order set theories", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E72", "originalCode": "03E72", "name": "Theory of fuzzy sets, etc.", "description": "Theory of fuzzy sets, etc.", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E75", "originalCode": "03E75", "name": "Applications of set theory", "description": "Applications of set theory", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03E99", "originalCode": "03E99", "name": "Set theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "03E", "page": 10 }, { "code": "03F", "originalCode": "03Fxx", "name": "Proof theory and constructive mathematics", "description": "Proof theory and constructive mathematics", "kind": "section", "parent": "03", "page": 10 }, { "code": "03F03", "originalCode": "03F03", "name": "Proof theory in general (including proof-theoretic semantics)", "description": "Proof theory in general (including proof-theoretic semantics)", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F05", "originalCode": "03F05", "name": "Cut-elimination and normal-form theorems", "description": "Cut-elimination and normal-form theorems", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F07", "originalCode": "03F07", "name": "Structure of proofs", "description": "Structure of proofs", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F10", "originalCode": "03F10", "name": "Functionals in proof theory", "description": "Functionals in proof theory", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F15", "originalCode": "03F15", "name": "Recursive ordinals and ordinal notations", "description": "Recursive ordinals and ordinal notations", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F20", "originalCode": "03F20", "name": "Complexity of proofs", "description": "Complexity of proofs", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F25", "originalCode": "03F25", "name": "Relative consistency and interpretations", "description": "Relative consistency and interpretations", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F30", "originalCode": "03F30", "name": "First-order arithmetic and fragments", "description": "First-order arithmetic and fragments", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F35", "originalCode": "03F35", "name": "Second- and higher-order arithmetic and fragments", "description": "Second- and higher-order arithmetic and fragments [See also 03B30]", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F40", "originalCode": "03F40", "name": "Gödel numberings and issues of incompleteness", "description": "Gödel numberings and issues of incompleteness", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F45", "originalCode": "03F45", "name": "Provability logics and related algebras (e.g., diagonalizable algebras)", "description": "Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F50", "originalCode": "03F50", "name": "Metamathematics of constructive systems", "description": "Metamathematics of constructive systems", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F52", "originalCode": "03F52", "name": "Proof-theoretic aspects of linear logic and other substructural logics", "description": "Proof-theoretic aspects of linear logic and other substructural logics [See also 03B47]", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F55", "originalCode": "03F55", "name": "Intuitionistic mathematics", "description": "Intuitionistic mathematics", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F60", "originalCode": "03F60", "name": "Constructive and recursive analysis", "description": "Constructive and recursive analysis [See also 03B30, 03D45, 03D78, 26E40, 46S30, 47S30]", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F65", "originalCode": "03F65", "name": "Other constructive mathematics", "description": "Other constructive mathematics [See also 03D45]", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03F99", "originalCode": "03F99", "name": "Proof theory and constructive mathematics", "description": "None of the above, but in this section", "kind": "subject", "parent": "03F", "page": 10 }, { "code": "03G", "originalCode": "03Gxx", "name": "Algebraic logic", "description": "Algebraic logic", "kind": "section", "parent": "03", "page": 11 }, { "code": "03G05", "originalCode": "03G05", "name": "Logical aspects of Boolean algebras", "description": "Logical aspects of Boolean algebras [See also 06Exx]", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03G10", "originalCode": "03G10", "name": "Logical aspects of lattices and related structures", "description": "Logical aspects of lattices and related structures [See also 06Bxx]", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03G12", "originalCode": "03G12", "name": "Quantum logic", "description": "Quantum logic [See also 06C15, 81P10]", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03G15", "originalCode": "03G15", "name": "Cylindric and polyadic algebras; relation algebras", "description": "Cylindric and polyadic algebras; relation algebras", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03G20", "originalCode": "03G20", "name": "Logical aspects of ?ukasiewicz and Post algebras", "description": "Logical aspects of ?ukasiewicz and Post algebras [See also 06D25, 06D30]", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03G25", "originalCode": "03G25", "name": "Other algebras related to logic", "description": "Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03G27", "originalCode": "03G27", "name": "Abstract algebraic logic", "description": "Abstract algebraic logic", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03G30", "originalCode": "03G30", "name": "Categorical logic, topoi", "description": "Categorical logic, topoi [See also 18B25, 18C05, 18C10]", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03G99", "originalCode": "03G99", "name": "Algebraic logic", "description": "None of the above, but in this section", "kind": "subject", "parent": "03G", "page": 11 }, { "code": "03H", "originalCode": "03Hxx", "name": "Nonstandard models", "description": "Nonstandard models [See also 03C62]", "kind": "section", "parent": "03", "page": 11 }, { "code": "03H05", "originalCode": "03H05", "name": "Nonstandard models in mathematics", "description": "Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]", "kind": "subject", "parent": "03H", "page": 11 }, { "code": "03H10", "originalCode": "03H10", "name": "Other applications of nonstandard models (economics, physics, etc.)", "description": "Other applications of nonstandard models (economics, physics, etc.)", "kind": "subject", "parent": "03H", "page": 11 }, { "code": "03H15", "originalCode": "03H15", "name": "Nonstandard models of arithmetic", "description": "Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05]", "kind": "subject", "parent": "03H", "page": 11 }, { "code": "03H99", "originalCode": "03H99", "name": "Nonstandard models", "description": "None of the above, but in this section", "kind": "subject", "parent": "03H", "page": 11 }, { "code": "05", "originalCode": "05-XX", "name": "Combinatorics", "description": "Combinatorics \\{For finite fields, see 11Txx\\}", "kind": "class", "parent": null, "page": 11 }, { "code": "05-00", "originalCode": "05-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to combinatorics", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to combinatorics", "kind": "subject", "parent": "05", "page": 11 }, { "code": "05-01", "originalCode": "05-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics", "kind": "subject", "parent": "05", "page": 11 }, { "code": "05-02", "originalCode": "05-02", "name": "Research exposition (monographs, survey articles) pertaining to combinatorics", "description": "Research exposition (monographs, survey articles) pertaining to combinatorics", "kind": "subject", "parent": "05", "page": 11 }, { "code": "05-03", "originalCode": "05-03", "name": "History of combinatorics", "description": "History of combinatorics [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "05", "page": 11 }, { "code": "05-04", "originalCode": "05-04", "name": "Software, source code, etc. for problems pertaining to combinatorics", "description": "Software, source code, etc. for problems pertaining to combinatorics", "kind": "subject", "parent": "05", "page": 11 }, { "code": "05-06", "originalCode": "05-06", "name": "Proceedings, conferences, collections, etc. pertaining to combinatorics", "description": "Proceedings, conferences, collections, etc. pertaining to combinatorics", "kind": "subject", "parent": "05", "page": 11 }, { "code": "05-08", "originalCode": "05-08", "name": "Computational methods for problems pertaining to combinatorics", "description": "Computational methods for problems pertaining to combinatorics", "kind": "subject", "parent": "05", "page": 11 }, { "code": "05-11", "originalCode": "05-11", "name": "Research data for problems pertaining to combinatorics", "description": "Research data for problems pertaining to combinatorics", "kind": "subject", "parent": "05", "page": 11 }, { "code": "05A", "originalCode": "05Axx", "name": "Enumerative combinatorics", "description": "Enumerative combinatorics \\{For enumeration in graph theory, see 05C30\\}", "kind": "section", "parent": "05", "page": 11 }, { "code": "05A05", "originalCode": "05A05", "name": "Permutations, words, matrices", "description": "Permutations, words, matrices", "kind": "subject", "parent": "05A", "page": 11 }, { "code": "05A10", "originalCode": "05A10", "name": "Factorials, binomial coefficients, combinatorial functions", "description": "Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx]", "kind": "subject", "parent": "05A", "page": 11 }, { "code": "05A15", "originalCode": "05A15", "name": "Exact enumeration problems, generating functions", "description": "Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]", "kind": "subject", "parent": "05A", "page": 11 }, { "code": "05A16", "originalCode": "05A16", "name": "Asymptotic enumeration", "description": "Asymptotic enumeration", "kind": "subject", "parent": "05A", "page": 11 }, { "code": "05A17", "originalCode": "05A17", "name": "Combinatorial aspects of partitions of integers", "description": "Combinatorial aspects of partitions of integers [See also 11P81, 11P82, 11P83]", "kind": "subject", "parent": "05A", "page": 11 }, { "code": "05A18", "originalCode": "05A18", "name": "Partitions of sets", "description": "Partitions of sets", "kind": "subject", "parent": "05A", "page": 11 }, { "code": "05A19", "originalCode": "05A19", "name": "Combinatorial identities, bijective combinatorics", "description": "Combinatorial identities, bijective combinatorics", "kind": "subject", "parent": "05A", "page": 11 }, { "code": "05A20", "originalCode": "05A20", "name": "Combinatorial inequalities", "description": "Combinatorial inequalities", "kind": "subject", "parent": "05A", "page": 12 }, { "code": "05A30", "originalCode": "05A30", "name": "\\(q\\)-calculus and related topics", "description": "\\(q\\)-calculus and related topics [See also 33Dxx]", "kind": "subject", "parent": "05A", "page": 12 }, { "code": "05A40", "originalCode": "05A40", "name": "Umbral calculus", "description": "Umbral calculus", "kind": "subject", "parent": "05A", "page": 12 }, { "code": "05A99", "originalCode": "05A99", "name": "Enumerative combinatorics", "description": "None of the above, but in this section", "kind": "subject", "parent": "05A", "page": 12 }, { "code": "05B", "originalCode": "05Bxx", "name": "Designs and configurations", "description": "Designs and configurations \\{For applications of design theory, see 94C30\\}", "kind": "section", "parent": "05", "page": 12 }, { "code": "05B05", "originalCode": "05B05", "name": "Combinatorial aspects of block designs", "description": "Combinatorial aspects of block designs [See also 51E05, 62K10]", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B07", "originalCode": "05B07", "name": "Triple systems", "description": "Triple systems", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B10", "originalCode": "05B10", "name": "Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)", "description": "Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B15", "originalCode": "05B15", "name": "Orthogonal arrays, Latin squares, Room squares", "description": "Orthogonal arrays, Latin squares, Room squares", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B20", "originalCode": "05B20", "name": "Combinatorial aspects of matrices (incidence, Hadamard, etc.)", "description": "Combinatorial aspects of matrices (incidence, Hadamard, etc.)", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B25", "originalCode": "05B25", "name": "Combinatorial aspects of finite geometries", "description": "Combinatorial aspects of finite geometries [See also 51D20, 51Exx]", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B30", "originalCode": "05B30", "name": "Other designs, configurations", "description": "Other designs, configurations [See also 51E30]", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B35", "originalCode": "05B35", "name": "Combinatorial aspects of matroids and geometric lattices", "description": "Combinatorial aspects of matroids and geometric lattices [See also 52B40, 90C27]", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B40", "originalCode": "05B40", "name": "Combinatorial aspects of packing and covering", "description": "Combinatorial aspects of packing and covering [See also 11H31, 52C15, 52C17]", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B45", "originalCode": "05B45", "name": "Combinatorial aspects of tessellation and tiling problems", "description": "Combinatorial aspects of tessellation and tiling problems [See also 52C20, 52C22]", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B50", "originalCode": "05B50", "name": "Polyominoes", "description": "Polyominoes", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05B99", "originalCode": "05B99", "name": "Designs and configurations", "description": "None of the above, but in this section", "kind": "subject", "parent": "05B", "page": 12 }, { "code": "05C", "originalCode": "05Cxx", "name": "Graph theory", "description": "Graph theory \\{For computer science, see 68R10\\}", "kind": "section", "parent": "05", "page": 12 }, { "code": "05C05", "originalCode": "05C05", "name": "Trees", "description": "Trees", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C07", "originalCode": "05C07", "name": "Vertex degrees", "description": "Vertex degrees [See also 05E30]", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C09", "originalCode": "05C09", "name": "Graphical indices (Wiener index, Zagreb index, Randi? index, etc.)", "description": "Graphical indices (Wiener index, Zagreb index, Randi? index, etc.)", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C10", "originalCode": "05C10", "name": "Planar graphs; geometric and topological aspects of graph theory", "description": "Planar graphs; geometric and topological aspects of graph theory [See also 57K10, 57M15]", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C12", "originalCode": "05C12", "name": "Distance in graphs", "description": "Distance in graphs", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C15", "originalCode": "05C15", "name": "Coloring of graphs and hypergraphs", "description": "Coloring of graphs and hypergraphs", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C17", "originalCode": "05C17", "name": "Perfect graphs", "description": "Perfect graphs", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C20", "originalCode": "05C20", "name": "Directed graphs (digraphs), tournaments", "description": "Directed graphs (digraphs), tournaments", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C21", "originalCode": "05C21", "name": "Flows in graphs", "description": "Flows in graphs", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C22", "originalCode": "05C22", "name": "Signed and weighted graphs", "description": "Signed and weighted graphs", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C25", "originalCode": "05C25", "name": "Graphs and abstract algebra (groups, rings, fields, etc.)", "description": "Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C30", "originalCode": "05C30", "name": "Enumeration in graph theory", "description": "Enumeration in graph theory", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C31", "originalCode": "05C31", "name": "Graph polynomials", "description": "Graph polynomials", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C35", "originalCode": "05C35", "name": "Extremal problems in graph theory", "description": "Extremal problems in graph theory [See also 90C35]", "kind": "subject", "parent": "05C", "page": 12 }, { "code": "05C38", "originalCode": "05C38", "name": "Paths and cycles", "description": "Paths and cycles [See also 90B10]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C40", "originalCode": "05C40", "name": "Connectivity", "description": "Connectivity", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C42", "originalCode": "05C42", "name": "Density (toughness, etc.)", "description": "Density (toughness, etc.)", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C45", "originalCode": "05C45", "name": "Eulerian and Hamiltonian graphs", "description": "Eulerian and Hamiltonian graphs", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C48", "originalCode": "05C48", "name": "Expander graphs", "description": "Expander graphs", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C50", "originalCode": "05C50", "name": "Graphs and linear algebra (matrices, eigenvalues, etc.)", "description": "Graphs and linear algebra (matrices, eigenvalues, etc.)", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C51", "originalCode": "05C51", "name": "Graph designs and isomorphic decomposition", "description": "Graph designs and isomorphic decomposition [See also 05B30]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C55", "originalCode": "05C55", "name": "Generalized Ramsey theory", "description": "Generalized Ramsey theory [See also 05D10]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C57", "originalCode": "05C57", "name": "Games on graphs (graph-theoretic aspects)", "description": "Games on graphs (graph-theoretic aspects) [See also 91A43, 91A46]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C60", "originalCode": "05C60", "name": "Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)", "description": "Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C62", "originalCode": "05C62", "name": "Graph representations (geometric and intersection representations, etc.)", "description": "Graph representations (geometric and intersection representations, etc.) \\{For graph drawing, see also 68R10\\}", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C63", "originalCode": "05C63", "name": "Infinite graphs", "description": "Infinite graphs", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C65", "originalCode": "05C65", "name": "Hypergraphs", "description": "Hypergraphs", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C69", "originalCode": "05C69", "name": "Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)", "description": "Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C70", "originalCode": "05C70", "name": "Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)", "description": "Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C72", "originalCode": "05C72", "name": "Fractional graph theory, fuzzy graph theory", "description": "Fractional graph theory, fuzzy graph theory", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C75", "originalCode": "05C75", "name": "Structural characterization of families of graphs", "description": "Structural characterization of families of graphs", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C76", "originalCode": "05C76", "name": "Graph operations (line graphs, products, etc.)", "description": "Graph operations (line graphs, products, etc.)", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C78", "originalCode": "05C78", "name": "Graph labelling (graceful graphs, bandwidth, etc.)", "description": "Graph labelling (graceful graphs, bandwidth, etc.)", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C80", "originalCode": "05C80", "name": "Random graphs (graph-theoretic aspects)", "description": "Random graphs (graph-theoretic aspects) [See also 60B20]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C81", "originalCode": "05C81", "name": "Random walks on graphs", "description": "Random walks on graphs", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C82", "originalCode": "05C82", "name": "Small world graphs, complex networks (graph-theoretic aspects)", "description": "Small world graphs, complex networks (graph-theoretic aspects) [See also 90Bxx, 91D30]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C83", "originalCode": "05C83", "name": "Graph minors", "description": "Graph minors", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C85", "originalCode": "05C85", "name": "Graph algorithms (graph-theoretic aspects)", "description": "Graph algorithms (graph-theoretic aspects) [See also 68R10, 68W05]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C90", "originalCode": "05C90", "name": "Applications of graph theory", "description": "Applications of graph theory [See also 68R10, 81Q30, 82B20, 82C20, 90C35, 92E10, 94C15]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C92", "originalCode": "05C92", "name": "Chemical graph theory", "description": "Chemical graph theory [See also 92E10]", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05C99", "originalCode": "05C99", "name": "Graph theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "05C", "page": 13 }, { "code": "05D", "originalCode": "05Dxx", "name": "Extremal combinatorics", "description": "Extremal combinatorics", "kind": "section", "parent": "05", "page": 13 }, { "code": "05D05", "originalCode": "05D05", "name": "Extremal set theory", "description": "Extremal set theory", "kind": "subject", "parent": "05D", "page": 13 }, { "code": "05D10", "originalCode": "05D10", "name": "Ramsey theory", "description": "Ramsey theory [See also 05C55]", "kind": "subject", "parent": "05D", "page": 13 }, { "code": "05D15", "originalCode": "05D15", "name": "Transversal (matching) theory", "description": "Transversal (matching) theory", "kind": "subject", "parent": "05D", "page": 13 }, { "code": "05D40", "originalCode": "05D40", "name": "Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.)", "description": "Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.)", "kind": "subject", "parent": "05D", "page": 13 }, { "code": "05D99", "originalCode": "05D99", "name": "Extremal combinatorics", "description": "None of the above, but in this section", "kind": "subject", "parent": "05D", "page": 13 }, { "code": "05E", "originalCode": "05Exx", "name": "Algebraic combinatorics", "description": "Algebraic combinatorics", "kind": "section", "parent": "05", "page": 14 }, { "code": "05E05", "originalCode": "05E05", "name": "Symmetric functions and generalizations", "description": "Symmetric functions and generalizations", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "05E10", "originalCode": "05E10", "name": "Combinatorial aspects of representation theory", "description": "Combinatorial aspects of representation theory [See also 20C30]", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "05E14", "originalCode": "05E14", "name": "Combinatorial aspects of algebraic geometry", "description": "Combinatorial aspects of algebraic geometry [See also 14Nxx]", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "05E16", "originalCode": "05E16", "name": "Combinatorial aspects of groups and algebras", "description": "Combinatorial aspects of groups and algebras [See also 22E45, 33C80]", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "05E18", "originalCode": "05E18", "name": "Group actions on combinatorial structures", "description": "Group actions on combinatorial structures", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "05E30", "originalCode": "05E30", "name": "Association schemes, strongly regular graphs", "description": "Association schemes, strongly regular graphs", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "05E40", "originalCode": "05E40", "name": "Combinatorial aspects of commutative algebra", "description": "Combinatorial aspects of commutative algebra", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "05E45", "originalCode": "05E45", "name": "Combinatorial aspects of simplicial complexes", "description": "Combinatorial aspects of simplicial complexes", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "05E99", "originalCode": "05E99", "name": "Algebraic combinatorics", "description": "None of the above, but in this section", "kind": "subject", "parent": "05E", "page": 14 }, { "code": "06", "originalCode": "06-XX", "name": "Order, lattices, ordered algebraic structures", "description": "Order, lattices, ordered algebraic structures [See also 18B35]", "kind": "class", "parent": null, "page": 14 }, { "code": "06-00", "originalCode": "06-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordered structures", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordered structures", "kind": "subject", "parent": "06", "page": 14 }, { "code": "06-01", "originalCode": "06-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures", "kind": "subject", "parent": "06", "page": 14 }, { "code": "06-02", "originalCode": "06-02", "name": "Research exposition (monographs, survey articles) pertaining to ordered structures", "description": "Research exposition (monographs, survey articles) pertaining to ordered structures", "kind": "subject", "parent": "06", "page": 14 }, { "code": "06-03", "originalCode": "06-03", "name": "History of ordered structures", "description": "History of ordered structures [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "06", "page": 14 }, { "code": "06-04", "originalCode": "06-04", "name": "Software, source code, etc. for problems pertaining to ordered structures", "description": "Software, source code, etc. for problems pertaining to ordered structures", "kind": "subject", "parent": "06", "page": 14 }, { "code": "06-06", "originalCode": "06-06", "name": "Proceedings, conferences, collections, etc. pertaining to ordered structures", "description": "Proceedings, conferences, collections, etc. pertaining to ordered structures", "kind": "subject", "parent": "06", "page": 14 }, { "code": "06-08", "originalCode": "06-08", "name": "Computational methods for problems pertaining to ordered structures", "description": "Computational methods for problems pertaining to ordered structures", "kind": "subject", "parent": "06", "page": 14 }, { "code": "06-11", "originalCode": "06-11", "name": "Research data for problems pertaining to ordered structures", "description": "Research data for problems pertaining to ordered structures", "kind": "subject", "parent": "06", "page": 14 }, { "code": "06A", "originalCode": "06Axx", "name": "Ordered sets", "description": "Ordered sets", "kind": "section", "parent": "06", "page": 14 }, { "code": "06A05", "originalCode": "06A05", "name": "Total orders", "description": "Total orders", "kind": "subject", "parent": "06A", "page": 14 }, { "code": "06A06", "originalCode": "06A06", "name": "Partial orders, general", "description": "Partial orders, general", "kind": "subject", "parent": "06A", "page": 14 }, { "code": "06A07", "originalCode": "06A07", "name": "Combinatorics of partially ordered sets", "description": "Combinatorics of partially ordered sets", "kind": "subject", "parent": "06A", "page": 14 }, { "code": "06A11", "originalCode": "06A11", "name": "Algebraic aspects of posets", "description": "Algebraic aspects of posets", "kind": "subject", "parent": "06A", "page": 14 }, { "code": "06A12", "originalCode": "06A12", "name": "Semilattices", "description": "Semilattices [See also 20M10] \\{For topological semilattices, see 22A26\\}", "kind": "subject", "parent": "06A", "page": 14 }, { "code": "06A15", "originalCode": "06A15", "name": "Galois correspondences, closure operators (in relation to ordered sets)", "description": "Galois correspondences, closure operators (in relation to ordered sets)", "kind": "subject", "parent": "06A", "page": 14 }, { "code": "06A75", "originalCode": "06A75", "name": "Generalizations of ordered sets", "description": "Generalizations of ordered sets", "kind": "subject", "parent": "06A", "page": 14 }, { "code": "06A99", "originalCode": "06A99", "name": "Ordered sets", "description": "None of the above, but in this section", "kind": "subject", "parent": "06A", "page": 14 }, { "code": "06B", "originalCode": "06Bxx", "name": "Lattices", "description": "Lattices [See also 03G10]", "kind": "section", "parent": "06", "page": 15 }, { "code": "06B05", "originalCode": "06B05", "name": "Structure theory of lattices", "description": "Structure theory of lattices", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B10", "originalCode": "06B10", "name": "Lattice ideals, congruence relations", "description": "Lattice ideals, congruence relations", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B15", "originalCode": "06B15", "name": "Representation theory of lattices", "description": "Representation theory of lattices", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B20", "originalCode": "06B20", "name": "Varieties of lattices", "description": "Varieties of lattices", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B23", "originalCode": "06B23", "name": "Complete lattices, completions", "description": "Complete lattices, completions", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B25", "originalCode": "06B25", "name": "Free lattices, projective lattices, word problems", "description": "Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10]", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B30", "originalCode": "06B30", "name": "Topological lattices", "description": "Topological lattices [See also 06F30, 22A26, 54F05, 54H12]", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B35", "originalCode": "06B35", "name": "Continuous lattices and posets, applications", "description": "Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B75", "originalCode": "06B75", "name": "Generalizations of lattices", "description": "Generalizations of lattices", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06B99", "originalCode": "06B99", "name": "Lattices", "description": "None of the above, but in this section", "kind": "subject", "parent": "06B", "page": 15 }, { "code": "06C", "originalCode": "06Cxx", "name": "Modular lattices, complemented lattices", "description": "Modular lattices, complemented lattices", "kind": "section", "parent": "06", "page": 15 }, { "code": "06C05", "originalCode": "06C05", "name": "Modular lattices, Desarguesian lattices", "description": "Modular lattices, Desarguesian lattices", "kind": "subject", "parent": "06C", "page": 15 }, { "code": "06C10", "originalCode": "06C10", "name": "Semimodular lattices, geometric lattices", "description": "Semimodular lattices, geometric lattices", "kind": "subject", "parent": "06C", "page": 15 }, { "code": "06C15", "originalCode": "06C15", "name": "Complemented lattices, orthocomplemented lattices and posets", "description": "Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]", "kind": "subject", "parent": "06C", "page": 15 }, { "code": "06C20", "originalCode": "06C20", "name": "Complemented modular lattices, continuous geometries", "description": "Complemented modular lattices, continuous geometries", "kind": "subject", "parent": "06C", "page": 15 }, { "code": "06C99", "originalCode": "06C99", "name": "Modular lattices, complemented lattices", "description": "None of the above, but in this section", "kind": "subject", "parent": "06C", "page": 15 }, { "code": "06D", "originalCode": "06Dxx", "name": "Distributive lattices", "description": "Distributive lattices", "kind": "section", "parent": "06", "page": 15 }, { "code": "06D05", "originalCode": "06D05", "name": "Structure and representation theory of distributive lattices", "description": "Structure and representation theory of distributive lattices", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D10", "originalCode": "06D10", "name": "Complete distributivity", "description": "Complete distributivity", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D15", "originalCode": "06D15", "name": "Pseudocomplemented lattices", "description": "Pseudocomplemented lattices", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D20", "originalCode": "06D20", "name": "Heyting algebras (lattice-theoretic aspects)", "description": "Heyting algebras (lattice-theoretic aspects) [See also 03G25]", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D22", "originalCode": "06D22", "name": "Frames, locales", "description": "Frames, locales \\{For topological questions, see 54-XX\\}", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D25", "originalCode": "06D25", "name": "Post algebras (lattice-theoretic aspects)", "description": "Post algebras (lattice-theoretic aspects) [See also 03G20]", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D30", "originalCode": "06D30", "name": "De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects)", "description": "De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects) [See also 03G20]", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D35", "originalCode": "06D35", "name": "MV-algebras", "description": "MV-algebras", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D50", "originalCode": "06D50", "name": "Lattices and duality", "description": "Lattices and duality", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D72", "originalCode": "06D72", "name": "Fuzzy lattices (soft algebras) and related topics", "description": "Fuzzy lattices (soft algebras) and related topics", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D75", "originalCode": "06D75", "name": "Other generalizations of distributive lattices", "description": "Other generalizations of distributive lattices", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06D99", "originalCode": "06D99", "name": "Distributive lattices", "description": "None of the above, but in this section", "kind": "subject", "parent": "06D", "page": 15 }, { "code": "06E", "originalCode": "06Exx", "name": "Boolean algebras (Boolean rings)", "description": "Boolean algebras (Boolean rings) [See also 03G05]", "kind": "section", "parent": "06", "page": 16 }, { "code": "06E05", "originalCode": "06E05", "name": "Structure theory of Boolean algebras", "description": "Structure theory of Boolean algebras", "kind": "subject", "parent": "06E", "page": 16 }, { "code": "06E10", "originalCode": "06E10", "name": "Chain conditions, complete algebras", "description": "Chain conditions, complete algebras", "kind": "subject", "parent": "06E", "page": 16 }, { "code": "06E15", "originalCode": "06E15", "name": "Stone spaces (Boolean spaces) and related structures", "description": "Stone spaces (Boolean spaces) and related structures", "kind": "subject", "parent": "06E", "page": 16 }, { "code": "06E20", "originalCode": "06E20", "name": "Ring-theoretic properties of Boolean algebras", "description": "Ring-theoretic properties of Boolean algebras [See also 16E50, 16G30]", "kind": "subject", "parent": "06E", "page": 16 }, { "code": "06E25", "originalCode": "06E25", "name": "Boolean algebras with additional operations (diagonalizable algebras, etc.)", "description": "Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45]", "kind": "subject", "parent": "06E", "page": 16 }, { "code": "06E30", "originalCode": "06E30", "name": "Boolean functions", "description": "Boolean functions [See also 94D10]", "kind": "subject", "parent": "06E", "page": 16 }, { "code": "06E75", "originalCode": "06E75", "name": "Generalizations of Boolean algebras", "description": "Generalizations of Boolean algebras", "kind": "subject", "parent": "06E", "page": 16 }, { "code": "06E99", "originalCode": "06E99", "name": "Boolean algebras (Boolean rings)", "description": "None of the above, but in this section", "kind": "subject", "parent": "06E", "page": 16 }, { "code": "06F", "originalCode": "06Fxx", "name": "Ordered structures", "description": "Ordered structures", "kind": "section", "parent": "06", "page": 16 }, { "code": "06F05", "originalCode": "06F05", "name": "Ordered semigroups and monoids", "description": "Ordered semigroups and monoids [See also 20Mxx]", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "06F07", "originalCode": "06F07", "name": "Quantales", "description": "Quantales", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "06F10", "originalCode": "06F10", "name": "Noether lattices", "description": "Noether lattices", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "06F15", "originalCode": "06F15", "name": "Ordered groups", "description": "Ordered groups [See also 20F60]", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "06F20", "originalCode": "06F20", "name": "Ordered abelian groups, Riesz groups, ordered linear spaces", "description": "Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "06F25", "originalCode": "06F25", "name": "Ordered rings, algebras, modules", "description": "Ordered rings, algebras, modules \\{For ordered fields, see 12J15\\} [See also 13J25, 16W80]", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "06F30", "originalCode": "06F30", "name": "Ordered topological structures", "description": "Ordered topological structures [See also 06B30, 22A26, 54F05, 54H12]", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "06F35", "originalCode": "06F35", "name": "BCK-algebras, BCI-algebras", "description": "BCK-algebras, BCI-algebras [See also 03G25]", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "06F99", "originalCode": "06F99", "name": "Ordered structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "06F", "page": 16 }, { "code": "08", "originalCode": "08-XX", "name": "General algebraic systems", "description": "General algebraic systems", "kind": "class", "parent": null, "page": 16 }, { "code": "08-00", "originalCode": "08-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general algebraic systems", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general algebraic systems", "kind": "subject", "parent": "08", "page": 16 }, { "code": "08-01", "originalCode": "08-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems", "kind": "subject", "parent": "08", "page": 16 }, { "code": "08-02", "originalCode": "08-02", "name": "Research exposition (monographs, survey articles) pertaining to general algebraic systems", "description": "Research exposition (monographs, survey articles) pertaining to general algebraic systems", "kind": "subject", "parent": "08", "page": 16 }, { "code": "08-03", "originalCode": "08-03", "name": "History of general algebraic systems", "description": "History of general algebraic systems [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "08", "page": 16 }, { "code": "08-04", "originalCode": "08-04", "name": "Software, source code, etc. for problems pertaining to general algebraic systems", "description": "Software, source code, etc. for problems pertaining to general algebraic systems", "kind": "subject", "parent": "08", "page": 16 }, { "code": "08-06", "originalCode": "08-06", "name": "Proceedings, conferences, collections, etc. pertaining to general algebraic systems", "description": "Proceedings, conferences, collections, etc. pertaining to general algebraic systems", "kind": "subject", "parent": "08", "page": 16 }, { "code": "08-08", "originalCode": "08-08", "name": "Computational methods for problems pertaining to general algebraic systems", "description": "Computational methods for problems pertaining to general algebraic systems", "kind": "subject", "parent": "08", "page": 16 }, { "code": "08-11", "originalCode": "08-11", "name": "Research data for problems pertaining to general algebraic systems", "description": "Research data for problems pertaining to general algebraic systems", "kind": "subject", "parent": "08", "page": 16 }, { "code": "08A", "originalCode": "08Axx", "name": "Algebraic structures", "description": "Algebraic structures [See also 03C05]", "kind": "section", "parent": "08", "page": 17 }, { "code": "08A02", "originalCode": "08A02", "name": "Relational systems, laws of composition", "description": "Relational systems, laws of composition", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A05", "originalCode": "08A05", "name": "Structure theory of algebraic structures", "description": "Structure theory of algebraic structures", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A30", "originalCode": "08A30", "name": "Subalgebras, congruence relations", "description": "Subalgebras, congruence relations", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A35", "originalCode": "08A35", "name": "Automorphisms and endomorphisms of algebraic structures", "description": "Automorphisms and endomorphisms of algebraic structures", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A40", "originalCode": "08A40", "name": "Operations and polynomials in algebraic structures, primal algebras", "description": "Operations and polynomials in algebraic structures, primal algebras", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A45", "originalCode": "08A45", "name": "Equational compactness", "description": "Equational compactness", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A50", "originalCode": "08A50", "name": "Word problems (aspects of algebraic structures)", "description": "Word problems (aspects of algebraic structures) [See also 03D40, 06B25, 20F10, 68R15]", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A55", "originalCode": "08A55", "name": "Partial algebras", "description": "Partial algebras", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A60", "originalCode": "08A60", "name": "Unary algebras", "description": "Unary algebras", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A62", "originalCode": "08A62", "name": "Finitary algebras", "description": "Finitary algebras", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A65", "originalCode": "08A65", "name": "Infinitary algebras", "description": "Infinitary algebras", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A68", "originalCode": "08A68", "name": "Heterogeneous algebras", "description": "Heterogeneous algebras", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A70", "originalCode": "08A70", "name": "Applications of universal algebra in computer science", "description": "Applications of universal algebra in computer science", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A72", "originalCode": "08A72", "name": "Fuzzy algebraic structures", "description": "Fuzzy algebraic structures", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08A99", "originalCode": "08A99", "name": "Algebraic structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "08A", "page": 17 }, { "code": "08B", "originalCode": "08Bxx", "name": "Varieties", "description": "Varieties [See also 03C05]", "kind": "section", "parent": "08", "page": 17 }, { "code": "08B05", "originalCode": "08B05", "name": "Equational logic, Mal'tsev conditions", "description": "Equational logic, Mal'tsev conditions", "kind": "subject", "parent": "08B", "page": 17 }, { "code": "08B10", "originalCode": "08B10", "name": "Congruence modularity, congruence distributivity", "description": "Congruence modularity, congruence distributivity", "kind": "subject", "parent": "08B", "page": 17 }, { "code": "08B15", "originalCode": "08B15", "name": "Lattices of varieties", "description": "Lattices of varieties", "kind": "subject", "parent": "08B", "page": 17 }, { "code": "08B20", "originalCode": "08B20", "name": "Free algebras", "description": "Free algebras", "kind": "subject", "parent": "08B", "page": 17 }, { "code": "08B25", "originalCode": "08B25", "name": "Products, amalgamated products, and other kinds of limits and colimits", "description": "Products, amalgamated products, and other kinds of limits and colimits [See also 18A30]", "kind": "subject", "parent": "08B", "page": 17 }, { "code": "08B26", "originalCode": "08B26", "name": "Subdirect products and subdirect irreducibility", "description": "Subdirect products and subdirect irreducibility", "kind": "subject", "parent": "08B", "page": 17 }, { "code": "08B30", "originalCode": "08B30", "name": "Injectives, projectives", "description": "Injectives, projectives", "kind": "subject", "parent": "08B", "page": 17 }, { "code": "08B99", "originalCode": "08B99", "name": "Varieties", "description": "None of the above, but in this section", "kind": "subject", "parent": "08B", "page": 17 }, { "code": "08C", "originalCode": "08Cxx", "name": "Other classes of algebras", "description": "Other classes of algebras", "kind": "section", "parent": "08", "page": 17 }, { "code": "08C05", "originalCode": "08C05", "name": "Categories of algebras", "description": "Categories of algebras [See also 18C05]", "kind": "subject", "parent": "08C", "page": 17 }, { "code": "08C10", "originalCode": "08C10", "name": "Axiomatic model classes", "description": "Axiomatic model classes [See also 03Cxx, in particular 03C60]", "kind": "subject", "parent": "08C", "page": 17 }, { "code": "08C15", "originalCode": "08C15", "name": "Quasivarieties", "description": "Quasivarieties", "kind": "subject", "parent": "08C", "page": 17 }, { "code": "08C20", "originalCode": "08C20", "name": "Natural dualities for classes of algebras", "description": "Natural dualities for classes of algebras [See also 06E15, 18A40, 22A30]", "kind": "subject", "parent": "08C", "page": 17 }, { "code": "08C99", "originalCode": "08C99", "name": "Other classes of algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "08C", "page": 17 }, { "code": "11", "originalCode": "11-XX", "name": "Number theory", "description": "Number theory", "kind": "class", "parent": null, "page": 18 }, { "code": "11-00", "originalCode": "11-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory", "kind": "subject", "parent": "11", "page": 18 }, { "code": "11-01", "originalCode": "11-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory", "kind": "subject", "parent": "11", "page": 18 }, { "code": "11-02", "originalCode": "11-02", "name": "Research exposition (monographs, survey articles) pertaining to number theory", "description": "Research exposition (monographs, survey articles) pertaining to number theory", "kind": "subject", "parent": "11", "page": 18 }, { "code": "11-03", "originalCode": "11-03", "name": "History of number theory", "description": "History of number theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "11", "page": 18 }, { "code": "11-04", "originalCode": "11-04", "name": "Software, source code, etc. for problems pertaining to number theory", "description": "Software, source code, etc. for problems pertaining to number theory", "kind": "subject", "parent": "11", "page": 18 }, { "code": "11-06", "originalCode": "11-06", "name": "Proceedings, conferences, collections, etc. pertaining to number theory", "description": "Proceedings, conferences, collections, etc. pertaining to number theory", "kind": "subject", "parent": "11", "page": 18 }, { "code": "11-11", "originalCode": "11-11", "name": "Research data for problems pertaining to number theory", "description": "Research data for problems pertaining to number theory", "kind": "subject", "parent": "11", "page": 18 }, { "code": "11A", "originalCode": "11Axx", "name": "Elementary number theory", "description": "Elementary number theory \\{For analogues in number fields, see 11R04\\}", "kind": "section", "parent": "11", "page": 18 }, { "code": "11A05", "originalCode": "11A05", "name": "Multiplicative structure; Euclidean algorithm; greatest common divisors", "description": "Multiplicative structure; Euclidean algorithm; greatest common divisors", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A07", "originalCode": "11A07", "name": "Congruences; primitive roots; residue systems", "description": "Congruences; primitive roots; residue systems", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A15", "originalCode": "11A15", "name": "Power residues, reciprocity", "description": "Power residues, reciprocity", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A25", "originalCode": "11A25", "name": "Arithmetic functions; related numbers; inversion formulas", "description": "Arithmetic functions; related numbers; inversion formulas", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A41", "originalCode": "11A41", "name": "Primes", "description": "Primes", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A51", "originalCode": "11A51", "name": "Factorization; primality", "description": "Factorization; primality", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A55", "originalCode": "11A55", "name": "Continued fractions", "description": "Continued fractions \\{For approximation results, see 11J70\\} [See also 11K50, 30B70, 40A15]", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A63", "originalCode": "11A63", "name": "Radix representation; digital problems", "description": "Radix representation; digital problems \\{For metric results, see 11K16\\}", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A67", "originalCode": "11A67", "name": "Other number representations", "description": "Other number representations", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11A99", "originalCode": "11A99", "name": "Elementary number theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "11A", "page": 18 }, { "code": "11B", "originalCode": "11Bxx", "name": "Sequences and sets", "description": "Sequences and sets", "kind": "section", "parent": "11", "page": 18 }, { "code": "11B05", "originalCode": "11B05", "name": "Density, gaps, topology", "description": "Density, gaps, topology", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B13", "originalCode": "11B13", "name": "Additive bases, including sumsets", "description": "Additive bases, including sumsets [See also 05B10]", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B25", "originalCode": "11B25", "name": "Arithmetic progressions", "description": "Arithmetic progressions [See also 11N13]", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B30", "originalCode": "11B30", "name": "Arithmetic combinatorics; higher degree uniformity", "description": "Arithmetic combinatorics; higher degree uniformity", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B34", "originalCode": "11B34", "name": "Representation functions", "description": "Representation functions", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B37", "originalCode": "11B37", "name": "Recurrences", "description": "Recurrences \\{For applications to special functions, see 33-XX\\}", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B39", "originalCode": "11B39", "name": "Fibonacci and Lucas numbers and polynomials and generalizations", "description": "Fibonacci and Lucas numbers and polynomials and generalizations", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B50", "originalCode": "11B50", "name": "Sequences (mod \\(m\\))", "description": "Sequences (mod \\(m\\))", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B57", "originalCode": "11B57", "name": "Farey sequences; the sequences \\(1^k, 2^k, \\dots\\)", "description": "Farey sequences; the sequences \\(1^k, 2^k, \\dots\\)", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B65", "originalCode": "11B65", "name": "Binomial coefficients; factorials; \\(q\\)-identities", "description": "Binomial coefficients; factorials; \\(q\\)-identities [See also 05A10, 05A30]", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B68", "originalCode": "11B68", "name": "Bernoulli and Euler numbers and polynomials", "description": "Bernoulli and Euler numbers and polynomials", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B73", "originalCode": "11B73", "name": "Bell and Stirling numbers", "description": "Bell and Stirling numbers", "kind": "subject", "parent": "11B", "page": 18 }, { "code": "11B75", "originalCode": "11B75", "name": "Other combinatorial number theory", "description": "Other combinatorial number theory", "kind": "subject", "parent": "11B", "page": 19 }, { "code": "11B83", "originalCode": "11B83", "name": "Special sequences and polynomials", "description": "Special sequences and polynomials", "kind": "subject", "parent": "11B", "page": 19 }, { "code": "11B85", "originalCode": "11B85", "name": "Automata sequences", "description": "Automata sequences", "kind": "subject", "parent": "11B", "page": 19 }, { "code": "11B99", "originalCode": "11B99", "name": "Sequences and sets", "description": "None of the above, but in this section", "kind": "subject", "parent": "11B", "page": 19 }, { "code": "11C", "originalCode": "11Cxx", "name": "Polynomials and matrices", "description": "Polynomials and matrices", "kind": "section", "parent": "11", "page": 19 }, { "code": "11C08", "originalCode": "11C08", "name": "Polynomials in number theory", "description": "Polynomials in number theory [See also 13F20]", "kind": "subject", "parent": "11C", "page": 19 }, { "code": "11C20", "originalCode": "11C20", "name": "Matrices, determinants in number theory", "description": "Matrices, determinants in number theory [See also 15B36]", "kind": "subject", "parent": "11C", "page": 19 }, { "code": "11C99", "originalCode": "11C99", "name": "Polynomials and matrices", "description": "None of the above, but in this section", "kind": "subject", "parent": "11C", "page": 19 }, { "code": "11D", "originalCode": "11Dxx", "name": "Diophantine equations", "description": "Diophantine equations [See also 11Gxx, 14Gxx]", "kind": "section", "parent": "11", "page": 19 }, { "code": "11D04", "originalCode": "11D04", "name": "Linear Diophantine equations", "description": "Linear Diophantine equations", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D07", "originalCode": "11D07", "name": "The Frobenius problem", "description": "The Frobenius problem", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D09", "originalCode": "11D09", "name": "Quadratic and bilinear Diophantine equations", "description": "Quadratic and bilinear Diophantine equations", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D25", "originalCode": "11D25", "name": "Cubic and quartic Diophantine equations", "description": "Cubic and quartic Diophantine equations", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D41", "originalCode": "11D41", "name": "Higher degree equations; Fermat's equation", "description": "Higher degree equations; Fermat's equation", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D45", "originalCode": "11D45", "name": "Counting solutions of Diophantine equations", "description": "Counting solutions of Diophantine equations", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D57", "originalCode": "11D57", "name": "Multiplicative and norm form equations", "description": "Multiplicative and norm form equations", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D59", "originalCode": "11D59", "name": "Thue-Mahler equations", "description": "Thue-Mahler equations", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D61", "originalCode": "11D61", "name": "Exponential Diophantine equations", "description": "Exponential Diophantine equations", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D68", "originalCode": "11D68", "name": "Rational numbers as sums of fractions", "description": "Rational numbers as sums of fractions", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D72", "originalCode": "11D72", "name": "Diophantine equations in many variables", "description": "Diophantine equations in many variables [See also 11P55]", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D75", "originalCode": "11D75", "name": "Diophantine inequalities", "description": "Diophantine inequalities [See also 11J25]", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D79", "originalCode": "11D79", "name": "Congruences in many variables", "description": "Congruences in many variables", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D85", "originalCode": "11D85", "name": "Representation problems", "description": "Representation problems [See also 11P55]", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D88", "originalCode": "11D88", "name": "\\(p\\)-adic and power series fields", "description": "\\(p\\)-adic and power series fields", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11D99", "originalCode": "11D99", "name": "Diophantine equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "11D", "page": 19 }, { "code": "11E", "originalCode": "11Exx", "name": "Forms and linear algebraic groups", "description": "Forms and linear algebraic groups [See also 19Gxx] \\{For quadratic forms in linear algebra, see 15A63\\}", "kind": "section", "parent": "11", "page": 19 }, { "code": "11E04", "originalCode": "11E04", "name": "Quadratic forms over general fields", "description": "Quadratic forms over general fields", "kind": "subject", "parent": "11E", "page": 19 }, { "code": "11E08", "originalCode": "11E08", "name": "Quadratic forms over local rings and fields", "description": "Quadratic forms over local rings and fields", "kind": "subject", "parent": "11E", "page": 19 }, { "code": "11E10", "originalCode": "11E10", "name": "Forms over real fields", "description": "Forms over real fields", "kind": "subject", "parent": "11E", "page": 19 }, { "code": "11E12", "originalCode": "11E12", "name": "Quadratic forms over global rings and fields", "description": "Quadratic forms over global rings and fields", "kind": "subject", "parent": "11E", "page": 19 }, { "code": "11E16", "originalCode": "11E16", "name": "General binary quadratic forms", "description": "General binary quadratic forms", "kind": "subject", "parent": "11E", "page": 19 }, { "code": "11E20", "originalCode": "11E20", "name": "General ternary and quaternary quadratic forms; forms of more than two variables", "description": "General ternary and quaternary quadratic forms; forms of more than two variables", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E25", "originalCode": "11E25", "name": "Sums of squares and representations by other particular quadratic forms", "description": "Sums of squares and representations by other particular quadratic forms", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E39", "originalCode": "11E39", "name": "Bilinear and Hermitian forms", "description": "Bilinear and Hermitian forms", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E41", "originalCode": "11E41", "name": "Class numbers of quadratic and Hermitian forms", "description": "Class numbers of quadratic and Hermitian forms", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E45", "originalCode": "11E45", "name": "Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)", "description": "Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E57", "originalCode": "11E57", "name": "Classical groups", "description": "Classical groups [See also 14Lxx, 20Gxx]", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E70", "originalCode": "11E70", "name": "\\(K\\)-theory of quadratic and Hermitian forms", "description": "\\(K\\)-theory of quadratic and Hermitian forms", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E72", "originalCode": "11E72", "name": "Galois cohomology of linear algebraic groups", "description": "Galois cohomology of linear algebraic groups [See also 20G10]", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E76", "originalCode": "11E76", "name": "Forms of degree higher than two", "description": "Forms of degree higher than two", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E81", "originalCode": "11E81", "name": "Algebraic theory of quadratic forms; Witt groups and rings", "description": "Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E88", "originalCode": "11E88", "name": "Quadratic spaces; Clifford algebras", "description": "Quadratic spaces; Clifford algebras [See also 15A63, 15A66]", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E95", "originalCode": "11E95", "name": "\\(p\\)-adic theory", "description": "\\(p\\)-adic theory", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11E99", "originalCode": "11E99", "name": "Forms and linear algebraic groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "11E", "page": 20 }, { "code": "11F", "originalCode": "11Fxx", "name": "Discontinuous groups and automorphic forms", "description": "Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] \\{For relations with quadratic forms, see 11E45\\}", "kind": "section", "parent": "11", "page": 20 }, { "code": "11F03", "originalCode": "11F03", "name": "Modular and automorphic functions", "description": "Modular and automorphic functions", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F06", "originalCode": "11F06", "name": "Structure of modular groups and generalizations; arithmetic groups", "description": "Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F11", "originalCode": "11F11", "name": "Holomorphic modular forms of integral weight", "description": "Holomorphic modular forms of integral weight", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F12", "originalCode": "11F12", "name": "Automorphic forms, one variable", "description": "Automorphic forms, one variable", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F20", "originalCode": "11F20", "name": "Dedekind eta function, Dedekind sums", "description": "Dedekind eta function, Dedekind sums", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F22", "originalCode": "11F22", "name": "Relationship to Lie algebras and finite simple groups", "description": "Relationship to Lie algebras and finite simple groups", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F23", "originalCode": "11F23", "name": "Relations with algebraic geometry and topology", "description": "Relations with algebraic geometry and topology", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F25", "originalCode": "11F25", "name": "Hecke-Petersson operators, differential operators (one variable)", "description": "Hecke-Petersson operators, differential operators (one variable)", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F27", "originalCode": "11F27", "name": "Theta series; Weil representation; theta correspondences", "description": "Theta series; Weil representation; theta correspondences", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F30", "originalCode": "11F30", "name": "Fourier coefficients of automorphic forms", "description": "Fourier coefficients of automorphic forms", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F32", "originalCode": "11F32", "name": "Modular correspondences, etc.", "description": "Modular correspondences, etc.", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F33", "originalCode": "11F33", "name": "Congruences for modular and \\(p\\)-adic modular forms", "description": "Congruences for modular and \\(p\\)-adic modular forms", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F37", "originalCode": "11F37", "name": "Forms of half-integer weight; nonholomorphic modular forms", "description": "Forms of half-integer weight; nonholomorphic modular forms", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F41", "originalCode": "11F41", "name": "Automorphic forms on \\(\\mbox{GL}(2)\\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces", "description": "Automorphic forms on \\(\\mbox{GL}(2)\\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14G35]", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F46", "originalCode": "11F46", "name": "Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms", "description": "Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F50", "originalCode": "11F50", "name": "Jacobi forms", "description": "Jacobi forms", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F52", "originalCode": "11F52", "name": "Modular forms associated to Drinfel'd modules", "description": "Modular forms associated to Drinfel'd modules", "kind": "subject", "parent": "11F", "page": 20 }, { "code": "11F55", "originalCode": "11F55", "name": "Other groups and their modular and automorphic forms (several variables)", "description": "Other groups and their modular and automorphic forms (several variables)", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F60", "originalCode": "11F60", "name": "Hecke-Petersson operators, differential operators (several variables)", "description": "Hecke-Petersson operators, differential operators (several variables)", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F66", "originalCode": "11F66", "name": "Langlands \\(L\\)-functions; one variable Dirichlet series and functional equations", "description": "Langlands \\(L\\)-functions; one variable Dirichlet series and functional equations", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F67", "originalCode": "11F67", "name": "Special values of automorphic \\(L\\)-series, periods of automorphic forms, cohomology, modular symbols", "description": "Special values of automorphic \\(L\\)-series, periods of automorphic forms, cohomology, modular symbols", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F68", "originalCode": "11F68", "name": "Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series", "description": "Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F70", "originalCode": "11F70", "name": "Representation-theoretic methods; automorphic representations over local and global fields", "description": "Representation-theoretic methods; automorphic representations over local and global fields", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F72", "originalCode": "11F72", "name": "Spectral theory; trace formulas (e.g., that of Selberg)", "description": "Spectral theory; trace formulas (e.g., that of Selberg)", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F75", "originalCode": "11F75", "name": "Cohomology of arithmetic groups", "description": "Cohomology of arithmetic groups", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F77", "originalCode": "11F77", "name": "Automorphic forms and their relations with perfectoid spaces", "description": "Automorphic forms and their relations with perfectoid spaces [See also 14G45]", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F80", "originalCode": "11F80", "name": "Galois representations", "description": "Galois representations", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F85", "originalCode": "11F85", "name": "\\(p\\)-adic theory, local fields", "description": "\\(p\\)-adic theory, local fields [See also 14G20, 22E50]", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11F99", "originalCode": "11F99", "name": "Discontinuous groups and automorphic forms", "description": "None of the above, but in this section", "kind": "subject", "parent": "11F", "page": 21 }, { "code": "11G", "originalCode": "11Gxx", "name": "Arithmetic algebraic geometry (Diophantine geometry)", "description": "Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx]", "kind": "section", "parent": "11", "page": 21 }, { "code": "11G05", "originalCode": "11G05", "name": "Elliptic curves over global fields", "description": "Elliptic curves over global fields [See also 14H52]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G07", "originalCode": "11G07", "name": "Elliptic curves over local fields", "description": "Elliptic curves over local fields [See also 14G20, 14H52]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G09", "originalCode": "11G09", "name": "Drinfel'd modules; higher-dimensional motives, etc.", "description": "Drinfel'd modules; higher-dimensional motives, etc. [See also 14L05]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G10", "originalCode": "11G10", "name": "Abelian varieties of dimension \\(> 1\\)", "description": "Abelian varieties of dimension \\(> 1\\) [See also 14Kxx]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G15", "originalCode": "11G15", "name": "Complex multiplication and moduli of abelian varieties", "description": "Complex multiplication and moduli of abelian varieties [See also 14K22]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G16", "originalCode": "11G16", "name": "Elliptic and modular units", "description": "Elliptic and modular units [See also 11R27]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G18", "originalCode": "11G18", "name": "Arithmetic aspects of modular and Shimura varieties", "description": "Arithmetic aspects of modular and Shimura varieties [See also 14G35]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G20", "originalCode": "11G20", "name": "Curves over finite and local fields", "description": "Curves over finite and local fields [See also 14H25]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G25", "originalCode": "11G25", "name": "Varieties over finite and local fields", "description": "Varieties over finite and local fields [See also 14G15, 14G20]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G30", "originalCode": "11G30", "name": "Curves of arbitrary genus or genus \\(\\ne 1\\) over global fields", "description": "Curves of arbitrary genus or genus \\(\\ne 1\\) over global fields [See also 14H25]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G32", "originalCode": "11G32", "name": "Arithmetic aspects of dessins d'enfants, Bely? theory", "description": "Arithmetic aspects of dessins d'enfants, Bely? theory", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G35", "originalCode": "11G35", "name": "Varieties over global fields", "description": "Varieties over global fields [See also 14G25]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G40", "originalCode": "11G40", "name": "\\(L\\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture", "description": "\\(L\\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G42", "originalCode": "11G42", "name": "Arithmetic mirror symmetry", "description": "Arithmetic mirror symmetry [See also 14J33]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G45", "originalCode": "11G45", "name": "Geometric class field theory", "description": "Geometric class field theory [See also 11R37, 14C35, 19F05]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G50", "originalCode": "11G50", "name": "Heights", "description": "Heights [See also 14G40, 37P30]", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G55", "originalCode": "11G55", "name": "Polylogarithms and relations with \\(K\\)-theory", "description": "Polylogarithms and relations with \\(K\\)-theory", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11G99", "originalCode": "11G99", "name": "Arithmetic algebraic geometry (Diophantine geometry)", "description": "None of the above, but in this section", "kind": "subject", "parent": "11G", "page": 21 }, { "code": "11H", "originalCode": "11Hxx", "name": "Geometry of numbers", "description": "Geometry of numbers \\{For applications in coding theory, see 94B75\\}", "kind": "section", "parent": "11", "page": 22 }, { "code": "11H06", "originalCode": "11H06", "name": "Lattices and convex bodies (number-theoretic aspects)", "description": "Lattices and convex bodies (number-theoretic aspects) [See also 11P21, 52C05, 52C07]", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H16", "originalCode": "11H16", "name": "Nonconvex bodies", "description": "Nonconvex bodies", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H31", "originalCode": "11H31", "name": "Lattice packing and covering (number-theoretic aspects)", "description": "Lattice packing and covering (number-theoretic aspects) [See also 05B40, 52C15, 52C17]", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H46", "originalCode": "11H46", "name": "Products of linear forms", "description": "Products of linear forms", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H50", "originalCode": "11H50", "name": "Minima of forms", "description": "Minima of forms", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H55", "originalCode": "11H55", "name": "Quadratic forms (reduction theory, extreme forms, etc.)", "description": "Quadratic forms (reduction theory, extreme forms, etc.)", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H56", "originalCode": "11H56", "name": "Automorphism groups of lattices", "description": "Automorphism groups of lattices", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H60", "originalCode": "11H60", "name": "Mean value and transfer theorems", "description": "Mean value and transfer theorems", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H71", "originalCode": "11H71", "name": "Relations with coding theory", "description": "Relations with coding theory", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11H99", "originalCode": "11H99", "name": "Geometry of numbers", "description": "None of the above, but in this section", "kind": "subject", "parent": "11H", "page": 22 }, { "code": "11J", "originalCode": "11Jxx", "name": "Diophantine approximation, transcendental number theory", "description": "Diophantine approximation, transcendental number theory [See also 11K60]", "kind": "section", "parent": "11", "page": 22 }, { "code": "11J04", "originalCode": "11J04", "name": "Homogeneous approximation to one number", "description": "Homogeneous approximation to one number", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J06", "originalCode": "11J06", "name": "Markov and Lagrange spectra and generalizations", "description": "Markov and Lagrange spectra and generalizations", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J13", "originalCode": "11J13", "name": "Simultaneous homogeneous approximation, linear forms", "description": "Simultaneous homogeneous approximation, linear forms", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J17", "originalCode": "11J17", "name": "Approximation by numbers from a fixed field", "description": "Approximation by numbers from a fixed field", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J20", "originalCode": "11J20", "name": "Inhomogeneous linear forms", "description": "Inhomogeneous linear forms", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J25", "originalCode": "11J25", "name": "Diophantine inequalities", "description": "Diophantine inequalities [See also 11D75]", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J54", "originalCode": "11J54", "name": "Small fractional parts of polynomials and generalizations", "description": "Small fractional parts of polynomials and generalizations", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J61", "originalCode": "11J61", "name": "Approximation in non-Archimedean valuations", "description": "Approximation in non-Archimedean valuations", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J68", "originalCode": "11J68", "name": "Approximation to algebraic numbers", "description": "Approximation to algebraic numbers", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J70", "originalCode": "11J70", "name": "Continued fractions and generalizations", "description": "Continued fractions and generalizations [See also 11A55, 11K50]", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J71", "originalCode": "11J71", "name": "Distribution modulo one", "description": "Distribution modulo one [See also 11K06]", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J72", "originalCode": "11J72", "name": "Irrationality; linear independence over a field", "description": "Irrationality; linear independence over a field", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J81", "originalCode": "11J81", "name": "Transcendence (general theory)", "description": "Transcendence (general theory)", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J82", "originalCode": "11J82", "name": "Measures of irrationality and of transcendence", "description": "Measures of irrationality and of transcendence", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J83", "originalCode": "11J83", "name": "Metric theory", "description": "Metric theory", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J85", "originalCode": "11J85", "name": "Algebraic independence; Gel'fond's method", "description": "Algebraic independence; Gel'fond's method", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J86", "originalCode": "11J86", "name": "Linear forms in logarithms; Baker's method", "description": "Linear forms in logarithms; Baker's method", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J87", "originalCode": "11J87", "name": "Schmidt Subspace Theorem and applications", "description": "Schmidt Subspace Theorem and applications", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J89", "originalCode": "11J89", "name": "Transcendence theory of elliptic and abelian functions", "description": "Transcendence theory of elliptic and abelian functions", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J91", "originalCode": "11J91", "name": "Transcendence theory of other special functions", "description": "Transcendence theory of other special functions", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J93", "originalCode": "11J93", "name": "Transcendence theory of Drinfel'd and \\(t\\)-modules", "description": "Transcendence theory of Drinfel'd and \\(t\\)-modules", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J95", "originalCode": "11J95", "name": "Results involving abelian varieties", "description": "Results involving abelian varieties", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J97", "originalCode": "11J97", "name": "Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.)", "description": "Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.)", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11J99", "originalCode": "11J99", "name": "Diophantine approximation, transcendental number theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "11J", "page": 22 }, { "code": "11K", "originalCode": "11Kxx", "name": "Probabilistic theory: distribution modulo \\(1\\); metric theory of algorithms", "description": "Probabilistic theory: distribution modulo \\(1\\); metric theory of algorithms", "kind": "section", "parent": "11", "page": 23 }, { "code": "11K06", "originalCode": "11K06", "name": "General theory of distribution modulo \\(1\\)", "description": "General theory of distribution modulo \\(1\\) [See also 11J71]", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K16", "originalCode": "11K16", "name": "Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.", "description": "Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K31", "originalCode": "11K31", "name": "Special sequences", "description": "Special sequences", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K36", "originalCode": "11K36", "name": "Well-distributed sequences and other variations", "description": "Well-distributed sequences and other variations", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K38", "originalCode": "11K38", "name": "Irregularities of distribution, discrepancy", "description": "Irregularities of distribution, discrepancy [See also 11Nxx]", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K41", "originalCode": "11K41", "name": "Continuous, \\(p\\)-adic and abstract analogues", "description": "Continuous, \\(p\\)-adic and abstract analogues", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K45", "originalCode": "11K45", "name": "Pseudo-random numbers; Monte Carlo methods", "description": "Pseudo-random numbers; Monte Carlo methods [See also 65C05, 65C10]", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K50", "originalCode": "11K50", "name": "Metric theory of continued fractions", "description": "Metric theory of continued fractions [See also 11A55, 11J70]", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K55", "originalCode": "11K55", "name": "Metric theory of other algorithms and expansions; measure and Hausdorff dimension", "description": "Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K60", "originalCode": "11K60", "name": "Diophantine approximation in probabilistic number theory", "description": "Diophantine approximation in probabilistic number theory [See also 11Jxx]", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K65", "originalCode": "11K65", "name": "Arithmetic functions in probabilistic number theory", "description": "Arithmetic functions in probabilistic number theory [See also 11Nxx]", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K70", "originalCode": "11K70", "name": "Harmonic analysis and almost periodicity in probabilistic number theory", "description": "Harmonic analysis and almost periodicity in probabilistic number theory", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11K99", "originalCode": "11K99", "name": "Probabilistic theory: distribution modulo \\(1\\); metric theory of algorithms", "description": "None of the above, but in this section", "kind": "subject", "parent": "11K", "page": 23 }, { "code": "11L", "originalCode": "11Lxx", "name": "Exponential sums and character sums", "description": "Exponential sums and character sums \\{For finite fields, see~11Txx\\}", "kind": "section", "parent": "11", "page": 23 }, { "code": "11L03", "originalCode": "11L03", "name": "Trigonometric and exponential sums (general theory)", "description": "Trigonometric and exponential sums (general theory)", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11L05", "originalCode": "11L05", "name": "Gauss and Kloosterman sums; generalizations", "description": "Gauss and Kloosterman sums; generalizations", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11L07", "originalCode": "11L07", "name": "Estimates on exponential sums", "description": "Estimates on exponential sums", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11L10", "originalCode": "11L10", "name": "Jacobsthal and Brewer sums; other complete character sums", "description": "Jacobsthal and Brewer sums; other complete character sums", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11L15", "originalCode": "11L15", "name": "Weyl sums", "description": "Weyl sums", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11L20", "originalCode": "11L20", "name": "Sums over primes", "description": "Sums over primes", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11L26", "originalCode": "11L26", "name": "Sums over arbitrary intervals", "description": "Sums over arbitrary intervals", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11L40", "originalCode": "11L40", "name": "Estimates on character sums", "description": "Estimates on character sums", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11L99", "originalCode": "11L99", "name": "Exponential sums and character sums", "description": "None of the above, but in this section", "kind": "subject", "parent": "11L", "page": 23 }, { "code": "11M", "originalCode": "11Mxx", "name": "Zeta and \\(L\\)-functions: analytic theory", "description": "Zeta and \\(L\\)-functions: analytic theory", "kind": "section", "parent": "11", "page": 23 }, { "code": "11M06", "originalCode": "11M06", "name": "\\(\\zeta (s)\\) and \\(L(s, \\chi)\\)", "description": "\\(\\zeta (s)\\) and \\(L(s, \\chi)\\)", "kind": "subject", "parent": "11M", "page": 23 }, { "code": "11M20", "originalCode": "11M20", "name": "Real zeros of \\(L(s, \\chi)\\); results on \\(L(1, \\chi)\\)", "description": "Real zeros of \\(L(s, \\chi)\\); results on \\(L(1, \\chi)\\)", "kind": "subject", "parent": "11M", "page": 23 }, { "code": "11M26", "originalCode": "11M26", "name": "Nonreal zeros of \\(\\zeta (s)\\) and \\(L(s, \\chi)\\); Riemann and other hypotheses", "description": "Nonreal zeros of \\(\\zeta (s)\\) and \\(L(s, \\chi)\\); Riemann and other hypotheses", "kind": "subject", "parent": "11M", "page": 23 }, { "code": "11M32", "originalCode": "11M32", "name": "Multiple Dirichlet series and zeta functions and multizeta values", "description": "Multiple Dirichlet series and zeta functions and multizeta values", "kind": "subject", "parent": "11M", "page": 23 }, { "code": "11M35", "originalCode": "11M35", "name": "Hurwitz and Lerch zeta functions", "description": "Hurwitz and Lerch zeta functions", "kind": "subject", "parent": "11M", "page": 23 }, { "code": "11M36", "originalCode": "11M36", "name": "Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)", "description": "Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)", "kind": "subject", "parent": "11M", "page": 23 }, { "code": "11M38", "originalCode": "11M38", "name": "Zeta and \\(L\\)-functions in characteristic \\(p\\)", "description": "Zeta and \\(L\\)-functions in characteristic \\(p\\)", "kind": "subject", "parent": "11M", "page": 23 }, { "code": "11M41", "originalCode": "11M41", "name": "Other Dirichlet series and zeta functions", "description": "Other Dirichlet series and zeta functions \\{For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10\\} [See also 11E45, 11F66, 11F70, 11F72]", "kind": "subject", "parent": "11M", "page": 24 }, { "code": "11M45", "originalCode": "11M45", "name": "Tauberian theorems", "description": "Tauberian theorems [See also 40E05]", "kind": "subject", "parent": "11M", "page": 24 }, { "code": "11M50", "originalCode": "11M50", "name": "Relations with random matrices", "description": "Relations with random matrices", "kind": "subject", "parent": "11M", "page": 24 }, { "code": "11M55", "originalCode": "11M55", "name": "Relations with noncommutative geometry", "description": "Relations with noncommutative geometry", "kind": "subject", "parent": "11M", "page": 24 }, { "code": "11M99", "originalCode": "11M99", "name": "Zeta and \\(L\\)-functions: analytic theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "11M", "page": 24 }, { "code": "11N", "originalCode": "11Nxx", "name": "Multiplicative number theory", "description": "Multiplicative number theory", "kind": "section", "parent": "11", "page": 24 }, { "code": "11N05", "originalCode": "11N05", "name": "Distribution of primes", "description": "Distribution of primes", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N13", "originalCode": "11N13", "name": "Primes in congruence classes", "description": "Primes in congruence classes", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N25", "originalCode": "11N25", "name": "Distribution of integers with specified multiplicative constraints", "description": "Distribution of integers with specified multiplicative constraints", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N30", "originalCode": "11N30", "name": "Turán theory", "description": "Turán theory [See also 30Bxx]", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N32", "originalCode": "11N32", "name": "Primes represented by polynomials; other multiplicative structures of polynomial values", "description": "Primes represented by polynomials; other multiplicative structures of polynomial values", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N35", "originalCode": "11N35", "name": "Sieves", "description": "Sieves", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N36", "originalCode": "11N36", "name": "Applications of sieve methods", "description": "Applications of sieve methods", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N37", "originalCode": "11N37", "name": "Asymptotic results on arithmetic functions", "description": "Asymptotic results on arithmetic functions", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N45", "originalCode": "11N45", "name": "Asymptotic results on counting functions for algebraic and topological structures", "description": "Asymptotic results on counting functions for algebraic and topological structures", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N56", "originalCode": "11N56", "name": "Rate of growth of arithmetic functions", "description": "Rate of growth of arithmetic functions", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N60", "originalCode": "11N60", "name": "Distribution functions associated with additive and positive multiplicative functions", "description": "Distribution functions associated with additive and positive multiplicative functions", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N64", "originalCode": "11N64", "name": "Other results on the distribution of values or the characterization of arithmetic functions", "description": "Other results on the distribution of values or the characterization of arithmetic functions", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N69", "originalCode": "11N69", "name": "Distribution of integers in special residue classes", "description": "Distribution of integers in special residue classes", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N75", "originalCode": "11N75", "name": "Applications of automorphic functions and forms to multiplicative problems", "description": "Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N80", "originalCode": "11N80", "name": "Generalized primes and integers", "description": "Generalized primes and integers", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11N99", "originalCode": "11N99", "name": "Multiplicative number theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "11N", "page": 24 }, { "code": "11P", "originalCode": "11Pxx", "name": "Additive number theory; partitions", "description": "Additive number theory; partitions", "kind": "section", "parent": "11", "page": 24 }, { "code": "11P05", "originalCode": "11P05", "name": "Waring's problem and variants", "description": "Waring's problem and variants", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P21", "originalCode": "11P21", "name": "Lattice points in specified regions", "description": "Lattice points in specified regions", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P32", "originalCode": "11P32", "name": "Goldbach-type theorems; other additive questions involving primes", "description": "Goldbach-type theorems; other additive questions involving primes", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P55", "originalCode": "11P55", "name": "Applications of the Hardy-Littlewood method", "description": "Applications of the Hardy-Littlewood method [See also 11D85]", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P70", "originalCode": "11P70", "name": "Inverse problems of additive number theory, including sumsets", "description": "Inverse problems of additive number theory, including sumsets", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P81", "originalCode": "11P81", "name": "Elementary theory of partitions", "description": "Elementary theory of partitions [See also 05A17]", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P82", "originalCode": "11P82", "name": "Analytic theory of partitions", "description": "Analytic theory of partitions", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P83", "originalCode": "11P83", "name": "Partitions; congruences and congruential restrictions", "description": "Partitions; congruences and congruential restrictions", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P84", "originalCode": "11P84", "name": "Partition identities; identities of Rogers-Ramanujan type", "description": "Partition identities; identities of Rogers-Ramanujan type", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11P99", "originalCode": "11P99", "name": "Additive number theory; partitions", "description": "None of the above, but in this section", "kind": "subject", "parent": "11P", "page": 24 }, { "code": "11R", "originalCode": "11Rxx", "name": "Algebraic number theory: global fields", "description": "Algebraic number theory: global fields \\{For complex multiplication, see 11G15\\}", "kind": "section", "parent": "11", "page": 25 }, { "code": "11R04", "originalCode": "11R04", "name": "Algebraic numbers; rings of algebraic integers", "description": "Algebraic numbers; rings of algebraic integers", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R06", "originalCode": "11R06", "name": "PV-numbers and generalizations; other special algebraic numbers; Mahler measure", "description": "PV-numbers and generalizations; other special algebraic numbers; Mahler measure", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R09", "originalCode": "11R09", "name": "Polynomials (irreducibility, etc.)", "description": "Polynomials (irreducibility, etc.)", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R11", "originalCode": "11R11", "name": "Quadratic extensions", "description": "Quadratic extensions", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R16", "originalCode": "11R16", "name": "Cubic and quartic extensions", "description": "Cubic and quartic extensions", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R18", "originalCode": "11R18", "name": "Cyclotomic extensions", "description": "Cyclotomic extensions", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R20", "originalCode": "11R20", "name": "Other abelian and metabelian extensions", "description": "Other abelian and metabelian extensions", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R21", "originalCode": "11R21", "name": "Other number fields", "description": "Other number fields", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R23", "originalCode": "11R23", "name": "Iwasawa theory", "description": "Iwasawa theory", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R27", "originalCode": "11R27", "name": "Units and factorization", "description": "Units and factorization", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R29", "originalCode": "11R29", "name": "Class numbers, class groups, discriminants", "description": "Class numbers, class groups, discriminants", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R32", "originalCode": "11R32", "name": "Galois theory", "description": "Galois theory", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R33", "originalCode": "11R33", "name": "Integral representations related to algebraic numbers; Galois module structure of rings of integers", "description": "Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R34", "originalCode": "11R34", "name": "Galois cohomology", "description": "Galois cohomology [See also 12Gxx, 19F05]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R37", "originalCode": "11R37", "name": "Class field theory", "description": "Class field theory", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R39", "originalCode": "11R39", "name": "Langlands-Weil conjectures, nonabelian class field theory", "description": "Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R42", "originalCode": "11R42", "name": "Zeta functions and \\(L\\)-functions of number fields", "description": "Zeta functions and \\(L\\)-functions of number fields [See also 11M41, 19F27]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R44", "originalCode": "11R44", "name": "Distribution of prime ideals", "description": "Distribution of prime ideals [See also 11N05]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R45", "originalCode": "11R45", "name": "Density theorems", "description": "Density theorems", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R47", "originalCode": "11R47", "name": "Other analytic theory", "description": "Other analytic theory [See also 11Nxx]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R52", "originalCode": "11R52", "name": "Quaternion and other division algebras: arithmetic, zeta functions", "description": "Quaternion and other division algebras: arithmetic, zeta functions", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R54", "originalCode": "11R54", "name": "Other algebras and orders, and their zeta and \\(L\\)-functions", "description": "Other algebras and orders, and their zeta and \\(L\\)-functions [See also 11S45, 16Hxx]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R56", "originalCode": "11R56", "name": "Adèle rings and groups", "description": "Adèle rings and groups", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R58", "originalCode": "11R58", "name": "Arithmetic theory of algebraic function fields", "description": "Arithmetic theory of algebraic function fields [See also 14Gxx, 14H05]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R59", "originalCode": "11R59", "name": "Zeta functions and \\(L\\)-functions of function fields", "description": "Zeta functions and \\(L\\)-functions of function fields", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R60", "originalCode": "11R60", "name": "Cyclotomic function fields (class groups, Bernoulli objects, etc.)", "description": "Cyclotomic function fields (class groups, Bernoulli objects, etc.)", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R65", "originalCode": "11R65", "name": "Class groups and Picard groups of orders", "description": "Class groups and Picard groups of orders", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R70", "originalCode": "11R70", "name": "\\(K\\)-theory of global fields", "description": "\\(K\\)-theory of global fields [See also 19Fxx]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R80", "originalCode": "11R80", "name": "Totally real fields", "description": "Totally real fields [See also 12J15]", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11R99", "originalCode": "11R99", "name": "Algebraic number theory: global fields", "description": "None of the above, but in this section", "kind": "subject", "parent": "11R", "page": 25 }, { "code": "11S", "originalCode": "11Sxx", "name": "Algebraic number theory: local fields", "description": "Algebraic number theory: local fields", "kind": "section", "parent": "11", "page": 26 }, { "code": "11S05", "originalCode": "11S05", "name": "Polynomials", "description": "Polynomials", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S15", "originalCode": "11S15", "name": "Ramification and extension theory", "description": "Ramification and extension theory", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S20", "originalCode": "11S20", "name": "Galois theory", "description": "Galois theory", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S23", "originalCode": "11S23", "name": "Integral representations", "description": "Integral representations", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S25", "originalCode": "11S25", "name": "Galois cohomology", "description": "Galois cohomology [See also 12Gxx, 16H05]", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S31", "originalCode": "11S31", "name": "Class field theory; \\(p\\)-adic formal groups", "description": "Class field theory; \\(p\\)-adic formal groups [See also 14L05]", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S37", "originalCode": "11S37", "name": "Langlands-Weil conjectures, nonabelian class field theory", "description": "Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S40", "originalCode": "11S40", "name": "Zeta functions and \\(L\\)-functions", "description": "Zeta functions and \\(L\\)-functions [See also 11M41, 19F27]", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S45", "originalCode": "11S45", "name": "Algebras and orders, and their zeta functions", "description": "Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16Hxx, 16Kxx]", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S70", "originalCode": "11S70", "name": "\\(K\\)-theory of local fields", "description": "\\(K\\)-theory of local fields [See also 19Fxx]", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S80", "originalCode": "11S80", "name": "Other analytic theory (analogues of beta and gamma functions, \\(p\\)-adic integration, etc.)", "description": "Other analytic theory (analogues of beta and gamma functions, \\(p\\)-adic integration, etc.)", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S82", "originalCode": "11S82", "name": "Non-Archimedean dynamical systems", "description": "Non-Archimedean dynamical systems [See mainly 37Pxx]", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S85", "originalCode": "11S85", "name": "Other nonanalytic theory", "description": "Other nonanalytic theory", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S90", "originalCode": "11S90", "name": "Prehomogeneous vector spaces", "description": "Prehomogeneous vector spaces", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11S99", "originalCode": "11S99", "name": "Algebraic number theory: local fields", "description": "None of the above, but in this section", "kind": "subject", "parent": "11S", "page": 26 }, { "code": "11T", "originalCode": "11Txx", "name": "Finite fields and commutative rings (number-theoretic aspects)", "description": "Finite fields and commutative rings (number-theoretic aspects)", "kind": "section", "parent": "11", "page": 26 }, { "code": "11T06", "originalCode": "11T06", "name": "Polynomials over finite fields", "description": "Polynomials over finite fields", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11T22", "originalCode": "11T22", "name": "Cyclotomy", "description": "Cyclotomy", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11T23", "originalCode": "11T23", "name": "Exponential sums", "description": "Exponential sums", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11T24", "originalCode": "11T24", "name": "Other character sums and Gauss sums", "description": "Other character sums and Gauss sums", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11T30", "originalCode": "11T30", "name": "Structure theory for finite fields and commutative rings (number-theoretic aspects)", "description": "Structure theory for finite fields and commutative rings (number-theoretic aspects)", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11T55", "originalCode": "11T55", "name": "Arithmetic theory of polynomial rings over finite fields", "description": "Arithmetic theory of polynomial rings over finite fields", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11T60", "originalCode": "11T60", "name": "Finite upper half-planes", "description": "Finite upper half-planes", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11T71", "originalCode": "11T71", "name": "Algebraic coding theory; cryptography (number-theoretic aspects)", "description": "Algebraic coding theory; cryptography (number-theoretic aspects)", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11T99", "originalCode": "11T99", "name": "Finite fields and commutative rings (number-theoretic aspects)", "description": "None of the above, but in this section", "kind": "subject", "parent": "11T", "page": 26 }, { "code": "11U", "originalCode": "11Uxx", "name": "Connections of number theory and logic", "description": "Connections of number theory and logic", "kind": "section", "parent": "11", "page": 26 }, { "code": "11U05", "originalCode": "11U05", "name": "Decidability (number-theoretic aspects)", "description": "Decidability (number-theoretic aspects) [See also 03B25]", "kind": "subject", "parent": "11U", "page": 26 }, { "code": "11U07", "originalCode": "11U07", "name": "Ultraproducts (number-theoretic aspects)", "description": "Ultraproducts (number-theoretic aspects) [See also 03C20]", "kind": "subject", "parent": "11U", "page": 26 }, { "code": "11U09", "originalCode": "11U09", "name": "Model theory (number-theoretic aspects)", "description": "Model theory (number-theoretic aspects) [See also 03Cxx]", "kind": "subject", "parent": "11U", "page": 26 }, { "code": "11U10", "originalCode": "11U10", "name": "Nonstandard arithmetic (number-theoretic aspects)", "description": "Nonstandard arithmetic (number-theoretic aspects) [See also 03H15]", "kind": "subject", "parent": "11U", "page": 26 }, { "code": "11U99", "originalCode": "11U99", "name": "Connections of number theory and logic", "description": "None of the above, but in this section", "kind": "subject", "parent": "11U", "page": 26 }, { "code": "11Y", "originalCode": "11Yxx", "name": "Computational number theory", "description": "Computational number theory \\{For software etc., see~11-04\\} [See also 68W30]", "kind": "section", "parent": "11", "page": 27 }, { "code": "11Y05", "originalCode": "11Y05", "name": "Factorization", "description": "Factorization", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y11", "originalCode": "11Y11", "name": "Primality", "description": "Primality", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y16", "originalCode": "11Y16", "name": "Number-theoretic algorithms; complexity", "description": "Number-theoretic algorithms; complexity [See also 68Q25]", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y35", "originalCode": "11Y35", "name": "Analytic computations", "description": "Analytic computations", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y40", "originalCode": "11Y40", "name": "Algebraic number theory computations", "description": "Algebraic number theory computations", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y50", "originalCode": "11Y50", "name": "Computer solution of Diophantine equations", "description": "Computer solution of Diophantine equations", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y55", "originalCode": "11Y55", "name": "Calculation of integer sequences", "description": "Calculation of integer sequences", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y60", "originalCode": "11Y60", "name": "Evaluation of number-theoretic constants", "description": "Evaluation of number-theoretic constants", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y65", "originalCode": "11Y65", "name": "Continued fraction calculations (number-theoretic aspects)", "description": "Continued fraction calculations (number-theoretic aspects)", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y70", "originalCode": "11Y70", "name": "Values of arithmetic functions; tables", "description": "Values of arithmetic functions; tables", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Y99", "originalCode": "11Y99", "name": "Computational number theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "11Y", "page": 27 }, { "code": "11Z", "originalCode": "11Zxx", "name": "Miscellaneous applications of number theory", "description": "Miscellaneous applications of number theory", "kind": "section", "parent": "11", "page": 27 }, { "code": "11Z05", "originalCode": "11Z05", "name": "Miscellaneous applications of number theory", "description": "Miscellaneous applications of number theory", "kind": "subject", "parent": "11Z", "page": 27 }, { "code": "11Z99", "originalCode": "11Z99", "name": "Miscellaneous applications of number theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "11Z", "page": 27 }, { "code": "12", "originalCode": "12-XX", "name": "Field theory and polynomials", "description": "Field theory and polynomials", "kind": "class", "parent": null, "page": 27 }, { "code": "12-00", "originalCode": "12-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory", "kind": "subject", "parent": "12", "page": 27 }, { "code": "12-01", "originalCode": "12-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory", "kind": "subject", "parent": "12", "page": 27 }, { "code": "12-02", "originalCode": "12-02", "name": "Research exposition (monographs, survey articles) pertaining to field theory", "description": "Research exposition (monographs, survey articles) pertaining to field theory", "kind": "subject", "parent": "12", "page": 27 }, { "code": "12-03", "originalCode": "12-03", "name": "History of field theory", "description": "History of field theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "12", "page": 27 }, { "code": "12-04", "originalCode": "12-04", "name": "Software, source code, etc. for problems pertaining to field theory", "description": "Software, source code, etc. for problems pertaining to field theory", "kind": "subject", "parent": "12", "page": 27 }, { "code": "12-06", "originalCode": "12-06", "name": "Proceedings, conferences, collections, etc. pertaining to field theory", "description": "Proceedings, conferences, collections, etc. pertaining to field theory", "kind": "subject", "parent": "12", "page": 27 }, { "code": "12-08", "originalCode": "12-08", "name": "Computational methods for problems pertaining to field theory", "description": "Computational methods for problems pertaining to field theory [See also 68W30]", "kind": "subject", "parent": "12", "page": 27 }, { "code": "12-11", "originalCode": "12-11", "name": "Research data for problems pertaining to field theory", "description": "Research data for problems pertaining to field theory", "kind": "subject", "parent": "12", "page": 27 }, { "code": "12D", "originalCode": "12Dxx", "name": "Real and complex fields", "description": "Real and complex fields", "kind": "section", "parent": "12", "page": 27 }, { "code": "12D05", "originalCode": "12D05", "name": "Polynomials in real and complex fields: factorization", "description": "Polynomials in real and complex fields: factorization", "kind": "subject", "parent": "12D", "page": 27 }, { "code": "12D10", "originalCode": "12D10", "name": "Polynomials in real and complex fields: location of zeros (algebraic theorems)", "description": "Polynomials in real and complex fields: location of zeros (algebraic theorems) \\{For the analytic theory, see 26C10, 30C15\\}", "kind": "subject", "parent": "12D", "page": 27 }, { "code": "12D15", "originalCode": "12D15", "name": "Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)", "description": "Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]", "kind": "subject", "parent": "12D", "page": 27 }, { "code": "12D99", "originalCode": "12D99", "name": "Real and complex fields", "description": "None of the above, but in this section", "kind": "subject", "parent": "12D", "page": 27 }, { "code": "12E", "originalCode": "12Exx", "name": "General field theory", "description": "General field theory", "kind": "section", "parent": "12", "page": 28 }, { "code": "12E05", "originalCode": "12E05", "name": "Polynomials in general fields (irreducibility, etc.)", "description": "Polynomials in general fields (irreducibility, etc.)", "kind": "subject", "parent": "12E", "page": 28 }, { "code": "12E10", "originalCode": "12E10", "name": "Special polynomials in general fields", "description": "Special polynomials in general fields", "kind": "subject", "parent": "12E", "page": 28 }, { "code": "12E12", "originalCode": "12E12", "name": "Equations in general fields", "description": "Equations in general fields", "kind": "subject", "parent": "12E", "page": 28 }, { "code": "12E15", "originalCode": "12E15", "name": "Skew fields, division rings", "description": "Skew fields, division rings [See also 11R52, 16Kxx]", "kind": "subject", "parent": "12E", "page": 28 }, { "code": "12E20", "originalCode": "12E20", "name": "Finite fields (field-theoretic aspects)", "description": "Finite fields (field-theoretic aspects)", "kind": "subject", "parent": "12E", "page": 28 }, { "code": "12E25", "originalCode": "12E25", "name": "Hilbertian fields; Hilbert's irreducibility theorem", "description": "Hilbertian fields; Hilbert's irreducibility theorem", "kind": "subject", "parent": "12E", "page": 28 }, { "code": "12E30", "originalCode": "12E30", "name": "Field arithmetic", "description": "Field arithmetic", "kind": "subject", "parent": "12E", "page": 28 }, { "code": "12E99", "originalCode": "12E99", "name": "General field theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "12E", "page": 28 }, { "code": "12F", "originalCode": "12Fxx", "name": "Field extensions", "description": "Field extensions", "kind": "section", "parent": "12", "page": 28 }, { "code": "12F05", "originalCode": "12F05", "name": "Algebraic field extensions", "description": "Algebraic field extensions", "kind": "subject", "parent": "12F", "page": 28 }, { "code": "12F10", "originalCode": "12F10", "name": "Separable extensions, Galois theory", "description": "Separable extensions, Galois theory", "kind": "subject", "parent": "12F", "page": 28 }, { "code": "12F12", "originalCode": "12F12", "name": "Inverse Galois theory", "description": "Inverse Galois theory", "kind": "subject", "parent": "12F", "page": 28 }, { "code": "12F15", "originalCode": "12F15", "name": "Inseparable field extensions", "description": "Inseparable field extensions", "kind": "subject", "parent": "12F", "page": 28 }, { "code": "12F20", "originalCode": "12F20", "name": "Transcendental field extensions", "description": "Transcendental field extensions", "kind": "subject", "parent": "12F", "page": 28 }, { "code": "12F99", "originalCode": "12F99", "name": "Field extensions", "description": "None of the above, but in this section", "kind": "subject", "parent": "12F", "page": 28 }, { "code": "12G", "originalCode": "12Gxx", "name": "Homological methods (field theory)", "description": "Homological methods (field theory)", "kind": "section", "parent": "12", "page": 28 }, { "code": "12G05", "originalCode": "12G05", "name": "Galois cohomology", "description": "Galois cohomology [See also 14F22, 16H05, 16K50]", "kind": "subject", "parent": "12G", "page": 28 }, { "code": "12G10", "originalCode": "12G10", "name": "Cohomological dimension of fields", "description": "Cohomological dimension of fields", "kind": "subject", "parent": "12G", "page": 28 }, { "code": "12G99", "originalCode": "12G99", "name": "Homological methods (field theory)", "description": "None of the above, but in this section", "kind": "subject", "parent": "12G", "page": 28 }, { "code": "12H", "originalCode": "12Hxx", "name": "Differential and difference algebra", "description": "Differential and difference algebra", "kind": "section", "parent": "12", "page": 28 }, { "code": "12H05", "originalCode": "12H05", "name": "Differential algebra", "description": "Differential algebra [See also 13Nxx]", "kind": "subject", "parent": "12H", "page": 28 }, { "code": "12H10", "originalCode": "12H10", "name": "Difference algebra", "description": "Difference algebra [See also 39Axx]", "kind": "subject", "parent": "12H", "page": 28 }, { "code": "12H20", "originalCode": "12H20", "name": "Abstract differential equations", "description": "Abstract differential equations [See also 34Mxx]", "kind": "subject", "parent": "12H", "page": 28 }, { "code": "12H25", "originalCode": "12H25", "name": "\\(p\\)-adic differential equations", "description": "\\(p\\)-adic differential equations [See also 11S80, 14G20]", "kind": "subject", "parent": "12H", "page": 28 }, { "code": "12H99", "originalCode": "12H99", "name": "Differential and difference algebra", "description": "None of the above, but in this section", "kind": "subject", "parent": "12H", "page": 28 }, { "code": "12J", "originalCode": "12Jxx", "name": "Topological fields", "description": "Topological fields", "kind": "section", "parent": "12", "page": 29 }, { "code": "12J05", "originalCode": "12J05", "name": "Normed fields", "description": "Normed fields", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12J10", "originalCode": "12J10", "name": "Valued fields", "description": "Valued fields", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12J12", "originalCode": "12J12", "name": "Formally \\(p\\)-adic fields", "description": "Formally \\(p\\)-adic fields", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12J15", "originalCode": "12J15", "name": "Ordered fields", "description": "Ordered fields", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12J17", "originalCode": "12J17", "name": "Topological semifields", "description": "Topological semifields", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12J20", "originalCode": "12J20", "name": "General valuation theory for fields", "description": "General valuation theory for fields [See also 13A18]", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12J25", "originalCode": "12J25", "name": "Non-Archimedean valued fields", "description": "Non-Archimedean valued fields [See also 30G06, 46S10]", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12J27", "originalCode": "12J27", "name": "Krasner-Tate algebras", "description": "Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12J99", "originalCode": "12J99", "name": "Topological fields", "description": "None of the above, but in this section", "kind": "subject", "parent": "12J", "page": 29 }, { "code": "12K", "originalCode": "12Kxx", "name": "Generalizations of fields", "description": "Generalizations of fields", "kind": "section", "parent": "12", "page": 29 }, { "code": "12K05", "originalCode": "12K05", "name": "Near-fields", "description": "Near-fields [See also 16Y30]", "kind": "subject", "parent": "12K", "page": 29 }, { "code": "12K10", "originalCode": "12K10", "name": "Semifields", "description": "Semifields [See also 16Y60]", "kind": "subject", "parent": "12K", "page": 29 }, { "code": "12K99", "originalCode": "12K99", "name": "Generalizations of fields", "description": "None of the above, but in this section", "kind": "subject", "parent": "12K", "page": 29 }, { "code": "12L", "originalCode": "12Lxx", "name": "Connections between field theory and logic", "description": "Connections between field theory and logic", "kind": "section", "parent": "12", "page": 29 }, { "code": "12L05", "originalCode": "12L05", "name": "Decidability and field theory", "description": "Decidability and field theory [See also 03B25]", "kind": "subject", "parent": "12L", "page": 29 }, { "code": "12L10", "originalCode": "12L10", "name": "Ultraproducts and field theory", "description": "Ultraproducts and field theory [See also 03C20]", "kind": "subject", "parent": "12L", "page": 29 }, { "code": "12L12", "originalCode": "12L12", "name": "Model theory of fields", "description": "Model theory of fields [See also 03C60]", "kind": "subject", "parent": "12L", "page": 29 }, { "code": "12L15", "originalCode": "12L15", "name": "Nonstandard arithmetic and field theory", "description": "Nonstandard arithmetic and field theory [See also 03H15]", "kind": "subject", "parent": "12L", "page": 29 }, { "code": "12L99", "originalCode": "12L99", "name": "Connections between field theory and logic", "description": "None of the above, but in this section", "kind": "subject", "parent": "12L", "page": 29 }, { "code": "13", "originalCode": "13-XX", "name": "Commutative algebra", "description": "Commutative algebra", "kind": "class", "parent": null, "page": 29 }, { "code": "13-00", "originalCode": "13-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra", "kind": "subject", "parent": "13", "page": 29 }, { "code": "13-01", "originalCode": "13-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra", "kind": "subject", "parent": "13", "page": 29 }, { "code": "13-02", "originalCode": "13-02", "name": "Research exposition (monographs, survey articles) pertaining to commutative algebra", "description": "Research exposition (monographs, survey articles) pertaining to commutative algebra", "kind": "subject", "parent": "13", "page": 29 }, { "code": "13-03", "originalCode": "13-03", "name": "History of commutative algebra", "description": "History of commutative algebra [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "13", "page": 29 }, { "code": "13-04", "originalCode": "13-04", "name": "Software, source code, etc. for problems pertaining to commutative algebra", "description": "Software, source code, etc. for problems pertaining to commutative algebra", "kind": "subject", "parent": "13", "page": 29 }, { "code": "13-06", "originalCode": "13-06", "name": "Proceedings, conferences, collections, etc. pertaining to commutative algebra", "description": "Proceedings, conferences, collections, etc. pertaining to commutative algebra", "kind": "subject", "parent": "13", "page": 29 }, { "code": "13-11", "originalCode": "13-11", "name": "Research data for problems pertaining to commutative algebra", "description": "Research data for problems pertaining to commutative algebra", "kind": "subject", "parent": "13", "page": 29 }, { "code": "13A", "originalCode": "13Axx", "name": "General commutative ring theory", "description": "General commutative ring theory", "kind": "section", "parent": "13", "page": 30 }, { "code": "13A02", "originalCode": "13A02", "name": "Graded rings", "description": "Graded rings [See also 16W50]", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13A05", "originalCode": "13A05", "name": "Divisibility and factorizations in commutative rings", "description": "Divisibility and factorizations in commutative rings [See also 13F15]", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13A15", "originalCode": "13A15", "name": "Ideals and multiplicative ideal theory in commutative rings", "description": "Ideals and multiplicative ideal theory in commutative rings", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13A18", "originalCode": "13A18", "name": "Valuations and their generalizations for commutative rings", "description": "Valuations and their generalizations for commutative rings [See also 12J20]", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13A30", "originalCode": "13A30", "name": "Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics", "description": "Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13A35", "originalCode": "13A35", "name": "Characteristic \\(p\\) methods (Frobenius endomorphism) and reduction to characteristic \\(p\\); tight closure", "description": "Characteristic \\(p\\) methods (Frobenius endomorphism) and reduction to characteristic \\(p\\); tight closure [See also 13B22]", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13A50", "originalCode": "13A50", "name": "Actions of groups on commutative rings; invariant theory", "description": "Actions of groups on commutative rings; invariant theory [See also 14L24]", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13A70", "originalCode": "13A70", "name": "General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.)", "description": "General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) [See also 05C25, 05E40]", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13A99", "originalCode": "13A99", "name": "General commutative ring theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "13A", "page": 30 }, { "code": "13B", "originalCode": "13Bxx", "name": "Commutative ring extensions and related topics", "description": "Commutative ring extensions and related topics", "kind": "section", "parent": "13", "page": 30 }, { "code": "13B02", "originalCode": "13B02", "name": "Extension theory of commutative rings", "description": "Extension theory of commutative rings", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B05", "originalCode": "13B05", "name": "Galois theory and commutative ring extensions", "description": "Galois theory and commutative ring extensions", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B10", "originalCode": "13B10", "name": "Morphisms of commutative rings", "description": "Morphisms of commutative rings", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B21", "originalCode": "13B21", "name": "Integral dependence in commutative rings; going up, going down", "description": "Integral dependence in commutative rings; going up, going down", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B22", "originalCode": "13B22", "name": "Integral closure of commutative rings and ideals", "description": "Integral closure of commutative rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B25", "originalCode": "13B25", "name": "Polynomials over commutative rings", "description": "Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10]", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B30", "originalCode": "13B30", "name": "Rings of fractions and localization for commutative rings", "description": "Rings of fractions and localization for commutative rings [See also 16S85]", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B35", "originalCode": "13B35", "name": "Completion of commutative rings", "description": "Completion of commutative rings [See also 13J10]", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B40", "originalCode": "13B40", "name": "Étale and flat extensions; Henselization; Artin approximation", "description": "Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13B99", "originalCode": "13B99", "name": "Commutative ring extensions and related topics", "description": "None of the above, but in this section", "kind": "subject", "parent": "13B", "page": 30 }, { "code": "13C", "originalCode": "13Cxx", "name": "Theory of modules and ideals in commutative rings", "description": "Theory of modules and ideals in commutative rings", "kind": "section", "parent": "13", "page": 30 }, { "code": "13C05", "originalCode": "13C05", "name": "Structure, classification theorems for modules and ideals in commutative rings", "description": "Structure, classification theorems for modules and ideals in commutative rings", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C10", "originalCode": "13C10", "name": "Projective and free modules and ideals in commutative rings", "description": "Projective and free modules and ideals in commutative rings [See also 19A13]", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C11", "originalCode": "13C11", "name": "Injective and flat modules and ideals in commutative rings", "description": "Injective and flat modules and ideals in commutative rings", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C12", "originalCode": "13C12", "name": "Torsion modules and ideals in commutative rings", "description": "Torsion modules and ideals in commutative rings", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C13", "originalCode": "13C13", "name": "Other special types of modules and ideals in commutative rings", "description": "Other special types of modules and ideals in commutative rings", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C14", "originalCode": "13C14", "name": "Cohen-Macaulay modules", "description": "Cohen-Macaulay modules [See also 13H10]", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C15", "originalCode": "13C15", "name": "Dimension theory, depth, related commutative rings (catenary, etc.)", "description": "Dimension theory, depth, related commutative rings (catenary, etc.)", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C20", "originalCode": "13C20", "name": "Class groups", "description": "Class groups [See also 11R29]", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C40", "originalCode": "13C40", "name": "Linkage, complete intersections and determinantal ideals", "description": "Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]", "kind": "subject", "parent": "13C", "page": 30 }, { "code": "13C60", "originalCode": "13C60", "name": "Module categories and commutative rings", "description": "Module categories and commutative rings", "kind": "subject", "parent": "13C", "page": 31 }, { "code": "13C70", "originalCode": "13C70", "name": "Theory of modules and ideals in commutative rings described by combinatorial properties", "description": "Theory of modules and ideals in commutative rings described by combinatorial properties [See also 05C25, 05E40]", "kind": "subject", "parent": "13C", "page": 31 }, { "code": "13C99", "originalCode": "13C99", "name": "Theory of modules and ideals in commutative rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "13C", "page": 31 }, { "code": "13D", "originalCode": "13Dxx", "name": "Homological methods in commutative ring theory", "description": "Homological methods in commutative ring theory \\{For noncommutative rings, see 16Exx; for general categories, see 18Gxx\\}", "kind": "section", "parent": "13", "page": 31 }, { "code": "13D02", "originalCode": "13D02", "name": "Syzygies, resolutions, complexes and commutative rings", "description": "Syzygies, resolutions, complexes and commutative rings", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D03", "originalCode": "13D03", "name": "(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)", "description": "(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D05", "originalCode": "13D05", "name": "Homological dimension and commutative rings", "description": "Homological dimension and commutative rings", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D07", "originalCode": "13D07", "name": "Homological functors on modules of commutative rings (Tor, Ext, etc.)", "description": "Homological functors on modules of commutative rings (Tor, Ext, etc.)", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D09", "originalCode": "13D09", "name": "Derived categories and commutative rings", "description": "Derived categories and commutative rings", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D10", "originalCode": "13D10", "name": "Deformations and infinitesimal methods in commutative ring theory", "description": "Deformations and infinitesimal methods in commutative ring theory [See also 14B10, 14B12, 14D15, 32Gxx]", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D15", "originalCode": "13D15", "name": "Grothendieck groups, \\(K\\)-theory and commutative rings", "description": "Grothendieck groups, \\(K\\)-theory and commutative rings [See also 14C35, 18F30, 19Axx, 19D50]", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D22", "originalCode": "13D22", "name": "Homological conjectures (intersection theorems) in commutative ring theory", "description": "Homological conjectures (intersection theorems) in commutative ring theory", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D30", "originalCode": "13D30", "name": "Torsion theory for commutative rings", "description": "Torsion theory for commutative rings [See also 13C12, 18E40]", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D40", "originalCode": "13D40", "name": "Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series", "description": "Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D45", "originalCode": "13D45", "name": "Local cohomology and commutative rings", "description": "Local cohomology and commutative rings [See also 14B15]", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13D99", "originalCode": "13D99", "name": "Homological methods in commutative ring theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "13D", "page": 31 }, { "code": "13E", "originalCode": "13Exx", "name": "Chain conditions, finiteness conditions in commutative ring theory", "description": "Chain conditions, finiteness conditions in commutative ring theory", "kind": "section", "parent": "13", "page": 31 }, { "code": "13E05", "originalCode": "13E05", "name": "Commutative Noetherian rings and modules", "description": "Commutative Noetherian rings and modules", "kind": "subject", "parent": "13E", "page": 31 }, { "code": "13E10", "originalCode": "13E10", "name": "Commutative Artinian rings and modules, finite-dimensional algebras", "description": "Commutative Artinian rings and modules, finite-dimensional algebras", "kind": "subject", "parent": "13E", "page": 31 }, { "code": "13E15", "originalCode": "13E15", "name": "Commutative rings and modules of finite generation or presentation; number of generators", "description": "Commutative rings and modules of finite generation or presentation; number of generators", "kind": "subject", "parent": "13E", "page": 31 }, { "code": "13E99", "originalCode": "13E99", "name": "Chain conditions, finiteness conditions in commutative ring theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "13E", "page": 31 }, { "code": "13F", "originalCode": "13Fxx", "name": "Arithmetic rings and other special commutative rings", "description": "Arithmetic rings and other special commutative rings", "kind": "section", "parent": "13", "page": 31 }, { "code": "13F05", "originalCode": "13F05", "name": "Dedekind, Prüfer, Krull and Mori rings and their generalizations", "description": "Dedekind, Prüfer, Krull and Mori rings and their generalizations", "kind": "subject", "parent": "13F", "page": 31 }, { "code": "13F07", "originalCode": "13F07", "name": "Euclidean rings and generalizations", "description": "Euclidean rings and generalizations", "kind": "subject", "parent": "13F", "page": 31 }, { "code": "13F10", "originalCode": "13F10", "name": "Principal ideal rings", "description": "Principal ideal rings", "kind": "subject", "parent": "13F", "page": 31 }, { "code": "13F15", "originalCode": "13F15", "name": "Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial)", "description": "Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05]", "kind": "subject", "parent": "13F", "page": 31 }, { "code": "13F20", "originalCode": "13F20", "name": "Polynomial rings and ideals; rings of integer-valued polynomials", "description": "Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]", "kind": "subject", "parent": "13F", "page": 31 }, { "code": "13F25", "originalCode": "13F25", "name": "Formal power series rings", "description": "Formal power series rings [See also 13J05]", "kind": "subject", "parent": "13F", "page": 31 }, { "code": "13F30", "originalCode": "13F30", "name": "Valuation rings", "description": "Valuation rings [See also 13A18]", "kind": "subject", "parent": "13F", "page": 31 }, { "code": "13F35", "originalCode": "13F35", "name": "Witt vectors and related rings", "description": "Witt vectors and related rings", "kind": "subject", "parent": "13F", "page": 31 }, { "code": "13F40", "originalCode": "13F40", "name": "Excellent rings", "description": "Excellent rings", "kind": "subject", "parent": "13F", "page": 32 }, { "code": "13F45", "originalCode": "13F45", "name": "Seminormal rings", "description": "Seminormal rings", "kind": "subject", "parent": "13F", "page": 32 }, { "code": "13F50", "originalCode": "13F50", "name": "Rings with straightening laws, Hodge algebras", "description": "Rings with straightening laws, Hodge algebras", "kind": "subject", "parent": "13F", "page": 32 }, { "code": "13F55", "originalCode": "13F55", "name": "Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes", "description": "Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes [See also 55U10]", "kind": "subject", "parent": "13F", "page": 32 }, { "code": "13F60", "originalCode": "13F60", "name": "Cluster algebras", "description": "Cluster algebras", "kind": "subject", "parent": "13F", "page": 32 }, { "code": "13F65", "originalCode": "13F65", "name": "Commutative rings defined by binomial ideals, toric rings, etc.", "description": "Commutative rings defined by binomial ideals, toric rings, etc. [See also 14M25]", "kind": "subject", "parent": "13F", "page": 32 }, { "code": "13F70", "originalCode": "13F70", "name": "Other commutative rings defined by combinatorial properties", "description": "Other commutative rings defined by combinatorial properties", "kind": "subject", "parent": "13F", "page": 32 }, { "code": "13F99", "originalCode": "13F99", "name": "Arithmetic rings and other special commutative rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "13F", "page": 32 }, { "code": "13G", "originalCode": "13Gxx", "name": "Integral domains", "description": "Integral domains", "kind": "section", "parent": "13", "page": 32 }, { "code": "13G05", "originalCode": "13G05", "name": "Integral domains", "description": "Integral domains", "kind": "subject", "parent": "13G", "page": 32 }, { "code": "13G99", "originalCode": "13G99", "name": "Integral domains", "description": "None of the above, but in this section", "kind": "subject", "parent": "13G", "page": 32 }, { "code": "13H", "originalCode": "13Hxx", "name": "Local rings and semilocal rings", "description": "Local rings and semilocal rings", "kind": "section", "parent": "13", "page": 32 }, { "code": "13H05", "originalCode": "13H05", "name": "Regular local rings", "description": "Regular local rings", "kind": "subject", "parent": "13H", "page": 32 }, { "code": "13H10", "originalCode": "13H10", "name": "Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)", "description": "Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]", "kind": "subject", "parent": "13H", "page": 32 }, { "code": "13H15", "originalCode": "13H15", "name": "Multiplicity theory and related topics", "description": "Multiplicity theory and related topics [See also 14C17]", "kind": "subject", "parent": "13H", "page": 32 }, { "code": "13H99", "originalCode": "13H99", "name": "Local rings and semilocal rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "13H", "page": 32 }, { "code": "13J", "originalCode": "13Jxx", "name": "Topological rings and modules", "description": "Topological rings and modules [See also 16W60, 16W80]", "kind": "section", "parent": "13", "page": 32 }, { "code": "13J05", "originalCode": "13J05", "name": "Power series rings", "description": "Power series rings [See also 13F25]", "kind": "subject", "parent": "13J", "page": 32 }, { "code": "13J07", "originalCode": "13J07", "name": "Analytical algebras and rings", "description": "Analytical algebras and rings [See also 32B05]", "kind": "subject", "parent": "13J", "page": 32 }, { "code": "13J10", "originalCode": "13J10", "name": "Complete rings, completion", "description": "Complete rings, completion [See also 13B35]", "kind": "subject", "parent": "13J", "page": 32 }, { "code": "13J15", "originalCode": "13J15", "name": "Henselian rings", "description": "Henselian rings [See also 13B40]", "kind": "subject", "parent": "13J", "page": 32 }, { "code": "13J20", "originalCode": "13J20", "name": "Global topological rings", "description": "Global topological rings", "kind": "subject", "parent": "13J", "page": 32 }, { "code": "13J25", "originalCode": "13J25", "name": "Ordered rings", "description": "Ordered rings [See also 06F25]", "kind": "subject", "parent": "13J", "page": 32 }, { "code": "13J30", "originalCode": "13J30", "name": "Real algebra", "description": "Real algebra [See also 12D15, 14Pxx]", "kind": "subject", "parent": "13J", "page": 32 }, { "code": "13J99", "originalCode": "13J99", "name": "Topological rings and modules", "description": "None of the above, but in this section", "kind": "subject", "parent": "13J", "page": 32 }, { "code": "13L", "originalCode": "13Lxx", "name": "Applications of logic to commutative algebra", "description": "Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]", "kind": "section", "parent": "13", "page": 32 }, { "code": "13L05", "originalCode": "13L05", "name": "Applications of logic to commutative algebra", "description": "Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]", "kind": "subject", "parent": "13L", "page": 32 }, { "code": "13L99", "originalCode": "13L99", "name": "Applications of logic to commutative algebra", "description": "None of the above, but in this section", "kind": "subject", "parent": "13L", "page": 32 }, { "code": "13M", "originalCode": "13Mxx", "name": "Finite commutative rings", "description": "Finite commutative rings \\{For number-theoretic aspects, see 11Txx\\}", "kind": "section", "parent": "13", "page": 32 }, { "code": "13M05", "originalCode": "13M05", "name": "Structure of finite commutative rings", "description": "Structure of finite commutative rings", "kind": "subject", "parent": "13M", "page": 32 }, { "code": "13M10", "originalCode": "13M10", "name": "Polynomials and finite commutative rings", "description": "Polynomials and finite commutative rings", "kind": "subject", "parent": "13M", "page": 32 }, { "code": "13M99", "originalCode": "13M99", "name": "Finite commutative rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "13M", "page": 32 }, { "code": "13N", "originalCode": "13Nxx", "name": "Differential algebra", "description": "Differential algebra [See also 12H05, 14F10]", "kind": "section", "parent": "13", "page": 33 }, { "code": "13N05", "originalCode": "13N05", "name": "Modules of differentials", "description": "Modules of differentials", "kind": "subject", "parent": "13N", "page": 33 }, { "code": "13N10", "originalCode": "13N10", "name": "Commutative rings of differential operators and their modules", "description": "Commutative rings of differential operators and their modules [See also 16S32, 32C38]", "kind": "subject", "parent": "13N", "page": 33 }, { "code": "13N15", "originalCode": "13N15", "name": "Derivations and commutative rings", "description": "Derivations and commutative rings", "kind": "subject", "parent": "13N", "page": 33 }, { "code": "13N99", "originalCode": "13N99", "name": "Differential algebra", "description": "None of the above, but in this section", "kind": "subject", "parent": "13N", "page": 33 }, { "code": "13P", "originalCode": "13Pxx", "name": "Computational aspects and applications of commutative rings", "description": "Computational aspects and applications of commutative rings [See also 14Qxx, 68W30] \\{For software etc., see 13-04\\}", "kind": "section", "parent": "13", "page": 33 }, { "code": "13P05", "originalCode": "13P05", "name": "Polynomials, factorization in commutative rings", "description": "Polynomials, factorization in commutative rings [See also 12-08]", "kind": "subject", "parent": "13P", "page": 33 }, { "code": "13P10", "originalCode": "13P10", "name": "Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)", "description": "Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)", "kind": "subject", "parent": "13P", "page": 33 }, { "code": "13P15", "originalCode": "13P15", "name": "Solving polynomial systems; resultants", "description": "Solving polynomial systems; resultants", "kind": "subject", "parent": "13P", "page": 33 }, { "code": "13P20", "originalCode": "13P20", "name": "Computational homological algebra", "description": "Computational homological algebra [See also 13Dxx]", "kind": "subject", "parent": "13P", "page": 33 }, { "code": "13P25", "originalCode": "13P25", "name": "Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)", "description": "Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)", "kind": "subject", "parent": "13P", "page": 33 }, { "code": "13P99", "originalCode": "13P99", "name": "Computational aspects and applications of commutative rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "13P", "page": 33 }, { "code": "14", "originalCode": "14-XX", "name": "Algebraic geometry", "description": "Algebraic geometry", "kind": "class", "parent": null, "page": 33 }, { "code": "14-00", "originalCode": "14-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry", "kind": "subject", "parent": "14", "page": 33 }, { "code": "14-01", "originalCode": "14-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry", "kind": "subject", "parent": "14", "page": 33 }, { "code": "14-02", "originalCode": "14-02", "name": "Research exposition (monographs, survey articles) pertaining to algebraic geometry", "description": "Research exposition (monographs, survey articles) pertaining to algebraic geometry", "kind": "subject", "parent": "14", "page": 33 }, { "code": "14-03", "originalCode": "14-03", "name": "History of algebraic geometry", "description": "History of algebraic geometry [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "14", "page": 33 }, { "code": "14-04", "originalCode": "14-04", "name": "Software, source code, etc. for problems pertaining to algebraic geometry", "description": "Software, source code, etc. for problems pertaining to algebraic geometry", "kind": "subject", "parent": "14", "page": 33 }, { "code": "14-06", "originalCode": "14-06", "name": "Proceedings, conferences, collections, etc. pertaining to algebraic geometry", "description": "Proceedings, conferences, collections, etc. pertaining to algebraic geometry", "kind": "subject", "parent": "14", "page": 33 }, { "code": "14-11", "originalCode": "14-11", "name": "Research data for problems pertaining to algebraic geometry", "description": "Research data for problems pertaining to algebraic geometry", "kind": "subject", "parent": "14", "page": 33 }, { "code": "14A", "originalCode": "14Axx", "name": "Foundations of algebraic geometry", "description": "Foundations of algebraic geometry", "kind": "section", "parent": "14", "page": 33 }, { "code": "14A05", "originalCode": "14A05", "name": "Relevant commutative algebra", "description": "Relevant commutative algebra [See also 13-XX]", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A10", "originalCode": "14A10", "name": "Varieties and morphisms", "description": "Varieties and morphisms", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A15", "originalCode": "14A15", "name": "Schemes and morphisms", "description": "Schemes and morphisms", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A20", "originalCode": "14A20", "name": "Generalizations (algebraic spaces, stacks)", "description": "Generalizations (algebraic spaces, stacks)", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A21", "originalCode": "14A21", "name": "Logarithmic algebraic geometry, log schemes", "description": "Logarithmic algebraic geometry, log schemes", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A22", "originalCode": "14A22", "name": "Noncommutative algebraic geometry", "description": "Noncommutative algebraic geometry [See also 16S38]", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A23", "originalCode": "14A23", "name": "Geometry over the field with one element", "description": "Geometry over the field with one element", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A25", "originalCode": "14A25", "name": "Elementary questions in algebraic geometry", "description": "Elementary questions in algebraic geometry", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A30", "originalCode": "14A30", "name": "Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.)", "description": "Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) \\{For categorical aspects, see 18Fxx, 18Gxx\\}", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14A99", "originalCode": "14A99", "name": "Foundations of algebraic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14A", "page": 33 }, { "code": "14B", "originalCode": "14Bxx", "name": "Local theory in algebraic geometry", "description": "Local theory in algebraic geometry", "kind": "section", "parent": "14", "page": 34 }, { "code": "14B05", "originalCode": "14B05", "name": "Singularities in algebraic geometry", "description": "Singularities in algebraic geometry [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]", "kind": "subject", "parent": "14B", "page": 34 }, { "code": "14B07", "originalCode": "14B07", "name": "Deformations of singularities", "description": "Deformations of singularities [See also 14D15, 32S30]", "kind": "subject", "parent": "14B", "page": 34 }, { "code": "14B10", "originalCode": "14B10", "name": "Infinitesimal methods in algebraic geometry", "description": "Infinitesimal methods in algebraic geometry [See also 13D10]", "kind": "subject", "parent": "14B", "page": 34 }, { "code": "14B12", "originalCode": "14B12", "name": "Local deformation theory, Artin approximation, etc.", "description": "Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]", "kind": "subject", "parent": "14B", "page": 34 }, { "code": "14B15", "originalCode": "14B15", "name": "Local cohomology and algebraic geometry", "description": "Local cohomology and algebraic geometry [See also 13D45, 32C36]", "kind": "subject", "parent": "14B", "page": 34 }, { "code": "14B20", "originalCode": "14B20", "name": "Formal neighborhoods in algebraic geometry", "description": "Formal neighborhoods in algebraic geometry", "kind": "subject", "parent": "14B", "page": 34 }, { "code": "14B25", "originalCode": "14B25", "name": "Local structure of morphisms in algebraic geometry: étale, flat, etc.", "description": "Local structure of morphisms in algebraic geometry: étale, flat, etc. [See also 13B40]", "kind": "subject", "parent": "14B", "page": 34 }, { "code": "14B99", "originalCode": "14B99", "name": "Local theory in algebraic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14B", "page": 34 }, { "code": "14C", "originalCode": "14Cxx", "name": "Cycles and subschemes", "description": "Cycles and subschemes", "kind": "section", "parent": "14", "page": 34 }, { "code": "14C05", "originalCode": "14C05", "name": "Parametrization (Chow and Hilbert schemes)", "description": "Parametrization (Chow and Hilbert schemes)", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C15", "originalCode": "14C15", "name": "(Equivariant) Chow groups and rings; motives", "description": "(Equivariant) Chow groups and rings; motives", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C17", "originalCode": "14C17", "name": "Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry", "description": "Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry [See also 13H15]", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C20", "originalCode": "14C20", "name": "Divisors, linear systems, invertible sheaves", "description": "Divisors, linear systems, invertible sheaves", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C21", "originalCode": "14C21", "name": "Pencils, nets, webs in algebraic geometry", "description": "Pencils, nets, webs in algebraic geometry [See also 53A60]", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C22", "originalCode": "14C22", "name": "Picard groups", "description": "Picard groups", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C25", "originalCode": "14C25", "name": "Algebraic cycles", "description": "Algebraic cycles", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C30", "originalCode": "14C30", "name": "Transcendental methods, Hodge theory (algebro-geometric aspects)", "description": "Transcendental methods, Hodge theory (algebro-geometric aspects) [See also 14D07, 32G20, 32J25, 32S35, 58A14], Hodge conjecture", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C34", "originalCode": "14C34", "name": "Torelli problem", "description": "Torelli problem [See also 32G20]", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C35", "originalCode": "14C35", "name": "Applications of methods of algebraic \\(K\\)-theory in algebraic geometry", "description": "Applications of methods of algebraic \\(K\\)-theory in algebraic geometry [See also 19Exx]", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C40", "originalCode": "14C40", "name": "Riemann-Roch theorems", "description": "Riemann-Roch theorems [See also 19E20, 19L10]", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14C99", "originalCode": "14C99", "name": "Cycles and subschemes", "description": "None of the above, but in this section", "kind": "subject", "parent": "14C", "page": 34 }, { "code": "14D", "originalCode": "14Dxx", "name": "Families, fibrations in algebraic geometry", "description": "Families, fibrations in algebraic geometry", "kind": "section", "parent": "14", "page": 34 }, { "code": "14D05", "originalCode": "14D05", "name": "Structure of families (Picard-Lefschetz, monodromy, etc.)", "description": "Structure of families (Picard-Lefschetz, monodromy, etc.)", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D06", "originalCode": "14D06", "name": "Fibrations, degenerations in algebraic geometry", "description": "Fibrations, degenerations in algebraic geometry", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D07", "originalCode": "14D07", "name": "Variation of Hodge structures (algebro-geometric aspects)", "description": "Variation of Hodge structures (algebro-geometric aspects) [See also 32G20]", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D10", "originalCode": "14D10", "name": "Arithmetic ground fields (finite, local, global) and families or fibrations", "description": "Arithmetic ground fields (finite, local, global) and families or fibrations", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D15", "originalCode": "14D15", "name": "Formal methods and deformations in algebraic geometry", "description": "Formal methods and deformations in algebraic geometry [See also 13D10, 14B07, 32Gxx]", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D20", "originalCode": "14D20", "name": "Algebraic moduli problems, moduli of vector bundles", "description": "Algebraic moduli problems, moduli of vector bundles \\{For analytic moduli problems, see 32G13\\}", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D21", "originalCode": "14D21", "name": "Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)", "description": "Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx]", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D22", "originalCode": "14D22", "name": "Fine and coarse moduli spaces", "description": "Fine and coarse moduli spaces", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D23", "originalCode": "14D23", "name": "Stacks and moduli problems", "description": "Stacks and moduli problems", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D24", "originalCode": "14D24", "name": "Geometric Langlands program (algebro-geometric aspects)", "description": "Geometric Langlands program (algebro-geometric aspects) [See also 22E57]", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14D99", "originalCode": "14D99", "name": "Families, fibrations in algebraic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14D", "page": 34 }, { "code": "14E", "originalCode": "14Exx", "name": "Birational geometry", "description": "Birational geometry", "kind": "section", "parent": "14", "page": 35 }, { "code": "14E05", "originalCode": "14E05", "name": "Rational and birational maps", "description": "Rational and birational maps", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E07", "originalCode": "14E07", "name": "Birational automorphisms, Cremona group and generalizations", "description": "Birational automorphisms, Cremona group and generalizations", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E08", "originalCode": "14E08", "name": "Rationality questions in algebraic geometry", "description": "Rationality questions in algebraic geometry [See also 14M20]", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E15", "originalCode": "14E15", "name": "Global theory and resolution of singularities (algebro-geometric aspects)", "description": "Global theory and resolution of singularities (algebro-geometric aspects) [See also 14B05, 32S20, 32S45]", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E16", "originalCode": "14E16", "name": "McKay correspondence", "description": "McKay correspondence", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E18", "originalCode": "14E18", "name": "Arcs and motivic integration", "description": "Arcs and motivic integration", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E20", "originalCode": "14E20", "name": "Coverings in algebraic geometry", "description": "Coverings in algebraic geometry [See also 14H30]", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E22", "originalCode": "14E22", "name": "Ramification problems in algebraic geometry", "description": "Ramification problems in algebraic geometry [See also 11S15]", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E25", "originalCode": "14E25", "name": "Embeddings in algebraic geometry", "description": "Embeddings in algebraic geometry", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E30", "originalCode": "14E30", "name": "Minimal model program (Mori theory, extremal rays)", "description": "Minimal model program (Mori theory, extremal rays)", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14E99", "originalCode": "14E99", "name": "Birational geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14E", "page": 35 }, { "code": "14F", "originalCode": "14Fxx", "name": "(Co)homology theory in algebraic geometry", "description": "(Co)homology theory in algebraic geometry [See also 13Dxx]", "kind": "section", "parent": "14", "page": 35 }, { "code": "14F06", "originalCode": "14F06", "name": "Sheaves in algebraic geometry", "description": "Sheaves in algebraic geometry [See also 14F08, 14H60, 14J60, 18F20, 32L10, 46M20]", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F08", "originalCode": "14F08", "name": "Derived categories of sheaves, dg categories, and related constructions in algebraic geometry", "description": "Derived categories of sheaves, dg categories, and related constructions in algebraic geometry [See also 14A30, 14F06, 18Gxx]", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F10", "originalCode": "14F10", "name": "Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials", "description": "Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F17", "originalCode": "14F17", "name": "Vanishing theorems in algebraic geometry", "description": "Vanishing theorems in algebraic geometry [See also 32L20]", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F18", "originalCode": "14F18", "name": "Multiplier ideals", "description": "Multiplier ideals", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F20", "originalCode": "14F20", "name": "Étale and other Grothendieck topologies and (co)homologies", "description": "Étale and other Grothendieck topologies and (co)homologies", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F22", "originalCode": "14F22", "name": "Brauer groups of schemes", "description": "Brauer groups of schemes [See also 12G05, 16K50]", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F25", "originalCode": "14F25", "name": "Classical real and complex (co)homology in algebraic geometry", "description": "Classical real and complex (co)homology in algebraic geometry", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F30", "originalCode": "14F30", "name": "\\(p\\)-adic cohomology, crystalline cohomology", "description": "\\(p\\)-adic cohomology, crystalline cohomology", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F35", "originalCode": "14F35", "name": "Homotopy theory and fundamental groups in algebraic geometry", "description": "Homotopy theory and fundamental groups in algebraic geometry [See also 14H30]", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F40", "originalCode": "14F40", "name": "de Rham cohomology and algebraic geometry", "description": "de Rham cohomology and algebraic geometry [See also 14C30, 32C35, 32L10]", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F42", "originalCode": "14F42", "name": "Motivic cohomology; motivic homotopy theory", "description": "Motivic cohomology; motivic homotopy theory [See also 19E15]", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F43", "originalCode": "14F43", "name": "Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)", "description": "Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F45", "originalCode": "14F45", "name": "Topological properties in algebraic geometry", "description": "Topological properties in algebraic geometry", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14F99", "originalCode": "14F99", "name": "(Co)homology theory in algebraic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14F", "page": 35 }, { "code": "14G", "originalCode": "14Gxx", "name": "Arithmetic problems in algebraic geometry; Diophantine geometry", "description": "Arithmetic problems in algebraic geometry; Diophantine geometry [See also 11Dxx, 11Gxx]", "kind": "section", "parent": "14", "page": 36 }, { "code": "14G05", "originalCode": "14G05", "name": "Rational points", "description": "Rational points", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G10", "originalCode": "14G10", "name": "Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)", "description": "Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) [See also 11G40]", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G12", "originalCode": "14G12", "name": "Hasse principle, weak and strong approximation, Brauer-Manin obstruction", "description": "Hasse principle, weak and strong approximation, Brauer-Manin obstruction [See also 14F22]", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G15", "originalCode": "14G15", "name": "Finite ground fields in algebraic geometry", "description": "Finite ground fields in algebraic geometry", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G17", "originalCode": "14G17", "name": "Positive characteristic ground fields in algebraic geometry", "description": "Positive characteristic ground fields in algebraic geometry", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G20", "originalCode": "14G20", "name": "Local ground fields in algebraic geometry", "description": "Local ground fields in algebraic geometry", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G22", "originalCode": "14G22", "name": "Rigid analytic geometry", "description": "Rigid analytic geometry", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G25", "originalCode": "14G25", "name": "Global ground fields in algebraic geometry", "description": "Global ground fields in algebraic geometry", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G27", "originalCode": "14G27", "name": "Other nonalgebraically closed ground fields in algebraic geometry", "description": "Other nonalgebraically closed ground fields in algebraic geometry", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G32", "originalCode": "14G32", "name": "Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)", "description": "Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G35", "originalCode": "14G35", "name": "Modular and Shimura varieties", "description": "Modular and Shimura varieties [See also 11F41, 11F46, 11G18]", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G40", "originalCode": "14G40", "name": "Arithmetic varieties and schemes; Arakelov theory; heights", "description": "Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G45", "originalCode": "14G45", "name": "Perfectoid spaces and mixed characteristic", "description": "Perfectoid spaces and mixed characteristic", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G50", "originalCode": "14G50", "name": "Applications to coding theory and cryptography of arithmetic geometry", "description": "Applications to coding theory and cryptography of arithmetic geometry [See also 94A60, 94B27, 94B40]", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14G99", "originalCode": "14G99", "name": "Arithmetic problems in algebraic geometry; Diophantine geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14G", "page": 36 }, { "code": "14H", "originalCode": "14Hxx", "name": "Curves in algebraic geometry", "description": "Curves in algebraic geometry", "kind": "section", "parent": "14", "page": 36 }, { "code": "14H05", "originalCode": "14H05", "name": "Algebraic functions and function fields in algebraic geometry", "description": "Algebraic functions and function fields in algebraic geometry [See also 11R58]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H10", "originalCode": "14H10", "name": "Families, moduli of curves (algebraic)", "description": "Families, moduli of curves (algebraic)", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H15", "originalCode": "14H15", "name": "Families, moduli of curves (analytic)", "description": "Families, moduli of curves (analytic) [See also 30F10, 32G15]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H20", "originalCode": "14H20", "name": "Singularities of curves, local rings", "description": "Singularities of curves, local rings [See also 13Hxx, 14B05]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H25", "originalCode": "14H25", "name": "Arithmetic ground fields for curves", "description": "Arithmetic ground fields for curves [See also 11Dxx, 11G05, 14Gxx]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H30", "originalCode": "14H30", "name": "Coverings of curves, fundamental group", "description": "Coverings of curves, fundamental group [See also 14E20, 14F35]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H37", "originalCode": "14H37", "name": "Automorphisms of curves", "description": "Automorphisms of curves", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H40", "originalCode": "14H40", "name": "Jacobians, Prym varieties", "description": "Jacobians, Prym varieties [See also 32G20]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H42", "originalCode": "14H42", "name": "Theta functions and curves; Schottky problem", "description": "Theta functions and curves; Schottky problem [See also 14K25, 32G20]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H45", "originalCode": "14H45", "name": "Special algebraic curves and curves of low genus", "description": "Special algebraic curves and curves of low genus", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H50", "originalCode": "14H50", "name": "Plane and space curves", "description": "Plane and space curves", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H51", "originalCode": "14H51", "name": "Special divisors on curves (gonality, Brill-Noether theory)", "description": "Special divisors on curves (gonality, Brill-Noether theory)", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H52", "originalCode": "14H52", "name": "Elliptic curves", "description": "Elliptic curves [See also 11G05, 11G07, 14Kxx]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H55", "originalCode": "14H55", "name": "Riemann surfaces; Weierstrass points; gap sequences", "description": "Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]", "kind": "subject", "parent": "14H", "page": 36 }, { "code": "14H57", "originalCode": "14H57", "name": "Dessins d'enfants theory", "description": "Dessins d'enfants theory \\{For arithmetic aspects, see 11G32\\}", "kind": "subject", "parent": "14H", "page": 37 }, { "code": "14H60", "originalCode": "14H60", "name": "Vector bundles on curves and their moduli", "description": "Vector bundles on curves and their moduli [See also 14D20, 14F06, 14J60]", "kind": "subject", "parent": "14H", "page": 37 }, { "code": "14H70", "originalCode": "14H70", "name": "Relationships between algebraic curves and integrable systems", "description": "Relationships between algebraic curves and integrable systems", "kind": "subject", "parent": "14H", "page": 37 }, { "code": "14H81", "originalCode": "14H81", "name": "Relationships between algebraic curves and physics", "description": "Relationships between algebraic curves and physics", "kind": "subject", "parent": "14H", "page": 37 }, { "code": "14H99", "originalCode": "14H99", "name": "Curves in algebraic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14H", "page": 37 }, { "code": "14J", "originalCode": "14Jxx", "name": "Surfaces and higher-dimensional varieties", "description": "Surfaces and higher-dimensional varieties \\{For analytic theory, see 32Jxx\\}", "kind": "section", "parent": "14", "page": 37 }, { "code": "14J10", "originalCode": "14J10", "name": "Families, moduli, classification: algebraic theory", "description": "Families, moduli, classification: algebraic theory", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J15", "originalCode": "14J15", "name": "Moduli, classification: analytic theory; relations with modular forms", "description": "Moduli, classification: analytic theory; relations with modular forms [See also 32G13]", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J17", "originalCode": "14J17", "name": "Singularities of surfaces or higher-dimensional varieties", "description": "Singularities of surfaces or higher-dimensional varieties [See also 14B05, 14E15, 32S05, 32S25]", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J20", "originalCode": "14J20", "name": "Arithmetic ground fields for surfaces or higher-dimensional varieties", "description": "Arithmetic ground fields for surfaces or higher-dimensional varieties [See also 11Dxx, 11G25, 11G35, 14Gxx]", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J25", "originalCode": "14J25", "name": "Special surfaces", "description": "Special surfaces \\{For Hilbert modular surfaces, see 14G35\\}", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J26", "originalCode": "14J26", "name": "Rational and ruled surfaces", "description": "Rational and ruled surfaces", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J27", "originalCode": "14J27", "name": "Elliptic surfaces, elliptic or Calabi-Yau fibrations", "description": "Elliptic surfaces, elliptic or Calabi-Yau fibrations", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J28", "originalCode": "14J28", "name": "\\(K3\\) surfaces and Enriques surfaces", "description": "\\(K3\\) surfaces and Enriques surfaces", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J29", "originalCode": "14J29", "name": "Surfaces of general type", "description": "Surfaces of general type", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J30", "originalCode": "14J30", "name": "\\(3\\)-folds", "description": "\\(3\\)-folds", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J32", "originalCode": "14J32", "name": "Calabi-Yau manifolds (algebro-geometric aspects)", "description": "Calabi-Yau manifolds (algebro-geometric aspects) [See also 32Q25]", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J33", "originalCode": "14J33", "name": "Mirror symmetry (algebro-geometric aspects)", "description": "Mirror symmetry (algebro-geometric aspects) [See also 11G42, 53D37]", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J35", "originalCode": "14J35", "name": "\\(4\\)-folds", "description": "\\(4\\)-folds", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J40", "originalCode": "14J40", "name": "\\(n\\)-folds (\\(n>4\\))", "description": "\\(n\\)-folds (\\(n>4\\))", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J42", "originalCode": "14J42", "name": "Holomorphic symplectic varieties, hyper-Kähler varieties", "description": "Holomorphic symplectic varieties, hyper-Kähler varieties", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J45", "originalCode": "14J45", "name": "Fano varieties", "description": "Fano varieties", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J50", "originalCode": "14J50", "name": "Automorphisms of surfaces and higher-dimensional varieties", "description": "Automorphisms of surfaces and higher-dimensional varieties", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J60", "originalCode": "14J60", "name": "Vector bundles on surfaces and higher-dimensional varieties, and their moduli", "description": "Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F06, 14H60, 32Lxx]", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J70", "originalCode": "14J70", "name": "Hypersurfaces and algebraic geometry", "description": "Hypersurfaces and algebraic geometry", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J80", "originalCode": "14J80", "name": "Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)", "description": "Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J81", "originalCode": "14J81", "name": "Relationships between surfaces, higher-dimensional varieties, and physics", "description": "Relationships between surfaces, higher-dimensional varieties, and physics", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14J99", "originalCode": "14J99", "name": "Surfaces and higher-dimensional varieties", "description": "None of the above, but in this section", "kind": "subject", "parent": "14J", "page": 37 }, { "code": "14K", "originalCode": "14Kxx", "name": "Abelian varieties and schemes", "description": "Abelian varieties and schemes", "kind": "section", "parent": "14", "page": 38 }, { "code": "14K02", "originalCode": "14K02", "name": "Isogeny", "description": "Isogeny", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K05", "originalCode": "14K05", "name": "Algebraic theory of abelian varieties", "description": "Algebraic theory of abelian varieties", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K10", "originalCode": "14K10", "name": "Algebraic moduli of abelian varieties, classification", "description": "Algebraic moduli of abelian varieties, classification [See also 11G15]", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K12", "originalCode": "14K12", "name": "Subvarieties of abelian varieties", "description": "Subvarieties of abelian varieties", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K15", "originalCode": "14K15", "name": "Arithmetic ground fields for abelian varieties", "description": "Arithmetic ground fields for abelian varieties [See also 11Dxx, 11Fxx, 11G10, 14Gxx]", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K20", "originalCode": "14K20", "name": "Analytic theory of abelian varieties; abelian integrals and differentials", "description": "Analytic theory of abelian varieties; abelian integrals and differentials", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K22", "originalCode": "14K22", "name": "Complex multiplication and abelian varieties", "description": "Complex multiplication and abelian varieties [See also 11G15]", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K25", "originalCode": "14K25", "name": "Theta functions and abelian varieties", "description": "Theta functions and abelian varieties [See also 14H42]", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K30", "originalCode": "14K30", "name": "Picard schemes, higher Jacobians", "description": "Picard schemes, higher Jacobians [See also 14H40, 32G20]", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14K99", "originalCode": "14K99", "name": "Abelian varieties and schemes", "description": "None of the above, but in this section", "kind": "subject", "parent": "14K", "page": 38 }, { "code": "14L", "originalCode": "14Lxx", "name": "Algebraic groups", "description": "Algebraic groups [See also 11E57] \\{For Lie algebras, see 17B45; for linear algebraic groups, see 20Gxx\\}", "kind": "section", "parent": "14", "page": 38 }, { "code": "14L05", "originalCode": "14L05", "name": "Formal groups, \\(p\\)-divisible groups", "description": "Formal groups, \\(p\\)-divisible groups [See also 55N22]", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14L10", "originalCode": "14L10", "name": "Group varieties", "description": "Group varieties", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14L15", "originalCode": "14L15", "name": "Group schemes", "description": "Group schemes", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14L17", "originalCode": "14L17", "name": "Affine algebraic groups, hyperalgebra constructions", "description": "Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18C40]", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14L24", "originalCode": "14L24", "name": "Geometric invariant theory", "description": "Geometric invariant theory [See also 13A50]", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14L30", "originalCode": "14L30", "name": "Group actions on varieties or schemes (quotients)", "description": "Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14L35", "originalCode": "14L35", "name": "Classical groups (algebro-geometric aspects)", "description": "Classical groups (algebro-geometric aspects) [See also 20Gxx, 51N30]", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14L40", "originalCode": "14L40", "name": "Other algebraic groups (geometric aspects)", "description": "Other algebraic groups (geometric aspects)", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14L99", "originalCode": "14L99", "name": "Algebraic groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "14L", "page": 38 }, { "code": "14M", "originalCode": "14Mxx", "name": "Special varieties", "description": "Special varieties", "kind": "section", "parent": "14", "page": 38 }, { "code": "14M05", "originalCode": "14M05", "name": "Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)", "description": "Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M06", "originalCode": "14M06", "name": "Linkage", "description": "Linkage [See also 13C40]", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M07", "originalCode": "14M07", "name": "Low codimension problems in algebraic geometry", "description": "Low codimension problems in algebraic geometry", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M10", "originalCode": "14M10", "name": "Complete intersections", "description": "Complete intersections [See also 13C40]", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M12", "originalCode": "14M12", "name": "Determinantal varieties", "description": "Determinantal varieties [See also 13C40]", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M15", "originalCode": "14M15", "name": "Grassmannians, Schubert varieties, flag manifolds", "description": "Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M17", "originalCode": "14M17", "name": "Homogeneous spaces and generalizations", "description": "Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M20", "originalCode": "14M20", "name": "Rational and unirational varieties", "description": "Rational and unirational varieties [See also 14E08]", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M22", "originalCode": "14M22", "name": "Rationally connected varieties", "description": "Rationally connected varieties", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M25", "originalCode": "14M25", "name": "Toric varieties, Newton polyhedra, Okounkov bodies", "description": "Toric varieties, Newton polyhedra, Okounkov bodies [See also 52B20]", "kind": "subject", "parent": "14M", "page": 38 }, { "code": "14M27", "originalCode": "14M27", "name": "Compactifications; symmetric and spherical varieties", "description": "Compactifications; symmetric and spherical varieties", "kind": "subject", "parent": "14M", "page": 39 }, { "code": "14M30", "originalCode": "14M30", "name": "Supervarieties", "description": "Supervarieties [See also 32C11, 58A50]", "kind": "subject", "parent": "14M", "page": 39 }, { "code": "14M35", "originalCode": "14M35", "name": "Character varieties", "description": "Character varieties", "kind": "subject", "parent": "14M", "page": 39 }, { "code": "14M99", "originalCode": "14M99", "name": "Special varieties", "description": "None of the above, but in this section", "kind": "subject", "parent": "14M", "page": 39 }, { "code": "14N", "originalCode": "14Nxx", "name": "Projective and enumerative algebraic geometry", "description": "Projective and enumerative algebraic geometry [See also 51-XX]", "kind": "section", "parent": "14", "page": 39 }, { "code": "14N05", "originalCode": "14N05", "name": "Projective techniques in algebraic geometry", "description": "Projective techniques in algebraic geometry [See also 51N35]", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14N07", "originalCode": "14N07", "name": "Secant varieties, tensor rank, varieties of sums of powers", "description": "Secant varieties, tensor rank, varieties of sums of powers", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14N10", "originalCode": "14N10", "name": "Enumerative problems (combinatorial problems) in algebraic geometry", "description": "Enumerative problems (combinatorial problems) in algebraic geometry", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14N15", "originalCode": "14N15", "name": "Classical problems, Schubert calculus", "description": "Classical problems, Schubert calculus", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14N20", "originalCode": "14N20", "name": "Configurations and arrangements of linear subspaces", "description": "Configurations and arrangements of linear subspaces", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14N25", "originalCode": "14N25", "name": "Varieties of low degree", "description": "Varieties of low degree", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14N30", "originalCode": "14N30", "name": "Adjunction problems", "description": "Adjunction problems", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14N35", "originalCode": "14N35", "name": "Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)", "description": "Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) [See also 53D45]", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14N99", "originalCode": "14N99", "name": "Projective and enumerative algebraic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14N", "page": 39 }, { "code": "14P", "originalCode": "14Pxx", "name": "Real algebraic and real-analytic geometry", "description": "Real algebraic and real-analytic geometry", "kind": "section", "parent": "14", "page": 39 }, { "code": "14P05", "originalCode": "14P05", "name": "Real algebraic sets", "description": "Real algebraic sets [See also 12D15, 13J30]", "kind": "subject", "parent": "14P", "page": 39 }, { "code": "14P10", "originalCode": "14P10", "name": "Semialgebraic sets and related spaces", "description": "Semialgebraic sets and related spaces", "kind": "subject", "parent": "14P", "page": 39 }, { "code": "14P15", "originalCode": "14P15", "name": "Real-analytic and semi-analytic sets", "description": "Real-analytic and semi-analytic sets [See also 32B20, 32C05]", "kind": "subject", "parent": "14P", "page": 39 }, { "code": "14P20", "originalCode": "14P20", "name": "Nash functions and manifolds", "description": "Nash functions and manifolds [See also 32C07, 58A07]", "kind": "subject", "parent": "14P", "page": 39 }, { "code": "14P25", "originalCode": "14P25", "name": "Topology of real algebraic varieties", "description": "Topology of real algebraic varieties", "kind": "subject", "parent": "14P", "page": 39 }, { "code": "14P99", "originalCode": "14P99", "name": "Real algebraic and real-analytic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14P", "page": 39 }, { "code": "14Q", "originalCode": "14Qxx", "name": "Computational aspects in algebraic geometry", "description": "Computational aspects in algebraic geometry \\{For software etc., see 14-04\\} [See also 12-08, 13Pxx, 68W30]", "kind": "section", "parent": "14", "page": 39 }, { "code": "14Q05", "originalCode": "14Q05", "name": "Computational aspects of algebraic curves", "description": "Computational aspects of algebraic curves [See also 14Hxx]", "kind": "subject", "parent": "14Q", "page": 39 }, { "code": "14Q10", "originalCode": "14Q10", "name": "Computational aspects of algebraic surfaces", "description": "Computational aspects of algebraic surfaces [See also 14Jxx]", "kind": "subject", "parent": "14Q", "page": 39 }, { "code": "14Q15", "originalCode": "14Q15", "name": "Computational aspects of higher-dimensional varieties", "description": "Computational aspects of higher-dimensional varieties [See also 14Jxx, 14Mxx]", "kind": "subject", "parent": "14Q", "page": 39 }, { "code": "14Q20", "originalCode": "14Q20", "name": "Effectivity, complexity and computational aspects of algebraic geometry", "description": "Effectivity, complexity and computational aspects of algebraic geometry", "kind": "subject", "parent": "14Q", "page": 39 }, { "code": "14Q25", "originalCode": "14Q25", "name": "Computational algebraic geometry over arithmetic ground fields", "description": "Computational algebraic geometry over arithmetic ground fields [See also 14Gxx, 14H25, 14Kxx]", "kind": "subject", "parent": "14Q", "page": 39 }, { "code": "14Q30", "originalCode": "14Q30", "name": "Computational real algebraic geometry", "description": "Computational real algebraic geometry [See also 14Pxx]", "kind": "subject", "parent": "14Q", "page": 39 }, { "code": "14Q65", "originalCode": "14Q65", "name": "Geometric aspects of numerical algebraic geometry", "description": "Geometric aspects of numerical algebraic geometry [See also 65H14]", "kind": "subject", "parent": "14Q", "page": 39 }, { "code": "14Q99", "originalCode": "14Q99", "name": "Computational aspects in algebraic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14Q", "page": 39 }, { "code": "14R", "originalCode": "14Rxx", "name": "Affine geometry", "description": "Affine geometry", "kind": "section", "parent": "14", "page": 40 }, { "code": "14R05", "originalCode": "14R05", "name": "Classification of affine varieties", "description": "Classification of affine varieties", "kind": "subject", "parent": "14R", "page": 40 }, { "code": "14R10", "originalCode": "14R10", "name": "Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)", "description": "Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)", "kind": "subject", "parent": "14R", "page": 40 }, { "code": "14R15", "originalCode": "14R15", "name": "Jacobian problem", "description": "Jacobian problem [See also 13F20]", "kind": "subject", "parent": "14R", "page": 40 }, { "code": "14R20", "originalCode": "14R20", "name": "Group actions on affine varieties", "description": "Group actions on affine varieties [See also 13A50, 14L30]", "kind": "subject", "parent": "14R", "page": 40 }, { "code": "14R25", "originalCode": "14R25", "name": "Affine fibrations", "description": "Affine fibrations [See also 14D06]", "kind": "subject", "parent": "14R", "page": 40 }, { "code": "14R99", "originalCode": "14R99", "name": "Affine geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14R", "page": 40 }, { "code": "14T", "originalCode": "14Txx", "name": "Tropical geometry", "description": "Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]", "kind": "section", "parent": "14", "page": 40 }, { "code": "14T10", "originalCode": "14T10", "name": "Foundations of tropical geometry and relations with algebra", "description": "Foundations of tropical geometry and relations with algebra \\{For algebraic aspects, see 15A80\\}", "kind": "subject", "parent": "14T", "page": 40 }, { "code": "14T15", "originalCode": "14T15", "name": "Combinatorial aspects of tropical varieties", "description": "Combinatorial aspects of tropical varieties", "kind": "subject", "parent": "14T", "page": 40 }, { "code": "14T20", "originalCode": "14T20", "name": "Geometric aspects of tropical varieties", "description": "Geometric aspects of tropical varieties", "kind": "subject", "parent": "14T", "page": 40 }, { "code": "14T25", "originalCode": "14T25", "name": "Arithmetic aspects of tropical varieties", "description": "Arithmetic aspects of tropical varieties", "kind": "subject", "parent": "14T", "page": 40 }, { "code": "14T90", "originalCode": "14T90", "name": "Applications of tropical geometry", "description": "Applications of tropical geometry", "kind": "subject", "parent": "14T", "page": 40 }, { "code": "14T99", "originalCode": "14T99", "name": "Tropical geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "14T", "page": 40 }, { "code": "15", "originalCode": "15-XX", "name": "Linear and multilinear algebra; matrix theory", "description": "Linear and multilinear algebra; matrix theory", "kind": "class", "parent": null, "page": 40 }, { "code": "15-00", "originalCode": "15-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to linear algebra", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to linear algebra", "kind": "subject", "parent": "15", "page": 40 }, { "code": "15-01", "originalCode": "15-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra", "kind": "subject", "parent": "15", "page": 40 }, { "code": "15-02", "originalCode": "15-02", "name": "Research exposition (monographs, survey articles) pertaining to linear algebra", "description": "Research exposition (monographs, survey articles) pertaining to linear algebra", "kind": "subject", "parent": "15", "page": 40 }, { "code": "15-03", "originalCode": "15-03", "name": "History of linear algebra", "description": "History of linear algebra [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "15", "page": 40 }, { "code": "15-04", "originalCode": "15-04", "name": "Software, source code, etc. for problems pertaining to linear algebra", "description": "Software, source code, etc. for problems pertaining to linear algebra", "kind": "subject", "parent": "15", "page": 40 }, { "code": "15-06", "originalCode": "15-06", "name": "Proceedings, conferences, collections, etc. pertaining to linear algebra", "description": "Proceedings, conferences, collections, etc. pertaining to linear algebra", "kind": "subject", "parent": "15", "page": 40 }, { "code": "15-11", "originalCode": "15-11", "name": "Research data for problems pertaining to linear algebra", "description": "Research data for problems pertaining to linear algebra", "kind": "subject", "parent": "15", "page": 40 }, { "code": "15A", "originalCode": "15Axx", "name": "Basic linear algebra", "description": "Basic linear algebra", "kind": "section", "parent": "15", "page": 40 }, { "code": "15A03", "originalCode": "15A03", "name": "Vector spaces, linear dependence, rank, lineability", "description": "Vector spaces, linear dependence, rank, lineability", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A04", "originalCode": "15A04", "name": "Linear transformations, semilinear transformations", "description": "Linear transformations, semilinear transformations", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A06", "originalCode": "15A06", "name": "Linear equations (linear algebraic aspects)", "description": "Linear equations (linear algebraic aspects)", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A09", "originalCode": "15A09", "name": "Theory of matrix inversion and generalized inverses", "description": "Theory of matrix inversion and generalized inverses", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A10", "originalCode": "15A10", "name": "Applications of generalized inverses", "description": "Applications of generalized inverses", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A12", "originalCode": "15A12", "name": "Conditioning of matrices", "description": "Conditioning of matrices [See also 65F35]", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A15", "originalCode": "15A15", "name": "Determinants, permanents, traces, other special matrix functions", "description": "Determinants, permanents, traces, other special matrix functions [See also 19B10, 19B14]", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A16", "originalCode": "15A16", "name": "Matrix exponential and similar functions of matrices", "description": "Matrix exponential and similar functions of matrices", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A18", "originalCode": "15A18", "name": "Eigenvalues, singular values, and eigenvectors", "description": "Eigenvalues, singular values, and eigenvectors", "kind": "subject", "parent": "15A", "page": 40 }, { "code": "15A20", "originalCode": "15A20", "name": "Diagonalization, Jordan forms", "description": "Diagonalization, Jordan forms", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A21", "originalCode": "15A21", "name": "Canonical forms, reductions, classification", "description": "Canonical forms, reductions, classification", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A22", "originalCode": "15A22", "name": "Matrix pencils", "description": "Matrix pencils [See also 47A56]", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A23", "originalCode": "15A23", "name": "Factorization of matrices", "description": "Factorization of matrices", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A24", "originalCode": "15A24", "name": "Matrix equations and identities", "description": "Matrix equations and identities", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A27", "originalCode": "15A27", "name": "Commutativity of matrices", "description": "Commutativity of matrices", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A29", "originalCode": "15A29", "name": "Inverse problems in linear algebra", "description": "Inverse problems in linear algebra", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A30", "originalCode": "15A30", "name": "Algebraic systems of matrices", "description": "Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A39", "originalCode": "15A39", "name": "Linear inequalities of matrices", "description": "Linear inequalities of matrices", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A42", "originalCode": "15A42", "name": "Inequalities involving eigenvalues and eigenvectors", "description": "Inequalities involving eigenvalues and eigenvectors", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A45", "originalCode": "15A45", "name": "Miscellaneous inequalities involving matrices", "description": "Miscellaneous inequalities involving matrices", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A54", "originalCode": "15A54", "name": "Matrices over function rings in one or more variables", "description": "Matrices over function rings in one or more variables", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A60", "originalCode": "15A60", "name": "Norms of matrices, numerical range, applications of functional analysis to matrix theory", "description": "Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A63", "originalCode": "15A63", "name": "Quadratic and bilinear forms, inner products", "description": "Quadratic and bilinear forms, inner products [See mainly 11Exx]", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A66", "originalCode": "15A66", "name": "Clifford algebras, spinors", "description": "Clifford algebras, spinors", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A67", "originalCode": "15A67", "name": "Applications of Clifford algebras to physics, etc.", "description": "Applications of Clifford algebras to physics, etc.", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A69", "originalCode": "15A69", "name": "Multilinear algebra, tensor calculus", "description": "Multilinear algebra, tensor calculus", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A72", "originalCode": "15A72", "name": "Vector and tensor algebra, theory of invariants", "description": "Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A75", "originalCode": "15A75", "name": "Exterior algebra, Grassmann algebras", "description": "Exterior algebra, Grassmann algebras", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A78", "originalCode": "15A78", "name": "Other algebras built from modules", "description": "Other algebras built from modules", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A80", "originalCode": "15A80", "name": "Max-plus and related algebras", "description": "Max-plus and related algebras", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A83", "originalCode": "15A83", "name": "Matrix completion problems", "description": "Matrix completion problems", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A86", "originalCode": "15A86", "name": "Linear preserver problems", "description": "Linear preserver problems", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15A99", "originalCode": "15A99", "name": "Basic linear algebra", "description": "None of the above, but in this section", "kind": "subject", "parent": "15A", "page": 41 }, { "code": "15B", "originalCode": "15Bxx", "name": "Special matrices", "description": "Special matrices", "kind": "section", "parent": "15", "page": 41 }, { "code": "15B05", "originalCode": "15B05", "name": "Toeplitz, Cauchy, and related matrices", "description": "Toeplitz, Cauchy, and related matrices", "kind": "subject", "parent": "15B", "page": 41 }, { "code": "15B10", "originalCode": "15B10", "name": "Orthogonal matrices", "description": "Orthogonal matrices", "kind": "subject", "parent": "15B", "page": 41 }, { "code": "15B15", "originalCode": "15B15", "name": "Fuzzy matrices", "description": "Fuzzy matrices", "kind": "subject", "parent": "15B", "page": 41 }, { "code": "15B30", "originalCode": "15B30", "name": "Matrix Lie algebras", "description": "Matrix Lie algebras", "kind": "subject", "parent": "15B", "page": 41 }, { "code": "15B33", "originalCode": "15B33", "name": "Matrices over special rings (quaternions, finite fields, etc.)", "description": "Matrices over special rings (quaternions, finite fields, etc.)", "kind": "subject", "parent": "15B", "page": 41 }, { "code": "15B34", "originalCode": "15B34", "name": "Boolean and Hadamard matrices", "description": "Boolean and Hadamard matrices", "kind": "subject", "parent": "15B", "page": 41 }, { "code": "15B35", "originalCode": "15B35", "name": "Sign pattern matrices", "description": "Sign pattern matrices", "kind": "subject", "parent": "15B", "page": 41 }, { "code": "15B36", "originalCode": "15B36", "name": "Matrices of integers", "description": "Matrices of integers [See also 11C20]", "kind": "subject", "parent": "15B", "page": 42 }, { "code": "15B48", "originalCode": "15B48", "name": "Positive matrices and their generalizations; cones of matrices", "description": "Positive matrices and their generalizations; cones of matrices", "kind": "subject", "parent": "15B", "page": 42 }, { "code": "15B51", "originalCode": "15B51", "name": "Stochastic matrices", "description": "Stochastic matrices", "kind": "subject", "parent": "15B", "page": 42 }, { "code": "15B52", "originalCode": "15B52", "name": "Random matrices (algebraic aspects)", "description": "Random matrices (algebraic aspects) \\{For probabilistic aspects, see 60B20\\}", "kind": "subject", "parent": "15B", "page": 42 }, { "code": "15B57", "originalCode": "15B57", "name": "Hermitian, skew-Hermitian, and related matrices", "description": "Hermitian, skew-Hermitian, and related matrices", "kind": "subject", "parent": "15B", "page": 42 }, { "code": "15B99", "originalCode": "15B99", "name": "Special matrices", "description": "None of the above, but in this section", "kind": "subject", "parent": "15B", "page": 42 }, { "code": "16", "originalCode": "16-XX", "name": "Associative rings and algebras", "description": "Associative rings and algebras \\{For the commutative case, see 13-XX\\}", "kind": "class", "parent": null, "page": 42 }, { "code": "16-00", "originalCode": "16-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras", "kind": "subject", "parent": "16", "page": 42 }, { "code": "16-01", "originalCode": "16-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras", "kind": "subject", "parent": "16", "page": 42 }, { "code": "16-02", "originalCode": "16-02", "name": "Research exposition (monographs, survey articles) pertaining to associative rings and algebras", "description": "Research exposition (monographs, survey articles) pertaining to associative rings and algebras", "kind": "subject", "parent": "16", "page": 42 }, { "code": "16-03", "originalCode": "16-03", "name": "History of associative rings and algebras", "description": "History of associative rings and algebras [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "16", "page": 42 }, { "code": "16-04", "originalCode": "16-04", "name": "Software, source code, etc. for problems pertaining to associative rings and algebras", "description": "Software, source code, etc. for problems pertaining to associative rings and algebras", "kind": "subject", "parent": "16", "page": 42 }, { "code": "16-06", "originalCode": "16-06", "name": "Proceedings, conferences, collections, etc. pertaining to associative rings and algebras", "description": "Proceedings, conferences, collections, etc. pertaining to associative rings and algebras", "kind": "subject", "parent": "16", "page": 42 }, { "code": "16-11", "originalCode": "16-11", "name": "Research data for problems pertaining to associative rings and algebras", "description": "Research data for problems pertaining to associative rings and algebras", "kind": "subject", "parent": "16", "page": 42 }, { "code": "16B", "originalCode": "16Bxx", "name": "General and miscellaneous", "description": "General and miscellaneous", "kind": "section", "parent": "16", "page": 42 }, { "code": "16B50", "originalCode": "16B50", "name": "Category-theoretic methods and results in associative algebras (except as in 16D90)", "description": "Category-theoretic methods and results in associative algebras (except as in 16D90) [See also 18-XX]", "kind": "subject", "parent": "16B", "page": 42 }, { "code": "16B70", "originalCode": "16B70", "name": "Applications of logic in associative algebras", "description": "Applications of logic in associative algebras [See also 03Cxx]", "kind": "subject", "parent": "16B", "page": 42 }, { "code": "16B99", "originalCode": "16B99", "name": "General and miscellaneous", "description": "None of the above, but in this section", "kind": "subject", "parent": "16B", "page": 42 }, { "code": "16D", "originalCode": "16Dxx", "name": "Modules, bimodules and ideals in associative algebras", "description": "Modules, bimodules and ideals in associative algebras", "kind": "section", "parent": "16", "page": 42 }, { "code": "16D10", "originalCode": "16D10", "name": "General module theory in associative algebras", "description": "General module theory in associative algebras", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D20", "originalCode": "16D20", "name": "Bimodules in associative algebras", "description": "Bimodules in associative algebras", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D25", "originalCode": "16D25", "name": "Ideals in associative algebras", "description": "Ideals in associative algebras", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D30", "originalCode": "16D30", "name": "Infinite-dimensional simple rings (except as in 16Kxx)", "description": "Infinite-dimensional simple rings (except as in 16Kxx)", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D40", "originalCode": "16D40", "name": "Free, projective, and flat modules and ideals in associative algebras", "description": "Free, projective, and flat modules and ideals in associative algebras [See also 19A13]", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D50", "originalCode": "16D50", "name": "Injective modules, self-injective associative rings", "description": "Injective modules, self-injective associative rings [See also 16L60]", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D60", "originalCode": "16D60", "name": "Simple and semisimple modules, primitive rings and ideals in associative algebras", "description": "Simple and semisimple modules, primitive rings and ideals in associative algebras", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D70", "originalCode": "16D70", "name": "Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)", "description": "Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D80", "originalCode": "16D80", "name": "Other classes of modules and ideals in associative algebras", "description": "Other classes of modules and ideals in associative algebras [See also 16G50]", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D90", "originalCode": "16D90", "name": "Module categories in associative algebras", "description": "Module categories in associative algebras [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16D99", "originalCode": "16D99", "name": "Modules, bimodules and ideals in associative algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "16D", "page": 42 }, { "code": "16E", "originalCode": "16Exx", "name": "Homological methods in associative algebras", "description": "Homological methods in associative algebras \\{For commutative rings, see 13Dxx; for general categories, see 18Gxx\\}", "kind": "section", "parent": "16", "page": 43 }, { "code": "16E05", "originalCode": "16E05", "name": "Syzygies, resolutions, complexes in associative algebras", "description": "Syzygies, resolutions, complexes in associative algebras", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E10", "originalCode": "16E10", "name": "Homological dimension in associative algebras", "description": "Homological dimension in associative algebras", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E20", "originalCode": "16E20", "name": "Grothendieck groups, \\(K\\)-theory, etc.", "description": "Grothendieck groups, \\(K\\)-theory, etc. [See also 18F30, 19Axx, 19D50]", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E30", "originalCode": "16E30", "name": "Homological functors on modules (Tor, Ext, etc.) in associative algebras", "description": "Homological functors on modules (Tor, Ext, etc.) in associative algebras", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E35", "originalCode": "16E35", "name": "Derived categories and associative algebras", "description": "Derived categories and associative algebras", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E40", "originalCode": "16E40", "name": "(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)", "description": "(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E45", "originalCode": "16E45", "name": "Differential graded algebras and applications (associative algebraic aspects)", "description": "Differential graded algebras and applications (associative algebraic aspects)", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E50", "originalCode": "16E50", "name": "von Neumann regular rings and generalizations (associative algebraic aspects)", "description": "von Neumann regular rings and generalizations (associative algebraic aspects)", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E60", "originalCode": "16E60", "name": "Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.", "description": "Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E65", "originalCode": "16E65", "name": "Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)", "description": "Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16E99", "originalCode": "16E99", "name": "Homological methods in associative algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "16E", "page": 43 }, { "code": "16G", "originalCode": "16Gxx", "name": "Representation theory of associative rings and algebras", "description": "Representation theory of associative rings and algebras", "kind": "section", "parent": "16", "page": 43 }, { "code": "16G10", "originalCode": "16G10", "name": "Representations of associative Artinian rings", "description": "Representations of associative Artinian rings", "kind": "subject", "parent": "16G", "page": 43 }, { "code": "16G20", "originalCode": "16G20", "name": "Representations of quivers and partially ordered sets", "description": "Representations of quivers and partially ordered sets", "kind": "subject", "parent": "16G", "page": 43 }, { "code": "16G30", "originalCode": "16G30", "name": "Representations of orders, lattices, algebras over commutative rings", "description": "Representations of orders, lattices, algebras over commutative rings [See also 16Hxx]", "kind": "subject", "parent": "16G", "page": 43 }, { "code": "16G50", "originalCode": "16G50", "name": "Cohen-Macaulay modules in associative algebras", "description": "Cohen-Macaulay modules in associative algebras", "kind": "subject", "parent": "16G", "page": 43 }, { "code": "16G60", "originalCode": "16G60", "name": "Representation type (finite, tame, wild, etc.) of associative algebras", "description": "Representation type (finite, tame, wild, etc.) of associative algebras", "kind": "subject", "parent": "16G", "page": 43 }, { "code": "16G70", "originalCode": "16G70", "name": "Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers", "description": "Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers", "kind": "subject", "parent": "16G", "page": 43 }, { "code": "16G99", "originalCode": "16G99", "name": "Representation theory of associative rings and algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "16G", "page": 43 }, { "code": "16H", "originalCode": "16Hxx", "name": "Associative algebras and orders", "description": "Associative algebras and orders \\{For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30\\}", "kind": "section", "parent": "16", "page": 43 }, { "code": "16H05", "originalCode": "16H05", "name": "Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)", "description": "Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)", "kind": "subject", "parent": "16H", "page": 43 }, { "code": "16H10", "originalCode": "16H10", "name": "Orders in separable algebras", "description": "Orders in separable algebras", "kind": "subject", "parent": "16H", "page": 43 }, { "code": "16H15", "originalCode": "16H15", "name": "Commutative orders", "description": "Commutative orders", "kind": "subject", "parent": "16H", "page": 43 }, { "code": "16H20", "originalCode": "16H20", "name": "Lattices over orders", "description": "Lattices over orders", "kind": "subject", "parent": "16H", "page": 43 }, { "code": "16H99", "originalCode": "16H99", "name": "Associative algebras and orders", "description": "None of the above, but in this section", "kind": "subject", "parent": "16H", "page": 43 }, { "code": "16K", "originalCode": "16Kxx", "name": "Division rings and semisimple Artin rings", "description": "Division rings and semisimple Artin rings [See also 12E15, 15A30]", "kind": "section", "parent": "16", "page": 43 }, { "code": "16K20", "originalCode": "16K20", "name": "Finite-dimensional division rings", "description": "Finite-dimensional division rings \\{For crossed products, see 16S35\\}", "kind": "subject", "parent": "16K", "page": 43 }, { "code": "16K40", "originalCode": "16K40", "name": "Infinite-dimensional and general division rings", "description": "Infinite-dimensional and general division rings", "kind": "subject", "parent": "16K", "page": 43 }, { "code": "16K50", "originalCode": "16K50", "name": "Brauer groups (algebraic aspects)", "description": "Brauer groups (algebraic aspects) [See also 12G05, 14F22]", "kind": "subject", "parent": "16K", "page": 43 }, { "code": "16K99", "originalCode": "16K99", "name": "Division rings and semisimple Artin rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "16K", "page": 43 }, { "code": "16L", "originalCode": "16Lxx", "name": "Local rings and generalizations", "description": "Local rings and generalizations", "kind": "section", "parent": "16", "page": 44 }, { "code": "16L30", "originalCode": "16L30", "name": "Noncommutative local and semilocal rings, perfect rings", "description": "Noncommutative local and semilocal rings, perfect rings", "kind": "subject", "parent": "16L", "page": 44 }, { "code": "16L60", "originalCode": "16L60", "name": "Quasi-Frobenius rings", "description": "Quasi-Frobenius rings [See also 16D50]", "kind": "subject", "parent": "16L", "page": 44 }, { "code": "16L99", "originalCode": "16L99", "name": "Local rings and generalizations", "description": "None of the above, but in this section", "kind": "subject", "parent": "16L", "page": 44 }, { "code": "16N", "originalCode": "16Nxx", "name": "Radicals and radical properties of associative rings", "description": "Radicals and radical properties of associative rings", "kind": "section", "parent": "16", "page": 44 }, { "code": "16N20", "originalCode": "16N20", "name": "Jacobson radical, quasimultiplication", "description": "Jacobson radical, quasimultiplication", "kind": "subject", "parent": "16N", "page": 44 }, { "code": "16N40", "originalCode": "16N40", "name": "Nil and nilpotent radicals, sets, ideals, associative rings", "description": "Nil and nilpotent radicals, sets, ideals, associative rings", "kind": "subject", "parent": "16N", "page": 44 }, { "code": "16N60", "originalCode": "16N60", "name": "Prime and semiprime associative rings", "description": "Prime and semiprime associative rings [See also 16D60, 16U10]", "kind": "subject", "parent": "16N", "page": 44 }, { "code": "16N80", "originalCode": "16N80", "name": "General radicals and associative rings", "description": "General radicals and associative rings \\{For radicals in module categories, see 16S90\\}", "kind": "subject", "parent": "16N", "page": 44 }, { "code": "16N99", "originalCode": "16N99", "name": "Radicals and radical properties of associative rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "16N", "page": 44 }, { "code": "16P", "originalCode": "16Pxx", "name": "Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras", "description": "Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras", "kind": "section", "parent": "16", "page": 44 }, { "code": "16P10", "originalCode": "16P10", "name": "Finite rings and finite-dimensional associative algebras", "description": "Finite rings and finite-dimensional associative algebras \\{For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx\\}", "kind": "subject", "parent": "16P", "page": 44 }, { "code": "16P20", "originalCode": "16P20", "name": "Artinian rings and modules (associative rings and algebras)", "description": "Artinian rings and modules (associative rings and algebras)", "kind": "subject", "parent": "16P", "page": 44 }, { "code": "16P40", "originalCode": "16P40", "name": "Noetherian rings and modules (associative rings and algebras)", "description": "Noetherian rings and modules (associative rings and algebras)", "kind": "subject", "parent": "16P", "page": 44 }, { "code": "16P50", "originalCode": "16P50", "name": "Localization and associative Noetherian rings", "description": "Localization and associative Noetherian rings [See also 16U20]", "kind": "subject", "parent": "16P", "page": 44 }, { "code": "16P60", "originalCode": "16P60", "name": "Chain conditions on annihilators and summands: Goldie-type conditions", "description": "Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension (associative rings and algebras)", "kind": "subject", "parent": "16P", "page": 44 }, { "code": "16P70", "originalCode": "16P70", "name": "Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)", "description": "Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)", "kind": "subject", "parent": "16P", "page": 44 }, { "code": "16P90", "originalCode": "16P90", "name": "Growth rate, Gelfand-Kirillov dimension", "description": "Growth rate, Gelfand-Kirillov dimension", "kind": "subject", "parent": "16P", "page": 44 }, { "code": "16P99", "originalCode": "16P99", "name": "Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "16P", "page": 44 }, { "code": "16R", "originalCode": "16Rxx", "name": "Rings with polynomial identity", "description": "Rings with polynomial identity", "kind": "section", "parent": "16", "page": 44 }, { "code": "16R10", "originalCode": "16R10", "name": "\\(T\\)-ideals, identities, varieties of associative rings and algebras", "description": "\\(T\\)-ideals, identities, varieties of associative rings and algebras", "kind": "subject", "parent": "16R", "page": 44 }, { "code": "16R20", "originalCode": "16R20", "name": "Semiprime p.i. rings, rings embeddable in matrices over commutative rings", "description": "Semiprime p.i. rings, rings embeddable in matrices over commutative rings", "kind": "subject", "parent": "16R", "page": 44 }, { "code": "16R30", "originalCode": "16R30", "name": "Trace rings and invariant theory (associative rings and algebras)", "description": "Trace rings and invariant theory (associative rings and algebras)", "kind": "subject", "parent": "16R", "page": 44 }, { "code": "16R40", "originalCode": "16R40", "name": "Identities other than those of matrices over commutative rings", "description": "Identities other than those of matrices over commutative rings", "kind": "subject", "parent": "16R", "page": 44 }, { "code": "16R50", "originalCode": "16R50", "name": "Other kinds of identities (generalized polynomial, rational, involution)", "description": "Other kinds of identities (generalized polynomial, rational, involution)", "kind": "subject", "parent": "16R", "page": 44 }, { "code": "16R60", "originalCode": "16R60", "name": "Functional identities (associative rings and algebras)", "description": "Functional identities (associative rings and algebras)", "kind": "subject", "parent": "16R", "page": 44 }, { "code": "16R99", "originalCode": "16R99", "name": "Rings with polynomial identity", "description": "None of the above, but in this section", "kind": "subject", "parent": "16R", "page": 44 }, { "code": "16S", "originalCode": "16Sxx", "name": "Associative rings and algebras arising under various constructions", "description": "Associative rings and algebras arising under various constructions", "kind": "section", "parent": "16", "page": 45 }, { "code": "16S10", "originalCode": "16S10", "name": "Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)", "description": "Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S15", "originalCode": "16S15", "name": "Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)", "description": "Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S20", "originalCode": "16S20", "name": "Centralizing and normalizing extensions", "description": "Centralizing and normalizing extensions", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S30", "originalCode": "16S30", "name": "Universal enveloping algebras of Lie algebras", "description": "Universal enveloping algebras of Lie algebras [See mainly 17B35]", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S32", "originalCode": "16S32", "name": "Rings of differential operators (associative algebraic aspects)", "description": "Rings of differential operators (associative algebraic aspects) [See also 13N10, 32C38]", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S34", "originalCode": "16S34", "name": "Group rings", "description": "Group rings [See also 20C05, 20C07], Laurent polynomial rings (associative algebraic aspects)", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S35", "originalCode": "16S35", "name": "Twisted and skew group rings, crossed products", "description": "Twisted and skew group rings, crossed products", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S36", "originalCode": "16S36", "name": "Ordinary and skew polynomial rings and semigroup rings", "description": "Ordinary and skew polynomial rings and semigroup rings [See also 20M25]", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S37", "originalCode": "16S37", "name": "Quadratic and Koszul algebras", "description": "Quadratic and Koszul algebras", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S38", "originalCode": "16S38", "name": "Rings arising from noncommutative algebraic geometry", "description": "Rings arising from noncommutative algebraic geometry [See also 14A22]", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S40", "originalCode": "16S40", "name": "Smash products of general Hopf actions", "description": "Smash products of general Hopf actions [See also 16T05]", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S50", "originalCode": "16S50", "name": "Endomorphism rings; matrix rings", "description": "Endomorphism rings; matrix rings [See also 15-XX]", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S60", "originalCode": "16S60", "name": "Associative rings of functions, subdirect products, sheaves of rings", "description": "Associative rings of functions, subdirect products, sheaves of rings", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S70", "originalCode": "16S70", "name": "Extensions of associative rings by ideals", "description": "Extensions of associative rings by ideals", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S80", "originalCode": "16S80", "name": "Deformations of associative rings", "description": "Deformations of associative rings [See also 13D10, 14D15]", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S85", "originalCode": "16S85", "name": "Associative rings of fractions and localizations", "description": "Associative rings of fractions and localizations [See also 13B30]", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S88", "originalCode": "16S88", "name": "Leavitt path algebras", "description": "Leavitt path algebras", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S90", "originalCode": "16S90", "name": "Torsion theories; radicals on module categories (associative algebraic aspects)", "description": "Torsion theories; radicals on module categories (associative algebraic aspects) [See also 13D30, 18E40] \\{For radicals of rings, see 16Nxx\\}", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16S99", "originalCode": "16S99", "name": "Associative rings and algebras arising under various constructions", "description": "None of the above, but in this section", "kind": "subject", "parent": "16S", "page": 45 }, { "code": "16T", "originalCode": "16Txx", "name": "Hopf algebras, quantum groups and related topics", "description": "Hopf algebras, quantum groups and related topics", "kind": "section", "parent": "16", "page": 45 }, { "code": "16T05", "originalCode": "16T05", "name": "Hopf algebras and their applications", "description": "Hopf algebras and their applications [See also 16S40, 57T05]", "kind": "subject", "parent": "16T", "page": 45 }, { "code": "16T10", "originalCode": "16T10", "name": "Bialgebras", "description": "Bialgebras", "kind": "subject", "parent": "16T", "page": 45 }, { "code": "16T15", "originalCode": "16T15", "name": "Coalgebras and comodules; corings", "description": "Coalgebras and comodules; corings", "kind": "subject", "parent": "16T", "page": 45 }, { "code": "16T20", "originalCode": "16T20", "name": "Ring-theoretic aspects of quantum groups", "description": "Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]", "kind": "subject", "parent": "16T", "page": 45 }, { "code": "16T25", "originalCode": "16T25", "name": "Yang-Baxter equations", "description": "Yang-Baxter equations", "kind": "subject", "parent": "16T", "page": 45 }, { "code": "16T30", "originalCode": "16T30", "name": "Connections of Hopf algebras with combinatorics", "description": "Connections of Hopf algebras with combinatorics [See also 05Exx]", "kind": "subject", "parent": "16T", "page": 45 }, { "code": "16T99", "originalCode": "16T99", "name": "Hopf algebras, quantum groups and related topics", "description": "None of the above, but in this section", "kind": "subject", "parent": "16T", "page": 45 }, { "code": "16U", "originalCode": "16Uxx", "name": "Conditions on elements", "description": "Conditions on elements", "kind": "section", "parent": "16", "page": 46 }, { "code": "16U10", "originalCode": "16U10", "name": "Integral domains (associative rings and algebras)", "description": "Integral domains (associative rings and algebras)", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16U20", "originalCode": "16U20", "name": "Ore rings, multiplicative sets, Ore localization", "description": "Ore rings, multiplicative sets, Ore localization", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16U30", "originalCode": "16U30", "name": "Divisibility, noncommutative UFDs", "description": "Divisibility, noncommutative UFDs", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16U40", "originalCode": "16U40", "name": "Idempotent elements (associative rings and algebras)", "description": "Idempotent elements (associative rings and algebras)", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16U60", "originalCode": "16U60", "name": "Units, groups of units (associative rings and algebras)", "description": "Units, groups of units (associative rings and algebras)", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16U70", "originalCode": "16U70", "name": "Center, normalizer (invariant elements) (associative rings and algebras)", "description": "Center, normalizer (invariant elements) (associative rings and algebras)", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16U80", "originalCode": "16U80", "name": "Generalizations of commutativity (associative rings and algebras)", "description": "Generalizations of commutativity (associative rings and algebras)", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16U90", "originalCode": "16U90", "name": "Generalized inverses (associative rings and algebras)", "description": "Generalized inverses (associative rings and algebras)", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16U99", "originalCode": "16U99", "name": "Conditions on elements", "description": "None of the above, but in this section", "kind": "subject", "parent": "16U", "page": 46 }, { "code": "16W", "originalCode": "16Wxx", "name": "Associative rings and algebras with additional structure", "description": "Associative rings and algebras with additional structure", "kind": "section", "parent": "16", "page": 46 }, { "code": "16W10", "originalCode": "16W10", "name": "Rings with involution; Lie, Jordan and other nonassociative structures", "description": "Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W20", "originalCode": "16W20", "name": "Automorphisms and endomorphisms", "description": "Automorphisms and endomorphisms", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W22", "originalCode": "16W22", "name": "Actions of groups and semigroups; invariant theory (associative rings and algebras)", "description": "Actions of groups and semigroups; invariant theory (associative rings and algebras)", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W25", "originalCode": "16W25", "name": "Derivations, actions of Lie algebras", "description": "Derivations, actions of Lie algebras", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W50", "originalCode": "16W50", "name": "Graded rings and modules (associative rings and algebras)", "description": "Graded rings and modules (associative rings and algebras)", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W55", "originalCode": "16W55", "name": "``Super'' (or ``skew'') structure", "description": "``Super'' (or ``skew'') structure [See also 17A70, 17Bxx, 17C70] \\{For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66\\}", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W60", "originalCode": "16W60", "name": "Valuations, completions, formal power series and related constructions (associative rings and algebras)", "description": "Valuations, completions, formal power series and related constructions (associative rings and algebras) [See also 13Jxx]", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W70", "originalCode": "16W70", "name": "Filtered associative rings; filtrational and graded techniques", "description": "Filtered associative rings; filtrational and graded techniques", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W80", "originalCode": "16W80", "name": "Topological and ordered rings and modules", "description": "Topological and ordered rings and modules [See also 06F25, 13Jxx]", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16W99", "originalCode": "16W99", "name": "Associative rings and algebras with additional structure", "description": "None of the above, but in this section", "kind": "subject", "parent": "16W", "page": 46 }, { "code": "16Y", "originalCode": "16Yxx", "name": "Generalizations", "description": "Generalizations \\{For nonassociative rings, see 17-XX\\}", "kind": "section", "parent": "16", "page": 46 }, { "code": "16Y20", "originalCode": "16Y20", "name": "Hyperrings", "description": "Hyperrings", "kind": "subject", "parent": "16Y", "page": 46 }, { "code": "16Y30", "originalCode": "16Y30", "name": "Near-rings", "description": "Near-rings [See also 12K05]", "kind": "subject", "parent": "16Y", "page": 46 }, { "code": "16Y60", "originalCode": "16Y60", "name": "Semirings", "description": "Semirings [See also 12K10]", "kind": "subject", "parent": "16Y", "page": 46 }, { "code": "16Y80", "originalCode": "16Y80", "name": "\\(\\Gamma\\) and fuzzy structures", "description": "\\(\\Gamma\\) and fuzzy structures", "kind": "subject", "parent": "16Y", "page": 46 }, { "code": "16Y99", "originalCode": "16Y99", "name": "Generalizations", "description": "None of the above, but in this section", "kind": "subject", "parent": "16Y", "page": 46 }, { "code": "16Z", "originalCode": "16Zxx", "name": "Computational aspects of associative rings", "description": "Computational aspects of associative rings \\{For software etc., see 16-04\\}", "kind": "section", "parent": "16", "page": 46 }, { "code": "16Z05", "originalCode": "16Z05", "name": "Computational aspects of associative rings (general theory)", "description": "Computational aspects of associative rings (general theory) [See also 68W30]", "kind": "subject", "parent": "16Z", "page": 46 }, { "code": "16Z10", "originalCode": "16Z10", "name": "Gröbner-Shirshov bases", "description": "Gröbner-Shirshov bases", "kind": "subject", "parent": "16Z", "page": 46 }, { "code": "16Z99", "originalCode": "16Z99", "name": "Computational aspects of associative rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "16Z", "page": 46 }, { "code": "17", "originalCode": "17-XX", "name": "Nonassociative rings and algebras", "description": "Nonassociative rings and algebras", "kind": "class", "parent": null, "page": 47 }, { "code": "17-00", "originalCode": "17-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to nonassociative rings and algebras", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to nonassociative rings and algebras", "kind": "subject", "parent": "17", "page": 47 }, { "code": "17-01", "originalCode": "17-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras", "kind": "subject", "parent": "17", "page": 47 }, { "code": "17-02", "originalCode": "17-02", "name": "Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras", "description": "Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras", "kind": "subject", "parent": "17", "page": 47 }, { "code": "17-03", "originalCode": "17-03", "name": "History of nonassociative rings and algebras", "description": "History of nonassociative rings and algebras [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "17", "page": 47 }, { "code": "17-04", "originalCode": "17-04", "name": "Software, source code, etc. for problems pertaining to nonassociative rings and algebras", "description": "Software, source code, etc. for problems pertaining to nonassociative rings and algebras", "kind": "subject", "parent": "17", "page": 47 }, { "code": "17-06", "originalCode": "17-06", "name": "Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras", "description": "Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras", "kind": "subject", "parent": "17", "page": 47 }, { "code": "17-08", "originalCode": "17-08", "name": "Computational methods for problems pertaining to nonassociative rings and algebras", "description": "Computational methods for problems pertaining to nonassociative rings and algebras [See also 68W30]", "kind": "subject", "parent": "17", "page": 47 }, { "code": "17-11", "originalCode": "17-11", "name": "Research data for problems pertaining to nonassociative rings and algebras", "description": "Research data for problems pertaining to nonassociative rings and algebras", "kind": "subject", "parent": "17", "page": 47 }, { "code": "17A", "originalCode": "17Axx", "name": "General nonassociative rings", "description": "General nonassociative rings", "kind": "section", "parent": "17", "page": 47 }, { "code": "17A01", "originalCode": "17A01", "name": "General theory of nonassociative rings and algebras", "description": "General theory of nonassociative rings and algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A05", "originalCode": "17A05", "name": "Power-associative rings", "description": "Power-associative rings", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A15", "originalCode": "17A15", "name": "Noncommutative Jordan algebras", "description": "Noncommutative Jordan algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A20", "originalCode": "17A20", "name": "Flexible algebras", "description": "Flexible algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A30", "originalCode": "17A30", "name": "Nonassociative algebras satisfying other identities", "description": "Nonassociative algebras satisfying other identities", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A32", "originalCode": "17A32", "name": "Leibniz algebras", "description": "Leibniz algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A35", "originalCode": "17A35", "name": "Nonassociative division algebras", "description": "Nonassociative division algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A36", "originalCode": "17A36", "name": "Automorphisms, derivations, other operators (nonassociative rings and algebras)", "description": "Automorphisms, derivations, other operators (nonassociative rings and algebras)", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A40", "originalCode": "17A40", "name": "Ternary compositions", "description": "Ternary compositions", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A42", "originalCode": "17A42", "name": "Other \\(n\\)-ary compositions \\((n \\ge 3)\\)", "description": "Other \\(n\\)-ary compositions \\((n \\ge 3)\\)", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A45", "originalCode": "17A45", "name": "Quadratic algebras (but not quadratic Jordan algebras)", "description": "Quadratic algebras (but not quadratic Jordan algebras)", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A50", "originalCode": "17A50", "name": "Free nonassociative algebras", "description": "Free nonassociative algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A60", "originalCode": "17A60", "name": "Structure theory for nonassociative algebras", "description": "Structure theory for nonassociative algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A61", "originalCode": "17A61", "name": "Gröbner-Shirshov bases in nonassociative algebras", "description": "Gröbner-Shirshov bases in nonassociative algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A65", "originalCode": "17A65", "name": "Radical theory (nonassociative rings and algebras)", "description": "Radical theory (nonassociative rings and algebras)", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A70", "originalCode": "17A70", "name": "Superalgebras", "description": "Superalgebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A75", "originalCode": "17A75", "name": "Composition algebras", "description": "Composition algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A80", "originalCode": "17A80", "name": "Valued algebras", "description": "Valued algebras", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17A99", "originalCode": "17A99", "name": "General nonassociative rings", "description": "None of the above, but in this section", "kind": "subject", "parent": "17A", "page": 47 }, { "code": "17B", "originalCode": "17Bxx", "name": "Lie algebras and Lie superalgebras", "description": "Lie algebras and Lie superalgebras \\{For Lie groups, see 22Exx\\}", "kind": "section", "parent": "17", "page": 48 }, { "code": "17B01", "originalCode": "17B01", "name": "Identities, free Lie (super)algebras", "description": "Identities, free Lie (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B05", "originalCode": "17B05", "name": "Structure theory for Lie algebras and superalgebras", "description": "Structure theory for Lie algebras and superalgebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B08", "originalCode": "17B08", "name": "Coadjoint orbits; nilpotent varieties", "description": "Coadjoint orbits; nilpotent varieties", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B10", "originalCode": "17B10", "name": "Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)", "description": "Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B15", "originalCode": "17B15", "name": "Representations of Lie algebras and Lie superalgebras, analytic theory", "description": "Representations of Lie algebras and Lie superalgebras, analytic theory", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B20", "originalCode": "17B20", "name": "Simple, semisimple, reductive (super)algebras", "description": "Simple, semisimple, reductive (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B22", "originalCode": "17B22", "name": "Root systems", "description": "Root systems", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B25", "originalCode": "17B25", "name": "Exceptional (super)algebras", "description": "Exceptional (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B30", "originalCode": "17B30", "name": "Solvable, nilpotent (super)algebras", "description": "Solvable, nilpotent (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B35", "originalCode": "17B35", "name": "Universal enveloping (super)algebras", "description": "Universal enveloping (super)algebras [See also 16S30]", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B37", "originalCode": "17B37", "name": "Quantum groups (quantized enveloping algebras) and related deformations", "description": "Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B38", "originalCode": "17B38", "name": "Yang-Baxter equations and Rota-Baxter operators", "description": "Yang-Baxter equations and Rota-Baxter operators", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B40", "originalCode": "17B40", "name": "Automorphisms, derivations, other operators for Lie algebras and super algebras", "description": "Automorphisms, derivations, other operators for Lie algebras and super algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B45", "originalCode": "17B45", "name": "Lie algebras of linear algebraic groups", "description": "Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B50", "originalCode": "17B50", "name": "Modular Lie (super)algebras", "description": "Modular Lie (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B55", "originalCode": "17B55", "name": "Homological methods in Lie (super)algebras", "description": "Homological methods in Lie (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B56", "originalCode": "17B56", "name": "Cohomology of Lie (super)algebras", "description": "Cohomology of Lie (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B60", "originalCode": "17B60", "name": "Lie (super)algebras associated with other structures (associative, Jordan, etc.)", "description": "Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B61", "originalCode": "17B61", "name": "Hom-Lie and related algebras", "description": "Hom-Lie and related algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B62", "originalCode": "17B62", "name": "Lie bialgebras; Lie coalgebras", "description": "Lie bialgebras; Lie coalgebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B63", "originalCode": "17B63", "name": "Poisson algebras", "description": "Poisson algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B65", "originalCode": "17B65", "name": "Infinite-dimensional Lie (super)algebras", "description": "Infinite-dimensional Lie (super)algebras [See also 22E65]", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B66", "originalCode": "17B66", "name": "Lie algebras of vector fields and related (super) algebras", "description": "Lie algebras of vector fields and related (super) algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B67", "originalCode": "17B67", "name": "Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras", "description": "Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B68", "originalCode": "17B68", "name": "Virasoro and related algebras", "description": "Virasoro and related algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B69", "originalCode": "17B69", "name": "Vertex operators; vertex operator algebras and related structures", "description": "Vertex operators; vertex operator algebras and related structures", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B70", "originalCode": "17B70", "name": "Graded Lie (super)algebras", "description": "Graded Lie (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B75", "originalCode": "17B75", "name": "Color Lie (super)algebras", "description": "Color Lie (super)algebras", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B80", "originalCode": "17B80", "name": "Applications of Lie algebras and superalgebras to integrable systems", "description": "Applications of Lie algebras and superalgebras to integrable systems", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B81", "originalCode": "17B81", "name": "Applications of Lie (super)algebras to physics, etc.", "description": "Applications of Lie (super)algebras to physics, etc.", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17B99", "originalCode": "17B99", "name": "Lie algebras and Lie superalgebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "17B", "page": 48 }, { "code": "17C", "originalCode": "17Cxx", "name": "Jordan algebras (algebras, triples and pairs)", "description": "Jordan algebras (algebras, triples and pairs)", "kind": "section", "parent": "17", "page": 49 }, { "code": "17C05", "originalCode": "17C05", "name": "Identities and free Jordan structures", "description": "Identities and free Jordan structures", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C10", "originalCode": "17C10", "name": "Structure theory for Jordan algebras", "description": "Structure theory for Jordan algebras", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C17", "originalCode": "17C17", "name": "Radicals in Jordan algebras", "description": "Radicals in Jordan algebras", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C20", "originalCode": "17C20", "name": "Simple, semisimple Jordan algebras", "description": "Simple, semisimple Jordan algebras", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C27", "originalCode": "17C27", "name": "Idempotents, Peirce decompositions", "description": "Idempotents, Peirce decompositions", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C30", "originalCode": "17C30", "name": "Associated groups, automorphisms of Jordan algebras", "description": "Associated groups, automorphisms of Jordan algebras", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C36", "originalCode": "17C36", "name": "Associated manifolds of Jordan algebras", "description": "Associated manifolds of Jordan algebras", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C37", "originalCode": "17C37", "name": "Associated geometries of Jordan algebras", "description": "Associated geometries of Jordan algebras", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C40", "originalCode": "17C40", "name": "Exceptional Jordan structures", "description": "Exceptional Jordan structures", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C50", "originalCode": "17C50", "name": "Jordan structures associated with other structures", "description": "Jordan structures associated with other structures [See also 16W10]", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C55", "originalCode": "17C55", "name": "Finite-dimensional structures of Jordan algebras", "description": "Finite-dimensional structures of Jordan algebras", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C60", "originalCode": "17C60", "name": "Division algebras and Jordan algebras", "description": "Division algebras and Jordan algebras", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C65", "originalCode": "17C65", "name": "Jordan structures on Banach spaces and algebras", "description": "Jordan structures on Banach spaces and algebras [See also 46H70, 46L70]", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C70", "originalCode": "17C70", "name": "Super structures", "description": "Super structures", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C90", "originalCode": "17C90", "name": "Applications of Jordan algebras to physics, etc.", "description": "Applications of Jordan algebras to physics, etc.", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17C99", "originalCode": "17C99", "name": "Jordan algebras (algebras, triples and pairs)", "description": "None of the above, but in this section", "kind": "subject", "parent": "17C", "page": 49 }, { "code": "17D", "originalCode": "17Dxx", "name": "Other nonassociative rings and algebras", "description": "Other nonassociative rings and algebras", "kind": "section", "parent": "17", "page": 49 }, { "code": "17D05", "originalCode": "17D05", "name": "Alternative rings", "description": "Alternative rings", "kind": "subject", "parent": "17D", "page": 49 }, { "code": "17D10", "originalCode": "17D10", "name": "Mal'tsev rings and algebras", "description": "Mal'tsev rings and algebras", "kind": "subject", "parent": "17D", "page": 49 }, { "code": "17D15", "originalCode": "17D15", "name": "Right alternative rings", "description": "Right alternative rings", "kind": "subject", "parent": "17D", "page": 49 }, { "code": "17D20", "originalCode": "17D20", "name": "\\((\\gamma, \\delta)\\)-rings, including \\((1,-1)\\)-rings", "description": "\\((\\gamma, \\delta)\\)-rings, including \\((1,-1)\\)-rings", "kind": "subject", "parent": "17D", "page": 49 }, { "code": "17D25", "originalCode": "17D25", "name": "Lie-admissible algebras", "description": "Lie-admissible algebras", "kind": "subject", "parent": "17D", "page": 49 }, { "code": "17D30", "originalCode": "17D30", "name": "(non-Lie) Hom algebras and topics", "description": "(non-Lie) Hom algebras and topics", "kind": "subject", "parent": "17D", "page": 49 }, { "code": "17D92", "originalCode": "17D92", "name": "Genetic algebras", "description": "Genetic algebras", "kind": "subject", "parent": "17D", "page": 49 }, { "code": "17D99", "originalCode": "17D99", "name": "Other nonassociative rings and algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "17D", "page": 49 }, { "code": "18", "originalCode": "18-XX", "name": "Category theory; homological algebra", "description": "Category theory; homological algebra \\{For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx\\}", "kind": "class", "parent": null, "page": 49 }, { "code": "18-00", "originalCode": "18-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory", "kind": "subject", "parent": "18", "page": 49 }, { "code": "18-01", "originalCode": "18-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory", "kind": "subject", "parent": "18", "page": 49 }, { "code": "18-02", "originalCode": "18-02", "name": "Research exposition (monographs, survey articles) pertaining to category theory", "description": "Research exposition (monographs, survey articles) pertaining to category theory", "kind": "subject", "parent": "18", "page": 50 }, { "code": "18-03", "originalCode": "18-03", "name": "History of category theory", "description": "History of category theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "18", "page": 50 }, { "code": "18-04", "originalCode": "18-04", "name": "Software, source code, etc. for problems pertaining to category theory", "description": "Software, source code, etc. for problems pertaining to category theory", "kind": "subject", "parent": "18", "page": 50 }, { "code": "18-06", "originalCode": "18-06", "name": "Proceedings, conferences, collections, etc. pertaining to category theory", "description": "Proceedings, conferences, collections, etc. pertaining to category theory", "kind": "subject", "parent": "18", "page": 50 }, { "code": "18-08", "originalCode": "18-08", "name": "Computational methods for problems pertaining to category theory", "description": "Computational methods for problems pertaining to category theory", "kind": "subject", "parent": "18", "page": 50 }, { "code": "18-11", "originalCode": "18-11", "name": "Research data for problems pertaining to category theory", "description": "Research data for problems pertaining to category theory", "kind": "subject", "parent": "18", "page": 50 }, { "code": "18A", "originalCode": "18Axx", "name": "General theory of categories and functors", "description": "General theory of categories and functors", "kind": "section", "parent": "18", "page": 50 }, { "code": "18A05", "originalCode": "18A05", "name": "Definitions and generalizations in theory of categories", "description": "Definitions and generalizations in theory of categories", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A10", "originalCode": "18A10", "name": "Graphs, diagram schemes, precategories", "description": "Graphs, diagram schemes, precategories", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A15", "originalCode": "18A15", "name": "Foundations, relations to logic and deductive systems", "description": "Foundations, relations to logic and deductive systems [See also 03-XX]", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A20", "originalCode": "18A20", "name": "Epimorphisms, monomorphisms, special classes of morphisms, null morphisms", "description": "Epimorphisms, monomorphisms, special classes of morphisms, null morphisms", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A22", "originalCode": "18A22", "name": "Special properties of functors (faithful, full, etc.)", "description": "Special properties of functors (faithful, full, etc.)", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A23", "originalCode": "18A23", "name": "Natural morphisms, dinatural morphisms", "description": "Natural morphisms, dinatural morphisms", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A25", "originalCode": "18A25", "name": "Functor categories, comma categories", "description": "Functor categories, comma categories", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A30", "originalCode": "18A30", "name": "Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)", "description": "Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A32", "originalCode": "18A32", "name": "Factorization systems, substructures, quotient structures, congruences, amalgams", "description": "Factorization systems, substructures, quotient structures, congruences, amalgams", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A35", "originalCode": "18A35", "name": "Categories admitting limits (complete categories), functors preserving limits, completions", "description": "Categories admitting limits (complete categories), functors preserving limits, completions", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A40", "originalCode": "18A40", "name": "Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)", "description": "Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A50", "originalCode": "18A50", "name": "Graded categories (general)", "description": "Graded categories (general) \\{For dg categories, see 18G35\\}", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18A99", "originalCode": "18A99", "name": "General theory of categories and functors", "description": "None of the above, but in this section", "kind": "subject", "parent": "18A", "page": 50 }, { "code": "18B", "originalCode": "18Bxx", "name": "Special categories", "description": "Special categories", "kind": "section", "parent": "18", "page": 50 }, { "code": "18B05", "originalCode": "18B05", "name": "Categories of sets, characterizations", "description": "Categories of sets, characterizations [See also 03-XX]", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18B10", "originalCode": "18B10", "name": "Categories of spans/cospans, relations, or partial maps", "description": "Categories of spans/cospans, relations, or partial maps", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18B15", "originalCode": "18B15", "name": "Embedding theorems, universal categories", "description": "Embedding theorems, universal categories [See also 18E20]", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18B20", "originalCode": "18B20", "name": "Categories of machines, automata", "description": "Categories of machines, automata [See also 03D05, 68Qxx]", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18B25", "originalCode": "18B25", "name": "Topoi", "description": "Topoi [See also 03G30, 18F10]", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18B35", "originalCode": "18B35", "name": "Preorders, orders, domains and lattices (viewed as categories)", "description": "Preorders, orders, domains and lattices (viewed as categories) [See also 06-XX]", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18B40", "originalCode": "18B40", "name": "Groupoids, semigroupoids, semigroups, groups (viewed as categories)", "description": "Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18B50", "originalCode": "18B50", "name": "Extensive, distributive, and adhesive categories", "description": "Extensive, distributive, and adhesive categories", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18B99", "originalCode": "18B99", "name": "Special categories", "description": "None of the above, but in this section", "kind": "subject", "parent": "18B", "page": 50 }, { "code": "18C", "originalCode": "18Cxx", "name": "Categories and theories", "description": "Categories and theories", "kind": "section", "parent": "18", "page": 51 }, { "code": "18C05", "originalCode": "18C05", "name": "Equational categories", "description": "Equational categories [See also 03C05, 08C05]", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18C10", "originalCode": "18C10", "name": "Theories (e.g., algebraic theories), structure, and semantics", "description": "Theories (e.g., algebraic theories), structure, and semantics [See also 03G30]", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18C15", "originalCode": "18C15", "name": "Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads", "description": "Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads [See also 18Gxx] \\{For functional programming, see also 68N18\\}", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18C20", "originalCode": "18C20", "name": "Eilenberg-Moore and Kleisli constructions for monads", "description": "Eilenberg-Moore and Kleisli constructions for monads", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18C30", "originalCode": "18C30", "name": "Sketches and generalizations", "description": "Sketches and generalizations", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18C35", "originalCode": "18C35", "name": "Accessible and locally presentable categories", "description": "Accessible and locally presentable categories", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18C40", "originalCode": "18C40", "name": "Structured objects in a category (group objects, etc.)", "description": "Structured objects in a category (group objects, etc.)", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18C50", "originalCode": "18C50", "name": "Categorical semantics of formal languages", "description": "Categorical semantics of formal languages [See also 68Q55, 68Q65]", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18C99", "originalCode": "18C99", "name": "Categories and theories", "description": "None of the above, but in this section", "kind": "subject", "parent": "18C", "page": 51 }, { "code": "18D", "originalCode": "18Dxx", "name": "Categorical structures", "description": "Categorical structures", "kind": "section", "parent": "18", "page": 51 }, { "code": "18D15", "originalCode": "18D15", "name": "Closed categories (closed monoidal and Cartesian closed categories, etc.)", "description": "Closed categories (closed monoidal and Cartesian closed categories, etc.)", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18D20", "originalCode": "18D20", "name": "Enriched categories (over closed or monoidal categories)", "description": "Enriched categories (over closed or monoidal categories)", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18D25", "originalCode": "18D25", "name": "Actions of a monoidal category, tensorial strength", "description": "Actions of a monoidal category, tensorial strength \\{For functional programming, see also 68N18\\}", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18D30", "originalCode": "18D30", "name": "Fibered categories", "description": "Fibered categories", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18D40", "originalCode": "18D40", "name": "Internal categories and groupoids", "description": "Internal categories and groupoids \\{For double categories, see 18N10; for topological groupoids, see 22A22; for Lie groupoids, see 58H05\\}", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18D60", "originalCode": "18D60", "name": "Profunctors (= correspondences, distributors, modules)", "description": "Profunctors (= correspondences, distributors, modules)", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18D65", "originalCode": "18D65", "name": "Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads)", "description": "Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads)", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18D70", "originalCode": "18D70", "name": "Formal category theory", "description": "Formal category theory", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18D99", "originalCode": "18D99", "name": "Categorical structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "18D", "page": 51 }, { "code": "18E", "originalCode": "18Exx", "name": "Categorical algebra", "description": "Categorical algebra", "kind": "section", "parent": "18", "page": 51 }, { "code": "18E05", "originalCode": "18E05", "name": "Preadditive, additive categories", "description": "Preadditive, additive categories", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E08", "originalCode": "18E08", "name": "Regular categories, Barr-exact categories", "description": "Regular categories, Barr-exact categories", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E10", "originalCode": "18E10", "name": "Abelian categories, Grothendieck categories", "description": "Abelian categories, Grothendieck categories", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E13", "originalCode": "18E13", "name": "Protomodular categories, semi-abelian categories, Mal'tsev categories", "description": "Protomodular categories, semi-abelian categories, Mal'tsev categories [See also 08B05 and 08B10]", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E20", "originalCode": "18E20", "name": "Categorical embedding theorems", "description": "Categorical embedding theorems [See also 18B15]", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E35", "originalCode": "18E35", "name": "Localization of categories, calculus of fractions", "description": "Localization of categories, calculus of fractions \\{For homotopical aspects, see also 18N55, 55P60\\}", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E40", "originalCode": "18E40", "name": "Torsion theories, radicals", "description": "Torsion theories, radicals [See also 13D30, 16S90]", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E45", "originalCode": "18E45", "name": "Definable subcategories and connections with model theory", "description": "Definable subcategories and connections with model theory [See also 13C60]", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E50", "originalCode": "18E50", "name": "Categorical Galois theory", "description": "Categorical Galois theory", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18E99", "originalCode": "18E99", "name": "Categorical algebra", "description": "None of the above, but in this section", "kind": "subject", "parent": "18E", "page": 51 }, { "code": "18F", "originalCode": "18Fxx", "name": "Categories in geometry and topology", "description": "Categories in geometry and topology", "kind": "section", "parent": "18", "page": 52 }, { "code": "18F05", "originalCode": "18F05", "name": "Local categories and functors", "description": "Local categories and functors", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F10", "originalCode": "18F10", "name": "Grothendieck topologies and Grothendieck topoi", "description": "Grothendieck topologies and Grothendieck topoi [See also 14F20, 18B25]", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F15", "originalCode": "18F15", "name": "Abstract manifolds and fiber bundles (category-theoretic aspects)", "description": "Abstract manifolds and fiber bundles (category-theoretic aspects) [See also 55Rxx, 57Pxx]", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F20", "originalCode": "18F20", "name": "Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)", "description": "Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) [See also 14F06, 14F08, 32C35, 32L10, 54B40, 55N30]", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F25", "originalCode": "18F25", "name": "Algebraic \\(K\\)-theory and \\(L\\)-theory (category-theoretic aspects)", "description": "Algebraic \\(K\\)-theory and \\(L\\)-theory (category-theoretic aspects) [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F30", "originalCode": "18F30", "name": "Grothendieck groups (category-theoretic aspects)", "description": "Grothendieck groups (category-theoretic aspects) [See also 13D15, 16E20, 19Axx]", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F40", "originalCode": "18F40", "name": "Synthetic differential geometry, tangent categories, differential categories", "description": "Synthetic differential geometry, tangent categories, differential categories", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F50", "originalCode": "18F50", "name": "Goodwillie calculus and functor calculus", "description": "Goodwillie calculus and functor calculus", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F60", "originalCode": "18F60", "name": "Categories of topological spaces and continuous mappings", "description": "Categories of topological spaces and continuous mappings [See also 54-XX]", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F70", "originalCode": "18F70", "name": "Frames and locales, pointfree topology, Stone duality", "description": "Frames and locales, pointfree topology, Stone duality [See also 06D22, 18B35]", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F75", "originalCode": "18F75", "name": "Quantales", "description": "Quantales [See also 06F07, 18B35]", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18F99", "originalCode": "18F99", "name": "Categories in geometry and topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "18F", "page": 52 }, { "code": "18G", "originalCode": "18Gxx", "name": "Homological algebra in category theory, derived categories and functors", "description": "Homological algebra in category theory, derived categories and functors [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]", "kind": "section", "parent": "18", "page": 52 }, { "code": "18G05", "originalCode": "18G05", "name": "Projectives and injectives (category-theoretic aspects)", "description": "Projectives and injectives (category-theoretic aspects) [See also 13C10, 13C11, 16D40, 16D50]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G10", "originalCode": "18G10", "name": "Resolutions; derived functors (category-theoretic aspects)", "description": "Resolutions; derived functors (category-theoretic aspects) [See also 13D02, 16E05, 18Gxx]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G15", "originalCode": "18G15", "name": "Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)", "description": "Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) [See also 55U25]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G20", "originalCode": "18G20", "name": "Homological dimension (category-theoretic aspects)", "description": "Homological dimension (category-theoretic aspects) [See also 13D05, 16E10]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G25", "originalCode": "18G25", "name": "Relative homological algebra, projective classes (category-theoretic aspects)", "description": "Relative homological algebra, projective classes (category-theoretic aspects)", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G31", "originalCode": "18G31", "name": "Simplicial modules and Dold-Kan correspondence", "description": "Simplicial modules and Dold-Kan correspondence", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G35", "originalCode": "18G35", "name": "Chain complexes (category-theoretic aspects), dg categories", "description": "Chain complexes (category-theoretic aspects), dg categories [See also 14F08, 18G80, 55U15]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G40", "originalCode": "18G40", "name": "Spectral sequences, hypercohomology", "description": "Spectral sequences, hypercohomology [See also 55Txx]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G45", "originalCode": "18G45", "name": "2-groups, crossed modules, crossed complexes", "description": "2-groups, crossed modules, crossed complexes", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G50", "originalCode": "18G50", "name": "Nonabelian homological algebra (category-theoretic aspects)", "description": "Nonabelian homological algebra (category-theoretic aspects)", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G65", "originalCode": "18G65", "name": "Stable module categories", "description": "Stable module categories [See also 20C20]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G70", "originalCode": "18G70", "name": "\\(A_{\\infty}\\)-categories, relations with homological mirror symmetry", "description": "\\(A_{\\infty}\\)-categories, relations with homological mirror symmetry [See also 14F08, 14J33, 53D37]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G80", "originalCode": "18G80", "name": "Derived categories, triangulated categories", "description": "Derived categories, triangulated categories", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G85", "originalCode": "18G85", "name": "Graph complexes and graph homology", "description": "Graph complexes and graph homology \\{For relations with deformation quantization, see 53D55\\}", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G90", "originalCode": "18G90", "name": "Other (co)homology theories (category-theoretic aspects)", "description": "Other (co)homology theories (category-theoretic aspects) [See also 19D55, 46L80, 58J20, 58J22]", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18G99", "originalCode": "18G99", "name": "Homological algebra in category theory, derived categories and functors", "description": "None of the above, but in this section", "kind": "subject", "parent": "18G", "page": 52 }, { "code": "18M", "originalCode": "18Mxx", "name": "Monoidal categories and operads", "description": "Monoidal categories and operads", "kind": "section", "parent": "18", "page": 53 }, { "code": "18M05", "originalCode": "18M05", "name": "Monoidal categories, symmetric monoidal categories", "description": "Monoidal categories, symmetric monoidal categories [See also 19D23]", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M10", "originalCode": "18M10", "name": "Traced monoidal categories, compact closed categories, star-autonomous categories", "description": "Traced monoidal categories, compact closed categories, star-autonomous categories", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M15", "originalCode": "18M15", "name": "Braided monoidal categories and ribbon categories", "description": "Braided monoidal categories and ribbon categories \\{For applications to knot theory, see also 57Kxx; for applications to quantum groups, see also 16T20, 17B37, 81R50\\}", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M20", "originalCode": "18M20", "name": "Fusion categories, modular tensor categories, modular functors", "description": "Fusion categories, modular tensor categories, modular functors \\{For applications to topological quantum field theories, see also 57R56; for applications to conformal field theories, see also 81T40\\}", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M25", "originalCode": "18M25", "name": "Tannakian categories", "description": "Tannakian categories \\{For applications to motives, see also 14C15, 19E15\\}", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M30", "originalCode": "18M30", "name": "String diagrams and graphical calculi", "description": "String diagrams and graphical calculi", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M35", "originalCode": "18M35", "name": "Categories of networks and processes, compositionality", "description": "Categories of networks and processes, compositionality", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M40", "originalCode": "18M40", "name": "Dagger categories, categorical quantum mechanics", "description": "Dagger categories, categorical quantum mechanics [See also 81P68]", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M45", "originalCode": "18M45", "name": "Categorical aspects of linear logic", "description": "Categorical aspects of linear logic [See also 03B47]", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M50", "originalCode": "18M50", "name": "Bimonoidal, skew-monoidal, duoidal categories", "description": "Bimonoidal, skew-monoidal, duoidal categories", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M60", "originalCode": "18M60", "name": "Operads (general)", "description": "Operads (general)", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M65", "originalCode": "18M65", "name": "Non-symmetric operads, multicategories, generalized multicategories", "description": "Non-symmetric operads, multicategories, generalized multicategories", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M70", "originalCode": "18M70", "name": "Algebraic operads, cooperads, and Koszul duality", "description": "Algebraic operads, cooperads, and Koszul duality", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M75", "originalCode": "18M75", "name": "Topological and simplicial operads", "description": "Topological and simplicial operads [See also 18N60]", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M80", "originalCode": "18M80", "name": "Species, Hopf monoids, operads in combinatorics", "description": "Species, Hopf monoids, operads in combinatorics", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M85", "originalCode": "18M85", "name": "Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads", "description": "Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M90", "originalCode": "18M90", "name": "Globular operads", "description": "Globular operads", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18M99", "originalCode": "18M99", "name": "Monoidal categories and operads", "description": "None of the above, but in this section", "kind": "subject", "parent": "18M", "page": 53 }, { "code": "18N", "originalCode": "18Nxx", "name": "Higher categories and homotopical algebra", "description": "Higher categories and homotopical algebra", "kind": "section", "parent": "18", "page": 53 }, { "code": "18N10", "originalCode": "18N10", "name": "2-categories, bicategories, double categories", "description": "2-categories, bicategories, double categories", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N15", "originalCode": "18N15", "name": "2-dimensional monad theory", "description": "2-dimensional monad theory [See also 18C15]", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N20", "originalCode": "18N20", "name": "Tricategories, weak \\(n\\)-categories, coherence, semi-strictification", "description": "Tricategories, weak \\(n\\)-categories, coherence, semi-strictification", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N25", "originalCode": "18N25", "name": "Categorification", "description": "Categorification", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N30", "originalCode": "18N30", "name": "Strict omega-categories, computads, polygraphs", "description": "Strict omega-categories, computads, polygraphs", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N40", "originalCode": "18N40", "name": "Homotopical algebra, Quillen model categories, derivators", "description": "Homotopical algebra, Quillen model categories, derivators [See also 55U35]", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N45", "originalCode": "18N45", "name": "Categories of fibrations, relations to \\(K\\)-theory, relations to type theory", "description": "Categories of fibrations, relations to \\(K\\)-theory, relations to type theory", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N50", "originalCode": "18N50", "name": "Simplicial sets, simplicial objects", "description": "Simplicial sets, simplicial objects [See also 55U10]", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N55", "originalCode": "18N55", "name": "Localizations (e.g., simplicial localization, Bousfield localization)", "description": "Localizations (e.g., simplicial localization, Bousfield localization) [See also 18E35, 55P60]", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N60", "originalCode": "18N60", "name": "\\((\\infty,1)\\)-categories (quasi-categories, Segal spaces, etc.); \\(\\infty\\)-topoi, stable \\(\\infty\\)-categories", "description": "\\((\\infty,1)\\)-categories (quasi-categories, Segal spaces, etc.); \\(\\infty\\)-topoi, stable \\(\\infty\\)-categories [See also 55U35, 55U40]", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N65", "originalCode": "18N65", "name": "\\((\\infty, n)\\)-categories and \\((\\infty,\\infty)\\)-categories", "description": "\\((\\infty, n)\\)-categories and \\((\\infty,\\infty)\\)-categories", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N70", "originalCode": "18N70", "name": "\\(\\infty\\)-operads and higher algebra", "description": "\\(\\infty\\)-operads and higher algebra [See also 18M75]", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "18N99", "originalCode": "18N99", "name": "Higher categories and homotopical algebra", "description": "None of the above, but in this section", "kind": "subject", "parent": "18N", "page": 53 }, { "code": "19", "originalCode": "19-XX", "name": "\\(K\\)-theory", "description": "\\(K\\)-theory [See also 16E20, 18F25]", "kind": "class", "parent": null, "page": 54 }, { "code": "19-00", "originalCode": "19-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to \\(K\\)-theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to \\(K\\)-theory", "kind": "subject", "parent": "19", "page": 54 }, { "code": "19-01", "originalCode": "19-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to \\(K\\)-theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to \\(K\\)-theory", "kind": "subject", "parent": "19", "page": 54 }, { "code": "19-02", "originalCode": "19-02", "name": "Research exposition (monographs, survey articles) pertaining to \\(K\\)-theory", "description": "Research exposition (monographs, survey articles) pertaining to \\(K\\)-theory", "kind": "subject", "parent": "19", "page": 54 }, { "code": "19-03", "originalCode": "19-03", "name": "History of \\(K\\)-theory", "description": "History of \\(K\\)-theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "19", "page": 54 }, { "code": "19-04", "originalCode": "19-04", "name": "Software, source code, etc. for problems pertaining to \\(K\\)-theory", "description": "Software, source code, etc. for problems pertaining to \\(K\\)-theory", "kind": "subject", "parent": "19", "page": 54 }, { "code": "19-06", "originalCode": "19-06", "name": "Proceedings, conferences, collections, etc. pertaining to \\(K\\)-theory", "description": "Proceedings, conferences, collections, etc. pertaining to \\(K\\)-theory", "kind": "subject", "parent": "19", "page": 54 }, { "code": "19-08", "originalCode": "19-08", "name": "Computational methods for problems pertaining to \\(K\\)-theory", "description": "Computational methods for problems pertaining to \\(K\\)-theory", "kind": "subject", "parent": "19", "page": 54 }, { "code": "19-11", "originalCode": "19-11", "name": "Research data for problems pertaining to \\(K\\)-theory", "description": "Research data for problems pertaining to \\(K\\)-theory", "kind": "subject", "parent": "19", "page": 54 }, { "code": "19A", "originalCode": "19Axx", "name": "Grothendieck groups and \\(K_0\\)", "description": "Grothendieck groups and \\(K_0\\) [See also 13D15, 18F30]", "kind": "section", "parent": "19", "page": 54 }, { "code": "19A13", "originalCode": "19A13", "name": "Stability for projective modules", "description": "Stability for projective modules [See also 13C10]", "kind": "subject", "parent": "19A", "page": 54 }, { "code": "19A15", "originalCode": "19A15", "name": "Efficient generation of modules", "description": "Efficient generation of modules", "kind": "subject", "parent": "19A", "page": 54 }, { "code": "19A22", "originalCode": "19A22", "name": "Frobenius induction, Burnside and representation rings", "description": "Frobenius induction, Burnside and representation rings", "kind": "subject", "parent": "19A", "page": 54 }, { "code": "19A31", "originalCode": "19A31", "name": "\\(K_0\\) of group rings and orders", "description": "\\(K_0\\) of group rings and orders", "kind": "subject", "parent": "19A", "page": 54 }, { "code": "19A49", "originalCode": "19A49", "name": "\\(K_0\\) of other rings", "description": "\\(K_0\\) of other rings", "kind": "subject", "parent": "19A", "page": 54 }, { "code": "19A99", "originalCode": "19A99", "name": "Grothendieck groups and \\(K_0\\)", "description": "None of the above, but in this section", "kind": "subject", "parent": "19A", "page": 54 }, { "code": "19B", "originalCode": "19Bxx", "name": "Whitehead groups and \\(K_1\\)", "description": "Whitehead groups and \\(K_1\\)", "kind": "section", "parent": "19", "page": 54 }, { "code": "19B10", "originalCode": "19B10", "name": "Stable range conditions", "description": "Stable range conditions", "kind": "subject", "parent": "19B", "page": 54 }, { "code": "19B14", "originalCode": "19B14", "name": "Stability for linear groups", "description": "Stability for linear groups", "kind": "subject", "parent": "19B", "page": 54 }, { "code": "19B28", "originalCode": "19B28", "name": "\\(K_1\\) of group rings and orders", "description": "\\(K_1\\) of group rings and orders [See also 57Q10]", "kind": "subject", "parent": "19B", "page": 54 }, { "code": "19B37", "originalCode": "19B37", "name": "Congruence subgroup problems", "description": "Congruence subgroup problems [See also 20H05]", "kind": "subject", "parent": "19B", "page": 54 }, { "code": "19B99", "originalCode": "19B99", "name": "Whitehead groups and \\(K_1\\)", "description": "None of the above, but in this section", "kind": "subject", "parent": "19B", "page": 54 }, { "code": "19C", "originalCode": "19Cxx", "name": "Steinberg groups and \\(K_2\\)", "description": "Steinberg groups and \\(K_2\\)", "kind": "section", "parent": "19", "page": 54 }, { "code": "19C09", "originalCode": "19C09", "name": "Central extensions and Schur multipliers", "description": "Central extensions and Schur multipliers", "kind": "subject", "parent": "19C", "page": 54 }, { "code": "19C20", "originalCode": "19C20", "name": "Symbols, presentations and stability of \\(K_2\\)", "description": "Symbols, presentations and stability of \\(K_2\\)", "kind": "subject", "parent": "19C", "page": 54 }, { "code": "19C30", "originalCode": "19C30", "name": "\\(K_2\\) and the Brauer group", "description": "\\(K_2\\) and the Brauer group", "kind": "subject", "parent": "19C", "page": 54 }, { "code": "19C40", "originalCode": "19C40", "name": "Excision for \\(K_2\\)", "description": "Excision for \\(K_2\\)", "kind": "subject", "parent": "19C", "page": 54 }, { "code": "19C99", "originalCode": "19C99", "name": "Steinberg groups and \\(K_2\\)", "description": "None of the above, but in this section", "kind": "subject", "parent": "19C", "page": 54 }, { "code": "19D", "originalCode": "19Dxx", "name": "Higher algebraic \\(K\\)-theory", "description": "Higher algebraic \\(K\\)-theory", "kind": "section", "parent": "19", "page": 55 }, { "code": "19D06", "originalCode": "19D06", "name": "\\(Q\\)- and plus-constructions", "description": "\\(Q\\)- and plus-constructions", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19D10", "originalCode": "19D10", "name": "Algebraic \\(K\\)-theory of spaces", "description": "Algebraic \\(K\\)-theory of spaces", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19D23", "originalCode": "19D23", "name": "Symmetric monoidal categories", "description": "Symmetric monoidal categories [See also 18M05]", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19D25", "originalCode": "19D25", "name": "Karoubi-Villamayor-Gersten \\(K\\)-theory", "description": "Karoubi-Villamayor-Gersten \\(K\\)-theory", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19D35", "originalCode": "19D35", "name": "Negative \\(K\\)-theory, NK and Nil", "description": "Negative \\(K\\)-theory, NK and Nil", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19D45", "originalCode": "19D45", "name": "Higher symbols, Milnor \\(K\\)-theory", "description": "Higher symbols, Milnor \\(K\\)-theory", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19D50", "originalCode": "19D50", "name": "Computations of higher \\(K\\)-theory of rings", "description": "Computations of higher \\(K\\)-theory of rings [See also 13D15, 16E20]", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19D55", "originalCode": "19D55", "name": "\\(K\\)-theory and homology; cyclic homology and cohomology", "description": "\\(K\\)-theory and homology; cyclic homology and cohomology [See also 18G90]", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19D99", "originalCode": "19D99", "name": "Higher algebraic \\(K\\)-theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "19D", "page": 55 }, { "code": "19E", "originalCode": "19Exx", "name": "\\(K\\)-theory in geometry", "description": "\\(K\\)-theory in geometry", "kind": "section", "parent": "19", "page": 55 }, { "code": "19E08", "originalCode": "19E08", "name": "\\(K\\)-theory of schemes", "description": "\\(K\\)-theory of schemes [See also 14C35]", "kind": "subject", "parent": "19E", "page": 55 }, { "code": "19E15", "originalCode": "19E15", "name": "Algebraic cycles and motivic cohomology (\\(K\\)-theoretic aspects)", "description": "Algebraic cycles and motivic cohomology (\\(K\\)-theoretic aspects) [See also 14C25, 14C35, 14F42]", "kind": "subject", "parent": "19E", "page": 55 }, { "code": "19E20", "originalCode": "19E20", "name": "Relations of \\(K\\)-theory with cohomology theories", "description": "Relations of \\(K\\)-theory with cohomology theories [See also 14Fxx]", "kind": "subject", "parent": "19E", "page": 55 }, { "code": "19E99", "originalCode": "19E99", "name": "\\(K\\)-theory in geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "19E", "page": 55 }, { "code": "19F", "originalCode": "19Fxx", "name": "\\(K\\)-theory in number theory", "description": "\\(K\\)-theory in number theory [See also 11R70, 11S70]", "kind": "section", "parent": "19", "page": 55 }, { "code": "19F05", "originalCode": "19F05", "name": "Generalized class field theory (\\(K\\)-theoretic aspects)", "description": "Generalized class field theory (\\(K\\)-theoretic aspects) [See also 11G45]", "kind": "subject", "parent": "19F", "page": 55 }, { "code": "19F15", "originalCode": "19F15", "name": "Symbols and arithmetic (\\(K\\)-theoretic aspects)", "description": "Symbols and arithmetic (\\(K\\)-theoretic aspects) [See also 11R37]", "kind": "subject", "parent": "19F", "page": 55 }, { "code": "19F27", "originalCode": "19F27", "name": "Étale cohomology, higher regulators, zeta and \\(L\\)-functions (\\(K\\)-theoretic aspects)", "description": "Étale cohomology, higher regulators, zeta and \\(L\\)-functions (\\(K\\)-theoretic aspects) [See also 11G40, 11R42, 11S40, 14F20, 14G10]", "kind": "subject", "parent": "19F", "page": 55 }, { "code": "19F99", "originalCode": "19F99", "name": "\\(K\\)-theory in number theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "19F", "page": 55 }, { "code": "19G", "originalCode": "19Gxx", "name": "\\(K\\)-theory of forms", "description": "\\(K\\)-theory of forms [See also 11Exx]", "kind": "section", "parent": "19", "page": 55 }, { "code": "19G05", "originalCode": "19G05", "name": "Stability for quadratic modules", "description": "Stability for quadratic modules", "kind": "subject", "parent": "19G", "page": 55 }, { "code": "19G12", "originalCode": "19G12", "name": "Witt groups of rings", "description": "Witt groups of rings [See also 11E81]", "kind": "subject", "parent": "19G", "page": 55 }, { "code": "19G24", "originalCode": "19G24", "name": "\\(L\\)-theory of group rings", "description": "\\(L\\)-theory of group rings [See also 11E81]", "kind": "subject", "parent": "19G", "page": 55 }, { "code": "19G38", "originalCode": "19G38", "name": "Hermitian \\(K\\)-theory, relations with \\(K\\)-theory of rings", "description": "Hermitian \\(K\\)-theory, relations with \\(K\\)-theory of rings", "kind": "subject", "parent": "19G", "page": 55 }, { "code": "19G99", "originalCode": "19G99", "name": "\\(K\\)-theory of forms", "description": "None of the above, but in this section", "kind": "subject", "parent": "19G", "page": 55 }, { "code": "19J", "originalCode": "19Jxx", "name": "Obstructions from topology", "description": "Obstructions from topology", "kind": "section", "parent": "19", "page": 55 }, { "code": "19J05", "originalCode": "19J05", "name": "Finiteness and other obstructions in \\(K_0\\)", "description": "Finiteness and other obstructions in \\(K_0\\)", "kind": "subject", "parent": "19J", "page": 55 }, { "code": "19J10", "originalCode": "19J10", "name": "Whitehead (and related) torsion", "description": "Whitehead (and related) torsion", "kind": "subject", "parent": "19J", "page": 55 }, { "code": "19J25", "originalCode": "19J25", "name": "Surgery obstructions (\\(K\\)-theoretic aspects)", "description": "Surgery obstructions (\\(K\\)-theoretic aspects) [See also 57R67]", "kind": "subject", "parent": "19J", "page": 55 }, { "code": "19J35", "originalCode": "19J35", "name": "Obstructions to group actions (\\(K\\)-theoretic aspects)", "description": "Obstructions to group actions (\\(K\\)-theoretic aspects)", "kind": "subject", "parent": "19J", "page": 55 }, { "code": "19J99", "originalCode": "19J99", "name": "Obstructions from topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "19J", "page": 55 }, { "code": "19K", "originalCode": "19Kxx", "name": "\\(K\\)-theory and operator algebras", "description": "\\(K\\)-theory and operator algebras [See mainly 46L80, and also 46M20]", "kind": "section", "parent": "19", "page": 56 }, { "code": "19K14", "originalCode": "19K14", "name": "\\(K_0\\) as an ordered group, traces", "description": "\\(K_0\\) as an ordered group, traces", "kind": "subject", "parent": "19K", "page": 56 }, { "code": "19K33", "originalCode": "19K33", "name": "Ext and \\(K\\)-homology", "description": "Ext and \\(K\\)-homology [See also 55N22]", "kind": "subject", "parent": "19K", "page": 56 }, { "code": "19K35", "originalCode": "19K35", "name": "Kasparov theory (\\(KK\\)-theory)", "description": "Kasparov theory (\\(KK\\)-theory) [See also 58J22]", "kind": "subject", "parent": "19K", "page": 56 }, { "code": "19K56", "originalCode": "19K56", "name": "Index theory", "description": "Index theory [See also 58J20, 58J22]", "kind": "subject", "parent": "19K", "page": 56 }, { "code": "19K99", "originalCode": "19K99", "name": "\\(K\\)-theory and operator algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "19K", "page": 56 }, { "code": "19L", "originalCode": "19Lxx", "name": "Topological \\(K\\)-theory", "description": "Topological \\(K\\)-theory [See also 55N15, 55R50, 55S25]", "kind": "section", "parent": "19", "page": 56 }, { "code": "19L10", "originalCode": "19L10", "name": "Riemann-Roch theorems, Chern characters", "description": "Riemann-Roch theorems, Chern characters", "kind": "subject", "parent": "19L", "page": 56 }, { "code": "19L20", "originalCode": "19L20", "name": "\\(J\\)-homomorphism, Adams operations", "description": "\\(J\\)-homomorphism, Adams operations [See also 55Q50]", "kind": "subject", "parent": "19L", "page": 56 }, { "code": "19L41", "originalCode": "19L41", "name": "Connective \\(K\\)-theory, cobordism", "description": "Connective \\(K\\)-theory, cobordism [See also 55N22]", "kind": "subject", "parent": "19L", "page": 56 }, { "code": "19L47", "originalCode": "19L47", "name": "Equivariant \\(K\\)-theory", "description": "Equivariant \\(K\\)-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]", "kind": "subject", "parent": "19L", "page": 56 }, { "code": "19L50", "originalCode": "19L50", "name": "Twisted \\(K\\)-theory; differential \\(K\\)-theory", "description": "Twisted \\(K\\)-theory; differential \\(K\\)-theory", "kind": "subject", "parent": "19L", "page": 56 }, { "code": "19L64", "originalCode": "19L64", "name": "Geometric applications of topological \\(K\\)-theory", "description": "Geometric applications of topological \\(K\\)-theory", "kind": "subject", "parent": "19L", "page": 56 }, { "code": "19L99", "originalCode": "19L99", "name": "Topological \\(K\\)-theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "19L", "page": 56 }, { "code": "19M", "originalCode": "19Mxx", "name": "Miscellaneous applications of \\(K\\)-theory", "description": "Miscellaneous applications of \\(K\\)-theory", "kind": "section", "parent": "19", "page": 56 }, { "code": "19M05", "originalCode": "19M05", "name": "Miscellaneous applications of \\(K\\)-theory", "description": "Miscellaneous applications of \\(K\\)-theory", "kind": "subject", "parent": "19M", "page": 56 }, { "code": "19M99", "originalCode": "19M99", "name": "Miscellaneous applications of \\(K\\)-theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "19M", "page": 56 }, { "code": "20", "originalCode": "20-XX", "name": "Group theory and generalizations", "description": "Group theory and generalizations", "kind": "class", "parent": null, "page": 56 }, { "code": "20-00", "originalCode": "20-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to group theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to group theory", "kind": "subject", "parent": "20", "page": 56 }, { "code": "20-01", "originalCode": "20-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory", "kind": "subject", "parent": "20", "page": 56 }, { "code": "20-02", "originalCode": "20-02", "name": "Research exposition (monographs, survey articles) pertaining to group theory", "description": "Research exposition (monographs, survey articles) pertaining to group theory", "kind": "subject", "parent": "20", "page": 56 }, { "code": "20-03", "originalCode": "20-03", "name": "History of group theory", "description": "History of group theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "20", "page": 56 }, { "code": "20-04", "originalCode": "20-04", "name": "Software, source code, etc. for problems pertaining to group theory", "description": "Software, source code, etc. for problems pertaining to group theory", "kind": "subject", "parent": "20", "page": 56 }, { "code": "20-06", "originalCode": "20-06", "name": "Proceedings, conferences, collections, etc. pertaining to group theory", "description": "Proceedings, conferences, collections, etc. pertaining to group theory", "kind": "subject", "parent": "20", "page": 56 }, { "code": "20-08", "originalCode": "20-08", "name": "Computational methods for problems pertaining to group theory", "description": "Computational methods for problems pertaining to group theory", "kind": "subject", "parent": "20", "page": 56 }, { "code": "20-11", "originalCode": "20-11", "name": "Research data for problems pertaining to group theory", "description": "Research data for problems pertaining to group theory", "kind": "subject", "parent": "20", "page": 56 }, { "code": "20A", "originalCode": "20Axx", "name": "Foundations", "description": "Foundations", "kind": "section", "parent": "20", "page": 56 }, { "code": "20A05", "originalCode": "20A05", "name": "Axiomatics and elementary properties of groups", "description": "Axiomatics and elementary properties of groups", "kind": "subject", "parent": "20A", "page": 56 }, { "code": "20A10", "originalCode": "20A10", "name": "Metamathematical considerations in group theory", "description": "Metamathematical considerations in group theory \\{For word problems, see 20F10\\}", "kind": "subject", "parent": "20A", "page": 56 }, { "code": "20A15", "originalCode": "20A15", "name": "Applications of logic to group theory", "description": "Applications of logic to group theory", "kind": "subject", "parent": "20A", "page": 56 }, { "code": "20A99", "originalCode": "20A99", "name": "Foundations", "description": "None of the above, but in this section", "kind": "subject", "parent": "20A", "page": 56 }, { "code": "20B", "originalCode": "20Bxx", "name": "Permutation groups", "description": "Permutation groups", "kind": "section", "parent": "20", "page": 57 }, { "code": "20B05", "originalCode": "20B05", "name": "General theory for finite permutation groups", "description": "General theory for finite permutation groups", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B07", "originalCode": "20B07", "name": "General theory for infinite permutation groups", "description": "General theory for infinite permutation groups", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B10", "originalCode": "20B10", "name": "Characterization theorems for permutation groups", "description": "Characterization theorems for permutation groups", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B15", "originalCode": "20B15", "name": "Primitive groups", "description": "Primitive groups", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B20", "originalCode": "20B20", "name": "Multiply transitive finite groups", "description": "Multiply transitive finite groups", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B22", "originalCode": "20B22", "name": "Multiply transitive infinite groups", "description": "Multiply transitive infinite groups", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B25", "originalCode": "20B25", "name": "Finite automorphism groups of algebraic, geometric, or combinatorial structures", "description": "Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B27", "originalCode": "20B27", "name": "Infinite automorphism groups", "description": "Infinite automorphism groups [See also 12F10]", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B30", "originalCode": "20B30", "name": "Symmetric groups", "description": "Symmetric groups", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B35", "originalCode": "20B35", "name": "Subgroups of symmetric groups", "description": "Subgroups of symmetric groups", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20B99", "originalCode": "20B99", "name": "Permutation groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "20B", "page": 57 }, { "code": "20C", "originalCode": "20Cxx", "name": "Representation theory of groups", "description": "Representation theory of groups \\{For representation rings and Burnside rings, see also 19A22\\}", "kind": "section", "parent": "20", "page": 57 }, { "code": "20C05", "originalCode": "20C05", "name": "Group rings of finite groups and their modules (group-theoretic aspects)", "description": "Group rings of finite groups and their modules (group-theoretic aspects) [See also 16S34]", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C07", "originalCode": "20C07", "name": "Group rings of infinite groups and their modules (group-theoretic aspects)", "description": "Group rings of infinite groups and their modules (group-theoretic aspects) [See also 16S34]", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C08", "originalCode": "20C08", "name": "Hecke algebras and their representations", "description": "Hecke algebras and their representations", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C10", "originalCode": "20C10", "name": "Integral representations of finite groups", "description": "Integral representations of finite groups", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C11", "originalCode": "20C11", "name": "\\(p\\)-adic representations of finite groups", "description": "\\(p\\)-adic representations of finite groups", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C12", "originalCode": "20C12", "name": "Integral representations of infinite groups", "description": "Integral representations of infinite groups", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C15", "originalCode": "20C15", "name": "Ordinary representations and characters", "description": "Ordinary representations and characters", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C20", "originalCode": "20C20", "name": "Modular representations and characters", "description": "Modular representations and characters", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C25", "originalCode": "20C25", "name": "Projective representations and multipliers", "description": "Projective representations and multipliers", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C30", "originalCode": "20C30", "name": "Representations of finite symmetric groups", "description": "Representations of finite symmetric groups", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C32", "originalCode": "20C32", "name": "Representations of infinite symmetric groups", "description": "Representations of infinite symmetric groups", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C33", "originalCode": "20C33", "name": "Representations of finite groups of Lie type", "description": "Representations of finite groups of Lie type", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C34", "originalCode": "20C34", "name": "Representations of sporadic groups", "description": "Representations of sporadic groups", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C35", "originalCode": "20C35", "name": "Applications of group representations to physics and other areas of science", "description": "Applications of group representations to physics and other areas of science", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20C99", "originalCode": "20C99", "name": "Representation theory of groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "20C", "page": 57 }, { "code": "20D", "originalCode": "20Dxx", "name": "Abstract finite groups", "description": "Abstract finite groups", "kind": "section", "parent": "20", "page": 58 }, { "code": "20D05", "originalCode": "20D05", "name": "Finite simple groups and their classification", "description": "Finite simple groups and their classification", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D06", "originalCode": "20D06", "name": "Simple groups: alternating groups and groups of Lie type", "description": "Simple groups: alternating groups and groups of Lie type [See also 20Gxx]", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D08", "originalCode": "20D08", "name": "Simple groups: sporadic groups", "description": "Simple groups: sporadic groups", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D10", "originalCode": "20D10", "name": "Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \\(\\pi\\)-length, ranks", "description": "Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \\(\\pi\\)-length, ranks [See also 20F17]", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D15", "originalCode": "20D15", "name": "Finite nilpotent groups, \\(p\\)-groups", "description": "Finite nilpotent groups, \\(p\\)-groups", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D20", "originalCode": "20D20", "name": "Sylow subgroups, Sylow properties, \\(\\pi\\)-groups, \\(\\pi\\)-structure", "description": "Sylow subgroups, Sylow properties, \\(\\pi\\)-groups, \\(\\pi\\)-structure", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D25", "originalCode": "20D25", "name": "Special subgroups (Frattini, Fitting, etc.)", "description": "Special subgroups (Frattini, Fitting, etc.)", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D30", "originalCode": "20D30", "name": "Series and lattices of subgroups", "description": "Series and lattices of subgroups", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D35", "originalCode": "20D35", "name": "Subnormal subgroups of abstract finite groups", "description": "Subnormal subgroups of abstract finite groups", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D40", "originalCode": "20D40", "name": "Products of subgroups of abstract finite groups", "description": "Products of subgroups of abstract finite groups", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D45", "originalCode": "20D45", "name": "Automorphisms of abstract finite groups", "description": "Automorphisms of abstract finite groups", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D60", "originalCode": "20D60", "name": "Arithmetic and combinatorial problems involving abstract finite groups", "description": "Arithmetic and combinatorial problems involving abstract finite groups", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20D99", "originalCode": "20D99", "name": "Abstract finite groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "20D", "page": 58 }, { "code": "20E", "originalCode": "20Exx", "name": "Structure and classification of infinite or finite groups", "description": "Structure and classification of infinite or finite groups", "kind": "section", "parent": "20", "page": 58 }, { "code": "20E05", "originalCode": "20E05", "name": "Free nonabelian groups", "description": "Free nonabelian groups", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E06", "originalCode": "20E06", "name": "Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations", "description": "Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E07", "originalCode": "20E07", "name": "Subgroup theorems; subgroup growth", "description": "Subgroup theorems; subgroup growth", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E08", "originalCode": "20E08", "name": "Groups acting on trees", "description": "Groups acting on trees [See also 20F65]", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E10", "originalCode": "20E10", "name": "Quasivarieties and varieties of groups", "description": "Quasivarieties and varieties of groups", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E15", "originalCode": "20E15", "name": "Chains and lattices of subgroups, subnormal subgroups", "description": "Chains and lattices of subgroups, subnormal subgroups [See also 20F22]", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E18", "originalCode": "20E18", "name": "Limits, profinite groups", "description": "Limits, profinite groups", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E22", "originalCode": "20E22", "name": "Extensions, wreath products, and other compositions of groups", "description": "Extensions, wreath products, and other compositions of groups [See also 20J05]", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E25", "originalCode": "20E25", "name": "Local properties of groups", "description": "Local properties of groups", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E26", "originalCode": "20E26", "name": "Residual properties and generalizations; residually finite groups", "description": "Residual properties and generalizations; residually finite groups", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E28", "originalCode": "20E28", "name": "Maximal subgroups", "description": "Maximal subgroups", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E32", "originalCode": "20E32", "name": "Simple groups", "description": "Simple groups [See also 20D05]", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E34", "originalCode": "20E34", "name": "General structure theorems for groups", "description": "General structure theorems for groups", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E36", "originalCode": "20E36", "name": "Automorphisms of infinite groups", "description": "Automorphisms of infinite groups \\{For automorphisms of finite groups, see 20D45\\}", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E42", "originalCode": "20E42", "name": "Groups with a \\(BN\\)-pair; buildings", "description": "Groups with a \\(BN\\)-pair; buildings [See also 51E24]", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E45", "originalCode": "20E45", "name": "Conjugacy classes for groups", "description": "Conjugacy classes for groups", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20E99", "originalCode": "20E99", "name": "Structure and classification of infinite or finite groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "20E", "page": 58 }, { "code": "20F", "originalCode": "20Fxx", "name": "Special aspects of infinite or finite groups", "description": "Special aspects of infinite or finite groups", "kind": "section", "parent": "20", "page": 59 }, { "code": "20F05", "originalCode": "20F05", "name": "Generators, relations, and presentations of groups", "description": "Generators, relations, and presentations of groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F06", "originalCode": "20F06", "name": "Cancellation theory of groups; application of van Kampen diagrams", "description": "Cancellation theory of groups; application of van Kampen diagrams [See also 57M05]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F10", "originalCode": "20F10", "name": "Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)", "description": "Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F11", "originalCode": "20F11", "name": "Groups of finite Morley rank", "description": "Groups of finite Morley rank [See also 03C45, 03C60]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F12", "originalCode": "20F12", "name": "Commutator calculus", "description": "Commutator calculus", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F14", "originalCode": "20F14", "name": "Derived series, central series, and generalizations for groups", "description": "Derived series, central series, and generalizations for groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F16", "originalCode": "20F16", "name": "Solvable groups, supersolvable groups", "description": "Solvable groups, supersolvable groups [See also 20D10]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F17", "originalCode": "20F17", "name": "Formations of groups, Fitting classes", "description": "Formations of groups, Fitting classes [See also 20D10]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F18", "originalCode": "20F18", "name": "Nilpotent groups", "description": "Nilpotent groups [See also 20D15]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F19", "originalCode": "20F19", "name": "Generalizations of solvable and nilpotent groups", "description": "Generalizations of solvable and nilpotent groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F22", "originalCode": "20F22", "name": "Other classes of groups defined by subgroup chains", "description": "Other classes of groups defined by subgroup chains", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F24", "originalCode": "20F24", "name": "FC-groups and their generalizations", "description": "FC-groups and their generalizations", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F28", "originalCode": "20F28", "name": "Automorphism groups of groups", "description": "Automorphism groups of groups [See also 20E36]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F29", "originalCode": "20F29", "name": "Representations of groups as automorphism groups of algebraic systems", "description": "Representations of groups as automorphism groups of algebraic systems", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F34", "originalCode": "20F34", "name": "Fundamental groups and their automorphisms (group-theoretic aspects)", "description": "Fundamental groups and their automorphisms (group-theoretic aspects) [See also 57M05, 57Sxx]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F36", "originalCode": "20F36", "name": "Braid groups; Artin groups", "description": "Braid groups; Artin groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F38", "originalCode": "20F38", "name": "Other groups related to topology or analysis", "description": "Other groups related to topology or analysis", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F40", "originalCode": "20F40", "name": "Associated Lie structures for groups", "description": "Associated Lie structures for groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F45", "originalCode": "20F45", "name": "Engel conditions", "description": "Engel conditions", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F50", "originalCode": "20F50", "name": "Periodic groups; locally finite groups", "description": "Periodic groups; locally finite groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F55", "originalCode": "20F55", "name": "Reflection and Coxeter groups (group-theoretic aspects)", "description": "Reflection and Coxeter groups (group-theoretic aspects) [See also 22E40, 51F15]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F60", "originalCode": "20F60", "name": "Ordered groups (group-theoretic aspects)", "description": "Ordered groups (group-theoretic aspects) [See mainly 06F15]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F65", "originalCode": "20F65", "name": "Geometric group theory", "description": "Geometric group theory [See also 05C25, 20E08, 57Mxx]", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F67", "originalCode": "20F67", "name": "Hyperbolic groups and nonpositively curved groups", "description": "Hyperbolic groups and nonpositively curved groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F69", "originalCode": "20F69", "name": "Asymptotic properties of groups", "description": "Asymptotic properties of groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F70", "originalCode": "20F70", "name": "Algebraic geometry over groups; equations over groups", "description": "Algebraic geometry over groups; equations over groups", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20F99", "originalCode": "20F99", "name": "Special aspects of infinite or finite groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "20F", "page": 59 }, { "code": "20G", "originalCode": "20Gxx", "name": "Linear algebraic groups and related topics", "description": "Linear algebraic groups and related topics \\{For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55\\}", "kind": "section", "parent": "20", "page": 60 }, { "code": "20G05", "originalCode": "20G05", "name": "Representation theory for linear algebraic groups", "description": "Representation theory for linear algebraic groups", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G07", "originalCode": "20G07", "name": "Structure theory for linear algebraic groups", "description": "Structure theory for linear algebraic groups", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G10", "originalCode": "20G10", "name": "Cohomology theory for linear algebraic groups", "description": "Cohomology theory for linear algebraic groups", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G15", "originalCode": "20G15", "name": "Linear algebraic groups over arbitrary fields", "description": "Linear algebraic groups over arbitrary fields", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G20", "originalCode": "20G20", "name": "Linear algebraic groups over the reals, the complexes, the quaternions", "description": "Linear algebraic groups over the reals, the complexes, the quaternions", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G25", "originalCode": "20G25", "name": "Linear algebraic groups over local fields and their integers", "description": "Linear algebraic groups over local fields and their integers", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G30", "originalCode": "20G30", "name": "Linear algebraic groups over global fields and their integers", "description": "Linear algebraic groups over global fields and their integers", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G35", "originalCode": "20G35", "name": "Linear algebraic groups over adèles and other rings and schemes", "description": "Linear algebraic groups over adèles and other rings and schemes", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G40", "originalCode": "20G40", "name": "Linear algebraic groups over finite fields", "description": "Linear algebraic groups over finite fields", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G41", "originalCode": "20G41", "name": "Exceptional groups", "description": "Exceptional groups", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G42", "originalCode": "20G42", "name": "Quantum groups (quantized function algebras) and their representations", "description": "Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G43", "originalCode": "20G43", "name": "Schur and \\(q\\)-Schur algebras", "description": "Schur and \\(q\\)-Schur algebras", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G44", "originalCode": "20G44", "name": "Kac-Moody groups", "description": "Kac-Moody groups", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G45", "originalCode": "20G45", "name": "Applications of linear algebraic groups to the sciences", "description": "Applications of linear algebraic groups to the sciences", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20G99", "originalCode": "20G99", "name": "Linear algebraic groups and related topics", "description": "None of the above, but in this section", "kind": "subject", "parent": "20G", "page": 60 }, { "code": "20H", "originalCode": "20Hxx", "name": "Other groups of matrices", "description": "Other groups of matrices [See also 15A30]", "kind": "section", "parent": "20", "page": 60 }, { "code": "20H05", "originalCode": "20H05", "name": "Unimodular groups, congruence subgroups (group-theoretic aspects)", "description": "Unimodular groups, congruence subgroups (group-theoretic aspects) [See also 11F06, 19B37, 22E40, 51F20]", "kind": "subject", "parent": "20H", "page": 60 }, { "code": "20H10", "originalCode": "20H10", "name": "Fuchsian groups and their generalizations (group-theoretic aspects)", "description": "Fuchsian groups and their generalizations (group-theoretic aspects) [See also 11F06, 22E40, 30F35, 32Nxx]", "kind": "subject", "parent": "20H", "page": 60 }, { "code": "20H15", "originalCode": "20H15", "name": "Other geometric groups, including crystallographic groups", "description": "Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]", "kind": "subject", "parent": "20H", "page": 60 }, { "code": "20H20", "originalCode": "20H20", "name": "Other matrix groups over fields", "description": "Other matrix groups over fields", "kind": "subject", "parent": "20H", "page": 60 }, { "code": "20H25", "originalCode": "20H25", "name": "Other matrix groups over rings", "description": "Other matrix groups over rings", "kind": "subject", "parent": "20H", "page": 60 }, { "code": "20H30", "originalCode": "20H30", "name": "Other matrix groups over finite fields", "description": "Other matrix groups over finite fields", "kind": "subject", "parent": "20H", "page": 60 }, { "code": "20H99", "originalCode": "20H99", "name": "Other groups of matrices", "description": "None of the above, but in this section", "kind": "subject", "parent": "20H", "page": 60 }, { "code": "20J", "originalCode": "20Jxx", "name": "Connections of group theory with homological algebra and category theory", "description": "Connections of group theory with homological algebra and category theory", "kind": "section", "parent": "20", "page": 60 }, { "code": "20J05", "originalCode": "20J05", "name": "Homological methods in group theory", "description": "Homological methods in group theory", "kind": "subject", "parent": "20J", "page": 60 }, { "code": "20J06", "originalCode": "20J06", "name": "Cohomology of groups", "description": "Cohomology of groups", "kind": "subject", "parent": "20J", "page": 60 }, { "code": "20J15", "originalCode": "20J15", "name": "Category of groups", "description": "Category of groups", "kind": "subject", "parent": "20J", "page": 60 }, { "code": "20J99", "originalCode": "20J99", "name": "Connections of group theory with homological algebra and category theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "20J", "page": 60 }, { "code": "20K", "originalCode": "20Kxx", "name": "Abelian groups", "description": "Abelian groups", "kind": "section", "parent": "20", "page": 61 }, { "code": "20K01", "originalCode": "20K01", "name": "Finite abelian groups", "description": "Finite abelian groups \\{For sumsets, see 11B13, 11P70\\}", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K10", "originalCode": "20K10", "name": "Torsion groups, primary groups and generalized primary groups", "description": "Torsion groups, primary groups and generalized primary groups", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K15", "originalCode": "20K15", "name": "Torsion-free groups, finite rank", "description": "Torsion-free groups, finite rank", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K20", "originalCode": "20K20", "name": "Torsion-free groups, infinite rank", "description": "Torsion-free groups, infinite rank", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K21", "originalCode": "20K21", "name": "Mixed groups", "description": "Mixed groups", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K25", "originalCode": "20K25", "name": "Direct sums, direct products, etc. for abelian groups", "description": "Direct sums, direct products, etc. for abelian groups", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K27", "originalCode": "20K27", "name": "Subgroups of abelian groups", "description": "Subgroups of abelian groups", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K30", "originalCode": "20K30", "name": "Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups", "description": "Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K35", "originalCode": "20K35", "name": "Extensions of abelian groups", "description": "Extensions of abelian groups", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K40", "originalCode": "20K40", "name": "Homological and categorical methods for abelian groups", "description": "Homological and categorical methods for abelian groups", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K45", "originalCode": "20K45", "name": "Topological methods for abelian groups", "description": "Topological methods for abelian groups [See also 22A05, 22B05]", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20K99", "originalCode": "20K99", "name": "Abelian groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "20K", "page": 61 }, { "code": "20L", "originalCode": "20Lxx", "name": "Groupoids (i.e. small categories in which all morphisms are isomorphisms)", "description": "Groupoids (i.e. small categories in which all morphisms are isomorphisms) \\{For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05\\}", "kind": "section", "parent": "20", "page": 61 }, { "code": "20L05", "originalCode": "20L05", "name": "Groupoids (i.e. small categories in which all morphisms are isomorphisms)", "description": "Groupoids (i.e. small categories in which all morphisms are isomorphisms) \\{For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05\\}", "kind": "subject", "parent": "20L", "page": 61 }, { "code": "20L99", "originalCode": "20L99", "name": "Groupoids (i.e. small categories in which all morphisms are isomorphisms)", "description": "None of the above, but in this section", "kind": "subject", "parent": "20L", "page": 61 }, { "code": "20M", "originalCode": "20Mxx", "name": "Semigroups", "description": "Semigroups", "kind": "section", "parent": "20", "page": 61 }, { "code": "20M05", "originalCode": "20M05", "name": "Free semigroups, generators and relations, word problems", "description": "Free semigroups, generators and relations, word problems [See also 03D40, 08A50, 20F10]", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M07", "originalCode": "20M07", "name": "Varieties and pseudovarieties of semigroups", "description": "Varieties and pseudovarieties of semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M10", "originalCode": "20M10", "name": "General structure theory for semigroups", "description": "General structure theory for semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M11", "originalCode": "20M11", "name": "Radical theory for semigroups", "description": "Radical theory for semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M12", "originalCode": "20M12", "name": "Ideal theory for semigroups", "description": "Ideal theory for semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M13", "originalCode": "20M13", "name": "Arithmetic theory of semigroups", "description": "Arithmetic theory of semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M14", "originalCode": "20M14", "name": "Commutative semigroups", "description": "Commutative semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M15", "originalCode": "20M15", "name": "Mappings of semigroups", "description": "Mappings of semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M17", "originalCode": "20M17", "name": "Regular semigroups", "description": "Regular semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M18", "originalCode": "20M18", "name": "Inverse semigroups", "description": "Inverse semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M19", "originalCode": "20M19", "name": "Orthodox semigroups", "description": "Orthodox semigroups", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M20", "originalCode": "20M20", "name": "Semigroups of transformations, relations, partitions, etc.", "description": "Semigroups of transformations, relations, partitions, etc. [See also 47D03, 47H20, 54H15]", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M25", "originalCode": "20M25", "name": "Semigroup rings, multiplicative semigroups of rings", "description": "Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]", "kind": "subject", "parent": "20M", "page": 61 }, { "code": "20M30", "originalCode": "20M30", "name": "Representation of semigroups; actions of semigroups on sets", "description": "Representation of semigroups; actions of semigroups on sets", "kind": "subject", "parent": "20M", "page": 62 }, { "code": "20M32", "originalCode": "20M32", "name": "Algebraic monoids", "description": "Algebraic monoids", "kind": "subject", "parent": "20M", "page": 62 }, { "code": "20M35", "originalCode": "20M35", "name": "Semigroups in automata theory, linguistics, etc.", "description": "Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]", "kind": "subject", "parent": "20M", "page": 62 }, { "code": "20M50", "originalCode": "20M50", "name": "Connections of semigroups with homological algebra and category theory", "description": "Connections of semigroups with homological algebra and category theory", "kind": "subject", "parent": "20M", "page": 62 }, { "code": "20M75", "originalCode": "20M75", "name": "Generalizations of semigroups", "description": "Generalizations of semigroups", "kind": "subject", "parent": "20M", "page": 62 }, { "code": "20M99", "originalCode": "20M99", "name": "Semigroups", "description": "None of the above, but in this section", "kind": "subject", "parent": "20M", "page": 62 }, { "code": "20N", "originalCode": "20Nxx", "name": "Other generalizations of groups", "description": "Other generalizations of groups", "kind": "section", "parent": "20", "page": 62 }, { "code": "20N02", "originalCode": "20N02", "name": "Sets with a single binary operation (groupoids)", "description": "Sets with a single binary operation (groupoids) \\{For groupoids in connection with category theory, see 20L05; for topological groupoids, see 22A22, 58H05\\}", "kind": "subject", "parent": "20N", "page": 62 }, { "code": "20N05", "originalCode": "20N05", "name": "Loops, quasigroups", "description": "Loops, quasigroups [See also 05Bxx]", "kind": "subject", "parent": "20N", "page": 62 }, { "code": "20N10", "originalCode": "20N10", "name": "Ternary systems (heaps, semiheaps, heapoids, etc.)", "description": "Ternary systems (heaps, semiheaps, heapoids, etc.)", "kind": "subject", "parent": "20N", "page": 62 }, { "code": "20N15", "originalCode": "20N15", "name": "\\(n\\)-ary systems \\((n\\ge 3)\\)", "description": "\\(n\\)-ary systems \\((n\\ge 3)\\)", "kind": "subject", "parent": "20N", "page": 62 }, { "code": "20N20", "originalCode": "20N20", "name": "Hypergroups", "description": "Hypergroups", "kind": "subject", "parent": "20N", "page": 62 }, { "code": "20N25", "originalCode": "20N25", "name": "Fuzzy groups", "description": "Fuzzy groups [See also 03E72]", "kind": "subject", "parent": "20N", "page": 62 }, { "code": "20N99", "originalCode": "20N99", "name": "Other generalizations of groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "20N", "page": 62 }, { "code": "20P", "originalCode": "20Pxx", "name": "Probabilistic methods in group theory", "description": "Probabilistic methods in group theory [See also 60Bxx]", "kind": "section", "parent": "20", "page": 62 }, { "code": "20P05", "originalCode": "20P05", "name": "Probabilistic methods in group theory", "description": "Probabilistic methods in group theory [See also 60Bxx]", "kind": "subject", "parent": "20P", "page": 62 }, { "code": "20P99", "originalCode": "20P99", "name": "Probabilistic methods in group theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "20P", "page": 62 }, { "code": "22", "originalCode": "22-XX", "name": "Topological groups, Lie groups", "description": "Topological groups, Lie groups \\{For transformation groups, see 54H15, 57Sxx, 58-XX; for abstract harmonic analysis, see 43-XX\\}", "kind": "class", "parent": null, "page": 62 }, { "code": "22-00", "originalCode": "22-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to topological groups", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to topological groups", "kind": "subject", "parent": "22", "page": 62 }, { "code": "22-01", "originalCode": "22-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups", "kind": "subject", "parent": "22", "page": 62 }, { "code": "22-02", "originalCode": "22-02", "name": "Research exposition (monographs, survey articles) pertaining to topological groups", "description": "Research exposition (monographs, survey articles) pertaining to topological groups", "kind": "subject", "parent": "22", "page": 62 }, { "code": "22-03", "originalCode": "22-03", "name": "History of topological groups", "description": "History of topological groups [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "22", "page": 62 }, { "code": "22-04", "originalCode": "22-04", "name": "Software, source code, etc. for problems pertaining to topological groups", "description": "Software, source code, etc. for problems pertaining to topological groups", "kind": "subject", "parent": "22", "page": 62 }, { "code": "22-06", "originalCode": "22-06", "name": "Proceedings, conferences, collections, etc. pertaining to topological groups", "description": "Proceedings, conferences, collections, etc. pertaining to topological groups", "kind": "subject", "parent": "22", "page": 62 }, { "code": "22-08", "originalCode": "22-08", "name": "Computational methods for problems pertaining to topological groups", "description": "Computational methods for problems pertaining to topological groups", "kind": "subject", "parent": "22", "page": 62 }, { "code": "22-11", "originalCode": "22-11", "name": "Research data for problems pertaining to topological groups", "description": "Research data for problems pertaining to topological groups", "kind": "subject", "parent": "22", "page": 62 }, { "code": "22A", "originalCode": "22Axx", "name": "Topological and differentiable algebraic systems", "description": "Topological and differentiable algebraic systems \\{For topological rings and fields, see 12Jxx, 13Jxx, 16W80\\}", "kind": "section", "parent": "22", "page": 63 }, { "code": "22A05", "originalCode": "22A05", "name": "Structure of general topological groups", "description": "Structure of general topological groups", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22A10", "originalCode": "22A10", "name": "Analysis on general topological groups", "description": "Analysis on general topological groups", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22A15", "originalCode": "22A15", "name": "Structure of topological semigroups", "description": "Structure of topological semigroups", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22A20", "originalCode": "22A20", "name": "Analysis on topological semigroups", "description": "Analysis on topological semigroups", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22A22", "originalCode": "22A22", "name": "Topological groupoids (including differentiable and Lie groupoids)", "description": "Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22A25", "originalCode": "22A25", "name": "Representations of general topological groups and semigroups", "description": "Representations of general topological groups and semigroups", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22A26", "originalCode": "22A26", "name": "Topological semilattices, lattices and applications", "description": "Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22A30", "originalCode": "22A30", "name": "Other topological algebraic systems and their representations", "description": "Other topological algebraic systems and their representations", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22A99", "originalCode": "22A99", "name": "Topological and differentiable algebraic systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "22A", "page": 63 }, { "code": "22B", "originalCode": "22Bxx", "name": "Locally compact abelian groups (LCA groups)", "description": "Locally compact abelian groups (LCA groups)", "kind": "section", "parent": "22", "page": 63 }, { "code": "22B05", "originalCode": "22B05", "name": "General properties and structure of LCA groups", "description": "General properties and structure of LCA groups", "kind": "subject", "parent": "22B", "page": 63 }, { "code": "22B10", "originalCode": "22B10", "name": "Structure of group algebras of LCA groups", "description": "Structure of group algebras of LCA groups", "kind": "subject", "parent": "22B", "page": 63 }, { "code": "22B99", "originalCode": "22B99", "name": "Locally compact abelian groups (LCA groups)", "description": "None of the above, but in this section", "kind": "subject", "parent": "22B", "page": 63 }, { "code": "22C", "originalCode": "22Cxx", "name": "Compact groups", "description": "Compact groups", "kind": "section", "parent": "22", "page": 63 }, { "code": "22C05", "originalCode": "22C05", "name": "Compact groups", "description": "Compact groups", "kind": "subject", "parent": "22C", "page": 63 }, { "code": "22C99", "originalCode": "22C99", "name": "Compact groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "22C", "page": 63 }, { "code": "22D", "originalCode": "22Dxx", "name": "Locally compact groups and their algebras", "description": "Locally compact groups and their algebras", "kind": "section", "parent": "22", "page": 63 }, { "code": "22D05", "originalCode": "22D05", "name": "General properties and structure of locally compact groups", "description": "General properties and structure of locally compact groups", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D10", "originalCode": "22D10", "name": "Unitary representations of locally compact groups", "description": "Unitary representations of locally compact groups", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D12", "originalCode": "22D12", "name": "Other representations of locally compact groups", "description": "Other representations of locally compact groups", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D15", "originalCode": "22D15", "name": "Group algebras of locally compact groups", "description": "Group algebras of locally compact groups", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D20", "originalCode": "22D20", "name": "Representations of group algebras", "description": "Representations of group algebras", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D25", "originalCode": "22D25", "name": "\\(C^*\\)-algebras and \\(W^*\\)-algebras in relation to group representations", "description": "\\(C^*\\)-algebras and \\(W^*\\)-algebras in relation to group representations [See also 46Lxx]", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D30", "originalCode": "22D30", "name": "Induced representations for locally compact groups", "description": "Induced representations for locally compact groups", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D35", "originalCode": "22D35", "name": "Duality theorems for locally compact groups", "description": "Duality theorems for locally compact groups", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D40", "originalCode": "22D40", "name": "Ergodic theory on groups", "description": "Ergodic theory on groups [See also 28Dxx]", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D45", "originalCode": "22D45", "name": "Automorphism groups of locally compact groups", "description": "Automorphism groups of locally compact groups", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D50", "originalCode": "22D50", "name": "Rigidity in locally compact groups", "description": "Rigidity in locally compact groups", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D55", "originalCode": "22D55", "name": "Kazhdan's property (T), the Haagerup property, and generalizations", "description": "Kazhdan's property (T), the Haagerup property, and generalizations", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22D99", "originalCode": "22D99", "name": "Locally compact groups and their algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "22D", "page": 63 }, { "code": "22E", "originalCode": "22Exx", "name": "Lie groups", "description": "Lie groups \\{For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90\\}", "kind": "section", "parent": "22", "page": 64 }, { "code": "22E05", "originalCode": "22E05", "name": "Local Lie groups", "description": "Local Lie groups [See also 34-XX, 35-XX, 58H05]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E10", "originalCode": "22E10", "name": "General properties and structure of complex Lie groups", "description": "General properties and structure of complex Lie groups [See also 32M05]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E15", "originalCode": "22E15", "name": "General properties and structure of real Lie groups", "description": "General properties and structure of real Lie groups", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E20", "originalCode": "22E20", "name": "General properties and structure of other Lie groups", "description": "General properties and structure of other Lie groups", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E25", "originalCode": "22E25", "name": "Nilpotent and solvable Lie groups", "description": "Nilpotent and solvable Lie groups", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E27", "originalCode": "22E27", "name": "Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)", "description": "Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E30", "originalCode": "22E30", "name": "Analysis on real and complex Lie groups", "description": "Analysis on real and complex Lie groups [See also 33C80, 43-XX]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E35", "originalCode": "22E35", "name": "Analysis on \\(p\\)-adic Lie groups", "description": "Analysis on \\(p\\)-adic Lie groups", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E40", "originalCode": "22E40", "name": "Discrete subgroups of Lie groups", "description": "Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E41", "originalCode": "22E41", "name": "Continuous cohomology of Lie groups", "description": "Continuous cohomology of Lie groups [See also 57R32, 57Txx, 58H10]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E43", "originalCode": "22E43", "name": "Structure and representation of the Lorentz group", "description": "Structure and representation of the Lorentz group", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E45", "originalCode": "22E45", "name": "Representations of Lie and linear algebraic groups over real fields: analytic methods", "description": "Representations of Lie and linear algebraic groups over real fields: analytic methods \\{For the purely algebraic theory, see 20G05\\}", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E46", "originalCode": "22E46", "name": "Semisimple Lie groups and their representations", "description": "Semisimple Lie groups and their representations", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E47", "originalCode": "22E47", "name": "Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)", "description": "Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E50", "originalCode": "22E50", "name": "Representations of Lie and linear algebraic groups over local fields", "description": "Representations of Lie and linear algebraic groups over local fields [See also 11F70, 20G05]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E55", "originalCode": "22E55", "name": "Representations of Lie and linear algebraic groups over global fields and adèle rings", "description": "Representations of Lie and linear algebraic groups over global fields and adèle rings [See also 11F70, 20G05]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E57", "originalCode": "22E57", "name": "Geometric Langlands program: representation-theoretic aspects", "description": "Geometric Langlands program: representation-theoretic aspects [See also 14D24]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E60", "originalCode": "22E60", "name": "Lie algebras of Lie groups", "description": "Lie algebras of Lie groups \\{For the algebraic theory of Lie algebras, see 17Bxx\\}", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E65", "originalCode": "22E65", "name": "Infinite-dimensional Lie groups and their Lie algebras: general properties", "description": "Infinite-dimensional Lie groups and their Lie algebras: general properties [See also 17B65, 58B25, 58D05 58H05]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E66", "originalCode": "22E66", "name": "Analysis on and representations of infinite-dimensional Lie groups", "description": "Analysis on and representations of infinite-dimensional Lie groups", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E67", "originalCode": "22E67", "name": "Loop groups and related constructions, group-theoretic treatment", "description": "Loop groups and related constructions, group-theoretic treatment [See also 58D05]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E70", "originalCode": "22E70", "name": "Applications of Lie groups to the sciences; explicit representations", "description": "Applications of Lie groups to the sciences; explicit representations [See also 81R05, 81R10]", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22E99", "originalCode": "22E99", "name": "Lie groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "22E", "page": 64 }, { "code": "22F", "originalCode": "22Fxx", "name": "Noncompact transformation groups", "description": "Noncompact transformation groups", "kind": "section", "parent": "22", "page": 64 }, { "code": "22F05", "originalCode": "22F05", "name": "General theory of group and pseudogroup actions", "description": "General theory of group and pseudogroup actions \\{For topological properties of spaces with an action, see 57S20\\}", "kind": "subject", "parent": "22F", "page": 64 }, { "code": "22F10", "originalCode": "22F10", "name": "Measurable group actions", "description": "Measurable group actions [See also 22D40, 28Dxx, 37Axx]", "kind": "subject", "parent": "22F", "page": 64 }, { "code": "22F30", "originalCode": "22F30", "name": "Homogeneous spaces", "description": "Homogeneous spaces \\{For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40\\}", "kind": "subject", "parent": "22F", "page": 64 }, { "code": "22F50", "originalCode": "22F50", "name": "Groups as automorphisms of other structures", "description": "Groups as automorphisms of other structures", "kind": "subject", "parent": "22F", "page": 64 }, { "code": "22F99", "originalCode": "22F99", "name": "Noncompact transformation groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "22F", "page": 64 }, { "code": "26", "originalCode": "26-XX", "name": "Real functions", "description": "Real functions [See also 54C30]", "kind": "class", "parent": null, "page": 65 }, { "code": "26-00", "originalCode": "26-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to real functions", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to real functions", "kind": "subject", "parent": "26", "page": 65 }, { "code": "26-01", "originalCode": "26-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions", "kind": "subject", "parent": "26", "page": 65 }, { "code": "26-02", "originalCode": "26-02", "name": "Research exposition (monographs, survey articles) pertaining to real functions", "description": "Research exposition (monographs, survey articles) pertaining to real functions", "kind": "subject", "parent": "26", "page": 65 }, { "code": "26-03", "originalCode": "26-03", "name": "History of real functions", "description": "History of real functions [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "26", "page": 65 }, { "code": "26-04", "originalCode": "26-04", "name": "Software, source code, etc. for problems pertaining to real functions", "description": "Software, source code, etc. for problems pertaining to real functions", "kind": "subject", "parent": "26", "page": 65 }, { "code": "26-06", "originalCode": "26-06", "name": "Proceedings, conferences, collections, etc. pertaining to real functions", "description": "Proceedings, conferences, collections, etc. pertaining to real functions", "kind": "subject", "parent": "26", "page": 65 }, { "code": "26-08", "originalCode": "26-08", "name": "Computational methods for problems pertaining to real functions", "description": "Computational methods for problems pertaining to real functions", "kind": "subject", "parent": "26", "page": 65 }, { "code": "26-11", "originalCode": "26-11", "name": "Research data for problems pertaining to real functions", "description": "Research data for problems pertaining to real functions", "kind": "subject", "parent": "26", "page": 65 }, { "code": "26A", "originalCode": "26Axx", "name": "Functions of one variable", "description": "Functions of one variable", "kind": "section", "parent": "26", "page": 65 }, { "code": "26A03", "originalCode": "26A03", "name": "Foundations: limits and generalizations, elementary topology of the line", "description": "Foundations: limits and generalizations, elementary topology of the line", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A06", "originalCode": "26A06", "name": "One-variable calculus", "description": "One-variable calculus", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A09", "originalCode": "26A09", "name": "Elementary functions", "description": "Elementary functions", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A12", "originalCode": "26A12", "name": "Rate of growth of functions, orders of infinity, slowly varying functions", "description": "Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A15", "originalCode": "26A15", "name": "Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable", "description": "Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable \\{For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27\\}", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A16", "originalCode": "26A16", "name": "Lipschitz (Hölder) classes", "description": "Lipschitz (Hölder) classes", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A18", "originalCode": "26A18", "name": "Iteration of real functions in one variable", "description": "Iteration of real functions in one variable [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A21", "originalCode": "26A21", "name": "Classification of real functions; Baire classification of sets and functions", "description": "Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A24", "originalCode": "26A24", "name": "Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems", "description": "Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems [See also 28A15]", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A27", "originalCode": "26A27", "name": "Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives", "description": "Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A30", "originalCode": "26A30", "name": "Singular functions, Cantor functions, functions with other special properties", "description": "Singular functions, Cantor functions, functions with other special properties", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A33", "originalCode": "26A33", "name": "Fractional derivatives and integrals", "description": "Fractional derivatives and integrals", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A36", "originalCode": "26A36", "name": "Antidifferentiation", "description": "Antidifferentiation", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A39", "originalCode": "26A39", "name": "Denjoy and Perron integrals, other special integrals", "description": "Denjoy and Perron integrals, other special integrals", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A42", "originalCode": "26A42", "name": "Integrals of Riemann, Stieltjes and Lebesgue type", "description": "Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A45", "originalCode": "26A45", "name": "Functions of bounded variation, generalizations", "description": "Functions of bounded variation, generalizations", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A46", "originalCode": "26A46", "name": "Absolutely continuous real functions in one variable", "description": "Absolutely continuous real functions in one variable", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A48", "originalCode": "26A48", "name": "Monotonic functions, generalizations", "description": "Monotonic functions, generalizations", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A51", "originalCode": "26A51", "name": "Convexity of real functions in one variable, generalizations", "description": "Convexity of real functions in one variable, generalizations", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26A99", "originalCode": "26A99", "name": "Functions of one variable", "description": "None of the above, but in this section", "kind": "subject", "parent": "26A", "page": 65 }, { "code": "26B", "originalCode": "26Bxx", "name": "Functions of several variables", "description": "Functions of several variables", "kind": "section", "parent": "26", "page": 66 }, { "code": "26B05", "originalCode": "26B05", "name": "Continuity and differentiation questions", "description": "Continuity and differentiation questions", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B10", "originalCode": "26B10", "name": "Implicit function theorems, Jacobians, transformations with several variables", "description": "Implicit function theorems, Jacobians, transformations with several variables", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B12", "originalCode": "26B12", "name": "Calculus of vector functions", "description": "Calculus of vector functions", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B15", "originalCode": "26B15", "name": "Integration of real functions of several variables: length, area, volume", "description": "Integration of real functions of several variables: length, area, volume [See also 28A75, 51M25]", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B20", "originalCode": "26B20", "name": "Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)", "description": "Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B25", "originalCode": "26B25", "name": "Convexity of real functions of several variables, generalizations", "description": "Convexity of real functions of several variables, generalizations", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B30", "originalCode": "26B30", "name": "Absolutely continuous real functions of several variables, functions of bounded variation", "description": "Absolutely continuous real functions of several variables, functions of bounded variation", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B35", "originalCode": "26B35", "name": "Special properties of functions of several variables, Hölder conditions, etc.", "description": "Special properties of functions of several variables, Hölder conditions, etc.", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B40", "originalCode": "26B40", "name": "Representation and superposition of functions", "description": "Representation and superposition of functions", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26B99", "originalCode": "26B99", "name": "Functions of several variables", "description": "None of the above, but in this section", "kind": "subject", "parent": "26B", "page": 66 }, { "code": "26C", "originalCode": "26Cxx", "name": "Polynomials, rational functions in real analysis", "description": "Polynomials, rational functions in real analysis", "kind": "section", "parent": "26", "page": 66 }, { "code": "26C05", "originalCode": "26C05", "name": "Real polynomials: analytic properties, etc.", "description": "Real polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]", "kind": "subject", "parent": "26C", "page": 66 }, { "code": "26C10", "originalCode": "26C10", "name": "Real polynomials: location of zeros", "description": "Real polynomials: location of zeros \\{For algebraic theory, see 12D10; for complex methods, see 30C15; for numerical methods, see 65H05\\}", "kind": "subject", "parent": "26C", "page": 66 }, { "code": "26C15", "originalCode": "26C15", "name": "Real rational functions", "description": "Real rational functions [See also 14Pxx]", "kind": "subject", "parent": "26C", "page": 66 }, { "code": "26C99", "originalCode": "26C99", "name": "Polynomials, rational functions in real analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "26C", "page": 66 }, { "code": "26D", "originalCode": "26Dxx", "name": "Inequalities in real analysis", "description": "Inequalities in real analysis \\{For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15\\}", "kind": "section", "parent": "26", "page": 66 }, { "code": "26D05", "originalCode": "26D05", "name": "Inequalities for trigonometric functions and polynomials", "description": "Inequalities for trigonometric functions and polynomials", "kind": "subject", "parent": "26D", "page": 66 }, { "code": "26D07", "originalCode": "26D07", "name": "Inequalities involving other types of functions", "description": "Inequalities involving other types of functions", "kind": "subject", "parent": "26D", "page": 66 }, { "code": "26D10", "originalCode": "26D10", "name": "Inequalities involving derivatives and differential and integral operators", "description": "Inequalities involving derivatives and differential and integral operators", "kind": "subject", "parent": "26D", "page": 66 }, { "code": "26D15", "originalCode": "26D15", "name": "Inequalities for sums, series and integrals", "description": "Inequalities for sums, series and integrals", "kind": "subject", "parent": "26D", "page": 66 }, { "code": "26D20", "originalCode": "26D20", "name": "Other analytical inequalities", "description": "Other analytical inequalities", "kind": "subject", "parent": "26D", "page": 66 }, { "code": "26D99", "originalCode": "26D99", "name": "Inequalities in real analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "26D", "page": 66 }, { "code": "26E", "originalCode": "26Exx", "name": "Miscellaneous topics in real functions", "description": "Miscellaneous topics in real functions [See also 58Cxx]", "kind": "section", "parent": "26", "page": 66 }, { "code": "26E05", "originalCode": "26E05", "name": "Real-analytic functions", "description": "Real-analytic functions [See also 32B05, 32C05]", "kind": "subject", "parent": "26E", "page": 66 }, { "code": "26E10", "originalCode": "26E10", "name": "\\(C^\\infty\\)-functions, quasi-analytic functions", "description": "\\(C^\\infty\\)-functions, quasi-analytic functions [See also 58C25]", "kind": "subject", "parent": "26E", "page": 66 }, { "code": "26E15", "originalCode": "26E15", "name": "Calculus of functions on infinite-dimensional spaces", "description": "Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]", "kind": "subject", "parent": "26E", "page": 66 }, { "code": "26E20", "originalCode": "26E20", "name": "Calculus of functions taking values in infinite-dimensional spaces", "description": "Calculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]", "kind": "subject", "parent": "26E", "page": 66 }, { "code": "26E25", "originalCode": "26E25", "name": "Set-valued functions", "description": "Set-valued functions [See also 28B20, 49J53, 54C60] \\{For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx\\}", "kind": "subject", "parent": "26E", "page": 66 }, { "code": "26E30", "originalCode": "26E30", "name": "Non-Archimedean analysis", "description": "Non-Archimedean analysis [See also 12J25]", "kind": "subject", "parent": "26E", "page": 66 }, { "code": "26E35", "originalCode": "26E35", "name": "Nonstandard analysis", "description": "Nonstandard analysis [See also 03H05, 28E05, 54J05]", "kind": "subject", "parent": "26E", "page": 66 }, { "code": "26E40", "originalCode": "26E40", "name": "Constructive real analysis", "description": "Constructive real analysis [See also 03F60]", "kind": "subject", "parent": "26E", "page": 67 }, { "code": "26E50", "originalCode": "26E50", "name": "Fuzzy real analysis", "description": "Fuzzy real analysis [See also 03E72, 28E10]", "kind": "subject", "parent": "26E", "page": 67 }, { "code": "26E60", "originalCode": "26E60", "name": "Means", "description": "Means [See also 47A64]", "kind": "subject", "parent": "26E", "page": 67 }, { "code": "26E70", "originalCode": "26E70", "name": "Real analysis on time scales or measure chains", "description": "Real analysis on time scales or measure chains \\{For dynamic equations on time scales or measure chains, see 34N05\\}", "kind": "subject", "parent": "26E", "page": 67 }, { "code": "26E99", "originalCode": "26E99", "name": "Miscellaneous topics in real functions", "description": "None of the above, but in this section", "kind": "subject", "parent": "26E", "page": 67 }, { "code": "28", "originalCode": "28-XX", "name": "Measure and integration", "description": "Measure and integration \\{For analysis on manifolds, see 58-XX\\}", "kind": "class", "parent": null, "page": 67 }, { "code": "28-00", "originalCode": "28-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and integration", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and integration", "kind": "subject", "parent": "28", "page": 67 }, { "code": "28-01", "originalCode": "28-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration", "kind": "subject", "parent": "28", "page": 67 }, { "code": "28-02", "originalCode": "28-02", "name": "Research exposition (monographs, survey articles) pertaining to measure and integration", "description": "Research exposition (monographs, survey articles) pertaining to measure and integration", "kind": "subject", "parent": "28", "page": 67 }, { "code": "28-03", "originalCode": "28-03", "name": "History of measure and integration", "description": "History of measure and integration [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "28", "page": 67 }, { "code": "28-04", "originalCode": "28-04", "name": "Software, source code, etc. for problems pertaining to measure and integration", "description": "Software, source code, etc. for problems pertaining to measure and integration", "kind": "subject", "parent": "28", "page": 67 }, { "code": "28-06", "originalCode": "28-06", "name": "Proceedings, conferences, collections, etc. pertaining to measure and integration", "description": "Proceedings, conferences, collections, etc. pertaining to measure and integration", "kind": "subject", "parent": "28", "page": 67 }, { "code": "28-08", "originalCode": "28-08", "name": "Computational methods for problems pertaining to measure and integration", "description": "Computational methods for problems pertaining to measure and integration", "kind": "subject", "parent": "28", "page": 67 }, { "code": "28-11", "originalCode": "28-11", "name": "Research data for problems pertaining to measure and integration", "description": "Research data for problems pertaining to measure and integration", "kind": "subject", "parent": "28", "page": 67 }, { "code": "28A", "originalCode": "28Axx", "name": "Classical measure theory", "description": "Classical measure theory", "kind": "section", "parent": "28", "page": 67 }, { "code": "28A05", "originalCode": "28A05", "name": "Classes of sets (Borel fields, \\(\\sigma\\)-rings, etc.), measurable sets, Suslin sets, analytic sets", "description": "Classes of sets (Borel fields, \\(\\sigma\\)-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A10", "originalCode": "28A10", "name": "Real- or complex-valued set functions", "description": "Real- or complex-valued set functions", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A12", "originalCode": "28A12", "name": "Contents, measures, outer measures, capacities", "description": "Contents, measures, outer measures, capacities", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A15", "originalCode": "28A15", "name": "Abstract differentiation theory, differentiation of set functions", "description": "Abstract differentiation theory, differentiation of set functions [See also 26A24]", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A20", "originalCode": "28A20", "name": "Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence", "description": "Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A25", "originalCode": "28A25", "name": "Integration with respect to measures and other set functions", "description": "Integration with respect to measures and other set functions", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A33", "originalCode": "28A33", "name": "Spaces of measures, convergence of measures", "description": "Spaces of measures, convergence of measures [See also 46E27, 60Bxx]", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A35", "originalCode": "28A35", "name": "Measures and integrals in product spaces", "description": "Measures and integrals in product spaces", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A50", "originalCode": "28A50", "name": "Integration and disintegration of measures", "description": "Integration and disintegration of measures", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A51", "originalCode": "28A51", "name": "Lifting theory", "description": "Lifting theory [See also 46G15]", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A60", "originalCode": "28A60", "name": "Measures on Boolean rings, measure algebras", "description": "Measures on Boolean rings, measure algebras [See also 54H10]", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A75", "originalCode": "28A75", "name": "Length, area, volume, other geometric measure theory", "description": "Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A78", "originalCode": "28A78", "name": "Hausdorff and packing measures", "description": "Hausdorff and packing measures", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A80", "originalCode": "28A80", "name": "Fractals", "description": "Fractals [See also 37Fxx]", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28A99", "originalCode": "28A99", "name": "Classical measure theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "28A", "page": 67 }, { "code": "28B", "originalCode": "28Bxx", "name": "Set functions, measures and integrals with values in abstract spaces", "description": "Set functions, measures and integrals with values in abstract spaces", "kind": "section", "parent": "28", "page": 68 }, { "code": "28B05", "originalCode": "28B05", "name": "Vector-valued set functions, measures and integrals", "description": "Vector-valued set functions, measures and integrals [See also 46G10]", "kind": "subject", "parent": "28B", "page": 68 }, { "code": "28B10", "originalCode": "28B10", "name": "Group- or semigroup-valued set functions, measures and integrals", "description": "Group- or semigroup-valued set functions, measures and integrals", "kind": "subject", "parent": "28B", "page": 68 }, { "code": "28B15", "originalCode": "28B15", "name": "Set functions, measures and integrals with values in ordered spaces", "description": "Set functions, measures and integrals with values in ordered spaces", "kind": "subject", "parent": "28B", "page": 68 }, { "code": "28B20", "originalCode": "28B20", "name": "Set-valued set functions and measures; integration of set-valued functions; measurable selections", "description": "Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14]", "kind": "subject", "parent": "28B", "page": 68 }, { "code": "28B99", "originalCode": "28B99", "name": "Set functions, measures and integrals with values in abstract spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "28B", "page": 68 }, { "code": "28C", "originalCode": "28Cxx", "name": "Set functions and measures on spaces with additional structure", "description": "Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]", "kind": "section", "parent": "28", "page": 68 }, { "code": "28C05", "originalCode": "28C05", "name": "Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures", "description": "Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures", "kind": "subject", "parent": "28C", "page": 68 }, { "code": "28C10", "originalCode": "28C10", "name": "Set functions and measures on topological groups or semigroups, Haar measures, invariant measures", "description": "Set functions and measures on topological groups or semigroups, Haar measures, invariant measures [See also 22Axx, 43A05]", "kind": "subject", "parent": "28C", "page": 68 }, { "code": "28C15", "originalCode": "28C15", "name": "Set functions and measures on topological spaces (regularity of measures, etc.)", "description": "Set functions and measures on topological spaces (regularity of measures, etc.)", "kind": "subject", "parent": "28C", "page": 68 }, { "code": "28C20", "originalCode": "28C20", "name": "Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)", "description": "Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]", "kind": "subject", "parent": "28C", "page": 68 }, { "code": "28C99", "originalCode": "28C99", "name": "Set functions and measures on spaces with additional structure", "description": "None of the above, but in this section", "kind": "subject", "parent": "28C", "page": 68 }, { "code": "28D", "originalCode": "28Dxx", "name": "Measure-theoretic ergodic theory", "description": "Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 60Fxx, 60G10]", "kind": "section", "parent": "28", "page": 68 }, { "code": "28D05", "originalCode": "28D05", "name": "Measure-preserving transformations", "description": "Measure-preserving transformations \\{For measure-preserving transformations and dynamical systems, see 37A05\\}", "kind": "subject", "parent": "28D", "page": 68 }, { "code": "28D10", "originalCode": "28D10", "name": "One-parameter continuous families of measure-preserving transformations", "description": "One-parameter continuous families of measure-preserving transformations \\{For dynamical systems aspect, see 37A10\\}", "kind": "subject", "parent": "28D", "page": 68 }, { "code": "28D15", "originalCode": "28D15", "name": "General groups of measure-preserving transformations", "description": "General groups of measure-preserving transformations \\{For dynamical systems aspects, see 37A15\\}", "kind": "subject", "parent": "28D", "page": 68 }, { "code": "28D20", "originalCode": "28D20", "name": "Entropy and other invariants", "description": "Entropy and other invariants", "kind": "subject", "parent": "28D", "page": 68 }, { "code": "28D99", "originalCode": "28D99", "name": "Measure-theoretic ergodic theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "28D", "page": 68 }, { "code": "28E", "originalCode": "28Exx", "name": "Miscellaneous topics in measure theory", "description": "Miscellaneous topics in measure theory", "kind": "section", "parent": "28", "page": 68 }, { "code": "28E05", "originalCode": "28E05", "name": "Nonstandard measure theory", "description": "Nonstandard measure theory [See also 03H05, 26E35]", "kind": "subject", "parent": "28E", "page": 68 }, { "code": "28E10", "originalCode": "28E10", "name": "Fuzzy measure theory", "description": "Fuzzy measure theory [See also 03E72, 26E50, 94D05]", "kind": "subject", "parent": "28E", "page": 68 }, { "code": "28E15", "originalCode": "28E15", "name": "Other connections with logic and set theory", "description": "Other connections with logic and set theory", "kind": "subject", "parent": "28E", "page": 68 }, { "code": "28E99", "originalCode": "28E99", "name": "Miscellaneous topics in measure theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "28E", "page": 68 }, { "code": "30", "originalCode": "30-XX", "name": "Functions of a complex variable", "description": "Functions of a complex variable", "kind": "class", "parent": null, "page": 69 }, { "code": "30-00", "originalCode": "30-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable", "kind": "subject", "parent": "30", "page": 69 }, { "code": "30-01", "originalCode": "30-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable", "kind": "subject", "parent": "30", "page": 69 }, { "code": "30-02", "originalCode": "30-02", "name": "Research exposition (monographs, survey articles) pertaining to functions of a complex variable", "description": "Research exposition (monographs, survey articles) pertaining to functions of a complex variable", "kind": "subject", "parent": "30", "page": 69 }, { "code": "30-03", "originalCode": "30-03", "name": "History of functions of a complex variable", "description": "History of functions of a complex variable [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "30", "page": 69 }, { "code": "30-04", "originalCode": "30-04", "name": "Software, source code, etc. for problems pertaining to functions of a complex variable", "description": "Software, source code, etc. for problems pertaining to functions of a complex variable", "kind": "subject", "parent": "30", "page": 69 }, { "code": "30-06", "originalCode": "30-06", "name": "Proceedings, conferences, collections, etc. pertaining to functions of a complex variable", "description": "Proceedings, conferences, collections, etc. pertaining to functions of a complex variable", "kind": "subject", "parent": "30", "page": 69 }, { "code": "30-08", "originalCode": "30-08", "name": "Computational methods for problems pertaining to functions of a complex variable", "description": "Computational methods for problems pertaining to functions of a complex variable [See also 65Exx]", "kind": "subject", "parent": "30", "page": 69 }, { "code": "30-11", "originalCode": "30-11", "name": "Research data for problems pertaining to functions of a complex variable", "description": "Research data for problems pertaining to functions of a complex variable", "kind": "subject", "parent": "30", "page": 69 }, { "code": "30A", "originalCode": "30Axx", "name": "General properties of functions of one complex variable", "description": "General properties of functions of one complex variable", "kind": "section", "parent": "30", "page": 69 }, { "code": "30A05", "originalCode": "30A05", "name": "Monogenic and polygenic functions of one complex variable", "description": "Monogenic and polygenic functions of one complex variable", "kind": "subject", "parent": "30A", "page": 69 }, { "code": "30A10", "originalCode": "30A10", "name": "Inequalities in the complex plane", "description": "Inequalities in the complex plane", "kind": "subject", "parent": "30A", "page": 69 }, { "code": "30A99", "originalCode": "30A99", "name": "General properties of functions of one complex variable", "description": "None of the above, but in this section", "kind": "subject", "parent": "30A", "page": 69 }, { "code": "30B", "originalCode": "30Bxx", "name": "Series expansions of functions of one complex variable", "description": "Series expansions of functions of one complex variable", "kind": "section", "parent": "30", "page": 69 }, { "code": "30B10", "originalCode": "30B10", "name": "Power series (including lacunary series) in one complex variable", "description": "Power series (including lacunary series) in one complex variable", "kind": "subject", "parent": "30B", "page": 69 }, { "code": "30B20", "originalCode": "30B20", "name": "Random power series in one complex variable", "description": "Random power series in one complex variable", "kind": "subject", "parent": "30B", "page": 69 }, { "code": "30B30", "originalCode": "30B30", "name": "Boundary behavior of power series in one complex variable; over-convergence", "description": "Boundary behavior of power series in one complex variable; over-convergence", "kind": "subject", "parent": "30B", "page": 69 }, { "code": "30B40", "originalCode": "30B40", "name": "Analytic continuation of functions of one complex variable", "description": "Analytic continuation of functions of one complex variable", "kind": "subject", "parent": "30B", "page": 69 }, { "code": "30B50", "originalCode": "30B50", "name": "Dirichlet series, exponential series and other series in one complex variable", "description": "Dirichlet series, exponential series and other series in one complex variable [See also 11M41, 42-XX]", "kind": "subject", "parent": "30B", "page": 69 }, { "code": "30B60", "originalCode": "30B60", "name": "Completeness problems, closure of a system of functions of one complex variable", "description": "Completeness problems, closure of a system of functions of one complex variable", "kind": "subject", "parent": "30B", "page": 69 }, { "code": "30B70", "originalCode": "30B70", "name": "Continued fractions; complex-analytic aspects", "description": "Continued fractions; complex-analytic aspects [See also 11A55, 40A15]", "kind": "subject", "parent": "30B", "page": 69 }, { "code": "30B99", "originalCode": "30B99", "name": "Series expansions of functions of one complex variable", "description": "None of the above, but in this section", "kind": "subject", "parent": "30B", "page": 69 }, { "code": "30C", "originalCode": "30Cxx", "name": "Geometric function theory", "description": "Geometric function theory", "kind": "section", "parent": "30", "page": 69 }, { "code": "30C10", "originalCode": "30C10", "name": "Polynomials and rational functions of one complex variable", "description": "Polynomials and rational functions of one complex variable", "kind": "subject", "parent": "30C", "page": 69 }, { "code": "30C15", "originalCode": "30C15", "name": "Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)", "description": "Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) \\{For algebraic theory, see 12D10; for real methods, see 26C10\\}", "kind": "subject", "parent": "30C", "page": 69 }, { "code": "30C20", "originalCode": "30C20", "name": "Conformal mappings of special domains", "description": "Conformal mappings of special domains", "kind": "subject", "parent": "30C", "page": 69 }, { "code": "30C25", "originalCode": "30C25", "name": "Covering theorems in conformal mapping theory", "description": "Covering theorems in conformal mapping theory", "kind": "subject", "parent": "30C", "page": 69 }, { "code": "30C30", "originalCode": "30C30", "name": "Schwarz-Christoffel-type mappings", "description": "Schwarz-Christoffel-type mappings [See also 65E10]", "kind": "subject", "parent": "30C", "page": 69 }, { "code": "30C35", "originalCode": "30C35", "name": "General theory of conformal mappings", "description": "General theory of conformal mappings", "kind": "subject", "parent": "30C", "page": 69 }, { "code": "30C40", "originalCode": "30C40", "name": "Kernel functions in one complex variable and applications", "description": "Kernel functions in one complex variable and applications", "kind": "subject", "parent": "30C", "page": 69 }, { "code": "30C45", "originalCode": "30C45", "name": "Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)", "description": "Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C50", "originalCode": "30C50", "name": "Coefficient problems for univalent and multivalent functions of one complex variable", "description": "Coefficient problems for univalent and multivalent functions of one complex variable", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C55", "originalCode": "30C55", "name": "General theory of univalent and multivalent functions of one complex variable", "description": "General theory of univalent and multivalent functions of one complex variable", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C62", "originalCode": "30C62", "name": "Quasiconformal mappings in the complex plane", "description": "Quasiconformal mappings in the complex plane", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C65", "originalCode": "30C65", "name": "Quasiconformal mappings in \\(\\mathbb{R}^n\\), other generalizations", "description": "Quasiconformal mappings in \\(\\mathbb{R}^n\\), other generalizations", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C70", "originalCode": "30C70", "name": "Extremal problems for conformal and quasiconformal mappings, variational methods", "description": "Extremal problems for conformal and quasiconformal mappings, variational methods", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C75", "originalCode": "30C75", "name": "Extremal problems for conformal and quasiconformal mappings, other methods", "description": "Extremal problems for conformal and quasiconformal mappings, other methods", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C80", "originalCode": "30C80", "name": "Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination", "description": "Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C85", "originalCode": "30C85", "name": "Capacity and harmonic measure in the complex plane", "description": "Capacity and harmonic measure in the complex plane [See also 31A15]", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30C99", "originalCode": "30C99", "name": "Geometric function theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "30C", "page": 70 }, { "code": "30D", "originalCode": "30Dxx", "name": "Entire and meromorphic functions of one complex variable, and related topics", "description": "Entire and meromorphic functions of one complex variable, and related topics", "kind": "section", "parent": "30", "page": 70 }, { "code": "30D05", "originalCode": "30D05", "name": "Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable", "description": "Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable [See also 34Mxx, 37Fxx, 39-XX]", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D10", "originalCode": "30D10", "name": "Representations of entire functions of one complex variable by series and integrals", "description": "Representations of entire functions of one complex variable by series and integrals", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D15", "originalCode": "30D15", "name": "Special classes of entire functions of one complex variable and growth estimates", "description": "Special classes of entire functions of one complex variable and growth estimates", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D20", "originalCode": "30D20", "name": "Entire functions of one complex variable (general theory)", "description": "Entire functions of one complex variable (general theory)", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D30", "originalCode": "30D30", "name": "Meromorphic functions of one complex variable (general theory)", "description": "Meromorphic functions of one complex variable (general theory)", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D35", "originalCode": "30D35", "name": "Value distribution of meromorphic functions of one complex variable, Nevanlinna theory", "description": "Value distribution of meromorphic functions of one complex variable, Nevanlinna theory", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D40", "originalCode": "30D40", "name": "Cluster sets, prime ends, boundary behavior", "description": "Cluster sets, prime ends, boundary behavior", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D45", "originalCode": "30D45", "name": "Normal functions of one complex variable, normal families", "description": "Normal functions of one complex variable, normal families", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D60", "originalCode": "30D60", "name": "Quasi-analytic and other classes of functions of one complex variable", "description": "Quasi-analytic and other classes of functions of one complex variable", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30D99", "originalCode": "30D99", "name": "Entire and meromorphic functions of one complex variable, and related topics", "description": "None of the above, but in this section", "kind": "subject", "parent": "30D", "page": 70 }, { "code": "30E", "originalCode": "30Exx", "name": "Miscellaneous topics of analysis in the complex plane", "description": "Miscellaneous topics of analysis in the complex plane", "kind": "section", "parent": "30", "page": 70 }, { "code": "30E05", "originalCode": "30E05", "name": "Moment problems and interpolation problems in the complex plane", "description": "Moment problems and interpolation problems in the complex plane", "kind": "subject", "parent": "30E", "page": 70 }, { "code": "30E10", "originalCode": "30E10", "name": "Approximation in the complex plane", "description": "Approximation in the complex plane", "kind": "subject", "parent": "30E", "page": 70 }, { "code": "30E15", "originalCode": "30E15", "name": "Asymptotic representations in the complex plane", "description": "Asymptotic representations in the complex plane", "kind": "subject", "parent": "30E", "page": 70 }, { "code": "30E20", "originalCode": "30E20", "name": "Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane", "description": "Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane [See also 45Exx]", "kind": "subject", "parent": "30E", "page": 70 }, { "code": "30E25", "originalCode": "30E25", "name": "Boundary value problems in the complex plane", "description": "Boundary value problems in the complex plane [See also 45Exx]", "kind": "subject", "parent": "30E", "page": 70 }, { "code": "30E99", "originalCode": "30E99", "name": "Miscellaneous topics of analysis in the complex plane", "description": "None of the above, but in this section", "kind": "subject", "parent": "30E", "page": 70 }, { "code": "30F", "originalCode": "30Fxx", "name": "Riemann surfaces", "description": "Riemann surfaces", "kind": "section", "parent": "30", "page": 71 }, { "code": "30F10", "originalCode": "30F10", "name": "Compact Riemann surfaces and uniformization", "description": "Compact Riemann surfaces and uniformization [See also 14H15, 32G15]", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F15", "originalCode": "30F15", "name": "Harmonic functions on Riemann surfaces", "description": "Harmonic functions on Riemann surfaces", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F20", "originalCode": "30F20", "name": "Classification theory of Riemann surfaces", "description": "Classification theory of Riemann surfaces", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F25", "originalCode": "30F25", "name": "Ideal boundary theory for Riemann surfaces", "description": "Ideal boundary theory for Riemann surfaces", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F30", "originalCode": "30F30", "name": "Differentials on Riemann surfaces", "description": "Differentials on Riemann surfaces", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F35", "originalCode": "30F35", "name": "Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)", "description": "Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F40", "originalCode": "30F40", "name": "Kleinian groups (aspects of compact Riemann surfaces and uniformization)", "description": "Kleinian groups (aspects of compact Riemann surfaces and uniformization) [See also 20H10]", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F45", "originalCode": "30F45", "name": "Conformal metrics (hyperbolic, Poincaré, distance functions)", "description": "Conformal metrics (hyperbolic, Poincaré, distance functions)", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F50", "originalCode": "30F50", "name": "Klein surfaces", "description": "Klein surfaces", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F60", "originalCode": "30F60", "name": "Teichmüller theory for Riemann surfaces", "description": "Teichmüller theory for Riemann surfaces [See also 32G15]", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30F99", "originalCode": "30F99", "name": "Riemann surfaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "30F", "page": 71 }, { "code": "30G", "originalCode": "30Gxx", "name": "Generalized function theory", "description": "Generalized function theory", "kind": "section", "parent": "30", "page": 71 }, { "code": "30G06", "originalCode": "30G06", "name": "Non-Archimedean function theory", "description": "Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05]", "kind": "subject", "parent": "30G", "page": 71 }, { "code": "30G12", "originalCode": "30G12", "name": "Finely holomorphic functions and topological function theory", "description": "Finely holomorphic functions and topological function theory", "kind": "subject", "parent": "30G", "page": 71 }, { "code": "30G20", "originalCode": "30G20", "name": "Generalizations of Bers and Vekua type (pseudoanalytic, \\(p\\)-analytic, etc.)", "description": "Generalizations of Bers and Vekua type (pseudoanalytic, \\(p\\)-analytic, etc.)", "kind": "subject", "parent": "30G", "page": 71 }, { "code": "30G25", "originalCode": "30G25", "name": "Discrete analytic functions", "description": "Discrete analytic functions", "kind": "subject", "parent": "30G", "page": 71 }, { "code": "30G30", "originalCode": "30G30", "name": "Other generalizations of analytic functions (including abstract-valued functions)", "description": "Other generalizations of analytic functions (including abstract-valued functions)", "kind": "subject", "parent": "30G", "page": 71 }, { "code": "30G35", "originalCode": "30G35", "name": "Functions of hypercomplex variables and generalized variables", "description": "Functions of hypercomplex variables and generalized variables", "kind": "subject", "parent": "30G", "page": 71 }, { "code": "30G99", "originalCode": "30G99", "name": "Generalized function theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "30G", "page": 71 }, { "code": "30H", "originalCode": "30Hxx", "name": "Spaces and algebras of analytic functions of one complex variable", "description": "Spaces and algebras of analytic functions of one complex variable", "kind": "section", "parent": "30", "page": 71 }, { "code": "30H05", "originalCode": "30H05", "name": "Spaces of bounded analytic functions of one complex variable", "description": "Spaces of bounded analytic functions of one complex variable", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H10", "originalCode": "30H10", "name": "Hardy spaces", "description": "Hardy spaces [See also 42B30, 46E30]", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H15", "originalCode": "30H15", "name": "Nevanlinna spaces and Smirnov spaces", "description": "Nevanlinna spaces and Smirnov spaces", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H20", "originalCode": "30H20", "name": "Bergman spaces and Fock spaces", "description": "Bergman spaces and Fock spaces [See also 46E30, 46E35]", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H25", "originalCode": "30H25", "name": "Besov spaces and \\(Q_p\\)-spaces", "description": "Besov spaces and \\(Q_p\\)-spaces", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H30", "originalCode": "30H30", "name": "Bloch spaces", "description": "Bloch spaces", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H35", "originalCode": "30H35", "name": "BMO-spaces", "description": "BMO-spaces", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H40", "originalCode": "30H40", "name": "Zygmund spaces", "description": "Zygmund spaces", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H45", "originalCode": "30H45", "name": "de Branges-Rovnyak spaces", "description": "de Branges-Rovnyak spaces", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H50", "originalCode": "30H50", "name": "Algebras of analytic functions of one complex variable", "description": "Algebras of analytic functions of one complex variable", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H80", "originalCode": "30H80", "name": "Corona theorems", "description": "Corona theorems", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30H99", "originalCode": "30H99", "name": "Spaces and algebras of analytic functions of one complex variable", "description": "None of the above, but in this section", "kind": "subject", "parent": "30H", "page": 71 }, { "code": "30J", "originalCode": "30Jxx", "name": "Function theory on the disc", "description": "Function theory on the disc", "kind": "section", "parent": "30", "page": 72 }, { "code": "30J05", "originalCode": "30J05", "name": "Inner functions of one complex variable", "description": "Inner functions of one complex variable", "kind": "subject", "parent": "30J", "page": 72 }, { "code": "30J10", "originalCode": "30J10", "name": "Blaschke products", "description": "Blaschke products", "kind": "subject", "parent": "30J", "page": 72 }, { "code": "30J15", "originalCode": "30J15", "name": "Singular inner functions of one complex variable", "description": "Singular inner functions of one complex variable", "kind": "subject", "parent": "30J", "page": 72 }, { "code": "30J99", "originalCode": "30J99", "name": "Function theory on the disc", "description": "None of the above, but in this section", "kind": "subject", "parent": "30J", "page": 72 }, { "code": "30K", "originalCode": "30Kxx", "name": "Universal holomorphic functions of one complex variable", "description": "Universal holomorphic functions of one complex variable", "kind": "section", "parent": "30", "page": 72 }, { "code": "30K05", "originalCode": "30K05", "name": "Universal Taylor series in one complex variable", "description": "Universal Taylor series in one complex variable", "kind": "subject", "parent": "30K", "page": 72 }, { "code": "30K10", "originalCode": "30K10", "name": "Universal Dirichlet series in one complex variable", "description": "Universal Dirichlet series in one complex variable", "kind": "subject", "parent": "30K", "page": 72 }, { "code": "30K15", "originalCode": "30K15", "name": "Universal functions of one complex variable", "description": "Universal functions of one complex variable", "kind": "subject", "parent": "30K", "page": 72 }, { "code": "30K20", "originalCode": "30K20", "name": "Compositional universality", "description": "Compositional universality", "kind": "subject", "parent": "30K", "page": 72 }, { "code": "30K99", "originalCode": "30K99", "name": "Universal holomorphic functions of one complex variable", "description": "None of the above, but in this section", "kind": "subject", "parent": "30K", "page": 72 }, { "code": "30L", "originalCode": "30Lxx", "name": "Analysis on metric spaces", "description": "Analysis on metric spaces", "kind": "section", "parent": "30", "page": 72 }, { "code": "30L05", "originalCode": "30L05", "name": "Geometric embeddings of metric spaces", "description": "Geometric embeddings of metric spaces", "kind": "subject", "parent": "30L", "page": 72 }, { "code": "30L10", "originalCode": "30L10", "name": "Quasiconformal mappings in metric spaces", "description": "Quasiconformal mappings in metric spaces", "kind": "subject", "parent": "30L", "page": 72 }, { "code": "30L15", "originalCode": "30L15", "name": "Inequalities in metric spaces", "description": "Inequalities in metric spaces", "kind": "subject", "parent": "30L", "page": 72 }, { "code": "30L99", "originalCode": "30L99", "name": "Analysis on metric spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "30L", "page": 72 }, { "code": "31", "originalCode": "31-XX", "name": "Potential theory", "description": "Potential theory \\{For probabilistic potential theory, see 60J45\\}", "kind": "class", "parent": null, "page": 72 }, { "code": "31-00", "originalCode": "31-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to potential theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to potential theory", "kind": "subject", "parent": "31", "page": 72 }, { "code": "31-01", "originalCode": "31-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory", "kind": "subject", "parent": "31", "page": 72 }, { "code": "31-02", "originalCode": "31-02", "name": "Research exposition (monographs, survey articles) pertaining to potential theory", "description": "Research exposition (monographs, survey articles) pertaining to potential theory", "kind": "subject", "parent": "31", "page": 72 }, { "code": "31-03", "originalCode": "31-03", "name": "History of potential theory", "description": "History of potential theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "31", "page": 72 }, { "code": "31-04", "originalCode": "31-04", "name": "Software, source code, etc. for problems pertaining to potential theory", "description": "Software, source code, etc. for problems pertaining to potential theory", "kind": "subject", "parent": "31", "page": 72 }, { "code": "31-06", "originalCode": "31-06", "name": "Proceedings, conferences, collections, etc. pertaining to potential theory", "description": "Proceedings, conferences, collections, etc. pertaining to potential theory", "kind": "subject", "parent": "31", "page": 72 }, { "code": "31-08", "originalCode": "31-08", "name": "Computational methods for problems pertaining to potential theory", "description": "Computational methods for problems pertaining to potential theory [See also 65Exx]", "kind": "subject", "parent": "31", "page": 72 }, { "code": "31-11", "originalCode": "31-11", "name": "Research data for problems pertaining to potential theory", "description": "Research data for problems pertaining to potential theory", "kind": "subject", "parent": "31", "page": 72 }, { "code": "31A", "originalCode": "31Axx", "name": "Two-dimensional potential theory", "description": "Two-dimensional potential theory", "kind": "section", "parent": "31", "page": 72 }, { "code": "31A05", "originalCode": "31A05", "name": "Harmonic, subharmonic, superharmonic functions in two dimensions", "description": "Harmonic, subharmonic, superharmonic functions in two dimensions", "kind": "subject", "parent": "31A", "page": 72 }, { "code": "31A10", "originalCode": "31A10", "name": "Integral representations, integral operators, integral equations methods in two dimensions", "description": "Integral representations, integral operators, integral equations methods in two dimensions", "kind": "subject", "parent": "31A", "page": 72 }, { "code": "31A15", "originalCode": "31A15", "name": "Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions", "description": "Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions [See also 30C85]", "kind": "subject", "parent": "31A", "page": 72 }, { "code": "31A20", "originalCode": "31A20", "name": "Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions", "description": "Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions", "kind": "subject", "parent": "31A", "page": 72 }, { "code": "31A25", "originalCode": "31A25", "name": "Boundary value and inverse problems for harmonic functions in two dimensions", "description": "Boundary value and inverse problems for harmonic functions in two dimensions", "kind": "subject", "parent": "31A", "page": 72 }, { "code": "31A30", "originalCode": "31A30", "name": "Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions", "description": "Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions", "kind": "subject", "parent": "31A", "page": 73 }, { "code": "31A35", "originalCode": "31A35", "name": "Connections of harmonic functions with differential equations in two dimensions", "description": "Connections of harmonic functions with differential equations in two dimensions", "kind": "subject", "parent": "31A", "page": 73 }, { "code": "31A99", "originalCode": "31A99", "name": "Two-dimensional potential theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "31A", "page": 73 }, { "code": "31B", "originalCode": "31Bxx", "name": "Higher-dimensional potential theory", "description": "Higher-dimensional potential theory", "kind": "section", "parent": "31", "page": 73 }, { "code": "31B05", "originalCode": "31B05", "name": "Harmonic, subharmonic, superharmonic functions in higher dimensions", "description": "Harmonic, subharmonic, superharmonic functions in higher dimensions", "kind": "subject", "parent": "31B", "page": 73 }, { "code": "31B10", "originalCode": "31B10", "name": "Integral representations, integral operators, integral equations methods in higher dimensions", "description": "Integral representations, integral operators, integral equations methods in higher dimensions", "kind": "subject", "parent": "31B", "page": 73 }, { "code": "31B15", "originalCode": "31B15", "name": "Potentials and capacities, extremal length and related notions in higher dimensions", "description": "Potentials and capacities, extremal length and related notions in higher dimensions", "kind": "subject", "parent": "31B", "page": 73 }, { "code": "31B20", "originalCode": "31B20", "name": "Boundary value and inverse problems for harmonic functions in higher dimensions", "description": "Boundary value and inverse problems for harmonic functions in higher dimensions", "kind": "subject", "parent": "31B", "page": 73 }, { "code": "31B25", "originalCode": "31B25", "name": "Boundary behavior of harmonic functions in higher dimensions", "description": "Boundary behavior of harmonic functions in higher dimensions", "kind": "subject", "parent": "31B", "page": 73 }, { "code": "31B30", "originalCode": "31B30", "name": "Biharmonic and polyharmonic equations and functions in higher dimensions", "description": "Biharmonic and polyharmonic equations and functions in higher dimensions", "kind": "subject", "parent": "31B", "page": 73 }, { "code": "31B35", "originalCode": "31B35", "name": "Connections of harmonic functions with differential equations in higher dimensions", "description": "Connections of harmonic functions with differential equations in higher dimensions", "kind": "subject", "parent": "31B", "page": 73 }, { "code": "31B99", "originalCode": "31B99", "name": "Higher-dimensional potential theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "31B", "page": 73 }, { "code": "31C", "originalCode": "31Cxx", "name": "Generalizations of potential theory", "description": "Generalizations of potential theory", "kind": "section", "parent": "31", "page": 73 }, { "code": "31C05", "originalCode": "31C05", "name": "Harmonic, subharmonic, superharmonic functions on other spaces", "description": "Harmonic, subharmonic, superharmonic functions on other spaces", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C10", "originalCode": "31C10", "name": "Pluriharmonic and plurisubharmonic functions", "description": "Pluriharmonic and plurisubharmonic functions [See also 32U05]", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C12", "originalCode": "31C12", "name": "Potential theory on Riemannian manifolds and other spaces", "description": "Potential theory on Riemannian manifolds and other spaces [See also 53C20] \\{For Hodge theory, see 58A14\\}", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C15", "originalCode": "31C15", "name": "Potentials and capacities on other spaces", "description": "Potentials and capacities on other spaces", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C20", "originalCode": "31C20", "name": "Discrete potential theory", "description": "Discrete potential theory", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C25", "originalCode": "31C25", "name": "Dirichlet forms", "description": "Dirichlet forms", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C35", "originalCode": "31C35", "name": "Martin boundary theory", "description": "Martin boundary theory [See also 60J50]", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C40", "originalCode": "31C40", "name": "Fine potential theory; fine properties of sets and functions", "description": "Fine potential theory; fine properties of sets and functions", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C45", "originalCode": "31C45", "name": "Other generalizations (nonlinear potential theory, etc.)", "description": "Other generalizations (nonlinear potential theory, etc.)", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31C99", "originalCode": "31C99", "name": "Generalizations of potential theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "31C", "page": 73 }, { "code": "31D", "originalCode": "31Dxx", "name": "Axiomatic potential theory", "description": "Axiomatic potential theory", "kind": "section", "parent": "31", "page": 73 }, { "code": "31D05", "originalCode": "31D05", "name": "Axiomatic potential theory", "description": "Axiomatic potential theory", "kind": "subject", "parent": "31D", "page": 73 }, { "code": "31D99", "originalCode": "31D99", "name": "Axiomatic potential theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "31D", "page": 73 }, { "code": "31E", "originalCode": "31Exx", "name": "Potential theory on fractals and metric spaces", "description": "Potential theory on fractals and metric spaces", "kind": "section", "parent": "31", "page": 73 }, { "code": "31E05", "originalCode": "31E05", "name": "Potential theory on fractals and metric spaces", "description": "Potential theory on fractals and metric spaces", "kind": "subject", "parent": "31E", "page": 73 }, { "code": "31E99", "originalCode": "31E99", "name": "Potential theory on fractals and metric spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "31E", "page": 73 }, { "code": "32", "originalCode": "32-XX", "name": "Several complex variables and analytic spaces", "description": "Several complex variables and analytic spaces \\{For infinite-dimensional holomorphy, see also 46G20, 58B12\\}", "kind": "class", "parent": null, "page": 74 }, { "code": "32-00", "originalCode": "32-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces", "kind": "subject", "parent": "32", "page": 74 }, { "code": "32-01", "originalCode": "32-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces", "kind": "subject", "parent": "32", "page": 74 }, { "code": "32-02", "originalCode": "32-02", "name": "Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces", "description": "Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces", "kind": "subject", "parent": "32", "page": 74 }, { "code": "32-03", "originalCode": "32-03", "name": "History of several complex variables and analytic spaces", "description": "History of several complex variables and analytic spaces [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "32", "page": 74 }, { "code": "32-04", "originalCode": "32-04", "name": "Software, source code, etc. for problems pertaining to several complex variables and analytic spaces", "description": "Software, source code, etc. for problems pertaining to several complex variables and analytic spaces", "kind": "subject", "parent": "32", "page": 74 }, { "code": "32-06", "originalCode": "32-06", "name": "Proceedings, conferences, collections, etc. pertaining to several complex variables and analytic spaces", "description": "Proceedings, conferences, collections, etc. pertaining to several complex variables and analytic spaces", "kind": "subject", "parent": "32", "page": 74 }, { "code": "32-08", "originalCode": "32-08", "name": "Computational methods for problems pertaining to several complex variables and analytic spaces", "description": "Computational methods for problems pertaining to several complex variables and analytic spaces [See also 65Exx]", "kind": "subject", "parent": "32", "page": 74 }, { "code": "32-11", "originalCode": "32-11", "name": "Research data for problems pertaining to several complex variables and analytic spaces", "description": "Research data for problems pertaining to several complex variables and analytic spaces", "kind": "subject", "parent": "32", "page": 74 }, { "code": "32A", "originalCode": "32Axx", "name": "Holomorphic functions of several complex variables", "description": "Holomorphic functions of several complex variables", "kind": "section", "parent": "32", "page": 74 }, { "code": "32A05", "originalCode": "32A05", "name": "Power series, series of functions of several complex variables", "description": "Power series, series of functions of several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A08", "originalCode": "32A08", "name": "Polynomials and rational functions of several complex variables", "description": "Polynomials and rational functions of several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A10", "originalCode": "32A10", "name": "Holomorphic functions of several complex variables", "description": "Holomorphic functions of several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A12", "originalCode": "32A12", "name": "Multifunctions of several complex variables", "description": "Multifunctions of several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A15", "originalCode": "32A15", "name": "Entire functions of several complex variables", "description": "Entire functions of several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A17", "originalCode": "32A17", "name": "Special families of functions of several complex variables", "description": "Special families of functions of several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A18", "originalCode": "32A18", "name": "Bloch functions, normal functions of several complex variables", "description": "Bloch functions, normal functions of several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A19", "originalCode": "32A19", "name": "Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.)", "description": "Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.)", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A20", "originalCode": "32A20", "name": "Meromorphic functions of several complex variables", "description": "Meromorphic functions of several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A22", "originalCode": "32A22", "name": "Nevanlinna theory; growth estimates; other inequalities of several complex variables", "description": "Nevanlinna theory; growth estimates; other inequalities of several complex variables \\{For geometric theory, see 32H25, 32H30\\}", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A25", "originalCode": "32A25", "name": "Integral representations; canonical kernels (Szeg?, Bergman, etc.)", "description": "Integral representations; canonical kernels (Szeg?, Bergman, etc.)", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A26", "originalCode": "32A26", "name": "Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)", "description": "Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A27", "originalCode": "32A27", "name": "Residues for several complex variables", "description": "Residues for several complex variables [See also 32C30]", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A30", "originalCode": "32A30", "name": "Other generalizations of function theory of one complex variable", "description": "Other generalizations of function theory of one complex variable [Should also be assigned at least one classification number from Section 30-XX] \\{For functions of several hypercomplex variables, see 30G35\\}", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A35", "originalCode": "32A35", "name": "\\(H^p\\)-spaces, Nevanlinna spaces of functions in several complex variables", "description": "\\(H^p\\)-spaces, Nevanlinna spaces of functions in several complex variables [See also 32M15, 42B30, 43A85, 46J15]", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A36", "originalCode": "32A36", "name": "Bergman spaces of functions in several complex variables", "description": "Bergman spaces of functions in several complex variables", "kind": "subject", "parent": "32A", "page": 74 }, { "code": "32A37", "originalCode": "32A37", "name": "Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))", "description": "Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A38", "originalCode": "32A38", "name": "Algebras of holomorphic functions of several complex variables", "description": "Algebras of holomorphic functions of several complex variables [See also 46J10, 46J15]", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A40", "originalCode": "32A40", "name": "Boundary behavior of holomorphic functions of several complex variables", "description": "Boundary behavior of holomorphic functions of several complex variables", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A45", "originalCode": "32A45", "name": "Hyperfunctions", "description": "Hyperfunctions [See also 46F15]", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A50", "originalCode": "32A50", "name": "Harmonic analysis of several complex variables", "description": "Harmonic analysis of several complex variables [See mainly 43-XX]", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A55", "originalCode": "32A55", "name": "Singular integrals of functions in several complex variables", "description": "Singular integrals of functions in several complex variables", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A60", "originalCode": "32A60", "name": "Zero sets of holomorphic functions of several complex variables", "description": "Zero sets of holomorphic functions of several complex variables", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A65", "originalCode": "32A65", "name": "Banach algebra techniques applied to functions of several complex variables", "description": "Banach algebra techniques applied to functions of several complex variables [See also 46Jxx]", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A70", "originalCode": "32A70", "name": "Functional analysis techniques applied to functions of several complex variables", "description": "Functional analysis techniques applied to functions of several complex variables [See also 46Exx]", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32A99", "originalCode": "32A99", "name": "Holomorphic functions of several complex variables", "description": "None of the above, but in this section", "kind": "subject", "parent": "32A", "page": 75 }, { "code": "32B", "originalCode": "32Bxx", "name": "Local analytic geometry", "description": "Local analytic geometry [See also 13-XX, 14-XX]", "kind": "section", "parent": "32", "page": 75 }, { "code": "32B05", "originalCode": "32B05", "name": "Analytic algebras and generalizations, preparation theorems", "description": "Analytic algebras and generalizations, preparation theorems", "kind": "subject", "parent": "32B", "page": 75 }, { "code": "32B10", "originalCode": "32B10", "name": "Germs of analytic sets, local parametrization", "description": "Germs of analytic sets, local parametrization", "kind": "subject", "parent": "32B", "page": 75 }, { "code": "32B15", "originalCode": "32B15", "name": "Analytic subsets of affine space", "description": "Analytic subsets of affine space", "kind": "subject", "parent": "32B", "page": 75 }, { "code": "32B20", "originalCode": "32B20", "name": "Semi-analytic sets, subanalytic sets, and generalizations", "description": "Semi-analytic sets, subanalytic sets, and generalizations [See also 14P15]", "kind": "subject", "parent": "32B", "page": 75 }, { "code": "32B25", "originalCode": "32B25", "name": "Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions", "description": "Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions", "kind": "subject", "parent": "32B", "page": 75 }, { "code": "32B99", "originalCode": "32B99", "name": "Local analytic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "32B", "page": 75 }, { "code": "32C", "originalCode": "32Cxx", "name": "Analytic spaces", "description": "Analytic spaces", "kind": "section", "parent": "32", "page": 75 }, { "code": "32C05", "originalCode": "32C05", "name": "Real-analytic manifolds, real-analytic spaces", "description": "Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C07", "originalCode": "32C07", "name": "Real-analytic sets, complex Nash functions", "description": "Real-analytic sets, complex Nash functions [See also 14P15, 14P20]", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C09", "originalCode": "32C09", "name": "Embedding of real-analytic manifolds", "description": "Embedding of real-analytic manifolds", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C11", "originalCode": "32C11", "name": "Complex supergeometry", "description": "Complex supergeometry [See also 14A22, 14M30, 58A50]", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C15", "originalCode": "32C15", "name": "Complex spaces", "description": "Complex spaces", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C18", "originalCode": "32C18", "name": "Topology of analytic spaces", "description": "Topology of analytic spaces", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C20", "originalCode": "32C20", "name": "Normal analytic spaces", "description": "Normal analytic spaces", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C22", "originalCode": "32C22", "name": "Embedding of analytic spaces", "description": "Embedding of analytic spaces", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C25", "originalCode": "32C25", "name": "Analytic subsets and submanifolds", "description": "Analytic subsets and submanifolds", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C30", "originalCode": "32C30", "name": "Integration on analytic sets and spaces, currents", "description": "Integration on analytic sets and spaces, currents [See also 32A25, 32A27]", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C35", "originalCode": "32C35", "name": "Analytic sheaves and cohomology groups", "description": "Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C36", "originalCode": "32C36", "name": "Local cohomology of analytic spaces", "description": "Local cohomology of analytic spaces", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C37", "originalCode": "32C37", "name": "Duality theorems for analytic spaces", "description": "Duality theorems for analytic spaces", "kind": "subject", "parent": "32C", "page": 75 }, { "code": "32C38", "originalCode": "32C38", "name": "Sheaves of differential operators and their modules, \\(D\\)-modules", "description": "Sheaves of differential operators and their modules, \\(D\\)-modules [See also 13N10, 14F10, 16S32, 35A27, 35S35, 58J15]", "kind": "subject", "parent": "32C", "page": 76 }, { "code": "32C55", "originalCode": "32C55", "name": "The Levi problem in complex spaces; generalizations", "description": "The Levi problem in complex spaces; generalizations", "kind": "subject", "parent": "32C", "page": 76 }, { "code": "32C81", "originalCode": "32C81", "name": "Applications of analytic spaces to physics and other areas of science", "description": "Applications of analytic spaces to physics and other areas of science", "kind": "subject", "parent": "32C", "page": 76 }, { "code": "32C99", "originalCode": "32C99", "name": "Analytic spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "32C", "page": 76 }, { "code": "32D", "originalCode": "32Dxx", "name": "Analytic continuation", "description": "Analytic continuation", "kind": "section", "parent": "32", "page": 76 }, { "code": "32D05", "originalCode": "32D05", "name": "Domains of holomorphy", "description": "Domains of holomorphy", "kind": "subject", "parent": "32D", "page": 76 }, { "code": "32D10", "originalCode": "32D10", "name": "Envelopes of holomorphy", "description": "Envelopes of holomorphy", "kind": "subject", "parent": "32D", "page": 76 }, { "code": "32D15", "originalCode": "32D15", "name": "Continuation of analytic objects in several complex variables", "description": "Continuation of analytic objects in several complex variables", "kind": "subject", "parent": "32D", "page": 76 }, { "code": "32D20", "originalCode": "32D20", "name": "Removable singularities in several complex variables", "description": "Removable singularities in several complex variables", "kind": "subject", "parent": "32D", "page": 76 }, { "code": "32D26", "originalCode": "32D26", "name": "Riemann domains", "description": "Riemann domains", "kind": "subject", "parent": "32D", "page": 76 }, { "code": "32D99", "originalCode": "32D99", "name": "Analytic continuation", "description": "None of the above, but in this section", "kind": "subject", "parent": "32D", "page": 76 }, { "code": "32E", "originalCode": "32Exx", "name": "Holomorphic convexity", "description": "Holomorphic convexity", "kind": "section", "parent": "32", "page": 76 }, { "code": "32E05", "originalCode": "32E05", "name": "Holomorphically convex complex spaces, reduction theory", "description": "Holomorphically convex complex spaces, reduction theory", "kind": "subject", "parent": "32E", "page": 76 }, { "code": "32E10", "originalCode": "32E10", "name": "Stein spaces", "description": "Stein spaces", "kind": "subject", "parent": "32E", "page": 76 }, { "code": "32E20", "originalCode": "32E20", "name": "Polynomial convexity, rational convexity, meromorphic convexity in several complex variables", "description": "Polynomial convexity, rational convexity, meromorphic convexity in several complex variables", "kind": "subject", "parent": "32E", "page": 76 }, { "code": "32E30", "originalCode": "32E30", "name": "Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs", "description": "Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs", "kind": "subject", "parent": "32E", "page": 76 }, { "code": "32E35", "originalCode": "32E35", "name": "Global boundary behavior of holomorphic functions of several complex variables", "description": "Global boundary behavior of holomorphic functions of several complex variables", "kind": "subject", "parent": "32E", "page": 76 }, { "code": "32E40", "originalCode": "32E40", "name": "The Levi problem", "description": "The Levi problem", "kind": "subject", "parent": "32E", "page": 76 }, { "code": "32E99", "originalCode": "32E99", "name": "Holomorphic convexity", "description": "None of the above, but in this section", "kind": "subject", "parent": "32E", "page": 76 }, { "code": "32F", "originalCode": "32Fxx", "name": "Geometric convexity in several complex variables", "description": "Geometric convexity in several complex variables", "kind": "section", "parent": "32", "page": 76 }, { "code": "32F10", "originalCode": "32F10", "name": "\\(q\\)-convexity, \\(q\\)-concavity", "description": "\\(q\\)-convexity, \\(q\\)-concavity", "kind": "subject", "parent": "32F", "page": 76 }, { "code": "32F17", "originalCode": "32F17", "name": "Other notions of convexity in relation to several complex variables", "description": "Other notions of convexity in relation to several complex variables", "kind": "subject", "parent": "32F", "page": 76 }, { "code": "32F18", "originalCode": "32F18", "name": "Finite-type conditions for the boundary of a domain", "description": "Finite-type conditions for the boundary of a domain", "kind": "subject", "parent": "32F", "page": 76 }, { "code": "32F27", "originalCode": "32F27", "name": "Topological consequences of geometric convexity", "description": "Topological consequences of geometric convexity", "kind": "subject", "parent": "32F", "page": 76 }, { "code": "32F32", "originalCode": "32F32", "name": "Analytical consequences of geometric convexity (vanishing theorems, etc.)", "description": "Analytical consequences of geometric convexity (vanishing theorems, etc.)", "kind": "subject", "parent": "32F", "page": 76 }, { "code": "32F45", "originalCode": "32F45", "name": "Invariant metrics and pseudodistances in several complex variables", "description": "Invariant metrics and pseudodistances in several complex variables", "kind": "subject", "parent": "32F", "page": 76 }, { "code": "32F99", "originalCode": "32F99", "name": "Geometric convexity in several complex variables", "description": "None of the above, but in this section", "kind": "subject", "parent": "32F", "page": 76 }, { "code": "32G", "originalCode": "32Gxx", "name": "Deformations of analytic structures", "description": "Deformations of analytic structures", "kind": "section", "parent": "32", "page": 77 }, { "code": "32G05", "originalCode": "32G05", "name": "Deformations of complex structures", "description": "Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G07", "originalCode": "32G07", "name": "Deformations of special (e.g., CR) structures", "description": "Deformations of special (e.g., CR) structures", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G08", "originalCode": "32G08", "name": "Deformations of fiber bundles", "description": "Deformations of fiber bundles", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G10", "originalCode": "32G10", "name": "Deformations of submanifolds and subspaces", "description": "Deformations of submanifolds and subspaces", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G13", "originalCode": "32G13", "name": "Complex-analytic moduli problems", "description": "Complex-analytic moduli problems \\{For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10\\} [See also 14H15, 14J15]", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G15", "originalCode": "32G15", "name": "Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)", "description": "Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) [See also 14H15, 30Fxx]", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G20", "originalCode": "32G20", "name": "Period matrices, variation of Hodge structure; degenerations", "description": "Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G34", "originalCode": "32G34", "name": "Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation)", "description": "Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) [See also 34Mxx]", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G81", "originalCode": "32G81", "name": "Applications of deformations of analytic structures to the sciences", "description": "Applications of deformations of analytic structures to the sciences", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32G99", "originalCode": "32G99", "name": "Deformations of analytic structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "32G", "page": 77 }, { "code": "32H", "originalCode": "32Hxx", "name": "Holomorphic mappings and correspondences", "description": "Holomorphic mappings and correspondences", "kind": "section", "parent": "32", "page": 77 }, { "code": "32H02", "originalCode": "32H02", "name": "Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables", "description": "Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32H04", "originalCode": "32H04", "name": "Meromorphic mappings in several complex variables", "description": "Meromorphic mappings in several complex variables", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32H12", "originalCode": "32H12", "name": "Boundary uniqueness of mappings in several complex variables", "description": "Boundary uniqueness of mappings in several complex variables", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32H25", "originalCode": "32H25", "name": "Picard-type theorems and generalizations for several complex variables", "description": "Picard-type theorems and generalizations for several complex variables \\{For function-theoretic properties, see 32A22\\}", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32H30", "originalCode": "32H30", "name": "Value distribution theory in higher dimensions", "description": "Value distribution theory in higher dimensions \\{For function-theoretic properties, see 32A22\\}", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32H35", "originalCode": "32H35", "name": "Proper holomorphic mappings, finiteness theorems", "description": "Proper holomorphic mappings, finiteness theorems", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32H40", "originalCode": "32H40", "name": "Boundary regularity of mappings in several complex variables", "description": "Boundary regularity of mappings in several complex variables", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32H50", "originalCode": "32H50", "name": "Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables", "description": "Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32H99", "originalCode": "32H99", "name": "Holomorphic mappings and correspondences", "description": "None of the above, but in this section", "kind": "subject", "parent": "32H", "page": 77 }, { "code": "32J", "originalCode": "32Jxx", "name": "Compact analytic spaces", "description": "Compact analytic spaces \\{For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx\\}", "kind": "section", "parent": "32", "page": 77 }, { "code": "32J05", "originalCode": "32J05", "name": "Compactification of analytic spaces", "description": "Compactification of analytic spaces", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32J10", "originalCode": "32J10", "name": "Algebraic dependence theorems", "description": "Algebraic dependence theorems", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32J15", "originalCode": "32J15", "name": "Compact complex surfaces", "description": "Compact complex surfaces", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32J17", "originalCode": "32J17", "name": "Compact complex \\(3\\)-folds", "description": "Compact complex \\(3\\)-folds", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32J18", "originalCode": "32J18", "name": "Compact complex \\(n\\)-folds", "description": "Compact complex \\(n\\)-folds", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32J25", "originalCode": "32J25", "name": "Transcendental methods of algebraic geometry (complex-analytic aspects)", "description": "Transcendental methods of algebraic geometry (complex-analytic aspects) [See also 14C30]", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32J27", "originalCode": "32J27", "name": "Compact Kähler manifolds: generalizations, classification", "description": "Compact Kähler manifolds: generalizations, classification", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32J81", "originalCode": "32J81", "name": "Applications of compact analytic spaces to the sciences", "description": "Applications of compact analytic spaces to the sciences", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32J99", "originalCode": "32J99", "name": "Compact analytic spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "32J", "page": 77 }, { "code": "32K", "originalCode": "32Kxx", "name": "Generalizations of analytic spaces", "description": "Generalizations of analytic spaces", "kind": "section", "parent": "32", "page": 78 }, { "code": "32K05", "originalCode": "32K05", "name": "Banach analytic manifolds and spaces", "description": "Banach analytic manifolds and spaces [See also 46G20, 58Bxx]", "kind": "subject", "parent": "32K", "page": 78 }, { "code": "32K07", "originalCode": "32K07", "name": "Formal and graded complex spaces", "description": "Formal and graded complex spaces [See also 58C50]", "kind": "subject", "parent": "32K", "page": 78 }, { "code": "32K12", "originalCode": "32K12", "name": "Holomorphic maps with infinite-dimensional arguments or values", "description": "Holomorphic maps with infinite-dimensional arguments or values [See also 46G20]", "kind": "subject", "parent": "32K", "page": 78 }, { "code": "32K15", "originalCode": "32K15", "name": "Differentiable functions on analytic spaces, differentiable spaces", "description": "Differentiable functions on analytic spaces, differentiable spaces [See also 58C25]", "kind": "subject", "parent": "32K", "page": 78 }, { "code": "32K99", "originalCode": "32K99", "name": "Generalizations of analytic spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "32K", "page": 78 }, { "code": "32L", "originalCode": "32Lxx", "name": "Holomorphic fiber spaces", "description": "Holomorphic fiber spaces [See also 55Rxx]", "kind": "section", "parent": "32", "page": 78 }, { "code": "32L05", "originalCode": "32L05", "name": "Holomorphic bundles and generalizations", "description": "Holomorphic bundles and generalizations", "kind": "subject", "parent": "32L", "page": 78 }, { "code": "32L10", "originalCode": "32L10", "name": "Sheaves and cohomology of sections of holomorphic vector bundles, general results", "description": "Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F06, 14H60, 14J60, 18F20, 55N30]", "kind": "subject", "parent": "32L", "page": 78 }, { "code": "32L15", "originalCode": "32L15", "name": "Bundle convexity", "description": "Bundle convexity [See also 32F10]", "kind": "subject", "parent": "32L", "page": 78 }, { "code": "32L20", "originalCode": "32L20", "name": "Vanishing theorems", "description": "Vanishing theorems", "kind": "subject", "parent": "32L", "page": 78 }, { "code": "32L25", "originalCode": "32L25", "name": "Twistor theory, double fibrations (complex-analytic aspects)", "description": "Twistor theory, double fibrations (complex-analytic aspects) [See also 53C28]", "kind": "subject", "parent": "32L", "page": 78 }, { "code": "32L81", "originalCode": "32L81", "name": "Applications of holomorphic fiber spaces to the sciences", "description": "Applications of holomorphic fiber spaces to the sciences", "kind": "subject", "parent": "32L", "page": 78 }, { "code": "32L99", "originalCode": "32L99", "name": "Holomorphic fiber spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "32L", "page": 78 }, { "code": "32M", "originalCode": "32Mxx", "name": "Complex spaces with a group of automorphisms", "description": "Complex spaces with a group of automorphisms", "kind": "section", "parent": "32", "page": 78 }, { "code": "32M05", "originalCode": "32M05", "name": "Complex Lie groups, group actions on complex spaces", "description": "Complex Lie groups, group actions on complex spaces [See also 22E10]", "kind": "subject", "parent": "32M", "page": 78 }, { "code": "32M10", "originalCode": "32M10", "name": "Homogeneous complex manifolds", "description": "Homogeneous complex manifolds [See also 14M17, 57T15]", "kind": "subject", "parent": "32M", "page": 78 }, { "code": "32M12", "originalCode": "32M12", "name": "Almost homogeneous manifolds and spaces", "description": "Almost homogeneous manifolds and spaces [See also 14M17]", "kind": "subject", "parent": "32M", "page": 78 }, { "code": "32M15", "originalCode": "32M15", "name": "Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)", "description": "Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) [See also 22E10, 22E40, 53C35, 57T15]", "kind": "subject", "parent": "32M", "page": 78 }, { "code": "32M17", "originalCode": "32M17", "name": "Automorphism groups of \\(\\mathbb{C}^n\\) and affine manifolds", "description": "Automorphism groups of \\(\\mathbb{C}^n\\) and affine manifolds", "kind": "subject", "parent": "32M", "page": 78 }, { "code": "32M18", "originalCode": "32M18", "name": "Automorphism groups of other complex spaces", "description": "Automorphism groups of other complex spaces", "kind": "subject", "parent": "32M", "page": 78 }, { "code": "32M25", "originalCode": "32M25", "name": "Complex vector fields, holomorphic foliations, \\(\\mathbb{C}\\)-actions", "description": "Complex vector fields, holomorphic foliations, \\(\\mathbb{C}\\)-actions", "kind": "subject", "parent": "32M", "page": 78 }, { "code": "32M99", "originalCode": "32M99", "name": "Complex spaces with a group of automorphisms", "description": "None of the above, but in this section", "kind": "subject", "parent": "32M", "page": 78 }, { "code": "32N", "originalCode": "32Nxx", "name": "Automorphic functions", "description": "Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]", "kind": "section", "parent": "32", "page": 78 }, { "code": "32N05", "originalCode": "32N05", "name": "General theory of automorphic functions of several complex variables", "description": "General theory of automorphic functions of several complex variables", "kind": "subject", "parent": "32N", "page": 78 }, { "code": "32N10", "originalCode": "32N10", "name": "Automorphic forms in several complex variables", "description": "Automorphic forms in several complex variables", "kind": "subject", "parent": "32N", "page": 78 }, { "code": "32N15", "originalCode": "32N15", "name": "Automorphic functions in symmetric domains", "description": "Automorphic functions in symmetric domains", "kind": "subject", "parent": "32N", "page": 78 }, { "code": "32N99", "originalCode": "32N99", "name": "Automorphic functions", "description": "None of the above, but in this section", "kind": "subject", "parent": "32N", "page": 78 }, { "code": "32P", "originalCode": "32Pxx", "name": "Non-Archimedean analysis", "description": "Non-Archimedean analysis [Should also be assigned at least one other classification number from Section 32-XX describing the type of problem]", "kind": "section", "parent": "32", "page": 79 }, { "code": "32P05", "originalCode": "32P05", "name": "Non-Archimedean analysis", "description": "Non-Archimedean analysis [Should also be assigned at least one other classification number from Section 32-XX describing the type of problem]", "kind": "subject", "parent": "32P", "page": 79 }, { "code": "32P99", "originalCode": "32P99", "name": "Non-Archimedean analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "32P", "page": 79 }, { "code": "32Q", "originalCode": "32Qxx", "name": "Complex manifolds", "description": "Complex manifolds", "kind": "section", "parent": "32", "page": 79 }, { "code": "32Q02", "originalCode": "32Q02", "name": "Special domains (Reinhardt, Hartogs, circular, tube, etc.) in \\(\\mathbb{C}^n\\) and complex manifolds", "description": "Special domains (Reinhardt, Hartogs, circular, tube, etc.) in \\(\\mathbb{C}^n\\) and complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q05", "originalCode": "32Q05", "name": "Negative curvature complex manifolds", "description": "Negative curvature complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q10", "originalCode": "32Q10", "name": "Positive curvature complex manifolds", "description": "Positive curvature complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q15", "originalCode": "32Q15", "name": "Kähler manifolds", "description": "Kähler manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q20", "originalCode": "32Q20", "name": "Kähler-Einstein manifolds", "description": "Kähler-Einstein manifolds [See also 53Cxx]", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q25", "originalCode": "32Q25", "name": "Calabi-Yau theory (complex-analytic aspects)", "description": "Calabi-Yau theory (complex-analytic aspects) [See also 14J32]", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q26", "originalCode": "32Q26", "name": "Notions of stability for complex manifolds", "description": "Notions of stability for complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q28", "originalCode": "32Q28", "name": "Stein manifolds", "description": "Stein manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q30", "originalCode": "32Q30", "name": "Uniformization of complex manifolds", "description": "Uniformization of complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q35", "originalCode": "32Q35", "name": "Complex manifolds as subdomains of Euclidean space", "description": "Complex manifolds as subdomains of Euclidean space", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q40", "originalCode": "32Q40", "name": "Embedding theorems for complex manifolds", "description": "Embedding theorems for complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q45", "originalCode": "32Q45", "name": "Hyperbolic and Kobayashi hyperbolic manifolds", "description": "Hyperbolic and Kobayashi hyperbolic manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q55", "originalCode": "32Q55", "name": "Topological aspects of complex manifolds", "description": "Topological aspects of complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q56", "originalCode": "32Q56", "name": "Oka principle and Oka manifolds", "description": "Oka principle and Oka manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q57", "originalCode": "32Q57", "name": "Classification theorems for complex manifolds", "description": "Classification theorems for complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q60", "originalCode": "32Q60", "name": "Almost complex manifolds", "description": "Almost complex manifolds", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q65", "originalCode": "32Q65", "name": "Pseudoholomorphic curves", "description": "Pseudoholomorphic curves", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32Q99", "originalCode": "32Q99", "name": "Complex manifolds", "description": "None of the above, but in this section", "kind": "subject", "parent": "32Q", "page": 79 }, { "code": "32S", "originalCode": "32Sxx", "name": "Complex singularities", "description": "Complex singularities [See also 58Kxx]", "kind": "section", "parent": "32", "page": 79 }, { "code": "32S05", "originalCode": "32S05", "name": "Local complex singularities", "description": "Local complex singularities [See also 14J17]", "kind": "subject", "parent": "32S", "page": 79 }, { "code": "32S10", "originalCode": "32S10", "name": "Invariants of analytic local rings", "description": "Invariants of analytic local rings", "kind": "subject", "parent": "32S", "page": 79 }, { "code": "32S15", "originalCode": "32S15", "name": "Equisingularity (topological and analytic)", "description": "Equisingularity (topological and analytic) [See also 14E15]", "kind": "subject", "parent": "32S", "page": 79 }, { "code": "32S20", "originalCode": "32S20", "name": "Global theory of complex singularities; cohomological properties", "description": "Global theory of complex singularities; cohomological properties [See also 14E15]", "kind": "subject", "parent": "32S", "page": 79 }, { "code": "32S22", "originalCode": "32S22", "name": "Relations with arrangements of hyperplanes", "description": "Relations with arrangements of hyperplanes [See also 52C35]", "kind": "subject", "parent": "32S", "page": 79 }, { "code": "32S25", "originalCode": "32S25", "name": "Complex surface and hypersurface singularities", "description": "Complex surface and hypersurface singularities [See also 14J17]", "kind": "subject", "parent": "32S", "page": 79 }, { "code": "32S30", "originalCode": "32S30", "name": "Deformations of complex singularities; vanishing cycles", "description": "Deformations of complex singularities; vanishing cycles [See also 14B07]", "kind": "subject", "parent": "32S", "page": 79 }, { "code": "32S35", "originalCode": "32S35", "name": "Mixed Hodge theory of singular varieties (complex-analytic aspects)", "description": "Mixed Hodge theory of singular varieties (complex-analytic aspects) [See also 14C30, 14D07]", "kind": "subject", "parent": "32S", "page": 79 }, { "code": "32S40", "originalCode": "32S40", "name": "Monodromy; relations with differential equations and \\(D\\)-modules (complex-analytic aspects)", "description": "Monodromy; relations with differential equations and \\(D\\)-modules (complex-analytic aspects)", "kind": "subject", "parent": "32S", "page": 80 }, { "code": "32S45", "originalCode": "32S45", "name": "Modifications; resolution of singularities (complex-analytic aspects)", "description": "Modifications; resolution of singularities (complex-analytic aspects) [See also 14E15]", "kind": "subject", "parent": "32S", "page": 80 }, { "code": "32S50", "originalCode": "32S50", "name": "Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants", "description": "Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants", "kind": "subject", "parent": "32S", "page": 80 }, { "code": "32S55", "originalCode": "32S55", "name": "Milnor fibration; relations with knot theory", "description": "Milnor fibration; relations with knot theory [See also 57K10, 57K45]", "kind": "subject", "parent": "32S", "page": 80 }, { "code": "32S60", "originalCode": "32S60", "name": "Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)", "description": "Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) [See also 58Kxx]", "kind": "subject", "parent": "32S", "page": 80 }, { "code": "32S65", "originalCode": "32S65", "name": "Singularities of holomorphic vector fields and foliations", "description": "Singularities of holomorphic vector fields and foliations", "kind": "subject", "parent": "32S", "page": 80 }, { "code": "32S70", "originalCode": "32S70", "name": "Other operations on complex singularities", "description": "Other operations on complex singularities", "kind": "subject", "parent": "32S", "page": 80 }, { "code": "32S99", "originalCode": "32S99", "name": "Complex singularities", "description": "None of the above, but in this section", "kind": "subject", "parent": "32S", "page": 80 }, { "code": "32T", "originalCode": "32Txx", "name": "Pseudoconvex domains", "description": "Pseudoconvex domains", "kind": "section", "parent": "32", "page": 80 }, { "code": "32T05", "originalCode": "32T05", "name": "Domains of holomorphy", "description": "Domains of holomorphy", "kind": "subject", "parent": "32T", "page": 80 }, { "code": "32T15", "originalCode": "32T15", "name": "Strongly pseudoconvex domains", "description": "Strongly pseudoconvex domains", "kind": "subject", "parent": "32T", "page": 80 }, { "code": "32T20", "originalCode": "32T20", "name": "Worm domains", "description": "Worm domains", "kind": "subject", "parent": "32T", "page": 80 }, { "code": "32T25", "originalCode": "32T25", "name": "Finite-type domains", "description": "Finite-type domains", "kind": "subject", "parent": "32T", "page": 80 }, { "code": "32T27", "originalCode": "32T27", "name": "Geometric and analytic invariants on weakly pseudoconvex boundaries", "description": "Geometric and analytic invariants on weakly pseudoconvex boundaries", "kind": "subject", "parent": "32T", "page": 80 }, { "code": "32T35", "originalCode": "32T35", "name": "Exhaustion functions", "description": "Exhaustion functions", "kind": "subject", "parent": "32T", "page": 80 }, { "code": "32T40", "originalCode": "32T40", "name": "Peak functions", "description": "Peak functions", "kind": "subject", "parent": "32T", "page": 80 }, { "code": "32T99", "originalCode": "32T99", "name": "Pseudoconvex domains", "description": "None of the above, but in this section", "kind": "subject", "parent": "32T", "page": 80 }, { "code": "32U", "originalCode": "32Uxx", "name": "Pluripotential theory", "description": "Pluripotential theory", "kind": "section", "parent": "32", "page": 80 }, { "code": "32U05", "originalCode": "32U05", "name": "Plurisubharmonic functions and generalizations", "description": "Plurisubharmonic functions and generalizations [See also 31C10]", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32U10", "originalCode": "32U10", "name": "Plurisubharmonic exhaustion functions", "description": "Plurisubharmonic exhaustion functions", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32U15", "originalCode": "32U15", "name": "General pluripotential theory", "description": "General pluripotential theory", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32U20", "originalCode": "32U20", "name": "Capacity theory and generalizations", "description": "Capacity theory and generalizations", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32U25", "originalCode": "32U25", "name": "Lelong numbers", "description": "Lelong numbers", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32U30", "originalCode": "32U30", "name": "Removable sets in pluripotential theory", "description": "Removable sets in pluripotential theory", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32U35", "originalCode": "32U35", "name": "Plurisubharmonic extremal functions, pluricomplex Green functions", "description": "Plurisubharmonic extremal functions, pluricomplex Green functions", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32U40", "originalCode": "32U40", "name": "Currents", "description": "Currents", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32U99", "originalCode": "32U99", "name": "Pluripotential theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "32U", "page": 80 }, { "code": "32V", "originalCode": "32Vxx", "name": "CR manifolds", "description": "CR manifolds", "kind": "section", "parent": "32", "page": 81 }, { "code": "32V05", "originalCode": "32V05", "name": "CR structures, CR operators, and generalizations", "description": "CR structures, CR operators, and generalizations", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32V10", "originalCode": "32V10", "name": "CR functions", "description": "CR functions", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32V15", "originalCode": "32V15", "name": "CR manifolds as boundaries of domains", "description": "CR manifolds as boundaries of domains", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32V20", "originalCode": "32V20", "name": "Analysis on CR manifolds", "description": "Analysis on CR manifolds", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32V25", "originalCode": "32V25", "name": "Extension of functions and other analytic objects from CR manifolds", "description": "Extension of functions and other analytic objects from CR manifolds", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32V30", "originalCode": "32V30", "name": "Embeddings of CR manifolds", "description": "Embeddings of CR manifolds", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32V35", "originalCode": "32V35", "name": "Finite-type conditions on CR manifolds", "description": "Finite-type conditions on CR manifolds", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32V40", "originalCode": "32V40", "name": "Real submanifolds in complex manifolds", "description": "Real submanifolds in complex manifolds", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32V99", "originalCode": "32V99", "name": "CR manifolds", "description": "None of the above, but in this section", "kind": "subject", "parent": "32V", "page": 81 }, { "code": "32W", "originalCode": "32Wxx", "name": "Differential operators in several variables", "description": "Differential operators in several variables", "kind": "section", "parent": "32", "page": 81 }, { "code": "32W05", "originalCode": "32W05", "name": "\\(\\overline\\partial\\) and \\(\\overline\\partial\\)-Neumann operators", "description": "\\(\\overline\\partial\\) and \\(\\overline\\partial\\)-Neumann operators", "kind": "subject", "parent": "32W", "page": 81 }, { "code": "32W10", "originalCode": "32W10", "name": "\\(\\overline\\partial_b\\) and \\(\\overline\\partial_b\\)-Neumann operators", "description": "\\(\\overline\\partial_b\\) and \\(\\overline\\partial_b\\)-Neumann operators", "kind": "subject", "parent": "32W", "page": 81 }, { "code": "32W20", "originalCode": "32W20", "name": "Complex Monge-Ampère operators", "description": "Complex Monge-Ampère operators", "kind": "subject", "parent": "32W", "page": 81 }, { "code": "32W25", "originalCode": "32W25", "name": "Pseudodifferential operators in several complex variables", "description": "Pseudodifferential operators in several complex variables", "kind": "subject", "parent": "32W", "page": 81 }, { "code": "32W30", "originalCode": "32W30", "name": "Heat kernels in several complex variables", "description": "Heat kernels in several complex variables", "kind": "subject", "parent": "32W", "page": 81 }, { "code": "32W50", "originalCode": "32W50", "name": "Other partial differential equations of complex analysis in several variables", "description": "Other partial differential equations of complex analysis in several variables", "kind": "subject", "parent": "32W", "page": 81 }, { "code": "32W99", "originalCode": "32W99", "name": "Differential operators in several variables", "description": "None of the above, but in this section", "kind": "subject", "parent": "32W", "page": 81 }, { "code": "33", "originalCode": "33-XX", "name": "Special functions", "description": "Special functions (33-XX deals with the properties of functions as functions) \\{For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11-XX; for representation theory, see 22Exx\\}", "kind": "class", "parent": null, "page": 81 }, { "code": "33-00", "originalCode": "33-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions", "kind": "subject", "parent": "33", "page": 81 }, { "code": "33-01", "originalCode": "33-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions", "kind": "subject", "parent": "33", "page": 81 }, { "code": "33-02", "originalCode": "33-02", "name": "Research exposition (monographs, survey articles) pertaining to special functions", "description": "Research exposition (monographs, survey articles) pertaining to special functions", "kind": "subject", "parent": "33", "page": 81 }, { "code": "33-03", "originalCode": "33-03", "name": "History of special functions", "description": "History of special functions [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "33", "page": 81 }, { "code": "33-04", "originalCode": "33-04", "name": "Software, source code, etc. for problems pertaining to special functions", "description": "Software, source code, etc. for problems pertaining to special functions", "kind": "subject", "parent": "33", "page": 81 }, { "code": "33-06", "originalCode": "33-06", "name": "Proceedings, conferences, collections, etc. pertaining to special functions", "description": "Proceedings, conferences, collections, etc. pertaining to special functions", "kind": "subject", "parent": "33", "page": 81 }, { "code": "33-11", "originalCode": "33-11", "name": "Research data for problems pertaining to special functions", "description": "Research data for problems pertaining to special functions", "kind": "subject", "parent": "33", "page": 81 }, { "code": "33B", "originalCode": "33Bxx", "name": "Elementary classical functions", "description": "Elementary classical functions", "kind": "section", "parent": "33", "page": 82 }, { "code": "33B10", "originalCode": "33B10", "name": "Exponential and trigonometric functions", "description": "Exponential and trigonometric functions", "kind": "subject", "parent": "33B", "page": 82 }, { "code": "33B15", "originalCode": "33B15", "name": "Gamma, beta and polygamma functions", "description": "Gamma, beta and polygamma functions", "kind": "subject", "parent": "33B", "page": 82 }, { "code": "33B20", "originalCode": "33B20", "name": "Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)", "description": "Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)", "kind": "subject", "parent": "33B", "page": 82 }, { "code": "33B30", "originalCode": "33B30", "name": "Higher logarithm functions", "description": "Higher logarithm functions", "kind": "subject", "parent": "33B", "page": 82 }, { "code": "33B99", "originalCode": "33B99", "name": "Elementary classical functions", "description": "None of the above, but in this section", "kind": "subject", "parent": "33B", "page": 82 }, { "code": "33C", "originalCode": "33Cxx", "name": "Hypergeometric functions", "description": "Hypergeometric functions", "kind": "section", "parent": "33", "page": 82 }, { "code": "33C05", "originalCode": "33C05", "name": "Classical hypergeometric functions, \\({}_2F_1\\)", "description": "Classical hypergeometric functions, \\({}_2F_1\\)", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C10", "originalCode": "33C10", "name": "Bessel and Airy functions, cylinder functions, \\({}_0F_1\\)", "description": "Bessel and Airy functions, cylinder functions, \\({}_0F_1\\)", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C15", "originalCode": "33C15", "name": "Confluent hypergeometric functions, Whittaker functions, \\({}_1F_1\\)", "description": "Confluent hypergeometric functions, Whittaker functions, \\({}_1F_1\\)", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C20", "originalCode": "33C20", "name": "Generalized hypergeometric series, \\({}_pF_q\\)", "description": "Generalized hypergeometric series, \\({}_pF_q\\)", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C45", "originalCode": "33C45", "name": "Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)", "description": "Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) \\{For general orthogonal polynomials and functions, see also 42C05\\}", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C47", "originalCode": "33C47", "name": "Other special orthogonal polynomials and functions", "description": "Other special orthogonal polynomials and functions", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C50", "originalCode": "33C50", "name": "Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable", "description": "Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C52", "originalCode": "33C52", "name": "Orthogonal polynomials and functions associated with root systems", "description": "Orthogonal polynomials and functions associated with root systems", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C55", "originalCode": "33C55", "name": "Spherical harmonics", "description": "Spherical harmonics", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C60", "originalCode": "33C60", "name": "Hypergeometric integrals and functions defined by them (\\(E\\), \\(G\\), \\(H\\) and \\(I\\) functions)", "description": "Hypergeometric integrals and functions defined by them (\\(E\\), \\(G\\), \\(H\\) and \\(I\\) functions)", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C65", "originalCode": "33C65", "name": "Appell, Horn and Lauricella functions", "description": "Appell, Horn and Lauricella functions", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C67", "originalCode": "33C67", "name": "Hypergeometric functions associated with root systems", "description": "Hypergeometric functions associated with root systems", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C70", "originalCode": "33C70", "name": "Other hypergeometric functions and integrals in several variables", "description": "Other hypergeometric functions and integrals in several variables", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C75", "originalCode": "33C75", "name": "Elliptic integrals as hypergeometric functions", "description": "Elliptic integrals as hypergeometric functions", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C80", "originalCode": "33C80", "name": "Connections of hypergeometric functions with groups and algebras, and related topics", "description": "Connections of hypergeometric functions with groups and algebras, and related topics", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C90", "originalCode": "33C90", "name": "Applications of hypergeometric functions", "description": "Applications of hypergeometric functions", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33C99", "originalCode": "33C99", "name": "Hypergeometric functions", "description": "None of the above, but in this section", "kind": "subject", "parent": "33C", "page": 82 }, { "code": "33D", "originalCode": "33Dxx", "name": "Basic hypergeometric functions", "description": "Basic hypergeometric functions", "kind": "section", "parent": "33", "page": 82 }, { "code": "33D05", "originalCode": "33D05", "name": "\\(q\\)-gamma functions, \\(q\\)-beta functions and integrals", "description": "\\(q\\)-gamma functions, \\(q\\)-beta functions and integrals", "kind": "subject", "parent": "33D", "page": 82 }, { "code": "33D15", "originalCode": "33D15", "name": "Basic hypergeometric functions in one variable, \\({}_r\\phi_s\\)", "description": "Basic hypergeometric functions in one variable, \\({}_r\\phi_s\\)", "kind": "subject", "parent": "33D", "page": 82 }, { "code": "33D45", "originalCode": "33D45", "name": "Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)", "description": "Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)", "kind": "subject", "parent": "33D", "page": 82 }, { "code": "33D50", "originalCode": "33D50", "name": "Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable", "description": "Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable", "kind": "subject", "parent": "33D", "page": 82 }, { "code": "33D52", "originalCode": "33D52", "name": "Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)", "description": "Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)", "kind": "subject", "parent": "33D", "page": 82 }, { "code": "33D60", "originalCode": "33D60", "name": "Basic hypergeometric integrals and functions defined by them", "description": "Basic hypergeometric integrals and functions defined by them", "kind": "subject", "parent": "33D", "page": 82 }, { "code": "33D65", "originalCode": "33D65", "name": "Bibasic functions and multiple bases", "description": "Bibasic functions and multiple bases", "kind": "subject", "parent": "33D", "page": 83 }, { "code": "33D67", "originalCode": "33D67", "name": "Basic hypergeometric functions associated with root systems", "description": "Basic hypergeometric functions associated with root systems", "kind": "subject", "parent": "33D", "page": 83 }, { "code": "33D70", "originalCode": "33D70", "name": "Other basic hypergeometric functions and integrals in several variables", "description": "Other basic hypergeometric functions and integrals in several variables", "kind": "subject", "parent": "33D", "page": 83 }, { "code": "33D80", "originalCode": "33D80", "name": "Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \\(p\\)-adic groups, Hecke algebras, and related topics", "description": "Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \\(p\\)-adic groups, Hecke algebras, and related topics", "kind": "subject", "parent": "33D", "page": 83 }, { "code": "33D90", "originalCode": "33D90", "name": "Applications of basic hypergeometric functions", "description": "Applications of basic hypergeometric functions", "kind": "subject", "parent": "33D", "page": 83 }, { "code": "33D99", "originalCode": "33D99", "name": "Basic hypergeometric functions", "description": "None of the above, but in this section", "kind": "subject", "parent": "33D", "page": 83 }, { "code": "33E", "originalCode": "33Exx", "name": "Other special functions", "description": "Other special functions", "kind": "section", "parent": "33", "page": 83 }, { "code": "33E05", "originalCode": "33E05", "name": "Elliptic functions and integrals", "description": "Elliptic functions and integrals", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33E10", "originalCode": "33E10", "name": "Lamé, Mathieu, and spheroidal wave functions", "description": "Lamé, Mathieu, and spheroidal wave functions", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33E12", "originalCode": "33E12", "name": "Mittag-Leffler functions and generalizations", "description": "Mittag-Leffler functions and generalizations", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33E15", "originalCode": "33E15", "name": "Other wave functions", "description": "Other wave functions", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33E17", "originalCode": "33E17", "name": "Painlevé-type functions", "description": "Painlevé-type functions", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33E20", "originalCode": "33E20", "name": "Other functions defined by series and integrals", "description": "Other functions defined by series and integrals", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33E30", "originalCode": "33E30", "name": "Other functions coming from differential, difference and integral equations", "description": "Other functions coming from differential, difference and integral equations", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33E50", "originalCode": "33E50", "name": "Special functions in characteristic \\(p\\) (gamma functions, etc.)", "description": "Special functions in characteristic \\(p\\) (gamma functions, etc.)", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33E99", "originalCode": "33E99", "name": "Other special functions", "description": "None of the above, but in this section", "kind": "subject", "parent": "33E", "page": 83 }, { "code": "33F", "originalCode": "33Fxx", "name": "Computational aspects of special functions", "description": "Computational aspects of special functions \\{For software etc., see 33-04\\}", "kind": "section", "parent": "33", "page": 83 }, { "code": "33F05", "originalCode": "33F05", "name": "Numerical approximation and evaluation of special functions", "description": "Numerical approximation and evaluation of special functions [See also 65D20]", "kind": "subject", "parent": "33F", "page": 83 }, { "code": "33F10", "originalCode": "33F10", "name": "Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)", "description": "Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) [See also 68W30]", "kind": "subject", "parent": "33F", "page": 83 }, { "code": "33F99", "originalCode": "33F99", "name": "Computational aspects of special functions", "description": "None of the above, but in this section", "kind": "subject", "parent": "33F", "page": 83 }, { "code": "34", "originalCode": "34-XX", "name": "Ordinary differential equations", "description": "Ordinary differential equations", "kind": "class", "parent": null, "page": 83 }, { "code": "34-00", "originalCode": "34-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations", "kind": "subject", "parent": "34", "page": 83 }, { "code": "34-01", "originalCode": "34-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations", "kind": "subject", "parent": "34", "page": 83 }, { "code": "34-02", "originalCode": "34-02", "name": "Research exposition (monographs, survey articles) pertaining to ordinary differential equations", "description": "Research exposition (monographs, survey articles) pertaining to ordinary differential equations", "kind": "subject", "parent": "34", "page": 83 }, { "code": "34-03", "originalCode": "34-03", "name": "History of ordinary differential equations", "description": "History of ordinary differential equations [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "34", "page": 83 }, { "code": "34-04", "originalCode": "34-04", "name": "Software, source code, etc. for problems pertaining to ordinary differential equations", "description": "Software, source code, etc. for problems pertaining to ordinary differential equations", "kind": "subject", "parent": "34", "page": 83 }, { "code": "34-06", "originalCode": "34-06", "name": "Proceedings, conferences, collections, etc. pertaining to ordinary differential equations", "description": "Proceedings, conferences, collections, etc. pertaining to ordinary differential equations", "kind": "subject", "parent": "34", "page": 83 }, { "code": "34-11", "originalCode": "34-11", "name": "Research data for problems pertaining to ordinary differential equations", "description": "Research data for problems pertaining to ordinary differential equations", "kind": "subject", "parent": "34", "page": 83 }, { "code": "34A", "originalCode": "34Axx", "name": "General theory for ordinary differential equations", "description": "General theory for ordinary differential equations", "kind": "section", "parent": "34", "page": 84 }, { "code": "34A05", "originalCode": "34A05", "name": "Explicit solutions, first integrals of ordinary differential equations", "description": "Explicit solutions, first integrals of ordinary differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A06", "originalCode": "34A06", "name": "Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.)", "description": "Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.)", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A07", "originalCode": "34A07", "name": "Fuzzy ordinary differential equations", "description": "Fuzzy ordinary differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A08", "originalCode": "34A08", "name": "Fractional ordinary differential equations", "description": "Fractional ordinary differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A09", "originalCode": "34A09", "name": "Implicit ordinary differential equations, differential-algebraic equations", "description": "Implicit ordinary differential equations, differential-algebraic equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A12", "originalCode": "34A12", "name": "Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations", "description": "Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A25", "originalCode": "34A25", "name": "Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.", "description": "Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. [See also 44-XX]", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A26", "originalCode": "34A26", "name": "Geometric methods in ordinary differential equations", "description": "Geometric methods in ordinary differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A30", "originalCode": "34A30", "name": "Linear ordinary differential equations and systems", "description": "Linear ordinary differential equations and systems", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A33", "originalCode": "34A33", "name": "Ordinary lattice differential equations", "description": "Ordinary lattice differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A34", "originalCode": "34A34", "name": "Nonlinear ordinary differential equations and systems", "description": "Nonlinear ordinary differential equations and systems", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A35", "originalCode": "34A35", "name": "Ordinary differential equations of infinite order", "description": "Ordinary differential equations of infinite order", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A36", "originalCode": "34A36", "name": "Discontinuous ordinary differential equations", "description": "Discontinuous ordinary differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A37", "originalCode": "34A37", "name": "Ordinary differential equations with impulses", "description": "Ordinary differential equations with impulses", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A38", "originalCode": "34A38", "name": "Hybrid systems of ordinary differential equations", "description": "Hybrid systems of ordinary differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A40", "originalCode": "34A40", "name": "Differential inequalities involving functions of a single real variable", "description": "Differential inequalities involving functions of a single real variable [See also 26D20]", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A45", "originalCode": "34A45", "name": "Theoretical approximation of solutions to ordinary differential equations", "description": "Theoretical approximation of solutions to ordinary differential equations \\{For numerical analysis, see 65Lxx\\}", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A55", "originalCode": "34A55", "name": "Inverse problems involving ordinary differential equations", "description": "Inverse problems involving ordinary differential equations", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A60", "originalCode": "34A60", "name": "Ordinary differential inclusions", "description": "Ordinary differential inclusions [See also 49J21, 49K21]", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34A99", "originalCode": "34A99", "name": "General theory for ordinary differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "34A", "page": 84 }, { "code": "34B", "originalCode": "34Bxx", "name": "Boundary value problems for ordinary differential equations", "description": "Boundary value problems for ordinary differential equations \\{For ordinary differential operators, see 34Lxx\\}", "kind": "section", "parent": "34", "page": 84 }, { "code": "34B05", "originalCode": "34B05", "name": "Linear boundary value problems for ordinary differential equations", "description": "Linear boundary value problems for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 84 }, { "code": "34B07", "originalCode": "34B07", "name": "Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter", "description": "Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter", "kind": "subject", "parent": "34B", "page": 84 }, { "code": "34B08", "originalCode": "34B08", "name": "Parameter dependent boundary value problems for ordinary differential equations", "description": "Parameter dependent boundary value problems for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 84 }, { "code": "34B09", "originalCode": "34B09", "name": "Boundary eigenvalue problems for ordinary differential equations", "description": "Boundary eigenvalue problems for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 84 }, { "code": "34B10", "originalCode": "34B10", "name": "Nonlocal and multipoint boundary value problems for ordinary differential equations", "description": "Nonlocal and multipoint boundary value problems for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 84 }, { "code": "34B15", "originalCode": "34B15", "name": "Nonlinear boundary value problems for ordinary differential equations", "description": "Nonlinear boundary value problems for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 84 }, { "code": "34B16", "originalCode": "34B16", "name": "Singular nonlinear boundary value problems for ordinary differential equations", "description": "Singular nonlinear boundary value problems for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 84 }, { "code": "34B18", "originalCode": "34B18", "name": "Positive solutions to nonlinear boundary value problems for ordinary differential equations", "description": "Positive solutions to nonlinear boundary value problems for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 84 }, { "code": "34B20", "originalCode": "34B20", "name": "Weyl theory and its generalizations for ordinary differential equations", "description": "Weyl theory and its generalizations for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34B24", "originalCode": "34B24", "name": "Sturm-Liouville theory", "description": "Sturm-Liouville theory [See also 34Lxx]", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34B27", "originalCode": "34B27", "name": "Green's functions for ordinary differential equations", "description": "Green's functions for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34B30", "originalCode": "34B30", "name": "Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)", "description": "Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34B37", "originalCode": "34B37", "name": "Boundary value problems with impulses for ordinary differential equations", "description": "Boundary value problems with impulses for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34B40", "originalCode": "34B40", "name": "Boundary value problems on infinite intervals for ordinary differential equations", "description": "Boundary value problems on infinite intervals for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34B45", "originalCode": "34B45", "name": "Boundary value problems on graphs and networks for ordinary differential equations", "description": "Boundary value problems on graphs and networks for ordinary differential equations", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34B60", "originalCode": "34B60", "name": "Applications of boundary value problems involving ordinary differential equations", "description": "Applications of boundary value problems involving ordinary differential equations", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34B99", "originalCode": "34B99", "name": "Boundary value problems for ordinary differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "34B", "page": 85 }, { "code": "34C", "originalCode": "34Cxx", "name": "Qualitative theory for ordinary differential equations", "description": "Qualitative theory for ordinary differential equations [See also 37-XX]", "kind": "section", "parent": "34", "page": 85 }, { "code": "34C05", "originalCode": "34C05", "name": "Topological structure of integral curves, singular points, limit cycles of ordinary differential equations", "description": "Topological structure of integral curves, singular points, limit cycles of ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C07", "originalCode": "34C07", "name": "Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations", "description": "Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C08", "originalCode": "34C08", "name": "Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.)", "description": "Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.)", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C10", "originalCode": "34C10", "name": "Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations", "description": "Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C11", "originalCode": "34C11", "name": "Growth and boundedness of solutions to ordinary differential equations", "description": "Growth and boundedness of solutions to ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C12", "originalCode": "34C12", "name": "Monotone systems involving ordinary differential equations", "description": "Monotone systems involving ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C14", "originalCode": "34C14", "name": "Symmetries, invariants of ordinary differential equations", "description": "Symmetries, invariants of ordinary differential equations [See also 37C79]", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C15", "originalCode": "34C15", "name": "Nonlinear oscillations and coupled oscillators for ordinary differential equations", "description": "Nonlinear oscillations and coupled oscillators for ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C20", "originalCode": "34C20", "name": "Transformation and reduction of ordinary differential equations and systems, normal forms", "description": "Transformation and reduction of ordinary differential equations and systems, normal forms", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C23", "originalCode": "34C23", "name": "Bifurcation theory for ordinary differential equations", "description": "Bifurcation theory for ordinary differential equations [See also 37Gxx]", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C25", "originalCode": "34C25", "name": "Periodic solutions to ordinary differential equations", "description": "Periodic solutions to ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C26", "originalCode": "34C26", "name": "Relaxation oscillations for ordinary differential equations", "description": "Relaxation oscillations for ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C27", "originalCode": "34C27", "name": "Almost and pseudo-almost periodic solutions to ordinary differential equations", "description": "Almost and pseudo-almost periodic solutions to ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C28", "originalCode": "34C28", "name": "Complex behavior and chaotic systems of ordinary differential equations", "description": "Complex behavior and chaotic systems of ordinary differential equations [See also 37Dxx]", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C29", "originalCode": "34C29", "name": "Averaging method for ordinary differential equations", "description": "Averaging method for ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C37", "originalCode": "34C37", "name": "Homoclinic and heteroclinic solutions to ordinary differential equations", "description": "Homoclinic and heteroclinic solutions to ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C40", "originalCode": "34C40", "name": "Ordinary differential equations and systems on manifolds", "description": "Ordinary differential equations and systems on manifolds", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C41", "originalCode": "34C41", "name": "Equivalence and asymptotic equivalence of ordinary differential equations", "description": "Equivalence and asymptotic equivalence of ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C45", "originalCode": "34C45", "name": "Invariant manifolds for ordinary differential equations", "description": "Invariant manifolds for ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C46", "originalCode": "34C46", "name": "Multifrequency systems of ordinary differential equations", "description": "Multifrequency systems of ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C55", "originalCode": "34C55", "name": "Hysteresis for ordinary differential equations", "description": "Hysteresis for ordinary differential equations", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C60", "originalCode": "34C60", "name": "Qualitative investigation and simulation of ordinary differential equation models", "description": "Qualitative investigation and simulation of ordinary differential equation models", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34C99", "originalCode": "34C99", "name": "Qualitative theory for ordinary differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "34C", "page": 85 }, { "code": "34D", "originalCode": "34Dxx", "name": "Stability theory for ordinary differential equations", "description": "Stability theory for ordinary differential equations [See also 37C75, 93Dxx]", "kind": "section", "parent": "34", "page": 86 }, { "code": "34D05", "originalCode": "34D05", "name": "Asymptotic properties of solutions to ordinary differential equations", "description": "Asymptotic properties of solutions to ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D06", "originalCode": "34D06", "name": "Synchronization of solutions to ordinary differential equations", "description": "Synchronization of solutions to ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D08", "originalCode": "34D08", "name": "Characteristic and Lyapunov exponents of ordinary differential equations", "description": "Characteristic and Lyapunov exponents of ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D09", "originalCode": "34D09", "name": "Dichotomy, trichotomy of solutions to ordinary differential equations", "description": "Dichotomy, trichotomy of solutions to ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D10", "originalCode": "34D10", "name": "Perturbations of ordinary differential equations", "description": "Perturbations of ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D15", "originalCode": "34D15", "name": "Singular perturbations of ordinary differential equations", "description": "Singular perturbations of ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D20", "originalCode": "34D20", "name": "Stability of solutions to ordinary differential equations", "description": "Stability of solutions to ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D23", "originalCode": "34D23", "name": "Global stability of solutions to ordinary differential equations", "description": "Global stability of solutions to ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D30", "originalCode": "34D30", "name": "Structural stability and analogous concepts of solutions to ordinary differential equations", "description": "Structural stability and analogous concepts of solutions to ordinary differential equations [See also 37C20]", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D35", "originalCode": "34D35", "name": "Stability of manifolds of solutions to ordinary differential equations", "description": "Stability of manifolds of solutions to ordinary differential equations", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D45", "originalCode": "34D45", "name": "Attractors of solutions to ordinary differential equations", "description": "Attractors of solutions to ordinary differential equations [See also 37C70, 37D45]", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34D99", "originalCode": "34D99", "name": "Stability theory for ordinary differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "34D", "page": 86 }, { "code": "34E", "originalCode": "34Exx", "name": "Asymptotic theory for ordinary differential equations", "description": "Asymptotic theory for ordinary differential equations", "kind": "section", "parent": "34", "page": 86 }, { "code": "34E05", "originalCode": "34E05", "name": "Asymptotic expansions of solutions to ordinary differential equations", "description": "Asymptotic expansions of solutions to ordinary differential equations", "kind": "subject", "parent": "34E", "page": 86 }, { "code": "34E10", "originalCode": "34E10", "name": "Perturbations, asymptotics of solutions to ordinary differential equations", "description": "Perturbations, asymptotics of solutions to ordinary differential equations", "kind": "subject", "parent": "34E", "page": 86 }, { "code": "34E13", "originalCode": "34E13", "name": "Multiple scale methods for ordinary differential equations", "description": "Multiple scale methods for ordinary differential equations", "kind": "subject", "parent": "34E", "page": 86 }, { "code": "34E15", "originalCode": "34E15", "name": "Singular perturbations for ordinary differential equations", "description": "Singular perturbations for ordinary differential equations", "kind": "subject", "parent": "34E", "page": 86 }, { "code": "34E17", "originalCode": "34E17", "name": "Canard solutions to ordinary differential equations", "description": "Canard solutions to ordinary differential equations", "kind": "subject", "parent": "34E", "page": 86 }, { "code": "34E18", "originalCode": "34E18", "name": "Methods of nonstandard analysis for ordinary differential equations", "description": "Methods of nonstandard analysis for ordinary differential equations", "kind": "subject", "parent": "34E", "page": 86 }, { "code": "34E20", "originalCode": "34E20", "name": "Singular perturbations, turning point theory, WKB methods for ordinary differential equations", "description": "Singular perturbations, turning point theory, WKB methods for ordinary differential equations", "kind": "subject", "parent": "34E", "page": 86 }, { "code": "34E99", "originalCode": "34E99", "name": "Asymptotic theory for ordinary differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "34E", "page": 86 }, { "code": "34F", "originalCode": "34Fxx", "name": "Ordinary differential equations and systems with randomness", "description": "Ordinary differential equations and systems with randomness [See also 34K50, 60H10, 93E03]", "kind": "section", "parent": "34", "page": 86 }, { "code": "34F05", "originalCode": "34F05", "name": "Ordinary differential equations and systems with randomness", "description": "Ordinary differential equations and systems with randomness", "kind": "subject", "parent": "34F", "page": 86 }, { "code": "34F10", "originalCode": "34F10", "name": "Bifurcation of solutions to ordinary differential equations involving randomness", "description": "Bifurcation of solutions to ordinary differential equations involving randomness", "kind": "subject", "parent": "34F", "page": 86 }, { "code": "34F15", "originalCode": "34F15", "name": "Resonance phenomena for ordinary differential equations involving randomness", "description": "Resonance phenomena for ordinary differential equations involving randomness", "kind": "subject", "parent": "34F", "page": 86 }, { "code": "34F99", "originalCode": "34F99", "name": "Ordinary differential equations and systems with randomness", "description": "None of the above, but in this section", "kind": "subject", "parent": "34F", "page": 86 }, { "code": "34G", "originalCode": "34Gxx", "name": "Differential equations in abstract spaces", "description": "Differential equations in abstract spaces [See also 34K30, 47Jxx, 58D25]", "kind": "section", "parent": "34", "page": 86 }, { "code": "34G10", "originalCode": "34G10", "name": "Linear differential equations in abstract spaces", "description": "Linear differential equations in abstract spaces [See also 47D06, 47D09]", "kind": "subject", "parent": "34G", "page": 86 }, { "code": "34G20", "originalCode": "34G20", "name": "Nonlinear differential equations in abstract spaces", "description": "Nonlinear differential equations in abstract spaces [See also 34K30, 47Jxx]", "kind": "subject", "parent": "34G", "page": 86 }, { "code": "34G25", "originalCode": "34G25", "name": "Evolution inclusions", "description": "Evolution inclusions", "kind": "subject", "parent": "34G", "page": 86 }, { "code": "34G99", "originalCode": "34G99", "name": "Differential equations in abstract spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "34G", "page": 86 }, { "code": "34H", "originalCode": "34Hxx", "name": "Control problems involving ordinary differential equations", "description": "Control problems involving ordinary differential equations [See also 49J15, 49K15, 93C15]", "kind": "section", "parent": "34", "page": 87 }, { "code": "34H05", "originalCode": "34H05", "name": "Control problems involving ordinary differential equations", "description": "Control problems involving ordinary differential equations", "kind": "subject", "parent": "34H", "page": 87 }, { "code": "34H10", "originalCode": "34H10", "name": "Chaos control for problems involving ordinary differential equations", "description": "Chaos control for problems involving ordinary differential equations", "kind": "subject", "parent": "34H", "page": 87 }, { "code": "34H15", "originalCode": "34H15", "name": "Stabilization of solutions to ordinary differential equations", "description": "Stabilization of solutions to ordinary differential equations", "kind": "subject", "parent": "34H", "page": 87 }, { "code": "34H20", "originalCode": "34H20", "name": "Bifurcation control of ordinary differential equations", "description": "Bifurcation control of ordinary differential equations", "kind": "subject", "parent": "34H", "page": 87 }, { "code": "34H99", "originalCode": "34H99", "name": "Control problems involving ordinary differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "34H", "page": 87 }, { "code": "34K", "originalCode": "34Kxx", "name": "Functional-differential equations (including equations with delayed, advanced or state-dependent argument)", "description": "Functional-differential equations (including equations with delayed, advanced or state-dependent argument)", "kind": "section", "parent": "34", "page": 87 }, { "code": "34K04", "originalCode": "34K04", "name": "Symmetries, invariants of functional-differential equations", "description": "Symmetries, invariants of functional-differential equations [See also 37C79]", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K05", "originalCode": "34K05", "name": "General theory of functional-differential equations", "description": "General theory of functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K06", "originalCode": "34K06", "name": "Linear functional-differential equations", "description": "Linear functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K07", "originalCode": "34K07", "name": "Theoretical approximation of solutions to functional-differential equations", "description": "Theoretical approximation of solutions to functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K08", "originalCode": "34K08", "name": "Spectral theory of functional-differential operators", "description": "Spectral theory of functional-differential operators", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K09", "originalCode": "34K09", "name": "Functional-differential inclusions", "description": "Functional-differential inclusions", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K10", "originalCode": "34K10", "name": "Boundary value problems for functional-differential equations", "description": "Boundary value problems for functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K11", "originalCode": "34K11", "name": "Oscillation theory of functional-differential equations", "description": "Oscillation theory of functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K12", "originalCode": "34K12", "name": "Growth, boundedness, comparison of solutions to functional-differential equations", "description": "Growth, boundedness, comparison of solutions to functional-differential equations [See also 37C35]", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K13", "originalCode": "34K13", "name": "Periodic solutions to functional-differential equations", "description": "Periodic solutions to functional-differential equations [See also 37C27]", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K14", "originalCode": "34K14", "name": "Almost and pseudo-almost periodic solutions to functional-differential equations", "description": "Almost and pseudo-almost periodic solutions to functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K16", "originalCode": "34K16", "name": "Heteroclinic and homoclinic orbits of functional-differential equations", "description": "Heteroclinic and homoclinic orbits of functional-differential equations [See also 37C29]", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K17", "originalCode": "34K17", "name": "Transformation and reduction of functional-differential equations and systems, normal forms", "description": "Transformation and reduction of functional-differential equations and systems, normal forms", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K18", "originalCode": "34K18", "name": "Bifurcation theory of functional-differential equations", "description": "Bifurcation theory of functional-differential equations [See also 37Gxx]", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K19", "originalCode": "34K19", "name": "Invariant manifolds of functional-differential equations", "description": "Invariant manifolds of functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K20", "originalCode": "34K20", "name": "Stability theory of functional-differential equations", "description": "Stability theory of functional-differential equations [See also 37C75]", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K21", "originalCode": "34K21", "name": "Stationary solutions of functional-differential equations", "description": "Stationary solutions of functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K23", "originalCode": "34K23", "name": "Complex (chaotic) behavior of solutions to functional-differential equations", "description": "Complex (chaotic) behavior of solutions to functional-differential equations [See also 37D45]", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K24", "originalCode": "34K24", "name": "Synchronization of functional-differential equations", "description": "Synchronization of functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K25", "originalCode": "34K25", "name": "Asymptotic theory of functional-differential equations", "description": "Asymptotic theory of functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K26", "originalCode": "34K26", "name": "Singular perturbations of functional-differential equations", "description": "Singular perturbations of functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K27", "originalCode": "34K27", "name": "Perturbations of functional-differential equations", "description": "Perturbations of functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K29", "originalCode": "34K29", "name": "Inverse problems for functional-differential equations", "description": "Inverse problems for functional-differential equations", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K30", "originalCode": "34K30", "name": "Functional-differential equations in abstract spaces", "description": "Functional-differential equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]", "kind": "subject", "parent": "34K", "page": 87 }, { "code": "34K31", "originalCode": "34K31", "name": "Lattice functional-differential equations", "description": "Lattice functional-differential equations", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K32", "originalCode": "34K32", "name": "Implicit functional-differential equations", "description": "Implicit functional-differential equations", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K33", "originalCode": "34K33", "name": "Averaging for functional-differential equations", "description": "Averaging for functional-differential equations", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K34", "originalCode": "34K34", "name": "Hybrid systems of functional-differential equations", "description": "Hybrid systems of functional-differential equations", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K35", "originalCode": "34K35", "name": "Control problems for functional-differential equations", "description": "Control problems for functional-differential equations [See also 49J21, 49K21, 93C23]", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K36", "originalCode": "34K36", "name": "Fuzzy functional-differential equations", "description": "Fuzzy functional-differential equations", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K37", "originalCode": "34K37", "name": "Functional-differential equations with fractional derivatives", "description": "Functional-differential equations with fractional derivatives", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K38", "originalCode": "34K38", "name": "Functional-differential inequalities", "description": "Functional-differential inequalities", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K39", "originalCode": "34K39", "name": "Discontinuous functional-differential equations", "description": "Discontinuous functional-differential equations", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K40", "originalCode": "34K40", "name": "Neutral functional-differential equations", "description": "Neutral functional-differential equations", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K41", "originalCode": "34K41", "name": "Functional-differential equations in the complex domain", "description": "Functional-differential equations in the complex domain", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K42", "originalCode": "34K42", "name": "Functional-differential equations on time scales or measure chains", "description": "Functional-differential equations on time scales or measure chains", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K43", "originalCode": "34K43", "name": "Functional-differential equations with state-dependent arguments", "description": "Functional-differential equations with state-dependent arguments", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K45", "originalCode": "34K45", "name": "Functional-differential equations with impulses", "description": "Functional-differential equations with impulses", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K50", "originalCode": "34K50", "name": "Stochastic functional-differential equations", "description": "Stochastic functional-differential equations [See also 34Fxx, 60Hxx]", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K60", "originalCode": "34K60", "name": "Qualitative investigation and simulation of models involving functional-differential equations", "description": "Qualitative investigation and simulation of models involving functional-differential equations", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34K99", "originalCode": "34K99", "name": "Functional-differential equations (including equations with delayed, advanced or state-dependent argument)", "description": "None of the above, but in this section", "kind": "subject", "parent": "34K", "page": 88 }, { "code": "34L", "originalCode": "34Lxx", "name": "Ordinary differential operators", "description": "Ordinary differential operators [See also 47E05]", "kind": "section", "parent": "34", "page": 88 }, { "code": "34L05", "originalCode": "34L05", "name": "General spectral theory of ordinary differential operators", "description": "General spectral theory of ordinary differential operators", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34L10", "originalCode": "34L10", "name": "Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators", "description": "Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34L15", "originalCode": "34L15", "name": "Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators", "description": "Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34L16", "originalCode": "34L16", "name": "Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators", "description": "Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34L20", "originalCode": "34L20", "name": "Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators", "description": "Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34L25", "originalCode": "34L25", "name": "Scattering theory, inverse scattering involving ordinary differential operators", "description": "Scattering theory, inverse scattering involving ordinary differential operators", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34L30", "originalCode": "34L30", "name": "Nonlinear ordinary differential operators", "description": "Nonlinear ordinary differential operators", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34L40", "originalCode": "34L40", "name": "Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)", "description": "Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34L99", "originalCode": "34L99", "name": "Ordinary differential operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "34L", "page": 88 }, { "code": "34M", "originalCode": "34Mxx", "name": "Ordinary differential equations in the complex domain", "description": "Ordinary differential equations in the complex domain [See also 30Dxx, 32G34]", "kind": "section", "parent": "34", "page": 89 }, { "code": "34M03", "originalCode": "34M03", "name": "Linear ordinary differential equations and systems in the complex domain", "description": "Linear ordinary differential equations and systems in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M04", "originalCode": "34M04", "name": "Nonlinear ordinary differential equations and systems in the complex domain", "description": "Nonlinear ordinary differential equations and systems in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M05", "originalCode": "34M05", "name": "Entire and meromorphic solutions to ordinary differential equations in the complex domain", "description": "Entire and meromorphic solutions to ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M10", "originalCode": "34M10", "name": "Oscillation, growth of solutions to ordinary differential equations in the complex domain", "description": "Oscillation, growth of solutions to ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M15", "originalCode": "34M15", "name": "Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain", "description": "Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M25", "originalCode": "34M25", "name": "Formal solutions and transform techniques for ordinary differential equations in the complex domain", "description": "Formal solutions and transform techniques for ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M30", "originalCode": "34M30", "name": "Asymptotics and summation methods for ordinary differential equations in the complex domain", "description": "Asymptotics and summation methods for ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M35", "originalCode": "34M35", "name": "Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms", "description": "Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M40", "originalCode": "34M40", "name": "Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain", "description": "Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M45", "originalCode": "34M45", "name": "Ordinary differential equations on complex manifolds", "description": "Ordinary differential equations on complex manifolds", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M46", "originalCode": "34M46", "name": "Spectral theory for ordinary differential operators in the complex domain", "description": "Spectral theory for ordinary differential operators in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M50", "originalCode": "34M50", "name": "Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain", "description": "Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M55", "originalCode": "34M55", "name": "Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies", "description": "Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M56", "originalCode": "34M56", "name": "Isomonodromic deformations for ordinary differential equations in the complex domain", "description": "Isomonodromic deformations for ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M60", "originalCode": "34M60", "name": "Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent)", "description": "Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M65", "originalCode": "34M65", "name": "Topological structure of trajectories of ordinary differential equations in the complex domain", "description": "Topological structure of trajectories of ordinary differential equations in the complex domain", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34M99", "originalCode": "34M99", "name": "Ordinary differential equations in the complex domain", "description": "None of the above, but in this section", "kind": "subject", "parent": "34M", "page": 89 }, { "code": "34N", "originalCode": "34Nxx", "name": "Dynamic equations on time scales or measure chains", "description": "Dynamic equations on time scales or measure chains \\{For real analysis on time scales, see 26E70\\}", "kind": "section", "parent": "34", "page": 89 }, { "code": "34N05", "originalCode": "34N05", "name": "Dynamic equations on time scales or measure chains", "description": "Dynamic equations on time scales or measure chains \\{For real analysis on time scales or measure chains, see 26E70\\}", "kind": "subject", "parent": "34N", "page": 89 }, { "code": "34N99", "originalCode": "34N99", "name": "Dynamic equations on time scales or measure chains", "description": "None of the above, but in this section", "kind": "subject", "parent": "34N", "page": 89 }, { "code": "35", "originalCode": "35-XX", "name": "Partial differential equations", "description": "Partial differential equations", "kind": "class", "parent": null, "page": 89 }, { "code": "35-00", "originalCode": "35-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to partial differential equations", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to partial differential equations", "kind": "subject", "parent": "35", "page": 89 }, { "code": "35-01", "originalCode": "35-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations", "kind": "subject", "parent": "35", "page": 89 }, { "code": "35-02", "originalCode": "35-02", "name": "Research exposition (monographs, survey articles) pertaining to partial differential equations", "description": "Research exposition (monographs, survey articles) pertaining to partial differential equations", "kind": "subject", "parent": "35", "page": 89 }, { "code": "35-03", "originalCode": "35-03", "name": "History of partial differential equations", "description": "History of partial differential equations [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "35", "page": 89 }, { "code": "35-04", "originalCode": "35-04", "name": "Software, source code, etc. for problems pertaining to partial differential equations", "description": "Software, source code, etc. for problems pertaining to partial differential equations", "kind": "subject", "parent": "35", "page": 89 }, { "code": "35-06", "originalCode": "35-06", "name": "Proceedings, conferences, collections, etc. pertaining to partial differential equations", "description": "Proceedings, conferences, collections, etc. pertaining to partial differential equations", "kind": "subject", "parent": "35", "page": 89 }, { "code": "35-11", "originalCode": "35-11", "name": "Research data for problems pertaining to partial differential equations", "description": "Research data for problems pertaining to partial differential equations", "kind": "subject", "parent": "35", "page": 89 }, { "code": "35A", "originalCode": "35Axx", "name": "General topics in partial differential equations", "description": "General topics in partial differential equations", "kind": "section", "parent": "35", "page": 90 }, { "code": "35A01", "originalCode": "35A01", "name": "Existence problems for PDEs: global existence, local existence, non-existence", "description": "Existence problems for PDEs: global existence, local existence, non-existence", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A02", "originalCode": "35A02", "name": "Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness", "description": "Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A08", "originalCode": "35A08", "name": "Fundamental solutions to PDEs", "description": "Fundamental solutions to PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A09", "originalCode": "35A09", "name": "Classical solutions to PDEs", "description": "Classical solutions to PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A10", "originalCode": "35A10", "name": "Cauchy-Kovalevskaya theorems", "description": "Cauchy-Kovalevskaya theorems", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A15", "originalCode": "35A15", "name": "Variational methods applied to PDEs", "description": "Variational methods applied to PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A16", "originalCode": "35A16", "name": "Topological and monotonicity methods applied to PDEs", "description": "Topological and monotonicity methods applied to PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A17", "originalCode": "35A17", "name": "Parametrices in context of PDEs", "description": "Parametrices in context of PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A18", "originalCode": "35A18", "name": "Wave front sets in context of PDEs", "description": "Wave front sets in context of PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A20", "originalCode": "35A20", "name": "Analyticity in context of PDEs", "description": "Analyticity in context of PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A21", "originalCode": "35A21", "name": "Singularity in context of PDEs", "description": "Singularity in context of PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A22", "originalCode": "35A22", "name": "Transform methods (e.g., integral transforms) applied to PDEs", "description": "Transform methods (e.g., integral transforms) applied to PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A23", "originalCode": "35A23", "name": "Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals", "description": "Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A24", "originalCode": "35A24", "name": "Methods of ordinary differential equations applied to PDEs", "description": "Methods of ordinary differential equations applied to PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A25", "originalCode": "35A25", "name": "Other special methods applied to PDEs", "description": "Other special methods applied to PDEs", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A27", "originalCode": "35A27", "name": "Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs", "description": "Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs [See also 32C38, 58J15]", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A30", "originalCode": "35A30", "name": "Geometric theory, characteristics, transformations in context of PDEs", "description": "Geometric theory, characteristics, transformations in context of PDEs [See also 58J70, 58J72]", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A35", "originalCode": "35A35", "name": "Theoretical approximation in context of PDEs", "description": "Theoretical approximation in context of PDEs \\{For numerical analysis, see 65Mxx, 65Nxx\\}", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35A99", "originalCode": "35A99", "name": "General topics in partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35A", "page": 90 }, { "code": "35B", "originalCode": "35Bxx", "name": "Qualitative properties of solutions to partial differential equations", "description": "Qualitative properties of solutions to partial differential equations", "kind": "section", "parent": "35", "page": 90 }, { "code": "35B05", "originalCode": "35B05", "name": "Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs", "description": "Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B06", "originalCode": "35B06", "name": "Symmetries, invariants, etc. in context of PDEs", "description": "Symmetries, invariants, etc. in context of PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B07", "originalCode": "35B07", "name": "Axially symmetric solutions to PDEs", "description": "Axially symmetric solutions to PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B08", "originalCode": "35B08", "name": "Entire solutions to PDEs", "description": "Entire solutions to PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B09", "originalCode": "35B09", "name": "Positive solutions to PDEs", "description": "Positive solutions to PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B10", "originalCode": "35B10", "name": "Periodic solutions to PDEs", "description": "Periodic solutions to PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B15", "originalCode": "35B15", "name": "Almost and pseudo-almost periodic solutions to PDEs", "description": "Almost and pseudo-almost periodic solutions to PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B20", "originalCode": "35B20", "name": "Perturbations in context of PDEs", "description": "Perturbations in context of PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B25", "originalCode": "35B25", "name": "Singular perturbations in context of PDEs", "description": "Singular perturbations in context of PDEs", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B27", "originalCode": "35B27", "name": "Homogenization in context of PDEs; PDEs in media with periodic structure", "description": "Homogenization in context of PDEs; PDEs in media with periodic structure [See also 74Q05, 74Q10, 76M50, 78M40, 80M40]", "kind": "subject", "parent": "35B", "page": 90 }, { "code": "35B30", "originalCode": "35B30", "name": "Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs", "description": "Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs [See also 37Cxx]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B32", "originalCode": "35B32", "name": "Bifurcations in context of PDEs", "description": "Bifurcations in context of PDEs [See also 34C23, 34F10, 34H20, 37F46, 37Gxx, 37H20, 37J20, 37K50, 37L10, 37M20, 47J15, 58E05, 58E07, 58J55]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B33", "originalCode": "35B33", "name": "Critical exponents in context of PDEs", "description": "Critical exponents in context of PDEs", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B34", "originalCode": "35B34", "name": "Resonance in context of PDEs", "description": "Resonance in context of PDEs [See also 34F15, 70J40, 70K28, 70K30, 81U24]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B35", "originalCode": "35B35", "name": "Stability in context of PDEs", "description": "Stability in context of PDEs [See also 34Dxx, 37B25, 37C20, 37C75, 37F15, 37J25, 37K45, 37L15, 49K40, 58K25, 93Dxx]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B36", "originalCode": "35B36", "name": "Pattern formations in context of PDEs", "description": "Pattern formations in context of PDEs [See also 92C15]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B38", "originalCode": "35B38", "name": "Critical points of functionals in context of PDEs (e.g., energy functionals)", "description": "Critical points of functionals in context of PDEs (e.g., energy functionals) [See also 57R70, 58K05, 58E05]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B40", "originalCode": "35B40", "name": "Asymptotic behavior of solutions to PDEs", "description": "Asymptotic behavior of solutions to PDEs", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B41", "originalCode": "35B41", "name": "Attractors", "description": "Attractors [See also 34D45, 37B35, 37C70, 37D45, 37G35, 37L30, 37M22]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B42", "originalCode": "35B42", "name": "Inertial manifolds", "description": "Inertial manifolds [See also 37L25]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B44", "originalCode": "35B44", "name": "Blow-up in context of PDEs", "description": "Blow-up in context of PDEs", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B45", "originalCode": "35B45", "name": "A priori estimates in context of PDEs", "description": "A priori estimates in context of PDEs", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B50", "originalCode": "35B50", "name": "Maximum principles in context of PDEs", "description": "Maximum principles in context of PDEs", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B51", "originalCode": "35B51", "name": "Comparison principles in context of PDEs", "description": "Comparison principles in context of PDEs", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B53", "originalCode": "35B53", "name": "Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs", "description": "Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B60", "originalCode": "35B60", "name": "Continuation and prolongation of solutions to PDEs", "description": "Continuation and prolongation of solutions to PDEs [See also 58A15, 58A17, 58Hxx]", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B65", "originalCode": "35B65", "name": "Smoothness and regularity of solutions to PDEs", "description": "Smoothness and regularity of solutions to PDEs", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35B99", "originalCode": "35B99", "name": "Qualitative properties of solutions to partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35B", "page": 91 }, { "code": "35C", "originalCode": "35Cxx", "name": "Representations of solutions to partial differential equations", "description": "Representations of solutions to partial differential equations", "kind": "section", "parent": "35", "page": 91 }, { "code": "35C05", "originalCode": "35C05", "name": "Solutions to PDEs in closed form", "description": "Solutions to PDEs in closed form", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C06", "originalCode": "35C06", "name": "Self-similar solutions to PDEs", "description": "Self-similar solutions to PDEs", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C07", "originalCode": "35C07", "name": "Traveling wave solutions", "description": "Traveling wave solutions", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C08", "originalCode": "35C08", "name": "Soliton solutions", "description": "Soliton solutions [See also 37K40]", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C09", "originalCode": "35C09", "name": "Trigonometric solutions to PDEs", "description": "Trigonometric solutions to PDEs", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C10", "originalCode": "35C10", "name": "Series solutions to PDEs", "description": "Series solutions to PDEs", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C11", "originalCode": "35C11", "name": "Polynomial solutions to PDEs", "description": "Polynomial solutions to PDEs", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C15", "originalCode": "35C15", "name": "Integral representations of solutions to PDEs", "description": "Integral representations of solutions to PDEs", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C20", "originalCode": "35C20", "name": "Asymptotic expansions of solutions to PDEs", "description": "Asymptotic expansions of solutions to PDEs", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35C99", "originalCode": "35C99", "name": "Representations of solutions to partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35C", "page": 91 }, { "code": "35D", "originalCode": "35Dxx", "name": "Generalized solutions to partial differential equations", "description": "Generalized solutions to partial differential equations", "kind": "section", "parent": "35", "page": 92 }, { "code": "35D30", "originalCode": "35D30", "name": "Weak solutions to PDEs", "description": "Weak solutions to PDEs", "kind": "subject", "parent": "35D", "page": 92 }, { "code": "35D35", "originalCode": "35D35", "name": "Strong solutions to PDEs", "description": "Strong solutions to PDEs", "kind": "subject", "parent": "35D", "page": 92 }, { "code": "35D40", "originalCode": "35D40", "name": "Viscosity solutions to PDEs", "description": "Viscosity solutions to PDEs", "kind": "subject", "parent": "35D", "page": 92 }, { "code": "35D99", "originalCode": "35D99", "name": "Generalized solutions to partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35D", "page": 92 }, { "code": "35E", "originalCode": "35Exx", "name": "Partial differential equations and systems of partial differential equations with constant coefficients", "description": "Partial differential equations and systems of partial differential equations with constant coefficients [See also 35N05]", "kind": "section", "parent": "35", "page": 92 }, { "code": "35E05", "originalCode": "35E05", "name": "Fundamental solutions to PDEs and systems of PDEs with constant coefficients", "description": "Fundamental solutions to PDEs and systems of PDEs with constant coefficients", "kind": "subject", "parent": "35E", "page": 92 }, { "code": "35E10", "originalCode": "35E10", "name": "Convexity properties of solutions to PDEs with constant coefficients", "description": "Convexity properties of solutions to PDEs with constant coefficients", "kind": "subject", "parent": "35E", "page": 92 }, { "code": "35E15", "originalCode": "35E15", "name": "Initial value problems for PDEs and systems of PDEs with constant coefficients", "description": "Initial value problems for PDEs and systems of PDEs with constant coefficients", "kind": "subject", "parent": "35E", "page": 92 }, { "code": "35E20", "originalCode": "35E20", "name": "General theory of PDEs and systems of PDEs with constant coefficients", "description": "General theory of PDEs and systems of PDEs with constant coefficients", "kind": "subject", "parent": "35E", "page": 92 }, { "code": "35E99", "originalCode": "35E99", "name": "Partial differential equations and systems of partial differential equations with constant coefficients", "description": "None of the above, but in this section", "kind": "subject", "parent": "35E", "page": 92 }, { "code": "35F", "originalCode": "35Fxx", "name": "General first-order partial differential equations and systems of first-order partial differential equations", "description": "General first-order partial differential equations and systems of first-order partial differential equations", "kind": "section", "parent": "35", "page": 92 }, { "code": "35F05", "originalCode": "35F05", "name": "Linear first-order PDEs", "description": "Linear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F10", "originalCode": "35F10", "name": "Initial value problems for linear first-order PDEs", "description": "Initial value problems for linear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F15", "originalCode": "35F15", "name": "Boundary value problems for linear first-order PDEs", "description": "Boundary value problems for linear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F16", "originalCode": "35F16", "name": "Initial-boundary value problems for linear first-order PDEs", "description": "Initial-boundary value problems for linear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F20", "originalCode": "35F20", "name": "Nonlinear first-order PDEs", "description": "Nonlinear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F21", "originalCode": "35F21", "name": "Hamilton-Jacobi equations", "description": "Hamilton-Jacobi equations \\{For calculus of variations and optimal control, see 49Lxx; for mechanics of particles and systems, see 70H20\\}", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F25", "originalCode": "35F25", "name": "Initial value problems for nonlinear first-order PDEs", "description": "Initial value problems for nonlinear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F30", "originalCode": "35F30", "name": "Boundary value problems for nonlinear first-order PDEs", "description": "Boundary value problems for nonlinear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F31", "originalCode": "35F31", "name": "Initial-boundary value problems for nonlinear first-order PDEs", "description": "Initial-boundary value problems for nonlinear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F35", "originalCode": "35F35", "name": "Systems of linear first-order PDEs", "description": "Systems of linear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F40", "originalCode": "35F40", "name": "Initial value problems for systems of linear first-order PDEs", "description": "Initial value problems for systems of linear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F45", "originalCode": "35F45", "name": "Boundary value problems for systems of linear first-order PDEs", "description": "Boundary value problems for systems of linear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F46", "originalCode": "35F46", "name": "Initial-boundary value problems for systems of linear first-order PDEs", "description": "Initial-boundary value problems for systems of linear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F50", "originalCode": "35F50", "name": "Systems of nonlinear first-order PDEs", "description": "Systems of nonlinear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F55", "originalCode": "35F55", "name": "Initial value problems for systems of nonlinear first-order PDEs", "description": "Initial value problems for systems of nonlinear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F60", "originalCode": "35F60", "name": "Boundary value problems for systems of nonlinear first-order PDEs", "description": "Boundary value problems for systems of nonlinear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F61", "originalCode": "35F61", "name": "Initial-boundary value problems for systems of nonlinear first-order PDEs", "description": "Initial-boundary value problems for systems of nonlinear first-order PDEs", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35F99", "originalCode": "35F99", "name": "General first-order partial differential equations and systems of first-order partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35F", "page": 92 }, { "code": "35G", "originalCode": "35Gxx", "name": "General higher-order partial differential equations and systems of higher-order partial differential equations", "description": "General higher-order partial differential equations and systems of higher-order partial differential equations", "kind": "section", "parent": "35", "page": 93 }, { "code": "35G05", "originalCode": "35G05", "name": "Linear higher-order PDEs", "description": "Linear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G10", "originalCode": "35G10", "name": "Initial value problems for linear higher-order PDEs", "description": "Initial value problems for linear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G15", "originalCode": "35G15", "name": "Boundary value problems for linear higher-order PDEs", "description": "Boundary value problems for linear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G16", "originalCode": "35G16", "name": "Initial-boundary value problems for linear higher-order PDEs", "description": "Initial-boundary value problems for linear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G20", "originalCode": "35G20", "name": "Nonlinear higher-order PDEs", "description": "Nonlinear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G25", "originalCode": "35G25", "name": "Initial value problems for nonlinear higher-order PDEs", "description": "Initial value problems for nonlinear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G30", "originalCode": "35G30", "name": "Boundary value problems for nonlinear higher-order PDEs", "description": "Boundary value problems for nonlinear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G31", "originalCode": "35G31", "name": "Initial-boundary value problems for nonlinear higher-order PDEs", "description": "Initial-boundary value problems for nonlinear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G35", "originalCode": "35G35", "name": "Systems of linear higher-order PDEs", "description": "Systems of linear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G40", "originalCode": "35G40", "name": "Initial value problems for systems of linear higher-order PDEs", "description": "Initial value problems for systems of linear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G45", "originalCode": "35G45", "name": "Boundary value problems for systems of linear higher-order PDEs", "description": "Boundary value problems for systems of linear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G46", "originalCode": "35G46", "name": "Initial-boundary value problems for systems of linear higher-order PDEs", "description": "Initial-boundary value problems for systems of linear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G50", "originalCode": "35G50", "name": "Systems of nonlinear higher-order PDEs", "description": "Systems of nonlinear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G55", "originalCode": "35G55", "name": "Initial value problems for systems of nonlinear higher-order PDEs", "description": "Initial value problems for systems of nonlinear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G60", "originalCode": "35G60", "name": "Boundary value problems for systems of nonlinear higher-order PDEs", "description": "Boundary value problems for systems of nonlinear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G61", "originalCode": "35G61", "name": "Initial-boundary value problems for systems of nonlinear higher-order PDEs", "description": "Initial-boundary value problems for systems of nonlinear higher-order PDEs", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35G99", "originalCode": "35G99", "name": "General higher-order partial differential equations and systems of higher-order partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35G", "page": 93 }, { "code": "35H", "originalCode": "35Hxx", "name": "Close-to-elliptic equations", "description": "Close-to-elliptic equations", "kind": "section", "parent": "35", "page": 93 }, { "code": "35H10", "originalCode": "35H10", "name": "Hypoelliptic equations", "description": "Hypoelliptic equations", "kind": "subject", "parent": "35H", "page": 93 }, { "code": "35H20", "originalCode": "35H20", "name": "Subelliptic equations", "description": "Subelliptic equations", "kind": "subject", "parent": "35H", "page": 93 }, { "code": "35H30", "originalCode": "35H30", "name": "Quasielliptic equations", "description": "Quasielliptic equations", "kind": "subject", "parent": "35H", "page": 93 }, { "code": "35H99", "originalCode": "35H99", "name": "Close-to-elliptic equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35H", "page": 93 }, { "code": "35J", "originalCode": "35Jxx", "name": "Elliptic equations and elliptic systems", "description": "Elliptic equations and elliptic systems \\{For global analysis, analysis on manifolds, see 58J10, 58J20\\}", "kind": "section", "parent": "35", "page": 93 }, { "code": "35J05", "originalCode": "35J05", "name": "Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation", "description": "Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation [See also 31Axx, 31Bxx]", "kind": "subject", "parent": "35J", "page": 93 }, { "code": "35J08", "originalCode": "35J08", "name": "Green's functions for elliptic equations", "description": "Green's functions for elliptic equations", "kind": "subject", "parent": "35J", "page": 93 }, { "code": "35J10", "originalCode": "35J10", "name": "Schrödinger operator, Schrödinger equation", "description": "Schrödinger operator, Schrödinger equation \\{For ordinary differential equations, see 34L40; for operator theory, see 47D08; for quantum theory, see 81Q05; for statistical mechanics, see 82B44\\}", "kind": "subject", "parent": "35J", "page": 93 }, { "code": "35J15", "originalCode": "35J15", "name": "Second-order elliptic equations", "description": "Second-order elliptic equations", "kind": "subject", "parent": "35J", "page": 93 }, { "code": "35J20", "originalCode": "35J20", "name": "Variational methods for second-order elliptic equations", "description": "Variational methods for second-order elliptic equations", "kind": "subject", "parent": "35J", "page": 93 }, { "code": "35J25", "originalCode": "35J25", "name": "Boundary value problems for second-order elliptic equations", "description": "Boundary value problems for second-order elliptic equations", "kind": "subject", "parent": "35J", "page": 93 }, { "code": "35J30", "originalCode": "35J30", "name": "Higher-order elliptic equations", "description": "Higher-order elliptic equations [See also 31A30, 31B30]", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J35", "originalCode": "35J35", "name": "Variational methods for higher-order elliptic equations", "description": "Variational methods for higher-order elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J40", "originalCode": "35J40", "name": "Boundary value problems for higher-order elliptic equations", "description": "Boundary value problems for higher-order elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J46", "originalCode": "35J46", "name": "First-order elliptic systems", "description": "First-order elliptic systems", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J47", "originalCode": "35J47", "name": "Second-order elliptic systems", "description": "Second-order elliptic systems", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J48", "originalCode": "35J48", "name": "Higher-order elliptic systems", "description": "Higher-order elliptic systems", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J50", "originalCode": "35J50", "name": "Variational methods for elliptic systems", "description": "Variational methods for elliptic systems", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J56", "originalCode": "35J56", "name": "Boundary value problems for first-order elliptic systems", "description": "Boundary value problems for first-order elliptic systems", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J57", "originalCode": "35J57", "name": "Boundary value problems for second-order elliptic systems", "description": "Boundary value problems for second-order elliptic systems", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J58", "originalCode": "35J58", "name": "Boundary value problems for higher-order elliptic systems", "description": "Boundary value problems for higher-order elliptic systems", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J60", "originalCode": "35J60", "name": "Nonlinear elliptic equations", "description": "Nonlinear elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J61", "originalCode": "35J61", "name": "Semilinear elliptic equations", "description": "Semilinear elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J62", "originalCode": "35J62", "name": "Quasilinear elliptic equations", "description": "Quasilinear elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J65", "originalCode": "35J65", "name": "Nonlinear boundary value problems for linear elliptic equations", "description": "Nonlinear boundary value problems for linear elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J66", "originalCode": "35J66", "name": "Nonlinear boundary value problems for nonlinear elliptic equations", "description": "Nonlinear boundary value problems for nonlinear elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J67", "originalCode": "35J67", "name": "Boundary values of solutions to elliptic equations and elliptic systems", "description": "Boundary values of solutions to elliptic equations and elliptic systems", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J70", "originalCode": "35J70", "name": "Degenerate elliptic equations", "description": "Degenerate elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J75", "originalCode": "35J75", "name": "Singular elliptic equations", "description": "Singular elliptic equations", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J86", "originalCode": "35J86", "name": "Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators", "description": "Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J87", "originalCode": "35J87", "name": "Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators", "description": "Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J88", "originalCode": "35J88", "name": "Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators", "description": "Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J91", "originalCode": "35J91", "name": "Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian", "description": "Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J92", "originalCode": "35J92", "name": "Quasilinear elliptic equations with \\(p\\)-Laplacian", "description": "Quasilinear elliptic equations with \\(p\\)-Laplacian", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J93", "originalCode": "35J93", "name": "Quasilinear elliptic equations with mean curvature operator", "description": "Quasilinear elliptic equations with mean curvature operator", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J94", "originalCode": "35J94", "name": "Elliptic equations with infinity-Laplacian", "description": "Elliptic equations with infinity-Laplacian", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J96", "originalCode": "35J96", "name": "Monge-Ampère equations", "description": "Monge-Ampère equations \\{For complex Monge-Ampère operators, see 32W20; for parabolic Monge-Ampère equations, see 35K96\\}", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35J99", "originalCode": "35J99", "name": "Elliptic equations and elliptic systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "35J", "page": 94 }, { "code": "35K", "originalCode": "35Kxx", "name": "Parabolic equations and parabolic systems", "description": "Parabolic equations and parabolic systems \\{For global analysis, analysis on manifolds, see 58J35\\}", "kind": "section", "parent": "35", "page": 95 }, { "code": "35K05", "originalCode": "35K05", "name": "Heat equation", "description": "Heat equation", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K08", "originalCode": "35K08", "name": "Heat kernel", "description": "Heat kernel", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K10", "originalCode": "35K10", "name": "Second-order parabolic equations", "description": "Second-order parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K15", "originalCode": "35K15", "name": "Initial value problems for second-order parabolic equations", "description": "Initial value problems for second-order parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K20", "originalCode": "35K20", "name": "Initial-boundary value problems for second-order parabolic equations", "description": "Initial-boundary value problems for second-order parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K25", "originalCode": "35K25", "name": "Higher-order parabolic equations", "description": "Higher-order parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K30", "originalCode": "35K30", "name": "Initial value problems for higher-order parabolic equations", "description": "Initial value problems for higher-order parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K35", "originalCode": "35K35", "name": "Initial-boundary value problems for higher-order parabolic equations", "description": "Initial-boundary value problems for higher-order parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K40", "originalCode": "35K40", "name": "Second-order parabolic systems", "description": "Second-order parabolic systems", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K41", "originalCode": "35K41", "name": "Higher-order parabolic systems", "description": "Higher-order parabolic systems", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K45", "originalCode": "35K45", "name": "Initial value problems for second-order parabolic systems", "description": "Initial value problems for second-order parabolic systems", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K46", "originalCode": "35K46", "name": "Initial value problems for higher-order parabolic systems", "description": "Initial value problems for higher-order parabolic systems", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K51", "originalCode": "35K51", "name": "Initial-boundary value problems for second-order parabolic systems", "description": "Initial-boundary value problems for second-order parabolic systems", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K52", "originalCode": "35K52", "name": "Initial-boundary value problems for higher-order parabolic systems", "description": "Initial-boundary value problems for higher-order parabolic systems", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K55", "originalCode": "35K55", "name": "Nonlinear parabolic equations", "description": "Nonlinear parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K57", "originalCode": "35K57", "name": "Reaction-diffusion equations", "description": "Reaction-diffusion equations \\{For diffusion processes and reaction effects, see 47D07, 58J65, 60J60, 60J70, 74N25, 76R50, 76V05, 80A23, 82B24, 82C24, 92E20\\}", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K58", "originalCode": "35K58", "name": "Semilinear parabolic equations", "description": "Semilinear parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K59", "originalCode": "35K59", "name": "Quasilinear parabolic equations", "description": "Quasilinear parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K60", "originalCode": "35K60", "name": "Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations", "description": "Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K61", "originalCode": "35K61", "name": "Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations", "description": "Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K65", "originalCode": "35K65", "name": "Degenerate parabolic equations", "description": "Degenerate parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K67", "originalCode": "35K67", "name": "Singular parabolic equations", "description": "Singular parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K70", "originalCode": "35K70", "name": "Ultraparabolic equations, pseudoparabolic equations, etc.", "description": "Ultraparabolic equations, pseudoparabolic equations, etc.", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K85", "originalCode": "35K85", "name": "Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators", "description": "Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K86", "originalCode": "35K86", "name": "Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators", "description": "Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K87", "originalCode": "35K87", "name": "Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators", "description": "Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K90", "originalCode": "35K90", "name": "Abstract parabolic equations", "description": "Abstract parabolic equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K91", "originalCode": "35K91", "name": "Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian", "description": "Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K92", "originalCode": "35K92", "name": "Quasilinear parabolic equations with \\(p\\)-Laplacian", "description": "Quasilinear parabolic equations with \\(p\\)-Laplacian", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K93", "originalCode": "35K93", "name": "Quasilinear parabolic equations with mean curvature operator", "description": "Quasilinear parabolic equations with mean curvature operator", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K96", "originalCode": "35K96", "name": "Parabolic Monge-Ampère equations", "description": "Parabolic Monge-Ampère equations", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35K99", "originalCode": "35K99", "name": "Parabolic equations and parabolic systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "35K", "page": 95 }, { "code": "35L", "originalCode": "35Lxx", "name": "Hyperbolic equations and hyperbolic systems", "description": "Hyperbolic equations and hyperbolic systems \\{For global analysis, see 58J45\\}", "kind": "section", "parent": "35", "page": 96 }, { "code": "35L02", "originalCode": "35L02", "name": "First-order hyperbolic equations", "description": "First-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L03", "originalCode": "35L03", "name": "Initial value problems for first-order hyperbolic equations", "description": "Initial value problems for first-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L04", "originalCode": "35L04", "name": "Initial-boundary value problems for first-order hyperbolic equations", "description": "Initial-boundary value problems for first-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L05", "originalCode": "35L05", "name": "Wave equation", "description": "Wave equation", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L10", "originalCode": "35L10", "name": "Second-order hyperbolic equations", "description": "Second-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L15", "originalCode": "35L15", "name": "Initial value problems for second-order hyperbolic equations", "description": "Initial value problems for second-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L20", "originalCode": "35L20", "name": "Initial-boundary value problems for second-order hyperbolic equations", "description": "Initial-boundary value problems for second-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L25", "originalCode": "35L25", "name": "Higher-order hyperbolic equations", "description": "Higher-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L30", "originalCode": "35L30", "name": "Initial value problems for higher-order hyperbolic equations", "description": "Initial value problems for higher-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L35", "originalCode": "35L35", "name": "Initial-boundary value problems for higher-order hyperbolic equations", "description": "Initial-boundary value problems for higher-order hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L40", "originalCode": "35L40", "name": "First-order hyperbolic systems", "description": "First-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L45", "originalCode": "35L45", "name": "Initial value problems for first-order hyperbolic systems", "description": "Initial value problems for first-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L50", "originalCode": "35L50", "name": "Initial-boundary value problems for first-order hyperbolic systems", "description": "Initial-boundary value problems for first-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L51", "originalCode": "35L51", "name": "Second-order hyperbolic systems", "description": "Second-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L52", "originalCode": "35L52", "name": "Initial value problems for second-order hyperbolic systems", "description": "Initial value problems for second-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L53", "originalCode": "35L53", "name": "Initial-boundary value problems for second-order hyperbolic systems", "description": "Initial-boundary value problems for second-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L55", "originalCode": "35L55", "name": "Higher-order hyperbolic systems", "description": "Higher-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L56", "originalCode": "35L56", "name": "Initial value problems for higher-order hyperbolic systems", "description": "Initial value problems for higher-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L57", "originalCode": "35L57", "name": "Initial-boundary value problems for higher-order hyperbolic systems", "description": "Initial-boundary value problems for higher-order hyperbolic systems", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L60", "originalCode": "35L60", "name": "First-order nonlinear hyperbolic equations", "description": "First-order nonlinear hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L65", "originalCode": "35L65", "name": "Hyperbolic conservation laws", "description": "Hyperbolic conservation laws", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L67", "originalCode": "35L67", "name": "Shocks and singularities for hyperbolic equations", "description": "Shocks and singularities for hyperbolic equations [See also 58Kxx, 74J40, 76L05]", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L70", "originalCode": "35L70", "name": "Second-order nonlinear hyperbolic equations", "description": "Second-order nonlinear hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L71", "originalCode": "35L71", "name": "Second-order semilinear hyperbolic equations", "description": "Second-order semilinear hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L72", "originalCode": "35L72", "name": "Second-order quasilinear hyperbolic equations", "description": "Second-order quasilinear hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L75", "originalCode": "35L75", "name": "Higher-order nonlinear hyperbolic equations", "description": "Higher-order nonlinear hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L76", "originalCode": "35L76", "name": "Higher-order semilinear hyperbolic equations", "description": "Higher-order semilinear hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L77", "originalCode": "35L77", "name": "Higher-order quasilinear hyperbolic equations", "description": "Higher-order quasilinear hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L80", "originalCode": "35L80", "name": "Degenerate hyperbolic equations", "description": "Degenerate hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L81", "originalCode": "35L81", "name": "Singular hyperbolic equations", "description": "Singular hyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L82", "originalCode": "35L82", "name": "Pseudohyperbolic equations", "description": "Pseudohyperbolic equations", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L85", "originalCode": "35L85", "name": "Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators", "description": "Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35L", "page": 96 }, { "code": "35L86", "originalCode": "35L86", "name": "Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators", "description": "Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35L", "page": 97 }, { "code": "35L87", "originalCode": "35L87", "name": "Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators", "description": "Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators [See also 35R35, 49J40]", "kind": "subject", "parent": "35L", "page": 97 }, { "code": "35L90", "originalCode": "35L90", "name": "Abstract hyperbolic equations", "description": "Abstract hyperbolic equations", "kind": "subject", "parent": "35L", "page": 97 }, { "code": "35L99", "originalCode": "35L99", "name": "Hyperbolic equations and hyperbolic systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "35L", "page": 97 }, { "code": "35M", "originalCode": "35Mxx", "name": "Partial differential equations of mixed type and mixed-type systems of partial differential equations", "description": "Partial differential equations of mixed type and mixed-type systems of partial differential equations", "kind": "section", "parent": "35", "page": 97 }, { "code": "35M10", "originalCode": "35M10", "name": "PDEs of mixed type", "description": "PDEs of mixed type", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M11", "originalCode": "35M11", "name": "Initial value problems for PDEs of mixed type", "description": "Initial value problems for PDEs of mixed type", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M12", "originalCode": "35M12", "name": "Boundary value problems for PDEs of mixed type", "description": "Boundary value problems for PDEs of mixed type", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M13", "originalCode": "35M13", "name": "Initial-boundary value problems for PDEs of mixed type", "description": "Initial-boundary value problems for PDEs of mixed type", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M30", "originalCode": "35M30", "name": "Mixed-type systems of PDEs", "description": "Mixed-type systems of PDEs", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M31", "originalCode": "35M31", "name": "Initial value problems for mixed-type systems of PDEs", "description": "Initial value problems for mixed-type systems of PDEs", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M32", "originalCode": "35M32", "name": "Boundary value problems for mixed-type systems of PDEs", "description": "Boundary value problems for mixed-type systems of PDEs", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M33", "originalCode": "35M33", "name": "Initial-boundary value problems for mixed-type systems of PDEs", "description": "Initial-boundary value problems for mixed-type systems of PDEs", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M85", "originalCode": "35M85", "name": "Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type", "description": "Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type [See also 35R35, 49J40]", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M86", "originalCode": "35M86", "name": "Unilateral problems for nonlinear PDEs of mixed type and variational inequalities with nonlinear partial differential operators of mixed type", "description": "Unilateral problems for nonlinear PDEs of mixed type and variational inequalities with nonlinear partial differential operators of mixed type [See also 35R35, 49J40]", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M87", "originalCode": "35M87", "name": "Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type", "description": "Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type [See also 35R35, 49J40]", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35M99", "originalCode": "35M99", "name": "Partial differential equations of mixed type and mixed-type systems of partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35M", "page": 97 }, { "code": "35N", "originalCode": "35Nxx", "name": "Overdetermined problems for partial differential equations and systems of partial differential equations", "description": "Overdetermined problems for partial differential equations and systems of partial differential equations \\{For global analysis, see 58Hxx, 58J10, 58J15\\}", "kind": "section", "parent": "35", "page": 97 }, { "code": "35N05", "originalCode": "35N05", "name": "Overdetermined systems of PDEs with constant coefficients", "description": "Overdetermined systems of PDEs with constant coefficients", "kind": "subject", "parent": "35N", "page": 97 }, { "code": "35N10", "originalCode": "35N10", "name": "Overdetermined systems of PDEs with variable coefficients", "description": "Overdetermined systems of PDEs with variable coefficients", "kind": "subject", "parent": "35N", "page": 97 }, { "code": "35N15", "originalCode": "35N15", "name": "\\(\\overline\\partial\\)-Neumann problems and formal complexes in context of PDEs", "description": "\\(\\overline\\partial\\)-Neumann problems and formal complexes in context of PDEs [See also 32W05, 32W10, 58J10]", "kind": "subject", "parent": "35N", "page": 97 }, { "code": "35N20", "originalCode": "35N20", "name": "Overdetermined initial value problems for PDEs and systems of PDEs", "description": "Overdetermined initial value problems for PDEs and systems of PDEs", "kind": "subject", "parent": "35N", "page": 97 }, { "code": "35N25", "originalCode": "35N25", "name": "Overdetermined boundary value problems for PDEs and systems of PDEs", "description": "Overdetermined boundary value problems for PDEs and systems of PDEs", "kind": "subject", "parent": "35N", "page": 97 }, { "code": "35N30", "originalCode": "35N30", "name": "Overdetermined initial-boundary value problems for PDEs and systems of PDEs", "description": "Overdetermined initial-boundary value problems for PDEs and systems of PDEs", "kind": "subject", "parent": "35N", "page": 97 }, { "code": "35N99", "originalCode": "35N99", "name": "Overdetermined problems for partial differential equations and systems of partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35N", "page": 97 }, { "code": "35P", "originalCode": "35Pxx", "name": "Spectral theory and eigenvalue problems for partial differential equations", "description": "Spectral theory and eigenvalue problems for partial differential equations \\{For operator theory, see 47Axx, 47Bxx, 47F05\\}", "kind": "section", "parent": "35", "page": 98 }, { "code": "35P05", "originalCode": "35P05", "name": "General topics in linear spectral theory for PDEs", "description": "General topics in linear spectral theory for PDEs", "kind": "subject", "parent": "35P", "page": 98 }, { "code": "35P10", "originalCode": "35P10", "name": "Completeness of eigenfunctions and eigenfunction expansions in context of PDEs", "description": "Completeness of eigenfunctions and eigenfunction expansions in context of PDEs", "kind": "subject", "parent": "35P", "page": 98 }, { "code": "35P15", "originalCode": "35P15", "name": "Estimates of eigenvalues in context of PDEs", "description": "Estimates of eigenvalues in context of PDEs", "kind": "subject", "parent": "35P", "page": 98 }, { "code": "35P20", "originalCode": "35P20", "name": "Asymptotic distributions of eigenvalues in context of PDEs", "description": "Asymptotic distributions of eigenvalues in context of PDEs", "kind": "subject", "parent": "35P", "page": 98 }, { "code": "35P25", "originalCode": "35P25", "name": "Scattering theory for PDEs", "description": "Scattering theory for PDEs [See also 47A40]", "kind": "subject", "parent": "35P", "page": 98 }, { "code": "35P30", "originalCode": "35P30", "name": "Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs", "description": "Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs", "kind": "subject", "parent": "35P", "page": 98 }, { "code": "35P99", "originalCode": "35P99", "name": "Spectral theory and eigenvalue problems for partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35P", "page": 98 }, { "code": "35Q", "originalCode": "35Qxx", "name": "Partial differential equations of mathematical physics and other areas of application", "description": "Partial differential equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]", "kind": "section", "parent": "35", "page": 98 }, { "code": "35Q05", "originalCode": "35Q05", "name": "Euler-Poisson-Darboux equations", "description": "Euler-Poisson-Darboux equations", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q07", "originalCode": "35Q07", "name": "Fuchsian PDEs", "description": "Fuchsian PDEs", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q15", "originalCode": "35Q15", "name": "Riemann-Hilbert problems in context of PDEs", "description": "Riemann-Hilbert problems in context of PDEs [See also 30E25, 31A25, 31B20]", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q20", "originalCode": "35Q20", "name": "Boltzmann equations", "description": "Boltzmann equations \\{For fluid mechanics, see 76P05; for statistical mechanics, see 82B40, 82C40, 82D05\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q30", "originalCode": "35Q30", "name": "Navier-Stokes equations", "description": "Navier-Stokes equations \\{For fluid mechanics, see 76D05, 76D07, 76N10\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q31", "originalCode": "35Q31", "name": "Euler equations", "description": "Euler equations \\{For fluid mechanics, see 76D05, 76D07, 76N10\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q35", "originalCode": "35Q35", "name": "PDEs in connection with fluid mechanics", "description": "PDEs in connection with fluid mechanics", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q40", "originalCode": "35Q40", "name": "PDEs in connection with quantum mechanics", "description": "PDEs in connection with quantum mechanics", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q41", "originalCode": "35Q41", "name": "Time-dependent Schrödinger equations and Dirac equations", "description": "Time-dependent Schrödinger equations and Dirac equations \\{For quantum theory, see 81Q05; for relativity and gravitational theory, see 83A05, 83C10\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q49", "originalCode": "35Q49", "name": "Transport equations", "description": "Transport equations \\{For calculus of variations and optimal control, see 49Q22; for fluid mechanics, see 76F25; for statistical mechanics, see 82C70, 82D75; for operations research, see 90B06; for mathematical programming, see 90C08\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q51", "originalCode": "35Q51", "name": "Soliton equations", "description": "Soliton equations \\{For dynamical systems and ergodic theory, see 37K40\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q53", "originalCode": "35Q53", "name": "KdV equations (Korteweg-de Vries equations)", "description": "KdV equations (Korteweg-de Vries equations) \\{For dynamical systems and ergodic theory, see 37K10\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q55", "originalCode": "35Q55", "name": "NLS equations (nonlinear Schrödinger equations)", "description": "NLS equations (nonlinear Schrödinger equations) \\{For dynamical systems and ergodic theory, see 37K10\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q56", "originalCode": "35Q56", "name": "Ginzburg-Landau equations", "description": "Ginzburg-Landau equations \\{For optics and electromagnetic theory, see 78A25\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q60", "originalCode": "35Q60", "name": "PDEs in connection with optics and electromagnetic theory", "description": "PDEs in connection with optics and electromagnetic theory", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q61", "originalCode": "35Q61", "name": "Maxwell equations", "description": "Maxwell equations \\{For optics and electromagnetic theory, see 78A25; for relativity and gravitational theory, see 83C22\\}", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q62", "originalCode": "35Q62", "name": "PDEs in connection with statistics", "description": "PDEs in connection with statistics", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q68", "originalCode": "35Q68", "name": "PDEs in connection with computer science", "description": "PDEs in connection with computer science", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q70", "originalCode": "35Q70", "name": "PDEs in connection with mechanics of particles and systems of particles", "description": "PDEs in connection with mechanics of particles and systems of particles", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q74", "originalCode": "35Q74", "name": "PDEs in connection with mechanics of deformable solids", "description": "PDEs in connection with mechanics of deformable solids", "kind": "subject", "parent": "35Q", "page": 98 }, { "code": "35Q75", "originalCode": "35Q75", "name": "PDEs in connection with relativity and gravitational theory", "description": "PDEs in connection with relativity and gravitational theory", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q76", "originalCode": "35Q76", "name": "Einstein equations", "description": "Einstein equations \\{For several complex variables and analytic spaces, see 32Q40; for differential geometry, see 53C07; for relativity and gravitational theory, see 83C05, 83C25, 83D05\\}", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q79", "originalCode": "35Q79", "name": "PDEs in connection with classical thermodynamics and heat transfer", "description": "PDEs in connection with classical thermodynamics and heat transfer", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q81", "originalCode": "35Q81", "name": "PDEs in connection with semiconductor devices", "description": "PDEs in connection with semiconductor devices \\{For statistical mechanics, see 82D37\\}", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q82", "originalCode": "35Q82", "name": "PDEs in connection with statistical mechanics", "description": "PDEs in connection with statistical mechanics", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q83", "originalCode": "35Q83", "name": "Vlasov equations", "description": "Vlasov equations \\{For statistical mechanics, see 82C70, 82D75\\}", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q84", "originalCode": "35Q84", "name": "Fokker-Planck equations", "description": "Fokker-Planck equations \\{For fluid mechanics, see 76X05, 76W05; for statistical mechanics, see 82C31\\}", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q85", "originalCode": "35Q85", "name": "PDEs in connection with astronomy and astrophysics", "description": "PDEs in connection with astronomy and astrophysics", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q86", "originalCode": "35Q86", "name": "PDEs in connection with geophysics", "description": "PDEs in connection with geophysics", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q89", "originalCode": "35Q89", "name": "PDEs in connection with mean field game theory", "description": "PDEs in connection with mean field game theory \\{For calculus of variations and optimal control, see 49N80; for game theory, see 91A16\\}", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q90", "originalCode": "35Q90", "name": "PDEs in connection with mathematical programming", "description": "PDEs in connection with mathematical programming", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q91", "originalCode": "35Q91", "name": "PDEs in connection with game theory, economics, social and behavioral sciences", "description": "PDEs in connection with game theory, economics, social and behavioral sciences", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q92", "originalCode": "35Q92", "name": "PDEs in connection with biology, chemistry and other natural sciences", "description": "PDEs in connection with biology, chemistry and other natural sciences", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q93", "originalCode": "35Q93", "name": "PDEs in connection with control and optimization", "description": "PDEs in connection with control and optimization", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q94", "originalCode": "35Q94", "name": "PDEs in connection with information and communication", "description": "PDEs in connection with information and communication", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35Q99", "originalCode": "35Q99", "name": "Partial differential equations of mathematical physics and other areas of application", "description": "None of the above, but in this section", "kind": "subject", "parent": "35Q", "page": 99 }, { "code": "35R", "originalCode": "35Rxx", "name": "Miscellaneous topics in partial differential equations", "description": "Miscellaneous topics in partial differential equations \\{For equations on manifolds, see 32Wxx, 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see 60H15\\}", "kind": "section", "parent": "35", "page": 99 }, { "code": "35R01", "originalCode": "35R01", "name": "PDEs on manifolds", "description": "PDEs on manifolds [See also 32Wxx, 53Cxx, 58Jxx]", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R02", "originalCode": "35R02", "name": "PDEs on graphs and networks (ramified or polygonal spaces)", "description": "PDEs on graphs and networks (ramified or polygonal spaces)", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R03", "originalCode": "35R03", "name": "PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.", "description": "PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R05", "originalCode": "35R05", "name": "PDEs with low regular coefficients and/or low regular data", "description": "PDEs with low regular coefficients and/or low regular data", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R06", "originalCode": "35R06", "name": "PDEs with measure", "description": "PDEs with measure", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R07", "originalCode": "35R07", "name": "PDEs on time scales", "description": "PDEs on time scales", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R09", "originalCode": "35R09", "name": "Integro-partial differential equations", "description": "Integro-partial differential equations [See also 34K30, 45K05]", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R10", "originalCode": "35R10", "name": "Partial functional-differential equations", "description": "Partial functional-differential equations", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R11", "originalCode": "35R11", "name": "Fractional partial differential equations", "description": "Fractional partial differential equations", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R12", "originalCode": "35R12", "name": "Impulsive partial differential equations", "description": "Impulsive partial differential equations", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R13", "originalCode": "35R13", "name": "Fuzzy partial differential equations", "description": "Fuzzy partial differential equations", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R15", "originalCode": "35R15", "name": "PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)", "description": "PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) [See also 46Gxx, 58D25]", "kind": "subject", "parent": "35R", "page": 99 }, { "code": "35R20", "originalCode": "35R20", "name": "Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)", "description": "Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R25", "originalCode": "35R25", "name": "Ill-posed problems for PDEs", "description": "Ill-posed problems for PDEs", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R30", "originalCode": "35R30", "name": "Inverse problems for PDEs", "description": "Inverse problems for PDEs", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R35", "originalCode": "35R35", "name": "Free boundary problems for PDEs", "description": "Free boundary problems for PDEs", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R37", "originalCode": "35R37", "name": "Moving boundary problems for PDEs", "description": "Moving boundary problems for PDEs", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R45", "originalCode": "35R45", "name": "Partial differential inequalities and systems of partial differential inequalities", "description": "Partial differential inequalities and systems of partial differential inequalities", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R50", "originalCode": "35R50", "name": "PDEs of infinite order", "description": "PDEs of infinite order", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R60", "originalCode": "35R60", "name": "PDEs with randomness, stochastic partial differential equations", "description": "PDEs with randomness, stochastic partial differential equations [See also 60H15]", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R70", "originalCode": "35R70", "name": "PDEs with multivalued right-hand sides", "description": "PDEs with multivalued right-hand sides", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35R99", "originalCode": "35R99", "name": "Miscellaneous topics in partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "35R", "page": 100 }, { "code": "35S", "originalCode": "35Sxx", "name": "Pseudodifferential operators and other generalizations of partial differential operators", "description": "Pseudodifferential operators and other generalizations of partial differential operators \\{For operator theory, see 47G30, 58J40\\}", "kind": "section", "parent": "35", "page": 100 }, { "code": "35S05", "originalCode": "35S05", "name": "Pseudodifferential operators as generalizations of partial differential operators", "description": "Pseudodifferential operators as generalizations of partial differential operators [See also 32W25, 47G30, 47L80, 58J40]", "kind": "subject", "parent": "35S", "page": 100 }, { "code": "35S10", "originalCode": "35S10", "name": "Initial value problems for PDEs with pseudodifferential operators", "description": "Initial value problems for PDEs with pseudodifferential operators", "kind": "subject", "parent": "35S", "page": 100 }, { "code": "35S15", "originalCode": "35S15", "name": "Boundary value problems for PDEs with pseudodifferential operators", "description": "Boundary value problems for PDEs with pseudodifferential operators", "kind": "subject", "parent": "35S", "page": 100 }, { "code": "35S16", "originalCode": "35S16", "name": "Initial-boundary value problems for PDEs with pseudodifferential operators", "description": "Initial-boundary value problems for PDEs with pseudodifferential operators", "kind": "subject", "parent": "35S", "page": 100 }, { "code": "35S30", "originalCode": "35S30", "name": "Fourier integral operators applied to PDEs", "description": "Fourier integral operators applied to PDEs [See also 43A32, 58J40]", "kind": "subject", "parent": "35S", "page": 100 }, { "code": "35S35", "originalCode": "35S35", "name": "Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc.", "description": "Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15]", "kind": "subject", "parent": "35S", "page": 100 }, { "code": "35S50", "originalCode": "35S50", "name": "Paradifferential operators as generalizations of partial differential operators in context of PDEs", "description": "Paradifferential operators as generalizations of partial differential operators in context of PDEs", "kind": "subject", "parent": "35S", "page": 100 }, { "code": "35S99", "originalCode": "35S99", "name": "Pseudodifferential operators and other generalizations of partial differential operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "35S", "page": 100 }, { "code": "37", "originalCode": "37-XX", "name": "Dynamical systems and ergodic theory", "description": "Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]", "kind": "class", "parent": null, "page": 100 }, { "code": "37-00", "originalCode": "37-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to dynamical systems and ergodic theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to dynamical systems and ergodic theory", "kind": "subject", "parent": "37", "page": 100 }, { "code": "37-01", "originalCode": "37-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory", "kind": "subject", "parent": "37", "page": 100 }, { "code": "37-02", "originalCode": "37-02", "name": "Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory", "description": "Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory", "kind": "subject", "parent": "37", "page": 100 }, { "code": "37-03", "originalCode": "37-03", "name": "History of dynamical systems and ergodic theory", "description": "History of dynamical systems and ergodic theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "37", "page": 100 }, { "code": "37-04", "originalCode": "37-04", "name": "Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory", "description": "Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory", "kind": "subject", "parent": "37", "page": 100 }, { "code": "37-06", "originalCode": "37-06", "name": "Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory", "description": "Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory", "kind": "subject", "parent": "37", "page": 100 }, { "code": "37-11", "originalCode": "37-11", "name": "Research data for problems pertaining to dynamical systems and ergodic theory", "description": "Research data for problems pertaining to dynamical systems and ergodic theory", "kind": "subject", "parent": "37", "page": 100 }, { "code": "37A", "originalCode": "37Axx", "name": "Ergodic theory", "description": "Ergodic theory [See also 28Dxx]", "kind": "section", "parent": "37", "page": 101 }, { "code": "37A05", "originalCode": "37A05", "name": "Dynamical aspects of measure-preserving transformations", "description": "Dynamical aspects of measure-preserving transformations", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A10", "originalCode": "37A10", "name": "Dynamical systems involving one-parameter continuous families of measure-preserving transformations", "description": "Dynamical systems involving one-parameter continuous families of measure-preserving transformations", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A15", "originalCode": "37A15", "name": "General groups of measure-preserving transformations and dynamical systems", "description": "General groups of measure-preserving transformations and dynamical systems [See mainly 22Fxx]", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A17", "originalCode": "37A17", "name": "Homogeneous flows", "description": "Homogeneous flows [See also 22Fxx]", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A20", "originalCode": "37A20", "name": "Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations", "description": "Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A25", "originalCode": "37A25", "name": "Ergodicity, mixing, rates of mixing", "description": "Ergodicity, mixing, rates of mixing", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A30", "originalCode": "37A30", "name": "Ergodic theorems, spectral theory, Markov operators", "description": "Ergodic theorems, spectral theory, Markov operators \\{For operator ergodic theory, see mainly 47A35\\}", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A35", "originalCode": "37A35", "name": "Entropy and other invariants, isomorphism, classification in ergodic theory", "description": "Entropy and other invariants, isomorphism, classification in ergodic theory", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A40", "originalCode": "37A40", "name": "Nonsingular (and infinite-measure preserving) transformations", "description": "Nonsingular (and infinite-measure preserving) transformations", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A44", "originalCode": "37A44", "name": "Relations between ergodic theory and number theory", "description": "Relations between ergodic theory and number theory [See also 11Kxx]", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A46", "originalCode": "37A46", "name": "Relations between ergodic theory and harmonic analysis", "description": "Relations between ergodic theory and harmonic analysis", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A50", "originalCode": "37A50", "name": "Dynamical systems and their relations with probability theory and stochastic processes", "description": "Dynamical systems and their relations with probability theory and stochastic processes [See also 60Fxx, 60G10]", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A55", "originalCode": "37A55", "name": "Dynamical systems and the theory of \\(C^*\\)-algebras", "description": "Dynamical systems and the theory of \\(C^*\\)-algebras [See mainly 46L55]", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A60", "originalCode": "37A60", "name": "Dynamical aspects of statistical mechanics", "description": "Dynamical aspects of statistical mechanics [See also 82Cxx]", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37A99", "originalCode": "37A99", "name": "Ergodic theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "37A", "page": 101 }, { "code": "37B", "originalCode": "37Bxx", "name": "Topological dynamics", "description": "Topological dynamics", "kind": "section", "parent": "37", "page": 101 }, { "code": "37B02", "originalCode": "37B02", "name": "Dynamics in general topological spaces", "description": "Dynamics in general topological spaces", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B05", "originalCode": "37B05", "name": "Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)", "description": "Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B10", "originalCode": "37B10", "name": "Symbolic dynamics", "description": "Symbolic dynamics", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B15", "originalCode": "37B15", "name": "Dynamical aspects of cellular automata", "description": "Dynamical aspects of cellular automata \\{For computational aspects, see 68Q80\\}", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B20", "originalCode": "37B20", "name": "Notions of recurrence and recurrent behavior in topological dynamical systems", "description": "Notions of recurrence and recurrent behavior in topological dynamical systems", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B25", "originalCode": "37B25", "name": "Stability of topological dynamical systems", "description": "Stability of topological dynamical systems", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B30", "originalCode": "37B30", "name": "Index theory for dynamical systems, Morse-Conley indices", "description": "Index theory for dynamical systems, Morse-Conley indices", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B35", "originalCode": "37B35", "name": "Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems", "description": "Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B40", "originalCode": "37B40", "name": "Topological entropy", "description": "Topological entropy", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B45", "originalCode": "37B45", "name": "Continua theory in dynamics", "description": "Continua theory in dynamics", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B51", "originalCode": "37B51", "name": "Multidimensional shifts of finite type", "description": "Multidimensional shifts of finite type", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B52", "originalCode": "37B52", "name": "Tiling dynamics", "description": "Tiling dynamics", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B55", "originalCode": "37B55", "name": "Topological dynamics of nonautonomous systems", "description": "Topological dynamics of nonautonomous systems", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B65", "originalCode": "37B65", "name": "Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems", "description": "Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37B99", "originalCode": "37B99", "name": "Topological dynamics", "description": "None of the above, but in this section", "kind": "subject", "parent": "37B", "page": 101 }, { "code": "37C", "originalCode": "37Cxx", "name": "Smooth dynamical systems: general theory", "description": "Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]", "kind": "section", "parent": "37", "page": 102 }, { "code": "37C05", "originalCode": "37C05", "name": "Dynamical systems involving smooth mappings and diffeomorphisms", "description": "Dynamical systems involving smooth mappings and diffeomorphisms", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C10", "originalCode": "37C10", "name": "Dynamics induced by flows and semiflows", "description": "Dynamics induced by flows and semiflows", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C15", "originalCode": "37C15", "name": "Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems", "description": "Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C20", "originalCode": "37C20", "name": "Generic properties, structural stability of dynamical systems", "description": "Generic properties, structural stability of dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C25", "originalCode": "37C25", "name": "Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics", "description": "Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C27", "originalCode": "37C27", "name": "Periodic orbits of vector fields and flows", "description": "Periodic orbits of vector fields and flows", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C29", "originalCode": "37C29", "name": "Homoclinic and heteroclinic orbits for dynamical systems", "description": "Homoclinic and heteroclinic orbits for dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C30", "originalCode": "37C30", "name": "Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.", "description": "Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C35", "originalCode": "37C35", "name": "Orbit growth in dynamical systems", "description": "Orbit growth in dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C40", "originalCode": "37C40", "name": "Smooth ergodic theory, invariant measures for smooth dynamical systems", "description": "Smooth ergodic theory, invariant measures for smooth dynamical systems [See also 37Dxx]", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C45", "originalCode": "37C45", "name": "Dimension theory of smooth dynamical systems", "description": "Dimension theory of smooth dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C50", "originalCode": "37C50", "name": "Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics", "description": "Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C55", "originalCode": "37C55", "name": "Periodic and quasi-periodic flows and diffeomorphisms", "description": "Periodic and quasi-periodic flows and diffeomorphisms", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C60", "originalCode": "37C60", "name": "Nonautonomous smooth dynamical systems", "description": "Nonautonomous smooth dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C65", "originalCode": "37C65", "name": "Monotone flows as dynamical systems", "description": "Monotone flows as dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C70", "originalCode": "37C70", "name": "Attractors and repellers of smooth dynamical systems and their topological structure", "description": "Attractors and repellers of smooth dynamical systems and their topological structure", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C75", "originalCode": "37C75", "name": "Stability theory for smooth dynamical systems", "description": "Stability theory for smooth dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C79", "originalCode": "37C79", "name": "Symmetries and invariants of dynamical systems", "description": "Symmetries and invariants of dynamical systems [See also 34C14, 34K04]", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C81", "originalCode": "37C81", "name": "Equivariant dynamical systems", "description": "Equivariant dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C83", "originalCode": "37C83", "name": "Dynamical systems with singularities (billiards, etc.)", "description": "Dynamical systems with singularities (billiards, etc.)", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C85", "originalCode": "37C85", "name": "Dynamics induced by group actions other than \\(\\mathbb{Z}\\) and \\(\\mathbb{R}\\), and \\(\\mathbb{C}\\)", "description": "Dynamics induced by group actions other than \\(\\mathbb{Z}\\) and \\(\\mathbb{R}\\), and \\(\\mathbb{C}\\) [See mainly 22Fxx, and also 32M25, 57R30, 57Sxx]", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C86", "originalCode": "37C86", "name": "Foliations generated by dynamical systems", "description": "Foliations generated by dynamical systems", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37C99", "originalCode": "37C99", "name": "Smooth dynamical systems: general theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "37C", "page": 102 }, { "code": "37D", "originalCode": "37Dxx", "name": "Dynamical systems with hyperbolic behavior", "description": "Dynamical systems with hyperbolic behavior", "kind": "section", "parent": "37", "page": 102 }, { "code": "37D05", "originalCode": "37D05", "name": "Dynamical systems with hyperbolic orbits and sets", "description": "Dynamical systems with hyperbolic orbits and sets", "kind": "subject", "parent": "37D", "page": 102 }, { "code": "37D10", "originalCode": "37D10", "name": "Invariant manifold theory for dynamical systems", "description": "Invariant manifold theory for dynamical systems", "kind": "subject", "parent": "37D", "page": 102 }, { "code": "37D15", "originalCode": "37D15", "name": "Morse-Smale systems", "description": "Morse-Smale systems", "kind": "subject", "parent": "37D", "page": 102 }, { "code": "37D20", "originalCode": "37D20", "name": "Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)", "description": "Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)", "kind": "subject", "parent": "37D", "page": 102 }, { "code": "37D25", "originalCode": "37D25", "name": "Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)", "description": "Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)", "kind": "subject", "parent": "37D", "page": 102 }, { "code": "37D30", "originalCode": "37D30", "name": "Partially hyperbolic systems and dominated splittings", "description": "Partially hyperbolic systems and dominated splittings", "kind": "subject", "parent": "37D", "page": 102 }, { "code": "37D35", "originalCode": "37D35", "name": "Thermodynamic formalism, variational principles, equilibrium states for dynamical systems", "description": "Thermodynamic formalism, variational principles, equilibrium states for dynamical systems", "kind": "subject", "parent": "37D", "page": 102 }, { "code": "37D40", "originalCode": "37D40", "name": "Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)", "description": "Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)", "kind": "subject", "parent": "37D", "page": 103 }, { "code": "37D45", "originalCode": "37D45", "name": "Strange attractors, chaotic dynamics of systems with hyperbolic behavior", "description": "Strange attractors, chaotic dynamics of systems with hyperbolic behavior", "kind": "subject", "parent": "37D", "page": 103 }, { "code": "37D99", "originalCode": "37D99", "name": "Dynamical systems with hyperbolic behavior", "description": "None of the above, but in this section", "kind": "subject", "parent": "37D", "page": 103 }, { "code": "37E", "originalCode": "37Exx", "name": "Low-dimensional dynamical systems", "description": "Low-dimensional dynamical systems", "kind": "section", "parent": "37", "page": 103 }, { "code": "37E05", "originalCode": "37E05", "name": "Dynamical systems involving maps of the interval", "description": "Dynamical systems involving maps of the interval", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E10", "originalCode": "37E10", "name": "Dynamical systems involving maps of the circle", "description": "Dynamical systems involving maps of the circle", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E15", "originalCode": "37E15", "name": "Combinatorial dynamics (types of periodic orbits)", "description": "Combinatorial dynamics (types of periodic orbits)", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E20", "originalCode": "37E20", "name": "Universality and renormalization of dynamical systems", "description": "Universality and renormalization of dynamical systems [See also 37F25]", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E25", "originalCode": "37E25", "name": "Dynamical systems involving maps of trees and graphs", "description": "Dynamical systems involving maps of trees and graphs", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E30", "originalCode": "37E30", "name": "Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces", "description": "Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E35", "originalCode": "37E35", "name": "Flows on surfaces", "description": "Flows on surfaces", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E40", "originalCode": "37E40", "name": "Dynamical aspects of twist maps", "description": "Dynamical aspects of twist maps", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E45", "originalCode": "37E45", "name": "Rotation numbers and vectors", "description": "Rotation numbers and vectors", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37E99", "originalCode": "37E99", "name": "Low-dimensional dynamical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37E", "page": 103 }, { "code": "37F", "originalCode": "37Fxx", "name": "Dynamical systems over complex numbers", "description": "Dynamical systems over complex numbers [See also 30D05, 32H50]", "kind": "section", "parent": "37", "page": 103 }, { "code": "37F05", "originalCode": "37F05", "name": "Dynamical systems involving relations and correspondences in one complex variable", "description": "Dynamical systems involving relations and correspondences in one complex variable", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F10", "originalCode": "37F10", "name": "Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets", "description": "Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets [See also 32A10, 32A20, 32H02, 32H04]", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F12", "originalCode": "37F12", "name": "Critical orbits for holomorphic dynamical systems", "description": "Critical orbits for holomorphic dynamical systems", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F15", "originalCode": "37F15", "name": "Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems", "description": "Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F20", "originalCode": "37F20", "name": "Combinatorics and topology in relation with holomorphic dynamical systems", "description": "Combinatorics and topology in relation with holomorphic dynamical systems", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F25", "originalCode": "37F25", "name": "Renormalization of holomorphic dynamical systems", "description": "Renormalization of holomorphic dynamical systems", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F31", "originalCode": "37F31", "name": "Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics", "description": "Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F32", "originalCode": "37F32", "name": "Fuchsian and Kleinian groups as dynamical systems", "description": "Fuchsian and Kleinian groups as dynamical systems", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F34", "originalCode": "37F34", "name": "Teichmüller theory; moduli spaces of holomorphic dynamical systems", "description": "Teichmüller theory; moduli spaces of holomorphic dynamical systems", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F35", "originalCode": "37F35", "name": "Conformal densities and Hausdorff dimension for holomorphic dynamical systems", "description": "Conformal densities and Hausdorff dimension for holomorphic dynamical systems", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F40", "originalCode": "37F40", "name": "Geometric limits in holomorphic dynamics", "description": "Geometric limits in holomorphic dynamics", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F44", "originalCode": "37F44", "name": "Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps", "description": "Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F46", "originalCode": "37F46", "name": "Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets", "description": "Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F50", "originalCode": "37F50", "name": "Small divisors, rotation domains and linearization in holomorphic dynamics", "description": "Small divisors, rotation domains and linearization in holomorphic dynamics", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F75", "originalCode": "37F75", "name": "Dynamical aspects of holomorphic foliations and vector fields", "description": "Dynamical aspects of holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F80", "originalCode": "37F80", "name": "Higher-dimensional holomorphic and meromorphic dynamics", "description": "Higher-dimensional holomorphic and meromorphic dynamics", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37F99", "originalCode": "37F99", "name": "Dynamical systems over complex numbers", "description": "None of the above, but in this section", "kind": "subject", "parent": "37F", "page": 103 }, { "code": "37G", "originalCode": "37Gxx", "name": "Local and nonlocal bifurcation theory for dynamical systems", "description": "Local and nonlocal bifurcation theory for dynamical systems [See also 34C23, 34K18]", "kind": "section", "parent": "37", "page": 104 }, { "code": "37G05", "originalCode": "37G05", "name": "Normal forms for dynamical systems", "description": "Normal forms for dynamical systems", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37G10", "originalCode": "37G10", "name": "Bifurcations of singular points in dynamical systems", "description": "Bifurcations of singular points in dynamical systems", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37G15", "originalCode": "37G15", "name": "Bifurcations of limit cycles and periodic orbits in dynamical systems", "description": "Bifurcations of limit cycles and periodic orbits in dynamical systems", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37G20", "originalCode": "37G20", "name": "Hyperbolic singular points with homoclinic trajectories in dynamical systems", "description": "Hyperbolic singular points with homoclinic trajectories in dynamical systems", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37G25", "originalCode": "37G25", "name": "Bifurcations connected with nontransversal intersection in dynamical systems", "description": "Bifurcations connected with nontransversal intersection in dynamical systems", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37G30", "originalCode": "37G30", "name": "Infinite nonwandering sets arising in bifurcations of dynamical systems", "description": "Infinite nonwandering sets arising in bifurcations of dynamical systems", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37G35", "originalCode": "37G35", "name": "Dynamical aspects of attractors and their bifurcations", "description": "Dynamical aspects of attractors and their bifurcations", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37G40", "originalCode": "37G40", "name": "Dynamical aspects of symmetries, equivariant bifurcation theory", "description": "Dynamical aspects of symmetries, equivariant bifurcation theory", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37G99", "originalCode": "37G99", "name": "Local and nonlocal bifurcation theory for dynamical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37G", "page": 104 }, { "code": "37H", "originalCode": "37Hxx", "name": "Random dynamical systems", "description": "Random dynamical systems [See also 15B52, 34Fxx, 47B80, 70L05, 82C05, 93Exx]", "kind": "section", "parent": "37", "page": 104 }, { "code": "37H05", "originalCode": "37H05", "name": "General theory of random and stochastic dynamical systems", "description": "General theory of random and stochastic dynamical systems", "kind": "subject", "parent": "37H", "page": 104 }, { "code": "37H10", "originalCode": "37H10", "name": "Generation, random and stochastic difference and differential equations", "description": "Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]", "kind": "subject", "parent": "37H", "page": 104 }, { "code": "37H12", "originalCode": "37H12", "name": "Random iteration", "description": "Random iteration", "kind": "subject", "parent": "37H", "page": 104 }, { "code": "37H15", "originalCode": "37H15", "name": "Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents", "description": "Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents [See also 34Fxx, 37Axx, 37Cxx, 37Dxx]", "kind": "subject", "parent": "37H", "page": 104 }, { "code": "37H20", "originalCode": "37H20", "name": "Bifurcation theory for random and stochastic dynamical systems", "description": "Bifurcation theory for random and stochastic dynamical systems [See also 37Gxx]", "kind": "subject", "parent": "37H", "page": 104 }, { "code": "37H30", "originalCode": "37H30", "name": "Stability theory for random and stochastic dynamical systems", "description": "Stability theory for random and stochastic dynamical systems", "kind": "subject", "parent": "37H", "page": 104 }, { "code": "37H99", "originalCode": "37H99", "name": "Random dynamical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37H", "page": 104 }, { "code": "37J", "originalCode": "37Jxx", "name": "Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems", "description": "Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems [See also 53Dxx, 70Fxx, 70Hxx]", "kind": "section", "parent": "37", "page": 104 }, { "code": "37J06", "originalCode": "37J06", "name": "General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants", "description": "General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants", "kind": "subject", "parent": "37J", "page": 104 }, { "code": "37J11", "originalCode": "37J11", "name": "Symplectic and canonical mappings", "description": "Symplectic and canonical mappings", "kind": "subject", "parent": "37J", "page": 104 }, { "code": "37J12", "originalCode": "37J12", "name": "Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems", "description": "Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37J", "page": 104 }, { "code": "37J20", "originalCode": "37J20", "name": "Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems", "description": "Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37J", "page": 104 }, { "code": "37J25", "originalCode": "37J25", "name": "Stability problems for finite-dimensional Hamiltonian and Lagrangian systems", "description": "Stability problems for finite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37J", "page": 104 }, { "code": "37J30", "originalCode": "37J30", "name": "Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)", "description": "Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)", "kind": "subject", "parent": "37J", "page": 104 }, { "code": "37J35", "originalCode": "37J35", "name": "Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests", "description": "Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests", "kind": "subject", "parent": "37J", "page": 104 }, { "code": "37J37", "originalCode": "37J37", "name": "Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures", "description": "Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures", "kind": "subject", "parent": "37J", "page": 104 }, { "code": "37J38", "originalCode": "37J38", "name": "Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions", "description": "Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J39", "originalCode": "37J39", "name": "Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.)", "description": "Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) [See also 53D20]", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J40", "originalCode": "37J40", "name": "Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion", "description": "Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J46", "originalCode": "37J46", "name": "Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems", "description": "Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J51", "originalCode": "37J51", "name": "Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods", "description": "Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J55", "originalCode": "37J55", "name": "Contact systems", "description": "Contact systems [See also 53D10]", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J60", "originalCode": "37J60", "name": "Nonholonomic dynamical systems", "description": "Nonholonomic dynamical systems [See also 70F25]", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J65", "originalCode": "37J65", "name": "Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.)", "description": "Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) [See also 34M55]", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J70", "originalCode": "37J70", "name": "Completely integrable discrete dynamical systems", "description": "Completely integrable discrete dynamical systems", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37J99", "originalCode": "37J99", "name": "Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37J", "page": 105 }, { "code": "37K", "originalCode": "37Kxx", "name": "Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems", "description": "Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems [See also 35Axx, 35Qxx]", "kind": "section", "parent": "37", "page": 105 }, { "code": "37K06", "originalCode": "37K06", "name": "General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws", "description": "General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K10", "originalCode": "37K10", "name": "Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)", "description": "Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K15", "originalCode": "37K15", "name": "Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems", "description": "Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K20", "originalCode": "37K20", "name": "Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions", "description": "Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions [See also 14H70]", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K25", "originalCode": "37K25", "name": "Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry", "description": "Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K30", "originalCode": "37K30", "name": "Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures", "description": "Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K35", "originalCode": "37K35", "name": "Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems", "description": "Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K40", "originalCode": "37K40", "name": "Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems", "description": "Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K45", "originalCode": "37K45", "name": "Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems", "description": "Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K50", "originalCode": "37K50", "name": "Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems", "description": "Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K55", "originalCode": "37K55", "name": "Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems", "description": "Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K58", "originalCode": "37K58", "name": "Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems", "description": "Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K60", "originalCode": "37K60", "name": "Lattice dynamics; integrable lattice equations", "description": "Lattice dynamics; integrable lattice equations [See also 37L60]", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K65", "originalCode": "37K65", "name": "Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics", "description": "Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37K99", "originalCode": "37K99", "name": "Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37K", "page": 105 }, { "code": "37L", "originalCode": "37Lxx", "name": "Infinite-dimensional dissipative dynamical systems", "description": "Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]", "kind": "section", "parent": "37", "page": 106 }, { "code": "37L05", "originalCode": "37L05", "name": "General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations", "description": "General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L10", "originalCode": "37L10", "name": "Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems", "description": "Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L15", "originalCode": "37L15", "name": "Stability problems for infinite-dimensional dissipative dynamical systems", "description": "Stability problems for infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L20", "originalCode": "37L20", "name": "Symmetries of infinite-dimensional dissipative dynamical systems", "description": "Symmetries of infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L25", "originalCode": "37L25", "name": "Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems", "description": "Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L30", "originalCode": "37L30", "name": "Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems", "description": "Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L40", "originalCode": "37L40", "name": "Invariant measures for infinite-dimensional dissipative dynamical systems", "description": "Invariant measures for infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L45", "originalCode": "37L45", "name": "Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems", "description": "Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L50", "originalCode": "37L50", "name": "Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems", "description": "Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L55", "originalCode": "37L55", "name": "Infinite-dimensional random dynamical systems; stochastic equations", "description": "Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L60", "originalCode": "37L60", "name": "Lattice dynamics and infinite-dimensional dissipative dynamical systems", "description": "Lattice dynamics and infinite-dimensional dissipative dynamical systems [See also 37K60]", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L65", "originalCode": "37L65", "name": "Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems", "description": "Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37L99", "originalCode": "37L99", "name": "Infinite-dimensional dissipative dynamical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37L", "page": 106 }, { "code": "37M", "originalCode": "37Mxx", "name": "Approximation methods and numerical treatment of dynamical systems", "description": "Approximation methods and numerical treatment of dynamical systems \\{For numerical analysis, see also 65Pxx; for software etc., see 37-04\\}", "kind": "section", "parent": "37", "page": 106 }, { "code": "37M05", "originalCode": "37M05", "name": "Simulation of dynamical systems", "description": "Simulation of dynamical systems", "kind": "subject", "parent": "37M", "page": 106 }, { "code": "37M10", "originalCode": "37M10", "name": "Time series analysis of dynamical systems", "description": "Time series analysis of dynamical systems", "kind": "subject", "parent": "37M", "page": 106 }, { "code": "37M15", "originalCode": "37M15", "name": "Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems", "description": "Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems", "kind": "subject", "parent": "37M", "page": 106 }, { "code": "37M20", "originalCode": "37M20", "name": "Computational methods for bifurcation problems in dynamical systems", "description": "Computational methods for bifurcation problems in dynamical systems", "kind": "subject", "parent": "37M", "page": 106 }, { "code": "37M21", "originalCode": "37M21", "name": "Computational methods for invariant manifolds of dynamical systems", "description": "Computational methods for invariant manifolds of dynamical systems", "kind": "subject", "parent": "37M", "page": 106 }, { "code": "37M22", "originalCode": "37M22", "name": "Computational methods for attractors of dynamical systems", "description": "Computational methods for attractors of dynamical systems", "kind": "subject", "parent": "37M", "page": 106 }, { "code": "37M25", "originalCode": "37M25", "name": "Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)", "description": "Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)", "kind": "subject", "parent": "37M", "page": 106 }, { "code": "37M99", "originalCode": "37M99", "name": "Approximation methods and numerical treatment of dynamical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37M", "page": 106 }, { "code": "37N", "originalCode": "37Nxx", "name": "Applications of dynamical systems", "description": "Applications of dynamical systems", "kind": "section", "parent": "37", "page": 106 }, { "code": "37N05", "originalCode": "37N05", "name": "Dynamical systems in classical and celestial mechanics", "description": "Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]", "kind": "subject", "parent": "37N", "page": 106 }, { "code": "37N10", "originalCode": "37N10", "name": "Dynamical systems in fluid mechanics, oceanography and meteorology", "description": "Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]", "kind": "subject", "parent": "37N", "page": 106 }, { "code": "37N15", "originalCode": "37N15", "name": "Dynamical systems in solid mechanics", "description": "Dynamical systems in solid mechanics [See mainly 74Hxx]", "kind": "subject", "parent": "37N", "page": 106 }, { "code": "37N20", "originalCode": "37N20", "name": "Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)", "description": "Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)", "kind": "subject", "parent": "37N", "page": 106 }, { "code": "37N25", "originalCode": "37N25", "name": "Dynamical systems in biology", "description": "Dynamical systems in biology [See also 92-XX]", "kind": "subject", "parent": "37N", "page": 107 }, { "code": "37N30", "originalCode": "37N30", "name": "Dynamical systems in numerical analysis", "description": "Dynamical systems in numerical analysis [See also 65-XX]", "kind": "subject", "parent": "37N", "page": 107 }, { "code": "37N35", "originalCode": "37N35", "name": "Dynamical systems in control", "description": "Dynamical systems in control [See also 93-XX]", "kind": "subject", "parent": "37N", "page": 107 }, { "code": "37N40", "originalCode": "37N40", "name": "Dynamical systems in optimization and economics", "description": "Dynamical systems in optimization and economics [See also 90-XX, 91-XX]", "kind": "subject", "parent": "37N", "page": 107 }, { "code": "37N99", "originalCode": "37N99", "name": "Applications of dynamical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37N", "page": 107 }, { "code": "37P", "originalCode": "37Pxx", "name": "Arithmetic and non-Archimedean dynamical systems", "description": "Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A44]", "kind": "section", "parent": "37", "page": 107 }, { "code": "37P05", "originalCode": "37P05", "name": "Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps", "description": "Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P10", "originalCode": "37P10", "name": "Arithmetic and non-Archimedean dynamical systems involving analytic and meromorphic maps", "description": "Arithmetic and non-Archimedean dynamical systems involving analytic and meromorphic maps", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P15", "originalCode": "37P15", "name": "Dynamical systems over global ground fields", "description": "Dynamical systems over global ground fields", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P20", "originalCode": "37P20", "name": "Dynamical systems over non-Archimedean local ground fields", "description": "Dynamical systems over non-Archimedean local ground fields", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P25", "originalCode": "37P25", "name": "Dynamical systems over finite ground fields", "description": "Dynamical systems over finite ground fields", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P30", "originalCode": "37P30", "name": "Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems", "description": "Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems [See also 11G50, 14G40]", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P35", "originalCode": "37P35", "name": "Arithmetic properties of periodic points", "description": "Arithmetic properties of periodic points", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P40", "originalCode": "37P40", "name": "Non-Archimedean Fatou and Julia sets", "description": "Non-Archimedean Fatou and Julia sets", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P45", "originalCode": "37P45", "name": "Families and moduli spaces in arithmetic and non-Archimedean dynamical systems", "description": "Families and moduli spaces in arithmetic and non-Archimedean dynamical systems", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P50", "originalCode": "37P50", "name": "Dynamical systems on Berkovich spaces", "description": "Dynamical systems on Berkovich spaces", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P55", "originalCode": "37P55", "name": "Arithmetic dynamics on general algebraic varieties", "description": "Arithmetic dynamics on general algebraic varieties", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "37P99", "originalCode": "37P99", "name": "Arithmetic and non-Archimedean dynamical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "37P", "page": 107 }, { "code": "39", "originalCode": "39-XX", "name": "Difference and functional equations", "description": "Difference and functional equations", "kind": "class", "parent": null, "page": 107 }, { "code": "39-00", "originalCode": "39-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to difference and functional equations", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to difference and functional equations", "kind": "subject", "parent": "39", "page": 107 }, { "code": "39-01", "originalCode": "39-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations", "kind": "subject", "parent": "39", "page": 107 }, { "code": "39-02", "originalCode": "39-02", "name": "Research exposition (monographs, survey articles) pertaining to difference and functional equations", "description": "Research exposition (monographs, survey articles) pertaining to difference and functional equations", "kind": "subject", "parent": "39", "page": 107 }, { "code": "39-03", "originalCode": "39-03", "name": "History of difference and functional equations", "description": "History of difference and functional equations [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "39", "page": 107 }, { "code": "39-04", "originalCode": "39-04", "name": "Software, source code, etc. for problems pertaining to difference and functional equations", "description": "Software, source code, etc. for problems pertaining to difference and functional equations", "kind": "subject", "parent": "39", "page": 107 }, { "code": "39-06", "originalCode": "39-06", "name": "Proceedings, conferences, collections, etc. pertaining to difference and functional equations", "description": "Proceedings, conferences, collections, etc. pertaining to difference and functional equations", "kind": "subject", "parent": "39", "page": 107 }, { "code": "39-08", "originalCode": "39-08", "name": "Computational methods for problems pertaining to difference and functional equations", "description": "Computational methods for problems pertaining to difference and functional equations", "kind": "subject", "parent": "39", "page": 107 }, { "code": "39-11", "originalCode": "39-11", "name": "Research data for problems pertaining to difference and functional equations", "description": "Research data for problems pertaining to difference and functional equations", "kind": "subject", "parent": "39", "page": 107 }, { "code": "39A", "originalCode": "39Axx", "name": "Difference equations", "description": "Difference equations \\{For dynamic equations on time scales, see 34N05; for dynamical systems, see 37-XX\\}", "kind": "section", "parent": "39", "page": 108 }, { "code": "39A05", "originalCode": "39A05", "name": "General theory of difference equations", "description": "General theory of difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A06", "originalCode": "39A06", "name": "Linear difference equations", "description": "Linear difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A10", "originalCode": "39A10", "name": "Additive difference equations", "description": "Additive difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A12", "originalCode": "39A12", "name": "Discrete version of topics in analysis", "description": "Discrete version of topics in analysis", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A13", "originalCode": "39A13", "name": "Difference equations, scaling (\\(q\\)-differences)", "description": "Difference equations, scaling (\\(q\\)-differences) [See also 33Dxx]", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A14", "originalCode": "39A14", "name": "Partial difference equations", "description": "Partial difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A20", "originalCode": "39A20", "name": "Multiplicative and other generalized difference equations", "description": "Multiplicative and other generalized difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A21", "originalCode": "39A21", "name": "Oscillation theory for difference equations", "description": "Oscillation theory for difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A22", "originalCode": "39A22", "name": "Growth, boundedness, comparison of solutions to difference equations", "description": "Growth, boundedness, comparison of solutions to difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A23", "originalCode": "39A23", "name": "Periodic solutions of difference equations", "description": "Periodic solutions of difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A24", "originalCode": "39A24", "name": "Almost periodic solutions of difference equations", "description": "Almost periodic solutions of difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A26", "originalCode": "39A26", "name": "Fuzzy difference equations", "description": "Fuzzy difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A27", "originalCode": "39A27", "name": "Boundary value problems for difference equations", "description": "Boundary value problems for difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A28", "originalCode": "39A28", "name": "Bifurcation theory for difference equations", "description": "Bifurcation theory for difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A30", "originalCode": "39A30", "name": "Stability theory for difference equations", "description": "Stability theory for difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A33", "originalCode": "39A33", "name": "Chaotic behavior of solutions of difference equations", "description": "Chaotic behavior of solutions of difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A36", "originalCode": "39A36", "name": "Integrable difference and lattice equations; integrability tests", "description": "Integrable difference and lattice equations; integrability tests", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A45", "originalCode": "39A45", "name": "Difference equations in the complex domain", "description": "Difference equations in the complex domain", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A50", "originalCode": "39A50", "name": "Stochastic difference equations", "description": "Stochastic difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A60", "originalCode": "39A60", "name": "Applications of difference equations", "description": "Applications of difference equations", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A70", "originalCode": "39A70", "name": "Difference operators", "description": "Difference operators [See also 47B39]", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39A99", "originalCode": "39A99", "name": "Difference equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "39A", "page": 108 }, { "code": "39B", "originalCode": "39Bxx", "name": "Functional equations and inequalities", "description": "Functional equations and inequalities [See also 30D05]", "kind": "section", "parent": "39", "page": 108 }, { "code": "39B05", "originalCode": "39B05", "name": "General theory of functional equations and inequalities", "description": "General theory of functional equations and inequalities", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B12", "originalCode": "39B12", "name": "Iteration theory, iterative and composite equations", "description": "Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B22", "originalCode": "39B22", "name": "Functional equations for real functions", "description": "Functional equations for real functions [See also 26A51, 26B25]", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B32", "originalCode": "39B32", "name": "Functional equations for complex functions", "description": "Functional equations for complex functions [See also 30D05]", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B42", "originalCode": "39B42", "name": "Matrix and operator functional equations", "description": "Matrix and operator functional equations [See also 47Jxx]", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B52", "originalCode": "39B52", "name": "Functional equations for functions with more general domains and/or ranges", "description": "Functional equations for functions with more general domains and/or ranges", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B55", "originalCode": "39B55", "name": "Orthogonal additivity and other conditional functional equations", "description": "Orthogonal additivity and other conditional functional equations", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B62", "originalCode": "39B62", "name": "Functional inequalities, including subadditivity, convexity, etc.", "description": "Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B72", "originalCode": "39B72", "name": "Systems of functional equations and inequalities", "description": "Systems of functional equations and inequalities", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B82", "originalCode": "39B82", "name": "Stability, separation, extension, and related topics for functional equations", "description": "Stability, separation, extension, and related topics for functional equations [See also 46A22]", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "39B99", "originalCode": "39B99", "name": "Functional equations and inequalities", "description": "None of the above, but in this section", "kind": "subject", "parent": "39B", "page": 108 }, { "code": "40", "originalCode": "40-XX", "name": "Sequences, series, summability", "description": "Sequences, series, summability", "kind": "class", "parent": null, "page": 109 }, { "code": "40-00", "originalCode": "40-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to sequences, series, summability", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to sequences, series, summability", "kind": "subject", "parent": "40", "page": 109 }, { "code": "40-01", "originalCode": "40-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summability", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summability", "kind": "subject", "parent": "40", "page": 109 }, { "code": "40-02", "originalCode": "40-02", "name": "Research exposition (monographs, survey articles) pertaining to sequences, series, summability", "description": "Research exposition (monographs, survey articles) pertaining to sequences, series, summability", "kind": "subject", "parent": "40", "page": 109 }, { "code": "40-03", "originalCode": "40-03", "name": "History of sequences, series, summability", "description": "History of sequences, series, summability [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "40", "page": 109 }, { "code": "40-04", "originalCode": "40-04", "name": "Software, source code, etc. for problems pertaining to sequences, series, summability", "description": "Software, source code, etc. for problems pertaining to sequences, series, summability", "kind": "subject", "parent": "40", "page": 109 }, { "code": "40-06", "originalCode": "40-06", "name": "Proceedings, conferences, collections, etc. pertaining to sequences, series, summability", "description": "Proceedings, conferences, collections, etc. pertaining to sequences, series, summability", "kind": "subject", "parent": "40", "page": 109 }, { "code": "40-08", "originalCode": "40-08", "name": "Computational methods for problems pertaining to sequences, series, summability", "description": "Computational methods for problems pertaining to sequences, series, summability", "kind": "subject", "parent": "40", "page": 109 }, { "code": "40-11", "originalCode": "40-11", "name": "Research data for problems pertaining to sequences, series, summability", "description": "Research data for problems pertaining to sequences, series, summability", "kind": "subject", "parent": "40", "page": 109 }, { "code": "40A", "originalCode": "40Axx", "name": "Convergence and divergence of infinite limiting processes", "description": "Convergence and divergence of infinite limiting processes", "kind": "section", "parent": "40", "page": 109 }, { "code": "40A05", "originalCode": "40A05", "name": "Convergence and divergence of series and sequences", "description": "Convergence and divergence of series and sequences", "kind": "subject", "parent": "40A", "page": 109 }, { "code": "40A10", "originalCode": "40A10", "name": "Convergence and divergence of integrals", "description": "Convergence and divergence of integrals", "kind": "subject", "parent": "40A", "page": 109 }, { "code": "40A15", "originalCode": "40A15", "name": "Convergence and divergence of continued fractions", "description": "Convergence and divergence of continued fractions [See also 30B70]", "kind": "subject", "parent": "40A", "page": 109 }, { "code": "40A20", "originalCode": "40A20", "name": "Convergence and divergence of infinite products", "description": "Convergence and divergence of infinite products", "kind": "subject", "parent": "40A", "page": 109 }, { "code": "40A25", "originalCode": "40A25", "name": "Approximation to limiting values (summation of series, etc.)", "description": "Approximation to limiting values (summation of series, etc.) \\{For the Euler-Maclaurin summation formula, see 65B15\\}", "kind": "subject", "parent": "40A", "page": 109 }, { "code": "40A30", "originalCode": "40A30", "name": "Convergence and divergence of series and sequences of functions", "description": "Convergence and divergence of series and sequences of functions", "kind": "subject", "parent": "40A", "page": 109 }, { "code": "40A35", "originalCode": "40A35", "name": "Ideal and statistical convergence", "description": "Ideal and statistical convergence [See also 40G15]", "kind": "subject", "parent": "40A", "page": 109 }, { "code": "40A99", "originalCode": "40A99", "name": "Convergence and divergence of infinite limiting processes", "description": "None of the above, but in this section", "kind": "subject", "parent": "40A", "page": 109 }, { "code": "40B", "originalCode": "40Bxx", "name": "Multiple sequences and series", "description": "Multiple sequences and series", "kind": "section", "parent": "40", "page": 109 }, { "code": "40B05", "originalCode": "40B05", "name": "Multiple sequences and series", "description": "Multiple sequences and series [Should also be assigned at least one other classification number in this section]", "kind": "subject", "parent": "40B", "page": 109 }, { "code": "40B99", "originalCode": "40B99", "name": "Multiple sequences and series", "description": "None of the above, but in this section", "kind": "subject", "parent": "40B", "page": 109 }, { "code": "40C", "originalCode": "40Cxx", "name": "General summability methods", "description": "General summability methods", "kind": "section", "parent": "40", "page": 109 }, { "code": "40C05", "originalCode": "40C05", "name": "Matrix methods for summability", "description": "Matrix methods for summability", "kind": "subject", "parent": "40C", "page": 109 }, { "code": "40C10", "originalCode": "40C10", "name": "Integral methods for summability", "description": "Integral methods for summability", "kind": "subject", "parent": "40C", "page": 109 }, { "code": "40C15", "originalCode": "40C15", "name": "Function-theoretic methods (including power series methods and semicontinuous methods) for summability", "description": "Function-theoretic methods (including power series methods and semicontinuous methods) for summability", "kind": "subject", "parent": "40C", "page": 109 }, { "code": "40C99", "originalCode": "40C99", "name": "General summability methods", "description": "None of the above, but in this section", "kind": "subject", "parent": "40C", "page": 109 }, { "code": "40D", "originalCode": "40Dxx", "name": "Direct theorems on summability", "description": "Direct theorems on summability", "kind": "section", "parent": "40", "page": 110 }, { "code": "40D05", "originalCode": "40D05", "name": "General theorems on summability", "description": "General theorems on summability", "kind": "subject", "parent": "40D", "page": 110 }, { "code": "40D09", "originalCode": "40D09", "name": "Structure of summability fields", "description": "Structure of summability fields", "kind": "subject", "parent": "40D", "page": 110 }, { "code": "40D10", "originalCode": "40D10", "name": "Tauberian constants and oscillation limits in summability theory", "description": "Tauberian constants and oscillation limits in summability theory", "kind": "subject", "parent": "40D", "page": 110 }, { "code": "40D15", "originalCode": "40D15", "name": "Convergence factors and summability factors", "description": "Convergence factors and summability factors", "kind": "subject", "parent": "40D", "page": 110 }, { "code": "40D20", "originalCode": "40D20", "name": "Summability and bounded fields of methods", "description": "Summability and bounded fields of methods", "kind": "subject", "parent": "40D", "page": 110 }, { "code": "40D25", "originalCode": "40D25", "name": "Inclusion and equivalence theorems in summability theory", "description": "Inclusion and equivalence theorems in summability theory", "kind": "subject", "parent": "40D", "page": 110 }, { "code": "40D99", "originalCode": "40D99", "name": "Direct theorems on summability", "description": "None of the above, but in this section", "kind": "subject", "parent": "40D", "page": 110 }, { "code": "40E", "originalCode": "40Exx", "name": "Inversion theorems", "description": "Inversion theorems", "kind": "section", "parent": "40", "page": 110 }, { "code": "40E05", "originalCode": "40E05", "name": "Tauberian theorems", "description": "Tauberian theorems", "kind": "subject", "parent": "40E", "page": 110 }, { "code": "40E10", "originalCode": "40E10", "name": "Growth estimates", "description": "Growth estimates", "kind": "subject", "parent": "40E", "page": 110 }, { "code": "40E15", "originalCode": "40E15", "name": "Lacunary inversion theorems", "description": "Lacunary inversion theorems", "kind": "subject", "parent": "40E", "page": 110 }, { "code": "40E20", "originalCode": "40E20", "name": "Tauberian constants", "description": "Tauberian constants", "kind": "subject", "parent": "40E", "page": 110 }, { "code": "40E99", "originalCode": "40E99", "name": "Inversion theorems", "description": "None of the above, but in this section", "kind": "subject", "parent": "40E", "page": 110 }, { "code": "40F", "originalCode": "40Fxx", "name": "Absolute and strong summability", "description": "Absolute and strong summability [Should also be assigned at least one other classification number in Section 40-XX]", "kind": "section", "parent": "40", "page": 110 }, { "code": "40F05", "originalCode": "40F05", "name": "Absolute and strong summability", "description": "Absolute and strong summability [Should also be assigned at least one other classification number in Section 40-XX]", "kind": "subject", "parent": "40F", "page": 110 }, { "code": "40F99", "originalCode": "40F99", "name": "Absolute and strong summability", "description": "None of the above, but in this section", "kind": "subject", "parent": "40F", "page": 110 }, { "code": "40G", "originalCode": "40Gxx", "name": "Special methods of summability", "description": "Special methods of summability", "kind": "section", "parent": "40", "page": 110 }, { "code": "40G05", "originalCode": "40G05", "name": "Cesàro, Euler, Nörlund and Hausdorff methods", "description": "Cesàro, Euler, Nörlund and Hausdorff methods", "kind": "subject", "parent": "40G", "page": 110 }, { "code": "40G10", "originalCode": "40G10", "name": "Abel, Borel and power series methods", "description": "Abel, Borel and power series methods", "kind": "subject", "parent": "40G", "page": 110 }, { "code": "40G15", "originalCode": "40G15", "name": "Summability methods using statistical convergence", "description": "Summability methods using statistical convergence [See also 40A35]", "kind": "subject", "parent": "40G", "page": 110 }, { "code": "40G99", "originalCode": "40G99", "name": "Special methods of summability", "description": "None of the above, but in this section", "kind": "subject", "parent": "40G", "page": 110 }, { "code": "40H", "originalCode": "40Hxx", "name": "Functional analytic methods in summability", "description": "Functional analytic methods in summability", "kind": "section", "parent": "40", "page": 110 }, { "code": "40H05", "originalCode": "40H05", "name": "Functional analytic methods in summability", "description": "Functional analytic methods in summability", "kind": "subject", "parent": "40H", "page": 110 }, { "code": "40H99", "originalCode": "40H99", "name": "Functional analytic methods in summability", "description": "None of the above, but in this section", "kind": "subject", "parent": "40H", "page": 110 }, { "code": "40J", "originalCode": "40Jxx", "name": "Summability in abstract structures", "description": "Summability in abstract structures [Should also be assigned at least one other classification number from Section 40-XX] [See also 43A55, 46A35, 46B15]", "kind": "section", "parent": "40", "page": 110 }, { "code": "40J05", "originalCode": "40J05", "name": "Summability in abstract structures", "description": "Summability in abstract structures [Should also be assigned at least one other classification number from Section 40-XX] [See also 43A55, 46A35, 46B15]", "kind": "subject", "parent": "40J", "page": 110 }, { "code": "40J99", "originalCode": "40J99", "name": "Summability in abstract structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "40J", "page": 110 }, { "code": "41", "originalCode": "41-XX", "name": "Approximations and expansions", "description": "Approximations and expansions \\{For approximation theory in the complex domain, see 30E05, 30E10; for trigonometric approximation and interpolation, see 42A10, 42A15; for numerical approximation, see 65Dxx\\}", "kind": "class", "parent": null, "page": 111 }, { "code": "41-00", "originalCode": "41-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to approximations and expansions", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to approximations and expansions", "kind": "subject", "parent": "41", "page": 111 }, { "code": "41-01", "originalCode": "41-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to approximations and expansions", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to approximations and expansions", "kind": "subject", "parent": "41", "page": 111 }, { "code": "41-02", "originalCode": "41-02", "name": "Research exposition (monographs, survey articles) pertaining to approximations and expansions", "description": "Research exposition (monographs, survey articles) pertaining to approximations and expansions", "kind": "subject", "parent": "41", "page": 111 }, { "code": "41-03", "originalCode": "41-03", "name": "History of approximations and expansions", "description": "History of approximations and expansions [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "41", "page": 111 }, { "code": "41-04", "originalCode": "41-04", "name": "Software, source code, etc. for problems pertaining to approximations and expansions", "description": "Software, source code, etc. for problems pertaining to approximations and expansions", "kind": "subject", "parent": "41", "page": 111 }, { "code": "41-06", "originalCode": "41-06", "name": "Proceedings, conferences, collections, etc. pertaining to approximations and expansions", "description": "Proceedings, conferences, collections, etc. pertaining to approximations and expansions", "kind": "subject", "parent": "41", "page": 111 }, { "code": "41-11", "originalCode": "41-11", "name": "Research data for problems pertaining to approximations and expansions", "description": "Research data for problems pertaining to approximations and expansions", "kind": "subject", "parent": "41", "page": 111 }, { "code": "41A", "originalCode": "41Axx", "name": "Approximations and expansions", "description": "Approximations and expansions \\{For approximation theory in the complex domain, see 30E05, 30E10; for trigonometric approximation and interpolation, see 42A10, 42A15; for numerical approximation, see 65Dxx\\}", "kind": "section", "parent": "41", "page": 111 }, { "code": "41A05", "originalCode": "41A05", "name": "Interpolation in approximation theory", "description": "Interpolation in approximation theory [See also 42A15, 65D05]", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A10", "originalCode": "41A10", "name": "Approximation by polynomials", "description": "Approximation by polynomials \\{For approximation by trigonometric polynomials, see 42A10\\}", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A15", "originalCode": "41A15", "name": "Spline approximation", "description": "Spline approximation", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A17", "originalCode": "41A17", "name": "Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities)", "description": "Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities)", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A20", "originalCode": "41A20", "name": "Approximation by rational functions", "description": "Approximation by rational functions", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A21", "originalCode": "41A21", "name": "Padé approximation", "description": "Padé approximation", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A25", "originalCode": "41A25", "name": "Rate of convergence, degree of approximation", "description": "Rate of convergence, degree of approximation", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A27", "originalCode": "41A27", "name": "Inverse theorems in approximation theory", "description": "Inverse theorems in approximation theory", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A28", "originalCode": "41A28", "name": "Simultaneous approximation", "description": "Simultaneous approximation", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A29", "originalCode": "41A29", "name": "Approximation with constraints", "description": "Approximation with constraints", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A30", "originalCode": "41A30", "name": "Approximation by other special function classes", "description": "Approximation by other special function classes", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A35", "originalCode": "41A35", "name": "Approximation by operators (in particular, by integral operators)", "description": "Approximation by operators (in particular, by integral operators)", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A36", "originalCode": "41A36", "name": "Approximation by positive operators", "description": "Approximation by positive operators", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A40", "originalCode": "41A40", "name": "Saturation in approximation theory", "description": "Saturation in approximation theory", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A44", "originalCode": "41A44", "name": "Best constants in approximation theory", "description": "Best constants in approximation theory", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A45", "originalCode": "41A45", "name": "Approximation by arbitrary linear expressions", "description": "Approximation by arbitrary linear expressions", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A46", "originalCode": "41A46", "name": "Approximation by arbitrary nonlinear expressions; widths and entropy", "description": "Approximation by arbitrary nonlinear expressions; widths and entropy", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A50", "originalCode": "41A50", "name": "Best approximation, Chebyshev systems", "description": "Best approximation, Chebyshev systems", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A52", "originalCode": "41A52", "name": "Uniqueness of best approximation", "description": "Uniqueness of best approximation", "kind": "subject", "parent": "41A", "page": 111 }, { "code": "41A55", "originalCode": "41A55", "name": "Approximate quadratures", "description": "Approximate quadratures", "kind": "subject", "parent": "41A", "page": 112 }, { "code": "41A58", "originalCode": "41A58", "name": "Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)", "description": "Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)", "kind": "subject", "parent": "41A", "page": 112 }, { "code": "41A60", "originalCode": "41A60", "name": "Asymptotic approximations, asymptotic expansions (steepest descent, etc.)", "description": "Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]", "kind": "subject", "parent": "41A", "page": 112 }, { "code": "41A63", "originalCode": "41A63", "name": "Multidimensional problems", "description": "Multidimensional problems [Should also be assigned at least one other classification number from Section 41-XX]", "kind": "subject", "parent": "41A", "page": 112 }, { "code": "41A65", "originalCode": "41A65", "name": "Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)", "description": "Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)", "kind": "subject", "parent": "41A", "page": 112 }, { "code": "41A80", "originalCode": "41A80", "name": "Remainders in approximation formulas", "description": "Remainders in approximation formulas", "kind": "subject", "parent": "41A", "page": 112 }, { "code": "41A81", "originalCode": "41A81", "name": "Weighted approximation", "description": "Weighted approximation", "kind": "subject", "parent": "41A", "page": 112 }, { "code": "41A99", "originalCode": "41A99", "name": "Approximations and expansions", "description": "None of the above, but in this section", "kind": "subject", "parent": "41A", "page": 112 }, { "code": "42", "originalCode": "42-XX", "name": "Harmonic analysis on Euclidean spaces", "description": "Harmonic analysis on Euclidean spaces", "kind": "class", "parent": null, "page": 112 }, { "code": "42-00", "originalCode": "42-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to harmonic analysis on Euclidean spaces", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to harmonic analysis on Euclidean spaces", "kind": "subject", "parent": "42", "page": 112 }, { "code": "42-01", "originalCode": "42-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces", "kind": "subject", "parent": "42", "page": 112 }, { "code": "42-02", "originalCode": "42-02", "name": "Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces", "description": "Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces", "kind": "subject", "parent": "42", "page": 112 }, { "code": "42-03", "originalCode": "42-03", "name": "History of harmonic analysis on Euclidean spaces", "description": "History of harmonic analysis on Euclidean spaces [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "42", "page": 112 }, { "code": "42-04", "originalCode": "42-04", "name": "Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces", "description": "Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces", "kind": "subject", "parent": "42", "page": 112 }, { "code": "42-06", "originalCode": "42-06", "name": "Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spaces", "description": "Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spaces", "kind": "subject", "parent": "42", "page": 112 }, { "code": "42-08", "originalCode": "42-08", "name": "Computational methods for problems pertaining to harmonic analysis on Euclidean spaces", "description": "Computational methods for problems pertaining to harmonic analysis on Euclidean spaces", "kind": "subject", "parent": "42", "page": 112 }, { "code": "42-11", "originalCode": "42-11", "name": "Research data for problems pertaining to harmonic analysis on Euclidean spaces", "description": "Research data for problems pertaining to harmonic analysis on Euclidean spaces", "kind": "subject", "parent": "42", "page": 112 }, { "code": "42A", "originalCode": "42Axx", "name": "Harmonic analysis in one variable", "description": "Harmonic analysis in one variable", "kind": "section", "parent": "42", "page": 112 }, { "code": "42A05", "originalCode": "42A05", "name": "Trigonometric polynomials, inequalities, extremal problems", "description": "Trigonometric polynomials, inequalities, extremal problems", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A10", "originalCode": "42A10", "name": "Trigonometric approximation", "description": "Trigonometric approximation", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A15", "originalCode": "42A15", "name": "Trigonometric interpolation", "description": "Trigonometric interpolation", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A16", "originalCode": "42A16", "name": "Fourier coefficients, Fourier series of functions with special properties, special Fourier series", "description": "Fourier coefficients, Fourier series of functions with special properties, special Fourier series \\{For automorphic theory, see mainly 11F30\\}", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A20", "originalCode": "42A20", "name": "Convergence and absolute convergence of Fourier and trigonometric series", "description": "Convergence and absolute convergence of Fourier and trigonometric series", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A24", "originalCode": "42A24", "name": "Summability and absolute summability of Fourier and trigonometric series", "description": "Summability and absolute summability of Fourier and trigonometric series", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A32", "originalCode": "42A32", "name": "Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)", "description": "Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A38", "originalCode": "42A38", "name": "Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type", "description": "Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A45", "originalCode": "42A45", "name": "Multipliers in one variable harmonic analysis", "description": "Multipliers in one variable harmonic analysis", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A50", "originalCode": "42A50", "name": "Conjugate functions, conjugate series, singular integrals", "description": "Conjugate functions, conjugate series, singular integrals", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A55", "originalCode": "42A55", "name": "Lacunary series of trigonometric and other functions; Riesz products", "description": "Lacunary series of trigonometric and other functions; Riesz products", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A61", "originalCode": "42A61", "name": "Probabilistic methods for one variable harmonic analysis", "description": "Probabilistic methods for one variable harmonic analysis", "kind": "subject", "parent": "42A", "page": 112 }, { "code": "42A63", "originalCode": "42A63", "name": "Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization", "description": "Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization", "kind": "subject", "parent": "42A", "page": 113 }, { "code": "42A65", "originalCode": "42A65", "name": "Completeness of sets of functions in one variable harmonic analysis", "description": "Completeness of sets of functions in one variable harmonic analysis", "kind": "subject", "parent": "42A", "page": 113 }, { "code": "42A70", "originalCode": "42A70", "name": "Trigonometric moment problems in one variable harmonic analysis", "description": "Trigonometric moment problems in one variable harmonic analysis", "kind": "subject", "parent": "42A", "page": 113 }, { "code": "42A75", "originalCode": "42A75", "name": "Classical almost periodic functions, mean periodic functions", "description": "Classical almost periodic functions, mean periodic functions [See also 43A60]", "kind": "subject", "parent": "42A", "page": 113 }, { "code": "42A82", "originalCode": "42A82", "name": "Positive definite functions in one variable harmonic analysis", "description": "Positive definite functions in one variable harmonic analysis", "kind": "subject", "parent": "42A", "page": 113 }, { "code": "42A85", "originalCode": "42A85", "name": "Convolution, factorization for one variable harmonic analysis", "description": "Convolution, factorization for one variable harmonic analysis", "kind": "subject", "parent": "42A", "page": 113 }, { "code": "42A99", "originalCode": "42A99", "name": "Harmonic analysis in one variable", "description": "None of the above, but in this section", "kind": "subject", "parent": "42A", "page": 113 }, { "code": "42B", "originalCode": "42Bxx", "name": "Harmonic analysis in several variables", "description": "Harmonic analysis in several variables \\{For automorphic theory, see mainly 11F30\\}", "kind": "section", "parent": "42", "page": 113 }, { "code": "42B05", "originalCode": "42B05", "name": "Fourier series and coefficients in several variables", "description": "Fourier series and coefficients in several variables", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B08", "originalCode": "42B08", "name": "Summability in several variables", "description": "Summability in several variables", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B10", "originalCode": "42B10", "name": "Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type", "description": "Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B15", "originalCode": "42B15", "name": "Multipliers for harmonic analysis in several variables", "description": "Multipliers for harmonic analysis in several variables", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B20", "originalCode": "42B20", "name": "Singular and oscillatory integrals (Calderón-Zygmund, etc.)", "description": "Singular and oscillatory integrals (Calderón-Zygmund, etc.)", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B25", "originalCode": "42B25", "name": "Maximal functions, Littlewood-Paley theory", "description": "Maximal functions, Littlewood-Paley theory", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B30", "originalCode": "42B30", "name": "\\(H^p\\)-spaces", "description": "\\(H^p\\)-spaces", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B35", "originalCode": "42B35", "name": "Function spaces arising in harmonic analysis", "description": "Function spaces arising in harmonic analysis", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B37", "originalCode": "42B37", "name": "Harmonic analysis and PDEs", "description": "Harmonic analysis and PDEs [See also 35-XX]", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42B99", "originalCode": "42B99", "name": "Harmonic analysis in several variables", "description": "None of the above, but in this section", "kind": "subject", "parent": "42B", "page": 113 }, { "code": "42C", "originalCode": "42Cxx", "name": "Nontrigonometric harmonic analysis", "description": "Nontrigonometric harmonic analysis", "kind": "section", "parent": "42", "page": 113 }, { "code": "42C05", "originalCode": "42C05", "name": "Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis", "description": "Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis [See also 33C45, 33C50, 33D45]", "kind": "subject", "parent": "42C", "page": 113 }, { "code": "42C10", "originalCode": "42C10", "name": "Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)", "description": "Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)", "kind": "subject", "parent": "42C", "page": 113 }, { "code": "42C15", "originalCode": "42C15", "name": "General harmonic expansions, frames", "description": "General harmonic expansions, frames", "kind": "subject", "parent": "42C", "page": 113 }, { "code": "42C20", "originalCode": "42C20", "name": "Other transformations of harmonic type", "description": "Other transformations of harmonic type", "kind": "subject", "parent": "42C", "page": 113 }, { "code": "42C25", "originalCode": "42C25", "name": "Uniqueness and localization for orthogonal series", "description": "Uniqueness and localization for orthogonal series", "kind": "subject", "parent": "42C", "page": 113 }, { "code": "42C30", "originalCode": "42C30", "name": "Completeness of sets of functions in nontrigonometric harmonic analysis", "description": "Completeness of sets of functions in nontrigonometric harmonic analysis", "kind": "subject", "parent": "42C", "page": 113 }, { "code": "42C40", "originalCode": "42C40", "name": "Nontrigonometric harmonic analysis involving wavelets and other special systems", "description": "Nontrigonometric harmonic analysis involving wavelets and other special systems", "kind": "subject", "parent": "42C", "page": 113 }, { "code": "42C99", "originalCode": "42C99", "name": "Nontrigonometric harmonic analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "42C", "page": 113 }, { "code": "43", "originalCode": "43-XX", "name": "Abstract harmonic analysis", "description": "Abstract harmonic analysis \\{For other analysis on topological and Lie groups, see 22Exx\\}", "kind": "class", "parent": null, "page": 114 }, { "code": "43-00", "originalCode": "43-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to abstract harmonic analysis", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to abstract harmonic analysis", "kind": "subject", "parent": "43", "page": 114 }, { "code": "43-01", "originalCode": "43-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to abstract harmonic analysis", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to abstract harmonic analysis", "kind": "subject", "parent": "43", "page": 114 }, { "code": "43-02", "originalCode": "43-02", "name": "Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis", "description": "Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis", "kind": "subject", "parent": "43", "page": 114 }, { "code": "43-03", "originalCode": "43-03", "name": "History of abstract harmonic analysis", "description": "History of abstract harmonic analysis [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "43", "page": 114 }, { "code": "43-04", "originalCode": "43-04", "name": "Software, source code, etc. for problems pertaining to abstract harmonic analysis", "description": "Software, source code, etc. for problems pertaining to abstract harmonic analysis", "kind": "subject", "parent": "43", "page": 114 }, { "code": "43-06", "originalCode": "43-06", "name": "Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis", "description": "Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis", "kind": "subject", "parent": "43", "page": 114 }, { "code": "43-08", "originalCode": "43-08", "name": "Computational methods for problems pertaining to abstract harmonic analysis", "description": "Computational methods for problems pertaining to abstract harmonic analysis", "kind": "subject", "parent": "43", "page": 114 }, { "code": "43-11", "originalCode": "43-11", "name": "Research data for problems pertaining to abstract harmonic analysis", "description": "Research data for problems pertaining to abstract harmonic analysis", "kind": "subject", "parent": "43", "page": 114 }, { "code": "43A", "originalCode": "43Axx", "name": "Abstract harmonic analysis", "description": "Abstract harmonic analysis \\{For other analysis on topological and Lie groups, see 22Exx\\}", "kind": "section", "parent": "43", "page": 114 }, { "code": "43A05", "originalCode": "43A05", "name": "Measures on groups and semigroups, etc.", "description": "Measures on groups and semigroups, etc.", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A07", "originalCode": "43A07", "name": "Means on groups, semigroups, etc.; amenable groups", "description": "Means on groups, semigroups, etc.; amenable groups", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A10", "originalCode": "43A10", "name": "Measure algebras on groups, semigroups, etc.", "description": "Measure algebras on groups, semigroups, etc.", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A15", "originalCode": "43A15", "name": "\\(L^p\\)-spaces and other function spaces on groups, semigroups, etc.", "description": "\\(L^p\\)-spaces and other function spaces on groups, semigroups, etc.", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A17", "originalCode": "43A17", "name": "Analysis on ordered groups, \\(H^p\\)-theory", "description": "Analysis on ordered groups, \\(H^p\\)-theory", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A20", "originalCode": "43A20", "name": "\\(L^1\\)-algebras on groups, semigroups, etc.", "description": "\\(L^1\\)-algebras on groups, semigroups, etc.", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A22", "originalCode": "43A22", "name": "Homomorphisms and multipliers of function spaces on groups, semigroups, etc.", "description": "Homomorphisms and multipliers of function spaces on groups, semigroups, etc.", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A25", "originalCode": "43A25", "name": "Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups", "description": "Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A30", "originalCode": "43A30", "name": "Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.", "description": "Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A32", "originalCode": "43A32", "name": "Other transforms and operators of Fourier type", "description": "Other transforms and operators of Fourier type", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A35", "originalCode": "43A35", "name": "Positive definite functions on groups, semigroups, etc.", "description": "Positive definite functions on groups, semigroups, etc.", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A40", "originalCode": "43A40", "name": "Character groups and dual objects", "description": "Character groups and dual objects", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A45", "originalCode": "43A45", "name": "Spectral synthesis on groups, semigroups, etc.", "description": "Spectral synthesis on groups, semigroups, etc.", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A46", "originalCode": "43A46", "name": "Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)", "description": "Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A50", "originalCode": "43A50", "name": "Convergence of Fourier series and of inverse transforms", "description": "Convergence of Fourier series and of inverse transforms", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A55", "originalCode": "43A55", "name": "Summability methods on groups, semigroups, etc.", "description": "Summability methods on groups, semigroups, etc. [See also 40J05]", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A60", "originalCode": "43A60", "name": "Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions", "description": "Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A62", "originalCode": "43A62", "name": "Harmonic analysis on hypergroups", "description": "Harmonic analysis on hypergroups", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A65", "originalCode": "43A65", "name": "Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)", "description": "Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) [See also 22A10, 22A20, 22Dxx, 22E45]", "kind": "subject", "parent": "43A", "page": 114 }, { "code": "43A70", "originalCode": "43A70", "name": "Analysis on specific locally compact and other abelian groups", "description": "Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05]", "kind": "subject", "parent": "43A", "page": 115 }, { "code": "43A75", "originalCode": "43A75", "name": "Harmonic analysis on specific compact groups", "description": "Harmonic analysis on specific compact groups", "kind": "subject", "parent": "43A", "page": 115 }, { "code": "43A77", "originalCode": "43A77", "name": "Harmonic analysis on general compact groups", "description": "Harmonic analysis on general compact groups", "kind": "subject", "parent": "43A", "page": 115 }, { "code": "43A80", "originalCode": "43A80", "name": "Analysis on other specific Lie groups", "description": "Analysis on other specific Lie groups [See also 22Exx]", "kind": "subject", "parent": "43A", "page": 115 }, { "code": "43A85", "originalCode": "43A85", "name": "Harmonic analysis on homogeneous spaces", "description": "Harmonic analysis on homogeneous spaces", "kind": "subject", "parent": "43A", "page": 115 }, { "code": "43A90", "originalCode": "43A90", "name": "Harmonic analysis and spherical functions", "description": "Harmonic analysis and spherical functions [See also 22E45, 22E46, 33C55]", "kind": "subject", "parent": "43A", "page": 115 }, { "code": "43A95", "originalCode": "43A95", "name": "Categorical methods for abstract harmonic analysis", "description": "Categorical methods for abstract harmonic analysis [See also 46Mxx]", "kind": "subject", "parent": "43A", "page": 115 }, { "code": "43A99", "originalCode": "43A99", "name": "Abstract harmonic analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "43A", "page": 115 }, { "code": "44", "originalCode": "44-XX", "name": "Integral transforms, operational calculus", "description": "Integral transforms, operational calculus \\{For fractional derivatives and integrals, see 26A33; for Fourier transforms, see 42A38, 42B10; for integral transforms in distribution spaces, see 46F12; for numerical methods, see 65R10\\}", "kind": "class", "parent": null, "page": 115 }, { "code": "44-00", "originalCode": "44-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral transforms", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral transforms", "kind": "subject", "parent": "44", "page": 115 }, { "code": "44-01", "originalCode": "44-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms", "kind": "subject", "parent": "44", "page": 115 }, { "code": "44-02", "originalCode": "44-02", "name": "Research exposition (monographs, survey articles) pertaining to integral transforms", "description": "Research exposition (monographs, survey articles) pertaining to integral transforms", "kind": "subject", "parent": "44", "page": 115 }, { "code": "44-03", "originalCode": "44-03", "name": "History of integral transforms", "description": "History of integral transforms [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "44", "page": 115 }, { "code": "44-04", "originalCode": "44-04", "name": "Software, source code, etc. for problems pertaining to integral transforms", "description": "Software, source code, etc. for problems pertaining to integral transforms", "kind": "subject", "parent": "44", "page": 115 }, { "code": "44-06", "originalCode": "44-06", "name": "Proceedings, conferences, collections, etc. pertaining to integral transforms", "description": "Proceedings, conferences, collections, etc. pertaining to integral transforms", "kind": "subject", "parent": "44", "page": 115 }, { "code": "44-11", "originalCode": "44-11", "name": "Research data for problems pertaining to integral transforms", "description": "Research data for problems pertaining to integral transforms", "kind": "subject", "parent": "44", "page": 115 }, { "code": "44A", "originalCode": "44Axx", "name": "Integral transforms, operational calculus", "description": "Integral transforms, operational calculus \\{For fractional derivatives and integrals, see 26A33; for Fourier transforms, see 42A38, 42B10; for integral transforms in distribution spaces, see 46F12; for numerical methods, see 65R10\\}", "kind": "section", "parent": "44", "page": 115 }, { "code": "44A05", "originalCode": "44A05", "name": "General integral transforms", "description": "General integral transforms [See also 42A38]", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A10", "originalCode": "44A10", "name": "Laplace transform", "description": "Laplace transform", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A12", "originalCode": "44A12", "name": "Radon transform", "description": "Radon transform [See also 92C55]", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A15", "originalCode": "44A15", "name": "Special integral transforms (Legendre, Hilbert, etc.)", "description": "Special integral transforms (Legendre, Hilbert, etc.)", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A20", "originalCode": "44A20", "name": "Integral transforms of special functions", "description": "Integral transforms of special functions", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A30", "originalCode": "44A30", "name": "Multiple integral transforms", "description": "Multiple integral transforms", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A35", "originalCode": "44A35", "name": "Convolution as an integral transform", "description": "Convolution as an integral transform", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A40", "originalCode": "44A40", "name": "Calculus of Mikusi?ski and other operational calculi", "description": "Calculus of Mikusi?ski and other operational calculi", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A45", "originalCode": "44A45", "name": "Classical operational calculus", "description": "Classical operational calculus", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A55", "originalCode": "44A55", "name": "Discrete operational calculus", "description": "Discrete operational calculus", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A60", "originalCode": "44A60", "name": "Moment problems", "description": "Moment problems \\{For trigonometric moment problems, see 42A70\\}", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "44A99", "originalCode": "44A99", "name": "Integral transforms, operational calculus", "description": "None of the above, but in this section", "kind": "subject", "parent": "44A", "page": 115 }, { "code": "45", "originalCode": "45-XX", "name": "Integral equations", "description": "Integral equations", "kind": "class", "parent": null, "page": 116 }, { "code": "45-00", "originalCode": "45-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral equations", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral equations", "kind": "subject", "parent": "45", "page": 116 }, { "code": "45-01", "originalCode": "45-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral equations", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral equations", "kind": "subject", "parent": "45", "page": 116 }, { "code": "45-02", "originalCode": "45-02", "name": "Research exposition (monographs, survey articles) pertaining to integral equations", "description": "Research exposition (monographs, survey articles) pertaining to integral equations", "kind": "subject", "parent": "45", "page": 116 }, { "code": "45-03", "originalCode": "45-03", "name": "History of integral equations", "description": "History of integral equations [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "45", "page": 116 }, { "code": "45-04", "originalCode": "45-04", "name": "Software, source code, etc. for problems pertaining to integral equations", "description": "Software, source code, etc. for problems pertaining to integral equations", "kind": "subject", "parent": "45", "page": 116 }, { "code": "45-06", "originalCode": "45-06", "name": "Proceedings, conferences, collections, etc. pertaining to integral equations", "description": "Proceedings, conferences, collections, etc. pertaining to integral equations", "kind": "subject", "parent": "45", "page": 116 }, { "code": "45-11", "originalCode": "45-11", "name": "Research data for problems pertaining to integral equations", "description": "Research data for problems pertaining to integral equations", "kind": "subject", "parent": "45", "page": 116 }, { "code": "45A", "originalCode": "45Axx", "name": "Linear integral equations", "description": "Linear integral equations", "kind": "section", "parent": "45", "page": 116 }, { "code": "45A05", "originalCode": "45A05", "name": "Linear integral equations", "description": "Linear integral equations", "kind": "subject", "parent": "45A", "page": 116 }, { "code": "45A99", "originalCode": "45A99", "name": "Linear integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45A", "page": 116 }, { "code": "45B", "originalCode": "45Bxx", "name": "Fredholm integral equations", "description": "Fredholm integral equations", "kind": "section", "parent": "45", "page": 116 }, { "code": "45B05", "originalCode": "45B05", "name": "Fredholm integral equations", "description": "Fredholm integral equations", "kind": "subject", "parent": "45B", "page": 116 }, { "code": "45B99", "originalCode": "45B99", "name": "Fredholm integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45B", "page": 116 }, { "code": "45C", "originalCode": "45Cxx", "name": "Eigenvalue problems for integral equations", "description": "Eigenvalue problems for integral equations [See also 34Lxx, 35Pxx, 45P05, 47A75]", "kind": "section", "parent": "45", "page": 116 }, { "code": "45C05", "originalCode": "45C05", "name": "Eigenvalue problems for integral equations", "description": "Eigenvalue problems for integral equations [See also 34Lxx, 35Pxx, 45P05, 47A75]", "kind": "subject", "parent": "45C", "page": 116 }, { "code": "45C99", "originalCode": "45C99", "name": "Eigenvalue problems for integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45C", "page": 116 }, { "code": "45D", "originalCode": "45Dxx", "name": "Volterra integral equations", "description": "Volterra integral equations [See also 34A12]", "kind": "section", "parent": "45", "page": 116 }, { "code": "45D05", "originalCode": "45D05", "name": "Volterra integral equations", "description": "Volterra integral equations [See also 34A12]", "kind": "subject", "parent": "45D", "page": 116 }, { "code": "45D99", "originalCode": "45D99", "name": "Volterra integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45D", "page": 116 }, { "code": "45E", "originalCode": "45Exx", "name": "Singular integral equations", "description": "Singular integral equations [See also 30E20, 30E25, 44A15, 44A35]", "kind": "section", "parent": "45", "page": 116 }, { "code": "45E05", "originalCode": "45E05", "name": "Integral equations with kernels of Cauchy type", "description": "Integral equations with kernels of Cauchy type [See also 35J15]", "kind": "subject", "parent": "45E", "page": 116 }, { "code": "45E10", "originalCode": "45E10", "name": "Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)", "description": "Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35]", "kind": "subject", "parent": "45E", "page": 116 }, { "code": "45E99", "originalCode": "45E99", "name": "Singular integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45E", "page": 116 }, { "code": "45F", "originalCode": "45Fxx", "name": "Systems of linear integral equations", "description": "Systems of linear integral equations", "kind": "section", "parent": "45", "page": 116 }, { "code": "45F05", "originalCode": "45F05", "name": "Systems of nonsingular linear integral equations", "description": "Systems of nonsingular linear integral equations", "kind": "subject", "parent": "45F", "page": 116 }, { "code": "45F10", "originalCode": "45F10", "name": "Dual, triple, etc., integral and series equations", "description": "Dual, triple, etc., integral and series equations", "kind": "subject", "parent": "45F", "page": 116 }, { "code": "45F15", "originalCode": "45F15", "name": "Systems of singular linear integral equations", "description": "Systems of singular linear integral equations", "kind": "subject", "parent": "45F", "page": 116 }, { "code": "45F99", "originalCode": "45F99", "name": "Systems of linear integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45F", "page": 116 }, { "code": "45G", "originalCode": "45Gxx", "name": "Nonlinear integral equations", "description": "Nonlinear integral equations [See also 47H30, 47Jxx]", "kind": "section", "parent": "45", "page": 117 }, { "code": "45G05", "originalCode": "45G05", "name": "Singular nonlinear integral equations", "description": "Singular nonlinear integral equations", "kind": "subject", "parent": "45G", "page": 117 }, { "code": "45G10", "originalCode": "45G10", "name": "Other nonlinear integral equations", "description": "Other nonlinear integral equations", "kind": "subject", "parent": "45G", "page": 117 }, { "code": "45G15", "originalCode": "45G15", "name": "Systems of nonlinear integral equations", "description": "Systems of nonlinear integral equations", "kind": "subject", "parent": "45G", "page": 117 }, { "code": "45G99", "originalCode": "45G99", "name": "Nonlinear integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45G", "page": 117 }, { "code": "45H", "originalCode": "45Hxx", "name": "Integral equations with miscellaneous special kernels", "description": "Integral equations with miscellaneous special kernels [See also 44A15]", "kind": "section", "parent": "45", "page": 117 }, { "code": "45H05", "originalCode": "45H05", "name": "Integral equations with miscellaneous special kernels", "description": "Integral equations with miscellaneous special kernels [See also 44A15]", "kind": "subject", "parent": "45H", "page": 117 }, { "code": "45H99", "originalCode": "45H99", "name": "Integral equations with miscellaneous special kernels", "description": "None of the above, but in this section", "kind": "subject", "parent": "45H", "page": 117 }, { "code": "45J", "originalCode": "45Jxx", "name": "Integro-ordinary differential equations", "description": "Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]", "kind": "section", "parent": "45", "page": 117 }, { "code": "45J05", "originalCode": "45J05", "name": "Integro-ordinary differential equations", "description": "Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]", "kind": "subject", "parent": "45J", "page": 117 }, { "code": "45J99", "originalCode": "45J99", "name": "Integro-ordinary differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45J", "page": 117 }, { "code": "45K", "originalCode": "45Kxx", "name": "Integro-partial differential equations", "description": "Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]", "kind": "section", "parent": "45", "page": 117 }, { "code": "45K05", "originalCode": "45K05", "name": "Integro-partial differential equations", "description": "Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]", "kind": "subject", "parent": "45K", "page": 117 }, { "code": "45K99", "originalCode": "45K99", "name": "Integro-partial differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45K", "page": 117 }, { "code": "45L", "originalCode": "45Lxx", "name": "Theoretical approximation of solutions to integral equations", "description": "Theoretical approximation of solutions to integral equations \\{For numerical analysis, see 65Rxx\\}", "kind": "section", "parent": "45", "page": 117 }, { "code": "45L05", "originalCode": "45L05", "name": "Theoretical approximation of solutions to integral equations", "description": "Theoretical approximation of solutions to integral equations \\{For numerical analysis, see 65Rxx\\}", "kind": "subject", "parent": "45L", "page": 117 }, { "code": "45L99", "originalCode": "45L99", "name": "Theoretical approximation of solutions to integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45L", "page": 117 }, { "code": "45M", "originalCode": "45Mxx", "name": "Qualitative behavior of solutions to integral equations", "description": "Qualitative behavior of solutions to integral equations", "kind": "section", "parent": "45", "page": 117 }, { "code": "45M05", "originalCode": "45M05", "name": "Asymptotics of solutions to integral equations", "description": "Asymptotics of solutions to integral equations", "kind": "subject", "parent": "45M", "page": 117 }, { "code": "45M10", "originalCode": "45M10", "name": "Stability theory for integral equations", "description": "Stability theory for integral equations", "kind": "subject", "parent": "45M", "page": 117 }, { "code": "45M15", "originalCode": "45M15", "name": "Periodic solutions of integral equations", "description": "Periodic solutions of integral equations", "kind": "subject", "parent": "45M", "page": 117 }, { "code": "45M20", "originalCode": "45M20", "name": "Positive solutions of integral equations", "description": "Positive solutions of integral equations", "kind": "subject", "parent": "45M", "page": 117 }, { "code": "45M99", "originalCode": "45M99", "name": "Qualitative behavior of solutions to integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45M", "page": 117 }, { "code": "45N", "originalCode": "45Nxx", "name": "Abstract integral equations, integral equations in abstract spaces", "description": "Abstract integral equations, integral equations in abstract spaces", "kind": "section", "parent": "45", "page": 117 }, { "code": "45N05", "originalCode": "45N05", "name": "Abstract integral equations, integral equations in abstract spaces", "description": "Abstract integral equations, integral equations in abstract spaces", "kind": "subject", "parent": "45N", "page": 117 }, { "code": "45N99", "originalCode": "45N99", "name": "Abstract integral equations, integral equations in abstract spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "45N", "page": 117 }, { "code": "45P", "originalCode": "45Pxx", "name": "Integral operators", "description": "Integral operators [See also 47B38, 47G10]", "kind": "section", "parent": "45", "page": 117 }, { "code": "45P05", "originalCode": "45P05", "name": "Integral operators", "description": "Integral operators [See also 47B38, 47G10]", "kind": "subject", "parent": "45P", "page": 117 }, { "code": "45P99", "originalCode": "45P99", "name": "Integral operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "45P", "page": 117 }, { "code": "45Q", "originalCode": "45Qxx", "name": "Inverse problems for integral equations", "description": "Inverse problems for integral equations", "kind": "section", "parent": "45", "page": 118 }, { "code": "45Q05", "originalCode": "45Q05", "name": "Inverse problems for integral equations", "description": "Inverse problems for integral equations", "kind": "subject", "parent": "45Q", "page": 118 }, { "code": "45Q99", "originalCode": "45Q99", "name": "Inverse problems for integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45Q", "page": 118 }, { "code": "45R", "originalCode": "45Rxx", "name": "Random integral equations", "description": "Random integral equations [See also 60H20]", "kind": "section", "parent": "45", "page": 118 }, { "code": "45R05", "originalCode": "45R05", "name": "Random integral equations", "description": "Random integral equations [See also 60H20]", "kind": "subject", "parent": "45R", "page": 118 }, { "code": "45R99", "originalCode": "45R99", "name": "Random integral equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "45R", "page": 118 }, { "code": "46", "originalCode": "46-XX", "name": "Functional analysis", "description": "Functional analysis \\{For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx\\}", "kind": "class", "parent": null, "page": 118 }, { "code": "46-00", "originalCode": "46-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functional analysis", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functional analysis", "kind": "subject", "parent": "46", "page": 118 }, { "code": "46-01", "originalCode": "46-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis", "kind": "subject", "parent": "46", "page": 118 }, { "code": "46-02", "originalCode": "46-02", "name": "Research exposition (monographs, survey articles) pertaining to functional analysis", "description": "Research exposition (monographs, survey articles) pertaining to functional analysis", "kind": "subject", "parent": "46", "page": 118 }, { "code": "46-03", "originalCode": "46-03", "name": "History of functional analysis", "description": "History of functional analysis [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "46", "page": 118 }, { "code": "46-04", "originalCode": "46-04", "name": "Software, source code, etc. for problems pertaining to functional analysis", "description": "Software, source code, etc. for problems pertaining to functional analysis", "kind": "subject", "parent": "46", "page": 118 }, { "code": "46-06", "originalCode": "46-06", "name": "Proceedings, conferences, collections, etc. pertaining to functional analysis", "description": "Proceedings, conferences, collections, etc. pertaining to functional analysis", "kind": "subject", "parent": "46", "page": 118 }, { "code": "46-08", "originalCode": "46-08", "name": "Computational methods for problems pertaining to functional analysis", "description": "Computational methods for problems pertaining to functional analysis", "kind": "subject", "parent": "46", "page": 118 }, { "code": "46-11", "originalCode": "46-11", "name": "Research data for problems pertaining to functional analysis", "description": "Research data for problems pertaining to functional analysis", "kind": "subject", "parent": "46", "page": 118 }, { "code": "46A", "originalCode": "46Axx", "name": "Topological linear spaces and related structures", "description": "Topological linear spaces and related structures \\{For function spaces, see 46Exx\\}", "kind": "section", "parent": "46", "page": 118 }, { "code": "46A03", "originalCode": "46A03", "name": "General theory of locally convex spaces", "description": "General theory of locally convex spaces", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A04", "originalCode": "46A04", "name": "Locally convex Fréchet spaces and (DF)-spaces", "description": "Locally convex Fréchet spaces and (DF)-spaces", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A08", "originalCode": "46A08", "name": "Barrelled spaces, bornological spaces", "description": "Barrelled spaces, bornological spaces", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A11", "originalCode": "46A11", "name": "Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)", "description": "Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A13", "originalCode": "46A13", "name": "Spaces defined by inductive or projective limits (LB, LF, etc.)", "description": "Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A16", "originalCode": "46A16", "name": "Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)", "description": "Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A17", "originalCode": "46A17", "name": "Bornologies and related structures; Mackey convergence, etc.", "description": "Bornologies and related structures; Mackey convergence, etc.", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A19", "originalCode": "46A19", "name": "Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \\(\\mathbb{R}\\), etc.)", "description": "Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \\(\\mathbb{R}\\), etc.)", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A20", "originalCode": "46A20", "name": "Duality theory for topological vector spaces", "description": "Duality theory for topological vector spaces", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A22", "originalCode": "46A22", "name": "Theorems of Hahn-Banach type; extension and lifting of functionals and operators", "description": "Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A25", "originalCode": "46A25", "name": "Reflexivity and semi-reflexivity", "description": "Reflexivity and semi-reflexivity [See also 46B10]", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A30", "originalCode": "46A30", "name": "Open mapping and closed graph theorems; completeness (including \\(B\\)-, \\(B_r\\)-completeness)", "description": "Open mapping and closed graph theorems; completeness (including \\(B\\)-, \\(B_r\\)-completeness)", "kind": "subject", "parent": "46A", "page": 118 }, { "code": "46A32", "originalCode": "46A32", "name": "Spaces of linear operators; topological tensor products; approximation properties", "description": "Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A35", "originalCode": "46A35", "name": "Summability and bases in topological vector spaces", "description": "Summability and bases in topological vector spaces [See also 46B15]", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A40", "originalCode": "46A40", "name": "Ordered topological linear spaces, vector lattices", "description": "Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A45", "originalCode": "46A45", "name": "Sequence spaces (including Köthe sequence spaces)", "description": "Sequence spaces (including Köthe sequence spaces) [See also 46B45]", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A50", "originalCode": "46A50", "name": "Compactness in topological linear spaces; angelic spaces, etc.", "description": "Compactness in topological linear spaces; angelic spaces, etc.", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A55", "originalCode": "46A55", "name": "Convex sets in topological linear spaces; Choquet theory", "description": "Convex sets in topological linear spaces; Choquet theory [See also 52A07]", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A61", "originalCode": "46A61", "name": "Graded Fréchet spaces and tame operators", "description": "Graded Fréchet spaces and tame operators", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A63", "originalCode": "46A63", "name": "Topological invariants ((DN), (\\(\\Omega\\)), etc.) for locally convex spaces", "description": "Topological invariants ((DN), (\\(\\Omega\\)), etc.) for locally convex spaces", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A70", "originalCode": "46A70", "name": "Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)", "description": "Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A80", "originalCode": "46A80", "name": "Modular spaces", "description": "Modular spaces", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46A99", "originalCode": "46A99", "name": "Topological linear spaces and related structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "46A", "page": 119 }, { "code": "46B", "originalCode": "46Bxx", "name": "Normed linear spaces and Banach spaces; Banach lattices", "description": "Normed linear spaces and Banach spaces; Banach lattices \\{For function spaces, see 46Exx\\}", "kind": "section", "parent": "46", "page": 119 }, { "code": "46B03", "originalCode": "46B03", "name": "Isomorphic theory (including renorming) of Banach spaces", "description": "Isomorphic theory (including renorming) of Banach spaces", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B04", "originalCode": "46B04", "name": "Isometric theory of Banach spaces", "description": "Isometric theory of Banach spaces", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B06", "originalCode": "46B06", "name": "Asymptotic theory of Banach spaces", "description": "Asymptotic theory of Banach spaces [See also 52A23]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B07", "originalCode": "46B07", "name": "Local theory of Banach spaces", "description": "Local theory of Banach spaces", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B08", "originalCode": "46B08", "name": "Ultraproduct techniques in Banach space theory", "description": "Ultraproduct techniques in Banach space theory [See also 46M07]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B09", "originalCode": "46B09", "name": "Probabilistic methods in Banach space theory", "description": "Probabilistic methods in Banach space theory [See also 60Bxx]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B10", "originalCode": "46B10", "name": "Duality and reflexivity in normed linear and Banach spaces", "description": "Duality and reflexivity in normed linear and Banach spaces [See also 46A25]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B15", "originalCode": "46B15", "name": "Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces", "description": "Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces [See also 46A35, 42C15]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B20", "originalCode": "46B20", "name": "Geometry and structure of normed linear spaces", "description": "Geometry and structure of normed linear spaces", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B22", "originalCode": "46B22", "name": "Radon-Nikodým, Kre?n-Milman and related properties", "description": "Radon-Nikodým, Kre?n-Milman and related properties [See also 46G10]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B25", "originalCode": "46B25", "name": "Classical Banach spaces in the general theory", "description": "Classical Banach spaces in the general theory", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B26", "originalCode": "46B26", "name": "Nonseparable Banach spaces", "description": "Nonseparable Banach spaces", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B28", "originalCode": "46B28", "name": "Spaces of operators; tensor products; approximation properties", "description": "Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B40", "originalCode": "46B40", "name": "Ordered normed spaces", "description": "Ordered normed spaces [See also 46A40, 46B42]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B42", "originalCode": "46B42", "name": "Banach lattices", "description": "Banach lattices [See also 46A40, 46B40]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B45", "originalCode": "46B45", "name": "Banach sequence spaces", "description": "Banach sequence spaces [See also 46A45]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B50", "originalCode": "46B50", "name": "Compactness in Banach (or normed) spaces", "description": "Compactness in Banach (or normed) spaces", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B70", "originalCode": "46B70", "name": "Interpolation between normed linear spaces", "description": "Interpolation between normed linear spaces [See also 46M35]", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B80", "originalCode": "46B80", "name": "Nonlinear classification of Banach spaces; nonlinear quotients", "description": "Nonlinear classification of Banach spaces; nonlinear quotients", "kind": "subject", "parent": "46B", "page": 119 }, { "code": "46B85", "originalCode": "46B85", "name": "Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science", "description": "Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx]", "kind": "subject", "parent": "46B", "page": 120 }, { "code": "46B87", "originalCode": "46B87", "name": "Lineability in functional analysis", "description": "Lineability in functional analysis [See also 15A03]", "kind": "subject", "parent": "46B", "page": 120 }, { "code": "46B99", "originalCode": "46B99", "name": "Normed linear spaces and Banach spaces; Banach lattices", "description": "None of the above, but in this section", "kind": "subject", "parent": "46B", "page": 120 }, { "code": "46C", "originalCode": "46Cxx", "name": "Inner product spaces and their generalizations, Hilbert spaces", "description": "Inner product spaces and their generalizations, Hilbert spaces \\{For function spaces, see 46Exx\\}", "kind": "section", "parent": "46", "page": 120 }, { "code": "46C05", "originalCode": "46C05", "name": "Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)", "description": "Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)", "kind": "subject", "parent": "46C", "page": 120 }, { "code": "46C07", "originalCode": "46C07", "name": "Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)", "description": "Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]", "kind": "subject", "parent": "46C", "page": 120 }, { "code": "46C15", "originalCode": "46C15", "name": "Characterizations of Hilbert spaces", "description": "Characterizations of Hilbert spaces", "kind": "subject", "parent": "46C", "page": 120 }, { "code": "46C20", "originalCode": "46C20", "name": "Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.)", "description": "Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) [See also 47B50]", "kind": "subject", "parent": "46C", "page": 120 }, { "code": "46C50", "originalCode": "46C50", "name": "Generalizations of inner products (semi-inner products, partial inner products, etc.)", "description": "Generalizations of inner products (semi-inner products, partial inner products, etc.)", "kind": "subject", "parent": "46C", "page": 120 }, { "code": "46C99", "originalCode": "46C99", "name": "Inner product spaces and their generalizations, Hilbert spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "46C", "page": 120 }, { "code": "46E", "originalCode": "46Exx", "name": "Linear function spaces and their duals", "description": "Linear function spaces and their duals [See also 30H05, 32A38, 46F05] \\{For function algebras, see 46J10\\}", "kind": "section", "parent": "46", "page": 120 }, { "code": "46E05", "originalCode": "46E05", "name": "Lattices of continuous, differentiable or analytic functions", "description": "Lattices of continuous, differentiable or analytic functions", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E10", "originalCode": "46E10", "name": "Topological linear spaces of continuous, differentiable or analytic functions", "description": "Topological linear spaces of continuous, differentiable or analytic functions", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E15", "originalCode": "46E15", "name": "Banach spaces of continuous, differentiable or analytic functions", "description": "Banach spaces of continuous, differentiable or analytic functions", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E20", "originalCode": "46E20", "name": "Hilbert spaces of continuous, differentiable or analytic functions", "description": "Hilbert spaces of continuous, differentiable or analytic functions", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E22", "originalCode": "46E22", "name": "Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)", "description": "Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E25", "originalCode": "46E25", "name": "Rings and algebras of continuous, differentiable or analytic functions", "description": "Rings and algebras of continuous, differentiable or analytic functions \\{For Banach function algebras, see 46J10, 46J15\\}", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E27", "originalCode": "46E27", "name": "Spaces of measures", "description": "Spaces of measures [See also 28A33, 46Gxx]", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E30", "originalCode": "46E30", "name": "Spaces of measurable functions (\\(L^p\\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)", "description": "Spaces of measurable functions (\\(L^p\\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E35", "originalCode": "46E35", "name": "Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems", "description": "Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E36", "originalCode": "46E36", "name": "Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces", "description": "Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E39", "originalCode": "46E39", "name": "Sobolev (and similar kinds of) spaces of functions of discrete variables", "description": "Sobolev (and similar kinds of) spaces of functions of discrete variables", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E40", "originalCode": "46E40", "name": "Spaces of vector- and operator-valued functions", "description": "Spaces of vector- and operator-valued functions", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E50", "originalCode": "46E50", "name": "Spaces of differentiable or holomorphic functions on infinite-dimensional spaces", "description": "Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46E99", "originalCode": "46E99", "name": "Linear function spaces and their duals", "description": "None of the above, but in this section", "kind": "subject", "parent": "46E", "page": 120 }, { "code": "46F", "originalCode": "46Fxx", "name": "Distributions, generalized functions, distribution spaces", "description": "Distributions, generalized functions, distribution spaces [See also 46T30]", "kind": "section", "parent": "46", "page": 121 }, { "code": "46F05", "originalCode": "46F05", "name": "Topological linear spaces of test functions, distributions and ultradistributions", "description": "Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]", "kind": "subject", "parent": "46F", "page": 121 }, { "code": "46F10", "originalCode": "46F10", "name": "Operations with distributions and generalized functions", "description": "Operations with distributions and generalized functions", "kind": "subject", "parent": "46F", "page": 121 }, { "code": "46F12", "originalCode": "46F12", "name": "Integral transforms in distribution spaces", "description": "Integral transforms in distribution spaces [See also 42-XX, 44-XX]", "kind": "subject", "parent": "46F", "page": 121 }, { "code": "46F15", "originalCode": "46F15", "name": "Hyperfunctions, analytic functionals", "description": "Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]", "kind": "subject", "parent": "46F", "page": 121 }, { "code": "46F20", "originalCode": "46F20", "name": "Distributions and ultradistributions as boundary values of analytic functions", "description": "Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]", "kind": "subject", "parent": "46F", "page": 121 }, { "code": "46F25", "originalCode": "46F25", "name": "Distributions on infinite-dimensional spaces", "description": "Distributions on infinite-dimensional spaces [See also 58C35]", "kind": "subject", "parent": "46F", "page": 121 }, { "code": "46F30", "originalCode": "46F30", "name": "Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)", "description": "Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)", "kind": "subject", "parent": "46F", "page": 121 }, { "code": "46F99", "originalCode": "46F99", "name": "Distributions, generalized functions, distribution spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "46F", "page": 121 }, { "code": "46G", "originalCode": "46Gxx", "name": "Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)", "description": "Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]", "kind": "section", "parent": "46", "page": 121 }, { "code": "46G05", "originalCode": "46G05", "name": "Derivatives of functions in infinite-dimensional spaces", "description": "Derivatives of functions in infinite-dimensional spaces [See also 46T20, 58C20, 58C25]", "kind": "subject", "parent": "46G", "page": 121 }, { "code": "46G10", "originalCode": "46G10", "name": "Vector-valued measures and integration", "description": "Vector-valued measures and integration [See also 26E20, 28B05, 46B22]", "kind": "subject", "parent": "46G", "page": 121 }, { "code": "46G12", "originalCode": "46G12", "name": "Measures and integration on abstract linear spaces", "description": "Measures and integration on abstract linear spaces [See also 28C20, 46T12]", "kind": "subject", "parent": "46G", "page": 121 }, { "code": "46G15", "originalCode": "46G15", "name": "Functional analytic lifting theory", "description": "Functional analytic lifting theory [See also 28A51]", "kind": "subject", "parent": "46G", "page": 121 }, { "code": "46G20", "originalCode": "46G20", "name": "Infinite-dimensional holomorphy", "description": "Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]", "kind": "subject", "parent": "46G", "page": 121 }, { "code": "46G25", "originalCode": "46G25", "name": "(Spaces of) multilinear mappings, polynomials", "description": "(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]", "kind": "subject", "parent": "46G", "page": 121 }, { "code": "46G99", "originalCode": "46G99", "name": "Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)", "description": "None of the above, but in this section", "kind": "subject", "parent": "46G", "page": 121 }, { "code": "46H", "originalCode": "46Hxx", "name": "Topological algebras, normed rings and algebras, Banach algebras", "description": "Topological algebras, normed rings and algebras, Banach algebras \\{For group algebras, convolution algebras and measure algebras, see 43A10, 43A20\\}", "kind": "section", "parent": "46", "page": 121 }, { "code": "46H05", "originalCode": "46H05", "name": "General theory of topological algebras", "description": "General theory of topological algebras", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H10", "originalCode": "46H10", "name": "Ideals and subalgebras", "description": "Ideals and subalgebras", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H15", "originalCode": "46H15", "name": "Representations of topological algebras", "description": "Representations of topological algebras", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H20", "originalCode": "46H20", "name": "Structure, classification of topological algebras", "description": "Structure, classification of topological algebras", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H25", "originalCode": "46H25", "name": "Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)", "description": "Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H30", "originalCode": "46H30", "name": "Functional calculus in topological algebras", "description": "Functional calculus in topological algebras [See also 47A60]", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H35", "originalCode": "46H35", "name": "Topological algebras of operators", "description": "Topological algebras of operators [See mainly 47Lxx]", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H40", "originalCode": "46H40", "name": "Automatic continuity", "description": "Automatic continuity", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H70", "originalCode": "46H70", "name": "Nonassociative topological algebras", "description": "Nonassociative topological algebras [See also 46K70, 46L70]", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46H99", "originalCode": "46H99", "name": "Topological algebras, normed rings and algebras, Banach algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "46H", "page": 121 }, { "code": "46J", "originalCode": "46Jxx", "name": "Commutative Banach algebras and commutative topological algebras", "description": "Commutative Banach algebras and commutative topological algebras [See also 46E25]", "kind": "section", "parent": "46", "page": 122 }, { "code": "46J05", "originalCode": "46J05", "name": "General theory of commutative topological algebras", "description": "General theory of commutative topological algebras", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46J10", "originalCode": "46J10", "name": "Banach algebras of continuous functions, function algebras", "description": "Banach algebras of continuous functions, function algebras [See also 46E25]", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46J15", "originalCode": "46J15", "name": "Banach algebras of differentiable or analytic functions, \\(H^p\\)-spaces", "description": "Banach algebras of differentiable or analytic functions, \\(H^p\\)-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46J20", "originalCode": "46J20", "name": "Ideals, maximal ideals, boundaries", "description": "Ideals, maximal ideals, boundaries", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46J25", "originalCode": "46J25", "name": "Representations of commutative topological algebras", "description": "Representations of commutative topological algebras", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46J30", "originalCode": "46J30", "name": "Subalgebras of commutative topological algebras", "description": "Subalgebras of commutative topological algebras", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46J40", "originalCode": "46J40", "name": "Structure and classification of commutative topological algebras", "description": "Structure and classification of commutative topological algebras", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46J45", "originalCode": "46J45", "name": "Radical Banach algebras", "description": "Radical Banach algebras", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46J99", "originalCode": "46J99", "name": "Commutative Banach algebras and commutative topological algebras", "description": "None of the above, but in this section", "kind": "subject", "parent": "46J", "page": 122 }, { "code": "46K", "originalCode": "46Kxx", "name": "Topological (rings and) algebras with an involution", "description": "Topological (rings and) algebras with an involution [See also 16W10]", "kind": "section", "parent": "46", "page": 122 }, { "code": "46K05", "originalCode": "46K05", "name": "General theory of topological algebras with involution", "description": "General theory of topological algebras with involution", "kind": "subject", "parent": "46K", "page": 122 }, { "code": "46K10", "originalCode": "46K10", "name": "Representations of topological algebras with involution", "description": "Representations of topological algebras with involution", "kind": "subject", "parent": "46K", "page": 122 }, { "code": "46K15", "originalCode": "46K15", "name": "Hilbert algebras", "description": "Hilbert algebras", "kind": "subject", "parent": "46K", "page": 122 }, { "code": "46K50", "originalCode": "46K50", "name": "Nonselfadjoint (sub)algebras in algebras with involution", "description": "Nonselfadjoint (sub)algebras in algebras with involution", "kind": "subject", "parent": "46K", "page": 122 }, { "code": "46K70", "originalCode": "46K70", "name": "Nonassociative topological algebras with an involution", "description": "Nonassociative topological algebras with an involution [See also 46H70, 46L70]", "kind": "subject", "parent": "46K", "page": 122 }, { "code": "46K99", "originalCode": "46K99", "name": "Topological (rings and) algebras with an involution", "description": "None of the above, but in this section", "kind": "subject", "parent": "46K", "page": 122 }, { "code": "46L", "originalCode": "46Lxx", "name": "Selfadjoint operator algebras (\\(C^*\\)-algebras, von Neumann (\\(W^*\\)-) algebras, etc.)", "description": "Selfadjoint operator algebras (\\(C^*\\)-algebras, von Neumann (\\(W^*\\)-) algebras, etc.) [See also 22D25, 47Lxx]", "kind": "section", "parent": "46", "page": 122 }, { "code": "46L05", "originalCode": "46L05", "name": "General theory of \\(C^*\\)-algebras", "description": "General theory of \\(C^*\\)-algebras", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L06", "originalCode": "46L06", "name": "Tensor products of \\(C^*\\)-algebras", "description": "Tensor products of \\(C^*\\)-algebras", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L07", "originalCode": "46L07", "name": "Operator spaces and completely bounded maps", "description": "Operator spaces and completely bounded maps [See also 47L25]", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L08", "originalCode": "46L08", "name": "\\(C^*\\)-modules", "description": "\\(C^*\\)-modules", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L09", "originalCode": "46L09", "name": "Free products of \\(C^*\\)-algebras", "description": "Free products of \\(C^*\\)-algebras", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L10", "originalCode": "46L10", "name": "General theory of von Neumann algebras", "description": "General theory of von Neumann algebras", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L30", "originalCode": "46L30", "name": "States of selfadjoint operator algebras", "description": "States of selfadjoint operator algebras", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L35", "originalCode": "46L35", "name": "Classifications of \\(C^*\\)-algebras", "description": "Classifications of \\(C^*\\)-algebras", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L36", "originalCode": "46L36", "name": "Classification of factors", "description": "Classification of factors", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L37", "originalCode": "46L37", "name": "Subfactors and their classification", "description": "Subfactors and their classification", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L40", "originalCode": "46L40", "name": "Automorphisms of selfadjoint operator algebras", "description": "Automorphisms of selfadjoint operator algebras", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L45", "originalCode": "46L45", "name": "Decomposition theory for \\(C^*\\)-algebras", "description": "Decomposition theory for \\(C^*\\)-algebras", "kind": "subject", "parent": "46L", "page": 122 }, { "code": "46L51", "originalCode": "46L51", "name": "Noncommutative measure and integration", "description": "Noncommutative measure and integration", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L52", "originalCode": "46L52", "name": "Noncommutative function spaces", "description": "Noncommutative function spaces", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L53", "originalCode": "46L53", "name": "Noncommutative probability and statistics", "description": "Noncommutative probability and statistics", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L54", "originalCode": "46L54", "name": "Free probability and free operator algebras", "description": "Free probability and free operator algebras", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L55", "originalCode": "46L55", "name": "Noncommutative dynamical systems", "description": "Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 37A55]", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L57", "originalCode": "46L57", "name": "Derivations, dissipations and positive semigroups in \\(C^*\\)-algebras", "description": "Derivations, dissipations and positive semigroups in \\(C^*\\)-algebras", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L60", "originalCode": "46L60", "name": "Applications of selfadjoint operator algebras to physics", "description": "Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L65", "originalCode": "46L65", "name": "Quantizations, deformations for selfadjoint operator algebras", "description": "Quantizations, deformations for selfadjoint operator algebras", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L67", "originalCode": "46L67", "name": "Quantum groups (operator algebraic aspects)", "description": "Quantum groups (operator algebraic aspects)", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L70", "originalCode": "46L70", "name": "Nonassociative selfadjoint operator algebras", "description": "Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L80", "originalCode": "46L80", "name": "\\(K\\)-theory and operator algebras (including cyclic theory)", "description": "\\(K\\)-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L85", "originalCode": "46L85", "name": "Noncommutative topology", "description": "Noncommutative topology [See also 58B32, 58B34, 58J22]", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L87", "originalCode": "46L87", "name": "Noncommutative differential geometry", "description": "Noncommutative differential geometry [See also 58B32, 58B34, 58J22]", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L89", "originalCode": "46L89", "name": "Other ``noncommutative'' mathematics based on \\(C^*\\)-algebra theory", "description": "Other ``noncommutative'' mathematics based on \\(C^*\\)-algebra theory [See also 58B32, 58B34, 58J22]", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46L99", "originalCode": "46L99", "name": "Selfadjoint operator algebras (\\(C^*\\)-algebras, von Neumann (\\(W^*\\)-) algebras, etc.)", "description": "None of the above, but in this section", "kind": "subject", "parent": "46L", "page": 123 }, { "code": "46M", "originalCode": "46Mxx", "name": "Methods of category theory in functional analysis", "description": "Methods of category theory in functional analysis [See also 18-XX]", "kind": "section", "parent": "46", "page": 123 }, { "code": "46M05", "originalCode": "46M05", "name": "Tensor products in functional analysis", "description": "Tensor products in functional analysis [See also 46A32, 46B28, 47A80]", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46M07", "originalCode": "46M07", "name": "Ultraproducts in functional analysis", "description": "Ultraproducts in functional analysis [See also 46B08, 46S20]", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46M10", "originalCode": "46M10", "name": "Projective and injective objects in functional analysis", "description": "Projective and injective objects in functional analysis [See also 46A22]", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46M15", "originalCode": "46M15", "name": "Categories, functors in functional analysis", "description": "Categories, functors in functional analysis \\{For \\(K\\)-theory, Ext, etc., see 19K33, 46L80, 46M18, 46M20\\}", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46M18", "originalCode": "46M18", "name": "Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.)", "description": "Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.)", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46M20", "originalCode": "46M20", "name": "Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)", "description": "Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) [See also 14F06, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46M35", "originalCode": "46M35", "name": "Abstract interpolation of topological vector spaces", "description": "Abstract interpolation of topological vector spaces [See also 46B70]", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46M40", "originalCode": "46M40", "name": "Inductive and projective limits in functional analysis", "description": "Inductive and projective limits in functional analysis [See also 46A13]", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46M99", "originalCode": "46M99", "name": "Methods of category theory in functional analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "46M", "page": 123 }, { "code": "46N", "originalCode": "46Nxx", "name": "Miscellaneous applications of functional analysis", "description": "Miscellaneous applications of functional analysis [See also 47Nxx]", "kind": "section", "parent": "46", "page": 123 }, { "code": "46N10", "originalCode": "46N10", "name": "Applications of functional analysis in optimization, convex analysis, mathematical programming, economics", "description": "Applications of functional analysis in optimization, convex analysis, mathematical programming, economics", "kind": "subject", "parent": "46N", "page": 123 }, { "code": "46N20", "originalCode": "46N20", "name": "Applications of functional analysis to differential and integral equations", "description": "Applications of functional analysis to differential and integral equations", "kind": "subject", "parent": "46N", "page": 123 }, { "code": "46N30", "originalCode": "46N30", "name": "Applications of functional analysis in probability theory and statistics", "description": "Applications of functional analysis in probability theory and statistics", "kind": "subject", "parent": "46N", "page": 123 }, { "code": "46N40", "originalCode": "46N40", "name": "Applications of functional analysis in numerical analysis", "description": "Applications of functional analysis in numerical analysis [See also 65Jxx]", "kind": "subject", "parent": "46N", "page": 123 }, { "code": "46N50", "originalCode": "46N50", "name": "Applications of functional analysis in quantum physics", "description": "Applications of functional analysis in quantum physics", "kind": "subject", "parent": "46N", "page": 123 }, { "code": "46N55", "originalCode": "46N55", "name": "Applications of functional analysis in statistical physics", "description": "Applications of functional analysis in statistical physics", "kind": "subject", "parent": "46N", "page": 123 }, { "code": "46N60", "originalCode": "46N60", "name": "Applications of functional analysis in biology and other sciences", "description": "Applications of functional analysis in biology and other sciences", "kind": "subject", "parent": "46N", "page": 123 }, { "code": "46N99", "originalCode": "46N99", "name": "Miscellaneous applications of functional analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "46N", "page": 123 }, { "code": "46S", "originalCode": "46Sxx", "name": "Other (nonclassical) types of functional analysis", "description": "Other (nonclassical) types of functional analysis [See also 47Sxx]", "kind": "section", "parent": "46", "page": 124 }, { "code": "46S05", "originalCode": "46S05", "name": "Quaternionic functional analysis", "description": "Quaternionic functional analysis", "kind": "subject", "parent": "46S", "page": 124 }, { "code": "46S10", "originalCode": "46S10", "name": "Functional analysis over fields other than \\(\\mathbb{R}\\) or \\(\\mathbb{C}\\) or the quaternions; non-Archimedean functional analysis", "description": "Functional analysis over fields other than \\(\\mathbb{R}\\) or \\(\\mathbb{C}\\) or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]", "kind": "subject", "parent": "46S", "page": 124 }, { "code": "46S20", "originalCode": "46S20", "name": "Nonstandard functional analysis", "description": "Nonstandard functional analysis [See also 03H05]", "kind": "subject", "parent": "46S", "page": 124 }, { "code": "46S30", "originalCode": "46S30", "name": "Constructive functional analysis", "description": "Constructive functional analysis [See also 03F60]", "kind": "subject", "parent": "46S", "page": 124 }, { "code": "46S40", "originalCode": "46S40", "name": "Fuzzy functional analysis", "description": "Fuzzy functional analysis [See also 03E72]", "kind": "subject", "parent": "46S", "page": 124 }, { "code": "46S50", "originalCode": "46S50", "name": "Functional analysis in probabilistic metric linear spaces", "description": "Functional analysis in probabilistic metric linear spaces", "kind": "subject", "parent": "46S", "page": 124 }, { "code": "46S60", "originalCode": "46S60", "name": "Functional analysis on superspaces (supermanifolds) or graded spaces", "description": "Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50, 58C50]", "kind": "subject", "parent": "46S", "page": 124 }, { "code": "46S99", "originalCode": "46S99", "name": "Other (nonclassical) types of functional analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "46S", "page": 124 }, { "code": "46T", "originalCode": "46Txx", "name": "Nonlinear functional analysis", "description": "Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]", "kind": "section", "parent": "46", "page": 124 }, { "code": "46T05", "originalCode": "46T05", "name": "Infinite-dimensional manifolds", "description": "Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx]", "kind": "subject", "parent": "46T", "page": 124 }, { "code": "46T10", "originalCode": "46T10", "name": "Manifolds of mappings", "description": "Manifolds of mappings", "kind": "subject", "parent": "46T", "page": 124 }, { "code": "46T12", "originalCode": "46T12", "name": "Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds", "description": "Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX]", "kind": "subject", "parent": "46T", "page": 124 }, { "code": "46T20", "originalCode": "46T20", "name": "Continuous and differentiable maps in nonlinear functional analysis", "description": "Continuous and differentiable maps in nonlinear functional analysis [See also 46G05]", "kind": "subject", "parent": "46T", "page": 124 }, { "code": "46T25", "originalCode": "46T25", "name": "Holomorphic maps in nonlinear functional analysis", "description": "Holomorphic maps in nonlinear functional analysis [See also 46G20]", "kind": "subject", "parent": "46T", "page": 124 }, { "code": "46T30", "originalCode": "46T30", "name": "Distributions and generalized functions on nonlinear spaces", "description": "Distributions and generalized functions on nonlinear spaces [See also 46Fxx]", "kind": "subject", "parent": "46T", "page": 124 }, { "code": "46T99", "originalCode": "46T99", "name": "Nonlinear functional analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "46T", "page": 124 }, { "code": "47", "originalCode": "47-XX", "name": "Operator theory", "description": "Operator theory", "kind": "class", "parent": null, "page": 124 }, { "code": "47-00", "originalCode": "47-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operator theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operator theory", "kind": "subject", "parent": "47", "page": 124 }, { "code": "47-01", "originalCode": "47-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory", "kind": "subject", "parent": "47", "page": 124 }, { "code": "47-02", "originalCode": "47-02", "name": "Research exposition (monographs, survey articles) pertaining to operator theory", "description": "Research exposition (monographs, survey articles) pertaining to operator theory", "kind": "subject", "parent": "47", "page": 124 }, { "code": "47-03", "originalCode": "47-03", "name": "History of operator theory", "description": "History of operator theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "47", "page": 124 }, { "code": "47-04", "originalCode": "47-04", "name": "Software, source code, etc. for problems pertaining to operator theory", "description": "Software, source code, etc. for problems pertaining to operator theory", "kind": "subject", "parent": "47", "page": 124 }, { "code": "47-06", "originalCode": "47-06", "name": "Proceedings, conferences, collections, etc. pertaining to operator theory", "description": "Proceedings, conferences, collections, etc. pertaining to operator theory", "kind": "subject", "parent": "47", "page": 124 }, { "code": "47-08", "originalCode": "47-08", "name": "Computational methods for problems pertaining to operator theory", "description": "Computational methods for problems pertaining to operator theory", "kind": "subject", "parent": "47", "page": 124 }, { "code": "47-11", "originalCode": "47-11", "name": "Research data for problems pertaining to operator theory", "description": "Research data for problems pertaining to operator theory", "kind": "subject", "parent": "47", "page": 124 }, { "code": "47A", "originalCode": "47Axx", "name": "General theory of linear operators", "description": "General theory of linear operators", "kind": "section", "parent": "47", "page": 125 }, { "code": "47A05", "originalCode": "47A05", "name": "General (adjoints, conjugates, products, inverses, domains, ranges, etc.)", "description": "General (adjoints, conjugates, products, inverses, domains, ranges, etc.)", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A06", "originalCode": "47A06", "name": "Linear relations (multivalued linear operators)", "description": "Linear relations (multivalued linear operators)", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A07", "originalCode": "47A07", "name": "Forms (bilinear, sesquilinear, multilinear)", "description": "Forms (bilinear, sesquilinear, multilinear)", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A08", "originalCode": "47A08", "name": "Operator matrices", "description": "Operator matrices [See also 47A13]", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A10", "originalCode": "47A10", "name": "Spectrum, resolvent", "description": "Spectrum, resolvent", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A11", "originalCode": "47A11", "name": "Local spectral properties of linear operators", "description": "Local spectral properties of linear operators", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A12", "originalCode": "47A12", "name": "Numerical range, numerical radius", "description": "Numerical range, numerical radius", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A13", "originalCode": "47A13", "name": "Several-variable operator theory (spectral, Fredholm, etc.)", "description": "Several-variable operator theory (spectral, Fredholm, etc.)", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A15", "originalCode": "47A15", "name": "Invariant subspaces of linear operators", "description": "Invariant subspaces of linear operators [See also 47A46]", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A16", "originalCode": "47A16", "name": "Cyclic vectors, hypercyclic and chaotic operators", "description": "Cyclic vectors, hypercyclic and chaotic operators", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A20", "originalCode": "47A20", "name": "Dilations, extensions, compressions of linear operators", "description": "Dilations, extensions, compressions of linear operators", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A25", "originalCode": "47A25", "name": "Spectral sets of linear operators", "description": "Spectral sets of linear operators", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A30", "originalCode": "47A30", "name": "Norms (inequalities, more than one norm, etc.) of linear operators", "description": "Norms (inequalities, more than one norm, etc.) of linear operators", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A35", "originalCode": "47A35", "name": "Ergodic theory of linear operators", "description": "Ergodic theory of linear operators [See also 28Dxx, 37Axx]", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A40", "originalCode": "47A40", "name": "Scattering theory of linear operators", "description": "Scattering theory of linear operators [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A45", "originalCode": "47A45", "name": "Canonical models for contractions and nonselfadjoint linear operators", "description": "Canonical models for contractions and nonselfadjoint linear operators", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A46", "originalCode": "47A46", "name": "Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.", "description": "Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A48", "originalCode": "47A48", "name": "Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.", "description": "Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A50", "originalCode": "47A50", "name": "Equations and inequalities involving linear operators, with vector unknowns", "description": "Equations and inequalities involving linear operators, with vector unknowns", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A52", "originalCode": "47A52", "name": "Linear operators and ill-posed problems, regularization", "description": "Linear operators and ill-posed problems, regularization [See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A53", "originalCode": "47A53", "name": "(Semi-) Fredholm operators; index theories", "description": "(Semi-) Fredholm operators; index theories [See also 58B15, 58J20]", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A55", "originalCode": "47A55", "name": "Perturbation theory of linear operators", "description": "Perturbation theory of linear operators [See also 47H14, 58J37, 70H09, 81Q15]", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A56", "originalCode": "47A56", "name": "Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)", "description": "Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A57", "originalCode": "47A57", "name": "Linear operator methods in interpolation, moment and extension problems", "description": "Linear operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A58", "originalCode": "47A58", "name": "Linear operator approximation theory", "description": "Linear operator approximation theory", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A60", "originalCode": "47A60", "name": "Functional calculus for linear operators", "description": "Functional calculus for linear operators", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A62", "originalCode": "47A62", "name": "Equations involving linear operators, with operator unknowns", "description": "Equations involving linear operators, with operator unknowns", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A63", "originalCode": "47A63", "name": "Linear operator inequalities", "description": "Linear operator inequalities", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A64", "originalCode": "47A64", "name": "Operator means involving linear operators, shorted linear operators, etc.", "description": "Operator means involving linear operators, shorted linear operators, etc.", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A65", "originalCode": "47A65", "name": "Structure theory of linear operators", "description": "Structure theory of linear operators", "kind": "subject", "parent": "47A", "page": 125 }, { "code": "47A66", "originalCode": "47A66", "name": "Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators", "description": "Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators", "kind": "subject", "parent": "47A", "page": 126 }, { "code": "47A67", "originalCode": "47A67", "name": "Representation theory of linear operators", "description": "Representation theory of linear operators", "kind": "subject", "parent": "47A", "page": 126 }, { "code": "47A68", "originalCode": "47A68", "name": "Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators", "description": "Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators", "kind": "subject", "parent": "47A", "page": 126 }, { "code": "47A70", "originalCode": "47A70", "name": "(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces", "description": "(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces", "kind": "subject", "parent": "47A", "page": 126 }, { "code": "47A75", "originalCode": "47A75", "name": "Eigenvalue problems for linear operators", "description": "Eigenvalue problems for linear operators [See also 47J10, 49R05]", "kind": "subject", "parent": "47A", "page": 126 }, { "code": "47A80", "originalCode": "47A80", "name": "Tensor products of linear operators", "description": "Tensor products of linear operators [See also 46M05]", "kind": "subject", "parent": "47A", "page": 126 }, { "code": "47A99", "originalCode": "47A99", "name": "General theory of linear operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "47A", "page": 126 }, { "code": "47B", "originalCode": "47Bxx", "name": "Special classes of linear operators", "description": "Special classes of linear operators", "kind": "section", "parent": "47", "page": 126 }, { "code": "47B01", "originalCode": "47B01", "name": "Operators on Banach spaces", "description": "Operators on Banach spaces", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B02", "originalCode": "47B02", "name": "Operators on Hilbert spaces (general)", "description": "Operators on Hilbert spaces (general)", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B06", "originalCode": "47B06", "name": "Riesz operators; eigenvalue distributions; approximation numbers, \\(s\\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators", "description": "Riesz operators; eigenvalue distributions; approximation numbers, \\(s\\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B07", "originalCode": "47B07", "name": "Linear operators defined by compactness properties", "description": "Linear operators defined by compactness properties", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B10", "originalCode": "47B10", "name": "Linear operators belonging to operator ideals (nuclear, \\(p\\)-summing, in the Schatten-von Neumann classes, etc.)", "description": "Linear operators belonging to operator ideals (nuclear, \\(p\\)-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B12", "originalCode": "47B12", "name": "Sectorial operators", "description": "Sectorial operators", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B13", "originalCode": "47B13", "name": "Cowen-Douglas operators", "description": "Cowen-Douglas operators", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B15", "originalCode": "47B15", "name": "Hermitian and normal operators (spectral measures, functional calculus, etc.)", "description": "Hermitian and normal operators (spectral measures, functional calculus, etc.)", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B20", "originalCode": "47B20", "name": "Subnormal operators, hyponormal operators, etc.", "description": "Subnormal operators, hyponormal operators, etc.", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B25", "originalCode": "47B25", "name": "Linear symmetric and selfadjoint operators (unbounded)", "description": "Linear symmetric and selfadjoint operators (unbounded)", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B28", "originalCode": "47B28", "name": "Nonselfadjoint operators", "description": "Nonselfadjoint operators [See also 47A45, 81Q12]", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B32", "originalCode": "47B32", "name": "Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)", "description": "Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B33", "originalCode": "47B33", "name": "Linear composition operators", "description": "Linear composition operators", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B34", "originalCode": "47B34", "name": "Kernel operators", "description": "Kernel operators", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B35", "originalCode": "47B35", "name": "Toeplitz operators, Hankel operators, Wiener-Hopf operators", "description": "Toeplitz operators, Hankel operators, Wiener-Hopf operators \\{For other integral operators, see also 45P05, 47G10\\} [See also 32A25, 32M15]", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B36", "originalCode": "47B36", "name": "Jacobi (tridiagonal) operators (matrices) and generalizations", "description": "Jacobi (tridiagonal) operators (matrices) and generalizations", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B37", "originalCode": "47B37", "name": "Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)", "description": "Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B38", "originalCode": "47B38", "name": "Linear operators on function spaces (general)", "description": "Linear operators on function spaces (general)", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B39", "originalCode": "47B39", "name": "Linear difference operators", "description": "Linear difference operators [See also 39A70]", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B40", "originalCode": "47B40", "name": "Spectral operators, decomposable operators, well-bounded operators, etc.", "description": "Spectral operators, decomposable operators, well-bounded operators, etc.", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B44", "originalCode": "47B44", "name": "Linear accretive operators, dissipative operators, etc.", "description": "Linear accretive operators, dissipative operators, etc.", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B47", "originalCode": "47B47", "name": "Commutators, derivations, elementary operators, etc.", "description": "Commutators, derivations, elementary operators, etc.", "kind": "subject", "parent": "47B", "page": 126 }, { "code": "47B48", "originalCode": "47B48", "name": "Linear operators on Banach algebras", "description": "Linear operators on Banach algebras", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B49", "originalCode": "47B49", "name": "Transformers, preservers (linear operators on spaces of linear operators)", "description": "Transformers, preservers (linear operators on spaces of linear operators)", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B50", "originalCode": "47B50", "name": "Linear operators on spaces with an indefinite metric", "description": "Linear operators on spaces with an indefinite metric [See also 46C20]", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B60", "originalCode": "47B60", "name": "Linear operators on ordered spaces", "description": "Linear operators on ordered spaces", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B65", "originalCode": "47B65", "name": "Positive linear operators and order-bounded operators", "description": "Positive linear operators and order-bounded operators", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B80", "originalCode": "47B80", "name": "Random linear operators", "description": "Random linear operators [See also 47H40, 60H25]", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B90", "originalCode": "47B90", "name": "Operator theory and harmonic analysis", "description": "Operator theory and harmonic analysis [See also 42-XX, 43-XX, 44-XX]", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B91", "originalCode": "47B91", "name": "Operators on complex function spaces", "description": "Operators on complex function spaces", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B92", "originalCode": "47B92", "name": "Operators on real function spaces", "description": "Operators on real function spaces", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B93", "originalCode": "47B93", "name": "Operators arising in mathematical physics", "description": "Operators arising in mathematical physics", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47B99", "originalCode": "47B99", "name": "Special classes of linear operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "47B", "page": 127 }, { "code": "47C", "originalCode": "47Cxx", "name": "Individual linear operators as elements of algebraic systems", "description": "Individual linear operators as elements of algebraic systems", "kind": "section", "parent": "47", "page": 127 }, { "code": "47C05", "originalCode": "47C05", "name": "Linear operators in algebras", "description": "Linear operators in algebras", "kind": "subject", "parent": "47C", "page": 127 }, { "code": "47C10", "originalCode": "47C10", "name": "Linear operators in \\({}^*\\)-algebras", "description": "Linear operators in \\({}^*\\)-algebras", "kind": "subject", "parent": "47C", "page": 127 }, { "code": "47C15", "originalCode": "47C15", "name": "Linear operators in \\(C^*\\)- or von Neumann algebras", "description": "Linear operators in \\(C^*\\)- or von Neumann algebras", "kind": "subject", "parent": "47C", "page": 127 }, { "code": "47C99", "originalCode": "47C99", "name": "Individual linear operators as elements of algebraic systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "47C", "page": 127 }, { "code": "47D", "originalCode": "47Dxx", "name": "Groups and semigroups of linear operators, their generalizations and applications", "description": "Groups and semigroups of linear operators, their generalizations and applications", "kind": "section", "parent": "47", "page": 127 }, { "code": "47D03", "originalCode": "47D03", "name": "Groups and semigroups of linear operators", "description": "Groups and semigroups of linear operators [See also 20M20] \\{For nonlinear operators, see 47H20\\}", "kind": "subject", "parent": "47D", "page": 127 }, { "code": "47D06", "originalCode": "47D06", "name": "One-parameter semigroups and linear evolution equations", "description": "One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]", "kind": "subject", "parent": "47D", "page": 127 }, { "code": "47D07", "originalCode": "47D07", "name": "Markov semigroups and applications to diffusion processes", "description": "Markov semigroups and applications to diffusion processes \\{For Markov processes, see 60Jxx\\}", "kind": "subject", "parent": "47D", "page": 127 }, { "code": "47D08", "originalCode": "47D08", "name": "Schrödinger and Feynman-Kac semigroups", "description": "Schrödinger and Feynman-Kac semigroups", "kind": "subject", "parent": "47D", "page": 127 }, { "code": "47D09", "originalCode": "47D09", "name": "Operator sine and cosine functions and higher-order Cauchy problems", "description": "Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10]", "kind": "subject", "parent": "47D", "page": 127 }, { "code": "47D60", "originalCode": "47D60", "name": "\\(C\\)-semigroups, regularized semigroups", "description": "\\(C\\)-semigroups, regularized semigroups", "kind": "subject", "parent": "47D", "page": 127 }, { "code": "47D62", "originalCode": "47D62", "name": "Integrated semigroups", "description": "Integrated semigroups", "kind": "subject", "parent": "47D", "page": 127 }, { "code": "47D99", "originalCode": "47D99", "name": "Groups and semigroups of linear operators, their generalizations and applications", "description": "None of the above, but in this section", "kind": "subject", "parent": "47D", "page": 127 }, { "code": "47E", "originalCode": "47Exx", "name": "Ordinary differential operators", "description": "Ordinary differential operators [See also 34Bxx, 34Lxx]", "kind": "section", "parent": "47", "page": 127 }, { "code": "47E05", "originalCode": "47E05", "name": "General theory of ordinary differential operators", "description": "General theory of ordinary differential operators [Should also be assigned at least one other classification number in Section 47-XX] [See also 34Bxx, 34Lxx]", "kind": "subject", "parent": "47E", "page": 127 }, { "code": "47E07", "originalCode": "47E07", "name": "Functional-differential and differential-difference operators", "description": "Functional-differential and differential-difference operators [See also 34K08]", "kind": "subject", "parent": "47E", "page": 127 }, { "code": "47E99", "originalCode": "47E99", "name": "Ordinary differential operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "47E", "page": 127 }, { "code": "47F", "originalCode": "47Fxx", "name": "Partial differential operators", "description": "Partial differential operators [See also 35Pxx, 58Jxx]", "kind": "section", "parent": "47", "page": 128 }, { "code": "47F05", "originalCode": "47F05", "name": "General theory of partial differential operators", "description": "General theory of partial differential operators [Should also be assigned at least one other classification number in Section 47-XX] [See also 35Pxx, 58Jxx]", "kind": "subject", "parent": "47F", "page": 128 }, { "code": "47F10", "originalCode": "47F10", "name": "Elliptic operators and their generalizations", "description": "Elliptic operators and their generalizations \\{For elliptic complexes, see 58J10\\}", "kind": "subject", "parent": "47F", "page": 128 }, { "code": "47F99", "originalCode": "47F99", "name": "Partial differential operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "47F", "page": 128 }, { "code": "47G", "originalCode": "47Gxx", "name": "Integral, integro-differential, and pseudodifferential operators", "description": "Integral, integro-differential, and pseudodifferential operators [See also 58Jxx]", "kind": "section", "parent": "47", "page": 128 }, { "code": "47G10", "originalCode": "47G10", "name": "Integral operators", "description": "Integral operators [See also 45P05]", "kind": "subject", "parent": "47G", "page": 128 }, { "code": "47G20", "originalCode": "47G20", "name": "Integro-differential operators", "description": "Integro-differential operators [See also 34K30, 35R09, 35R10, 45J05, 45K05]", "kind": "subject", "parent": "47G", "page": 128 }, { "code": "47G30", "originalCode": "47G30", "name": "Pseudodifferential operators", "description": "Pseudodifferential operators [See also 35Sxx, 58Jxx]", "kind": "subject", "parent": "47G", "page": 128 }, { "code": "47G40", "originalCode": "47G40", "name": "Potential operators", "description": "Potential operators [See also 31-XX]", "kind": "subject", "parent": "47G", "page": 128 }, { "code": "47G99", "originalCode": "47G99", "name": "Integral, integro-differential, and pseudodifferential operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "47G", "page": 128 }, { "code": "47H", "originalCode": "47Hxx", "name": "Nonlinear operators and their properties", "description": "Nonlinear operators and their properties \\{For global and geometric aspects, see 49J53, 58-XX, especially 58Cxx\\}", "kind": "section", "parent": "47", "page": 128 }, { "code": "47H04", "originalCode": "47H04", "name": "Set-valued operators", "description": "Set-valued operators [See also 28B20, 54C60, 58C06]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H05", "originalCode": "47H05", "name": "Monotone operators and generalizations", "description": "Monotone operators and generalizations", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H06", "originalCode": "47H06", "name": "Nonlinear accretive operators, dissipative operators, etc.", "description": "Nonlinear accretive operators, dissipative operators, etc.", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H07", "originalCode": "47H07", "name": "Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces", "description": "Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H08", "originalCode": "47H08", "name": "Measures of noncompactness and condensing mappings, \\(K\\)-set contractions, etc.", "description": "Measures of noncompactness and condensing mappings, \\(K\\)-set contractions, etc.", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H09", "originalCode": "47H09", "name": "Contraction-type mappings, nonexpansive mappings, \\(A\\)-proper mappings, etc.", "description": "Contraction-type mappings, nonexpansive mappings, \\(A\\)-proper mappings, etc.", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H10", "originalCode": "47H10", "name": "Fixed-point theorems", "description": "Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H11", "originalCode": "47H11", "name": "Degree theory for nonlinear operators", "description": "Degree theory for nonlinear operators [See also 55M25, 58C30]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H14", "originalCode": "47H14", "name": "Perturbations of nonlinear operators", "description": "Perturbations of nonlinear operators [See also 47A55, 58J37, 70H09, 70K60, 81Q15]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H20", "originalCode": "47H20", "name": "Semigroups of nonlinear operators", "description": "Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H25", "originalCode": "47H25", "name": "Nonlinear ergodic theorems", "description": "Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H30", "originalCode": "47H30", "name": "Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.)", "description": "Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) [See also 45Gxx, 45P05]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H40", "originalCode": "47H40", "name": "Random nonlinear operators", "description": "Random nonlinear operators [See also 47B80, 60H25]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H60", "originalCode": "47H60", "name": "Multilinear and polynomial operators", "description": "Multilinear and polynomial operators [See also 46G25]", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47H99", "originalCode": "47H99", "name": "Nonlinear operators and their properties", "description": "None of the above, but in this section", "kind": "subject", "parent": "47H", "page": 128 }, { "code": "47J", "originalCode": "47Jxx", "name": "Equations and inequalities involving nonlinear operators", "description": "Equations and inequalities involving nonlinear operators [See also 46Txx] \\{For global and geometric aspects, see 58-XX\\}", "kind": "section", "parent": "47", "page": 129 }, { "code": "47J05", "originalCode": "47J05", "name": "Equations involving nonlinear operators (general)", "description": "Equations involving nonlinear operators (general) [See also 47H10, 47J25]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J06", "originalCode": "47J06", "name": "Nonlinear ill-posed problems", "description": "Nonlinear ill-posed problems [See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J07", "originalCode": "47J07", "name": "Abstract inverse mapping and implicit function theorems involving nonlinear operators", "description": "Abstract inverse mapping and implicit function theorems involving nonlinear operators [See also 46T20, 58C15]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J10", "originalCode": "47J10", "name": "Nonlinear spectral theory, nonlinear eigenvalue problems", "description": "Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J15", "originalCode": "47J15", "name": "Abstract bifurcation theory involving nonlinear operators", "description": "Abstract bifurcation theory involving nonlinear operators [See also 34C23, 37Gxx, 58E07, 58E09]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J20", "originalCode": "47J20", "name": "Variational and other types of inequalities involving nonlinear operators (general)", "description": "Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J22", "originalCode": "47J22", "name": "Variational and other types of inclusions", "description": "Variational and other types of inclusions [See also 34A60, 49J21, 49K21]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J25", "originalCode": "47J25", "name": "Iterative procedures involving nonlinear operators", "description": "Iterative procedures involving nonlinear operators [See also 47J26, 65J15]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J26", "originalCode": "47J26", "name": "Fixed-point iterations", "description": "Fixed-point iterations [See also 47J25]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J30", "originalCode": "47J30", "name": "Variational methods involving nonlinear operators", "description": "Variational methods involving nonlinear operators [See also 58Exx]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J35", "originalCode": "47J35", "name": "Nonlinear evolution equations", "description": "Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J40", "originalCode": "47J40", "name": "Equations with nonlinear hysteresis operators", "description": "Equations with nonlinear hysteresis operators [See also 34C55, 74N30]", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47J99", "originalCode": "47J99", "name": "Equations and inequalities involving nonlinear operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "47J", "page": 129 }, { "code": "47L", "originalCode": "47Lxx", "name": "Linear spaces and algebras of operators", "description": "Linear spaces and algebras of operators [See also 46Lxx]", "kind": "section", "parent": "47", "page": 129 }, { "code": "47L05", "originalCode": "47L05", "name": "Linear spaces of operators", "description": "Linear spaces of operators [See also 46A32, 46B28]", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L07", "originalCode": "47L07", "name": "Convex sets and cones of operators", "description": "Convex sets and cones of operators [See also 46A55]", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L10", "originalCode": "47L10", "name": "Algebras of operators on Banach spaces and other topological linear spaces", "description": "Algebras of operators on Banach spaces and other topological linear spaces", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L15", "originalCode": "47L15", "name": "Operator algebras with symbol structure", "description": "Operator algebras with symbol structure", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L20", "originalCode": "47L20", "name": "Operator ideals", "description": "Operator ideals [See also 47B10]", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L22", "originalCode": "47L22", "name": "Ideals of polynomials and of multilinear mappings in operator theory", "description": "Ideals of polynomials and of multilinear mappings in operator theory", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L25", "originalCode": "47L25", "name": "Operator spaces (= matricially normed spaces)", "description": "Operator spaces (= matricially normed spaces) [See also 46L07]", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L30", "originalCode": "47L30", "name": "Abstract operator algebras on Hilbert spaces", "description": "Abstract operator algebras on Hilbert spaces", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L35", "originalCode": "47L35", "name": "Nest algebras, CSL algebras", "description": "Nest algebras, CSL algebras", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L40", "originalCode": "47L40", "name": "Limit algebras, subalgebras of \\(C^*\\)-algebras", "description": "Limit algebras, subalgebras of \\(C^*\\)-algebras", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L45", "originalCode": "47L45", "name": "Dual algebras; weakly closed singly generated operator algebras", "description": "Dual algebras; weakly closed singly generated operator algebras", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L50", "originalCode": "47L50", "name": "Dual spaces of operator algebras", "description": "Dual spaces of operator algebras", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L55", "originalCode": "47L55", "name": "Representations of (nonselfadjoint) operator algebras", "description": "Representations of (nonselfadjoint) operator algebras", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L60", "originalCode": "47L60", "name": "Algebras of unbounded operators; partial algebras of operators", "description": "Algebras of unbounded operators; partial algebras of operators", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L65", "originalCode": "47L65", "name": "Crossed product algebras (analytic crossed products)", "description": "Crossed product algebras (analytic crossed products)", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L70", "originalCode": "47L70", "name": "Nonassociative nonselfadjoint operator algebras", "description": "Nonassociative nonselfadjoint operator algebras", "kind": "subject", "parent": "47L", "page": 129 }, { "code": "47L75", "originalCode": "47L75", "name": "Other nonselfadjoint operator algebras", "description": "Other nonselfadjoint operator algebras", "kind": "subject", "parent": "47L", "page": 130 }, { "code": "47L80", "originalCode": "47L80", "name": "Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)", "description": "Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)", "kind": "subject", "parent": "47L", "page": 130 }, { "code": "47L90", "originalCode": "47L90", "name": "Applications of operator algebras to the sciences", "description": "Applications of operator algebras to the sciences", "kind": "subject", "parent": "47L", "page": 130 }, { "code": "47L99", "originalCode": "47L99", "name": "Linear spaces and algebras of operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "47L", "page": 130 }, { "code": "47N", "originalCode": "47Nxx", "name": "Miscellaneous applications of operator theory", "description": "Miscellaneous applications of operator theory [See also 46Nxx]", "kind": "section", "parent": "47", "page": 130 }, { "code": "47N10", "originalCode": "47N10", "name": "Applications of operator theory in optimization, convex analysis, mathematical programming, economics", "description": "Applications of operator theory in optimization, convex analysis, mathematical programming, economics", "kind": "subject", "parent": "47N", "page": 130 }, { "code": "47N20", "originalCode": "47N20", "name": "Applications of operator theory to differential and integral equations", "description": "Applications of operator theory to differential and integral equations", "kind": "subject", "parent": "47N", "page": 130 }, { "code": "47N30", "originalCode": "47N30", "name": "Applications of operator theory in probability theory and statistics", "description": "Applications of operator theory in probability theory and statistics", "kind": "subject", "parent": "47N", "page": 130 }, { "code": "47N40", "originalCode": "47N40", "name": "Applications of operator theory in numerical analysis", "description": "Applications of operator theory in numerical analysis [See also 65Jxx]", "kind": "subject", "parent": "47N", "page": 130 }, { "code": "47N50", "originalCode": "47N50", "name": "Applications of operator theory in the physical sciences", "description": "Applications of operator theory in the physical sciences", "kind": "subject", "parent": "47N", "page": 130 }, { "code": "47N60", "originalCode": "47N60", "name": "Applications of operator theory in chemistry and life sciences", "description": "Applications of operator theory in chemistry and life sciences", "kind": "subject", "parent": "47N", "page": 130 }, { "code": "47N70", "originalCode": "47N70", "name": "Applications of operator theory in systems, signals, circuits, and control theory", "description": "Applications of operator theory in systems, signals, circuits, and control theory", "kind": "subject", "parent": "47N", "page": 130 }, { "code": "47N99", "originalCode": "47N99", "name": "Miscellaneous applications of operator theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "47N", "page": 130 }, { "code": "47S", "originalCode": "47Sxx", "name": "Other (nonclassical) types of operator theory", "description": "Other (nonclassical) types of operator theory [See also 46Sxx]", "kind": "section", "parent": "47", "page": 130 }, { "code": "47S05", "originalCode": "47S05", "name": "Quaternionic operator theory", "description": "Quaternionic operator theory", "kind": "subject", "parent": "47S", "page": 130 }, { "code": "47S10", "originalCode": "47S10", "name": "Operator theory over fields other than \\(\\mathbb{R}\\), \\(\\mathbb{C}\\) or the quaternions; non-Archimedean operator theory", "description": "Operator theory over fields other than \\(\\mathbb{R}\\), \\(\\mathbb{C}\\) or the quaternions; non-Archimedean operator theory", "kind": "subject", "parent": "47S", "page": 130 }, { "code": "47S20", "originalCode": "47S20", "name": "Nonstandard operator theory", "description": "Nonstandard operator theory [See also 03H05]", "kind": "subject", "parent": "47S", "page": 130 }, { "code": "47S30", "originalCode": "47S30", "name": "Constructive operator theory", "description": "Constructive operator theory [See also 03F60]", "kind": "subject", "parent": "47S", "page": 130 }, { "code": "47S40", "originalCode": "47S40", "name": "Fuzzy operator theory", "description": "Fuzzy operator theory [See also 03E72]", "kind": "subject", "parent": "47S", "page": 130 }, { "code": "47S50", "originalCode": "47S50", "name": "Operator theory in probabilistic metric linear spaces", "description": "Operator theory in probabilistic metric linear spaces [See also 54E70]", "kind": "subject", "parent": "47S", "page": 130 }, { "code": "47S99", "originalCode": "47S99", "name": "Other (nonclassical) types of operator theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "47S", "page": 130 }, { "code": "49", "originalCode": "49-XX", "name": "Calculus of variations and optimal control; optimization", "description": "Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]", "kind": "class", "parent": null, "page": 130 }, { "code": "49-00", "originalCode": "49-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to calculus of variations and optimal control", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to calculus of variations and optimal control", "kind": "subject", "parent": "49", "page": 130 }, { "code": "49-01", "originalCode": "49-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control", "kind": "subject", "parent": "49", "page": 130 }, { "code": "49-02", "originalCode": "49-02", "name": "Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control", "description": "Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control", "kind": "subject", "parent": "49", "page": 130 }, { "code": "49-03", "originalCode": "49-03", "name": "History of calculus of variations and optimal control", "description": "History of calculus of variations and optimal control [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "49", "page": 130 }, { "code": "49-04", "originalCode": "49-04", "name": "Software, source code, etc. for problems pertaining to calculus of variations and optimal control", "description": "Software, source code, etc. for problems pertaining to calculus of variations and optimal control", "kind": "subject", "parent": "49", "page": 130 }, { "code": "49-06", "originalCode": "49-06", "name": "Proceedings, conferences, collections, etc. pertaining to calculus of variations and optimal control", "description": "Proceedings, conferences, collections, etc. pertaining to calculus of variations and optimal control", "kind": "subject", "parent": "49", "page": 130 }, { "code": "49-11", "originalCode": "49-11", "name": "Research data for problems pertaining to calculus of variations and optimal control", "description": "Research data for problems pertaining to calculus of variations and optimal control", "kind": "subject", "parent": "49", "page": 130 }, { "code": "49J", "originalCode": "49Jxx", "name": "Existence theories in calculus of variations and optimal control", "description": "Existence theories in calculus of variations and optimal control", "kind": "section", "parent": "49", "page": 131 }, { "code": "49J05", "originalCode": "49J05", "name": "Existence theories for free problems in one independent variable", "description": "Existence theories for free problems in one independent variable", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J10", "originalCode": "49J10", "name": "Existence theories for free problems in two or more independent variables", "description": "Existence theories for free problems in two or more independent variables", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J15", "originalCode": "49J15", "name": "Existence theories for optimal control problems involving ordinary differential equations", "description": "Existence theories for optimal control problems involving ordinary differential equations", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J20", "originalCode": "49J20", "name": "Existence theories for optimal control problems involving partial differential equations", "description": "Existence theories for optimal control problems involving partial differential equations", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J21", "originalCode": "49J21", "name": "Existence theories for optimal control problems involving relations other than differential equations", "description": "Existence theories for optimal control problems involving relations other than differential equations", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J27", "originalCode": "49J27", "name": "Existence theories for problems in abstract spaces", "description": "Existence theories for problems in abstract spaces [See also 90C48, 93C25]", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J30", "originalCode": "49J30", "name": "Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)", "description": "Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J35", "originalCode": "49J35", "name": "Existence of solutions for minimax problems", "description": "Existence of solutions for minimax problems", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J40", "originalCode": "49J40", "name": "Variational inequalities", "description": "Variational inequalities [See also 47J20]", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J45", "originalCode": "49J45", "name": "Methods involving semicontinuity and convergence; relaxation", "description": "Methods involving semicontinuity and convergence; relaxation", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J50", "originalCode": "49J50", "name": "Fréchet and Gateaux differentiability in optimization", "description": "Fréchet and Gateaux differentiability in optimization [See also 46G05, 58C20]", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J52", "originalCode": "49J52", "name": "Nonsmooth analysis", "description": "Nonsmooth analysis [See also 46G05, 58C50, 90C56]", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J53", "originalCode": "49J53", "name": "Set-valued and variational analysis", "description": "Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J55", "originalCode": "49J55", "name": "Existence of optimal solutions to problems involving randomness", "description": "Existence of optimal solutions to problems involving randomness [See also 93E20]", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49J99", "originalCode": "49J99", "name": "Existence theories in calculus of variations and optimal control", "description": "None of the above, but in this section", "kind": "subject", "parent": "49J", "page": 131 }, { "code": "49K", "originalCode": "49Kxx", "name": "Optimality conditions", "description": "Optimality conditions", "kind": "section", "parent": "49", "page": 131 }, { "code": "49K05", "originalCode": "49K05", "name": "Optimality conditions for free problems in one independent variable", "description": "Optimality conditions for free problems in one independent variable", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K10", "originalCode": "49K10", "name": "Optimality conditions for free problems in two or more independent variables", "description": "Optimality conditions for free problems in two or more independent variables", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K15", "originalCode": "49K15", "name": "Optimality conditions for problems involving ordinary differential equations", "description": "Optimality conditions for problems involving ordinary differential equations", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K20", "originalCode": "49K20", "name": "Optimality conditions for problems involving partial differential equations", "description": "Optimality conditions for problems involving partial differential equations", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K21", "originalCode": "49K21", "name": "Optimality conditions for problems involving relations other than differential equations", "description": "Optimality conditions for problems involving relations other than differential equations", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K27", "originalCode": "49K27", "name": "Optimality conditions for problems in abstract spaces", "description": "Optimality conditions for problems in abstract spaces [See also 90C48, 93C25]", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K30", "originalCode": "49K30", "name": "Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)", "description": "Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K35", "originalCode": "49K35", "name": "Optimality conditions for minimax problems", "description": "Optimality conditions for minimax problems", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K40", "originalCode": "49K40", "name": "Sensitivity, stability, well-posedness", "description": "Sensitivity, stability, well-posedness [See also 90C31]", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K45", "originalCode": "49K45", "name": "Optimality conditions for problems involving randomness", "description": "Optimality conditions for problems involving randomness [See also 93E20]", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49K99", "originalCode": "49K99", "name": "Optimality conditions", "description": "None of the above, but in this section", "kind": "subject", "parent": "49K", "page": 131 }, { "code": "49L", "originalCode": "49Lxx", "name": "Hamilton-Jacobi theories", "description": "Hamilton-Jacobi theories [See also 70H20, 35F21]", "kind": "section", "parent": "49", "page": 131 }, { "code": "49L12", "originalCode": "49L12", "name": "Hamilton-Jacobi equations in optimal control and differential games", "description": "Hamilton-Jacobi equations in optimal control and differential games", "kind": "subject", "parent": "49L", "page": 131 }, { "code": "49L20", "originalCode": "49L20", "name": "Dynamic programming in optimal control and differential games", "description": "Dynamic programming in optimal control and differential games", "kind": "subject", "parent": "49L", "page": 131 }, { "code": "49L25", "originalCode": "49L25", "name": "Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games", "description": "Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games", "kind": "subject", "parent": "49L", "page": 131 }, { "code": "49L99", "originalCode": "49L99", "name": "Hamilton-Jacobi theories", "description": "None of the above, but in this section", "kind": "subject", "parent": "49L", "page": 131 }, { "code": "49M", "originalCode": "49Mxx", "name": "Numerical methods in optimal control", "description": "Numerical methods in optimal control [See also 65Kxx, 90-08, 90Cxx]", "kind": "section", "parent": "49", "page": 132 }, { "code": "49M05", "originalCode": "49M05", "name": "Numerical methods based on necessary conditions", "description": "Numerical methods based on necessary conditions", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49M15", "originalCode": "49M15", "name": "Newton-type methods", "description": "Newton-type methods [See also 90C53]", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49M20", "originalCode": "49M20", "name": "Numerical methods of relaxation type", "description": "Numerical methods of relaxation type", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49M25", "originalCode": "49M25", "name": "Discrete approximations in optimal control", "description": "Discrete approximations in optimal control", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49M27", "originalCode": "49M27", "name": "Decomposition methods", "description": "Decomposition methods", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49M29", "originalCode": "49M29", "name": "Numerical methods involving duality", "description": "Numerical methods involving duality", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49M37", "originalCode": "49M37", "name": "Numerical methods based on nonlinear programming", "description": "Numerical methods based on nonlinear programming [See also 65Kxx, 90C30]", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49M41", "originalCode": "49M41", "name": "PDE constrained optimization (numerical aspects)", "description": "PDE constrained optimization (numerical aspects)", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49M99", "originalCode": "49M99", "name": "Numerical methods in optimal control", "description": "None of the above, but in this section", "kind": "subject", "parent": "49M", "page": 132 }, { "code": "49N", "originalCode": "49Nxx", "name": "Miscellaneous topics in calculus of variations and optimal control", "description": "Miscellaneous topics in calculus of variations and optimal control", "kind": "section", "parent": "49", "page": 132 }, { "code": "49N05", "originalCode": "49N05", "name": "Linear optimal control problems", "description": "Linear optimal control problems [See also 93C05]", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N10", "originalCode": "49N10", "name": "Linear-quadratic optimal control problems", "description": "Linear-quadratic optimal control problems", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N15", "originalCode": "49N15", "name": "Duality theory (optimization)", "description": "Duality theory (optimization) [See also 90C46]", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N20", "originalCode": "49N20", "name": "Periodic optimal control problems", "description": "Periodic optimal control problems", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N25", "originalCode": "49N25", "name": "Impulsive optimal control problems", "description": "Impulsive optimal control problems", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N30", "originalCode": "49N30", "name": "Problems with incomplete information (optimization)", "description": "Problems with incomplete information (optimization) [See also 93C41]", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N35", "originalCode": "49N35", "name": "Optimal feedback synthesis", "description": "Optimal feedback synthesis [See also 93B52]", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N45", "originalCode": "49N45", "name": "Inverse problems in optimal control", "description": "Inverse problems in optimal control", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N60", "originalCode": "49N60", "name": "Regularity of solutions in optimal control", "description": "Regularity of solutions in optimal control", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N70", "originalCode": "49N70", "name": "Differential games and control", "description": "Differential games and control [See also 91A23]", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N75", "originalCode": "49N75", "name": "Pursuit and evasion games", "description": "Pursuit and evasion games [See also 91A24]", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N80", "originalCode": "49N80", "name": "Mean field games and control", "description": "Mean field games and control \\{For partial differential equations, see 35Q89; for game theory, see 91A16\\}", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N90", "originalCode": "49N90", "name": "Applications of optimal control and differential games", "description": "Applications of optimal control and differential games [See also 90C90, 91A80, 93C95]", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49N99", "originalCode": "49N99", "name": "Miscellaneous topics in calculus of variations and optimal control", "description": "None of the above, but in this section", "kind": "subject", "parent": "49N", "page": 132 }, { "code": "49Q", "originalCode": "49Qxx", "name": "Manifolds and measure-geometric topics", "description": "Manifolds and measure-geometric topics [See also 58Exx]", "kind": "section", "parent": "49", "page": 132 }, { "code": "49Q05", "originalCode": "49Q05", "name": "Minimal surfaces and optimization", "description": "Minimal surfaces and optimization [See also 53A10, 58E12]", "kind": "subject", "parent": "49Q", "page": 132 }, { "code": "49Q10", "originalCode": "49Q10", "name": "Optimization of shapes other than minimal surfaces", "description": "Optimization of shapes other than minimal surfaces [See also 90C90]", "kind": "subject", "parent": "49Q", "page": 132 }, { "code": "49Q12", "originalCode": "49Q12", "name": "Sensitivity analysis for optimization problems on manifolds", "description": "Sensitivity analysis for optimization problems on manifolds", "kind": "subject", "parent": "49Q", "page": 132 }, { "code": "49Q15", "originalCode": "49Q15", "name": "Geometric measure and integration theory, integral and normal currents in optimization", "description": "Geometric measure and integration theory, integral and normal currents in optimization [See also 28A75, 32C30, 58A25, 58C35]", "kind": "subject", "parent": "49Q", "page": 132 }, { "code": "49Q20", "originalCode": "49Q20", "name": "Variational problems in a geometric measure-theoretic setting", "description": "Variational problems in a geometric measure-theoretic setting", "kind": "subject", "parent": "49Q", "page": 132 }, { "code": "49Q22", "originalCode": "49Q22", "name": "Optimal transportation", "description": "Optimal transportation [See also 90B06]", "kind": "subject", "parent": "49Q", "page": 132 }, { "code": "49Q99", "originalCode": "49Q99", "name": "Manifolds and measure-geometric topics", "description": "None of the above, but in this section", "kind": "subject", "parent": "49Q", "page": 132 }, { "code": "49R", "originalCode": "49Rxx", "name": "Variational methods for eigenvalues of operators", "description": "Variational methods for eigenvalues of operators [Should also be assigned at least one other classification number in Section 49-XX] [See also 47A75]", "kind": "section", "parent": "49", "page": 133 }, { "code": "49R05", "originalCode": "49R05", "name": "Variational methods for eigenvalues of operators", "description": "Variational methods for eigenvalues of operators [Should also be assigned at least one other classification number in Section 49-XX] [See also 47A75]", "kind": "subject", "parent": "49R", "page": 133 }, { "code": "49R99", "originalCode": "49R99", "name": "Variational methods for eigenvalues of operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "49R", "page": 133 }, { "code": "49S", "originalCode": "49Sxx", "name": "Variational principles of physics", "description": "Variational principles of physics [Should also be assigned at least one other classification number in Section 49-XX]", "kind": "section", "parent": "49", "page": 133 }, { "code": "49S05", "originalCode": "49S05", "name": "Variational principles of physics", "description": "Variational principles of physics [Should also be assigned at least one other classification number in Section 49-XX]", "kind": "subject", "parent": "49S", "page": 133 }, { "code": "49S99", "originalCode": "49S99", "name": "Variational principles of physics", "description": "None of the above, but in this section", "kind": "subject", "parent": "49S", "page": 133 }, { "code": "51", "originalCode": "51-XX", "name": "Geometry", "description": "Geometry \\{For algebraic geometry, see 14-XX; for differential geometry, see 53-XX\\}", "kind": "class", "parent": null, "page": 133 }, { "code": "51-00", "originalCode": "51-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geometry", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geometry", "kind": "subject", "parent": "51", "page": 133 }, { "code": "51-01", "originalCode": "51-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry", "kind": "subject", "parent": "51", "page": 133 }, { "code": "51-02", "originalCode": "51-02", "name": "Research exposition (monographs, survey articles) pertaining to geometry", "description": "Research exposition (monographs, survey articles) pertaining to geometry", "kind": "subject", "parent": "51", "page": 133 }, { "code": "51-03", "originalCode": "51-03", "name": "History of geometry", "description": "History of geometry [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "51", "page": 133 }, { "code": "51-04", "originalCode": "51-04", "name": "Software, source code, etc. for problems pertaining to geometry", "description": "Software, source code, etc. for problems pertaining to geometry", "kind": "subject", "parent": "51", "page": 133 }, { "code": "51-06", "originalCode": "51-06", "name": "Proceedings, conferences, collections, etc. pertaining to geometry", "description": "Proceedings, conferences, collections, etc. pertaining to geometry", "kind": "subject", "parent": "51", "page": 133 }, { "code": "51-08", "originalCode": "51-08", "name": "Computational methods for problems pertaining to geometry", "description": "Computational methods for problems pertaining to geometry", "kind": "subject", "parent": "51", "page": 133 }, { "code": "51-11", "originalCode": "51-11", "name": "Research data for problems pertaining to geometry", "description": "Research data for problems pertaining to geometry", "kind": "subject", "parent": "51", "page": 133 }, { "code": "51A", "originalCode": "51Axx", "name": "Linear incidence geometry", "description": "Linear incidence geometry", "kind": "section", "parent": "51", "page": 133 }, { "code": "51A05", "originalCode": "51A05", "name": "General theory of linear incidence geometry and projective geometries", "description": "General theory of linear incidence geometry and projective geometries", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A10", "originalCode": "51A10", "name": "Homomorphism, automorphism and dualities in linear incidence geometry", "description": "Homomorphism, automorphism and dualities in linear incidence geometry", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A15", "originalCode": "51A15", "name": "Linear incidence geometric structures with parallelism", "description": "Linear incidence geometric structures with parallelism", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A20", "originalCode": "51A20", "name": "Configuration theorems in linear incidence geometry", "description": "Configuration theorems in linear incidence geometry", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A25", "originalCode": "51A25", "name": "Algebraization in linear incidence geometry", "description": "Algebraization in linear incidence geometry [See also 12Kxx, 20N05]", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A30", "originalCode": "51A30", "name": "Desarguesian and Pappian geometries", "description": "Desarguesian and Pappian geometries", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A35", "originalCode": "51A35", "name": "Non-Desarguesian affine and projective planes", "description": "Non-Desarguesian affine and projective planes", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A40", "originalCode": "51A40", "name": "Translation planes and spreads in linear incidence geometry", "description": "Translation planes and spreads in linear incidence geometry", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A45", "originalCode": "51A45", "name": "Incidence structures embeddable into projective geometries", "description": "Incidence structures embeddable into projective geometries", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A50", "originalCode": "51A50", "name": "Polar geometry, symplectic spaces, orthogonal spaces", "description": "Polar geometry, symplectic spaces, orthogonal spaces", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51A99", "originalCode": "51A99", "name": "Linear incidence geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "51A", "page": 133 }, { "code": "51B", "originalCode": "51Bxx", "name": "Nonlinear incidence geometry", "description": "Nonlinear incidence geometry", "kind": "section", "parent": "51", "page": 134 }, { "code": "51B05", "originalCode": "51B05", "name": "General theory of nonlinear incidence geometry", "description": "General theory of nonlinear incidence geometry", "kind": "subject", "parent": "51B", "page": 134 }, { "code": "51B10", "originalCode": "51B10", "name": "Möbius geometries", "description": "Möbius geometries", "kind": "subject", "parent": "51B", "page": 134 }, { "code": "51B15", "originalCode": "51B15", "name": "Laguerre geometries", "description": "Laguerre geometries", "kind": "subject", "parent": "51B", "page": 134 }, { "code": "51B20", "originalCode": "51B20", "name": "Minkowski geometries in nonlinear incidence geometry", "description": "Minkowski geometries in nonlinear incidence geometry", "kind": "subject", "parent": "51B", "page": 134 }, { "code": "51B25", "originalCode": "51B25", "name": "Lie geometries in nonlinear incidence geometry", "description": "Lie geometries in nonlinear incidence geometry", "kind": "subject", "parent": "51B", "page": 134 }, { "code": "51B99", "originalCode": "51B99", "name": "Nonlinear incidence geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "51B", "page": 134 }, { "code": "51C", "originalCode": "51Cxx", "name": "Ring geometry (Hjelmslev, Barbilian, etc.)", "description": "Ring geometry (Hjelmslev, Barbilian, etc.)", "kind": "section", "parent": "51", "page": 134 }, { "code": "51C05", "originalCode": "51C05", "name": "Ring geometry (Hjelmslev, Barbilian, etc.)", "description": "Ring geometry (Hjelmslev, Barbilian, etc.)", "kind": "subject", "parent": "51C", "page": 134 }, { "code": "51C99", "originalCode": "51C99", "name": "Ring geometry (Hjelmslev, Barbilian, etc.)", "description": "None of the above, but in this section", "kind": "subject", "parent": "51C", "page": 134 }, { "code": "51D", "originalCode": "51Dxx", "name": "Geometric closure systems", "description": "Geometric closure systems", "kind": "section", "parent": "51", "page": 134 }, { "code": "51D05", "originalCode": "51D05", "name": "Abstract (Maeda) geometries", "description": "Abstract (Maeda) geometries", "kind": "subject", "parent": "51D", "page": 134 }, { "code": "51D10", "originalCode": "51D10", "name": "Abstract geometries with exchange axiom", "description": "Abstract geometries with exchange axiom", "kind": "subject", "parent": "51D", "page": 134 }, { "code": "51D15", "originalCode": "51D15", "name": "Abstract geometries with parallelism", "description": "Abstract geometries with parallelism", "kind": "subject", "parent": "51D", "page": 134 }, { "code": "51D20", "originalCode": "51D20", "name": "Combinatorial geometries and geometric closure systems", "description": "Combinatorial geometries and geometric closure systems [See also 05B25, 05B35]", "kind": "subject", "parent": "51D", "page": 134 }, { "code": "51D25", "originalCode": "51D25", "name": "Lattices of subspaces and geometric closure systems", "description": "Lattices of subspaces and geometric closure systems [See also 05B35]", "kind": "subject", "parent": "51D", "page": 134 }, { "code": "51D30", "originalCode": "51D30", "name": "Continuous geometries, geometric closure systems and related topics", "description": "Continuous geometries, geometric closure systems and related topics [See also 06Cxx]", "kind": "subject", "parent": "51D", "page": 134 }, { "code": "51D99", "originalCode": "51D99", "name": "Geometric closure systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "51D", "page": 134 }, { "code": "51E", "originalCode": "51Exx", "name": "Finite geometry and special incidence structures", "description": "Finite geometry and special incidence structures", "kind": "section", "parent": "51", "page": 134 }, { "code": "51E05", "originalCode": "51E05", "name": "General block designs in finite geometry", "description": "General block designs in finite geometry [See also 05B05]", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E10", "originalCode": "51E10", "name": "Steiner systems in finite geometry", "description": "Steiner systems in finite geometry [See also 05B05]", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E12", "originalCode": "51E12", "name": "Generalized quadrangles and generalized polygons in finite geometry", "description": "Generalized quadrangles and generalized polygons in finite geometry", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E14", "originalCode": "51E14", "name": "Finite partial geometries (general), nets, partial spreads", "description": "Finite partial geometries (general), nets, partial spreads", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E15", "originalCode": "51E15", "name": "Finite affine and projective planes (geometric aspects)", "description": "Finite affine and projective planes (geometric aspects)", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E20", "originalCode": "51E20", "name": "Combinatorial structures in finite projective spaces", "description": "Combinatorial structures in finite projective spaces [See also 05Bxx]", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E21", "originalCode": "51E21", "name": "Blocking sets, ovals, \\(k\\)-arcs", "description": "Blocking sets, ovals, \\(k\\)-arcs", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E22", "originalCode": "51E22", "name": "Linear codes and caps in Galois spaces", "description": "Linear codes and caps in Galois spaces [See also 94B05]", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E23", "originalCode": "51E23", "name": "Spreads and packing problems in finite geometry", "description": "Spreads and packing problems in finite geometry", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E24", "originalCode": "51E24", "name": "Buildings and the geometry of diagrams", "description": "Buildings and the geometry of diagrams", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E25", "originalCode": "51E25", "name": "Other finite nonlinear geometries", "description": "Other finite nonlinear geometries", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E26", "originalCode": "51E26", "name": "Other finite linear geometries", "description": "Other finite linear geometries", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E30", "originalCode": "51E30", "name": "Other finite incidence structures (geometric aspects)", "description": "Other finite incidence structures (geometric aspects) [See also 05B30]", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51E99", "originalCode": "51E99", "name": "Finite geometry and special incidence structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "51E", "page": 134 }, { "code": "51F", "originalCode": "51Fxx", "name": "Metric geometry", "description": "Metric geometry", "kind": "section", "parent": "51", "page": 135 }, { "code": "51F05", "originalCode": "51F05", "name": "Absolute planes in metric geometry", "description": "Absolute planes in metric geometry", "kind": "subject", "parent": "51F", "page": 135 }, { "code": "51F10", "originalCode": "51F10", "name": "Absolute spaces in metric geometry", "description": "Absolute spaces in metric geometry", "kind": "subject", "parent": "51F", "page": 135 }, { "code": "51F15", "originalCode": "51F15", "name": "Reflection groups, reflection geometries", "description": "Reflection groups, reflection geometries [See also 20H10, 20H15] \\{For Coxeter groups, see 20F55\\}", "kind": "subject", "parent": "51F", "page": 135 }, { "code": "51F20", "originalCode": "51F20", "name": "Congruence and orthogonality in metric geometry", "description": "Congruence and orthogonality in metric geometry [See also 20H05]", "kind": "subject", "parent": "51F", "page": 135 }, { "code": "51F25", "originalCode": "51F25", "name": "Orthogonal and unitary groups in metric geometry", "description": "Orthogonal and unitary groups in metric geometry [See also 20H05]", "kind": "subject", "parent": "51F", "page": 135 }, { "code": "51F30", "originalCode": "51F30", "name": "Lipschitz and coarse geometry of metric spaces", "description": "Lipschitz and coarse geometry of metric spaces [See also 53C23]", "kind": "subject", "parent": "51F", "page": 135 }, { "code": "51F99", "originalCode": "51F99", "name": "Metric geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "51F", "page": 135 }, { "code": "51G", "originalCode": "51Gxx", "name": "Ordered geometries (ordered incidence structures, etc.)", "description": "Ordered geometries (ordered incidence structures, etc.)", "kind": "section", "parent": "51", "page": 135 }, { "code": "51G05", "originalCode": "51G05", "name": "Ordered geometries (ordered incidence structures, etc.)", "description": "Ordered geometries (ordered incidence structures, etc.)", "kind": "subject", "parent": "51G", "page": 135 }, { "code": "51G99", "originalCode": "51G99", "name": "Ordered geometries (ordered incidence structures, etc.)", "description": "None of the above, but in this section", "kind": "subject", "parent": "51G", "page": 135 }, { "code": "51H", "originalCode": "51Hxx", "name": "Topological geometry", "description": "Topological geometry", "kind": "section", "parent": "51", "page": 135 }, { "code": "51H05", "originalCode": "51H05", "name": "General theory of topological geometry", "description": "General theory of topological geometry", "kind": "subject", "parent": "51H", "page": 135 }, { "code": "51H10", "originalCode": "51H10", "name": "Topological linear incidence structures", "description": "Topological linear incidence structures", "kind": "subject", "parent": "51H", "page": 135 }, { "code": "51H15", "originalCode": "51H15", "name": "Topological nonlinear incidence structures", "description": "Topological nonlinear incidence structures", "kind": "subject", "parent": "51H", "page": 135 }, { "code": "51H20", "originalCode": "51H20", "name": "Topological geometries on manifolds", "description": "Topological geometries on manifolds [See also 57-XX]", "kind": "subject", "parent": "51H", "page": 135 }, { "code": "51H25", "originalCode": "51H25", "name": "Geometries with differentiable structure", "description": "Geometries with differentiable structure [See also 53Cxx, especially 53C70]", "kind": "subject", "parent": "51H", "page": 135 }, { "code": "51H30", "originalCode": "51H30", "name": "Geometries with algebraic manifold structure", "description": "Geometries with algebraic manifold structure [See also 14-XX]", "kind": "subject", "parent": "51H", "page": 135 }, { "code": "51H99", "originalCode": "51H99", "name": "Topological geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "51H", "page": 135 }, { "code": "51J", "originalCode": "51Jxx", "name": "Incidence groups", "description": "Incidence groups", "kind": "section", "parent": "51", "page": 135 }, { "code": "51J05", "originalCode": "51J05", "name": "General theory of incidence groups", "description": "General theory of incidence groups", "kind": "subject", "parent": "51J", "page": 135 }, { "code": "51J10", "originalCode": "51J10", "name": "Projective incidence groups", "description": "Projective incidence groups", "kind": "subject", "parent": "51J", "page": 135 }, { "code": "51J15", "originalCode": "51J15", "name": "Kinematic spaces", "description": "Kinematic spaces", "kind": "subject", "parent": "51J", "page": 135 }, { "code": "51J20", "originalCode": "51J20", "name": "Representation by near-fields and near-algebras", "description": "Representation by near-fields and near-algebras [See also 12K05, 16Y30]", "kind": "subject", "parent": "51J", "page": 135 }, { "code": "51J99", "originalCode": "51J99", "name": "Incidence groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "51J", "page": 135 }, { "code": "51K", "originalCode": "51Kxx", "name": "Distance geometry", "description": "Distance geometry", "kind": "section", "parent": "51", "page": 135 }, { "code": "51K05", "originalCode": "51K05", "name": "General theory of distance geometry", "description": "General theory of distance geometry", "kind": "subject", "parent": "51K", "page": 135 }, { "code": "51K10", "originalCode": "51K10", "name": "Synthetic differential geometry", "description": "Synthetic differential geometry", "kind": "subject", "parent": "51K", "page": 135 }, { "code": "51K99", "originalCode": "51K99", "name": "Distance geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "51K", "page": 135 }, { "code": "51L", "originalCode": "51Lxx", "name": "Geometric order structures", "description": "Geometric order structures [See also 53C75]", "kind": "section", "parent": "51", "page": 136 }, { "code": "51L05", "originalCode": "51L05", "name": "Geometry of orders of nondifferentiable curves", "description": "Geometry of orders of nondifferentiable curves", "kind": "subject", "parent": "51L", "page": 136 }, { "code": "51L10", "originalCode": "51L10", "name": "Directly differentiable curves in geometric order structures", "description": "Directly differentiable curves in geometric order structures", "kind": "subject", "parent": "51L", "page": 136 }, { "code": "51L15", "originalCode": "51L15", "name": "\\(n\\)-vertex theorems via direct methods", "description": "\\(n\\)-vertex theorems via direct methods", "kind": "subject", "parent": "51L", "page": 136 }, { "code": "51L20", "originalCode": "51L20", "name": "Geometry of orders of surfaces", "description": "Geometry of orders of surfaces", "kind": "subject", "parent": "51L", "page": 136 }, { "code": "51L99", "originalCode": "51L99", "name": "Geometric order structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "51L", "page": 136 }, { "code": "51M", "originalCode": "51Mxx", "name": "Real and complex geometry", "description": "Real and complex geometry", "kind": "section", "parent": "51", "page": 136 }, { "code": "51M04", "originalCode": "51M04", "name": "Elementary problems in Euclidean geometries", "description": "Elementary problems in Euclidean geometries", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M05", "originalCode": "51M05", "name": "Euclidean geometries (general) and generalizations", "description": "Euclidean geometries (general) and generalizations", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M09", "originalCode": "51M09", "name": "Elementary problems in hyperbolic and elliptic geometries", "description": "Elementary problems in hyperbolic and elliptic geometries", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M10", "originalCode": "51M10", "name": "Hyperbolic and elliptic geometries (general) and generalizations", "description": "Hyperbolic and elliptic geometries (general) and generalizations", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M15", "originalCode": "51M15", "name": "Geometric constructions in real or complex geometry", "description": "Geometric constructions in real or complex geometry", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M16", "originalCode": "51M16", "name": "Inequalities and extremum problems in real or complex geometry", "description": "Inequalities and extremum problems in real or complex geometry \\{For convex problems, see 52A40\\}", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M20", "originalCode": "51M20", "name": "Polyhedra and polytopes; regular figures, division of spaces", "description": "Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M25", "originalCode": "51M25", "name": "Length, area and volume in real or complex geometry", "description": "Length, area and volume in real or complex geometry [See also 26B15]", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M30", "originalCode": "51M30", "name": "Line geometries and their generalizations", "description": "Line geometries and their generalizations [See also 53A25]", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M35", "originalCode": "51M35", "name": "Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)", "description": "Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51M99", "originalCode": "51M99", "name": "Real and complex geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "51M", "page": 136 }, { "code": "51N", "originalCode": "51Nxx", "name": "Analytic and descriptive geometry", "description": "Analytic and descriptive geometry", "kind": "section", "parent": "51", "page": 136 }, { "code": "51N05", "originalCode": "51N05", "name": "Descriptive geometry", "description": "Descriptive geometry [See also 65D17, 68U07]", "kind": "subject", "parent": "51N", "page": 136 }, { "code": "51N10", "originalCode": "51N10", "name": "Affine analytic geometry", "description": "Affine analytic geometry", "kind": "subject", "parent": "51N", "page": 136 }, { "code": "51N15", "originalCode": "51N15", "name": "Projective analytic geometry", "description": "Projective analytic geometry", "kind": "subject", "parent": "51N", "page": 136 }, { "code": "51N20", "originalCode": "51N20", "name": "Euclidean analytic geometry", "description": "Euclidean analytic geometry", "kind": "subject", "parent": "51N", "page": 136 }, { "code": "51N25", "originalCode": "51N25", "name": "Analytic geometry with other transformation groups", "description": "Analytic geometry with other transformation groups", "kind": "subject", "parent": "51N", "page": 136 }, { "code": "51N30", "originalCode": "51N30", "name": "Geometry of classical groups", "description": "Geometry of classical groups [See also 14L35, 20Gxx]", "kind": "subject", "parent": "51N", "page": 136 }, { "code": "51N35", "originalCode": "51N35", "name": "Questions of classical algebraic geometry", "description": "Questions of classical algebraic geometry [See also 14Nxx]", "kind": "subject", "parent": "51N", "page": 136 }, { "code": "51N99", "originalCode": "51N99", "name": "Analytic and descriptive geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "51N", "page": 136 }, { "code": "51P", "originalCode": "51Pxx", "name": "Classical or axiomatic geometry and physics", "description": "Classical or axiomatic geometry and physics [Should also be assigned at least one other classification number from Sections 70-XX through 86-XX]", "kind": "section", "parent": "51", "page": 136 }, { "code": "51P05", "originalCode": "51P05", "name": "Classical or axiomatic geometry and physics", "description": "Classical or axiomatic geometry and physics [Should also be assigned at least one other classification number from Sections 70-XX through 86-XX]", "kind": "subject", "parent": "51P", "page": 136 }, { "code": "51P99", "originalCode": "51P99", "name": "Classical or axiomatic geometry and physics", "description": "None of the above, but in this section", "kind": "subject", "parent": "51P", "page": 136 }, { "code": "52", "originalCode": "52-XX", "name": "Convex and discrete geometry", "description": "Convex and discrete geometry", "kind": "class", "parent": null, "page": 137 }, { "code": "52-00", "originalCode": "52-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to convex and discrete geometry", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to convex and discrete geometry", "kind": "subject", "parent": "52", "page": 137 }, { "code": "52-01", "originalCode": "52-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry", "kind": "subject", "parent": "52", "page": 137 }, { "code": "52-02", "originalCode": "52-02", "name": "Research exposition (monographs, survey articles) pertaining to convex and discrete geometry", "description": "Research exposition (monographs, survey articles) pertaining to convex and discrete geometry", "kind": "subject", "parent": "52", "page": 137 }, { "code": "52-03", "originalCode": "52-03", "name": "History of convex and discrete geometry", "description": "History of convex and discrete geometry [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "52", "page": 137 }, { "code": "52-04", "originalCode": "52-04", "name": "Software, source code, etc. for problems pertaining to convex and discrete geometry", "description": "Software, source code, etc. for problems pertaining to convex and discrete geometry", "kind": "subject", "parent": "52", "page": 137 }, { "code": "52-06", "originalCode": "52-06", "name": "Proceedings, conferences, collections, etc. pertaining to convex and discrete geometry", "description": "Proceedings, conferences, collections, etc. pertaining to convex and discrete geometry", "kind": "subject", "parent": "52", "page": 137 }, { "code": "52-08", "originalCode": "52-08", "name": "Computational methods for problems pertaining to convex and discrete geometry", "description": "Computational methods for problems pertaining to convex and discrete geometry", "kind": "subject", "parent": "52", "page": 137 }, { "code": "52-11", "originalCode": "52-11", "name": "Research data for problems pertaining to convex and discrete geometry", "description": "Research data for problems pertaining to convex and discrete geometry", "kind": "subject", "parent": "52", "page": 137 }, { "code": "52A", "originalCode": "52Axx", "name": "General convexity", "description": "General convexity", "kind": "section", "parent": "52", "page": 137 }, { "code": "52A01", "originalCode": "52A01", "name": "Axiomatic and generalized convexity", "description": "Axiomatic and generalized convexity", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A05", "originalCode": "52A05", "name": "Convex sets without dimension restrictions (aspects of convex geometry)", "description": "Convex sets without dimension restrictions (aspects of convex geometry)", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A07", "originalCode": "52A07", "name": "Convex sets in topological vector spaces (aspects of convex geometry)", "description": "Convex sets in topological vector spaces (aspects of convex geometry) [See also 46A55]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A10", "originalCode": "52A10", "name": "Convex sets in \\(2\\) dimensions (including convex curves)", "description": "Convex sets in \\(2\\) dimensions (including convex curves) [See also 53A04]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A15", "originalCode": "52A15", "name": "Convex sets in \\(3\\) dimensions (including convex surfaces)", "description": "Convex sets in \\(3\\) dimensions (including convex surfaces) [See also 53A05, 53C45]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A20", "originalCode": "52A20", "name": "Convex sets in \\(n\\) dimensions (including convex hypersurfaces)", "description": "Convex sets in \\(n\\) dimensions (including convex hypersurfaces) [See also 53A07, 53C45]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A21", "originalCode": "52A21", "name": "Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)", "description": "Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) [See also 46Bxx]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A22", "originalCode": "52A22", "name": "Random convex sets and integral geometry (aspects of convex geometry)", "description": "Random convex sets and integral geometry (aspects of convex geometry) [See also 53C65, 60D05]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A23", "originalCode": "52A23", "name": "Asymptotic theory of convex bodies", "description": "Asymptotic theory of convex bodies [See also 46B06]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A27", "originalCode": "52A27", "name": "Approximation by convex sets", "description": "Approximation by convex sets", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A30", "originalCode": "52A30", "name": "Variants of convex sets (star-shaped, (\\(m, n\\))-convex, etc.)", "description": "Variants of convex sets (star-shaped, (\\(m, n\\))-convex, etc.)", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A35", "originalCode": "52A35", "name": "Helly-type theorems and geometric transversal theory", "description": "Helly-type theorems and geometric transversal theory", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A37", "originalCode": "52A37", "name": "Other problems of combinatorial convexity", "description": "Other problems of combinatorial convexity", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A38", "originalCode": "52A38", "name": "Length, area, volume and convex sets (aspects of convex geometry)", "description": "Length, area, volume and convex sets (aspects of convex geometry) [See also 26B15, 28A75, 49Q20]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A39", "originalCode": "52A39", "name": "Mixed volumes and related topics in convex geometry", "description": "Mixed volumes and related topics in convex geometry", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A40", "originalCode": "52A40", "name": "Inequalities and extremum problems involving convexity in convex geometry", "description": "Inequalities and extremum problems involving convexity in convex geometry", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A41", "originalCode": "52A41", "name": "Convex functions and convex programs in convex geometry", "description": "Convex functions and convex programs in convex geometry [See also 26B25, 90C25]", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A55", "originalCode": "52A55", "name": "Spherical and hyperbolic convexity", "description": "Spherical and hyperbolic convexity", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52A99", "originalCode": "52A99", "name": "General convexity", "description": "None of the above, but in this section", "kind": "subject", "parent": "52A", "page": 137 }, { "code": "52B", "originalCode": "52Bxx", "name": "Polytopes and polyhedra", "description": "Polytopes and polyhedra", "kind": "section", "parent": "52", "page": 138 }, { "code": "52B05", "originalCode": "52B05", "name": "Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)", "description": "Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) [See also 05Cxx]", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B10", "originalCode": "52B10", "name": "Three-dimensional polytopes", "description": "Three-dimensional polytopes", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B11", "originalCode": "52B11", "name": "\\(n\\)-dimensional polytopes", "description": "\\(n\\)-dimensional polytopes", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B12", "originalCode": "52B12", "name": "Special polytopes (linear programming, centrally symmetric, etc.)", "description": "Special polytopes (linear programming, centrally symmetric, etc.)", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B15", "originalCode": "52B15", "name": "Symmetry properties of polytopes", "description": "Symmetry properties of polytopes", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B20", "originalCode": "52B20", "name": "Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)", "description": "Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13F55, 13Hxx, 52C05, 52C07]", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B22", "originalCode": "52B22", "name": "Shellability for polytopes and polyhedra", "description": "Shellability for polytopes and polyhedra", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B35", "originalCode": "52B35", "name": "Gale and other diagrams", "description": "Gale and other diagrams", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B40", "originalCode": "52B40", "name": "Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)", "description": "Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B45", "originalCode": "52B45", "name": "Dissections and valuations (Hilbert's third problem, etc.)", "description": "Dissections and valuations (Hilbert's third problem, etc.)", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B55", "originalCode": "52B55", "name": "Computational aspects related to convexity", "description": "Computational aspects related to convexity \\{For computational methods, see 52-08; for computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx\\} [See also 68Uxx]", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B60", "originalCode": "52B60", "name": "Isoperimetric problems for polytopes", "description": "Isoperimetric problems for polytopes", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B70", "originalCode": "52B70", "name": "Polyhedral manifolds", "description": "Polyhedral manifolds", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52B99", "originalCode": "52B99", "name": "Polytopes and polyhedra", "description": "None of the above, but in this section", "kind": "subject", "parent": "52B", "page": 138 }, { "code": "52C", "originalCode": "52Cxx", "name": "Discrete geometry", "description": "Discrete geometry", "kind": "section", "parent": "52", "page": 138 }, { "code": "52C05", "originalCode": "52C05", "name": "Lattices and convex bodies in \\(2\\) dimensions (aspects of discrete geometry)", "description": "Lattices and convex bodies in \\(2\\) dimensions (aspects of discrete geometry) [See also 11H06, 11H31, 11P21]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C07", "originalCode": "52C07", "name": "Lattices and convex bodies in \\(n\\) dimensions (aspects of discrete geometry)", "description": "Lattices and convex bodies in \\(n\\) dimensions (aspects of discrete geometry) [See also 11H06, 11H31, 11P21]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C10", "originalCode": "52C10", "name": "Erd?s problems and related topics of discrete geometry", "description": "Erd?s problems and related topics of discrete geometry [See also 11Hxx]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C15", "originalCode": "52C15", "name": "Packing and covering in \\(2\\) dimensions (aspects of discrete geometry)", "description": "Packing and covering in \\(2\\) dimensions (aspects of discrete geometry) [See also 05B40, 11H31]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C17", "originalCode": "52C17", "name": "Packing and covering in \\(n\\) dimensions (aspects of discrete geometry)", "description": "Packing and covering in \\(n\\) dimensions (aspects of discrete geometry) [See also 05B40, 11H31]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C20", "originalCode": "52C20", "name": "Tilings in \\(2\\) dimensions (aspects of discrete geometry)", "description": "Tilings in \\(2\\) dimensions (aspects of discrete geometry) [See also 05B45, 51M20]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C22", "originalCode": "52C22", "name": "Tilings in \\(n\\) dimensions (aspects of discrete geometry)", "description": "Tilings in \\(n\\) dimensions (aspects of discrete geometry) [See also 05B45, 51M20]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C23", "originalCode": "52C23", "name": "Quasicrystals and aperiodic tilings in discrete geometry", "description": "Quasicrystals and aperiodic tilings in discrete geometry", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C25", "originalCode": "52C25", "name": "Rigidity and flexibility of structures (aspects of discrete geometry)", "description": "Rigidity and flexibility of structures (aspects of discrete geometry) [See also 70B15]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C26", "originalCode": "52C26", "name": "Circle packings and discrete conformal geometry", "description": "Circle packings and discrete conformal geometry", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C30", "originalCode": "52C30", "name": "Planar arrangements of lines and pseudolines (aspects of discrete geometry)", "description": "Planar arrangements of lines and pseudolines (aspects of discrete geometry)", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C35", "originalCode": "52C35", "name": "Arrangements of points, flats, hyperplanes (aspects of discrete geometry)", "description": "Arrangements of points, flats, hyperplanes (aspects of discrete geometry) [See also 14N20, 32S22]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C40", "originalCode": "52C40", "name": "Oriented matroids in discrete geometry", "description": "Oriented matroids in discrete geometry", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C45", "originalCode": "52C45", "name": "Combinatorial complexity of geometric structures", "description": "Combinatorial complexity of geometric structures [See also 68U05]", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "52C99", "originalCode": "52C99", "name": "Discrete geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "52C", "page": 138 }, { "code": "53", "originalCode": "53-XX", "name": "Differential geometry", "description": "Differential geometry \\{For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx\\}", "kind": "class", "parent": null, "page": 139 }, { "code": "53-00", "originalCode": "53-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to differential geometry", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to differential geometry", "kind": "subject", "parent": "53", "page": 139 }, { "code": "53-01", "originalCode": "53-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry", "kind": "subject", "parent": "53", "page": 139 }, { "code": "53-02", "originalCode": "53-02", "name": "Research exposition (monographs, survey articles) pertaining to differential geometry", "description": "Research exposition (monographs, survey articles) pertaining to differential geometry", "kind": "subject", "parent": "53", "page": 139 }, { "code": "53-03", "originalCode": "53-03", "name": "History of differential geometry", "description": "History of differential geometry [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "53", "page": 139 }, { "code": "53-04", "originalCode": "53-04", "name": "Software, source code, etc. for problems pertaining to differential geometry", "description": "Software, source code, etc. for problems pertaining to differential geometry", "kind": "subject", "parent": "53", "page": 139 }, { "code": "53-06", "originalCode": "53-06", "name": "Proceedings, conferences, collections, etc. pertaining to differential geometry", "description": "Proceedings, conferences, collections, etc. pertaining to differential geometry", "kind": "subject", "parent": "53", "page": 139 }, { "code": "53-08", "originalCode": "53-08", "name": "Computational methods for problems pertaining to differential geometry", "description": "Computational methods for problems pertaining to differential geometry", "kind": "subject", "parent": "53", "page": 139 }, { "code": "53-11", "originalCode": "53-11", "name": "Research data for problems pertaining to differential geometry", "description": "Research data for problems pertaining to differential geometry", "kind": "subject", "parent": "53", "page": 139 }, { "code": "53A", "originalCode": "53Axx", "name": "Classical differential geometry", "description": "Classical differential geometry", "kind": "section", "parent": "53", "page": 139 }, { "code": "53A04", "originalCode": "53A04", "name": "Curves in Euclidean and related spaces", "description": "Curves in Euclidean and related spaces", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A05", "originalCode": "53A05", "name": "Surfaces in Euclidean and related spaces", "description": "Surfaces in Euclidean and related spaces", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A07", "originalCode": "53A07", "name": "Higher-dimensional and -codimensional surfaces in Euclidean and related \\(n\\)-spaces", "description": "Higher-dimensional and -codimensional surfaces in Euclidean and related \\(n\\)-spaces", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A10", "originalCode": "53A10", "name": "Minimal surfaces in differential geometry, surfaces with prescribed mean curvature", "description": "Minimal surfaces in differential geometry, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A15", "originalCode": "53A15", "name": "Affine differential geometry", "description": "Affine differential geometry", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A17", "originalCode": "53A17", "name": "Differential geometric aspects in kinematics", "description": "Differential geometric aspects in kinematics", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A20", "originalCode": "53A20", "name": "Projective differential geometry", "description": "Projective differential geometry", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A25", "originalCode": "53A25", "name": "Differential line geometry", "description": "Differential line geometry", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A31", "originalCode": "53A31", "name": "Differential geometry of submanifolds of Möbius space", "description": "Differential geometry of submanifolds of Möbius space", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A35", "originalCode": "53A35", "name": "Non-Euclidean differential geometry", "description": "Non-Euclidean differential geometry", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A40", "originalCode": "53A40", "name": "Other special differential geometries", "description": "Other special differential geometries", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A45", "originalCode": "53A45", "name": "Differential geometric aspects in vector and tensor analysis", "description": "Differential geometric aspects in vector and tensor analysis", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A55", "originalCode": "53A55", "name": "Differential invariants (local theory), geometric objects", "description": "Differential invariants (local theory), geometric objects", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A60", "originalCode": "53A60", "name": "Differential geometry of webs", "description": "Differential geometry of webs [See also 14C21, 20N05]", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A70", "originalCode": "53A70", "name": "Discrete differential geometry", "description": "Discrete differential geometry", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53A99", "originalCode": "53A99", "name": "Classical differential geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "53A", "page": 139 }, { "code": "53B", "originalCode": "53Bxx", "name": "Local differential geometry", "description": "Local differential geometry", "kind": "section", "parent": "53", "page": 140 }, { "code": "53B05", "originalCode": "53B05", "name": "Linear and affine connections", "description": "Linear and affine connections", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B10", "originalCode": "53B10", "name": "Projective connections", "description": "Projective connections", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B12", "originalCode": "53B12", "name": "Differential geometric aspects of statistical manifolds and information geometry", "description": "Differential geometric aspects of statistical manifolds and information geometry", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B15", "originalCode": "53B15", "name": "Other connections", "description": "Other connections", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B20", "originalCode": "53B20", "name": "Local Riemannian geometry", "description": "Local Riemannian geometry", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B21", "originalCode": "53B21", "name": "Methods of local Riemannian geometry", "description": "Methods of local Riemannian geometry", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B25", "originalCode": "53B25", "name": "Local submanifolds", "description": "Local submanifolds [See also 53C40]", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B30", "originalCode": "53B30", "name": "Local differential geometry of Lorentz metrics, indefinite metrics", "description": "Local differential geometry of Lorentz metrics, indefinite metrics", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B35", "originalCode": "53B35", "name": "Local differential geometry of Hermitian and Kählerian structures", "description": "Local differential geometry of Hermitian and Kählerian structures [See also 32Qxx]", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B40", "originalCode": "53B40", "name": "Local differential geometry of Finsler spaces and generalizations (areal metrics)", "description": "Local differential geometry of Finsler spaces and generalizations (areal metrics)", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B50", "originalCode": "53B50", "name": "Applications of local differential geometry to the sciences", "description": "Applications of local differential geometry to the sciences", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53B99", "originalCode": "53B99", "name": "Local differential geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "53B", "page": 140 }, { "code": "53C", "originalCode": "53Cxx", "name": "Global differential geometry", "description": "Global differential geometry [See also 51H25, 58-XX] \\{For related bundle theory, see 55Rxx, 57Rxx\\}", "kind": "section", "parent": "53", "page": 140 }, { "code": "53C05", "originalCode": "53C05", "name": "Connections (general theory)", "description": "Connections (general theory)", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C07", "originalCode": "53C07", "name": "Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)", "description": "Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) [See also 32Q20]", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C08", "originalCode": "53C08", "name": "Differential geometric aspects of gerbes and differential characters", "description": "Differential geometric aspects of gerbes and differential characters", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C10", "originalCode": "53C10", "name": "\\(G\\)-structures", "description": "\\(G\\)-structures", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C12", "originalCode": "53C12", "name": "Foliations (differential geometric aspects)", "description": "Foliations (differential geometric aspects) [See also 57R30, 57R32]", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C15", "originalCode": "53C15", "name": "General geometric structures on manifolds (almost complex, almost product structures, etc.)", "description": "General geometric structures on manifolds (almost complex, almost product structures, etc.)", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C17", "originalCode": "53C17", "name": "Sub-Riemannian geometry", "description": "Sub-Riemannian geometry", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C18", "originalCode": "53C18", "name": "Conformal structures on manifolds", "description": "Conformal structures on manifolds", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C20", "originalCode": "53C20", "name": "Global Riemannian geometry, including pinching", "description": "Global Riemannian geometry, including pinching [See also 31C12, 58B20]", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C21", "originalCode": "53C21", "name": "Methods of global Riemannian geometry, including PDE methods; curvature restrictions", "description": "Methods of global Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C22", "originalCode": "53C22", "name": "Geodesics in global differential geometry", "description": "Geodesics in global differential geometry [See also 58E10]", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C23", "originalCode": "53C23", "name": "Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces", "description": "Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C24", "originalCode": "53C24", "name": "Rigidity results", "description": "Rigidity results", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C25", "originalCode": "53C25", "name": "Special Riemannian manifolds (Einstein, Sasakian, etc.)", "description": "Special Riemannian manifolds (Einstein, Sasakian, etc.)", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C26", "originalCode": "53C26", "name": "Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry", "description": "Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C27", "originalCode": "53C27", "name": "Spin and Spin\\({}^c\\) geometry", "description": "Spin and Spin\\({}^c\\) geometry", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C28", "originalCode": "53C28", "name": "Twistor methods in differential geometry", "description": "Twistor methods in differential geometry [See also 32L25]", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C29", "originalCode": "53C29", "name": "Issues of holonomy in differential geometry", "description": "Issues of holonomy in differential geometry", "kind": "subject", "parent": "53C", "page": 140 }, { "code": "53C30", "originalCode": "53C30", "name": "Differential geometry of homogeneous manifolds", "description": "Differential geometry of homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C35", "originalCode": "53C35", "name": "Differential geometry of symmetric spaces", "description": "Differential geometry of symmetric spaces [See also 32M15, 57T15]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C38", "originalCode": "53C38", "name": "Calibrations and calibrated geometries", "description": "Calibrations and calibrated geometries", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C40", "originalCode": "53C40", "name": "Global submanifolds", "description": "Global submanifolds [See also 53B25]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C42", "originalCode": "53C42", "name": "Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)", "description": "Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C43", "originalCode": "53C43", "name": "Differential geometric aspects of harmonic maps", "description": "Differential geometric aspects of harmonic maps [See also 58E20]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C45", "originalCode": "53C45", "name": "Global surface theory (convex surfaces à la A. D. Aleksandrov)", "description": "Global surface theory (convex surfaces à la A. D. Aleksandrov)", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C50", "originalCode": "53C50", "name": "Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics", "description": "Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C55", "originalCode": "53C55", "name": "Global differential geometry of Hermitian and Kählerian manifolds", "description": "Global differential geometry of Hermitian and Kählerian manifolds [See also 32Qxx]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C56", "originalCode": "53C56", "name": "Other complex differential geometry", "description": "Other complex differential geometry [See also 32Qxx]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C60", "originalCode": "53C60", "name": "Global differential geometry of Finsler spaces and generalizations (areal metrics)", "description": "Global differential geometry of Finsler spaces and generalizations (areal metrics) [See also 58B20]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C65", "originalCode": "53C65", "name": "Integral geometry", "description": "Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C70", "originalCode": "53C70", "name": "Direct methods (\\(G\\)-spaces of Busemann, etc.)", "description": "Direct methods (\\(G\\)-spaces of Busemann, etc.)", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C75", "originalCode": "53C75", "name": "Geometric orders, order geometry", "description": "Geometric orders, order geometry [See also 51Lxx]", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C80", "originalCode": "53C80", "name": "Applications of global differential geometry to the sciences", "description": "Applications of global differential geometry to the sciences", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53C99", "originalCode": "53C99", "name": "Global differential geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "53C", "page": 141 }, { "code": "53D", "originalCode": "53Dxx", "name": "Symplectic geometry, contact geometry", "description": "Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]", "kind": "section", "parent": "53", "page": 141 }, { "code": "53D05", "originalCode": "53D05", "name": "Symplectic manifolds (general theory)", "description": "Symplectic manifolds (general theory)", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D10", "originalCode": "53D10", "name": "Contact manifolds (general theory)", "description": "Contact manifolds (general theory)", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D12", "originalCode": "53D12", "name": "Lagrangian submanifolds; Maslov index", "description": "Lagrangian submanifolds; Maslov index", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D15", "originalCode": "53D15", "name": "Almost contact and almost symplectic manifolds", "description": "Almost contact and almost symplectic manifolds", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D17", "originalCode": "53D17", "name": "Poisson manifolds; Poisson groupoids and algebroids", "description": "Poisson manifolds; Poisson groupoids and algebroids", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D18", "originalCode": "53D18", "name": "Generalized geometries (à la Hitchin)", "description": "Generalized geometries (à la Hitchin)", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D20", "originalCode": "53D20", "name": "Momentum maps; symplectic reduction", "description": "Momentum maps; symplectic reduction", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D22", "originalCode": "53D22", "name": "Canonical transformations in symplectic and contact geometry", "description": "Canonical transformations in symplectic and contact geometry", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D25", "originalCode": "53D25", "name": "Geodesic flows in symplectic geometry and contact geometry", "description": "Geodesic flows in symplectic geometry and contact geometry", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D30", "originalCode": "53D30", "name": "Symplectic structures of moduli spaces", "description": "Symplectic structures of moduli spaces", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D35", "originalCode": "53D35", "name": "Global theory of symplectic and contact manifolds", "description": "Global theory of symplectic and contact manifolds [See also 57Rxx]", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D37", "originalCode": "53D37", "name": "Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category", "description": "Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category [See also 14J33]", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D40", "originalCode": "53D40", "name": "Symplectic aspects of Floer homology and cohomology", "description": "Symplectic aspects of Floer homology and cohomology", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D42", "originalCode": "53D42", "name": "Symplectic field theory; contact homology", "description": "Symplectic field theory; contact homology", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D45", "originalCode": "53D45", "name": "Gromov-Witten invariants, quantum cohomology, Frobenius manifolds", "description": "Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D50", "originalCode": "53D50", "name": "Geometric quantization", "description": "Geometric quantization", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D55", "originalCode": "53D55", "name": "Deformation quantization, star products", "description": "Deformation quantization, star products", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53D99", "originalCode": "53D99", "name": "Symplectic geometry, contact geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "53D", "page": 141 }, { "code": "53E", "originalCode": "53Exx", "name": "Geometric evolution equations", "description": "Geometric evolution equations", "kind": "section", "parent": "53", "page": 142 }, { "code": "53E10", "originalCode": "53E10", "name": "Flows related to mean curvature", "description": "Flows related to mean curvature", "kind": "subject", "parent": "53E", "page": 142 }, { "code": "53E20", "originalCode": "53E20", "name": "Ricci flows", "description": "Ricci flows", "kind": "subject", "parent": "53E", "page": 142 }, { "code": "53E30", "originalCode": "53E30", "name": "Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows)", "description": "Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows)", "kind": "subject", "parent": "53E", "page": 142 }, { "code": "53E40", "originalCode": "53E40", "name": "Higher-order geometric flows", "description": "Higher-order geometric flows", "kind": "subject", "parent": "53E", "page": 142 }, { "code": "53E50", "originalCode": "53E50", "name": "Flows related to symplectic and contact structures", "description": "Flows related to symplectic and contact structures", "kind": "subject", "parent": "53E", "page": 142 }, { "code": "53E99", "originalCode": "53E99", "name": "Geometric evolution equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "53E", "page": 142 }, { "code": "53Z", "originalCode": "53Zxx", "name": "Applications of differential geometry to sciences and engineering", "description": "Applications of differential geometry to sciences and engineering", "kind": "section", "parent": "53", "page": 142 }, { "code": "53Z05", "originalCode": "53Z05", "name": "Applications of differential geometry to physics", "description": "Applications of differential geometry to physics", "kind": "subject", "parent": "53Z", "page": 142 }, { "code": "53Z10", "originalCode": "53Z10", "name": "Applications of differential geometry to biology", "description": "Applications of differential geometry to biology", "kind": "subject", "parent": "53Z", "page": 142 }, { "code": "53Z15", "originalCode": "53Z15", "name": "Applications of differential geometry to chemistry", "description": "Applications of differential geometry to chemistry", "kind": "subject", "parent": "53Z", "page": 142 }, { "code": "53Z30", "originalCode": "53Z30", "name": "Applications of differential geometry to engineering", "description": "Applications of differential geometry to engineering", "kind": "subject", "parent": "53Z", "page": 142 }, { "code": "53Z50", "originalCode": "53Z50", "name": "Applications of differential geometry to data and computer science", "description": "Applications of differential geometry to data and computer science", "kind": "subject", "parent": "53Z", "page": 142 }, { "code": "53Z99", "originalCode": "53Z99", "name": "Applications of differential geometry to sciences and engineering", "description": "None of the above, but in this section", "kind": "subject", "parent": "53Z", "page": 142 }, { "code": "54", "originalCode": "54-XX", "name": "General topology", "description": "General topology \\{For the topology of manifolds of all dimensions, see 57Nxx\\}", "kind": "class", "parent": null, "page": 142 }, { "code": "54-00", "originalCode": "54-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general topology", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general topology", "kind": "subject", "parent": "54", "page": 142 }, { "code": "54-01", "originalCode": "54-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology", "kind": "subject", "parent": "54", "page": 142 }, { "code": "54-02", "originalCode": "54-02", "name": "Research exposition (monographs, survey articles) pertaining to general topology", "description": "Research exposition (monographs, survey articles) pertaining to general topology", "kind": "subject", "parent": "54", "page": 142 }, { "code": "54-03", "originalCode": "54-03", "name": "History of general topology", "description": "History of general topology [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "54", "page": 142 }, { "code": "54-04", "originalCode": "54-04", "name": "Software, source code, etc. for problems pertaining to general topology", "description": "Software, source code, etc. for problems pertaining to general topology", "kind": "subject", "parent": "54", "page": 142 }, { "code": "54-06", "originalCode": "54-06", "name": "Proceedings, conferences, collections, etc. pertaining to general topology", "description": "Proceedings, conferences, collections, etc. pertaining to general topology", "kind": "subject", "parent": "54", "page": 142 }, { "code": "54-08", "originalCode": "54-08", "name": "Computational methods for problems pertaining to general topology", "description": "Computational methods for problems pertaining to general topology", "kind": "subject", "parent": "54", "page": 142 }, { "code": "54-11", "originalCode": "54-11", "name": "Research data for problems pertaining to general topology", "description": "Research data for problems pertaining to general topology", "kind": "subject", "parent": "54", "page": 142 }, { "code": "54A", "originalCode": "54Axx", "name": "Generalities in topology", "description": "Generalities in topology", "kind": "section", "parent": "54", "page": 142 }, { "code": "54A05", "originalCode": "54A05", "name": "Topological spaces and generalizations (closure spaces, etc.)", "description": "Topological spaces and generalizations (closure spaces, etc.)", "kind": "subject", "parent": "54A", "page": 142 }, { "code": "54A10", "originalCode": "54A10", "name": "Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)", "description": "Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)", "kind": "subject", "parent": "54A", "page": 142 }, { "code": "54A15", "originalCode": "54A15", "name": "Syntopogeneous structures", "description": "Syntopogeneous structures", "kind": "subject", "parent": "54A", "page": 142 }, { "code": "54A20", "originalCode": "54A20", "name": "Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)", "description": "Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)", "kind": "subject", "parent": "54A", "page": 142 }, { "code": "54A25", "originalCode": "54A25", "name": "Cardinality properties (cardinal functions and inequalities, discrete subsets)", "description": "Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] \\{For ultrafilters, see 54D80\\}", "kind": "subject", "parent": "54A", "page": 142 }, { "code": "54A35", "originalCode": "54A35", "name": "Consistency and independence results in general topology", "description": "Consistency and independence results in general topology [See also 03E35]", "kind": "subject", "parent": "54A", "page": 142 }, { "code": "54A40", "originalCode": "54A40", "name": "Fuzzy topology", "description": "Fuzzy topology [See also 03E72]", "kind": "subject", "parent": "54A", "page": 142 }, { "code": "54A99", "originalCode": "54A99", "name": "Generalities in topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "54A", "page": 142 }, { "code": "54B", "originalCode": "54Bxx", "name": "Basic constructions in general topology", "description": "Basic constructions in general topology", "kind": "section", "parent": "54", "page": 143 }, { "code": "54B05", "originalCode": "54B05", "name": "Subspaces in general topology", "description": "Subspaces in general topology", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54B10", "originalCode": "54B10", "name": "Product spaces in general topology", "description": "Product spaces in general topology", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54B15", "originalCode": "54B15", "name": "Quotient spaces, decompositions in general topology", "description": "Quotient spaces, decompositions in general topology", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54B17", "originalCode": "54B17", "name": "Adjunction spaces and similar constructions in general topology", "description": "Adjunction spaces and similar constructions in general topology", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54B20", "originalCode": "54B20", "name": "Hyperspaces in general topology", "description": "Hyperspaces in general topology", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54B30", "originalCode": "54B30", "name": "Categorical methods in general topology", "description": "Categorical methods in general topology [See also 18F60]", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54B35", "originalCode": "54B35", "name": "Spectra in general topology", "description": "Spectra in general topology", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54B40", "originalCode": "54B40", "name": "Presheaves and sheaves in general topology", "description": "Presheaves and sheaves in general topology [See also 18F20]", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54B99", "originalCode": "54B99", "name": "Basic constructions in general topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "54B", "page": 143 }, { "code": "54C", "originalCode": "54Cxx", "name": "Maps and general types of topological spaces defined by maps", "description": "Maps and general types of topological spaces defined by maps", "kind": "section", "parent": "54", "page": 143 }, { "code": "54C05", "originalCode": "54C05", "name": "Continuous maps", "description": "Continuous maps", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C08", "originalCode": "54C08", "name": "Weak and generalized continuity", "description": "Weak and generalized continuity", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C10", "originalCode": "54C10", "name": "Special maps on topological spaces (open, closed, perfect, etc.)", "description": "Special maps on topological spaces (open, closed, perfect, etc.)", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C15", "originalCode": "54C15", "name": "Retraction", "description": "Retraction", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C20", "originalCode": "54C20", "name": "Extension of maps", "description": "Extension of maps", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C25", "originalCode": "54C25", "name": "Embedding", "description": "Embedding", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C30", "originalCode": "54C30", "name": "Real-valued functions in general topology", "description": "Real-valued functions in general topology [See also 26-XX]", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C35", "originalCode": "54C35", "name": "Function spaces in general topology", "description": "Function spaces in general topology [See also 46Exx, 58D15]", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C40", "originalCode": "54C40", "name": "Algebraic properties of function spaces in general topology", "description": "Algebraic properties of function spaces in general topology [See also 46Exx]", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C45", "originalCode": "54C45", "name": "\\(C\\)- and \\(C^*\\)-embedding", "description": "\\(C\\)- and \\(C^*\\)-embedding", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C50", "originalCode": "54C50", "name": "Topology of special sets defined by functions", "description": "Topology of special sets defined by functions [See also 26A21]", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C55", "originalCode": "54C55", "name": "Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)", "description": "Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15]", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C56", "originalCode": "54C56", "name": "Shape theory in general topology", "description": "Shape theory in general topology [See also 55P55, 57N25]", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C60", "originalCode": "54C60", "name": "Set-valued maps in general topology", "description": "Set-valued maps in general topology [See also 26E25, 28B20, 47H04, 58C06]", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C65", "originalCode": "54C65", "name": "Selections in general topology", "description": "Selections in general topology [See also 28B20]", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C70", "originalCode": "54C70", "name": "Entropy in general topology", "description": "Entropy in general topology", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54C99", "originalCode": "54C99", "name": "Maps and general types of topological spaces defined by maps", "description": "None of the above, but in this section", "kind": "subject", "parent": "54C", "page": 143 }, { "code": "54D", "originalCode": "54Dxx", "name": "Fairly general properties of topological spaces", "description": "Fairly general properties of topological spaces", "kind": "section", "parent": "54", "page": 144 }, { "code": "54D05", "originalCode": "54D05", "name": "Connected and locally connected spaces (general aspects)", "description": "Connected and locally connected spaces (general aspects)", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D10", "originalCode": "54D10", "name": "Lower separation axioms (\\(T_0\\)--\\(T_3\\), etc.)", "description": "Lower separation axioms (\\(T_0\\)--\\(T_3\\), etc.)", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D15", "originalCode": "54D15", "name": "Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)", "description": "Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D20", "originalCode": "54D20", "name": "Noncompact covering properties (paracompact, Lindelöf, etc.)", "description": "Noncompact covering properties (paracompact, Lindelöf, etc.)", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D25", "originalCode": "54D25", "name": "``\\(P\\)-minimal'' and ``\\(P\\)-closed'' spaces", "description": "``\\(P\\)-minimal'' and ``\\(P\\)-closed'' spaces", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D30", "originalCode": "54D30", "name": "Compactness", "description": "Compactness", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D35", "originalCode": "54D35", "name": "Extensions of spaces (compactifications, supercompactifications, completions, etc.)", "description": "Extensions of spaces (compactifications, supercompactifications, completions, etc.)", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D40", "originalCode": "54D40", "name": "Remainders in general topology", "description": "Remainders in general topology", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D45", "originalCode": "54D45", "name": "Local compactness, \\(\\sigma\\)-compactness", "description": "Local compactness, \\(\\sigma\\)-compactness", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D50", "originalCode": "54D50", "name": "\\(k\\)-spaces", "description": "\\(k\\)-spaces", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D55", "originalCode": "54D55", "name": "Sequential spaces", "description": "Sequential spaces", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D60", "originalCode": "54D60", "name": "Realcompactness and realcompactification", "description": "Realcompactness and realcompactification", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D65", "originalCode": "54D65", "name": "Separability of topological spaces", "description": "Separability of topological spaces", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D70", "originalCode": "54D70", "name": "Base properties of topological spaces", "description": "Base properties of topological spaces", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D80", "originalCode": "54D80", "name": "Special constructions of topological spaces (spaces of ultrafilters, etc.)", "description": "Special constructions of topological spaces (spaces of ultrafilters, etc.)", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54D99", "originalCode": "54D99", "name": "Fairly general properties of topological spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "54D", "page": 144 }, { "code": "54E", "originalCode": "54Exx", "name": "Topological spaces with richer structures", "description": "Topological spaces with richer structures", "kind": "section", "parent": "54", "page": 144 }, { "code": "54E05", "originalCode": "54E05", "name": "Proximity structures and generalizations", "description": "Proximity structures and generalizations", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E15", "originalCode": "54E15", "name": "Uniform structures and generalizations", "description": "Uniform structures and generalizations", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E17", "originalCode": "54E17", "name": "Nearness spaces", "description": "Nearness spaces", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E18", "originalCode": "54E18", "name": "\\(p\\)-spaces, \\(M\\)-spaces, \\(\\sigma\\)-spaces, etc.", "description": "\\(p\\)-spaces, \\(M\\)-spaces, \\(\\sigma\\)-spaces, etc.", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E20", "originalCode": "54E20", "name": "Stratifiable spaces, cosmic spaces, etc.", "description": "Stratifiable spaces, cosmic spaces, etc.", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E25", "originalCode": "54E25", "name": "Semimetric spaces", "description": "Semimetric spaces", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E30", "originalCode": "54E30", "name": "Moore spaces", "description": "Moore spaces", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E35", "originalCode": "54E35", "name": "Metric spaces, metrizability", "description": "Metric spaces, metrizability", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E40", "originalCode": "54E40", "name": "Special maps on metric spaces", "description": "Special maps on metric spaces", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E45", "originalCode": "54E45", "name": "Compact (locally compact) metric spaces", "description": "Compact (locally compact) metric spaces", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E50", "originalCode": "54E50", "name": "Complete metric spaces", "description": "Complete metric spaces", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E52", "originalCode": "54E52", "name": "Baire category, Baire spaces", "description": "Baire category, Baire spaces", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E55", "originalCode": "54E55", "name": "Bitopologies", "description": "Bitopologies", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E70", "originalCode": "54E70", "name": "Probabilistic metric spaces", "description": "Probabilistic metric spaces", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54E99", "originalCode": "54E99", "name": "Topological spaces with richer structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "54E", "page": 144 }, { "code": "54F", "originalCode": "54Fxx", "name": "Special properties of topological spaces", "description": "Special properties of topological spaces", "kind": "section", "parent": "54", "page": 145 }, { "code": "54F05", "originalCode": "54F05", "name": "Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces", "description": "Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F15", "originalCode": "54F15", "name": "Continua and generalizations", "description": "Continua and generalizations", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F16", "originalCode": "54F16", "name": "Hyperspaces of continua", "description": "Hyperspaces of continua", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F17", "originalCode": "54F17", "name": "Inverse limits of set-valued functions", "description": "Inverse limits of set-valued functions", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F35", "originalCode": "54F35", "name": "Higher-dimensional local connectedness", "description": "Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F45", "originalCode": "54F45", "name": "Dimension theory in general topology", "description": "Dimension theory in general topology [See also 55M10]", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F50", "originalCode": "54F50", "name": "Topological spaces of dimension \\(\\leq 1\\); curves, dendrites", "description": "Topological spaces of dimension \\(\\leq 1\\); curves, dendrites [See also 26A03]", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F55", "originalCode": "54F55", "name": "Unicoherence, multicoherence", "description": "Unicoherence, multicoherence", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F65", "originalCode": "54F65", "name": "Topological characterizations of particular spaces", "description": "Topological characterizations of particular spaces", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54F99", "originalCode": "54F99", "name": "Special properties of topological spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "54F", "page": 145 }, { "code": "54G", "originalCode": "54Gxx", "name": "Peculiar topological spaces", "description": "Peculiar topological spaces", "kind": "section", "parent": "54", "page": 145 }, { "code": "54G05", "originalCode": "54G05", "name": "Extremally disconnected spaces, \\(F\\)-spaces, etc.", "description": "Extremally disconnected spaces, \\(F\\)-spaces, etc.", "kind": "subject", "parent": "54G", "page": 145 }, { "code": "54G10", "originalCode": "54G10", "name": "\\(P\\)-spaces", "description": "\\(P\\)-spaces", "kind": "subject", "parent": "54G", "page": 145 }, { "code": "54G12", "originalCode": "54G12", "name": "Scattered spaces", "description": "Scattered spaces", "kind": "subject", "parent": "54G", "page": 145 }, { "code": "54G15", "originalCode": "54G15", "name": "Pathological topological spaces", "description": "Pathological topological spaces", "kind": "subject", "parent": "54G", "page": 145 }, { "code": "54G20", "originalCode": "54G20", "name": "Counterexamples in general topology", "description": "Counterexamples in general topology", "kind": "subject", "parent": "54G", "page": 145 }, { "code": "54G99", "originalCode": "54G99", "name": "Peculiar topological spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "54G", "page": 145 }, { "code": "54H", "originalCode": "54Hxx", "name": "Connections of general topology with other structures, applications", "description": "Connections of general topology with other structures, applications", "kind": "section", "parent": "54", "page": 145 }, { "code": "54H05", "originalCode": "54H05", "name": "Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)", "description": "Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54H10", "originalCode": "54H10", "name": "Topological representations of algebraic systems", "description": "Topological representations of algebraic systems [See also 22-XX]", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54H11", "originalCode": "54H11", "name": "Topological groups (topological aspects)", "description": "Topological groups (topological aspects) [See also 22A05]", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54H12", "originalCode": "54H12", "name": "Topological lattices, etc. (topological aspects)", "description": "Topological lattices, etc. (topological aspects) [See also 06B30, 06F30]", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54H13", "originalCode": "54H13", "name": "Topological fields, rings, etc. (topological aspects)", "description": "Topological fields, rings, etc. (topological aspects) [See also 12Jxx] \\{For algebraic aspects, see 13Jxx, 16W80\\}", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54H15", "originalCode": "54H15", "name": "Transformation groups and semigroups (topological aspects)", "description": "Transformation groups and semigroups (topological aspects) [See also 20M20, 22-XX, 57Sxx]", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54H25", "originalCode": "54H25", "name": "Fixed-point and coincidence theorems (topological aspects)", "description": "Fixed-point and coincidence theorems (topological aspects) [See also 47H10, 55M20]", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54H30", "originalCode": "54H30", "name": "Applications of general topology to computer science (e.g., digital topology, image processing)", "description": "Applications of general topology to computer science (e.g., digital topology, image processing) [See also 68U03]", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54H99", "originalCode": "54H99", "name": "Connections of general topology with other structures, applications", "description": "None of the above, but in this section", "kind": "subject", "parent": "54H", "page": 145 }, { "code": "54J", "originalCode": "54Jxx", "name": "Nonstandard topology", "description": "Nonstandard topology [See also 03H05]", "kind": "section", "parent": "54", "page": 145 }, { "code": "54J05", "originalCode": "54J05", "name": "Nonstandard topology", "description": "Nonstandard topology [See also 03H05]", "kind": "subject", "parent": "54J", "page": 145 }, { "code": "54J99", "originalCode": "54J99", "name": "Nonstandard topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "54J", "page": 145 }, { "code": "55", "originalCode": "55-XX", "name": "Algebraic topology", "description": "Algebraic topology", "kind": "class", "parent": null, "page": 146 }, { "code": "55-00", "originalCode": "55-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic topology", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic topology", "kind": "subject", "parent": "55", "page": 146 }, { "code": "55-01", "originalCode": "55-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology", "kind": "subject", "parent": "55", "page": 146 }, { "code": "55-02", "originalCode": "55-02", "name": "Research exposition (monographs, survey articles) pertaining to algebraic topology", "description": "Research exposition (monographs, survey articles) pertaining to algebraic topology", "kind": "subject", "parent": "55", "page": 146 }, { "code": "55-03", "originalCode": "55-03", "name": "History of algebraic topology", "description": "History of algebraic topology [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "55", "page": 146 }, { "code": "55-04", "originalCode": "55-04", "name": "Software, source code, etc. for problems pertaining to algebraic topology", "description": "Software, source code, etc. for problems pertaining to algebraic topology", "kind": "subject", "parent": "55", "page": 146 }, { "code": "55-06", "originalCode": "55-06", "name": "Proceedings, conferences, collections, etc. pertaining to algebraic topology", "description": "Proceedings, conferences, collections, etc. pertaining to algebraic topology", "kind": "subject", "parent": "55", "page": 146 }, { "code": "55-08", "originalCode": "55-08", "name": "Computational methods for problems pertaining to algebraic topology", "description": "Computational methods for problems pertaining to algebraic topology", "kind": "subject", "parent": "55", "page": 146 }, { "code": "55-11", "originalCode": "55-11", "name": "Research data for problems pertaining to algebraic topology", "description": "Research data for problems pertaining to algebraic topology", "kind": "subject", "parent": "55", "page": 146 }, { "code": "55M", "originalCode": "55Mxx", "name": "Classical topics in algebraic topology", "description": "Classical topics in algebraic topology \\{For the topology of Euclidean spaces and manifolds, see 57Nxx\\}", "kind": "section", "parent": "55", "page": 146 }, { "code": "55M05", "originalCode": "55M05", "name": "Duality in algebraic topology", "description": "Duality in algebraic topology", "kind": "subject", "parent": "55M", "page": 146 }, { "code": "55M10", "originalCode": "55M10", "name": "Dimension theory in algebraic topology", "description": "Dimension theory in algebraic topology [See also 54F45]", "kind": "subject", "parent": "55M", "page": 146 }, { "code": "55M15", "originalCode": "55M15", "name": "Absolute neighborhood retracts", "description": "Absolute neighborhood retracts [See also 54C55]", "kind": "subject", "parent": "55M", "page": 146 }, { "code": "55M20", "originalCode": "55M20", "name": "Fixed points and coincidences in algebraic topology", "description": "Fixed points and coincidences in algebraic topology [See also 54H25]", "kind": "subject", "parent": "55M", "page": 146 }, { "code": "55M25", "originalCode": "55M25", "name": "Degree, winding number", "description": "Degree, winding number", "kind": "subject", "parent": "55M", "page": 146 }, { "code": "55M30", "originalCode": "55M30", "name": "Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects)", "description": "Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects)", "kind": "subject", "parent": "55M", "page": 146 }, { "code": "55M35", "originalCode": "55M35", "name": "Finite groups of transformations in algebraic topology (including Smith theory)", "description": "Finite groups of transformations in algebraic topology (including Smith theory) [See also 57S17]", "kind": "subject", "parent": "55M", "page": 146 }, { "code": "55M99", "originalCode": "55M99", "name": "Classical topics in algebraic topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "55M", "page": 146 }, { "code": "55N", "originalCode": "55Nxx", "name": "Homology and cohomology theories in algebraic topology", "description": "Homology and cohomology theories in algebraic topology \\{For homology and cohomology of topological groups and related structures, see 57Txx\\}", "kind": "section", "parent": "55", "page": 146 }, { "code": "55N05", "originalCode": "55N05", "name": "?ech types", "description": "?ech types", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N07", "originalCode": "55N07", "name": "Steenrod-Sitnikov homologies", "description": "Steenrod-Sitnikov homologies", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N10", "originalCode": "55N10", "name": "Singular homology and cohomology theory", "description": "Singular homology and cohomology theory", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N15", "originalCode": "55N15", "name": "Topological \\(K\\)-theory", "description": "Topological \\(K\\)-theory [See also 19Lxx] \\{For algebraic \\(K\\)-theory, see 18F25, 19-XX\\}", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N20", "originalCode": "55N20", "name": "Generalized (extraordinary) homology and cohomology theories in algebraic topology", "description": "Generalized (extraordinary) homology and cohomology theories in algebraic topology", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N22", "originalCode": "55N22", "name": "Bordism and cobordism theories and formal group laws in algebraic topology", "description": "Bordism and cobordism theories and formal group laws in algebraic topology [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N25", "originalCode": "55N25", "name": "Homology with local coefficients, equivariant cohomology", "description": "Homology with local coefficients, equivariant cohomology", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N30", "originalCode": "55N30", "name": "Sheaf cohomology in algebraic topology", "description": "Sheaf cohomology in algebraic topology [See also 18F20, 32C35, 32L10]", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N31", "originalCode": "55N31", "name": "Persistent homology and applications, topological data analysis", "description": "Persistent homology and applications, topological data analysis [See also 62R40, 68T09]", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N32", "originalCode": "55N32", "name": "Orbifold cohomology", "description": "Orbifold cohomology", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N33", "originalCode": "55N33", "name": "Intersection homology and cohomology in algebraic topology", "description": "Intersection homology and cohomology in algebraic topology", "kind": "subject", "parent": "55N", "page": 146 }, { "code": "55N34", "originalCode": "55N34", "name": "Elliptic cohomology", "description": "Elliptic cohomology", "kind": "subject", "parent": "55N", "page": 147 }, { "code": "55N35", "originalCode": "55N35", "name": "Other homology theories in algebraic topology", "description": "Other homology theories in algebraic topology", "kind": "subject", "parent": "55N", "page": 147 }, { "code": "55N40", "originalCode": "55N40", "name": "Axioms for homology theory and uniqueness theorems in algebraic topology", "description": "Axioms for homology theory and uniqueness theorems in algebraic topology", "kind": "subject", "parent": "55N", "page": 147 }, { "code": "55N45", "originalCode": "55N45", "name": "Products and intersections in homology and cohomology", "description": "Products and intersections in homology and cohomology", "kind": "subject", "parent": "55N", "page": 147 }, { "code": "55N91", "originalCode": "55N91", "name": "Equivariant homology and cohomology in algebraic topology", "description": "Equivariant homology and cohomology in algebraic topology [See also 19L47]", "kind": "subject", "parent": "55N", "page": 147 }, { "code": "55N99", "originalCode": "55N99", "name": "Homology and cohomology theories in algebraic topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "55N", "page": 147 }, { "code": "55P", "originalCode": "55Pxx", "name": "Homotopy theory", "description": "Homotopy theory \\{For simple homotopy type, see 57Q10\\}", "kind": "section", "parent": "55", "page": 147 }, { "code": "55P05", "originalCode": "55P05", "name": "Homotopy extension properties, cofibrations in algebraic topology", "description": "Homotopy extension properties, cofibrations in algebraic topology", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P10", "originalCode": "55P10", "name": "Homotopy equivalences in algebraic topology", "description": "Homotopy equivalences in algebraic topology", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P15", "originalCode": "55P15", "name": "Classification of homotopy type", "description": "Classification of homotopy type", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P20", "originalCode": "55P20", "name": "Eilenberg-Mac Lane spaces", "description": "Eilenberg-Mac Lane spaces", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P25", "originalCode": "55P25", "name": "Spanier-Whitehead duality", "description": "Spanier-Whitehead duality", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P30", "originalCode": "55P30", "name": "Eckmann-Hilton duality", "description": "Eckmann-Hilton duality", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P35", "originalCode": "55P35", "name": "Loop spaces", "description": "Loop spaces", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P40", "originalCode": "55P40", "name": "Suspensions", "description": "Suspensions", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P42", "originalCode": "55P42", "name": "Stable homotopy theory, spectra", "description": "Stable homotopy theory, spectra", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P43", "originalCode": "55P43", "name": "Spectra with additional structure (\\(E_\\infty\\), \\(A_\\infty\\), ring spectra, etc.)", "description": "Spectra with additional structure (\\(E_\\infty\\), \\(A_\\infty\\), ring spectra, etc.)", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P45", "originalCode": "55P45", "name": "\\(H\\)-spaces and duals", "description": "\\(H\\)-spaces and duals", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P47", "originalCode": "55P47", "name": "Infinite loop spaces", "description": "Infinite loop spaces", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P48", "originalCode": "55P48", "name": "Loop space machines and operads in algebraic topology", "description": "Loop space machines and operads in algebraic topology [See also 18Mxx]", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P50", "originalCode": "55P50", "name": "String topology", "description": "String topology", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P55", "originalCode": "55P55", "name": "Shape theory", "description": "Shape theory [See also 54C56, 55Q07]", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P57", "originalCode": "55P57", "name": "Proper homotopy theory", "description": "Proper homotopy theory", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P60", "originalCode": "55P60", "name": "Localization and completion in homotopy theory", "description": "Localization and completion in homotopy theory", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P62", "originalCode": "55P62", "name": "Rational homotopy theory", "description": "Rational homotopy theory", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P65", "originalCode": "55P65", "name": "Homotopy functors in algebraic topology", "description": "Homotopy functors in algebraic topology", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P91", "originalCode": "55P91", "name": "Equivariant homotopy theory in algebraic topology", "description": "Equivariant homotopy theory in algebraic topology [See also 19L47]", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P92", "originalCode": "55P92", "name": "Relations between equivariant and nonequivariant homotopy theory in algebraic topology", "description": "Relations between equivariant and nonequivariant homotopy theory in algebraic topology", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55P99", "originalCode": "55P99", "name": "Homotopy theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "55P", "page": 147 }, { "code": "55Q", "originalCode": "55Qxx", "name": "Homotopy groups", "description": "Homotopy groups", "kind": "section", "parent": "55", "page": 148 }, { "code": "55Q05", "originalCode": "55Q05", "name": "Homotopy groups, general; sets of homotopy classes", "description": "Homotopy groups, general; sets of homotopy classes", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q07", "originalCode": "55Q07", "name": "Shape groups", "description": "Shape groups", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q10", "originalCode": "55Q10", "name": "Stable homotopy groups", "description": "Stable homotopy groups", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q15", "originalCode": "55Q15", "name": "Whitehead products and generalizations", "description": "Whitehead products and generalizations", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q20", "originalCode": "55Q20", "name": "Homotopy groups of wedges, joins, and simple spaces", "description": "Homotopy groups of wedges, joins, and simple spaces", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q25", "originalCode": "55Q25", "name": "Hopf invariants", "description": "Hopf invariants", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q35", "originalCode": "55Q35", "name": "Operations in homotopy groups", "description": "Operations in homotopy groups", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q40", "originalCode": "55Q40", "name": "Homotopy groups of spheres", "description": "Homotopy groups of spheres", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q45", "originalCode": "55Q45", "name": "Stable homotopy of spheres", "description": "Stable homotopy of spheres", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q50", "originalCode": "55Q50", "name": "\\(J\\)-morphism", "description": "\\(J\\)-morphism [See also 19L20]", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q51", "originalCode": "55Q51", "name": "\\(v_n\\)-periodicity", "description": "\\(v_n\\)-periodicity", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q52", "originalCode": "55Q52", "name": "Homotopy groups of special spaces", "description": "Homotopy groups of special spaces", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q55", "originalCode": "55Q55", "name": "Cohomotopy groups", "description": "Cohomotopy groups", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q70", "originalCode": "55Q70", "name": "Homotopy groups of special types", "description": "Homotopy groups of special types [See also 55N05, 55N07]", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q91", "originalCode": "55Q91", "name": "Equivariant homotopy groups", "description": "Equivariant homotopy groups [See also 19L47]", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55Q99", "originalCode": "55Q99", "name": "Homotopy groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "55Q", "page": 148 }, { "code": "55R", "originalCode": "55Rxx", "name": "Fiber spaces and bundles in algebraic topology", "description": "Fiber spaces and bundles in algebraic topology [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]", "kind": "section", "parent": "55", "page": 148 }, { "code": "55R05", "originalCode": "55R05", "name": "Fiber spaces in algebraic topology", "description": "Fiber spaces in algebraic topology", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R10", "originalCode": "55R10", "name": "Fiber bundles in algebraic topology", "description": "Fiber bundles in algebraic topology", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R12", "originalCode": "55R12", "name": "Transfer for fiber spaces and bundles in algebraic topology", "description": "Transfer for fiber spaces and bundles in algebraic topology", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R15", "originalCode": "55R15", "name": "Classification of fiber spaces or bundles in algebraic topology", "description": "Classification of fiber spaces or bundles in algebraic topology", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R20", "originalCode": "55R20", "name": "Spectral sequences and homology of fiber spaces in algebraic topology", "description": "Spectral sequences and homology of fiber spaces in algebraic topology [See also 55Txx]", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R25", "originalCode": "55R25", "name": "Sphere bundles and vector bundles in algebraic topology", "description": "Sphere bundles and vector bundles in algebraic topology", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R35", "originalCode": "55R35", "name": "Classifying spaces of groups and \\(H\\)-spaces in algebraic topology", "description": "Classifying spaces of groups and \\(H\\)-spaces in algebraic topology", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R37", "originalCode": "55R37", "name": "Maps between classifying spaces in algebraic topology", "description": "Maps between classifying spaces in algebraic topology", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R40", "originalCode": "55R40", "name": "Homology of classifying spaces and characteristic classes in algebraic topology", "description": "Homology of classifying spaces and characteristic classes in algebraic topology [See also 57Txx, 57R20]", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R45", "originalCode": "55R45", "name": "Homology and homotopy of \\(B\\mathrm{O}\\) and \\(B\\mathrm{U}\\); Bott periodicity", "description": "Homology and homotopy of \\(B\\mathrm{O}\\) and \\(B\\mathrm{U}\\); Bott periodicity", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R50", "originalCode": "55R50", "name": "Stable classes of vector space bundles in algebraic topology and relations to \\(K\\)-theory", "description": "Stable classes of vector space bundles in algebraic topology and relations to \\(K\\)-theory [See also 19Lxx] \\{For algebraic \\(K\\)-theory, see 18F25, 19-XX\\}", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R55", "originalCode": "55R55", "name": "Fiberings with singularities in algebraic topology", "description": "Fiberings with singularities in algebraic topology", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R60", "originalCode": "55R60", "name": "Microbundles and block bundles in algebraic topology", "description": "Microbundles and block bundles in algebraic topology [See also 57N55, 57Q50]", "kind": "subject", "parent": "55R", "page": 148 }, { "code": "55R65", "originalCode": "55R65", "name": "Generalizations of fiber spaces and bundles in algebraic topology", "description": "Generalizations of fiber spaces and bundles in algebraic topology", "kind": "subject", "parent": "55R", "page": 149 }, { "code": "55R70", "originalCode": "55R70", "name": "Fibrewise topology", "description": "Fibrewise topology", "kind": "subject", "parent": "55R", "page": 149 }, { "code": "55R80", "originalCode": "55R80", "name": "Discriminantal varieties and configuration spaces in algebraic topology", "description": "Discriminantal varieties and configuration spaces in algebraic topology", "kind": "subject", "parent": "55R", "page": 149 }, { "code": "55R91", "originalCode": "55R91", "name": "Equivariant fiber spaces and bundles in algebraic topology", "description": "Equivariant fiber spaces and bundles in algebraic topology [See also 19L47]", "kind": "subject", "parent": "55R", "page": 149 }, { "code": "55R99", "originalCode": "55R99", "name": "Fiber spaces and bundles in algebraic topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "55R", "page": 149 }, { "code": "55S", "originalCode": "55Sxx", "name": "Operations and obstructions in algebraic topology", "description": "Operations and obstructions in algebraic topology", "kind": "section", "parent": "55", "page": 149 }, { "code": "55S05", "originalCode": "55S05", "name": "Primary cohomology operations in algebraic topology", "description": "Primary cohomology operations in algebraic topology", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S10", "originalCode": "55S10", "name": "Steenrod algebra", "description": "Steenrod algebra", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S12", "originalCode": "55S12", "name": "Dyer-Lashof operations", "description": "Dyer-Lashof operations", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S15", "originalCode": "55S15", "name": "Symmetric products and cyclic products in algebraic topology", "description": "Symmetric products and cyclic products in algebraic topology", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S20", "originalCode": "55S20", "name": "Secondary and higher cohomology operations in algebraic topology", "description": "Secondary and higher cohomology operations in algebraic topology", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S25", "originalCode": "55S25", "name": "\\(K\\)-theory operations and generalized cohomology operations in algebraic topology", "description": "\\(K\\)-theory operations and generalized cohomology operations in algebraic topology [See also 19D55, 19Lxx]", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S30", "originalCode": "55S30", "name": "Massey products", "description": "Massey products", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S35", "originalCode": "55S35", "name": "Obstruction theory in algebraic topology", "description": "Obstruction theory in algebraic topology", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S36", "originalCode": "55S36", "name": "Extension and compression of mappings in algebraic topology", "description": "Extension and compression of mappings in algebraic topology", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S37", "originalCode": "55S37", "name": "Classification of mappings in algebraic topology", "description": "Classification of mappings in algebraic topology", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S40", "originalCode": "55S40", "name": "Sectioning fiber spaces and bundles in algebraic topology", "description": "Sectioning fiber spaces and bundles in algebraic topology", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S45", "originalCode": "55S45", "name": "Postnikov systems, \\(k\\)-invariants", "description": "Postnikov systems, \\(k\\)-invariants", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S91", "originalCode": "55S91", "name": "Equivariant operations and obstructions in algebraic topology", "description": "Equivariant operations and obstructions in algebraic topology [See also 19L47]", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55S99", "originalCode": "55S99", "name": "Operations and obstructions in algebraic topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "55S", "page": 149 }, { "code": "55T", "originalCode": "55Txx", "name": "Spectral sequences in algebraic topology", "description": "Spectral sequences in algebraic topology [See also 18G40, 55R20]", "kind": "section", "parent": "55", "page": 149 }, { "code": "55T05", "originalCode": "55T05", "name": "General theory of spectral sequences in algebraic topology", "description": "General theory of spectral sequences in algebraic topology", "kind": "subject", "parent": "55T", "page": 149 }, { "code": "55T10", "originalCode": "55T10", "name": "Serre spectral sequences", "description": "Serre spectral sequences", "kind": "subject", "parent": "55T", "page": 149 }, { "code": "55T15", "originalCode": "55T15", "name": "Adams spectral sequences", "description": "Adams spectral sequences", "kind": "subject", "parent": "55T", "page": 149 }, { "code": "55T20", "originalCode": "55T20", "name": "Eilenberg-Moore spectral sequences", "description": "Eilenberg-Moore spectral sequences [See also 57T35]", "kind": "subject", "parent": "55T", "page": 149 }, { "code": "55T25", "originalCode": "55T25", "name": "Generalized cohomology and spectral sequences in algebraic topology", "description": "Generalized cohomology and spectral sequences in algebraic topology", "kind": "subject", "parent": "55T", "page": 149 }, { "code": "55T99", "originalCode": "55T99", "name": "Spectral sequences in algebraic topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "55T", "page": 149 }, { "code": "55U", "originalCode": "55Uxx", "name": "Applied homological algebra and category theory in algebraic topology", "description": "Applied homological algebra and category theory in algebraic topology [See also 18Gxx]", "kind": "section", "parent": "55", "page": 150 }, { "code": "55U05", "originalCode": "55U05", "name": "Abstract complexes in algebraic topology", "description": "Abstract complexes in algebraic topology", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "55U10", "originalCode": "55U10", "name": "Simplicial sets and complexes in algebraic topology", "description": "Simplicial sets and complexes in algebraic topology", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "55U15", "originalCode": "55U15", "name": "Chain complexes in algebraic topology", "description": "Chain complexes in algebraic topology", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "55U20", "originalCode": "55U20", "name": "Universal coefficient theorems, Bockstein operator", "description": "Universal coefficient theorems, Bockstein operator", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "55U25", "originalCode": "55U25", "name": "Homology of a product, Künneth formula", "description": "Homology of a product, Künneth formula", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "55U30", "originalCode": "55U30", "name": "Duality in applied homological algebra and category theory (aspects of algebraic topology)", "description": "Duality in applied homological algebra and category theory (aspects of algebraic topology)", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "55U35", "originalCode": "55U35", "name": "Abstract and axiomatic homotopy theory in algebraic topology", "description": "Abstract and axiomatic homotopy theory in algebraic topology", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "55U40", "originalCode": "55U40", "name": "Topological categories, foundations of homotopy theory", "description": "Topological categories, foundations of homotopy theory", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "55U99", "originalCode": "55U99", "name": "Applied homological algebra and category theory in algebraic topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "55U", "page": 150 }, { "code": "57", "originalCode": "57-XX", "name": "Manifolds and cell complexes", "description": "Manifolds and cell complexes \\{For complex manifolds, see 32Qxx\\}", "kind": "class", "parent": null, "page": 150 }, { "code": "57-00", "originalCode": "57-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and cell complexes", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and cell complexes", "kind": "subject", "parent": "57", "page": 150 }, { "code": "57-01", "originalCode": "57-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes", "kind": "subject", "parent": "57", "page": 150 }, { "code": "57-02", "originalCode": "57-02", "name": "Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes", "description": "Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes", "kind": "subject", "parent": "57", "page": 150 }, { "code": "57-03", "originalCode": "57-03", "name": "History of manifolds and cell complexes", "description": "History of manifolds and cell complexes [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "57", "page": 150 }, { "code": "57-04", "originalCode": "57-04", "name": "Software, source code, etc. for problems pertaining to manifolds and cell complexes", "description": "Software, source code, etc. for problems pertaining to manifolds and cell complexes", "kind": "subject", "parent": "57", "page": 150 }, { "code": "57-06", "originalCode": "57-06", "name": "Proceedings, conferences, collections, etc. pertaining to manifolds and cell complexes", "description": "Proceedings, conferences, collections, etc. pertaining to manifolds and cell complexes", "kind": "subject", "parent": "57", "page": 150 }, { "code": "57-08", "originalCode": "57-08", "name": "Computational methods for problems pertaining to manifolds and cell complexes", "description": "Computational methods for problems pertaining to manifolds and cell complexes", "kind": "subject", "parent": "57", "page": 150 }, { "code": "57-11", "originalCode": "57-11", "name": "Research data for problems pertaining to manifolds and cell complexes", "description": "Research data for problems pertaining to manifolds and cell complexes", "kind": "subject", "parent": "57", "page": 150 }, { "code": "57K", "originalCode": "57Kxx", "name": "Low-dimensional topology in specific dimensions", "description": "Low-dimensional topology in specific dimensions", "kind": "section", "parent": "57", "page": 150 }, { "code": "57K10", "originalCode": "57K10", "name": "Knot theory", "description": "Knot theory", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K12", "originalCode": "57K12", "name": "Generalized knots (virtual knots, welded knots, quandles, etc.)", "description": "Generalized knots (virtual knots, welded knots, quandles, etc.)", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K14", "originalCode": "57K14", "name": "Knot polynomials", "description": "Knot polynomials", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K16", "originalCode": "57K16", "name": "Finite-type and quantum invariants, topological quantum field theories (TQFT)", "description": "Finite-type and quantum invariants, topological quantum field theories (TQFT)", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K18", "originalCode": "57K18", "name": "Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.)", "description": "Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.)", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K20", "originalCode": "57K20", "name": "2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.)", "description": "2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.)", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K30", "originalCode": "57K30", "name": "General topology of 3-manifolds", "description": "General topology of 3-manifolds", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K31", "originalCode": "57K31", "name": "Invariants of 3-manifolds (including skein modules, character varieties)", "description": "Invariants of 3-manifolds (including skein modules, character varieties)", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K32", "originalCode": "57K32", "name": "Hyperbolic 3-manifolds", "description": "Hyperbolic 3-manifolds", "kind": "subject", "parent": "57K", "page": 150 }, { "code": "57K33", "originalCode": "57K33", "name": "Contact structures in 3 dimensions", "description": "Contact structures in 3 dimensions [See also 57R17]", "kind": "subject", "parent": "57K", "page": 151 }, { "code": "57K35", "originalCode": "57K35", "name": "Other geometric structures on 3-manifolds", "description": "Other geometric structures on 3-manifolds", "kind": "subject", "parent": "57K", "page": 151 }, { "code": "57K40", "originalCode": "57K40", "name": "General topology of 4-manifolds", "description": "General topology of 4-manifolds", "kind": "subject", "parent": "57K", "page": 151 }, { "code": "57K41", "originalCode": "57K41", "name": "Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants)", "description": "Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants)", "kind": "subject", "parent": "57K", "page": 151 }, { "code": "57K43", "originalCode": "57K43", "name": "Symplectic structures in 4 dimensions", "description": "Symplectic structures in 4 dimensions [See also 57R17]", "kind": "subject", "parent": "57K", "page": 151 }, { "code": "57K45", "originalCode": "57K45", "name": "Higher-dimensional knots and links", "description": "Higher-dimensional knots and links", "kind": "subject", "parent": "57K", "page": 151 }, { "code": "57K50", "originalCode": "57K50", "name": "Low-dimensional manifolds of specific dimension 5 or higher", "description": "Low-dimensional manifolds of specific dimension 5 or higher", "kind": "subject", "parent": "57K", "page": 151 }, { "code": "57K99", "originalCode": "57K99", "name": "Low-dimensional topology in specific dimensions", "description": "None of the above, but in this section", "kind": "subject", "parent": "57K", "page": 151 }, { "code": "57M", "originalCode": "57Mxx", "name": "General low-dimensional topology", "description": "General low-dimensional topology", "kind": "section", "parent": "57", "page": 151 }, { "code": "57M05", "originalCode": "57M05", "name": "Fundamental group, presentations, free differential calculus", "description": "Fundamental group, presentations, free differential calculus", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57M07", "originalCode": "57M07", "name": "Topological methods in group theory", "description": "Topological methods in group theory", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57M10", "originalCode": "57M10", "name": "Covering spaces and low-dimensional topology", "description": "Covering spaces and low-dimensional topology", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57M12", "originalCode": "57M12", "name": "Low-dimensional topology of special (e.g., branched) coverings", "description": "Low-dimensional topology of special (e.g., branched) coverings", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57M15", "originalCode": "57M15", "name": "Relations of low-dimensional topology with graph theory", "description": "Relations of low-dimensional topology with graph theory [See also 05C10]", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57M30", "originalCode": "57M30", "name": "Wild embeddings", "description": "Wild embeddings", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57M50", "originalCode": "57M50", "name": "General geometric structures on low-dimensional manifolds", "description": "General geometric structures on low-dimensional manifolds", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57M60", "originalCode": "57M60", "name": "Group actions on manifolds and cell complexes in low dimensions", "description": "Group actions on manifolds and cell complexes in low dimensions", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57M99", "originalCode": "57M99", "name": "General low-dimensional topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "57M", "page": 151 }, { "code": "57N", "originalCode": "57Nxx", "name": "Topological manifolds", "description": "Topological manifolds", "kind": "section", "parent": "57", "page": 151 }, { "code": "57N16", "originalCode": "57N16", "name": "Geometric structures on manifolds of high or arbitrary dimension", "description": "Geometric structures on manifolds of high or arbitrary dimension [See also 57M50]", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N17", "originalCode": "57N17", "name": "Topology of topological vector spaces", "description": "Topology of topological vector spaces", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N20", "originalCode": "57N20", "name": "Topology of infinite-dimensional manifolds", "description": "Topology of infinite-dimensional manifolds [See also 58Bxx]", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N25", "originalCode": "57N25", "name": "Shapes (aspects of topological manifolds)", "description": "Shapes (aspects of topological manifolds) [See also 54C56, 55P55, 55Q07]", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N30", "originalCode": "57N30", "name": "Engulfing in topological manifolds", "description": "Engulfing in topological manifolds", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N35", "originalCode": "57N35", "name": "Embeddings and immersions in topological manifolds", "description": "Embeddings and immersions in topological manifolds", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N37", "originalCode": "57N37", "name": "Isotopy and pseudo-isotopy", "description": "Isotopy and pseudo-isotopy", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N40", "originalCode": "57N40", "name": "Neighborhoods of submanifolds", "description": "Neighborhoods of submanifolds", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N45", "originalCode": "57N45", "name": "Flatness and tameness of topological manifolds", "description": "Flatness and tameness of topological manifolds", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N50", "originalCode": "57N50", "name": "\\(S^{n-1}\\subset E^n\\), Schoenflies problem", "description": "\\(S^{n-1}\\subset E^n\\), Schoenflies problem", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N55", "originalCode": "57N55", "name": "Microbundles and block bundles", "description": "Microbundles and block bundles [See also 55R60, 57Q50]", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N60", "originalCode": "57N60", "name": "Cellularity in topological manifolds", "description": "Cellularity in topological manifolds", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N65", "originalCode": "57N65", "name": "Algebraic topology of manifolds", "description": "Algebraic topology of manifolds", "kind": "subject", "parent": "57N", "page": 151 }, { "code": "57N70", "originalCode": "57N70", "name": "Cobordism and concordance in topological manifolds", "description": "Cobordism and concordance in topological manifolds", "kind": "subject", "parent": "57N", "page": 152 }, { "code": "57N75", "originalCode": "57N75", "name": "General position and transversality", "description": "General position and transversality", "kind": "subject", "parent": "57N", "page": 152 }, { "code": "57N80", "originalCode": "57N80", "name": "Stratifications in topological manifolds", "description": "Stratifications in topological manifolds", "kind": "subject", "parent": "57N", "page": 152 }, { "code": "57N99", "originalCode": "57N99", "name": "Topological manifolds", "description": "None of the above, but in this section", "kind": "subject", "parent": "57N", "page": 152 }, { "code": "57P", "originalCode": "57Pxx", "name": "Generalized manifolds", "description": "Generalized manifolds [See also 18F15]", "kind": "section", "parent": "57", "page": 152 }, { "code": "57P05", "originalCode": "57P05", "name": "Local properties of generalized manifolds", "description": "Local properties of generalized manifolds", "kind": "subject", "parent": "57P", "page": 152 }, { "code": "57P10", "originalCode": "57P10", "name": "Poincaré duality spaces", "description": "Poincaré duality spaces", "kind": "subject", "parent": "57P", "page": 152 }, { "code": "57P99", "originalCode": "57P99", "name": "Generalized manifolds", "description": "None of the above, but in this section", "kind": "subject", "parent": "57P", "page": 152 }, { "code": "57Q", "originalCode": "57Qxx", "name": "PL-topology", "description": "PL-topology", "kind": "section", "parent": "57", "page": 152 }, { "code": "57Q05", "originalCode": "57Q05", "name": "General topology of complexes", "description": "General topology of complexes", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q10", "originalCode": "57Q10", "name": "Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.", "description": "Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q12", "originalCode": "57Q12", "name": "Wall finiteness obstruction for CW-complexes", "description": "Wall finiteness obstruction for CW-complexes", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q15", "originalCode": "57Q15", "name": "Triangulating manifolds", "description": "Triangulating manifolds", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q20", "originalCode": "57Q20", "name": "Cobordism in PL-topology", "description": "Cobordism in PL-topology", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q25", "originalCode": "57Q25", "name": "Comparison of PL-structures: classification, Hauptvermutung", "description": "Comparison of PL-structures: classification, Hauptvermutung", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q30", "originalCode": "57Q30", "name": "Engulfing", "description": "Engulfing", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q35", "originalCode": "57Q35", "name": "Embeddings and immersions in PL-topology", "description": "Embeddings and immersions in PL-topology", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q37", "originalCode": "57Q37", "name": "Isotopy in PL-topology", "description": "Isotopy in PL-topology", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q40", "originalCode": "57Q40", "name": "Regular neighborhoods in PL-topology", "description": "Regular neighborhoods in PL-topology", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q50", "originalCode": "57Q50", "name": "Microbundles and block bundles", "description": "Microbundles and block bundles [See also 55R60, 57N55]", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q55", "originalCode": "57Q55", "name": "Approximations in PL-topology", "description": "Approximations in PL-topology", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q60", "originalCode": "57Q60", "name": "Cobordism and concordance in PL-topology", "description": "Cobordism and concordance in PL-topology", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q65", "originalCode": "57Q65", "name": "General position and transversality", "description": "General position and transversality", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q70", "originalCode": "57Q70", "name": "Discrete Morse theory and related ideas in manifold topology", "description": "Discrete Morse theory and related ideas in manifold topology", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q91", "originalCode": "57Q91", "name": "Equivariant PL-topology", "description": "Equivariant PL-topology", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57Q99", "originalCode": "57Q99", "name": "PL-topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "57Q", "page": 152 }, { "code": "57R", "originalCode": "57Rxx", "name": "Differential topology", "description": "Differential topology \\{For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx\\}", "kind": "section", "parent": "57", "page": 153 }, { "code": "57R05", "originalCode": "57R05", "name": "Triangulating", "description": "Triangulating", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R10", "originalCode": "57R10", "name": "Smoothing in differential topology", "description": "Smoothing in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R12", "originalCode": "57R12", "name": "Smooth approximations in differential topology", "description": "Smooth approximations in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R15", "originalCode": "57R15", "name": "Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)", "description": "Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R17", "originalCode": "57R17", "name": "Symplectic and contact topology in high or arbitrary dimension", "description": "Symplectic and contact topology in high or arbitrary dimension \\{For dimensions 3 and 4, see 57K33, 57K43\\}", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R18", "originalCode": "57R18", "name": "Topology and geometry of orbifolds", "description": "Topology and geometry of orbifolds", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R19", "originalCode": "57R19", "name": "Algebraic topology on manifolds and differential topology", "description": "Algebraic topology on manifolds and differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R20", "originalCode": "57R20", "name": "Characteristic classes and numbers in differential topology", "description": "Characteristic classes and numbers in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R22", "originalCode": "57R22", "name": "Topology of vector bundles and fiber bundles", "description": "Topology of vector bundles and fiber bundles [See also 55Rxx]", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R25", "originalCode": "57R25", "name": "Vector fields, frame fields in differential topology", "description": "Vector fields, frame fields in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R27", "originalCode": "57R27", "name": "Controllability of vector fields on \\(C^\\infty\\) and real-analytic manifolds", "description": "Controllability of vector fields on \\(C^\\infty\\) and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R30", "originalCode": "57R30", "name": "Foliations in differential topology; geometric theory", "description": "Foliations in differential topology; geometric theory [See also 53C12]", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R32", "originalCode": "57R32", "name": "Classifying spaces for foliations; Gelfand-Fuks cohomology", "description": "Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R35", "originalCode": "57R35", "name": "Differentiable mappings in differential topology", "description": "Differentiable mappings in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R40", "originalCode": "57R40", "name": "Embeddings in differential topology", "description": "Embeddings in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R42", "originalCode": "57R42", "name": "Immersions in differential topology", "description": "Immersions in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R45", "originalCode": "57R45", "name": "Singularities of differentiable mappings in differential topology", "description": "Singularities of differentiable mappings in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R50", "originalCode": "57R50", "name": "Differential topological aspects of diffeomorphisms", "description": "Differential topological aspects of diffeomorphisms", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R52", "originalCode": "57R52", "name": "Isotopy in differential topology", "description": "Isotopy in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R55", "originalCode": "57R55", "name": "Differentiable structures in differential topology", "description": "Differentiable structures in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R56", "originalCode": "57R56", "name": "Topological quantum field theories (aspects of differential topology)", "description": "Topological quantum field theories (aspects of differential topology)", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R57", "originalCode": "57R57", "name": "Applications of global analysis to structures on manifolds", "description": "Applications of global analysis to structures on manifolds [See also 57K41, 58-XX]", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R58", "originalCode": "57R58", "name": "Floer homology", "description": "Floer homology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R60", "originalCode": "57R60", "name": "Homotopy spheres, Poincaré conjecture", "description": "Homotopy spheres, Poincaré conjecture", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R65", "originalCode": "57R65", "name": "Surgery and handlebodies", "description": "Surgery and handlebodies", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R67", "originalCode": "57R67", "name": "Surgery obstructions, Wall groups", "description": "Surgery obstructions, Wall groups [See also 19J25]", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R70", "originalCode": "57R70", "name": "Critical points and critical submanifolds in differential topology", "description": "Critical points and critical submanifolds in differential topology", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R75", "originalCode": "57R75", "name": "\\(\\mathrm{O}\\)- and \\(\\mathrm{SO}\\)-cobordism", "description": "\\(\\mathrm{O}\\)- and \\(\\mathrm{SO}\\)-cobordism", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R77", "originalCode": "57R77", "name": "Complex cobordism (\\(\\mathrm{U}\\)- and \\(\\mathrm{SU}\\)-cobordism)", "description": "Complex cobordism (\\(\\mathrm{U}\\)- and \\(\\mathrm{SU}\\)-cobordism) [See also 55N22]", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R80", "originalCode": "57R80", "name": "\\(h\\)- and \\(s\\)-cobordism", "description": "\\(h\\)- and \\(s\\)-cobordism", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R85", "originalCode": "57R85", "name": "Equivariant cobordism", "description": "Equivariant cobordism", "kind": "subject", "parent": "57R", "page": 153 }, { "code": "57R90", "originalCode": "57R90", "name": "Other types of cobordism", "description": "Other types of cobordism [See also 55N22]", "kind": "subject", "parent": "57R", "page": 154 }, { "code": "57R91", "originalCode": "57R91", "name": "Equivariant algebraic topology of manifolds", "description": "Equivariant algebraic topology of manifolds", "kind": "subject", "parent": "57R", "page": 154 }, { "code": "57R95", "originalCode": "57R95", "name": "Realizing cycles by submanifolds", "description": "Realizing cycles by submanifolds", "kind": "subject", "parent": "57R", "page": 154 }, { "code": "57R99", "originalCode": "57R99", "name": "Differential topology", "description": "None of the above, but in this section", "kind": "subject", "parent": "57R", "page": 154 }, { "code": "57S", "originalCode": "57Sxx", "name": "Topological transformation groups", "description": "Topological transformation groups [See also 20F34, 22-XX, 37-XX, 54H15, 58D05]", "kind": "section", "parent": "57", "page": 154 }, { "code": "57S05", "originalCode": "57S05", "name": "Topological properties of groups of homeomorphisms or diffeomorphisms", "description": "Topological properties of groups of homeomorphisms or diffeomorphisms", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57S10", "originalCode": "57S10", "name": "Compact groups of homeomorphisms", "description": "Compact groups of homeomorphisms", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57S12", "originalCode": "57S12", "name": "Toric topology", "description": "Toric topology", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57S15", "originalCode": "57S15", "name": "Compact Lie groups of differentiable transformations", "description": "Compact Lie groups of differentiable transformations", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57S17", "originalCode": "57S17", "name": "Finite transformation groups", "description": "Finite transformation groups", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57S20", "originalCode": "57S20", "name": "Noncompact Lie groups of transformations", "description": "Noncompact Lie groups of transformations", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57S25", "originalCode": "57S25", "name": "Groups acting on specific manifolds", "description": "Groups acting on specific manifolds", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57S30", "originalCode": "57S30", "name": "Discontinuous groups of transformations", "description": "Discontinuous groups of transformations", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57S99", "originalCode": "57S99", "name": "Topological transformation groups", "description": "None of the above, but in this section", "kind": "subject", "parent": "57S", "page": 154 }, { "code": "57T", "originalCode": "57Txx", "name": "Homology and homotopy of topological groups and related structures", "description": "Homology and homotopy of topological groups and related structures", "kind": "section", "parent": "57", "page": 154 }, { "code": "57T05", "originalCode": "57T05", "name": "Hopf algebras (aspects of homology and homotopy of topological groups)", "description": "Hopf algebras (aspects of homology and homotopy of topological groups) [See also 16T05]", "kind": "subject", "parent": "57T", "page": 154 }, { "code": "57T10", "originalCode": "57T10", "name": "Homology and cohomology of Lie groups", "description": "Homology and cohomology of Lie groups", "kind": "subject", "parent": "57T", "page": 154 }, { "code": "57T15", "originalCode": "57T15", "name": "Homology and cohomology of homogeneous spaces of Lie groups", "description": "Homology and cohomology of homogeneous spaces of Lie groups", "kind": "subject", "parent": "57T", "page": 154 }, { "code": "57T20", "originalCode": "57T20", "name": "Homotopy groups of topological groups and homogeneous spaces", "description": "Homotopy groups of topological groups and homogeneous spaces", "kind": "subject", "parent": "57T", "page": 154 }, { "code": "57T25", "originalCode": "57T25", "name": "Homology and cohomology of \\(H\\)-spaces", "description": "Homology and cohomology of \\(H\\)-spaces", "kind": "subject", "parent": "57T", "page": 154 }, { "code": "57T30", "originalCode": "57T30", "name": "Bar and cobar constructions", "description": "Bar and cobar constructions [See also 18N40, 55Uxx]", "kind": "subject", "parent": "57T", "page": 154 }, { "code": "57T35", "originalCode": "57T35", "name": "Applications of Eilenberg-Moore spectral sequences", "description": "Applications of Eilenberg-Moore spectral sequences [See also 55R20, 55T20]", "kind": "subject", "parent": "57T", "page": 154 }, { "code": "57T99", "originalCode": "57T99", "name": "Homology and homotopy of topological groups and related structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "57T", "page": 154 }, { "code": "57Z", "originalCode": "57Zxx", "name": "Relations of manifolds and cell complexes with science and engineering", "description": "Relations of manifolds and cell complexes with science and engineering", "kind": "section", "parent": "57", "page": 154 }, { "code": "57Z05", "originalCode": "57Z05", "name": "Relations of manifolds and cell complexes with physics", "description": "Relations of manifolds and cell complexes with physics", "kind": "subject", "parent": "57Z", "page": 154 }, { "code": "57Z10", "originalCode": "57Z10", "name": "Relations of manifolds and cell complexes with biology", "description": "Relations of manifolds and cell complexes with biology", "kind": "subject", "parent": "57Z", "page": 154 }, { "code": "57Z15", "originalCode": "57Z15", "name": "Relations of manifolds and cell complexes with chemistry", "description": "Relations of manifolds and cell complexes with chemistry", "kind": "subject", "parent": "57Z", "page": 154 }, { "code": "57Z20", "originalCode": "57Z20", "name": "Relations of manifolds and cell complexes with engineering", "description": "Relations of manifolds and cell complexes with engineering", "kind": "subject", "parent": "57Z", "page": 154 }, { "code": "57Z25", "originalCode": "57Z25", "name": "Relations of manifolds and cell complexes with computer and data science", "description": "Relations of manifolds and cell complexes with computer and data science", "kind": "subject", "parent": "57Z", "page": 154 }, { "code": "57Z99", "originalCode": "57Z99", "name": "Relations of manifolds and cell complexes with science and engineering", "description": "None of the above, but in this section", "kind": "subject", "parent": "57Z", "page": 154 }, { "code": "58", "originalCode": "58-XX", "name": "Global analysis, analysis on manifolds", "description": "Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 53Cxx] \\{For nonlinear operators, see 47Hxx; for geometric integration theory, see 49Q15\\}", "kind": "class", "parent": null, "page": 155 }, { "code": "58-00", "originalCode": "58-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to global analysis", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to global analysis", "kind": "subject", "parent": "58", "page": 155 }, { "code": "58-01", "originalCode": "58-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis", "kind": "subject", "parent": "58", "page": 155 }, { "code": "58-02", "originalCode": "58-02", "name": "Research exposition (monographs, survey articles) pertaining to global analysis", "description": "Research exposition (monographs, survey articles) pertaining to global analysis", "kind": "subject", "parent": "58", "page": 155 }, { "code": "58-03", "originalCode": "58-03", "name": "History of global analysis", "description": "History of global analysis [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "58", "page": 155 }, { "code": "58-04", "originalCode": "58-04", "name": "Software, source code, etc. for problems pertaining to global analysis", "description": "Software, source code, etc. for problems pertaining to global analysis", "kind": "subject", "parent": "58", "page": 155 }, { "code": "58-06", "originalCode": "58-06", "name": "Proceedings, conferences, collections, etc. pertaining to global analysis", "description": "Proceedings, conferences, collections, etc. pertaining to global analysis", "kind": "subject", "parent": "58", "page": 155 }, { "code": "58-08", "originalCode": "58-08", "name": "Computational methods for problems pertaining to global analysis", "description": "Computational methods for problems pertaining to global analysis", "kind": "subject", "parent": "58", "page": 155 }, { "code": "58-11", "originalCode": "58-11", "name": "Research data for problems pertaining to global analysis", "description": "Research data for problems pertaining to global analysis", "kind": "subject", "parent": "58", "page": 155 }, { "code": "58A", "originalCode": "58Axx", "name": "General theory of differentiable manifolds", "description": "General theory of differentiable manifolds [See also 32Cxx]", "kind": "section", "parent": "58", "page": 155 }, { "code": "58A03", "originalCode": "58A03", "name": "Topos-theoretic approach to differentiable manifolds", "description": "Topos-theoretic approach to differentiable manifolds", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A05", "originalCode": "58A05", "name": "Differentiable manifolds, foundations", "description": "Differentiable manifolds, foundations", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A07", "originalCode": "58A07", "name": "Real-analytic and Nash manifolds", "description": "Real-analytic and Nash manifolds [See also 14P20, 32C07]", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A10", "originalCode": "58A10", "name": "Differential forms in global analysis", "description": "Differential forms in global analysis", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A12", "originalCode": "58A12", "name": "de Rham theory in global analysis", "description": "de Rham theory in global analysis [See also 14Fxx]", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A14", "originalCode": "58A14", "name": "Hodge theory in global analysis", "description": "Hodge theory in global analysis [See also 14C30, 14Fxx, 32J25, 32S35]", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A15", "originalCode": "58A15", "name": "Exterior differential systems (Cartan theory)", "description": "Exterior differential systems (Cartan theory)", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A17", "originalCode": "58A17", "name": "Pfaffian systems", "description": "Pfaffian systems", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A20", "originalCode": "58A20", "name": "Jets in global analysis", "description": "Jets in global analysis", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A25", "originalCode": "58A25", "name": "Currents in global analysis", "description": "Currents in global analysis [See also 32C30, 53C65]", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A30", "originalCode": "58A30", "name": "Vector distributions (subbundles of the tangent bundles)", "description": "Vector distributions (subbundles of the tangent bundles)", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A32", "originalCode": "58A32", "name": "Natural bundles", "description": "Natural bundles", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A35", "originalCode": "58A35", "name": "Stratified sets", "description": "Stratified sets [See also 32S60]", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A40", "originalCode": "58A40", "name": "Differential spaces", "description": "Differential spaces", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A50", "originalCode": "58A50", "name": "Supermanifolds and graded manifolds", "description": "Supermanifolds and graded manifolds [See also 14A22, 32C11]", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58A99", "originalCode": "58A99", "name": "General theory of differentiable manifolds", "description": "None of the above, but in this section", "kind": "subject", "parent": "58A", "page": 155 }, { "code": "58B", "originalCode": "58Bxx", "name": "Infinite-dimensional manifolds", "description": "Infinite-dimensional manifolds", "kind": "section", "parent": "58", "page": 156 }, { "code": "58B05", "originalCode": "58B05", "name": "Homotopy and topological questions for infinite-dimensional manifolds", "description": "Homotopy and topological questions for infinite-dimensional manifolds", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58B10", "originalCode": "58B10", "name": "Differentiability questions for infinite-dimensional manifolds", "description": "Differentiability questions for infinite-dimensional manifolds", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58B12", "originalCode": "58B12", "name": "Questions of holomorphy and infinite-dimensional manifolds", "description": "Questions of holomorphy and infinite-dimensional manifolds [See also 32-XX, 46G20]", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58B15", "originalCode": "58B15", "name": "Fredholm structures on infinite-dimensional manifolds", "description": "Fredholm structures on infinite-dimensional manifolds [See also 47A53]", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58B20", "originalCode": "58B20", "name": "Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds", "description": "Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds [See also 53C20, 53C60]", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58B25", "originalCode": "58B25", "name": "Group structures and generalizations on infinite-dimensional manifolds", "description": "Group structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58B32", "originalCode": "58B32", "name": "Geometry of quantum groups", "description": "Geometry of quantum groups", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58B34", "originalCode": "58B34", "name": "Noncommutative geometry (à la Connes)", "description": "Noncommutative geometry (à la Connes)", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58B99", "originalCode": "58B99", "name": "Infinite-dimensional manifolds", "description": "None of the above, but in this section", "kind": "subject", "parent": "58B", "page": 156 }, { "code": "58C", "originalCode": "58Cxx", "name": "Calculus on manifolds; nonlinear operators", "description": "Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]", "kind": "section", "parent": "58", "page": 156 }, { "code": "58C05", "originalCode": "58C05", "name": "Real-valued functions on manifolds", "description": "Real-valued functions on manifolds", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C06", "originalCode": "58C06", "name": "Set-valued and function-space-valued mappings on manifolds", "description": "Set-valued and function-space-valued mappings on manifolds [See also 47H04, 54C60]", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C07", "originalCode": "58C07", "name": "Continuity properties of mappings on manifolds", "description": "Continuity properties of mappings on manifolds", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C10", "originalCode": "58C10", "name": "Holomorphic maps on manifolds", "description": "Holomorphic maps on manifolds [See also 32-XX]", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C15", "originalCode": "58C15", "name": "Implicit function theorems; global Newton methods on manifolds", "description": "Implicit function theorems; global Newton methods on manifolds", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C20", "originalCode": "58C20", "name": "Differentiation theory (Gateaux, Fréchet, etc.) on manifolds", "description": "Differentiation theory (Gateaux, Fréchet, etc.) on manifolds [See also 26Exx, 46G05]", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C25", "originalCode": "58C25", "name": "Differentiable maps on manifolds", "description": "Differentiable maps on manifolds", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C30", "originalCode": "58C30", "name": "Fixed-point theorems on manifolds", "description": "Fixed-point theorems on manifolds [See also 47H10]", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C35", "originalCode": "58C35", "name": "Integration on manifolds; measures on manifolds", "description": "Integration on manifolds; measures on manifolds [See also 28Cxx]", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C40", "originalCode": "58C40", "name": "Spectral theory; eigenvalue problems on manifolds", "description": "Spectral theory; eigenvalue problems on manifolds [See also 47J10, 58E07]", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C50", "originalCode": "58C50", "name": "Analysis on supermanifolds or graded manifolds", "description": "Analysis on supermanifolds or graded manifolds", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58C99", "originalCode": "58C99", "name": "Calculus on manifolds; nonlinear operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "58C", "page": 156 }, { "code": "58D", "originalCode": "58Dxx", "name": "Spaces and manifolds of mappings (including nonlinear versions of 46Exx)", "description": "Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]", "kind": "section", "parent": "58", "page": 156 }, { "code": "58D05", "originalCode": "58D05", "name": "Groups of diffeomorphisms and homeomorphisms as manifolds", "description": "Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]", "kind": "subject", "parent": "58D", "page": 156 }, { "code": "58D07", "originalCode": "58D07", "name": "Groups and semigroups of nonlinear operators", "description": "Groups and semigroups of nonlinear operators [See also 17B65, 47H20]", "kind": "subject", "parent": "58D", "page": 156 }, { "code": "58D10", "originalCode": "58D10", "name": "Spaces of embeddings and immersions", "description": "Spaces of embeddings and immersions", "kind": "subject", "parent": "58D", "page": 156 }, { "code": "58D15", "originalCode": "58D15", "name": "Manifolds of mappings", "description": "Manifolds of mappings [See also 46T10, 54C35]", "kind": "subject", "parent": "58D", "page": 156 }, { "code": "58D17", "originalCode": "58D17", "name": "Manifolds of metrics (especially Riemannian)", "description": "Manifolds of metrics (especially Riemannian)", "kind": "subject", "parent": "58D", "page": 156 }, { "code": "58D19", "originalCode": "58D19", "name": "Group actions and symmetry properties", "description": "Group actions and symmetry properties", "kind": "subject", "parent": "58D", "page": 156 }, { "code": "58D20", "originalCode": "58D20", "name": "Measures (Gaussian, cylindrical, etc.) on manifolds of maps", "description": "Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12]", "kind": "subject", "parent": "58D", "page": 156 }, { "code": "58D25", "originalCode": "58D25", "name": "Equations in function spaces; evolution equations", "description": "Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]", "kind": "subject", "parent": "58D", "page": 156 }, { "code": "58D27", "originalCode": "58D27", "name": "Moduli problems for differential geometric structures", "description": "Moduli problems for differential geometric structures", "kind": "subject", "parent": "58D", "page": 157 }, { "code": "58D29", "originalCode": "58D29", "name": "Moduli problems for topological structures", "description": "Moduli problems for topological structures", "kind": "subject", "parent": "58D", "page": 157 }, { "code": "58D30", "originalCode": "58D30", "name": "Applications of manifolds of mappings to the sciences", "description": "Applications of manifolds of mappings to the sciences", "kind": "subject", "parent": "58D", "page": 157 }, { "code": "58D99", "originalCode": "58D99", "name": "Spaces and manifolds of mappings (including nonlinear versions of 46Exx)", "description": "None of the above, but in this section", "kind": "subject", "parent": "58D", "page": 157 }, { "code": "58E", "originalCode": "58Exx", "name": "Variational problems in infinite-dimensional spaces", "description": "Variational problems in infinite-dimensional spaces", "kind": "section", "parent": "58", "page": 157 }, { "code": "58E05", "originalCode": "58E05", "name": "Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces", "description": "Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E07", "originalCode": "58E07", "name": "Variational problems in abstract bifurcation theory in infinite-dimensional spaces", "description": "Variational problems in abstract bifurcation theory in infinite-dimensional spaces", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E09", "originalCode": "58E09", "name": "Group-invariant bifurcation theory in infinite-dimensional spaces", "description": "Group-invariant bifurcation theory in infinite-dimensional spaces", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E10", "originalCode": "58E10", "name": "Variational problems in applications to the theory of geodesics (problems in one independent variable)", "description": "Variational problems in applications to the theory of geodesics (problems in one independent variable)", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E11", "originalCode": "58E11", "name": "Critical metrics", "description": "Critical metrics", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E12", "originalCode": "58E12", "name": "Variational problems concerning minimal surfaces (problems in two independent variables)", "description": "Variational problems concerning minimal surfaces (problems in two independent variables) [See also 49Q05]", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E15", "originalCode": "58E15", "name": "Variational problems concerning extremal problems in several variables; Yang-Mills functionals", "description": "Variational problems concerning extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E17", "originalCode": "58E17", "name": "Multiobjective variational problems, Pareto optimality, applications to economics, etc.", "description": "Multiobjective variational problems, Pareto optimality, applications to economics, etc. [See also 90C29, 91Bxx]", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E20", "originalCode": "58E20", "name": "Harmonic maps, etc.", "description": "Harmonic maps, etc. [See also 53C43]", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E25", "originalCode": "58E25", "name": "Applications of variational problems to control theory", "description": "Applications of variational problems to control theory [See also 49-XX, 93-XX]", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E30", "originalCode": "58E30", "name": "Variational principles in infinite-dimensional spaces", "description": "Variational principles in infinite-dimensional spaces", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E35", "originalCode": "58E35", "name": "Variational inequalities (global problems) in infinite-dimensional spaces", "description": "Variational inequalities (global problems) in infinite-dimensional spaces", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E40", "originalCode": "58E40", "name": "Variational aspects of group actions in infinite-dimensional spaces", "description": "Variational aspects of group actions in infinite-dimensional spaces", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E50", "originalCode": "58E50", "name": "Applications of variational problems in infinite-dimensional spaces to the sciences", "description": "Applications of variational problems in infinite-dimensional spaces to the sciences", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58E99", "originalCode": "58E99", "name": "Variational problems in infinite-dimensional spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "58E", "page": 157 }, { "code": "58H", "originalCode": "58Hxx", "name": "Pseudogroups, differentiable groupoids and general structures on manifolds", "description": "Pseudogroups, differentiable groupoids and general structures on manifolds", "kind": "section", "parent": "58", "page": 157 }, { "code": "58H05", "originalCode": "58H05", "name": "Pseudogroups and differentiable groupoids", "description": "Pseudogroups and differentiable groupoids [See also 22A22, 22E65]", "kind": "subject", "parent": "58H", "page": 157 }, { "code": "58H10", "originalCode": "58H10", "name": "Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)", "description": "Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]", "kind": "subject", "parent": "58H", "page": 157 }, { "code": "58H15", "originalCode": "58H15", "name": "Deformations of general structures on manifolds", "description": "Deformations of general structures on manifolds [See also 32Gxx, 58J10]", "kind": "subject", "parent": "58H", "page": 157 }, { "code": "58H99", "originalCode": "58H99", "name": "Pseudogroups, differentiable groupoids and general structures on manifolds", "description": "None of the above, but in this section", "kind": "subject", "parent": "58H", "page": 157 }, { "code": "58J", "originalCode": "58Jxx", "name": "Partial differential equations on manifolds; differential operators", "description": "Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]", "kind": "section", "parent": "58", "page": 158 }, { "code": "58J05", "originalCode": "58J05", "name": "Elliptic equations on manifolds, general theory", "description": "Elliptic equations on manifolds, general theory [See also 35Jxx]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J10", "originalCode": "58J10", "name": "Differential complexes", "description": "Differential complexes [See also 35Nxx]; elliptic complexes", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J15", "originalCode": "58J15", "name": "Relations of PDEs on manifolds with hyperfunctions", "description": "Relations of PDEs on manifolds with hyperfunctions", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J20", "originalCode": "58J20", "name": "Index theory and related fixed-point theorems on manifolds", "description": "Index theory and related fixed-point theorems on manifolds [See also 19K56, 46L80]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J22", "originalCode": "58J22", "name": "Exotic index theories on manifolds", "description": "Exotic index theories on manifolds [See also 19K56, 46L05, 46L10, 46L80, 46M20]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J26", "originalCode": "58J26", "name": "Elliptic genera", "description": "Elliptic genera", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J28", "originalCode": "58J28", "name": "Eta-invariants, Chern-Simons invariants", "description": "Eta-invariants, Chern-Simons invariants", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J30", "originalCode": "58J30", "name": "Spectral flows", "description": "Spectral flows", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J32", "originalCode": "58J32", "name": "Boundary value problems on manifolds", "description": "Boundary value problems on manifolds", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J35", "originalCode": "58J35", "name": "Heat and other parabolic equation methods for PDEs on manifolds", "description": "Heat and other parabolic equation methods for PDEs on manifolds", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J37", "originalCode": "58J37", "name": "Perturbations of PDEs on manifolds; asymptotics", "description": "Perturbations of PDEs on manifolds; asymptotics", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J40", "originalCode": "58J40", "name": "Pseudodifferential and Fourier integral operators on manifolds", "description": "Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J42", "originalCode": "58J42", "name": "Noncommutative global analysis, noncommutative residues", "description": "Noncommutative global analysis, noncommutative residues", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J45", "originalCode": "58J45", "name": "Hyperbolic equations on manifolds", "description": "Hyperbolic equations on manifolds [See also 35Lxx]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J47", "originalCode": "58J47", "name": "Propagation of singularities; initial value problems on manifolds", "description": "Propagation of singularities; initial value problems on manifolds", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J50", "originalCode": "58J50", "name": "Spectral problems; spectral geometry; scattering theory on manifolds", "description": "Spectral problems; spectral geometry; scattering theory on manifolds [See also 35Pxx]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J51", "originalCode": "58J51", "name": "Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity", "description": "Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J52", "originalCode": "58J52", "name": "Determinants and determinant bundles, analytic torsion", "description": "Determinants and determinant bundles, analytic torsion", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J53", "originalCode": "58J53", "name": "Isospectrality", "description": "Isospectrality", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J55", "originalCode": "58J55", "name": "Bifurcation theory for PDEs on manifolds", "description": "Bifurcation theory for PDEs on manifolds [See also 35B32]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J60", "originalCode": "58J60", "name": "Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)", "description": "Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J65", "originalCode": "58J65", "name": "Diffusion processes and stochastic analysis on manifolds", "description": "Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J70", "originalCode": "58J70", "name": "Invariance and symmetry properties for PDEs on manifolds", "description": "Invariance and symmetry properties for PDEs on manifolds [See also 35A30]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J72", "originalCode": "58J72", "name": "Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds", "description": "Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds [See also 35A22]", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J90", "originalCode": "58J90", "name": "Applications of PDEs on manifolds", "description": "Applications of PDEs on manifolds", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58J99", "originalCode": "58J99", "name": "Partial differential equations on manifolds; differential operators", "description": "None of the above, but in this section", "kind": "subject", "parent": "58J", "page": 158 }, { "code": "58K", "originalCode": "58Kxx", "name": "Theory of singularities and catastrophe theory", "description": "Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]", "kind": "section", "parent": "58", "page": 159 }, { "code": "58K05", "originalCode": "58K05", "name": "Critical points of functions and mappings on manifolds", "description": "Critical points of functions and mappings on manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K10", "originalCode": "58K10", "name": "Monodromy on manifolds", "description": "Monodromy on manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K15", "originalCode": "58K15", "name": "Topological properties of mappings on manifolds", "description": "Topological properties of mappings on manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K20", "originalCode": "58K20", "name": "Algebraic and analytic properties of mappings on manifolds", "description": "Algebraic and analytic properties of mappings on manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K25", "originalCode": "58K25", "name": "Stability theory for manifolds", "description": "Stability theory for manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K30", "originalCode": "58K30", "name": "Global theory of singularities", "description": "Global theory of singularities", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K35", "originalCode": "58K35", "name": "Catastrophe theory", "description": "Catastrophe theory", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K40", "originalCode": "58K40", "name": "Classification; finite determinacy of map germs", "description": "Classification; finite determinacy of map germs", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K45", "originalCode": "58K45", "name": "Singularities of vector fields, topological aspects", "description": "Singularities of vector fields, topological aspects", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K50", "originalCode": "58K50", "name": "Normal forms on manifolds", "description": "Normal forms on manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K55", "originalCode": "58K55", "name": "Asymptotic behavior of solutions to equations on manifolds", "description": "Asymptotic behavior of solutions to equations on manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K60", "originalCode": "58K60", "name": "Deformation of singularities", "description": "Deformation of singularities", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K65", "originalCode": "58K65", "name": "Topological invariants on manifolds", "description": "Topological invariants on manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K70", "originalCode": "58K70", "name": "Symmetries, equivariance on manifolds", "description": "Symmetries, equivariance on manifolds", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58K99", "originalCode": "58K99", "name": "Theory of singularities and catastrophe theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "58K", "page": 159 }, { "code": "58Z", "originalCode": "58Zxx", "name": "Applications of global analysis to the sciences", "description": "Applications of global analysis to the sciences", "kind": "section", "parent": "58", "page": 159 }, { "code": "58Z05", "originalCode": "58Z05", "name": "Applications of global analysis to the sciences", "description": "Applications of global analysis to the sciences", "kind": "subject", "parent": "58Z", "page": 159 }, { "code": "58Z99", "originalCode": "58Z99", "name": "Applications of global analysis to the sciences", "description": "None of the above, but in this section", "kind": "subject", "parent": "58Z", "page": 159 }, { "code": "60", "originalCode": "60-XX", "name": "Probability theory and stochastic processes", "description": "Probability theory and stochastic processes \\{For additional applications, see 05Cxx, 11Kxx, 34-XX, 35-XX, 62-XX, 76-XX, 81-XX, 82-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX\\}", "kind": "class", "parent": null, "page": 159 }, { "code": "60-00", "originalCode": "60-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to probability theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to probability theory", "kind": "subject", "parent": "60", "page": 159 }, { "code": "60-01", "originalCode": "60-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory", "kind": "subject", "parent": "60", "page": 159 }, { "code": "60-02", "originalCode": "60-02", "name": "Research exposition (monographs, survey articles) pertaining to probability theory", "description": "Research exposition (monographs, survey articles) pertaining to probability theory", "kind": "subject", "parent": "60", "page": 159 }, { "code": "60-03", "originalCode": "60-03", "name": "History of probability theory", "description": "History of probability theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "60", "page": 159 }, { "code": "60-04", "originalCode": "60-04", "name": "Software, source code, etc. for problems pertaining to probability theory", "description": "Software, source code, etc. for problems pertaining to probability theory", "kind": "subject", "parent": "60", "page": 159 }, { "code": "60-06", "originalCode": "60-06", "name": "Proceedings, conferences, collections, etc. pertaining to probability theory", "description": "Proceedings, conferences, collections, etc. pertaining to probability theory", "kind": "subject", "parent": "60", "page": 159 }, { "code": "60-08", "originalCode": "60-08", "name": "Computational methods for problems pertaining to probability theory", "description": "Computational methods for problems pertaining to probability theory", "kind": "subject", "parent": "60", "page": 159 }, { "code": "60-11", "originalCode": "60-11", "name": "Research data for problems pertaining to probability theory", "description": "Research data for problems pertaining to probability theory", "kind": "subject", "parent": "60", "page": 159 }, { "code": "60A", "originalCode": "60Axx", "name": "Foundations of probability theory", "description": "Foundations of probability theory", "kind": "section", "parent": "60", "page": 160 }, { "code": "60A05", "originalCode": "60A05", "name": "Axioms; other general questions in probability", "description": "Axioms; other general questions in probability", "kind": "subject", "parent": "60A", "page": 160 }, { "code": "60A10", "originalCode": "60A10", "name": "Probabilistic measure theory", "description": "Probabilistic measure theory \\{For ergodic theory, see 28Dxx, 60Fxx\\}", "kind": "subject", "parent": "60A", "page": 160 }, { "code": "60A86", "originalCode": "60A86", "name": "Fuzzy probability", "description": "Fuzzy probability", "kind": "subject", "parent": "60A", "page": 160 }, { "code": "60A99", "originalCode": "60A99", "name": "Foundations of probability theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "60A", "page": 160 }, { "code": "60B", "originalCode": "60Bxx", "name": "Probability theory on algebraic and topological structures", "description": "Probability theory on algebraic and topological structures", "kind": "section", "parent": "60", "page": 160 }, { "code": "60B05", "originalCode": "60B05", "name": "Probability measures on topological spaces", "description": "Probability measures on topological spaces", "kind": "subject", "parent": "60B", "page": 160 }, { "code": "60B10", "originalCode": "60B10", "name": "Convergence of probability measures", "description": "Convergence of probability measures", "kind": "subject", "parent": "60B", "page": 160 }, { "code": "60B11", "originalCode": "60B11", "name": "Probability theory on linear topological spaces", "description": "Probability theory on linear topological spaces [See also 28C20]", "kind": "subject", "parent": "60B", "page": 160 }, { "code": "60B12", "originalCode": "60B12", "name": "Limit theorems for vector-valued random variables (infinite-dimensional case)", "description": "Limit theorems for vector-valued random variables (infinite-dimensional case)", "kind": "subject", "parent": "60B", "page": 160 }, { "code": "60B15", "originalCode": "60B15", "name": "Probability measures on groups or semigroups, Fourier transforms, factorization", "description": "Probability measures on groups or semigroups, Fourier transforms, factorization", "kind": "subject", "parent": "60B", "page": 160 }, { "code": "60B20", "originalCode": "60B20", "name": "Random matrices (probabilistic aspects)", "description": "Random matrices (probabilistic aspects) \\{For algebraic aspects, see 15B52\\}", "kind": "subject", "parent": "60B", "page": 160 }, { "code": "60B99", "originalCode": "60B99", "name": "Probability theory on algebraic and topological structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "60B", "page": 160 }, { "code": "60C", "originalCode": "60Cxx", "name": "Combinatorial probability", "description": "Combinatorial probability", "kind": "section", "parent": "60", "page": 160 }, { "code": "60C05", "originalCode": "60C05", "name": "Combinatorial probability", "description": "Combinatorial probability", "kind": "subject", "parent": "60C", "page": 160 }, { "code": "60C99", "originalCode": "60C99", "name": "Combinatorial probability", "description": "None of the above, but in this section", "kind": "subject", "parent": "60C", "page": 160 }, { "code": "60D", "originalCode": "60Dxx", "name": "Geometric probability and stochastic geometry", "description": "Geometric probability and stochastic geometry [See also 52A22, 53C65]", "kind": "section", "parent": "60", "page": 160 }, { "code": "60D05", "originalCode": "60D05", "name": "Geometric probability and stochastic geometry", "description": "Geometric probability and stochastic geometry [See also 52A22, 53C65]", "kind": "subject", "parent": "60D", "page": 160 }, { "code": "60D99", "originalCode": "60D99", "name": "Geometric probability and stochastic geometry", "description": "None of the above, but in this section", "kind": "subject", "parent": "60D", "page": 160 }, { "code": "60E", "originalCode": "60Exx", "name": "Distribution theory", "description": "Distribution theory [See also 62Exx, 62Hxx]", "kind": "section", "parent": "60", "page": 160 }, { "code": "60E05", "originalCode": "60E05", "name": "Probability distributions: general theory", "description": "Probability distributions: general theory", "kind": "subject", "parent": "60E", "page": 160 }, { "code": "60E07", "originalCode": "60E07", "name": "Infinitely divisible distributions; stable distributions", "description": "Infinitely divisible distributions; stable distributions", "kind": "subject", "parent": "60E", "page": 160 }, { "code": "60E10", "originalCode": "60E10", "name": "Characteristic functions; other transforms", "description": "Characteristic functions; other transforms", "kind": "subject", "parent": "60E", "page": 160 }, { "code": "60E15", "originalCode": "60E15", "name": "Inequalities; stochastic orderings", "description": "Inequalities; stochastic orderings", "kind": "subject", "parent": "60E", "page": 160 }, { "code": "60E99", "originalCode": "60E99", "name": "Distribution theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "60E", "page": 160 }, { "code": "60F", "originalCode": "60Fxx", "name": "Limit theorems in probability theory", "description": "Limit theorems in probability theory [See also 28Dxx, 60B12]", "kind": "section", "parent": "60", "page": 160 }, { "code": "60F05", "originalCode": "60F05", "name": "Central limit and other weak theorems", "description": "Central limit and other weak theorems", "kind": "subject", "parent": "60F", "page": 160 }, { "code": "60F10", "originalCode": "60F10", "name": "Large deviations", "description": "Large deviations", "kind": "subject", "parent": "60F", "page": 160 }, { "code": "60F15", "originalCode": "60F15", "name": "Strong limit theorems", "description": "Strong limit theorems", "kind": "subject", "parent": "60F", "page": 160 }, { "code": "60F17", "originalCode": "60F17", "name": "Functional limit theorems; invariance principles", "description": "Functional limit theorems; invariance principles", "kind": "subject", "parent": "60F", "page": 160 }, { "code": "60F20", "originalCode": "60F20", "name": "Zero-one laws", "description": "Zero-one laws", "kind": "subject", "parent": "60F", "page": 160 }, { "code": "60F25", "originalCode": "60F25", "name": "\\(L^p\\)-limit theorems", "description": "\\(L^p\\)-limit theorems", "kind": "subject", "parent": "60F", "page": 160 }, { "code": "60F99", "originalCode": "60F99", "name": "Limit theorems in probability theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "60F", "page": 160 }, { "code": "60G", "originalCode": "60Gxx", "name": "Stochastic processes", "description": "Stochastic processes", "kind": "section", "parent": "60", "page": 161 }, { "code": "60G05", "originalCode": "60G05", "name": "Foundations of stochastic processes", "description": "Foundations of stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G07", "originalCode": "60G07", "name": "General theory of stochastic processes", "description": "General theory of stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G09", "originalCode": "60G09", "name": "Exchangeability for stochastic processes", "description": "Exchangeability for stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G10", "originalCode": "60G10", "name": "Stationary stochastic processes", "description": "Stationary stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G12", "originalCode": "60G12", "name": "General second-order stochastic processes", "description": "General second-order stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G15", "originalCode": "60G15", "name": "Gaussian processes", "description": "Gaussian processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G17", "originalCode": "60G17", "name": "Sample path properties", "description": "Sample path properties", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G18", "originalCode": "60G18", "name": "Self-similar stochastic processes", "description": "Self-similar stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G20", "originalCode": "60G20", "name": "Generalized stochastic processes", "description": "Generalized stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G22", "originalCode": "60G22", "name": "Fractional processes, including fractional Brownian motion", "description": "Fractional processes, including fractional Brownian motion", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G25", "originalCode": "60G25", "name": "Prediction theory (aspects of stochastic processes)", "description": "Prediction theory (aspects of stochastic processes) [See also 62M20]", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G30", "originalCode": "60G30", "name": "Continuity and singularity of induced measures", "description": "Continuity and singularity of induced measures", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G35", "originalCode": "60G35", "name": "Signal detection and filtering (aspects of stochastic processes)", "description": "Signal detection and filtering (aspects of stochastic processes) [See also 62M20, 93E10, 93E11, 94Axx]", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G40", "originalCode": "60G40", "name": "Stopping times; optimal stopping problems; gambling theory", "description": "Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G42", "originalCode": "60G42", "name": "Martingales with discrete parameter", "description": "Martingales with discrete parameter", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G44", "originalCode": "60G44", "name": "Martingales with continuous parameter", "description": "Martingales with continuous parameter", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G46", "originalCode": "60G46", "name": "Martingales and classical analysis", "description": "Martingales and classical analysis", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G48", "originalCode": "60G48", "name": "Generalizations of martingales", "description": "Generalizations of martingales", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G50", "originalCode": "60G50", "name": "Sums of independent random variables; random walks", "description": "Sums of independent random variables; random walks", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G51", "originalCode": "60G51", "name": "Processes with independent increments; Lévy processes", "description": "Processes with independent increments; Lévy processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G52", "originalCode": "60G52", "name": "Stable stochastic processes", "description": "Stable stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G53", "originalCode": "60G53", "name": "Feller processes", "description": "Feller processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G55", "originalCode": "60G55", "name": "Point processes (e.g., Poisson, Cox, Hawkes processes)", "description": "Point processes (e.g., Poisson, Cox, Hawkes processes)", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G57", "originalCode": "60G57", "name": "Random measures", "description": "Random measures", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G60", "originalCode": "60G60", "name": "Random fields", "description": "Random fields", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G65", "originalCode": "60G65", "name": "Nonlinear processes (e.g., \\(G\\)-Brownian motion, \\(G\\)-Lévy processes)", "description": "Nonlinear processes (e.g., \\(G\\)-Brownian motion, \\(G\\)-Lévy processes)", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G70", "originalCode": "60G70", "name": "Extreme value theory; extremal stochastic processes", "description": "Extreme value theory; extremal stochastic processes", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60G99", "originalCode": "60G99", "name": "Stochastic processes", "description": "None of the above, but in this section", "kind": "subject", "parent": "60G", "page": 161 }, { "code": "60H", "originalCode": "60Hxx", "name": "Stochastic analysis", "description": "Stochastic analysis [See also 58J65]", "kind": "section", "parent": "60", "page": 162 }, { "code": "60H05", "originalCode": "60H05", "name": "Stochastic integrals", "description": "Stochastic integrals", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H07", "originalCode": "60H07", "name": "Stochastic calculus of variations and the Malliavin calculus", "description": "Stochastic calculus of variations and the Malliavin calculus", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H10", "originalCode": "60H10", "name": "Stochastic ordinary differential equations (aspects of stochastic analysis)", "description": "Stochastic ordinary differential equations (aspects of stochastic analysis) [See also 34F05]", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H15", "originalCode": "60H15", "name": "Stochastic partial differential equations (aspects of stochastic analysis)", "description": "Stochastic partial differential equations (aspects of stochastic analysis) [See also 35R60]", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H17", "originalCode": "60H17", "name": "Singular stochastic partial differential equations", "description": "Singular stochastic partial differential equations", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H20", "originalCode": "60H20", "name": "Stochastic integral equations", "description": "Stochastic integral equations", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H25", "originalCode": "60H25", "name": "Random operators and equations (aspects of stochastic analysis)", "description": "Random operators and equations (aspects of stochastic analysis) [See also 47B80]", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H30", "originalCode": "60H30", "name": "Applications of stochastic analysis (to PDEs, etc.)", "description": "Applications of stochastic analysis (to PDEs, etc.)", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H35", "originalCode": "60H35", "name": "Computational methods for stochastic equations (aspects of stochastic analysis)", "description": "Computational methods for stochastic equations (aspects of stochastic analysis) [See also 65C30]", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H40", "originalCode": "60H40", "name": "White noise theory", "description": "White noise theory", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H50", "originalCode": "60H50", "name": "Regularization by noise", "description": "Regularization by noise", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60H99", "originalCode": "60H99", "name": "Stochastic analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "60H", "page": 162 }, { "code": "60J", "originalCode": "60Jxx", "name": "Markov processes", "description": "Markov processes", "kind": "section", "parent": "60", "page": 162 }, { "code": "60J05", "originalCode": "60J05", "name": "Discrete-time Markov processes on general state spaces", "description": "Discrete-time Markov processes on general state spaces", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J10", "originalCode": "60J10", "name": "Markov chains (discrete-time Markov processes on discrete state spaces)", "description": "Markov chains (discrete-time Markov processes on discrete state spaces)", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J20", "originalCode": "60J20", "name": "Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)", "description": "Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91E40]", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J22", "originalCode": "60J22", "name": "Computational methods in Markov chains", "description": "Computational methods in Markov chains [See also 65C40]", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J25", "originalCode": "60J25", "name": "Continuous-time Markov processes on general state spaces", "description": "Continuous-time Markov processes on general state spaces", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J27", "originalCode": "60J27", "name": "Continuous-time Markov processes on discrete state spaces", "description": "Continuous-time Markov processes on discrete state spaces", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J28", "originalCode": "60J28", "name": "Applications of continuous-time Markov processes on discrete state spaces", "description": "Applications of continuous-time Markov processes on discrete state spaces", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J35", "originalCode": "60J35", "name": "Transition functions, generators and resolvents", "description": "Transition functions, generators and resolvents [See also 47D03, 47D07]", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J40", "originalCode": "60J40", "name": "Right processes", "description": "Right processes", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J45", "originalCode": "60J45", "name": "Probabilistic potential theory", "description": "Probabilistic potential theory [See also 31Cxx, 31D05]", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J46", "originalCode": "60J46", "name": "Dirichlet form methods in Markov processes", "description": "Dirichlet form methods in Markov processes", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J50", "originalCode": "60J50", "name": "Boundary theory for Markov processes", "description": "Boundary theory for Markov processes", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J55", "originalCode": "60J55", "name": "Local time and additive functionals", "description": "Local time and additive functionals", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J57", "originalCode": "60J57", "name": "Multiplicative functionals and Markov processes", "description": "Multiplicative functionals and Markov processes", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J60", "originalCode": "60J60", "name": "Diffusion processes", "description": "Diffusion processes [See also 58J65]", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J65", "originalCode": "60J65", "name": "Brownian motion", "description": "Brownian motion [See also 58J65]", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J67", "originalCode": "60J67", "name": "Stochastic (Schramm-)Loewner evolution (SLE)", "description": "Stochastic (Schramm-)Loewner evolution (SLE)", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J68", "originalCode": "60J68", "name": "Superprocesses", "description": "Superprocesses", "kind": "subject", "parent": "60J", "page": 162 }, { "code": "60J70", "originalCode": "60J70", "name": "Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)", "description": "Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]", "kind": "subject", "parent": "60J", "page": 163 }, { "code": "60J74", "originalCode": "60J74", "name": "Jump processes on discrete state spaces", "description": "Jump processes on discrete state spaces", "kind": "subject", "parent": "60J", "page": 163 }, { "code": "60J76", "originalCode": "60J76", "name": "Jump processes on general state spaces", "description": "Jump processes on general state spaces", "kind": "subject", "parent": "60J", "page": 163 }, { "code": "60J80", "originalCode": "60J80", "name": "Branching processes (Galton-Watson, birth-and-death, etc.)", "description": "Branching processes (Galton-Watson, birth-and-death, etc.)", "kind": "subject", "parent": "60J", "page": 163 }, { "code": "60J85", "originalCode": "60J85", "name": "Applications of branching processes", "description": "Applications of branching processes [See also 92Dxx]", "kind": "subject", "parent": "60J", "page": 163 }, { "code": "60J90", "originalCode": "60J90", "name": "Coalescent processes", "description": "Coalescent processes", "kind": "subject", "parent": "60J", "page": 163 }, { "code": "60J95", "originalCode": "60J95", "name": "Applications of coalescent processes", "description": "Applications of coalescent processes [See also 92Dxx]", "kind": "subject", "parent": "60J", "page": 163 }, { "code": "60J99", "originalCode": "60J99", "name": "Markov processes", "description": "None of the above, but in this section", "kind": "subject", "parent": "60J", "page": 163 }, { "code": "60K", "originalCode": "60Kxx", "name": "Special processes", "description": "Special processes", "kind": "section", "parent": "60", "page": 163 }, { "code": "60K05", "originalCode": "60K05", "name": "Renewal theory", "description": "Renewal theory", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K10", "originalCode": "60K10", "name": "Applications of renewal theory (reliability, demand theory, etc.)", "description": "Applications of renewal theory (reliability, demand theory, etc.)", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K15", "originalCode": "60K15", "name": "Markov renewal processes, semi-Markov processes", "description": "Markov renewal processes, semi-Markov processes", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K20", "originalCode": "60K20", "name": "Applications of Markov renewal processes (reliability, queueing networks, etc.)", "description": "Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K25", "originalCode": "60K25", "name": "Queueing theory (aspects of probability theory)", "description": "Queueing theory (aspects of probability theory) [See also 68M20, 90B22]", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K30", "originalCode": "60K30", "name": "Applications of queueing theory (congestion, allocation, storage, traffic, etc.)", "description": "Applications of queueing theory (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K35", "originalCode": "60K35", "name": "Interacting random processes; statistical mechanics type models; percolation theory", "description": "Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K37", "originalCode": "60K37", "name": "Processes in random environments", "description": "Processes in random environments", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K40", "originalCode": "60K40", "name": "Other physical applications of random processes", "description": "Other physical applications of random processes", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K50", "originalCode": "60K50", "name": "Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.)", "description": "Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) [See also 60G22, 60G55, 60J74, 60J76] \\{For applications to physics and the sciences, see 76-XX, 82Cxx, 92-XX\\}", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60K99", "originalCode": "60K99", "name": "Special processes", "description": "None of the above, but in this section", "kind": "subject", "parent": "60K", "page": 163 }, { "code": "60L", "originalCode": "60Lxx", "name": "Rough analysis", "description": "Rough analysis", "kind": "section", "parent": "60", "page": 163 }, { "code": "60L10", "originalCode": "60L10", "name": "Signatures and data streams", "description": "Signatures and data streams", "kind": "subject", "parent": "60L", "page": 163 }, { "code": "60L20", "originalCode": "60L20", "name": "Rough paths", "description": "Rough paths", "kind": "subject", "parent": "60L", "page": 163 }, { "code": "60L30", "originalCode": "60L30", "name": "Regularity structures", "description": "Regularity structures", "kind": "subject", "parent": "60L", "page": 163 }, { "code": "60L40", "originalCode": "60L40", "name": "Paracontrolled distributions and alternative approaches", "description": "Paracontrolled distributions and alternative approaches", "kind": "subject", "parent": "60L", "page": 163 }, { "code": "60L50", "originalCode": "60L50", "name": "Rough partial differential equations", "description": "Rough partial differential equations", "kind": "subject", "parent": "60L", "page": 163 }, { "code": "60L70", "originalCode": "60L70", "name": "Algebraic structures and computation", "description": "Algebraic structures and computation", "kind": "subject", "parent": "60L", "page": 163 }, { "code": "60L90", "originalCode": "60L90", "name": "Applications of rough analysis", "description": "Applications of rough analysis", "kind": "subject", "parent": "60L", "page": 163 }, { "code": "60L99", "originalCode": "60L99", "name": "Rough analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "60L", "page": 163 }, { "code": "62", "originalCode": "62-XX", "name": "Statistics", "description": "Statistics", "kind": "class", "parent": null, "page": 164 }, { "code": "62-00", "originalCode": "62-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistics", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistics", "kind": "subject", "parent": "62", "page": 164 }, { "code": "62-01", "originalCode": "62-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics", "kind": "subject", "parent": "62", "page": 164 }, { "code": "62-02", "originalCode": "62-02", "name": "Research exposition (monographs, survey articles) pertaining to statistics", "description": "Research exposition (monographs, survey articles) pertaining to statistics", "kind": "subject", "parent": "62", "page": 164 }, { "code": "62-03", "originalCode": "62-03", "name": "History of statistics", "description": "History of statistics [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "62", "page": 164 }, { "code": "62-04", "originalCode": "62-04", "name": "Software, source code, etc. for problems pertaining to statistics", "description": "Software, source code, etc. for problems pertaining to statistics", "kind": "subject", "parent": "62", "page": 164 }, { "code": "62-06", "originalCode": "62-06", "name": "Proceedings, conferences, collections, etc. pertaining to statistics", "description": "Proceedings, conferences, collections, etc. pertaining to statistics", "kind": "subject", "parent": "62", "page": 164 }, { "code": "62-08", "originalCode": "62-08", "name": "Computational methods for problems pertaining to statistics", "description": "Computational methods for problems pertaining to statistics", "kind": "subject", "parent": "62", "page": 164 }, { "code": "62-11", "originalCode": "62-11", "name": "Research data for problems pertaining to statistics", "description": "Research data for problems pertaining to statistics", "kind": "subject", "parent": "62", "page": 164 }, { "code": "62A", "originalCode": "62Axx", "name": "Foundational topics in statistics", "description": "Foundational topics in statistics", "kind": "section", "parent": "62", "page": 164 }, { "code": "62A01", "originalCode": "62A01", "name": "Foundations and philosophical topics in statistics", "description": "Foundations and philosophical topics in statistics", "kind": "subject", "parent": "62A", "page": 164 }, { "code": "62A09", "originalCode": "62A09", "name": "Graphical methods in statistics", "description": "Graphical methods in statistics", "kind": "subject", "parent": "62A", "page": 164 }, { "code": "62A86", "originalCode": "62A86", "name": "Fuzzy analysis in statistics", "description": "Fuzzy analysis in statistics", "kind": "subject", "parent": "62A", "page": 164 }, { "code": "62A99", "originalCode": "62A99", "name": "Foundational topics in statistics", "description": "None of the above, but in this section", "kind": "subject", "parent": "62A", "page": 164 }, { "code": "62B", "originalCode": "62Bxx", "name": "Sufficiency and information", "description": "Sufficiency and information", "kind": "section", "parent": "62", "page": 164 }, { "code": "62B05", "originalCode": "62B05", "name": "Sufficient statistics and fields", "description": "Sufficient statistics and fields", "kind": "subject", "parent": "62B", "page": 164 }, { "code": "62B10", "originalCode": "62B10", "name": "Statistical aspects of information-theoretic topics", "description": "Statistical aspects of information-theoretic topics [See also 94A17]", "kind": "subject", "parent": "62B", "page": 164 }, { "code": "62B11", "originalCode": "62B11", "name": "Information geometry (statistical aspects)", "description": "Information geometry (statistical aspects) \\{For differential geometric aspects, see 53B12\\}", "kind": "subject", "parent": "62B", "page": 164 }, { "code": "62B15", "originalCode": "62B15", "name": "Theory of statistical experiments", "description": "Theory of statistical experiments", "kind": "subject", "parent": "62B", "page": 164 }, { "code": "62B86", "originalCode": "62B86", "name": "Statistical aspects of fuzziness, sufficiency, and information", "description": "Statistical aspects of fuzziness, sufficiency, and information", "kind": "subject", "parent": "62B", "page": 164 }, { "code": "62B99", "originalCode": "62B99", "name": "Sufficiency and information", "description": "None of the above, but in this section", "kind": "subject", "parent": "62B", "page": 164 }, { "code": "62C", "originalCode": "62Cxx", "name": "Statistical decision theory", "description": "Statistical decision theory [See also 90B50, 91B06] \\{For game theory, see 91A35\\}", "kind": "section", "parent": "62", "page": 164 }, { "code": "62C05", "originalCode": "62C05", "name": "General considerations in statistical decision theory", "description": "General considerations in statistical decision theory", "kind": "subject", "parent": "62C", "page": 164 }, { "code": "62C07", "originalCode": "62C07", "name": "Complete class results in statistical decision theory", "description": "Complete class results in statistical decision theory", "kind": "subject", "parent": "62C", "page": 164 }, { "code": "62C10", "originalCode": "62C10", "name": "Bayesian 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problems in statistical decision theory", "kind": "subject", "parent": "62C", "page": 164 }, { "code": "62C86", "originalCode": "62C86", "name": "Statistical decision theory and fuzziness", "description": "Statistical decision theory and fuzziness", "kind": "subject", "parent": "62C", "page": 164 }, { "code": "62C99", "originalCode": "62C99", "name": "Statistical decision theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "62C", "page": 164 }, { "code": "62D", "originalCode": "62Dxx", "name": "Statistical sampling theory and related topics", "description": "Statistical sampling theory and related topics", "kind": "section", "parent": "62", "page": 165 }, { "code": "62D05", "originalCode": "62D05", "name": "Sampling theory, sample surveys", "description": "Sampling theory, sample surveys", "kind": "subject", "parent": "62D", "page": 165 }, { "code": "62D10", "originalCode": "62D10", "name": "Missing data", "description": "Missing data", "kind": "subject", "parent": "62D", "page": 165 }, { "code": "62D20", "originalCode": "62D20", "name": "Causal inference from observational studies", "description": "Causal inference from observational studies", "kind": "subject", "parent": "62D", "page": 165 }, { "code": "62D99", "originalCode": "62D99", "name": "Statistical sampling theory and related topics", "description": "None of the above, but in this section", "kind": "subject", "parent": "62D", "page": 165 }, { "code": "62E", "originalCode": "62Exx", "name": "Statistical distribution theory", "description": "Statistical distribution theory [See also 60Exx]", "kind": "section", "parent": "62", "page": 165 }, { "code": "62E10", "originalCode": "62E10", "name": "Characterization and structure theory of statistical distributions", "description": "Characterization and structure theory of statistical distributions", "kind": "subject", "parent": "62E", "page": 165 }, { "code": "62E15", "originalCode": "62E15", "name": "Exact distribution theory in statistics", "description": "Exact distribution theory in statistics", "kind": "subject", "parent": "62E", "page": 165 }, { "code": "62E17", "originalCode": "62E17", "name": "Approximations to statistical distributions (nonasymptotic)", "description": "Approximations to statistical distributions (nonasymptotic)", "kind": "subject", "parent": "62E", "page": 165 }, { "code": "62E20", "originalCode": "62E20", "name": "Asymptotic distribution theory in statistics", "description": "Asymptotic distribution theory in statistics", "kind": "subject", "parent": "62E", "page": 165 }, { "code": "62E86", "originalCode": "62E86", "name": "Fuzziness in connection with statistical distributions", "description": "Fuzziness in connection with statistical distributions", "kind": "subject", "parent": "62E", "page": 165 }, { "code": "62E99", "originalCode": "62E99", "name": "Statistical distribution theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "62E", "page": 165 }, { "code": "62F", "originalCode": "62Fxx", "name": "Parametric inference", "description": "Parametric inference", "kind": "section", "parent": "62", "page": 165 }, { "code": "62F03", "originalCode": "62F03", "name": "Parametric hypothesis testing", "description": "Parametric hypothesis testing", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F05", "originalCode": "62F05", "name": "Asymptotic properties of parametric tests", "description": "Asymptotic properties of parametric tests", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F07", "originalCode": "62F07", "name": "Statistical ranking and selection procedures", "description": "Statistical ranking and selection procedures", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F10", "originalCode": "62F10", "name": "Point estimation", "description": "Point estimation", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F12", "originalCode": "62F12", "name": "Asymptotic properties of parametric estimators", "description": "Asymptotic properties of parametric estimators", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F15", "originalCode": "62F15", "name": "Bayesian inference", "description": "Bayesian inference", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F25", "originalCode": "62F25", "name": "Parametric tolerance and confidence regions", "description": "Parametric tolerance and confidence regions", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F30", "originalCode": "62F30", "name": "Parametric inference under constraints", "description": "Parametric inference under constraints", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F35", "originalCode": "62F35", "name": "Robustness and adaptive procedures (parametric inference)", "description": "Robustness and adaptive procedures (parametric inference)", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F40", "originalCode": "62F40", "name": "Bootstrap, jackknife and other resampling methods", "description": "Bootstrap, jackknife and other resampling methods", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F86", "originalCode": "62F86", "name": "Parametric inference and fuzziness", "description": "Parametric inference and fuzziness", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62F99", "originalCode": "62F99", "name": "Parametric inference", "description": "None of the above, but in this section", "kind": "subject", "parent": "62F", "page": 165 }, { "code": "62G", "originalCode": "62Gxx", "name": "Nonparametric inference", "description": "Nonparametric inference", "kind": "section", "parent": "62", "page": 165 }, { "code": "62G05", "originalCode": "62G05", "name": "Nonparametric estimation", "description": "Nonparametric estimation", "kind": "subject", "parent": "62G", "page": 165 }, { "code": "62G07", "originalCode": "62G07", "name": "Density estimation", "description": "Density estimation", "kind": "subject", "parent": "62G", "page": 165 }, { "code": "62G08", "originalCode": "62G08", "name": "Nonparametric regression and quantile regression", "description": "Nonparametric regression and quantile regression", "kind": "subject", "parent": "62G", "page": 165 }, { "code": "62G09", "originalCode": "62G09", "name": "Nonparametric statistical resampling methods", "description": "Nonparametric statistical resampling methods", "kind": "subject", "parent": "62G", "page": 165 }, { "code": "62G10", "originalCode": "62G10", "name": "Nonparametric hypothesis testing", "description": "Nonparametric hypothesis testing", "kind": "subject", "parent": "62G", "page": 165 }, { "code": "62G15", "originalCode": "62G15", "name": "Nonparametric tolerance and confidence regions", "description": "Nonparametric tolerance and confidence regions", "kind": "subject", "parent": "62G", "page": 165 }, { "code": "62G20", "originalCode": "62G20", "name": "Asymptotic properties of nonparametric inference", "description": "Asymptotic properties of nonparametric inference", "kind": "subject", "parent": "62G", "page": 166 }, { "code": "62G30", "originalCode": "62G30", "name": "Order statistics; empirical distribution functions", "description": "Order statistics; empirical distribution functions", "kind": "subject", "parent": "62G", "page": 166 }, { "code": "62G32", "originalCode": "62G32", "name": "Statistics of extreme values; tail inference", "description": "Statistics of extreme values; tail inference", "kind": "subject", "parent": "62G", "page": 166 }, { "code": "62G35", "originalCode": "62G35", "name": "Nonparametric robustness", "description": "Nonparametric robustness", "kind": "subject", "parent": "62G", "page": 166 }, { "code": "62G86", "originalCode": "62G86", "name": "Nonparametric inference and fuzziness", "description": "Nonparametric inference and fuzziness", "kind": "subject", "parent": "62G", "page": 166 }, { "code": "62G99", "originalCode": "62G99", "name": "Nonparametric inference", "description": "None of the above, but in this section", "kind": "subject", "parent": "62G", "page": 166 }, { "code": "62H", "originalCode": "62Hxx", "name": "Multivariate analysis", "description": "Multivariate analysis [See also 60Exx]", "kind": "section", "parent": "62", "page": 166 }, { "code": "62H05", "originalCode": "62H05", "name": "Characterization and structure theory for multivariate probability distributions; copulas", "description": "Characterization and structure theory for multivariate probability distributions; copulas", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H10", "originalCode": "62H10", "name": "Multivariate distribution of statistics", "description": "Multivariate distribution of statistics", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H11", "originalCode": "62H11", "name": "Directional data; spatial statistics", "description": "Directional data; spatial statistics", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H12", "originalCode": "62H12", "name": "Estimation in multivariate analysis", "description": "Estimation in multivariate analysis", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H15", "originalCode": "62H15", "name": "Hypothesis testing in multivariate analysis", "description": "Hypothesis testing in multivariate analysis", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H17", "originalCode": "62H17", "name": "Contingency tables", "description": "Contingency tables", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H20", "originalCode": "62H20", "name": "Measures of association (correlation, canonical correlation, etc.)", "description": "Measures of association (correlation, canonical correlation, etc.)", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H22", "originalCode": "62H22", "name": "Probabilistic graphical models", "description": "Probabilistic graphical models", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H25", "originalCode": "62H25", "name": "Factor analysis and principal components; correspondence analysis", "description": "Factor analysis and principal components; correspondence analysis", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H30", "originalCode": "62H30", "name": "Classification and discrimination; cluster analysis (statistical aspects)", "description": "Classification and discrimination; cluster analysis (statistical aspects) [See also 68T10, 91C20]; mixture models", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H35", "originalCode": "62H35", "name": "Image analysis in multivariate analysis", "description": "Image analysis in multivariate analysis", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H86", "originalCode": "62H86", "name": "Multivariate analysis and fuzziness", "description": "Multivariate analysis and fuzziness", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62H99", "originalCode": "62H99", "name": "Multivariate analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "62H", "page": 166 }, { "code": "62J", "originalCode": "62Jxx", "name": "Linear inference, regression", "description": "Linear inference, regression", "kind": "section", "parent": "62", "page": 166 }, { "code": "62J02", "originalCode": "62J02", "name": "General nonlinear regression", "description": "General nonlinear regression", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62J05", "originalCode": "62J05", "name": "Linear regression; mixed models", "description": "Linear regression; mixed models", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62J07", "originalCode": "62J07", "name": "Ridge regression; shrinkage estimators (Lasso)", "description": "Ridge regression; shrinkage estimators (Lasso)", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62J10", "originalCode": "62J10", "name": "Analysis of variance and covariance (ANOVA)", "description": "Analysis of variance and covariance (ANOVA)", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62J12", "originalCode": "62J12", "name": "Generalized linear models (logistic models)", "description": "Generalized linear models (logistic models)", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62J15", "originalCode": "62J15", "name": "Paired and multiple comparisons; multiple testing", "description": "Paired and multiple comparisons; multiple testing", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62J20", "originalCode": "62J20", "name": "Diagnostics, and linear inference and regression", "description": "Diagnostics, and linear inference and regression", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62J86", "originalCode": "62J86", "name": "Fuzziness, and linear inference and regression", "description": "Fuzziness, and linear inference and regression", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62J99", "originalCode": "62J99", "name": "Linear inference, regression", "description": "None of the above, but in this section", "kind": "subject", "parent": "62J", "page": 166 }, { "code": "62K", "originalCode": "62Kxx", "name": "Design of statistical experiments", "description": "Design of statistical experiments [See also 05Bxx]", "kind": "section", "parent": "62", "page": 167 }, { "code": "62K05", "originalCode": "62K05", "name": "Optimal statistical designs", "description": "Optimal statistical designs", "kind": "subject", "parent": "62K", "page": 167 }, { "code": "62K10", "originalCode": "62K10", "name": "Statistical block designs", "description": "Statistical block designs", "kind": "subject", "parent": "62K", "page": 167 }, { "code": "62K15", "originalCode": "62K15", "name": "Factorial statistical designs", "description": "Factorial statistical designs", "kind": "subject", "parent": "62K", "page": 167 }, { "code": "62K20", "originalCode": "62K20", "name": "Response surface designs", "description": "Response surface designs", "kind": "subject", "parent": "62K", "page": 167 }, { "code": "62K25", "originalCode": "62K25", "name": "Robust parameter designs", "description": "Robust parameter designs", "kind": "subject", "parent": "62K", "page": 167 }, { "code": "62K86", "originalCode": "62K86", "name": "Fuzziness and design of statistical experiments", "description": "Fuzziness and design of statistical experiments", "kind": "subject", "parent": "62K", "page": 167 }, { "code": "62K99", "originalCode": "62K99", "name": "Design of statistical experiments", "description": "None of the above, but in this section", "kind": "subject", "parent": "62K", "page": 167 }, { "code": "62L", "originalCode": "62Lxx", "name": "Sequential statistical methods", "description": "Sequential statistical methods", "kind": "section", "parent": "62", "page": 167 }, { "code": "62L05", "originalCode": "62L05", "name": "Sequential statistical design", "description": "Sequential statistical design", "kind": "subject", "parent": "62L", "page": 167 }, { "code": "62L10", "originalCode": "62L10", "name": "Sequential statistical analysis", "description": "Sequential statistical analysis", "kind": "subject", "parent": "62L", "page": 167 }, { "code": "62L12", "originalCode": "62L12", "name": "Sequential estimation", "description": "Sequential estimation", "kind": "subject", "parent": "62L", "page": 167 }, { "code": "62L15", "originalCode": "62L15", "name": "Optimal stopping in statistics", "description": "Optimal stopping in statistics [See also 60G40, 91A60]", "kind": "subject", "parent": "62L", "page": 167 }, { "code": "62L20", "originalCode": "62L20", "name": "Stochastic approximation", "description": "Stochastic approximation", "kind": "subject", "parent": "62L", "page": 167 }, { "code": "62L86", "originalCode": "62L86", "name": "Fuzziness and sequential statistical methods", "description": "Fuzziness and sequential statistical methods", "kind": "subject", "parent": "62L", "page": 167 }, { "code": "62L99", "originalCode": "62L99", "name": "Sequential statistical methods", "description": "None of the above, but in this section", "kind": "subject", "parent": "62L", "page": 167 }, { "code": "62M", "originalCode": "62Mxx", "name": "Inference from stochastic processes", "description": "Inference from stochastic processes", "kind": "section", "parent": "62", "page": 167 }, { "code": "62M02", "originalCode": "62M02", "name": "Markov processes: hypothesis testing", "description": "Markov processes: hypothesis testing", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M05", "originalCode": "62M05", "name": "Markov processes: estimation; hidden Markov models", "description": "Markov processes: estimation; hidden Markov models", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M07", "originalCode": "62M07", "name": "Non-Markovian processes: hypothesis testing", "description": "Non-Markovian processes: hypothesis testing", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M09", "originalCode": "62M09", "name": "Non-Markovian processes: estimation", "description": "Non-Markovian processes: estimation", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M10", "originalCode": "62M10", "name": "Time series, auto-correlation, regression, etc. in statistics (GARCH)", "description": "Time series, auto-correlation, regression, etc. in statistics (GARCH) [See also 91B84]", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M15", "originalCode": "62M15", "name": "Inference from stochastic processes and spectral analysis", "description": "Inference from stochastic processes and spectral analysis", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M20", "originalCode": "62M20", "name": "Inference from stochastic processes and prediction", "description": "Inference from stochastic processes and prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M30", "originalCode": "62M30", "name": "Inference from spatial processes", "description": "Inference from spatial processes", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M40", "originalCode": "62M40", "name": "Random fields; image analysis", "description": "Random fields; image analysis", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M45", "originalCode": "62M45", "name": "Neural nets and related approaches to inference from stochastic processes", "description": "Neural nets and related approaches to inference from stochastic processes", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M86", "originalCode": "62M86", "name": "Inference from stochastic processes and fuzziness", "description": "Inference from stochastic processes and fuzziness", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62M99", "originalCode": "62M99", "name": "Inference from stochastic processes", "description": "None of the above, but in this section", "kind": "subject", "parent": "62M", "page": 167 }, { "code": "62N", "originalCode": "62Nxx", "name": "Survival analysis and censored data", "description": "Survival analysis and censored data", "kind": "section", "parent": "62", "page": 168 }, { "code": "62N01", "originalCode": "62N01", "name": "Censored data models", "description": "Censored data models", "kind": "subject", "parent": "62N", "page": 168 }, { "code": "62N02", "originalCode": "62N02", "name": "Estimation in survival analysis and censored data", "description": "Estimation in survival analysis and censored data", "kind": "subject", "parent": "62N", "page": 168 }, { "code": "62N03", "originalCode": "62N03", "name": "Testing in survival analysis and censored data", "description": "Testing in survival analysis and censored data", "kind": "subject", "parent": "62N", "page": 168 }, { "code": "62N05", "originalCode": "62N05", "name": "Reliability and life testing", "description": "Reliability and life testing [See also 90B25]", "kind": "subject", "parent": "62N", "page": 168 }, { "code": "62N86", "originalCode": "62N86", "name": "Fuzziness, and survival analysis and censored data", "description": "Fuzziness, and survival analysis and censored data", "kind": "subject", "parent": "62N", "page": 168 }, { "code": "62N99", "originalCode": "62N99", "name": "Survival analysis and censored data", "description": "None of the above, but in this section", "kind": "subject", "parent": "62N", "page": 168 }, { "code": "62P", "originalCode": "62Pxx", "name": "Applications of statistics", "description": "Applications of statistics [See also 90-XX, 91-XX, 92-XX]", "kind": "section", "parent": "62", "page": 168 }, { "code": "62P05", "originalCode": "62P05", "name": "Applications of statistics to actuarial sciences and financial mathematics", "description": "Applications of statistics to actuarial sciences and financial mathematics", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62P10", "originalCode": "62P10", "name": "Applications of statistics to biology and medical sciences; meta analysis", "description": "Applications of statistics to biology and medical sciences; meta analysis", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62P12", "originalCode": "62P12", "name": "Applications of statistics to environmental and related topics", "description": "Applications of statistics to environmental and related topics", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62P15", "originalCode": "62P15", "name": "Applications of statistics to psychology", "description": "Applications of statistics to psychology", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62P20", "originalCode": "62P20", "name": "Applications of statistics to economics", "description": "Applications of statistics to economics [See also 91Bxx]", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62P25", "originalCode": "62P25", "name": "Applications of statistics to social sciences", "description": "Applications of statistics to social sciences", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62P30", "originalCode": "62P30", "name": "Applications of statistics in engineering and industry; control charts", "description": "Applications of statistics in engineering and industry; control charts", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62P35", "originalCode": "62P35", "name": "Applications of statistics to physics", "description": "Applications of statistics to physics", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62P99", "originalCode": "62P99", "name": "Applications of statistics", "description": "None of the above, but in this section", "kind": "subject", "parent": "62P", "page": 168 }, { "code": "62Q", "originalCode": "62Qxx", "name": "Statistical tables", "description": "Statistical tables", "kind": "section", "parent": "62", "page": 168 }, { "code": "62Q05", "originalCode": "62Q05", "name": "Statistical tables", "description": "Statistical tables", "kind": "subject", "parent": "62Q", "page": 168 }, { "code": "62Q99", "originalCode": "62Q99", "name": "Statistical tables", "description": "None of the above, but in this section", "kind": "subject", "parent": "62Q", "page": 168 }, { "code": "62R", "originalCode": "62Rxx", "name": "Statistics on algebraic and topological structures", "description": "Statistics on algebraic and topological structures", "kind": "section", "parent": "62", "page": 168 }, { "code": "62R01", "originalCode": "62R01", "name": "Algebraic statistics", "description": "Algebraic statistics", "kind": "subject", "parent": "62R", "page": 168 }, { "code": "62R07", "originalCode": "62R07", "name": "Statistical aspects of big data and data science", "description": "Statistical aspects of big data and data science \\{For computer science aspects, see 68T09; for information-theoretic aspects, see 94A16\\}", "kind": "subject", "parent": "62R", "page": 168 }, { "code": "62R10", "originalCode": "62R10", "name": "Functional data analysis", "description": "Functional data analysis", "kind": "subject", "parent": "62R", "page": 168 }, { "code": "62R20", "originalCode": "62R20", "name": "Statistics on metric spaces", "description": "Statistics on metric spaces", "kind": "subject", "parent": "62R", "page": 168 }, { "code": "62R30", "originalCode": "62R30", "name": "Statistics on manifolds", "description": "Statistics on manifolds", "kind": "subject", "parent": "62R", "page": 168 }, { "code": "62R40", "originalCode": "62R40", "name": "Topological data analysis", "description": "Topological data analysis [See also 55N31]", "kind": "subject", "parent": "62R", "page": 168 }, { "code": "62R99", "originalCode": "62R99", "name": "Statistics on algebraic and topological structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "62R", "page": 168 }, { "code": "65", "originalCode": "65-XX", "name": "Numerical analysis", "description": "Numerical analysis", "kind": "class", "parent": null, "page": 169 }, { "code": "65-00", "originalCode": "65-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to numerical analysis", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to numerical analysis", "kind": "subject", "parent": "65", "page": 169 }, { "code": "65-01", "originalCode": "65-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis", "kind": "subject", "parent": "65", "page": 169 }, { "code": "65-02", "originalCode": "65-02", "name": "Research exposition (monographs, survey articles) pertaining to numerical analysis", "description": "Research exposition (monographs, survey articles) pertaining to numerical analysis", "kind": "subject", "parent": "65", "page": 169 }, { "code": "65-03", "originalCode": "65-03", "name": "History of numerical analysis", "description": "History of numerical analysis [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "65", "page": 169 }, { "code": "65-04", "originalCode": "65-04", "name": "Software, source code, etc. for problems pertaining to numerical analysis", "description": "Software, source code, etc. for problems pertaining to numerical analysis", "kind": "subject", "parent": "65", "page": 169 }, { "code": "65-06", "originalCode": "65-06", "name": "Proceedings, conferences, collections, etc. pertaining to numerical analysis", "description": "Proceedings, conferences, collections, etc. pertaining to numerical analysis", "kind": "subject", "parent": "65", "page": 169 }, { "code": "65-11", "originalCode": "65-11", "name": "Research data for problems pertaining to numerical analysis", "description": "Research data for problems pertaining to numerical analysis", "kind": "subject", "parent": "65", "page": 169 }, { "code": "65A", "originalCode": "65Axx", "name": "Tables in numerical analysis", "description": "Tables in numerical analysis", "kind": "section", "parent": "65", "page": 169 }, { "code": "65A05", "originalCode": "65A05", "name": "Tables in numerical analysis", "description": "Tables in numerical analysis", "kind": "subject", "parent": "65A", "page": 169 }, { "code": "65A99", "originalCode": "65A99", "name": "Tables in numerical analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "65A", "page": 169 }, { "code": "65B", "originalCode": "65Bxx", "name": "Acceleration of convergence in numerical analysis", "description": "Acceleration of convergence in numerical analysis", "kind": "section", "parent": "65", "page": 169 }, { "code": "65B05", "originalCode": "65B05", "name": "Extrapolation to the limit, deferred corrections", "description": "Extrapolation to the limit, deferred corrections", "kind": "subject", "parent": "65B", "page": 169 }, { "code": "65B10", "originalCode": "65B10", "name": "Numerical summation of series", "description": "Numerical summation of series", "kind": "subject", "parent": "65B", "page": 169 }, { "code": "65B15", "originalCode": "65B15", "name": "Euler-Maclaurin formula in numerical analysis", "description": "Euler-Maclaurin formula in numerical analysis", "kind": "subject", "parent": "65B", "page": 169 }, { "code": "65B99", "originalCode": "65B99", "name": "Acceleration of convergence in numerical analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "65B", "page": 169 }, { "code": "65C", "originalCode": "65Cxx", "name": "Probabilistic methods, stochastic differential equations", "description": "Probabilistic methods, stochastic differential equations", "kind": "section", "parent": "65", "page": 169 }, { "code": "65C05", "originalCode": "65C05", "name": "Monte Carlo methods", "description": "Monte Carlo methods [See also 82M31]", "kind": "subject", "parent": "65C", "page": 169 }, { "code": "65C10", "originalCode": "65C10", "name": "Random number generation in numerical analysis", "description": "Random number generation in numerical analysis [See also 11K45]", "kind": "subject", "parent": "65C", "page": 169 }, { "code": "65C20", "originalCode": "65C20", "name": "Probabilistic models, generic numerical methods in probability and statistics", "description": "Probabilistic models, generic numerical methods in probability and statistics [See also 60-08, 62-08]", "kind": "subject", "parent": "65C", "page": 169 }, { "code": "65C30", "originalCode": "65C30", "name": "Numerical solutions to stochastic differential and integral equations", "description": "Numerical solutions to stochastic differential and integral equations \\{For theoretical aspects, see 60H35\\} [See also 65M75, 65N75]", "kind": "subject", "parent": "65C", "page": 169 }, { "code": "65C35", "originalCode": "65C35", "name": "Stochastic particle methods", "description": "Stochastic particle methods [See also 82M60]", "kind": "subject", "parent": "65C", "page": 169 }, { "code": "65C40", "originalCode": "65C40", "name": "Numerical analysis or methods applied to Markov chains", "description": "Numerical analysis or methods applied to Markov chains [See also 60J22]", "kind": "subject", "parent": "65C", "page": 169 }, { "code": "65C99", "originalCode": "65C99", "name": "Probabilistic methods, stochastic differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "65C", "page": 169 }, { "code": "65D", "originalCode": "65Dxx", "name": "Numerical approximation and computational geometry (primarily algorithms)", "description": "Numerical approximation and computational geometry (primarily algorithms) \\{For theoretical aspects, see 41-XX, 68Uxx\\}", "kind": "section", "parent": "65", "page": 169 }, { "code": "65D05", "originalCode": "65D05", "name": "Numerical interpolation", "description": "Numerical interpolation", "kind": "subject", "parent": "65D", "page": 169 }, { "code": "65D07", "originalCode": "65D07", "name": "Numerical computation using splines", "description": "Numerical computation using splines", "kind": "subject", "parent": "65D", "page": 169 }, { "code": "65D10", "originalCode": "65D10", "name": "Numerical smoothing, curve fitting", "description": "Numerical smoothing, curve fitting", "kind": "subject", "parent": "65D", "page": 169 }, { "code": "65D12", "originalCode": "65D12", "name": "Numerical radial basis function approximation", "description": "Numerical radial basis function approximation", "kind": "subject", "parent": "65D", "page": 169 }, { "code": "65D15", "originalCode": "65D15", "name": "Algorithms for approximation of functions", "description": "Algorithms for approximation of functions", "kind": "subject", "parent": "65D", "page": 169 }, { "code": "65D17", "originalCode": "65D17", "name": "Computer-aided design (modeling of curves and surfaces)", "description": "Computer-aided design (modeling of curves and surfaces) [See also 68U07]", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65D18", "originalCode": "65D18", "name": "Numerical aspects of computer graphics, image analysis, and computational geometry", "description": "Numerical aspects of computer graphics, image analysis, and computational geometry [See also 51N05, 68U05]", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65D19", "originalCode": "65D19", "name": "Computational issues in computer and robotic vision", "description": "Computational issues in computer and robotic vision", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65D20", "originalCode": "65D20", "name": "Computation of special functions and constants, construction of tables", "description": "Computation of special functions and constants, construction of tables [See also 33F05]", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65D25", "originalCode": "65D25", "name": "Numerical differentiation", "description": "Numerical differentiation", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65D30", "originalCode": "65D30", "name": "Numerical integration", "description": "Numerical integration", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65D32", "originalCode": "65D32", "name": "Numerical quadrature and cubature formulas", "description": "Numerical quadrature and cubature formulas", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65D40", "originalCode": "65D40", "name": "Numerical approximation of high-dimensional functions; sparse grids", "description": "Numerical approximation of high-dimensional functions; sparse grids", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65D99", "originalCode": "65D99", "name": "Numerical approximation and computational geometry (primarily algorithms)", "description": "None of the above, but in this section", "kind": "subject", "parent": "65D", "page": 170 }, { "code": "65E", "originalCode": "65Exx", "name": "Numerical methods in complex analysis (potential theory, etc.)", "description": "Numerical methods in complex analysis (potential theory, etc.)", "kind": "section", "parent": "65", "page": 170 }, { "code": "65E05", "originalCode": "65E05", "name": "General theory of numerical methods in complex analysis (potential theory, etc.)", "description": "General theory of numerical methods in complex analysis (potential theory, etc.) [See also 30-08, 31-08, 32-08]", "kind": "subject", "parent": "65E", "page": 170 }, { "code": "65E10", "originalCode": "65E10", "name": "Numerical methods in conformal mappings", "description": "Numerical methods in conformal mappings [See also 30C30]", "kind": "subject", "parent": "65E", "page": 170 }, { "code": "65E99", "originalCode": "65E99", "name": "Numerical methods in complex analysis (potential theory, etc.)", "description": "None of the above, but in this section", "kind": "subject", "parent": "65E", "page": 170 }, { "code": "65F", "originalCode": "65Fxx", "name": "Numerical linear algebra", "description": "Numerical linear algebra", "kind": "section", "parent": "65", "page": 170 }, { "code": "65F05", "originalCode": "65F05", "name": "Direct numerical methods for linear systems and matrix inversion", "description": "Direct numerical methods for linear systems and matrix inversion", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F08", "originalCode": "65F08", "name": "Preconditioners for iterative methods", "description": "Preconditioners for iterative methods", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F10", "originalCode": "65F10", "name": "Iterative numerical methods for linear systems", "description": "Iterative numerical methods for linear systems [See also 65N22]", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F15", "originalCode": "65F15", "name": "Numerical computation of eigenvalues and eigenvectors of matrices", "description": "Numerical computation of eigenvalues and eigenvectors of matrices", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F18", "originalCode": "65F18", "name": "Numerical solutions to inverse eigenvalue problems", "description": "Numerical solutions to inverse eigenvalue problems", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F20", "originalCode": "65F20", "name": "Numerical solutions to overdetermined systems, pseudoinverses", "description": "Numerical solutions to overdetermined systems, pseudoinverses", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F22", "originalCode": "65F22", "name": "Ill-posedness and regularization problems in numerical linear algebra", "description": "Ill-posedness and regularization problems in numerical linear algebra", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F25", "originalCode": "65F25", "name": "Orthogonalization in numerical linear algebra", "description": "Orthogonalization in numerical linear algebra", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F35", "originalCode": "65F35", "name": "Numerical computation of matrix norms, conditioning, scaling", "description": "Numerical computation of matrix norms, conditioning, scaling [See also 15A12, 15A60]", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F40", "originalCode": "65F40", "name": "Numerical computation of determinants", "description": "Numerical computation of determinants", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F45", "originalCode": "65F45", "name": "Numerical methods for matrix equations", "description": "Numerical methods for matrix equations", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F50", "originalCode": "65F50", "name": "Computational methods for sparse matrices", "description": "Computational methods for sparse matrices", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F55", "originalCode": "65F55", "name": "Numerical methods for low-rank matrix approximation; matrix compression", "description": "Numerical methods for low-rank matrix approximation; matrix compression", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F60", "originalCode": "65F60", "name": "Numerical computation of matrix exponential and similar matrix functions", "description": "Numerical computation of matrix exponential and similar matrix functions", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65F99", "originalCode": "65F99", "name": "Numerical linear algebra", "description": "None of the above, but in this section", "kind": "subject", "parent": "65F", "page": 170 }, { "code": "65G", "originalCode": "65Gxx", "name": "Error analysis and interval analysis", "description": "Error analysis and interval analysis", "kind": "section", "parent": "65", "page": 171 }, { "code": "65G20", "originalCode": "65G20", "name": "Algorithms with automatic result verification", "description": "Algorithms with automatic result verification", "kind": "subject", "parent": "65G", "page": 171 }, { "code": "65G30", "originalCode": "65G30", "name": "Interval and finite arithmetic", "description": "Interval and finite arithmetic", "kind": "subject", "parent": "65G", "page": 171 }, { "code": "65G40", "originalCode": "65G40", "name": "General methods in interval analysis", "description": "General methods in interval analysis", "kind": "subject", "parent": "65G", "page": 171 }, { "code": "65G50", "originalCode": "65G50", "name": "Roundoff error", "description": "Roundoff error", "kind": "subject", "parent": "65G", "page": 171 }, { "code": "65G99", "originalCode": "65G99", "name": "Error analysis and interval analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "65G", "page": 171 }, { "code": "65H", "originalCode": "65Hxx", "name": "Nonlinear algebraic or transcendental equations", "description": "Nonlinear algebraic or transcendental equations", "kind": "section", "parent": "65", "page": 171 }, { "code": "65H04", "originalCode": "65H04", "name": "Numerical computation of roots of polynomial equations", "description": "Numerical computation of roots of polynomial equations", "kind": "subject", "parent": "65H", "page": 171 }, { "code": "65H05", "originalCode": "65H05", "name": "Numerical computation of solutions to single equations", "description": "Numerical computation of solutions to single equations", "kind": "subject", "parent": "65H", "page": 171 }, { "code": "65H10", "originalCode": "65H10", "name": "Numerical computation of solutions to systems of equations", "description": "Numerical computation of solutions to systems of equations", "kind": "subject", "parent": "65H", "page": 171 }, { "code": "65H14", "originalCode": "65H14", "name": "Numerical algebraic geometry", "description": "Numerical algebraic geometry", "kind": "subject", "parent": "65H", "page": 171 }, { "code": "65H17", "originalCode": "65H17", "name": "Numerical solution of nonlinear eigenvalue and eigenvector problems", "description": "Numerical solution of nonlinear eigenvalue and eigenvector problems [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30]", "kind": "subject", "parent": "65H", "page": 171 }, { "code": "65H20", "originalCode": "65H20", "name": "Global methods, including homotopy approaches to the numerical solution of nonlinear equations", "description": "Global methods, including homotopy approaches to the numerical solution of nonlinear equations [See also 58C30, 90C30]", "kind": "subject", "parent": "65H", "page": 171 }, { "code": "65H99", "originalCode": "65H99", "name": "Nonlinear algebraic or transcendental equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "65H", "page": 171 }, { "code": "65J", "originalCode": "65Jxx", "name": "Numerical analysis in abstract spaces", "description": "Numerical analysis in abstract spaces", "kind": "section", "parent": "65", "page": 171 }, { "code": "65J05", "originalCode": "65J05", "name": "General theory of numerical analysis in abstract spaces", "description": "General theory of numerical analysis in abstract spaces", "kind": "subject", "parent": "65J", "page": 171 }, { "code": "65J08", "originalCode": "65J08", "name": "Numerical solutions to abstract evolution equations", "description": "Numerical solutions to abstract evolution equations", "kind": "subject", "parent": "65J", "page": 171 }, { "code": "65J10", "originalCode": "65J10", "name": "Numerical solutions to equations with linear operators", "description": "Numerical solutions to equations with linear operators [do not use 65Fxx]", "kind": "subject", "parent": "65J", "page": 171 }, { "code": "65J15", "originalCode": "65J15", "name": "Numerical solutions to equations with nonlinear operators", "description": "Numerical solutions to equations with nonlinear operators [do not use 65Hxx]", "kind": "subject", "parent": "65J", "page": 171 }, { "code": "65J20", "originalCode": "65J20", "name": "Numerical solutions of ill-posed problems in abstract spaces; regularization", "description": "Numerical solutions of ill-posed problems in abstract spaces; regularization", "kind": "subject", "parent": "65J", "page": 171 }, { "code": "65J22", "originalCode": "65J22", "name": "Numerical solution to inverse problems in abstract spaces", "description": "Numerical solution to inverse problems in abstract spaces", "kind": "subject", "parent": "65J", "page": 171 }, { "code": "65J99", "originalCode": "65J99", "name": "Numerical analysis in abstract spaces", "description": "None of the above, but in this section", "kind": "subject", "parent": "65J", "page": 171 }, { "code": "65K", "originalCode": "65Kxx", "name": "Numerical methods for mathematical programming, optimization and variational techniques", "description": "Numerical methods for mathematical programming, optimization and variational techniques", "kind": "section", "parent": "65", "page": 171 }, { "code": "65K05", "originalCode": "65K05", "name": "Numerical mathematical programming methods", "description": "Numerical mathematical programming methods [See also 90Cxx]", "kind": "subject", "parent": "65K", "page": 171 }, { "code": "65K10", "originalCode": "65K10", "name": "Numerical optimization and variational techniques", "description": "Numerical optimization and variational techniques [See also 49Mxx, 93-08]", "kind": "subject", "parent": "65K", "page": 171 }, { "code": "65K15", "originalCode": "65K15", "name": "Numerical methods for variational inequalities and related problems", "description": "Numerical methods for variational inequalities and related problems", "kind": "subject", "parent": "65K", "page": 171 }, { "code": "65K99", "originalCode": "65K99", "name": "Numerical methods for mathematical programming, optimization and variational techniques", "description": "None of the above, but in this section", "kind": "subject", "parent": "65K", "page": 171 }, { "code": "65L", "originalCode": "65Lxx", "name": "Numerical methods for ordinary differential equations", "description": "Numerical methods for ordinary differential equations", "kind": "section", "parent": "65", "page": 172 }, { "code": "65L03", "originalCode": "65L03", "name": "Numerical methods for functional-differential equations", "description": "Numerical methods for functional-differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L04", "originalCode": "65L04", "name": "Numerical methods for stiff equations", "description": "Numerical methods for stiff equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L05", "originalCode": "65L05", "name": "Numerical methods for initial value problems involving ordinary differential equations", "description": "Numerical methods for initial value problems involving ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L06", "originalCode": "65L06", "name": "Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations", "description": "Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L07", "originalCode": "65L07", "name": "Numerical investigation of stability of solutions to ordinary differential equations", "description": "Numerical investigation of stability of solutions to ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L08", "originalCode": "65L08", "name": "Numerical solution of ill-posed problems involving ordinary differential equations", "description": "Numerical solution of ill-posed problems involving ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L09", "originalCode": "65L09", "name": "Numerical solution of inverse problems involving ordinary differential equations", "description": "Numerical solution of inverse problems involving ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L10", "originalCode": "65L10", "name": "Numerical solution of boundary value problems involving ordinary differential equations", "description": "Numerical solution of boundary value problems involving ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L11", "originalCode": "65L11", "name": "Numerical solution of singularly perturbed problems involving ordinary differential equations", "description": "Numerical solution of singularly perturbed problems involving ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L12", "originalCode": "65L12", "name": "Finite difference and finite volume methods for ordinary differential equations", "description": "Finite difference and finite volume methods for ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L15", "originalCode": "65L15", "name": "Numerical solution of eigenvalue problems involving ordinary differential equations", "description": "Numerical solution of eigenvalue problems involving ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L20", "originalCode": "65L20", "name": "Stability and convergence of numerical methods for ordinary differential equations", "description": "Stability and convergence of numerical methods for ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L50", "originalCode": "65L50", "name": "Mesh generation, refinement, and adaptive methods for ordinary differential equations", "description": "Mesh generation, refinement, and adaptive methods for ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L60", "originalCode": "65L60", "name": "Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations", "description": "Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L70", "originalCode": "65L70", "name": "Error bounds for numerical methods for ordinary differential equations", "description": "Error bounds for numerical methods for ordinary differential equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L80", "originalCode": "65L80", "name": "Numerical methods for differential-algebraic equations", "description": "Numerical methods for differential-algebraic equations", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65L99", "originalCode": "65L99", "name": "Numerical methods for ordinary differential equations", "description": "None of the above, but in this section", "kind": "subject", "parent": "65L", "page": 172 }, { "code": "65M", "originalCode": "65Mxx", "name": "Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems", "description": "Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems", "kind": "section", "parent": "65", "page": 172 }, { "code": "65M06", "originalCode": "65M06", "name": "Finite difference methods for initial value and initial-boundary value problems involving PDEs", "description": "Finite difference methods for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M08", "originalCode": "65M08", "name": "Finite volume methods for initial value and initial-boundary value problems involving PDEs", "description": "Finite volume methods for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M12", "originalCode": "65M12", "name": "Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs", "description": "Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M15", "originalCode": "65M15", "name": "Error bounds for initial value and initial-boundary value problems involving PDEs", "description": "Error bounds for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M20", "originalCode": "65M20", "name": "Method of lines for initial value and initial-boundary value problems involving PDEs", "description": "Method of lines for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M22", "originalCode": "65M22", "name": "Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs", "description": "Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs [See also 65Fxx, 65Hxx]", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M25", "originalCode": "65M25", "name": "Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs", "description": "Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M30", "originalCode": "65M30", "name": "Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs", "description": "Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M32", "originalCode": "65M32", "name": "Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs", "description": "Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M38", "originalCode": "65M38", "name": "Boundary element methods for initial value and initial-boundary value problems involving PDEs", "description": "Boundary element methods for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 172 }, { "code": "65M50", "originalCode": "65M50", "name": "Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs", "description": "Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 173 }, { "code": "65M55", "originalCode": "65M55", "name": "Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs", "description": "Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 173 }, { "code": "65M60", "originalCode": "65M60", "name": "Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs", "description": "Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 173 }, { "code": "65M70", "originalCode": "65M70", "name": "Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs", "description": "Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 173 }, { "code": "65M75", "originalCode": "65M75", "name": "Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs", "description": "Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 173 }, { "code": "65M80", "originalCode": "65M80", "name": "Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs", "description": "Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 173 }, { "code": "65M85", "originalCode": "65M85", "name": "Fictitious domain methods for initial value and initial-boundary value problems involving PDEs", "description": "Fictitious domain methods for initial value and initial-boundary value problems involving PDEs", "kind": "subject", "parent": "65M", "page": 173 }, { "code": "65M99", "originalCode": "65M99", "name": "Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems", "description": "None of the above, but in this section", "kind": "subject", "parent": "65M", "page": 173 }, { "code": "65N", "originalCode": "65Nxx", "name": "Numerical methods for partial differential equations, boundary value problems", "description": "Numerical methods for partial differential equations, boundary value problems", "kind": "section", "parent": "65", "page": 173 }, { "code": "65N06", "originalCode": "65N06", "name": "Finite difference methods for boundary value problems involving PDEs", "description": "Finite difference methods for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N08", "originalCode": "65N08", "name": "Finite volume methods for boundary value problems involving PDEs", "description": "Finite volume methods for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N12", "originalCode": "65N12", "name": "Stability and convergence of numerical methods for boundary value problems involving PDEs", "description": "Stability and convergence of numerical methods for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N15", "originalCode": "65N15", "name": "Error bounds for boundary value problems involving PDEs", "description": "Error bounds for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N20", "originalCode": "65N20", "name": "Numerical methods for ill-posed problems for boundary value problems involving PDEs", "description": "Numerical methods for ill-posed problems for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N21", "originalCode": "65N21", "name": "Numerical methods for inverse problems for boundary value problems involving PDEs", "description": "Numerical methods for inverse problems for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N22", "originalCode": "65N22", "name": "Numerical solution of discretized equations for boundary value problems involving PDEs", "description": "Numerical solution of discretized equations for boundary value problems involving PDEs [See also 65Fxx, 65Hxx]", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N25", "originalCode": "65N25", "name": "Numerical methods for eigenvalue problems for boundary value problems involving PDEs", "description": "Numerical methods for eigenvalue problems for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N30", "originalCode": "65N30", "name": "Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs", "description": "Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N35", "originalCode": "65N35", "name": "Spectral, collocation and related methods for boundary value problems involving PDEs", "description": "Spectral, collocation and related methods for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N38", "originalCode": "65N38", "name": "Boundary element methods for boundary value problems involving PDEs", "description": "Boundary element methods for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N40", "originalCode": "65N40", "name": "Method of lines for boundary value problems involving PDEs", "description": "Method of lines for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N45", "originalCode": "65N45", "name": "Method of contraction of the boundary for boundary value problems involving PDEs", "description": "Method of contraction of the boundary for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N50", "originalCode": "65N50", "name": "Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs", "description": "Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N55", "originalCode": "65N55", "name": "Multigrid methods; domain decomposition for boundary value problems involving PDEs", "description": "Multigrid methods; domain decomposition for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N75", "originalCode": "65N75", "name": "Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs", "description": "Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N80", "originalCode": "65N80", "name": "Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs", "description": "Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N85", "originalCode": "65N85", "name": "Fictitious domain methods for boundary value problems involving PDEs", "description": "Fictitious domain methods for boundary value problems involving PDEs", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65N99", "originalCode": "65N99", "name": "Numerical methods for partial differential equations, boundary value problems", "description": "None of the above, but in this section", "kind": "subject", "parent": "65N", "page": 173 }, { "code": "65P", "originalCode": "65Pxx", "name": "Numerical problems in dynamical systems", "description": "Numerical problems in dynamical systems [See also 37Mxx]", "kind": "section", "parent": "65", "page": 174 }, { "code": "65P10", "originalCode": "65P10", "name": "Numerical methods for Hamiltonian systems including symplectic integrators", "description": "Numerical methods for Hamiltonian systems including symplectic integrators", "kind": "subject", "parent": "65P", "page": 174 }, { "code": "65P20", "originalCode": "65P20", "name": "Numerical chaos", "description": "Numerical chaos", "kind": "subject", "parent": "65P", "page": 174 }, { "code": "65P30", "originalCode": "65P30", "name": "Numerical bifurcation problems", "description": "Numerical bifurcation problems", "kind": "subject", "parent": "65P", "page": 174 }, { "code": "65P40", "originalCode": "65P40", "name": "Numerical nonlinear stabilities in dynamical systems", "description": "Numerical nonlinear stabilities in dynamical systems", "kind": "subject", "parent": "65P", "page": 174 }, { "code": "65P99", "originalCode": "65P99", "name": "Numerical problems in dynamical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "65P", "page": 174 }, { "code": "65Q", "originalCode": "65Qxx", "name": "Numerical methods for difference and functional equations, recurrence relations", "description": "Numerical methods for difference and functional equations, recurrence relations", "kind": "section", "parent": "65", "page": 174 }, { "code": "65Q10", "originalCode": "65Q10", "name": "Numerical methods for difference equations", "description": "Numerical methods for difference equations", "kind": "subject", "parent": "65Q", "page": 174 }, { "code": "65Q20", "originalCode": "65Q20", "name": "Numerical methods for functional equations", "description": "Numerical methods for functional equations", "kind": "subject", "parent": "65Q", "page": 174 }, { "code": "65Q30", "originalCode": "65Q30", "name": "Numerical aspects of recurrence relations", "description": "Numerical aspects of recurrence relations", "kind": "subject", "parent": "65Q", "page": 174 }, { "code": "65Q99", "originalCode": "65Q99", "name": "Numerical methods for difference and functional equations, recurrence relations", "description": "None of the above, but in this section", "kind": "subject", "parent": "65Q", "page": 174 }, { "code": "65R", "originalCode": "65Rxx", "name": "Numerical methods for integral equations, integral transforms", "description": "Numerical methods for integral equations, integral transforms", "kind": "section", "parent": "65", "page": 174 }, { "code": "65R10", "originalCode": "65R10", "name": "Numerical methods for integral transforms", "description": "Numerical methods for integral transforms", "kind": "subject", "parent": "65R", "page": 174 }, { "code": "65R15", "originalCode": "65R15", "name": "Numerical methods for eigenvalue problems in integral equations", "description": "Numerical methods for eigenvalue problems in integral equations", "kind": "subject", "parent": "65R", "page": 174 }, { "code": "65R20", "originalCode": "65R20", "name": "Numerical methods for integral equations", "description": "Numerical methods for integral equations", "kind": "subject", "parent": "65R", "page": 174 }, { "code": "65R30", "originalCode": "65R30", "name": "Numerical methods for ill-posed problems for integral equations", "description": "Numerical methods for ill-posed problems for integral equations", "kind": "subject", "parent": "65R", "page": 174 }, { "code": "65R32", "originalCode": "65R32", "name": "Numerical methods for inverse problems for integral equations", "description": "Numerical methods for inverse problems for integral equations", "kind": "subject", "parent": "65R", "page": 174 }, { "code": "65R99", "originalCode": "65R99", "name": "Numerical methods for integral equations, integral transforms", "description": "None of the above, but in this section", "kind": "subject", "parent": "65R", "page": 174 }, { "code": "65S", "originalCode": "65Sxx", "name": "Graphical methods in numerical analysis", "description": "Graphical methods in numerical analysis", "kind": "section", "parent": "65", "page": 174 }, { "code": "65S05", "originalCode": "65S05", "name": "Graphical methods in numerical analysis", "description": "Graphical methods in numerical analysis", "kind": "subject", "parent": "65S", "page": 174 }, { "code": "65S99", "originalCode": "65S99", "name": "Graphical methods in numerical analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "65S", "page": 174 }, { "code": "65T", "originalCode": "65Txx", "name": "Numerical methods in Fourier analysis", "description": "Numerical methods in Fourier analysis", "kind": "section", "parent": "65", "page": 174 }, { "code": "65T40", "originalCode": "65T40", "name": "Numerical methods for trigonometric approximation and interpolation", "description": "Numerical methods for trigonometric approximation and interpolation", "kind": "subject", "parent": "65T", "page": 174 }, { "code": "65T50", "originalCode": "65T50", "name": "Numerical methods for discrete and fast Fourier transforms", "description": "Numerical methods for discrete and fast Fourier transforms", "kind": "subject", "parent": "65T", "page": 174 }, { "code": "65T60", "originalCode": "65T60", "name": "Numerical methods for wavelets", "description": "Numerical methods for wavelets", "kind": "subject", "parent": "65T", "page": 174 }, { "code": "65T99", "originalCode": "65T99", "name": "Numerical methods in Fourier analysis", "description": "None of the above, but in this section", "kind": "subject", "parent": "65T", "page": 174 }, { "code": "65Y", "originalCode": "65Yxx", "name": "Computer aspects of numerical algorithms", "description": "Computer aspects of numerical algorithms", "kind": "section", "parent": "65", "page": 174 }, { "code": "65Y04", "originalCode": "65Y04", "name": "Numerical algorithms for computer arithmetic, etc.", "description": "Numerical algorithms for computer arithmetic, etc. [See also 68M07]", "kind": "subject", "parent": "65Y", "page": 174 }, { "code": "65Y05", "originalCode": "65Y05", "name": "Parallel numerical computation", "description": "Parallel numerical computation", "kind": "subject", "parent": "65Y", "page": 174 }, { "code": "65Y10", "originalCode": "65Y10", "name": "Numerical algorithms for specific classes of architectures", "description": "Numerical algorithms for specific classes of architectures", "kind": "subject", "parent": "65Y", "page": 174 }, { "code": "65Y15", "originalCode": "65Y15", "name": "Packaged methods for numerical algorithms", "description": "Packaged methods for numerical algorithms", "kind": "subject", "parent": "65Y", "page": 174 }, { "code": "65Y20", "originalCode": "65Y20", "name": "Complexity and performance of numerical algorithms", "description": "Complexity and performance of numerical algorithms [See also 68Q25]", "kind": "subject", "parent": "65Y", "page": 174 }, { "code": "65Y99", "originalCode": "65Y99", "name": "Computer aspects of numerical algorithms", "description": "None of the above, but in this section", "kind": "subject", "parent": "65Y", "page": 174 }, { "code": "65Z", "originalCode": "65Zxx", "name": "Applications to the sciences", "description": "Applications to the sciences", "kind": "section", "parent": "65", "page": 175 }, { "code": "65Z05", "originalCode": "65Z05", "name": "Applications to the sciences", "description": "Applications to the sciences", "kind": "subject", "parent": "65Z", "page": 175 }, { "code": "65Z99", "originalCode": "65Z99", "name": "Applications to the sciences", "description": "None of the above, but in this section", "kind": "subject", "parent": "65Z", "page": 175 }, { "code": "68", "originalCode": "68-XX", "name": "Computer science", "description": "Computer science \\{For papers containing software, source code, etc. in a specific mathematical area, see the classification number --04 in that area\\}", "kind": "class", "parent": null, "page": 175 }, { "code": "68-00", "originalCode": "68-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to computer science", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to computer science", "kind": "subject", "parent": "68", "page": 175 }, { "code": "68-01", "originalCode": "68-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science", "kind": "subject", "parent": "68", "page": 175 }, { "code": "68-02", "originalCode": "68-02", "name": "Research exposition (monographs, survey articles) pertaining to computer science", "description": "Research exposition (monographs, survey articles) pertaining to computer science", "kind": "subject", "parent": "68", "page": 175 }, { "code": "68-03", "originalCode": "68-03", "name": "History of computer science", "description": "History of computer science [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "68", "page": 175 }, { "code": "68-04", "originalCode": "68-04", "name": "Software, source code, etc. for problems pertaining to computer science", "description": "Software, source code, etc. for problems pertaining to computer science", "kind": "subject", "parent": "68", "page": 175 }, { "code": "68-06", "originalCode": "68-06", "name": "Proceedings, conferences, collections, etc. pertaining to computer science", "description": "Proceedings, conferences, collections, etc. pertaining to computer science", "kind": "subject", "parent": "68", "page": 175 }, { "code": "68-11", "originalCode": "68-11", "name": "Research data for problems pertaining to computer science", "description": "Research data for problems pertaining to computer science", "kind": "subject", "parent": "68", "page": 175 }, { "code": "68M", "originalCode": "68Mxx", "name": "Computer system organization", "description": "Computer system organization", "kind": "section", "parent": "68", "page": 175 }, { "code": "68M01", "originalCode": "68M01", "name": "General theory of computer systems", "description": "General theory of computer systems", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M07", "originalCode": "68M07", "name": "Mathematical problems of computer architecture", "description": "Mathematical problems of computer architecture [See also 68W35]", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M10", "originalCode": "68M10", "name": "Network design and communication in computer systems", "description": "Network design and communication in computer systems [See also 68R10, 90B18]", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M11", "originalCode": "68M11", "name": "Internet topics", "description": "Internet topics [See also 68U35]", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M12", "originalCode": "68M12", "name": "Network protocols", "description": "Network protocols", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M14", "originalCode": "68M14", "name": "Distributed systems", "description": "Distributed systems", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M15", "originalCode": "68M15", "name": "Reliability, testing and fault tolerance of networks and computer systems", "description": "Reliability, testing and fault tolerance of networks and computer systems", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M18", "originalCode": "68M18", "name": "Wireless sensor networks as related to computer science", "description": "Wireless sensor networks as related to computer science [See also 90B18, 90B80]", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M20", "originalCode": "68M20", "name": "Performance evaluation, queueing, and scheduling in the context of computer systems", "description": "Performance evaluation, queueing, and scheduling in the context of computer systems [See also 60K20, 60K25, 90B22, 90B35, 90B36]", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M25", "originalCode": "68M25", "name": "Computer security", "description": "Computer security", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68M99", "originalCode": "68M99", "name": "Computer system organization", "description": "None of the above, but in this section", "kind": "subject", "parent": "68M", "page": 175 }, { "code": "68N", "originalCode": "68Nxx", "name": "Theory of software", "description": "Theory of software", "kind": "section", "parent": "68", "page": 175 }, { "code": "68N01", "originalCode": "68N01", "name": "General topics in the theory of software", "description": "General topics in the theory of software", "kind": "subject", "parent": "68N", "page": 175 }, { "code": "68N15", "originalCode": "68N15", "name": "Theory of programming languages", "description": "Theory of programming languages", "kind": "subject", "parent": "68N", "page": 175 }, { "code": "68N17", "originalCode": "68N17", "name": "Logic programming", "description": "Logic programming", "kind": "subject", "parent": "68N", "page": 175 }, { "code": "68N18", "originalCode": "68N18", "name": "Functional programming and lambda calculus", "description": "Functional programming and lambda calculus [See also 03B40]", "kind": "subject", "parent": "68N", "page": 175 }, { "code": "68N19", "originalCode": "68N19", "name": "Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.)", "description": "Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.)", "kind": "subject", "parent": "68N", "page": 175 }, { "code": "68N20", "originalCode": "68N20", "name": "Theory of compilers and interpreters", "description": "Theory of compilers and interpreters", "kind": "subject", "parent": "68N", "page": 176 }, { "code": "68N25", "originalCode": "68N25", "name": "Theory of operating systems", "description": "Theory of operating systems", "kind": "subject", "parent": "68N", "page": 176 }, { "code": "68N30", "originalCode": "68N30", "name": "Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)", "description": "Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)", "kind": "subject", "parent": "68N", "page": 176 }, { "code": "68N99", "originalCode": "68N99", "name": "Theory of software", "description": "None of the above, but in this section", "kind": "subject", "parent": "68N", "page": 176 }, { "code": "68P", "originalCode": "68Pxx", "name": "Theory of data", "description": "Theory of data", "kind": "section", "parent": "68", "page": 176 }, { "code": "68P01", "originalCode": "68P01", "name": "General topics in the theory of data", "description": "General topics in the theory of data", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68P05", "originalCode": "68P05", "name": "Data structures", "description": "Data structures", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68P10", "originalCode": "68P10", "name": "Searching and sorting", "description": "Searching and sorting", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68P15", "originalCode": "68P15", "name": "Database theory", "description": "Database theory", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68P20", "originalCode": "68P20", "name": "Information storage and retrieval of data", "description": "Information storage and retrieval of data", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68P25", "originalCode": "68P25", "name": "Data encryption (aspects in computer science)", "description": "Data encryption (aspects in computer science) [See also 81P94, 94A60]", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68P27", "originalCode": "68P27", "name": "Privacy of data", "description": "Privacy of data", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68P30", "originalCode": "68P30", "name": "Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)", "description": "Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science) [See also 94Axx, 94Bxx]", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68P99", "originalCode": "68P99", "name": "Theory of data", "description": "None of the above, but in this section", "kind": "subject", "parent": "68P", "page": 176 }, { "code": "68Q", "originalCode": "68Qxx", "name": "Theory of computing", "description": "Theory of computing", "kind": "section", "parent": "68", "page": 176 }, { "code": "68Q01", "originalCode": "68Q01", "name": "General topics in the theory of computing", "description": "General topics in the theory of computing", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q04", "originalCode": "68Q04", "name": "Classical models of computation (Turing machines, etc.)", "description": "Classical models of computation (Turing machines, etc.) [See also 03D10]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q06", "originalCode": "68Q06", "name": "Networks and circuits as models of computation; circuit complexity", "description": "Networks and circuits as models of computation; circuit complexity [See also 94C11]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q07", "originalCode": "68Q07", "name": "Biologically inspired models of computation (DNA computing, membrane computing, etc.)", "description": "Biologically inspired models of computation (DNA computing, membrane computing, etc.)", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q09", "originalCode": "68Q09", "name": "Other nonclassical models of computation", "description": "Other nonclassical models of computation \\{For quantum computing, see mainly 68Q12, 81P68\\}", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q10", "originalCode": "68Q10", "name": "Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)", "description": "Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q11", "originalCode": "68Q11", "name": "Communication complexity, information complexity", "description": "Communication complexity, information complexity", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q12", "originalCode": "68Q12", "name": "Quantum algorithms and complexity in the theory of computing", "description": "Quantum algorithms and complexity in the theory of computing [See also 68Q09, 81P68]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q15", "originalCode": "68Q15", "name": "Complexity classes (hierarchies, relations among complexity classes, etc.)", "description": "Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q17", "originalCode": "68Q17", "name": "Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)", "description": "Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q19", "originalCode": "68Q19", "name": "Descriptive complexity and finite models", "description": "Descriptive complexity and finite models [See also 03C13]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q25", "originalCode": "68Q25", "name": "Analysis of algorithms and problem complexity", "description": "Analysis of algorithms and problem complexity [See also 68W40]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q27", "originalCode": "68Q27", "name": "Parameterized complexity, tractability and kernelization", "description": "Parameterized complexity, tractability and kernelization", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q30", "originalCode": "68Q30", "name": "Algorithmic information theory (Kolmogorov complexity, etc.)", "description": "Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q32", "originalCode": "68Q32", "name": "Computational learning theory", "description": "Computational learning theory [See also 68T05]", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q42", "originalCode": "68Q42", "name": "Grammars and rewriting systems", "description": "Grammars and rewriting systems", "kind": "subject", "parent": "68Q", "page": 176 }, { "code": "68Q45", "originalCode": "68Q45", "name": "Formal languages and automata", "description": "Formal languages and automata [See also 03D05, 68Q70, 94A45]", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68Q55", "originalCode": "68Q55", "name": "Semantics in the theory of computing", "description": "Semantics in the theory of computing [See also 03B70, 06B35, 18C50]", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68Q60", "originalCode": "68Q60", "name": "Specification and verification (program logics, model checking, etc.)", "description": "Specification and verification (program logics, model checking, etc.) [See also 03B70]", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68Q65", "originalCode": "68Q65", "name": "Abstract data types; algebraic specification", "description": "Abstract data types; algebraic specification [See also 18C50]", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68Q70", "originalCode": "68Q70", "name": "Algebraic theory of languages and automata", "description": "Algebraic theory of languages and automata [See also 18B20, 20M35]", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68Q80", "originalCode": "68Q80", "name": "Cellular automata (computational aspects)", "description": "Cellular automata (computational aspects) \\{For cellular automata as dynamical systems, see 37B15\\}", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68Q85", "originalCode": "68Q85", "name": "Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)", "description": "Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68Q87", "originalCode": "68Q87", "name": "Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)", "description": "Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40]", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68Q99", "originalCode": "68Q99", "name": "Theory of computing", "description": "None of the above, but in this section", "kind": "subject", "parent": "68Q", "page": 177 }, { "code": "68R", "originalCode": "68Rxx", "name": "Discrete mathematics in relation to computer science", "description": "Discrete mathematics in relation to computer science", "kind": "section", "parent": "68", "page": 177 }, { "code": "68R01", "originalCode": "68R01", "name": "General topics of discrete mathematics in relation to computer science", "description": "General topics of discrete mathematics in relation to computer science", "kind": "subject", "parent": "68R", "page": 177 }, { "code": "68R05", "originalCode": "68R05", "name": "Combinatorics in computer science", "description": "Combinatorics in computer science", "kind": "subject", "parent": "68R", "page": 177 }, { "code": "68R07", "originalCode": "68R07", "name": "Computational aspects of satisfiability", "description": "Computational aspects of satisfiability [See also 68T20]", "kind": "subject", "parent": "68R", "page": 177 }, { "code": "68R10", "originalCode": "68R10", "name": "Graph theory (including graph drawing) in computer science", "description": "Graph theory (including graph drawing) in computer science [See also 05Cxx, 90B10, 90C35]", "kind": "subject", "parent": "68R", "page": 177 }, { "code": "68R12", "originalCode": "68R12", "name": "Metric embeddings as related to computational problems and algorithms", "description": "Metric embeddings as related to computational problems and algorithms", "kind": "subject", "parent": "68R", "page": 177 }, { "code": "68R15", "originalCode": "68R15", "name": "Combinatorics on words", "description": "Combinatorics on words", "kind": "subject", "parent": "68R", "page": 177 }, { "code": "68R99", "originalCode": "68R99", "name": "Discrete mathematics in relation to computer science", "description": "None of the above, but in this section", "kind": "subject", "parent": "68R", "page": 177 }, { "code": "68T", "originalCode": "68Txx", "name": "Artificial intelligence", "description": "Artificial intelligence", "kind": "section", "parent": "68", "page": 177 }, { "code": "68T01", "originalCode": "68T01", "name": "General topics in artificial intelligence", "description": "General topics in artificial intelligence", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T05", "originalCode": "68T05", "name": "Learning and adaptive systems in artificial intelligence", "description": "Learning and adaptive systems in artificial intelligence [See also 68Q32]", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T07", "originalCode": "68T07", "name": "Artificial neural networks and deep learning", "description": "Artificial neural networks and deep learning", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T09", "originalCode": "68T09", "name": "Computational aspects of data analysis and big data", "description": "Computational aspects of data analysis and big data [See also 62R07] \\{For homological aspects, see 55N31\\}", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T10", "originalCode": "68T10", "name": "Pattern recognition, speech recognition", "description": "Pattern recognition, speech recognition \\{For cluster analysis, see 62H30\\}", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T20", "originalCode": "68T20", "name": "Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)", "description": "Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T27", "originalCode": "68T27", "name": "Logic in artificial intelligence", "description": "Logic in artificial intelligence", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T30", "originalCode": "68T30", "name": "Knowledge representation", "description": "Knowledge representation", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T35", "originalCode": "68T35", "name": "Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence", "description": "Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T37", "originalCode": "68T37", "name": "Reasoning under uncertainty in the context of artificial intelligence", "description": "Reasoning under uncertainty in the context of artificial intelligence", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T40", "originalCode": "68T40", "name": "Artificial intelligence for robotics", "description": "Artificial intelligence for robotics [See also 93C85]", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T42", "originalCode": "68T42", "name": "Agent technology and artificial intelligence", "description": "Agent technology and artificial intelligence", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T45", "originalCode": "68T45", "name": "Machine vision and scene understanding", "description": "Machine vision and scene understanding", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T50", "originalCode": "68T50", "name": "Natural language processing", "description": "Natural language processing [See also 03B65, 91F20]", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68T99", "originalCode": "68T99", "name": "Artificial intelligence", "description": "None of the above, but in this section", "kind": "subject", "parent": "68T", "page": 177 }, { "code": "68U", "originalCode": "68Uxx", "name": "Computing methodologies and applications", "description": "Computing methodologies and applications", "kind": "section", "parent": "68", "page": 178 }, { "code": "68U01", "originalCode": "68U01", "name": "General topics in computing methodologies", "description": "General topics in computing methodologies", "kind": "subject", "parent": "68U", "page": 178 }, { "code": "68U03", "originalCode": "68U03", "name": "Computational aspects of digital topology", "description": "Computational aspects of digital topology \\{For topological aspects, see 54H30; for homological aspects, see 55-XX\\}", "kind": "subject", "parent": "68U", "page": 178 }, { "code": "68U05", "originalCode": "68U05", "name": "Computer graphics; computational geometry (digital and algorithmic aspects)", "description": "Computer graphics; computational geometry (digital and algorithmic aspects) \\{For methods of numerical mathematics, see 65D18\\}", "kind": "subject", "parent": "68U", "page": 178 }, { "code": "68U07", "originalCode": "68U07", "name": "Computer science aspects of computer-aided design", "description": "Computer science aspects of computer-aided design \\{For methods of numerical mathematics, see 65D17\\}", "kind": "subject", "parent": "68U", "page": 178 }, { "code": "68U10", "originalCode": "68U10", "name": "Computing methodologies for image processing", "description": "Computing methodologies for image processing", "kind": "subject", "parent": "68U", "page": 178 }, { "code": "68U15", "originalCode": "68U15", "name": "Computing methodologies for text processing; mathematical typography", "description": "Computing methodologies for text processing; mathematical typography", "kind": "subject", "parent": "68U", "page": 178 }, { "code": "68U35", "originalCode": "68U35", "name": "Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)", "description": "Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.) [See also 68M11]", "kind": "subject", "parent": "68U", "page": 178 }, { "code": "68U99", "originalCode": "68U99", "name": "Computing methodologies and applications", "description": "None of the above, but in this section", "kind": "subject", "parent": "68U", "page": 178 }, { "code": "68V", "originalCode": "68Vxx", "name": "Computer science support for mathematical research and practice", "description": "Computer science support for mathematical research and practice", "kind": "section", "parent": "68", "page": 178 }, { "code": "68V05", "originalCode": "68V05", "name": "Computer assisted proofs of proofs-by-exhaustion type", "description": "Computer assisted proofs of proofs-by-exhaustion type \\{For rigorous numerics, see 65Gxx; for proofs employing automated or interactive theorem provers, see 68V15\\}", "kind": "subject", "parent": "68V", "page": 178 }, { "code": "68V15", "originalCode": "68V15", "name": "Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)", "description": "Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.) [See also 03B35]", "kind": "subject", "parent": "68V", "page": 178 }, { "code": "68V20", "originalCode": "68V20", "name": "Formalization of mathematics in connection with theorem provers", "description": "Formalization of mathematics in connection with theorem provers [See also 03B35, 68V15]", "kind": "subject", "parent": "68V", "page": 178 }, { "code": "68V25", "originalCode": "68V25", "name": "Presentation and content markup for mathematics", "description": "Presentation and content markup for mathematics", "kind": "subject", "parent": "68V", "page": 178 }, { "code": "68V30", "originalCode": "68V30", "name": "Mathematical knowledge management", "description": "Mathematical knowledge management", "kind": "subject", "parent": "68V", "page": 178 }, { "code": "68V35", "originalCode": "68V35", "name": "Digital mathematics libraries and repositories", "description": "Digital mathematics libraries and repositories", "kind": "subject", "parent": "68V", "page": 178 }, { "code": "68V99", "originalCode": "68V99", "name": "Computer science support for mathematical research and practice", "description": "None of the above, but in this section", "kind": "subject", "parent": "68V", "page": 178 }, { "code": "68W", "originalCode": "68Wxx", "name": "Algorithms in computer science", "description": "Algorithms in computer science \\{For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx\\}", "kind": "section", "parent": "68", "page": 178 }, { "code": "68W01", "originalCode": "68W01", "name": "General topics in the theory of algorithms", "description": "General topics in the theory of algorithms", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W05", "originalCode": "68W05", "name": "Nonnumerical algorithms", "description": "Nonnumerical algorithms", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W10", "originalCode": "68W10", "name": "Parallel algorithms in computer science", "description": "Parallel algorithms in computer science", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W15", "originalCode": "68W15", "name": "Distributed algorithms", "description": "Distributed algorithms", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W20", "originalCode": "68W20", "name": "Randomized algorithms", "description": "Randomized algorithms", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W25", "originalCode": "68W25", "name": "Approximation algorithms", "description": "Approximation algorithms", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W27", "originalCode": "68W27", "name": "Online algorithms; streaming algorithms", "description": "Online algorithms; streaming algorithms", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W30", "originalCode": "68W30", "name": "Symbolic computation and algebraic computation", "description": "Symbolic computation and algebraic computation [See also 11Yxx, 12-08, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W32", "originalCode": "68W32", "name": "Algorithms on strings", "description": "Algorithms on strings", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W35", "originalCode": "68W35", "name": "Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.)", "description": "Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.) [See also 68M07]", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W40", "originalCode": "68W40", "name": "Analysis of algorithms", "description": "Analysis of algorithms [See also 68Q25]", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W50", "originalCode": "68W50", "name": "Evolutionary algorithms, genetic algorithms (computational aspects)", "description": "Evolutionary algorithms, genetic algorithms (computational aspects) [See also 68T05, 68T20, 90C59]", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "68W99", "originalCode": "68W99", "name": "Algorithms in computer science", "description": "None of the above, but in this section", "kind": "subject", "parent": "68W", "page": 178 }, { "code": "70", "originalCode": "70-XX", "name": "Mechanics of particles and systems", "description": "Mechanics of particles and systems \\{For relativistic mechanics, see 83A05, 83C10; for statistical mechanics, see 82-XX\\}", "kind": "class", "parent": null, "page": 179 }, { "code": "70-00", "originalCode": "70-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of particles and systems", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-01", "originalCode": "70-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-02", "originalCode": "70-02", "name": "Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems", "description": "Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-03", "originalCode": "70-03", "name": "History of mechanics of particles and systems", "description": "History of mechanics of particles and systems [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-04", "originalCode": "70-04", "name": "Software, source code, etc. for problems pertaining to mechanics of particles and systems", "description": "Software, source code, etc. for problems pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-05", "originalCode": "70-05", "name": "Experimental work for problems pertaining to mechanics of particles and systems", "description": "Experimental work for problems pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-06", "originalCode": "70-06", "name": "Proceedings, conferences, collections, etc. pertaining to mechanics of particles and systems", "description": "Proceedings, conferences, collections, etc. pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-08", "originalCode": "70-08", "name": "Computational methods for problems pertaining to mechanics of particles and systems", "description": "Computational methods for problems pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-10", "originalCode": "70-10", "name": "Mathematical modeling or simulation for problems pertaining to mechanics of particles and systems", "description": "Mathematical modeling or simulation for problems pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70-11", "originalCode": "70-11", "name": "Research data for problems pertaining to mechanics of particles and systems", "description": "Research data for problems pertaining to mechanics of particles and systems", "kind": "subject", "parent": "70", "page": 179 }, { "code": "70A", "originalCode": "70Axx", "name": "Axiomatics, foundations", "description": "Axiomatics, foundations", "kind": "section", "parent": "70", "page": 179 }, { "code": "70A05", "originalCode": "70A05", "name": "Axiomatics, foundations", "description": "Axiomatics, foundations", "kind": "subject", "parent": "70A", "page": 179 }, { "code": "70A99", "originalCode": "70A99", "name": "Axiomatics, foundations", "description": "None of the above, but in this section", "kind": "subject", "parent": "70A", "page": 179 }, { "code": "70B", "originalCode": "70Bxx", "name": "Kinematics", "description": "Kinematics [See also 53A17]", "kind": "section", "parent": "70", "page": 179 }, { "code": "70B05", "originalCode": "70B05", "name": "Kinematics of a particle", "description": "Kinematics of a particle", "kind": "subject", "parent": "70B", "page": 179 }, { "code": "70B10", "originalCode": "70B10", "name": "Kinematics of a rigid body", "description": "Kinematics of a rigid body", "kind": "subject", "parent": "70B", "page": 179 }, { "code": "70B15", "originalCode": "70B15", "name": "Kinematics of mechanisms and robots", "description": "Kinematics of mechanisms and robots [See also 68T40, 70Q05, 93C85]", "kind": "subject", "parent": "70B", "page": 179 }, { "code": "70B99", "originalCode": "70B99", "name": "Kinematics", "description": "None of the above, but in this section", "kind": "subject", "parent": "70B", "page": 179 }, { "code": "70C", "originalCode": "70Cxx", "name": "Statics", "description": "Statics", "kind": "section", "parent": "70", "page": 179 }, { "code": "70C20", "originalCode": "70C20", "name": "Statics", "description": "Statics", "kind": "subject", "parent": "70C", "page": 179 }, { "code": "70C99", "originalCode": "70C99", "name": "Statics", "description": "None of the above, but in this section", "kind": "subject", "parent": "70C", "page": 179 }, { "code": "70E", "originalCode": "70Exx", "name": "Dynamics of a rigid body and of multibody systems", "description": "Dynamics of a rigid body and of multibody systems", "kind": "section", "parent": "70", "page": 179 }, { "code": "70E05", "originalCode": "70E05", "name": "Motion of the gyroscope", "description": "Motion of the gyroscope", "kind": "subject", "parent": "70E", "page": 179 }, { "code": "70E15", "originalCode": "70E15", "name": "Free motion of a rigid body", "description": "Free motion of a rigid body [See also 70M20]", "kind": "subject", "parent": "70E", "page": 179 }, { "code": "70E17", "originalCode": "70E17", "name": "Motion of a rigid body with a fixed point", "description": "Motion of a rigid body with a fixed point", "kind": "subject", "parent": "70E", "page": 179 }, { "code": "70E18", "originalCode": "70E18", "name": "Motion of a rigid body in contact with a solid surface", "description": "Motion of a rigid body in contact with a solid surface [See also 70F25]", "kind": "subject", "parent": "70E", "page": 179 }, { "code": "70E20", "originalCode": "70E20", "name": "Perturbation methods for rigid body dynamics", "description": "Perturbation methods for rigid body dynamics", "kind": "subject", "parent": "70E", "page": 179 }, { "code": "70E40", "originalCode": "70E40", "name": "Integrable cases of motion in rigid body dynamics", "description": "Integrable cases of motion in rigid body dynamics", "kind": "subject", "parent": "70E", "page": 179 }, { "code": "70E45", "originalCode": "70E45", "name": "Higher-dimensional generalizations in rigid body dynamics", "description": "Higher-dimensional generalizations in rigid body dynamics", "kind": "subject", "parent": "70E", "page": 179 }, { "code": "70E50", "originalCode": "70E50", "name": "Stability problems in rigid body dynamics", "description": "Stability problems in rigid body dynamics", "kind": "subject", "parent": "70E", "page": 180 }, { "code": "70E55", "originalCode": "70E55", "name": "Dynamics of multibody systems", "description": "Dynamics of multibody systems", "kind": "subject", "parent": "70E", "page": 180 }, { "code": "70E60", "originalCode": "70E60", "name": "Robot dynamics and control of rigid bodies", "description": "Robot dynamics and control of rigid bodies [See also 68T40, 70Q05, 93C85]", "kind": "subject", "parent": "70E", "page": 180 }, { "code": "70E99", "originalCode": "70E99", "name": "Dynamics of a rigid body and of multibody systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "70E", "page": 180 }, { "code": "70F", "originalCode": "70Fxx", "name": "Dynamics of a system of particles, including celestial mechanics", "description": "Dynamics of a system of particles, including celestial mechanics", "kind": "section", "parent": "70", "page": 180 }, { "code": "70F05", "originalCode": "70F05", "name": "Two-body problems", "description": "Two-body problems", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F07", "originalCode": "70F07", "name": "Three-body problems", "description": "Three-body problems", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F10", "originalCode": "70F10", "name": "\\(n\\)-body problems", "description": "\\(n\\)-body problems", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F15", "originalCode": "70F15", "name": "Celestial mechanics", "description": "Celestial mechanics", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F16", "originalCode": "70F16", "name": "Collisions in celestial mechanics, regularization", "description": "Collisions in celestial mechanics, regularization", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F17", "originalCode": "70F17", "name": "Inverse problems for systems of particles", "description": "Inverse problems for systems of particles", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F20", "originalCode": "70F20", "name": "Holonomic systems related to the dynamics of a system of particles", "description": "Holonomic systems related to the dynamics of a system of particles", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F25", "originalCode": "70F25", "name": "Nonholonomic systems related to the dynamics of a system of particles", "description": "Nonholonomic systems related to the dynamics of a system of particles", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F35", "originalCode": "70F35", "name": "Collision of rigid or pseudo-rigid bodies", "description": "Collision of rigid or pseudo-rigid bodies", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F40", "originalCode": "70F40", "name": "Problems involving a system of particles with friction", "description": "Problems involving a system of particles with friction", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F45", "originalCode": "70F45", "name": "The dynamics of infinite particle systems", "description": "The dynamics of infinite particle systems", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70F99", "originalCode": "70F99", "name": "Dynamics of a system of particles, including celestial mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "70F", "page": 180 }, { "code": "70G", "originalCode": "70Gxx", "name": "General models, approaches, and methods in mechanics of particles and systems", "description": "General models, approaches, and methods in mechanics of particles and systems [See also 37-XX]", "kind": "section", "parent": "70", "page": 180 }, { "code": "70G10", "originalCode": "70G10", "name": "Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics", "description": "Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70G40", "originalCode": "70G40", "name": "Topological and differential topological methods for problems in mechanics", "description": "Topological and differential topological methods for problems in mechanics", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70G45", "originalCode": "70G45", "name": "Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics", "description": "Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics [See also 53Cxx, 53Dxx, 58Axx]", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70G55", "originalCode": "70G55", "name": "Algebraic geometry methods for problems in mechanics", "description": "Algebraic geometry methods for problems in mechanics", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70G60", "originalCode": "70G60", "name": "Dynamical systems methods for problems in mechanics", "description": "Dynamical systems methods for problems in mechanics", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70G65", "originalCode": "70G65", "name": "Symmetries, Lie group and Lie algebra methods for problems in mechanics", "description": "Symmetries, Lie group and Lie algebra methods for problems in mechanics", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70G70", "originalCode": "70G70", "name": "Functional analytic methods for problems in mechanics", "description": "Functional analytic methods for problems in mechanics", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70G75", "originalCode": "70G75", "name": "Variational methods for problems in mechanics", "description": "Variational methods for problems in mechanics", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70G99", "originalCode": "70G99", "name": "General models, approaches, and methods in mechanics of particles and systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "70G", "page": 180 }, { "code": "70H", "originalCode": "70Hxx", "name": "Hamiltonian and Lagrangian mechanics", "description": "Hamiltonian and Lagrangian mechanics [See also 37Jxx]", "kind": "section", "parent": "70", "page": 181 }, { "code": "70H03", "originalCode": "70H03", "name": "Lagrange's equations", "description": "Lagrange's equations", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H05", "originalCode": "70H05", "name": "Hamilton's equations", "description": "Hamilton's equations", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H06", "originalCode": "70H06", "name": "Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics", "description": "Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H07", "originalCode": "70H07", "name": "Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics", "description": "Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H08", "originalCode": "70H08", "name": "Nearly integrable Hamiltonian systems, KAM theory", "description": "Nearly integrable Hamiltonian systems, KAM theory", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H09", "originalCode": "70H09", "name": "Perturbation theories for problems in Hamiltonian and Lagrangian mechanics", "description": "Perturbation theories for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H11", "originalCode": "70H11", "name": "Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics", "description": "Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H12", "originalCode": "70H12", "name": "Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics", "description": "Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H14", "originalCode": "70H14", "name": "Stability problems for problems in Hamiltonian and Lagrangian mechanics", "description": "Stability problems for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H15", "originalCode": "70H15", "name": "Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics", "description": "Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H20", "originalCode": "70H20", "name": "Hamilton-Jacobi equations in mechanics", "description": "Hamilton-Jacobi equations in mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H25", "originalCode": "70H25", "name": "Hamilton's principle", "description": "Hamilton's principle", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H30", "originalCode": "70H30", "name": "Other variational principles in mechanics", "description": "Other variational principles in mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H33", "originalCode": "70H33", "name": "Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics", "description": "Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H40", "originalCode": "70H40", "name": "Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics", "description": "Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H45", "originalCode": "70H45", "name": "Constrained dynamics, Dirac's theory of constraints", "description": "Constrained dynamics, Dirac's theory of constraints [See also 70F20, 70F25, 70Gxx]", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H50", "originalCode": "70H50", "name": "Higher-order theories for problems in Hamiltonian and Lagrangian mechanics", "description": "Higher-order theories for problems in Hamiltonian and Lagrangian mechanics", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70H99", "originalCode": "70H99", "name": "Hamiltonian and Lagrangian mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "70H", "page": 181 }, { "code": "70J", "originalCode": "70Jxx", "name": "Linear vibration theory", "description": "Linear vibration theory", "kind": "section", "parent": "70", "page": 181 }, { "code": "70J10", "originalCode": "70J10", "name": "Modal analysis in linear vibration theory", "description": "Modal analysis in linear vibration theory", "kind": "subject", "parent": "70J", "page": 181 }, { "code": "70J25", "originalCode": "70J25", "name": "Stability for problems in linear vibration theory", "description": "Stability for problems in linear vibration theory", "kind": "subject", "parent": "70J", "page": 181 }, { "code": "70J30", "originalCode": "70J30", "name": "Free motions in linear vibration theory", "description": "Free motions in linear vibration theory", "kind": "subject", "parent": "70J", "page": 181 }, { "code": "70J35", "originalCode": "70J35", "name": "Forced motions in linear vibration theory", "description": "Forced motions in linear vibration theory", "kind": "subject", "parent": "70J", "page": 181 }, { "code": "70J40", "originalCode": "70J40", "name": "Parametric resonances in linear vibration theory", "description": "Parametric resonances in linear vibration theory", "kind": "subject", "parent": "70J", "page": 181 }, { "code": "70J50", "originalCode": "70J50", "name": "Systems arising from the discretization of structural vibration problems", "description": "Systems arising from the discretization of structural vibration problems", "kind": "subject", "parent": "70J", "page": 181 }, { "code": "70J99", "originalCode": "70J99", "name": "Linear vibration theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "70J", "page": 181 }, { "code": "70K", "originalCode": "70Kxx", "name": "Nonlinear dynamics in mechanics", "description": "Nonlinear dynamics in mechanics [See also 34Cxx, 37-XX]", "kind": "section", "parent": "70", "page": 182 }, { "code": "70K05", "originalCode": "70K05", "name": "Phase plane analysis, limit cycles for nonlinear problems in mechanics", "description": "Phase plane analysis, limit cycles for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K20", "originalCode": "70K20", "name": "Stability for nonlinear problems in mechanics", "description": "Stability for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K25", "originalCode": "70K25", "name": "Free motions for nonlinear problems in mechanics", "description": "Free motions for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K28", "originalCode": "70K28", "name": "Parametric resonances for nonlinear problems in mechanics", "description": "Parametric resonances for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K30", "originalCode": "70K30", "name": "Nonlinear resonances for nonlinear problems in mechanics", "description": "Nonlinear resonances for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K40", "originalCode": "70K40", "name": "Forced motions for nonlinear problems in mechanics", "description": "Forced motions for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K42", "originalCode": "70K42", "name": "Equilibria and periodic trajectories for nonlinear problems in mechanics", "description": "Equilibria and periodic trajectories for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K43", "originalCode": "70K43", "name": "Quasi-periodic motions and invariant tori for nonlinear problems in mechanics", "description": "Quasi-periodic motions and invariant tori for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K44", "originalCode": "70K44", "name": "Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics", "description": "Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K45", "originalCode": "70K45", "name": "Normal forms for nonlinear problems in mechanics", "description": "Normal forms for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K50", "originalCode": "70K50", "name": "Bifurcations and instability for nonlinear problems in mechanics", "description": "Bifurcations and instability for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K55", "originalCode": "70K55", "name": "Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics", "description": "Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics [See also 37D45]", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K60", "originalCode": "70K60", "name": "General perturbation schemes for nonlinear problems in mechanics", "description": "General perturbation schemes for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K65", "originalCode": "70K65", "name": "Averaging of perturbations for nonlinear problems in mechanics", "description": "Averaging of perturbations for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K70", "originalCode": "70K70", "name": "Systems with slow and fast motions for nonlinear problems in mechanics", "description": "Systems with slow and fast motions for nonlinear problems in mechanics", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K75", "originalCode": "70K75", "name": "Nonlinear modes", "description": "Nonlinear modes", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70K99", "originalCode": "70K99", "name": "Nonlinear dynamics in mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "70K", "page": 182 }, { "code": "70L", "originalCode": "70Lxx", "name": "Random and stochastic aspects of the mechanics of particles and systems", "description": "Random and stochastic aspects of the mechanics of particles and systems", "kind": "section", "parent": "70", "page": 182 }, { "code": "70L05", "originalCode": "70L05", "name": "Random vibrations in mechanics of particles and systems", "description": "Random vibrations in mechanics of particles and systems [See also 74H50]", "kind": "subject", "parent": "70L", "page": 182 }, { "code": "70L10", "originalCode": "70L10", "name": "Stochastic geometric mechanics", "description": "Stochastic geometric mechanics", "kind": "subject", "parent": "70L", "page": 182 }, { "code": "70L99", "originalCode": "70L99", "name": "Random and stochastic aspects of the mechanics of particles and systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "70L", "page": 182 }, { "code": "70M", "originalCode": "70Mxx", "name": "Orbital mechanics", "description": "Orbital mechanics", "kind": "section", "parent": "70", "page": 182 }, { "code": "70M20", "originalCode": "70M20", "name": "Orbital mechanics", "description": "Orbital mechanics", "kind": "subject", "parent": "70M", "page": 182 }, { "code": "70M99", "originalCode": "70M99", "name": "Orbital mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "70M", "page": 182 }, { "code": "70P", "originalCode": "70Pxx", "name": "Variable mass, rockets", "description": "Variable mass, rockets", "kind": "section", "parent": "70", "page": 182 }, { "code": "70P05", "originalCode": "70P05", "name": "Variable mass, rockets", "description": "Variable mass, rockets", "kind": "subject", "parent": "70P", "page": 182 }, { "code": "70P99", "originalCode": "70P99", "name": "Variable mass, rockets", "description": "None of the above, but in this section", "kind": "subject", "parent": "70P", "page": 182 }, { "code": "70Q", "originalCode": "70Qxx", "name": "Control of mechanical systems", "description": "Control of mechanical systems [See also 60Gxx, 60Jxx]", "kind": "section", "parent": "70", "page": 182 }, { "code": "70Q05", "originalCode": "70Q05", "name": "Control of mechanical systems", "description": "Control of mechanical systems", "kind": "subject", "parent": "70Q", "page": 182 }, { "code": "70Q99", "originalCode": "70Q99", "name": "Control of mechanical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "70Q", "page": 182 }, { "code": "70S", "originalCode": "70Sxx", "name": "Classical field theories", "description": "Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]", "kind": "section", "parent": "70", "page": 183 }, { "code": "70S05", "originalCode": "70S05", "name": "Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems", "description": "Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems", "kind": "subject", "parent": "70S", "page": 183 }, { "code": "70S10", "originalCode": "70S10", "name": "Symmetries and conservation laws in mechanics of particles and systems", "description": "Symmetries and conservation laws in mechanics of particles and systems", "kind": "subject", "parent": "70S", "page": 183 }, { "code": "70S15", "originalCode": "70S15", "name": "Yang-Mills and other gauge theories in mechanics of particles and systems", "description": "Yang-Mills and other gauge theories in mechanics of particles and systems", "kind": "subject", "parent": "70S", "page": 183 }, { "code": "70S20", "originalCode": "70S20", "name": "More general nonquantum field theories in mechanics of particles and systems", "description": "More general nonquantum field theories in mechanics of particles and systems", "kind": "subject", "parent": "70S", "page": 183 }, { "code": "70S99", "originalCode": "70S99", "name": "Classical field theories", "description": "None of the above, but in this section", "kind": "subject", "parent": "70S", "page": 183 }, { "code": "74", "originalCode": "74-XX", "name": "Mechanics of deformable solids", "description": "Mechanics of deformable solids", "kind": "class", "parent": null, "page": 183 }, { "code": "74-00", "originalCode": "74-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of deformable solids", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of deformable solids", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74-01", "originalCode": "74-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74-02", "originalCode": "74-02", "name": "Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids", "description": "Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74-03", "originalCode": "74-03", "name": "History of mechanics of deformable solids", "description": "History of mechanics of deformable solids [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74-04", "originalCode": "74-04", "name": "Software, source code, etc. for problems pertaining to mechanics of deformable solids", "description": "Software, source code, etc. for problems pertaining to mechanics of deformable solids", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74-05", "originalCode": "74-05", "name": "Experimental work for problems pertaining to mechanics of deformable solids", "description": "Experimental work for problems pertaining to mechanics of deformable solids", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74-06", "originalCode": "74-06", "name": "Proceedings, conferences, collections, etc. pertaining to mechanics of deformable solids", "description": "Proceedings, conferences, collections, etc. pertaining to mechanics of deformable solids", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74-10", "originalCode": "74-10", "name": "Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids", "description": "Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74-11", "originalCode": "74-11", "name": "Research data for problems pertaining to mechanics of deformable solids", "description": "Research data for problems pertaining to mechanics of deformable solids", "kind": "subject", "parent": "74", "page": 183 }, { "code": "74A", "originalCode": "74Axx", "name": "Generalities, axiomatics, foundations of continuum mechanics of solids", "description": "Generalities, axiomatics, foundations of continuum mechanics of solids", "kind": "section", "parent": "74", "page": 183 }, { "code": "74A05", "originalCode": "74A05", "name": "Kinematics of deformation", "description": "Kinematics of deformation", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A10", "originalCode": "74A10", "name": "Stress", "description": "Stress", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A15", "originalCode": "74A15", "name": "Thermodynamics in solid mechanics", "description": "Thermodynamics in solid mechanics", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A20", "originalCode": "74A20", "name": "Theory of constitutive functions in solid mechanics", "description": "Theory of constitutive functions in solid mechanics", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A25", "originalCode": "74A25", "name": "Molecular, statistical, and kinetic theories in solid mechanics", "description": "Molecular, statistical, and kinetic theories in solid mechanics", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A30", "originalCode": "74A30", "name": "Nonsimple materials", "description": "Nonsimple materials", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A35", "originalCode": "74A35", "name": "Polar materials", "description": "Polar materials", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A40", "originalCode": "74A40", "name": "Random materials and composite materials", "description": "Random materials and composite materials", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A45", "originalCode": "74A45", "name": "Theories of fracture and damage", "description": "Theories of fracture and damage", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A50", "originalCode": "74A50", "name": "Structured surfaces and interfaces, coexistent phases", "description": "Structured surfaces and interfaces, coexistent phases", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A55", "originalCode": "74A55", "name": "Theories of friction (tribology)", "description": "Theories of friction (tribology)", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A60", "originalCode": "74A60", "name": "Micromechanical theories", "description": "Micromechanical theories", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A65", "originalCode": "74A65", "name": "Reactive materials", "description": "Reactive materials", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A70", "originalCode": "74A70", "name": "Peridynamics", "description": "Peridynamics", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74A99", "originalCode": "74A99", "name": "Generalities, axiomatics, foundations of continuum mechanics of solids", "description": "None of the above, but in this section", "kind": "subject", "parent": "74A", "page": 183 }, { "code": "74B", "originalCode": "74Bxx", "name": "Elastic materials", "description": "Elastic materials", "kind": "section", "parent": "74", "page": 184 }, { "code": "74B05", "originalCode": "74B05", "name": "Classical linear elasticity", "description": "Classical linear elasticity", "kind": "subject", "parent": "74B", "page": 184 }, { "code": "74B10", "originalCode": "74B10", "name": "Linear elasticity with initial stresses", "description": "Linear elasticity with initial stresses", "kind": "subject", "parent": "74B", "page": 184 }, { "code": "74B15", "originalCode": "74B15", "name": "Equations linearized about a deformed state (small deformations superposed on large)", "description": "Equations linearized about a deformed state (small deformations superposed on large)", "kind": "subject", "parent": "74B", "page": 184 }, { "code": "74B20", "originalCode": "74B20", "name": "Nonlinear elasticity", "description": "Nonlinear elasticity", "kind": "subject", "parent": "74B", "page": 184 }, { "code": "74B99", "originalCode": "74B99", "name": "Elastic materials", "description": "None of the above, but in this section", "kind": "subject", "parent": "74B", "page": 184 }, { "code": "74C", "originalCode": "74Cxx", "name": "Plastic materials, materials of stress-rate and internal-variable type", "description": "Plastic materials, materials of stress-rate and internal-variable type", "kind": "section", "parent": "74", "page": 184 }, { "code": "74C05", "originalCode": "74C05", "name": "Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)", "description": "Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)", "kind": "subject", "parent": "74C", "page": 184 }, { "code": "74C10", "originalCode": "74C10", "name": "Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)", "description": "Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)", "kind": "subject", "parent": "74C", "page": 184 }, { "code": "74C15", "originalCode": "74C15", "name": "Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)", "description": "Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)", "kind": "subject", "parent": "74C", "page": 184 }, { "code": "74C20", "originalCode": "74C20", "name": "Large-strain, rate-dependent theories of plasticity", "description": "Large-strain, rate-dependent theories of plasticity", "kind": "subject", "parent": "74C", "page": 184 }, { "code": "74C99", "originalCode": "74C99", "name": "Plastic materials, materials of stress-rate and internal-variable type", "description": "None of the above, but in this section", "kind": "subject", "parent": "74C", "page": 184 }, { "code": "74D", "originalCode": "74Dxx", "name": "Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)", "description": "Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)", "kind": "section", "parent": "74", "page": 184 }, { "code": "74D05", "originalCode": "74D05", "name": "Linear constitutive equations for materials with memory", "description": "Linear constitutive equations for materials with memory", "kind": "subject", "parent": "74D", "page": 184 }, { "code": "74D10", "originalCode": "74D10", "name": "Nonlinear constitutive equations for materials with memory", "description": "Nonlinear constitutive equations for materials with memory", "kind": "subject", "parent": "74D", "page": 184 }, { "code": "74D99", "originalCode": "74D99", "name": "Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)", "description": "None of the above, but in this section", "kind": "subject", "parent": "74D", "page": 184 }, { "code": "74E", "originalCode": "74Exx", "name": "Material properties given special treatment", "description": "Material properties given special treatment", "kind": "section", "parent": "74", "page": 184 }, { "code": "74E05", "originalCode": "74E05", "name": "Inhomogeneity in solid mechanics", "description": "Inhomogeneity in solid mechanics", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74E10", "originalCode": "74E10", "name": "Anisotropy in solid mechanics", "description": "Anisotropy in solid mechanics", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74E15", "originalCode": "74E15", "name": "Crystalline structure", "description": "Crystalline structure", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74E20", "originalCode": "74E20", "name": "Granularity", "description": "Granularity", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74E25", "originalCode": "74E25", "name": "Texture in solid mechanics", "description": "Texture in solid mechanics", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74E30", "originalCode": "74E30", "name": "Composite and mixture properties", "description": "Composite and mixture properties", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74E35", "originalCode": "74E35", "name": "Random structure in solid mechanics", "description": "Random structure in solid mechanics", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74E40", "originalCode": "74E40", "name": "Chemical structure in solid mechanics", "description": "Chemical structure in solid mechanics", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74E99", "originalCode": "74E99", "name": "Material properties given special treatment", "description": "None of the above, but in this section", "kind": "subject", "parent": "74E", "page": 184 }, { "code": "74F", "originalCode": "74Fxx", "name": "Coupling of solid mechanics with other effects", "description": "Coupling of solid mechanics with other effects", "kind": "section", "parent": "74", "page": 184 }, { "code": "74F05", "originalCode": "74F05", "name": "Thermal effects in solid mechanics", "description": "Thermal effects in solid mechanics", "kind": "subject", "parent": "74F", "page": 184 }, { "code": "74F10", "originalCode": "74F10", "name": "Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)", "description": "Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)", "kind": "subject", "parent": "74F", "page": 184 }, { "code": "74F15", "originalCode": "74F15", "name": "Electromagnetic effects in solid mechanics", "description": "Electromagnetic effects in solid mechanics", "kind": "subject", "parent": "74F", "page": 184 }, { "code": "74F20", "originalCode": "74F20", "name": "Mixture effects in solid mechanics", "description": "Mixture effects in solid mechanics", "kind": "subject", "parent": "74F", "page": 184 }, { "code": "74F25", "originalCode": "74F25", "name": "Chemical and reactive effects in solid mechanics", "description": "Chemical and reactive effects in solid mechanics", "kind": "subject", "parent": "74F", "page": 184 }, { "code": "74F99", "originalCode": "74F99", "name": "Coupling of solid mechanics with other effects", "description": "None of the above, but in this section", "kind": "subject", "parent": "74F", "page": 184 }, { "code": "74G", "originalCode": "74Gxx", "name": "Equilibrium (steady-state) problems in solid mechanics", "description": "Equilibrium (steady-state) problems in solid mechanics", "kind": "section", "parent": "74", "page": 185 }, { "code": "74G05", "originalCode": "74G05", "name": "Explicit solutions of equilibrium problems in solid mechanics", "description": "Explicit solutions of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G10", "originalCode": "74G10", "name": "Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics", "description": "Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G15", "originalCode": "74G15", "name": "Numerical approximation of solutions of equilibrium problems in solid mechanics", "description": "Numerical approximation of solutions of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G22", "originalCode": "74G22", "name": "Existence of solutions of equilibrium problems in solid mechanics", "description": "Existence of solutions of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G30", "originalCode": "74G30", "name": "Uniqueness of solutions of equilibrium problems in solid mechanics", "description": "Uniqueness of solutions of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G35", "originalCode": "74G35", "name": "Multiplicity of solutions of equilibrium problems in solid mechanics", "description": "Multiplicity of solutions of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G40", "originalCode": "74G40", "name": "Regularity of solutions of equilibrium problems in solid mechanics", "description": "Regularity of solutions of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G45", "originalCode": "74G45", "name": "Bounds for solutions of equilibrium problems in solid mechanics", "description": "Bounds for solutions of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G50", "originalCode": "74G50", "name": "Saint-Venant's principle", "description": "Saint-Venant's principle", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G55", "originalCode": "74G55", "name": "Qualitative behavior of solutions of equilibrium problems in solid mechanics", "description": "Qualitative behavior of solutions of equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G60", "originalCode": "74G60", "name": "Bifurcation and buckling", "description": "Bifurcation and buckling", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G65", "originalCode": "74G65", "name": "Energy minimization in equilibrium problems in solid mechanics", "description": "Energy minimization in equilibrium problems in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G70", "originalCode": "74G70", "name": "Stress concentrations, singularities in solid mechanics", "description": "Stress concentrations, singularities in solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G75", "originalCode": "74G75", "name": "Inverse problems in equilibrium solid mechanics", "description": "Inverse problems in equilibrium solid mechanics", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74G99", "originalCode": "74G99", "name": "Equilibrium (steady-state) problems in solid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "74G", "page": 185 }, { "code": "74H", "originalCode": "74Hxx", "name": "Dynamical problems in solid mechanics", "description": "Dynamical problems in solid mechanics", "kind": "section", "parent": "74", "page": 185 }, { "code": "74H05", "originalCode": "74H05", "name": "Explicit solutions of dynamical problems in solid mechanics", "description": "Explicit solutions of dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H10", "originalCode": "74H10", "name": "Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics", "description": "Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H15", "originalCode": "74H15", "name": "Numerical approximation of solutions of dynamical problems in solid mechanics", "description": "Numerical approximation of solutions of dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H20", "originalCode": "74H20", "name": "Existence of solutions of dynamical problems in solid mechanics", "description": "Existence of solutions of dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H25", "originalCode": "74H25", "name": "Uniqueness of solutions of dynamical problems in solid mechanics", "description": "Uniqueness of solutions of dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H30", "originalCode": "74H30", "name": "Regularity of solutions of dynamical problems in solid mechanics", "description": "Regularity of solutions of dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H35", "originalCode": "74H35", "name": "Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics", "description": "Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H40", "originalCode": "74H40", "name": "Long-time behavior of solutions for dynamical problems in solid mechanics", "description": "Long-time behavior of solutions for dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H45", "originalCode": "74H45", "name": "Vibrations in dynamical problems in solid mechanics", "description": "Vibrations in dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H50", "originalCode": "74H50", "name": "Random vibrations in dynamical problems in solid mechanics", "description": "Random vibrations in dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H55", "originalCode": "74H55", "name": "Stability of dynamical problems in solid mechanics", "description": "Stability of dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H60", "originalCode": "74H60", "name": "Dynamical bifurcation of solutions to dynamical problems in solid mechanics", "description": "Dynamical bifurcation of solutions to dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H65", "originalCode": "74H65", "name": "Chaotic behavior of solutions to dynamical problems in solid mechanics", "description": "Chaotic behavior of solutions to dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H75", "originalCode": "74H75", "name": "Inverse problems in dynamical solid mechanics", "description": "Inverse problems in dynamical solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H80", "originalCode": "74H80", "name": "Energy minimization in dynamical problems in solid mechanics", "description": "Energy minimization in dynamical problems in solid mechanics", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74H99", "originalCode": "74H99", "name": "Dynamical problems in solid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "74H", "page": 185 }, { "code": "74J", "originalCode": "74Jxx", "name": "Waves in solid mechanics", "description": "Waves in solid mechanics", "kind": "section", "parent": "74", "page": 186 }, { "code": "74J05", "originalCode": "74J05", "name": "Linear waves in solid mechanics", "description": "Linear waves in solid mechanics", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74J10", "originalCode": "74J10", "name": "Bulk waves in solid mechanics", "description": "Bulk waves in solid mechanics", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74J15", "originalCode": "74J15", "name": "Surface waves in solid mechanics", "description": "Surface waves in solid mechanics", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74J20", "originalCode": "74J20", "name": "Wave scattering in solid mechanics", "description": "Wave scattering in solid mechanics", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74J25", "originalCode": "74J25", "name": "Inverse problems for waves in solid mechanics", "description": "Inverse problems for waves in solid mechanics", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74J30", "originalCode": "74J30", "name": "Nonlinear waves in solid mechanics", "description": "Nonlinear waves in solid mechanics", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74J35", "originalCode": "74J35", "name": "Solitary waves in solid mechanics", "description": "Solitary waves in solid mechanics", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74J40", "originalCode": "74J40", "name": "Shocks and related discontinuities in solid mechanics", "description": "Shocks and related discontinuities in solid mechanics", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74J99", "originalCode": "74J99", "name": "Waves in solid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "74J", "page": 186 }, { "code": "74K", "originalCode": "74Kxx", "name": "Thin bodies, structures", "description": "Thin bodies, structures", "kind": "section", "parent": "74", "page": 186 }, { "code": "74K05", "originalCode": "74K05", "name": "Strings", "description": "Strings", "kind": "subject", "parent": "74K", "page": 186 }, { "code": "74K10", "originalCode": "74K10", "name": "Rods (beams, columns, shafts, arches, rings, etc.)", "description": "Rods (beams, columns, shafts, arches, rings, etc.)", "kind": "subject", "parent": "74K", "page": 186 }, { "code": "74K15", "originalCode": "74K15", "name": "Membranes", "description": "Membranes", "kind": "subject", "parent": "74K", "page": 186 }, { "code": "74K20", "originalCode": "74K20", "name": "Plates", "description": "Plates", "kind": "subject", "parent": "74K", "page": 186 }, { "code": "74K25", "originalCode": "74K25", "name": "Shells", "description": "Shells", "kind": "subject", "parent": "74K", "page": 186 }, { "code": "74K30", "originalCode": "74K30", "name": "Junctions", "description": "Junctions", "kind": "subject", "parent": "74K", "page": 186 }, { "code": "74K35", "originalCode": "74K35", "name": "Thin films", "description": "Thin films", "kind": "subject", "parent": "74K", "page": 186 }, { "code": "74K99", "originalCode": "74K99", "name": "Thin bodies, structures", "description": "None of the above, but in this section", "kind": "subject", "parent": "74K", "page": 186 }, { "code": "74L", "originalCode": "74Lxx", "name": "Special subfields of solid mechanics", "description": "Special subfields of solid mechanics", "kind": "section", "parent": "74", "page": 186 }, { "code": "74L05", "originalCode": "74L05", "name": "Geophysical solid mechanics", "description": "Geophysical solid mechanics [See also 86-XX]", "kind": "subject", "parent": "74L", "page": 186 }, { "code": "74L10", "originalCode": "74L10", "name": "Soil and rock mechanics", "description": "Soil and rock mechanics", "kind": "subject", "parent": "74L", "page": 186 }, { "code": "74L15", "originalCode": "74L15", "name": "Biomechanical solid mechanics", "description": "Biomechanical solid mechanics [See also 92C10]", "kind": "subject", "parent": "74L", "page": 186 }, { "code": "74L99", "originalCode": "74L99", "name": "Special subfields of solid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "74L", "page": 186 }, { "code": "74M", "originalCode": "74Mxx", "name": "Special kinds of problems in solid mechanics", "description": "Special kinds of problems in solid mechanics", "kind": "section", "parent": "74", "page": 186 }, { "code": "74M05", "originalCode": "74M05", "name": "Control, switches and devices (``smart materials'') in solid mechanics", "description": "Control, switches and devices (``smart materials'') in solid mechanics [See also 93Cxx]", "kind": "subject", "parent": "74M", "page": 186 }, { "code": "74M10", "originalCode": "74M10", "name": "Friction in solid mechanics", "description": "Friction in solid mechanics", "kind": "subject", "parent": "74M", "page": 186 }, { "code": "74M15", "originalCode": "74M15", "name": "Contact in solid mechanics", "description": "Contact in solid mechanics", "kind": "subject", "parent": "74M", "page": 186 }, { "code": "74M20", "originalCode": "74M20", "name": "Impact in solid mechanics", "description": "Impact in solid mechanics", "kind": "subject", "parent": "74M", "page": 186 }, { "code": "74M25", "originalCode": "74M25", "name": "Micromechanics of solids", "description": "Micromechanics of solids", "kind": "subject", "parent": "74M", "page": 186 }, { "code": "74M99", "originalCode": "74M99", "name": "Special kinds of problems in solid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "74M", "page": 186 }, { "code": "74N", "originalCode": "74Nxx", "name": "Phase transformations in solids", "description": "Phase transformations in solids [See also 74A50, 80A22, 82B26, 82C26]", "kind": "section", "parent": "74", "page": 187 }, { "code": "74N05", "originalCode": "74N05", "name": "Crystals in solids", "description": "Crystals in solids", "kind": "subject", "parent": "74N", "page": 187 }, { "code": "74N10", "originalCode": "74N10", "name": "Displacive transformations in solids", "description": "Displacive transformations in solids", "kind": "subject", "parent": "74N", "page": 187 }, { "code": "74N15", "originalCode": "74N15", "name": "Analysis of microstructure in solids", "description": "Analysis of microstructure in solids", "kind": "subject", "parent": "74N", "page": 187 }, { "code": "74N20", "originalCode": "74N20", "name": "Dynamics of phase boundaries in solids", "description": "Dynamics of phase boundaries in solids", "kind": "subject", "parent": "74N", "page": 187 }, { "code": "74N25", "originalCode": "74N25", "name": "Transformations involving diffusion in solids", "description": "Transformations involving diffusion in solids", "kind": "subject", "parent": "74N", "page": 187 }, { "code": "74N30", "originalCode": "74N30", "name": "Problems involving hysteresis in solids", "description": "Problems involving hysteresis in solids", "kind": "subject", "parent": "74N", "page": 187 }, { "code": "74N99", "originalCode": "74N99", "name": "Phase transformations in solids", "description": "None of the above, but in this section", "kind": "subject", "parent": "74N", "page": 187 }, { "code": "74P", "originalCode": "74Pxx", "name": "Optimization problems in solid mechanics", "description": "Optimization problems in solid mechanics [See also 49Qxx]", "kind": "section", "parent": "74", "page": 187 }, { "code": "74P05", "originalCode": "74P05", "name": "Compliance or weight optimization in solid mechanics", "description": "Compliance or weight optimization in solid mechanics", "kind": "subject", "parent": "74P", "page": 187 }, { "code": "74P10", "originalCode": "74P10", "name": "Optimization of other properties in solid mechanics", "description": "Optimization of other properties in solid mechanics", "kind": "subject", "parent": "74P", "page": 187 }, { "code": "74P15", "originalCode": "74P15", "name": "Topological methods for optimization problems in solid mechanics", "description": "Topological methods for optimization problems in solid mechanics", "kind": "subject", "parent": "74P", "page": 187 }, { "code": "74P20", "originalCode": "74P20", "name": "Geometrical methods for optimization problems in solid mechanics", "description": "Geometrical methods for optimization problems in solid mechanics", "kind": "subject", "parent": "74P", "page": 187 }, { "code": "74P99", "originalCode": "74P99", "name": "Optimization problems in solid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "74P", "page": 187 }, { "code": "74Q", "originalCode": "74Qxx", "name": "Homogenization, determination of effective properties in solid mechanics", "description": "Homogenization, determination of effective properties in solid mechanics", "kind": "section", "parent": "74", "page": 187 }, { "code": "74Q05", "originalCode": "74Q05", "name": "Homogenization in equilibrium problems of solid mechanics", "description": "Homogenization in equilibrium problems of solid mechanics", "kind": "subject", "parent": "74Q", "page": 187 }, { "code": "74Q10", "originalCode": "74Q10", "name": "Homogenization and oscillations in dynamical problems of solid mechanics", "description": "Homogenization and oscillations in dynamical problems of solid mechanics", "kind": "subject", "parent": "74Q", "page": 187 }, { "code": "74Q15", "originalCode": "74Q15", "name": "Effective constitutive equations in solid mechanics", "description": "Effective constitutive equations in solid mechanics", "kind": "subject", "parent": "74Q", "page": 187 }, { "code": "74Q20", "originalCode": "74Q20", "name": "Bounds on effective properties in solid mechanics", "description": "Bounds on effective properties in solid mechanics", "kind": "subject", "parent": "74Q", "page": 187 }, { "code": "74Q99", "originalCode": "74Q99", "name": "Homogenization, determination of effective properties in solid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "74Q", "page": 187 }, { "code": "74R", "originalCode": "74Rxx", "name": "Fracture and damage", "description": "Fracture and damage", "kind": "section", "parent": "74", "page": 187 }, { "code": "74R05", "originalCode": "74R05", "name": "Brittle damage", "description": "Brittle damage", "kind": "subject", "parent": "74R", "page": 187 }, { "code": "74R10", "originalCode": "74R10", "name": "Brittle fracture", "description": "Brittle fracture", "kind": "subject", "parent": "74R", "page": 187 }, { "code": "74R15", "originalCode": "74R15", "name": "High-velocity fracture", "description": "High-velocity fracture", "kind": "subject", "parent": "74R", "page": 187 }, { "code": "74R20", "originalCode": "74R20", "name": "Anelastic fracture and damage", "description": "Anelastic fracture and damage", "kind": "subject", "parent": "74R", "page": 187 }, { "code": "74R99", "originalCode": "74R99", "name": "Fracture and damage", "description": "None of the above, but in this section", "kind": "subject", "parent": "74R", "page": 187 }, { "code": "74S", "originalCode": "74Sxx", "name": "Numerical and other methods in solid mechanics", "description": "Numerical and other methods in solid mechanics [See also 65-XX, 74G15, 74H15]", "kind": "section", "parent": "74", "page": 188 }, { "code": "74S05", "originalCode": "74S05", "name": "Finite element methods applied to problems in solid mechanics", "description": "Finite element methods applied to problems in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S10", "originalCode": "74S10", "name": "Finite volume methods applied to problems in solid mechanics", "description": "Finite volume methods applied to problems in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S15", "originalCode": "74S15", "name": "Boundary element methods applied to problems in solid mechanics", "description": "Boundary element methods applied to problems in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S20", "originalCode": "74S20", "name": "Finite difference methods applied to problems in solid mechanics", "description": "Finite difference methods applied to problems in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S22", "originalCode": "74S22", "name": "Isogeometric methods applied to problems in solid mechanics", "description": "Isogeometric methods applied to problems in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S25", "originalCode": "74S25", "name": "Spectral and related methods applied to problems in solid mechanics", "description": "Spectral and related methods applied to problems in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S40", "originalCode": "74S40", "name": "Applications of fractional calculus in solid mechanics", "description": "Applications of fractional calculus in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S50", "originalCode": "74S50", "name": "Applications of graph theory in solid mechanics", "description": "Applications of graph theory in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S60", "originalCode": "74S60", "name": "Stochastic and other probabilistic methods applied to problems in solid mechanics", "description": "Stochastic and other probabilistic methods applied to problems in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S70", "originalCode": "74S70", "name": "Complex-variable methods applied to problems in solid mechanics", "description": "Complex-variable methods applied to problems in solid mechanics", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "74S99", "originalCode": "74S99", "name": "Numerical and other methods in solid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "74S", "page": 188 }, { "code": "76", "originalCode": "76-XX", "name": "Fluid mechanics", "description": "Fluid mechanics \\{For general continuum mechanics, see 74Axx, or other parts of 74-XX\\}", "kind": "class", "parent": null, "page": 188 }, { "code": "76-00", "originalCode": "76-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to fluid mechanics", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to fluid mechanics", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76-01", "originalCode": "76-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76-02", "originalCode": "76-02", "name": "Research exposition (monographs, survey articles) pertaining to fluid mechanics", "description": "Research exposition (monographs, survey articles) pertaining to fluid mechanics", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76-03", "originalCode": "76-03", "name": "History of fluid mechanics", "description": "History of fluid mechanics [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76-04", "originalCode": "76-04", "name": "Software, source code, etc. for problems pertaining to fluid mechanics", "description": "Software, source code, etc. for problems pertaining to fluid mechanics", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76-05", "originalCode": "76-05", "name": "Experimental work for problems pertaining to fluid mechanics", "description": "Experimental work for problems pertaining to fluid mechanics", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76-06", "originalCode": "76-06", "name": "Proceedings, conferences, collections, etc. pertaining to fluid mechanics", "description": "Proceedings, conferences, collections, etc. pertaining to fluid mechanics", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76-10", "originalCode": "76-10", "name": "Mathematical modeling or simulation for problems pertaining to fluid mechanics", "description": "Mathematical modeling or simulation for problems pertaining to fluid mechanics", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76-11", "originalCode": "76-11", "name": "Research data for problems pertaining to fluid mechanics", "description": "Research data for problems pertaining to fluid mechanics", "kind": "subject", "parent": "76", "page": 188 }, { "code": "76A", "originalCode": "76Axx", "name": "Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena", "description": "Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena", "kind": "section", "parent": "76", "page": 188 }, { "code": "76A02", "originalCode": "76A02", "name": "Foundations of fluid mechanics", "description": "Foundations of fluid mechanics", "kind": "subject", "parent": "76A", "page": 188 }, { "code": "76A05", "originalCode": "76A05", "name": "Non-Newtonian fluids", "description": "Non-Newtonian fluids", "kind": "subject", "parent": "76A", "page": 188 }, { "code": "76A10", "originalCode": "76A10", "name": "Viscoelastic fluids", "description": "Viscoelastic fluids", "kind": "subject", "parent": "76A", "page": 188 }, { "code": "76A15", "originalCode": "76A15", "name": "Liquid crystals", "description": "Liquid crystals [See also 82D30]", "kind": "subject", "parent": "76A", "page": 188 }, { "code": "76A20", "originalCode": "76A20", "name": "Thin fluid films", "description": "Thin fluid films", "kind": "subject", "parent": "76A", "page": 188 }, { "code": "76A25", "originalCode": "76A25", "name": "Superfluids (classical aspects)", "description": "Superfluids (classical aspects)", "kind": "subject", "parent": "76A", "page": 188 }, { "code": "76A30", "originalCode": "76A30", "name": "Traffic and pedestrian flow models", "description": "Traffic and pedestrian flow models", "kind": "subject", "parent": "76A", "page": 188 }, { "code": "76A99", "originalCode": "76A99", "name": "Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena", "description": "None of the above, but in this section", "kind": "subject", "parent": "76A", "page": 188 }, { "code": "76B", "originalCode": "76Bxx", "name": "Incompressible inviscid fluids", "description": "Incompressible inviscid fluids", "kind": "section", "parent": "76", "page": 189 }, { "code": "76B03", "originalCode": "76B03", "name": "Existence, uniqueness, and regularity theory for incompressible inviscid fluids", "description": "Existence, uniqueness, and regularity theory for incompressible inviscid fluids [See also 35Q35]", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B07", "originalCode": "76B07", "name": "Free-surface potential flows for incompressible inviscid fluids", "description": "Free-surface potential flows for incompressible inviscid fluids", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B10", "originalCode": "76B10", "name": "Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing", "description": "Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B15", "originalCode": "76B15", "name": "Water waves, gravity waves; dispersion and scattering, nonlinear interaction", "description": "Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B20", "originalCode": "76B20", "name": "Ship waves", "description": "Ship waves", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B25", "originalCode": "76B25", "name": "Solitary waves for incompressible inviscid fluids", "description": "Solitary waves for incompressible inviscid fluids [See also 35C11]", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B45", "originalCode": "76B45", "name": "Capillarity (surface tension) for incompressible inviscid fluids", "description": "Capillarity (surface tension) for incompressible inviscid fluids [See also 76D45]", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B47", "originalCode": "76B47", "name": "Vortex flows for incompressible inviscid fluids", "description": "Vortex flows for incompressible inviscid fluids", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B55", "originalCode": "76B55", "name": "Internal waves for incompressible inviscid fluids", "description": "Internal waves for incompressible inviscid fluids", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B70", "originalCode": "76B70", "name": "Stratification effects in inviscid fluids", "description": "Stratification effects in inviscid fluids", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B75", "originalCode": "76B75", "name": "Flow control and optimization for incompressible inviscid fluids", "description": "Flow control and optimization for incompressible inviscid fluids [See also 49Q10, 93C20, 93C95]", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76B99", "originalCode": "76B99", "name": "Incompressible inviscid fluids", "description": "None of the above, but in this section", "kind": "subject", "parent": "76B", "page": 189 }, { "code": "76D", "originalCode": "76Dxx", "name": "Incompressible viscous fluids", "description": "Incompressible viscous fluids", "kind": "section", "parent": "76", "page": 189 }, { "code": "76D03", "originalCode": "76D03", "name": "Existence, uniqueness, and regularity theory for incompressible viscous fluids", "description": "Existence, uniqueness, and regularity theory for incompressible viscous fluids [See also 35Q30]", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D05", "originalCode": "76D05", "name": "Navier-Stokes equations for incompressible viscous fluids", "description": "Navier-Stokes equations for incompressible viscous fluids [See also 35Q30]", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D06", "originalCode": "76D06", "name": "Statistical solutions of Navier-Stokes and related equations", "description": "Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35]", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D07", "originalCode": "76D07", "name": "Stokes and related (Oseen, etc.) flows", "description": "Stokes and related (Oseen, etc.) flows", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D08", "originalCode": "76D08", "name": "Lubrication theory", "description": "Lubrication theory", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D09", "originalCode": "76D09", "name": "Viscous-inviscid interaction", "description": "Viscous-inviscid interaction", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D10", "originalCode": "76D10", "name": "Boundary-layer theory, separation and reattachment, higher-order effects", "description": "Boundary-layer theory, separation and reattachment, higher-order effects", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D17", "originalCode": "76D17", "name": "Viscous vortex flows", "description": "Viscous vortex flows", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D25", "originalCode": "76D25", "name": "Wakes and jets", "description": "Wakes and jets", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D27", "originalCode": "76D27", "name": "Other free boundary flows; Hele-Shaw flows", "description": "Other free boundary flows; Hele-Shaw flows", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D33", "originalCode": "76D33", "name": "Waves for incompressible viscous fluids", "description": "Waves for incompressible viscous fluids", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D45", "originalCode": "76D45", "name": "Capillarity (surface tension) for incompressible viscous fluids", "description": "Capillarity (surface tension) for incompressible viscous fluids [See also 76B45]", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D50", "originalCode": "76D50", "name": "Stratification effects in viscous fluids", "description": "Stratification effects in viscous fluids", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D55", "originalCode": "76D55", "name": "Flow control and optimization for incompressible viscous fluids", "description": "Flow control and optimization for incompressible viscous fluids [See also 49Q10, 93C20, 93C95]", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76D99", "originalCode": "76D99", "name": "Incompressible viscous fluids", "description": "None of the above, but in this section", "kind": "subject", "parent": "76D", "page": 189 }, { "code": "76E", "originalCode": "76Exx", "name": "Hydrodynamic stability", "description": "Hydrodynamic stability", "kind": "section", "parent": "76", "page": 190 }, { "code": "76E05", "originalCode": "76E05", "name": "Parallel shear flows in hydrodynamic stability", "description": "Parallel shear flows in hydrodynamic stability", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E06", "originalCode": "76E06", "name": "Convection in hydrodynamic stability", "description": "Convection in hydrodynamic stability", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E07", "originalCode": "76E07", "name": "Rotation in hydrodynamic stability", "description": "Rotation in hydrodynamic stability", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E09", "originalCode": "76E09", "name": "Stability and instability of nonparallel flows in hydrodynamic stability", "description": "Stability and instability of nonparallel flows in hydrodynamic stability", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E15", "originalCode": "76E15", "name": "Absolute and convective instability and stability in hydrodynamic stability", "description": "Absolute and convective instability and stability in hydrodynamic stability", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E17", "originalCode": "76E17", "name": "Interfacial stability and instability in hydrodynamic stability", "description": "Interfacial stability and instability in hydrodynamic stability", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E19", "originalCode": "76E19", "name": "Compressibility effects in hydrodynamic stability", "description": "Compressibility effects in hydrodynamic stability", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E20", "originalCode": "76E20", "name": "Stability and instability of geophysical and astrophysical flows", "description": "Stability and instability of geophysical and astrophysical flows", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E25", "originalCode": "76E25", "name": "Stability and instability of magnetohydrodynamic and electrohydrodynamic flows", "description": "Stability and instability of magnetohydrodynamic and electrohydrodynamic flows", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E30", "originalCode": "76E30", "name": "Nonlinear effects in hydrodynamic stability", "description": "Nonlinear effects in hydrodynamic stability", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76E99", "originalCode": "76E99", "name": "Hydrodynamic stability", "description": "None of the above, but in this section", "kind": "subject", "parent": "76E", "page": 190 }, { "code": "76F", "originalCode": "76Fxx", "name": "Turbulence", "description": "Turbulence [See also 37-XX, 60Gxx, 60Jxx]", "kind": "section", "parent": "76", "page": 190 }, { "code": "76F02", "originalCode": "76F02", "name": "Fundamentals of turbulence", "description": "Fundamentals of turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F05", "originalCode": "76F05", "name": "Isotropic turbulence; homogeneous turbulence", "description": "Isotropic turbulence; homogeneous turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F06", "originalCode": "76F06", "name": "Transition to turbulence", "description": "Transition to turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F10", "originalCode": "76F10", "name": "Shear flows and turbulence", "description": "Shear flows and turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F20", "originalCode": "76F20", "name": "Dynamical systems approach to turbulence", "description": "Dynamical systems approach to turbulence [See also 37-XX]", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F25", "originalCode": "76F25", "name": "Turbulent transport, mixing", "description": "Turbulent transport, mixing", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F30", "originalCode": "76F30", "name": "Renormalization and other field-theoretical methods for turbulence", "description": "Renormalization and other field-theoretical methods for turbulence [See also 81T99]", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F35", "originalCode": "76F35", "name": "Convective turbulence", "description": "Convective turbulence [See also 76E15, 76Rxx]", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F40", "originalCode": "76F40", "name": "Turbulent boundary layers", "description": "Turbulent boundary layers", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F45", "originalCode": "76F45", "name": "Stratification effects in turbulence", "description": "Stratification effects in turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F50", "originalCode": "76F50", "name": "Compressibility effects in turbulence", "description": "Compressibility effects in turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F55", "originalCode": "76F55", "name": "Statistical turbulence modeling", "description": "Statistical turbulence modeling [See also 76M35]", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F60", "originalCode": "76F60", "name": "\\(k\\)-\\(\\varepsilon\\) modeling in turbulence", "description": "\\(k\\)-\\(\\varepsilon\\) modeling in turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F65", "originalCode": "76F65", "name": "Direct numerical and large eddy simulation of turbulence", "description": "Direct numerical and large eddy simulation of turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F70", "originalCode": "76F70", "name": "Control of turbulent flows", "description": "Control of turbulent flows", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F80", "originalCode": "76F80", "name": "Turbulent combustion; reactive turbulence", "description": "Turbulent combustion; reactive turbulence", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76F99", "originalCode": "76F99", "name": "Turbulence", "description": "None of the above, but in this section", "kind": "subject", "parent": "76F", "page": 190 }, { "code": "76G", "originalCode": "76Gxx", "name": "General aerodynamics and subsonic flows", "description": "General aerodynamics and subsonic flows", "kind": "section", "parent": "76", "page": 190 }, { "code": "76G25", "originalCode": "76G25", "name": "General aerodynamics and subsonic flows", "description": "General aerodynamics and subsonic flows", "kind": "subject", "parent": "76G", "page": 190 }, { "code": "76G99", "originalCode": "76G99", "name": "General aerodynamics and subsonic flows", "description": "None of the above, but in this section", "kind": "subject", "parent": "76G", "page": 190 }, { "code": "76H", "originalCode": "76Hxx", "name": "Transonic flows", "description": "Transonic flows", "kind": "section", "parent": "76", "page": 191 }, { "code": "76H05", "originalCode": "76H05", "name": "Transonic flows", "description": "Transonic flows", "kind": "subject", "parent": "76H", "page": 191 }, { "code": "76H99", "originalCode": "76H99", "name": "Transonic flows", "description": "None of the above, but in this section", "kind": "subject", "parent": "76H", "page": 191 }, { "code": "76J", "originalCode": "76Jxx", "name": "Supersonic flows", "description": "Supersonic flows", "kind": "section", "parent": "76", "page": 191 }, { "code": "76J20", "originalCode": "76J20", "name": "Supersonic flows", "description": "Supersonic flows", "kind": "subject", "parent": "76J", "page": 191 }, { "code": "76J99", "originalCode": "76J99", "name": "Supersonic flows", "description": "None of the above, but in this section", "kind": "subject", "parent": "76J", "page": 191 }, { "code": "76K", "originalCode": "76Kxx", "name": "Hypersonic flows", "description": "Hypersonic flows", "kind": "section", "parent": "76", "page": 191 }, { "code": "76K05", "originalCode": "76K05", "name": "Hypersonic flows", "description": "Hypersonic flows", "kind": "subject", "parent": "76K", "page": 191 }, { "code": "76K99", "originalCode": "76K99", "name": "Hypersonic flows", "description": "None of the above, but in this section", "kind": "subject", "parent": "76K", "page": 191 }, { "code": "76L", "originalCode": "76Lxx", "name": "Shock waves and blast waves in fluid mechanics", "description": "Shock waves and blast waves in fluid mechanics [See also 35L67]", "kind": "section", "parent": "76", "page": 191 }, { "code": "76L05", "originalCode": "76L05", "name": "Shock waves and blast waves in fluid mechanics", "description": "Shock waves and blast waves in fluid mechanics [See also 35L67]", "kind": "subject", "parent": "76L", "page": 191 }, { "code": "76L99", "originalCode": "76L99", "name": "Shock waves and blast waves in fluid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "76L", "page": 191 }, { "code": "76M", "originalCode": "76Mxx", "name": "Basic methods in fluid mechanics", "description": "Basic methods in fluid mechanics [See also 65-XX]", "kind": "section", "parent": "76", "page": 191 }, { "code": "76M10", "originalCode": "76M10", "name": "Finite element methods applied to problems in fluid mechanics", "description": "Finite element methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M12", "originalCode": "76M12", "name": "Finite volume methods applied to problems in fluid mechanics", "description": "Finite volume methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M15", "originalCode": "76M15", "name": "Boundary element methods applied to problems in fluid mechanics", "description": "Boundary element methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M20", "originalCode": "76M20", "name": "Finite difference methods applied to problems in fluid mechanics", "description": "Finite difference methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M21", "originalCode": "76M21", "name": "Inverse problems in fluid mechanics", "description": "Inverse problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M22", "originalCode": "76M22", "name": "Spectral methods applied to problems in fluid mechanics", "description": "Spectral methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M23", "originalCode": "76M23", "name": "Vortex methods applied to problems in fluid mechanics", "description": "Vortex methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M27", "originalCode": "76M27", "name": "Visualization algorithms applied to problems in fluid mechanics", "description": "Visualization algorithms applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M28", "originalCode": "76M28", "name": "Particle methods and lattice-gas methods", "description": "Particle methods and lattice-gas methods", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M30", "originalCode": "76M30", "name": "Variational methods applied to problems in fluid mechanics", "description": "Variational methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M35", "originalCode": "76M35", "name": "Stochastic analysis applied to problems in fluid mechanics", "description": "Stochastic analysis applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M40", "originalCode": "76M40", "name": "Complex variables methods applied to problems in fluid mechanics", "description": "Complex variables methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M45", "originalCode": "76M45", "name": "Asymptotic methods, singular perturbations applied to problems in fluid mechanics", "description": "Asymptotic methods, singular perturbations applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M50", "originalCode": "76M50", "name": "Homogenization applied to problems in fluid mechanics", "description": "Homogenization applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M55", "originalCode": "76M55", "name": "Dimensional analysis and similarity applied to problems in fluid mechanics", "description": "Dimensional analysis and similarity applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M60", "originalCode": "76M60", "name": "Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics", "description": "Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76M99", "originalCode": "76M99", "name": "Basic methods in fluid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "76M", "page": 191 }, { "code": "76N", "originalCode": "76Nxx", "name": "Compressible fluids and gas dynamics", "description": "Compressible fluids and gas dynamics", "kind": "section", "parent": "76", "page": 192 }, { "code": "76N06", "originalCode": "76N06", "name": "Compressible Navier-Stokes equations", "description": "Compressible Navier-Stokes equations", "kind": "subject", "parent": "76N", "page": 192 }, { "code": "76N10", "originalCode": "76N10", "name": "Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics", "description": "Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics [See also 35L60, 35L65, 35Q30]", "kind": "subject", "parent": "76N", "page": 192 }, { "code": "76N15", "originalCode": "76N15", "name": "Gas dynamics (general theory)", "description": "Gas dynamics (general theory)", "kind": "subject", "parent": "76N", "page": 192 }, { "code": "76N17", "originalCode": "76N17", "name": "Viscous-inviscid interaction for compressible fluids and gas dynamics", "description": "Viscous-inviscid interaction for compressible fluids and gas dynamics", "kind": "subject", "parent": "76N", "page": 192 }, { "code": "76N20", "originalCode": "76N20", "name": "Boundary-layer theory for compressible fluids and gas dynamics", "description": "Boundary-layer theory for compressible fluids and gas dynamics", "kind": "subject", "parent": "76N", "page": 192 }, { "code": "76N25", "originalCode": "76N25", "name": "Flow control and optimization for compressible fluids and gas dynamics", "description": "Flow control and optimization for compressible fluids and gas dynamics", "kind": "subject", "parent": "76N", "page": 192 }, { "code": "76N30", "originalCode": "76N30", "name": "Waves in compressible fluids", "description": "Waves in compressible fluids", "kind": "subject", "parent": "76N", "page": 192 }, { "code": "76N99", "originalCode": "76N99", "name": "Compressible fluids and gas dynamics", "description": "None of the above, but in this section", "kind": "subject", "parent": "76N", "page": 192 }, { "code": "76P", "originalCode": "76Pxx", "name": "Rarefied gas flows, Boltzmann equation in fluid mechanics", "description": "Rarefied gas flows, Boltzmann equation in fluid mechanics [See also 82B40, 82C40, 82D05]", "kind": "section", "parent": "76", "page": 192 }, { "code": "76P05", "originalCode": "76P05", "name": "Rarefied gas flows, Boltzmann equation in fluid mechanics", "description": "Rarefied gas flows, Boltzmann equation in fluid mechanics [See also 82B40, 82C40, 82D05]", "kind": "subject", "parent": "76P", "page": 192 }, { "code": "76P99", "originalCode": "76P99", "name": "Rarefied gas flows, Boltzmann equation in fluid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "76P", "page": 192 }, { "code": "76Q", "originalCode": "76Qxx", "name": "Hydro- and aero-acoustics", "description": "Hydro- and aero-acoustics", "kind": "section", "parent": "76", "page": 192 }, { "code": "76Q05", "originalCode": "76Q05", "name": "Hydro- and aero-acoustics", "description": "Hydro- and aero-acoustics", "kind": "subject", "parent": "76Q", "page": 192 }, { "code": "76Q99", "originalCode": "76Q99", "name": "Hydro- and aero-acoustics", "description": "None of the above, but in this section", "kind": "subject", "parent": "76Q", "page": 192 }, { "code": "76R", "originalCode": "76Rxx", "name": "Diffusion and convection", "description": "Diffusion and convection", "kind": "section", "parent": "76", "page": 192 }, { "code": "76R05", "originalCode": "76R05", "name": "Forced convection", "description": "Forced convection", "kind": "subject", "parent": "76R", "page": 192 }, { "code": "76R10", "originalCode": "76R10", "name": "Free convection", "description": "Free convection", "kind": "subject", "parent": "76R", "page": 192 }, { "code": "76R50", "originalCode": "76R50", "name": "Diffusion", "description": "Diffusion [See also 60J60]", "kind": "subject", "parent": "76R", "page": 192 }, { "code": "76R99", "originalCode": "76R99", "name": "Diffusion and convection", "description": "None of the above, but in this section", "kind": "subject", "parent": "76R", "page": 192 }, { "code": "76S", "originalCode": "76Sxx", "name": "Flows in porous media; filtration; seepage", "description": "Flows in porous media; filtration; seepage", "kind": "section", "parent": "76", "page": 192 }, { "code": "76S05", "originalCode": "76S05", "name": "Flows in porous media; filtration; seepage", "description": "Flows in porous media; filtration; seepage", "kind": "subject", "parent": "76S", "page": 192 }, { "code": "76S99", "originalCode": "76S99", "name": "Flows in porous media; filtration; seepage", "description": "None of the above, but in this section", "kind": "subject", "parent": "76S", "page": 192 }, { "code": "76T", "originalCode": "76Txx", "name": "Multiphase and multicomponent flows", "description": "Multiphase and multicomponent flows", "kind": "section", "parent": "76", "page": 192 }, { "code": "76T06", "originalCode": "76T06", "name": "Liquid-liquid two component flows", "description": "Liquid-liquid two component flows", "kind": "subject", "parent": "76T", "page": 192 }, { "code": "76T10", "originalCode": "76T10", "name": "Liquid-gas two-phase flows, bubbly flows", "description": "Liquid-gas two-phase flows, bubbly flows", "kind": "subject", "parent": "76T", "page": 192 }, { "code": "76T15", "originalCode": "76T15", "name": "Dusty-gas two-phase flows", "description": "Dusty-gas two-phase flows", "kind": "subject", "parent": "76T", "page": 192 }, { "code": "76T17", "originalCode": "76T17", "name": "Two gas multicomponent flows", "description": "Two gas multicomponent flows", "kind": "subject", "parent": "76T", "page": 192 }, { "code": "76T20", "originalCode": "76T20", "name": "Suspensions", "description": "Suspensions", "kind": "subject", "parent": "76T", "page": 192 }, { "code": "76T25", "originalCode": "76T25", "name": "Granular flows", "description": "Granular flows [See also 74C99, 74E20]", "kind": "subject", "parent": "76T", "page": 192 }, { "code": "76T30", "originalCode": "76T30", "name": "Three or more component flows", "description": "Three or more component flows", "kind": "subject", "parent": "76T", "page": 192 }, { "code": "76T99", "originalCode": "76T99", "name": "Multiphase and multicomponent flows", "description": "None of the above, but in this section", "kind": "subject", "parent": "76T", "page": 192 }, { "code": "76U", "originalCode": "76Uxx", "name": "Rotating fluids", "description": "Rotating fluids", "kind": "section", "parent": "76", "page": 193 }, { "code": "76U05", "originalCode": "76U05", "name": "General theory of rotating fluids", "description": "General theory of rotating fluids", "kind": "subject", "parent": "76U", "page": 193 }, { "code": "76U60", "originalCode": "76U60", "name": "Geophysical flows", "description": "Geophysical flows [See also 86A05, 86A10]", "kind": "subject", "parent": "76U", "page": 193 }, { "code": "76U65", "originalCode": "76U65", "name": "Rossby waves", "description": "Rossby waves [See also 86A05, 86A10]", "kind": "subject", "parent": "76U", "page": 193 }, { "code": "76U99", "originalCode": "76U99", "name": "Rotating fluids", "description": "None of the above, but in this section", "kind": "subject", "parent": "76U", "page": 193 }, { "code": "76V", "originalCode": "76Vxx", "name": "Reaction effects in flows", "description": "Reaction effects in flows [See also 80A32]", "kind": "section", "parent": "76", "page": 193 }, { "code": "76V05", "originalCode": "76V05", "name": "Reaction effects in flows", "description": "Reaction effects in flows [See also 80A32]", "kind": "subject", "parent": "76V", "page": 193 }, { "code": "76V99", "originalCode": "76V99", "name": "Reaction effects in flows", "description": "None of the above, but in this section", "kind": "subject", "parent": "76V", "page": 193 }, { "code": "76W", "originalCode": "76Wxx", "name": "Magnetohydrodynamics and electrohydrodynamics", "description": "Magnetohydrodynamics and electrohydrodynamics", "kind": "section", "parent": "76", "page": 193 }, { "code": "76W05", "originalCode": "76W05", "name": "Magnetohydrodynamics and electrohydrodynamics", "description": "Magnetohydrodynamics and electrohydrodynamics", "kind": "subject", "parent": "76W", "page": 193 }, { "code": "76W99", "originalCode": "76W99", "name": "Magnetohydrodynamics and electrohydrodynamics", "description": "None of the above, but in this section", "kind": "subject", "parent": "76W", "page": 193 }, { "code": "76X", "originalCode": "76Xxx", "name": "Ionized gas flow in electromagnetic fields; plasmic flow", "description": "Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]", "kind": "section", "parent": "76", "page": 193 }, { "code": "76X05", "originalCode": "76X05", "name": "Ionized gas flow in electromagnetic fields; plasmic flow", "description": "Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]", "kind": "subject", "parent": "76X", "page": 193 }, { "code": "76X99", "originalCode": "76X99", "name": "Ionized gas flow in electromagnetic fields; plasmic flow", "description": "None of the above, but in this section", "kind": "subject", "parent": "76X", "page": 193 }, { "code": "76Y", "originalCode": "76Yxx", "name": "Quantum hydrodynamics and relativistic hydrodynamics", "description": "Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]", "kind": "section", "parent": "76", "page": 193 }, { "code": "76Y05", "originalCode": "76Y05", "name": "Quantum hydrodynamics and relativistic hydrodynamics", "description": "Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]", "kind": "subject", "parent": "76Y", "page": 193 }, { "code": "76Y99", "originalCode": "76Y99", "name": "Quantum hydrodynamics and relativistic hydrodynamics", "description": "None of the above, but in this section", "kind": "subject", "parent": "76Y", "page": 193 }, { "code": "76Z", "originalCode": "76Zxx", "name": "Biological fluid mechanics", "description": "Biological fluid mechanics [See also 74F10, 74L15, 92Cxx]", "kind": "section", "parent": "76", "page": 193 }, { "code": "76Z05", "originalCode": "76Z05", "name": "Physiological flows", "description": "Physiological flows [See also 92C35]", "kind": "subject", "parent": "76Z", "page": 193 }, { "code": "76Z10", "originalCode": "76Z10", "name": "Biopropulsion in water and in air", "description": "Biopropulsion in water and in air", "kind": "subject", "parent": "76Z", "page": 193 }, { "code": "76Z99", "originalCode": "76Z99", "name": "Biological fluid mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "76Z", "page": 193 }, { "code": "78", "originalCode": "78-XX", "name": "Optics, electromagnetic theory", "description": "Optics, electromagnetic theory \\{For quantum optics, see 81V80\\}", "kind": "class", "parent": null, "page": 193 }, { "code": "78-00", "originalCode": "78-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to optics and electromagnetic theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to optics and electromagnetic theory", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78-01", "originalCode": "78-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78-02", "originalCode": "78-02", "name": "Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory", "description": "Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78-03", "originalCode": "78-03", "name": "History of optics and electromagnetic theory", "description": "History of optics and electromagnetic theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78-04", "originalCode": "78-04", "name": "Software, source code, etc. for problems pertaining to optics and electromagnetic theory", "description": "Software, source code, etc. for problems pertaining to optics and electromagnetic theory", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78-05", "originalCode": "78-05", "name": "Experimental work for problems pertaining to optics and electromagnetic theory", "description": "Experimental work for problems pertaining to optics and electromagnetic theory", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78-06", "originalCode": "78-06", "name": "Proceedings, conferences, collections, etc. pertaining to optics and electromagnetic theory", "description": "Proceedings, conferences, collections, etc. pertaining to optics and electromagnetic theory", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78-10", "originalCode": "78-10", "name": "Mathematical modeling or simulation for problems pertaining to optics and electromagnetic theory", "description": "Mathematical modeling or simulation for problems pertaining to optics and electromagnetic theory", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78-11", "originalCode": "78-11", "name": "Research data for problems pertaining to optics and electromagnetic theory", "description": "Research data for problems pertaining to optics and electromagnetic theory", "kind": "subject", "parent": "78", "page": 193 }, { "code": "78A", "originalCode": "78Axx", "name": "General topics in optics and electromagnetic theory", "description": "General topics in optics and electromagnetic theory", "kind": "section", "parent": "78", "page": 194 }, { "code": "78A02", "originalCode": "78A02", "name": "Foundations in optics and electromagnetic theory", "description": "Foundations in optics and electromagnetic theory", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A05", "originalCode": "78A05", "name": "Geometric optics", "description": "Geometric optics", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A10", "originalCode": "78A10", "name": "Physical optics", "description": "Physical optics", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A15", "originalCode": "78A15", "name": "Electron optics", "description": "Electron optics", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A20", "originalCode": "78A20", "name": "Space charge waves", "description": "Space charge waves", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A25", "originalCode": "78A25", "name": "Electromagnetic theory (general)", "description": "Electromagnetic theory (general)", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A30", "originalCode": "78A30", "name": "Electro- and magnetostatics", "description": "Electro- and magnetostatics", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A35", "originalCode": "78A35", "name": "Motion of charged particles", "description": "Motion of charged particles", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A37", "originalCode": "78A37", "name": "Ion traps", "description": "Ion traps", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A40", "originalCode": "78A40", "name": "Waves and radiation in optics and electromagnetic theory", "description": "Waves and radiation in optics and electromagnetic theory", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A45", "originalCode": "78A45", "name": "Diffraction, scattering", "description": "Diffraction, scattering \\{For WKB methods, see also 34E20\\}", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A46", "originalCode": "78A46", "name": "Inverse problems (including inverse scattering) in optics and electromagnetic theory", "description": "Inverse problems (including inverse scattering) in optics and electromagnetic theory", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A48", "originalCode": "78A48", "name": "Composite media; random media in optics and electromagnetic theory", "description": "Composite media; random media in optics and electromagnetic theory", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A50", "originalCode": "78A50", "name": "Antennas, waveguides in optics and electromagnetic theory", "description": "Antennas, waveguides in optics and electromagnetic theory", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A55", "originalCode": "78A55", "name": "Technical applications of optics and electromagnetic theory", "description": "Technical applications of optics and electromagnetic theory", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A57", "originalCode": "78A57", "name": "Electrochemistry", "description": "Electrochemistry", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A60", "originalCode": "78A60", "name": "Lasers, masers, optical bistability, nonlinear optics", "description": "Lasers, masers, optical bistability, nonlinear optics [See also 81V80]", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A70", "originalCode": "78A70", "name": "Biological applications of optics and electromagnetic theory", "description": "Biological applications of optics and electromagnetic theory [See also 92-XX]", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A97", "originalCode": "78A97", "name": "Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in Section 78-XX)", "description": "Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in Section 78-XX)", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78A99", "originalCode": "78A99", "name": "General topics in optics and electromagnetic theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "78A", "page": 194 }, { "code": "78M", "originalCode": "78Mxx", "name": "Basic methods for problems in optics and electromagnetic theory", "description": "Basic methods for problems in optics and electromagnetic theory [See also 65-XX]", "kind": "section", "parent": "78", "page": 194 }, { "code": "78M05", "originalCode": "78M05", "name": "Method of moments applied to problems in optics and electromagnetic theory", "description": "Method of moments applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M10", "originalCode": "78M10", "name": "Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory", "description": "Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M12", "originalCode": "78M12", "name": "Finite volume methods, finite integration techniques applied to problems in optics and electromagnetic theory", "description": "Finite volume methods, finite integration techniques applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M15", "originalCode": "78M15", "name": "Boundary element methods applied to problems in optics and electromagnetic theory", "description": "Boundary element methods applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M16", "originalCode": "78M16", "name": "Multipole methods applied to problems in optics and electromagnetic theory", "description": "Multipole methods applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M20", "originalCode": "78M20", "name": "Finite difference methods applied to problems in optics and electromagnetic theory", "description": "Finite difference methods applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M22", "originalCode": "78M22", "name": "Spectral, collocation and related methods applied to problems in optics and electromagnetic theory", "description": "Spectral, collocation and related methods applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M30", "originalCode": "78M30", "name": "Variational methods applied to problems in optics and electromagnetic theory", "description": "Variational methods applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M31", "originalCode": "78M31", "name": "Monte Carlo methods applied to problems in optics and electromagnetic theory", "description": "Monte Carlo methods applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 194 }, { "code": "78M32", "originalCode": "78M32", "name": "Neural and heuristic methods applied to problems in optics and electromagnetic theory", "description": "Neural and heuristic methods applied to problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 195 }, { "code": "78M34", "originalCode": "78M34", "name": "Model reduction in optics and electromagnetic theory", "description": "Model reduction in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 195 }, { "code": "78M35", "originalCode": "78M35", "name": "Asymptotic analysis in optics and electromagnetic theory", "description": "Asymptotic analysis in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 195 }, { "code": "78M40", "originalCode": "78M40", "name": "Homogenization in optics and electromagnetic theory", "description": "Homogenization in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 195 }, { "code": "78M50", "originalCode": "78M50", "name": "Optimization problems in optics and electromagnetic theory", "description": "Optimization problems in optics and electromagnetic theory", "kind": "subject", "parent": "78M", "page": 195 }, { "code": "78M99", "originalCode": "78M99", "name": "Basic methods for problems in optics and electromagnetic theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "78M", "page": 195 }, { "code": "80", "originalCode": "80-XX", "name": "Classical thermodynamics, heat transfer", "description": "Classical thermodynamics, heat transfer \\{For thermodynamics of solids, see 74A15\\}", "kind": "class", "parent": null, "page": 195 }, { "code": "80-00", "originalCode": "80-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to classical thermodynamics", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to classical thermodynamics", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80-01", "originalCode": "80-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80-02", "originalCode": "80-02", "name": "Research exposition (monographs, survey articles) pertaining to classical thermodynamics", "description": "Research exposition (monographs, survey articles) pertaining to classical thermodynamics", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80-03", "originalCode": "80-03", "name": "History of classical thermodynamics", "description": "History of classical thermodynamics [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80-04", "originalCode": "80-04", "name": "Software, source code, etc. for problems pertaining to classical thermodynamics", "description": "Software, source code, etc. for problems pertaining to classical thermodynamics", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80-05", "originalCode": "80-05", "name": "Experimental work for problems pertaining to classical thermodynamics", "description": "Experimental work for problems pertaining to classical thermodynamics", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80-06", "originalCode": "80-06", "name": "Proceedings, conferences, collections, etc. pertaining to classical thermodynamics", "description": "Proceedings, conferences, collections, etc. pertaining to classical thermodynamics", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80-10", "originalCode": "80-10", "name": "Mathematical modeling or simulation for problems pertaining to classical thermodynamics", "description": "Mathematical modeling or simulation for problems pertaining to classical thermodynamics", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80-11", "originalCode": "80-11", "name": "Research data for problems pertaining to classical thermodynamics", "description": "Research data for problems pertaining to classical thermodynamics", "kind": "subject", "parent": "80", "page": 195 }, { "code": "80A", "originalCode": "80Axx", "name": "Thermodynamics and heat transfer", "description": "Thermodynamics and heat transfer", "kind": "section", "parent": "80", "page": 195 }, { "code": "80A05", "originalCode": "80A05", "name": "Foundations of thermodynamics and heat transfer", "description": "Foundations of thermodynamics and heat transfer", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A10", "originalCode": "80A10", "name": "Classical and relativistic thermodynamics", "description": "Classical and relativistic thermodynamics", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A17", "originalCode": "80A17", "name": "Thermodynamics of continua", "description": "Thermodynamics of continua [See also 74A15]", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A19", "originalCode": "80A19", "name": "Diffusive and convective heat and mass transfer, heat flow", "description": "Diffusive and convective heat and mass transfer, heat flow", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A21", "originalCode": "80A21", "name": "Radiative heat transfer", "description": "Radiative heat transfer", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A22", "originalCode": "80A22", "name": "Stefan problems, phase changes, etc.", "description": "Stefan problems, phase changes, etc. [See also 74Nxx]", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A23", "originalCode": "80A23", "name": "Inverse problems in thermodynamics and heat transfer", "description": "Inverse problems in thermodynamics and heat transfer", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A25", "originalCode": "80A25", "name": "Combustion", "description": "Combustion", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A30", "originalCode": "80A30", "name": "Chemical kinetics in thermodynamics and heat transfer", "description": "Chemical kinetics in thermodynamics and heat transfer [See also 76V05, 92C45, 92E20]", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A32", "originalCode": "80A32", "name": "Chemically reacting flows", "description": "Chemically reacting flows [See also 92C45, 92E20]", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A50", "originalCode": "80A50", "name": "Chemistry (general) in thermodynamics and heat transfer", "description": "Chemistry (general) in thermodynamics and heat transfer [See mainly 92Exx]", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80A99", "originalCode": "80A99", "name": "Thermodynamics and heat transfer", "description": "None of the above, but in this section", "kind": "subject", "parent": "80A", "page": 195 }, { "code": "80M", "originalCode": "80Mxx", "name": "Basic methods in thermodynamics and heat transfer", "description": "Basic methods in thermodynamics and heat transfer [See also 65-XX]", "kind": "section", "parent": "80", "page": 196 }, { "code": "80M10", "originalCode": "80M10", "name": "Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer", "description": "Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "80M12", "originalCode": "80M12", "name": "Finite volume methods applied to problems 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to problems in thermodynamics and heat transfer", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "80M30", "originalCode": "80M30", "name": "Variational methods applied to problems in thermodynamics and heat transfer", "description": "Variational methods applied to problems in thermodynamics and heat transfer", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "80M31", "originalCode": "80M31", "name": "Monte Carlo methods applied to problems in thermodynamics and heat transfer", "description": "Monte Carlo methods applied to problems in thermodynamics and heat transfer", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "80M35", "originalCode": "80M35", "name": "Asymptotic analysis for problems in thermodynamics and heat transfer", "description": "Asymptotic analysis for problems in thermodynamics and heat transfer", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "80M40", "originalCode": "80M40", "name": "Homogenization for problems in thermodynamics and heat transfer", "description": "Homogenization for problems in thermodynamics and heat transfer", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "80M50", "originalCode": "80M50", "name": "Optimization problems in thermodynamics and heat transfer", "description": "Optimization problems in thermodynamics and heat transfer", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "80M60", "originalCode": "80M60", "name": "Stochastic analysis in thermodynamics and heat transfer", "description": "Stochastic analysis in thermodynamics and heat transfer", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "80M99", "originalCode": "80M99", "name": "Basic methods in thermodynamics and heat transfer", "description": "None of the above, but in this section", "kind": "subject", "parent": "80M", "page": 196 }, { "code": "81", "originalCode": "81-XX", "name": "Quantum theory", "description": "Quantum theory", "kind": "class", "parent": null, "page": 196 }, { "code": "81-00", "originalCode": "81-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to quantum theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to quantum theory", "kind": "subject", "parent": "81", "page": 196 }, { "code": "81-01", "originalCode": "81-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory", "kind": "subject", "parent": "81", "page": 196 }, { "code": "81-02", "originalCode": "81-02", "name": "Research exposition (monographs, survey articles) pertaining to quantum theory", "description": "Research exposition (monographs, survey articles) pertaining to quantum theory", "kind": "subject", "parent": "81", "page": 196 }, { "code": "81-03", "originalCode": "81-03", "name": "History of quantum theory", "description": "History of quantum theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "81", "page": 196 }, { "code": "81-04", "originalCode": "81-04", "name": "Software, source code, etc. for problems pertaining to quantum theory", "description": "Software, source code, etc. for problems pertaining to quantum theory", "kind": "subject", "parent": "81", "page": 196 }, { "code": "81-05", "originalCode": "81-05", "name": "Experimental work for problems pertaining to quantum theory", "description": "Experimental work for problems pertaining to quantum theory", "kind": "subject", "parent": "81", "page": 196 }, { "code": "81-06", "originalCode": "81-06", "name": "Proceedings, conferences, collections, etc. pertaining to quantum theory", "description": "Proceedings, conferences, collections, etc. pertaining to quantum theory", "kind": "subject", "parent": "81", "page": 196 }, { "code": "81-08", "originalCode": "81-08", "name": "Computational 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"81P05", "originalCode": "81P05", "name": "General and philosophical questions in quantum theory", "description": "General and philosophical questions in quantum theory", "kind": "subject", "parent": "81P", "page": 196 }, { "code": "81P10", "originalCode": "81P10", "name": "Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)", "description": "Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) [See also 03G12, 06C15]", "kind": "subject", "parent": "81P", "page": 196 }, { "code": "81P13", "originalCode": "81P13", "name": "Contextuality in quantum theory", "description": "Contextuality in quantum theory", "kind": "subject", "parent": "81P", "page": 196 }, { "code": "81P15", "originalCode": "81P15", "name": "Quantum measurement theory, state operations, state preparations", "description": "Quantum measurement theory, state operations, state preparations", "kind": "subject", "parent": "81P", "page": 196 }, { "code": "81P16", "originalCode": "81P16", "name": "Quantum state spaces, operational and probabilistic concepts", "description": "Quantum state spaces, operational and probabilistic concepts", "kind": "subject", "parent": "81P", "page": 196 }, { "code": "81P17", "originalCode": "81P17", "name": "Quantum entropies", "description": "Quantum entropies", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P18", "originalCode": "81P18", "name": "Quantum state tomography, quantum state discrimination", "description": "Quantum state tomography, quantum state discrimination", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P20", "originalCode": "81P20", "name": "Stochastic mechanics (including stochastic electrodynamics)", "description": "Stochastic mechanics (including stochastic electrodynamics)", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P40", "originalCode": "81P40", "name": "Quantum coherence, entanglement, quantum correlations", "description": "Quantum coherence, entanglement, quantum correlations", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P42", "originalCode": "81P42", "name": "Entanglement measures, concurrencies, separability criteria", "description": "Entanglement measures, concurrencies, separability criteria", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P43", "originalCode": "81P43", "name": "Quantum discord", "description": "Quantum discord", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P45", "originalCode": "81P45", "name": "Quantum information, communication, networks (quantum-theoretic aspects)", "description": "Quantum information, communication, networks (quantum-theoretic aspects) [See also 94A15, 94A17]", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P47", "originalCode": "81P47", "name": "Quantum channels, fidelity", "description": "Quantum channels, fidelity [See also 94A40]", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P48", "originalCode": "81P48", "name": "LOCC, teleportation, dense coding, remote state operations, distillation", "description": "LOCC, teleportation, dense coding, remote state operations, distillation", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P50", "originalCode": "81P50", "name": "Quantum state estimation, approximate cloning", "description": "Quantum state estimation, approximate cloning", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P55", "originalCode": "81P55", "name": "Special bases (entangled, mutual unbiased, etc.)", "description": "Special bases (entangled, mutual unbiased, etc.)", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P65", "originalCode": "81P65", "name": "Quantum gates", "description": "Quantum gates", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P68", "originalCode": "81P68", "name": "Quantum computation", "description": "Quantum computation [See also 68Q09] \\{For algorithmic aspects, see 68Q12\\}", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P70", "originalCode": "81P70", "name": "Quantum coding (general)", "description": "Quantum coding (general)", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P73", "originalCode": "81P73", "name": "Computational stability and error-correcting codes for quantum computation and communication processing", "description": "Computational stability and error-correcting codes for quantum computation and communication processing", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P94", "originalCode": "81P94", "name": "Quantum cryptography (quantum-theoretic aspects)", "description": "Quantum cryptography (quantum-theoretic aspects) [See also 94A60]", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81P99", "originalCode": "81P99", "name": "Foundations, quantum information and its processing, quantum axioms, and philosophy", "description": "None of the above, but in this section", "kind": "subject", "parent": "81P", "page": 197 }, { "code": "81Q", "originalCode": "81Qxx", "name": "General mathematical topics and methods in quantum theory", "description": "General mathematical topics and methods in quantum theory", "kind": "section", "parent": "81", "page": 197 }, { "code": "81Q05", "originalCode": "81Q05", "name": "Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics", "description": "Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q10", "originalCode": "81Q10", "name": "Selfadjoint operator theory in quantum theory, including spectral analysis", "description": "Selfadjoint operator theory in quantum theory, including spectral analysis", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q12", "originalCode": "81Q12", "name": "Nonselfadjoint 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"description": "Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 05Cxx, 14D05, 32S40]", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q35", "originalCode": "81Q35", "name": "Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices", "description": "Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices [See also 81R20]", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q37", "originalCode": "81Q37", "name": "Quantum dots, waveguides, ratchets, etc.", "description": "Quantum dots, waveguides, ratchets, etc. [See also 82D20, 82D77]", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q40", "originalCode": "81Q40", "name": "Bethe-Salpeter and other integral equations arising in quantum theory", "description": "Bethe-Salpeter and other integral equations arising in quantum theory", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q50", "originalCode": "81Q50", "name": "Quantum chaos", "description": "Quantum chaos [See also 37D45]", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q60", "originalCode": "81Q60", "name": "Supersymmetry and quantum mechanics", "description": "Supersymmetry and quantum mechanics", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q65", "originalCode": "81Q65", "name": "Alternative quantum mechanics (including hidden variables, etc.)", "description": "Alternative quantum mechanics (including hidden variables, etc.)", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q70", "originalCode": "81Q70", "name": "Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory", "description": "Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q80", "originalCode": "81Q80", "name": "Special quantum systems, such as solvable systems", "description": "Special quantum systems, such as solvable systems", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q93", "originalCode": "81Q93", "name": "Quantum control", "description": "Quantum control", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81Q99", "originalCode": "81Q99", "name": "General mathematical topics and methods in quantum theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "81Q", "page": 197 }, { "code": "81R", "originalCode": "81Rxx", "name": "Groups and algebras in quantum theory", "description": "Groups and algebras in quantum theory", "kind": "section", "parent": "81", "page": 198 }, { "code": "81R05", "originalCode": "81R05", "name": "Finite-dimensional groups and algebras motivated by physics and their representations", "description": "Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R10", "originalCode": "81R10", "name": "Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \\(W\\)-algebras and other current algebras and their representations", "description": "Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \\(W\\)-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R12", "originalCode": "81R12", "name": "Groups and algebras in quantum theory and relations with integrable systems", "description": "Groups and algebras in quantum theory and relations with integrable systems [See also 17Bxx, 37J35]", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R15", "originalCode": "81R15", "name": "Operator algebra methods applied to problems in quantum theory", "description": "Operator algebra methods applied to problems in quantum theory [See also 46Lxx, 81T05]", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R20", "originalCode": "81R20", "name": "Covariant wave equations in quantum theory, relativistic quantum mechanics", "description": "Covariant wave equations in quantum theory, relativistic quantum mechanics [See also 81Q35]", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R25", "originalCode": "81R25", "name": "Spinor and twistor methods applied to problems in quantum theory", "description": "Spinor and twistor methods applied to problems in quantum theory [See also 32L25]", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R30", "originalCode": "81R30", "name": "Coherent states", "description": "Coherent states [See also 22E45]; squeezed states in quantum theory [See also 81V80]", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R40", "originalCode": "81R40", "name": "Symmetry breaking in quantum theory", "description": "Symmetry breaking in quantum theory", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R50", "originalCode": "81R50", "name": "Quantum groups and related algebraic methods applied to problems in quantum theory", "description": "Quantum groups and related algebraic methods applied to problems in quantum theory [See also 16T20, 17B37]", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R60", "originalCode": "81R60", "name": "Noncommutative geometry in quantum theory", "description": "Noncommutative geometry in quantum theory", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81R99", "originalCode": "81R99", "name": "Groups and algebras in quantum theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "81R", "page": 198 }, { "code": "81S", "originalCode": "81Sxx", "name": "General quantum mechanics and problems of quantization", "description": "General quantum mechanics and problems of quantization", "kind": "section", "parent": "81", "page": 198 }, { "code": "81S05", "originalCode": "81S05", "name": "Commutation relations and statistics as related to quantum mechanics (general)", "description": "Commutation relations and statistics as related to quantum mechanics (general)", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S07", "originalCode": "81S07", "name": "Uncertainty relations, also entropic", "description": "Uncertainty relations, also entropic", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S08", "originalCode": "81S08", "name": "Canonical quantization", "description": "Canonical quantization", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S10", "originalCode": "81S10", "name": "Geometry and quantization, symplectic methods", "description": "Geometry and quantization, symplectic methods [See also 53D50]", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S20", "originalCode": "81S20", "name": "Stochastic quantization", "description": "Stochastic quantization", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S22", "originalCode": "81S22", "name": "Open systems, reduced dynamics, master equations, decoherence", "description": "Open systems, reduced dynamics, master equations, decoherence [See also 82C31]", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S25", "originalCode": "81S25", "name": "Quantum stochastic calculus", "description": "Quantum stochastic calculus", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S30", "originalCode": "81S30", "name": "Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics", "description": "Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S40", "originalCode": "81S40", "name": "Path integrals in quantum mechanics", "description": "Path integrals in quantum mechanics [See also 58D30, 81Q30, 81T18]", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81S99", "originalCode": "81S99", "name": "General quantum mechanics and problems of quantization", "description": "None of the above, but in this section", "kind": "subject", "parent": "81S", "page": 198 }, { "code": "81T", "originalCode": "81Txx", "name": "Quantum field theory; related classical field theories", "description": "Quantum field theory; related classical field theories [See also 70Sxx]", "kind": "section", "parent": "81", "page": 198 }, { "code": "81T05", "originalCode": "81T05", "name": "Axiomatic quantum field theory; operator algebras", "description": "Axiomatic quantum field theory; operator algebras", "kind": "subject", "parent": "81T", "page": 198 }, { "code": "81T08", "originalCode": "81T08", "name": "Constructive quantum field theory", "description": "Constructive quantum field theory", "kind": "subject", "parent": "81T", "page": 198 }, { "code": "81T10", "originalCode": "81T10", "name": "Model quantum field theories", "description": "Model quantum field theories", "kind": "subject", "parent": "81T", "page": 198 }, { "code": "81T11", "originalCode": "81T11", "name": "Higher spin theories", "description": "Higher spin theories", "kind": "subject", "parent": "81T", "page": 198 }, { "code": "81T12", "originalCode": "81T12", "name": "Effective quantum field theories", "description": "Effective quantum field theories", "kind": "subject", "parent": "81T", "page": 198 }, { "code": "81T13", "originalCode": "81T13", "name": "Yang-Mills and other gauge theories in quantum field theory", "description": "Yang-Mills and other gauge theories in quantum field theory [See also 53C07, 58E15]", "kind": "subject", "parent": "81T", "page": 198 }, { "code": "81T15", "originalCode": "81T15", "name": "Perturbative methods of renormalization applied to problems in quantum field theory", "description": "Perturbative methods of renormalization applied to problems in quantum field theory", "kind": "subject", "parent": "81T", "page": 198 }, { "code": "81T16", "originalCode": "81T16", "name": "Nonperturbative methods of renormalization applied to problems in quantum field theory", "description": "Nonperturbative methods of renormalization applied to problems in quantum field theory", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T17", "originalCode": "81T17", "name": "Renormalization group methods applied to problems in quantum field theory", "description": "Renormalization group methods applied to problems in quantum field theory", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T18", "originalCode": "81T18", "name": "Feynman diagrams", "description": "Feynman diagrams", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T20", "originalCode": "81T20", "name": "Quantum field theory on curved space or space-time backgrounds", "description": "Quantum field theory on curved space or space-time backgrounds", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T25", "originalCode": "81T25", "name": "Quantum field theory on lattices", "description": "Quantum field theory on lattices", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T27", "originalCode": "81T27", "name": "Continuum limits in quantum field theory", "description": "Continuum limits in quantum field theory", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T28", "originalCode": "81T28", "name": "Thermal quantum field theory", "description": "Thermal quantum field theory [See also 82B30]", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T30", "originalCode": "81T30", "name": "String and superstring theories; other extended objects (e.g., branes) in quantum field theory", "description": "String and superstring theories; other extended objects (e.g., branes) in quantum field theory [See also 83E30]", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T32", "originalCode": "81T32", "name": "Matrix models and tensor models for quantum field theory", "description": "Matrix models and tensor models for quantum field theory", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T33", "originalCode": "81T33", "name": "Dimensional compactification in quantum field theory", "description": "Dimensional compactification in quantum field theory", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T35", "originalCode": "81T35", "name": "Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.)", "description": "Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) [See also 83E05]", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T40", "originalCode": "81T40", "name": "Two-dimensional field theories, conformal field theories, etc. in quantum mechanics", "description": "Two-dimensional field theories, conformal field theories, etc. in quantum mechanics", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T45", "originalCode": "81T45", "name": "Topological field theories in quantum mechanics", "description": "Topological field theories in quantum mechanics [See also 57R56, 58Dxx]", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T50", "originalCode": "81T50", "name": "Anomalies in quantum field theory", "description": "Anomalies in quantum field theory", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T55", "originalCode": "81T55", "name": "Casimir effect in quantum field theory", "description": "Casimir effect in quantum field theory", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T60", "originalCode": "81T60", "name": "Supersymmetric field theories in quantum mechanics", "description": "Supersymmetric field theories in quantum mechanics", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T70", "originalCode": "81T70", "name": "Quantization in field theory; cohomological methods", "description": "Quantization in field theory; cohomological methods [See also 58D29]", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T75", "originalCode": "81T75", "name": "Noncommutative geometry methods in quantum field theory", "description": "Noncommutative geometry methods in quantum field theory [See also 46L85, 46L87, 58B34]", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81T99", "originalCode": "81T99", "name": "Quantum field theory; related classical field theories", "description": "None of the above, but in this section", "kind": "subject", "parent": "81T", "page": 199 }, { "code": "81U", "originalCode": "81Uxx", "name": "Quantum scattering theory", "description": "Quantum scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40]", "kind": "section", "parent": "81", "page": 199 }, { "code": "81U05", "originalCode": "81U05", "name": "\\(2\\)-body potential quantum scattering theory", "description": "\\(2\\)-body potential quantum scattering theory \\{For WKB methods, see also 34E20\\}", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U10", "originalCode": "81U10", "name": "\\(n\\)-body potential quantum scattering theory", "description": "\\(n\\)-body potential quantum scattering theory", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U15", "originalCode": "81U15", "name": "Exactly and quasi-solvable systems arising in quantum theory", "description": "Exactly and quasi-solvable systems arising in quantum theory", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U20", "originalCode": "81U20", "name": "\\(S\\)-matrix theory, etc. in quantum theory", "description": "\\(S\\)-matrix theory, etc. in quantum theory", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U24", "originalCode": "81U24", "name": "Resonances in quantum scattering theory", "description": "Resonances in quantum scattering theory", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U26", "originalCode": "81U26", "name": "Tunneling in quantum theory", "description": "Tunneling in quantum theory", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U30", "originalCode": "81U30", "name": "Dispersion theory, dispersion relations arising in quantum theory", "description": "Dispersion theory, dispersion relations arising in quantum theory", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U35", "originalCode": "81U35", "name": "Inelastic and multichannel quantum scattering", "description": "Inelastic and multichannel quantum scattering", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U40", "originalCode": "81U40", "name": "Inverse scattering problems in quantum theory", "description": "Inverse scattering problems in quantum theory", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U90", "originalCode": "81U90", "name": "Particle decays", "description": "Particle decays", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81U99", "originalCode": "81U99", "name": "Quantum scattering theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "81U", "page": 199 }, { "code": "81V", "originalCode": "81Vxx", "name": "Applications of quantum theory to specific physical systems", "description": "Applications of quantum theory to specific physical systems", "kind": "section", "parent": "81", "page": 200 }, { "code": "81V05", "originalCode": "81V05", "name": "Strong interaction, including quantum chromodynamics", "description": "Strong interaction, including quantum chromodynamics", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V10", "originalCode": "81V10", "name": "Electromagnetic interaction; quantum electrodynamics", "description": "Electromagnetic interaction; quantum electrodynamics", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V15", "originalCode": "81V15", "name": "Weak interaction in quantum theory", "description": "Weak interaction in quantum theory", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V17", "originalCode": "81V17", "name": "Gravitational interaction in quantum theory", "description": "Gravitational interaction in quantum theory [See also 83Cxx, 83Exx]", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V19", "originalCode": "81V19", "name": "Other fundamental interactions in quantum theory", "description": "Other fundamental interactions in quantum theory", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V22", "originalCode": "81V22", "name": "Unified quantum theories", "description": "Unified quantum theories", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V25", "originalCode": "81V25", "name": "Other elementary particle theory in quantum theory", "description": "Other elementary particle theory in quantum theory", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V27", "originalCode": "81V27", "name": "Anyons", "description": "Anyons", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V35", "originalCode": "81V35", "name": "Nuclear physics", "description": "Nuclear physics", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V45", "originalCode": "81V45", "name": "Atomic physics", "description": "Atomic physics", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V55", "originalCode": "81V55", "name": "Molecular physics", "description": "Molecular physics [See also 92E10]", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V60", "originalCode": "81V60", "name": "Mono-, di- and multipole moments (EM and other), gyromagnetic relations", "description": "Mono-, di- and multipole moments (EM and other), gyromagnetic relations", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V65", "originalCode": "81V65", "name": "Quantum dots as quasi particles", "description": "Quantum dots as quasi particles [See also 82D20]", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V70", "originalCode": "81V70", "name": "Many-body theory; quantum Hall effect", "description": "Many-body theory; quantum Hall effect", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V72", "originalCode": "81V72", "name": "Particle exchange symmetries in quantum theory (general)", "description": "Particle exchange symmetries in quantum theory (general)", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V73", "originalCode": "81V73", "name": "Bosonic systems in quantum theory", "description": "Bosonic systems in quantum theory", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V74", "originalCode": "81V74", "name": "Fermionic systems in quantum theory", "description": "Fermionic systems in quantum theory", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V80", "originalCode": "81V80", "name": "Quantum optics", "description": "Quantum optics", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "81V99", "originalCode": "81V99", "name": "Applications of quantum theory to specific physical systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "81V", "page": 200 }, { "code": "82", "originalCode": "82-XX", "name": "Statistical mechanics, structure of matter", "description": "Statistical mechanics, structure of matter", "kind": "class", "parent": null, "page": 200 }, { "code": "82-00", "originalCode": "82-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistical mechanics", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistical mechanics", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82-01", "originalCode": "82-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82-02", "originalCode": "82-02", "name": "Research exposition (monographs, survey articles) pertaining to statistical mechanics", "description": "Research exposition (monographs, survey articles) pertaining to statistical mechanics", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82-03", "originalCode": "82-03", "name": "History of statistical mechanics", "description": "History of statistical mechanics [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82-04", "originalCode": "82-04", "name": "Software, source code, etc. for problems pertaining to statistical mechanics", "description": "Software, source code, etc. for problems pertaining to statistical mechanics", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82-05", "originalCode": "82-05", "name": "Experimental work for problems pertaining to statistical mechanics", "description": "Experimental work for problems pertaining to statistical mechanics", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82-06", "originalCode": "82-06", "name": "Proceedings, conferences, collections, etc. pertaining to statistical mechanics", "description": "Proceedings, conferences, collections, etc. pertaining to statistical mechanics", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82-10", "originalCode": "82-10", "name": "Mathematical modeling or simulation for problems pertaining to statistical mechanics", "description": "Mathematical modeling or simulation for problems pertaining to statistical mechanics", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82-11", "originalCode": "82-11", "name": "Research data for problems pertaining to statistical mechanics", "description": "Research data for problems pertaining to statistical mechanics", "kind": "subject", "parent": "82", "page": 200 }, { "code": "82B", "originalCode": "82Bxx", "name": "Equilibrium statistical mechanics", "description": "Equilibrium statistical mechanics", "kind": "section", "parent": "82", "page": 201 }, { "code": "82B03", "originalCode": "82B03", "name": "Foundations of equilibrium statistical mechanics", "description": "Foundations of equilibrium statistical mechanics", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B05", "originalCode": "82B05", "name": "Classical equilibrium statistical mechanics (general)", "description": "Classical equilibrium statistical mechanics (general)", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B10", "originalCode": "82B10", "name": "Quantum equilibrium statistical mechanics (general)", "description": "Quantum equilibrium statistical mechanics (general)", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B20", "originalCode": "82B20", "name": "Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics", "description": "Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics [See also 05Cxx]", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B21", "originalCode": "82B21", "name": "Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics", "description": "Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B23", "originalCode": "82B23", "name": "Exactly solvable models; Bethe ansatz", "description": "Exactly solvable models; Bethe ansatz", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B24", "originalCode": "82B24", "name": "Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics", "description": "Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B26", "originalCode": "82B26", "name": "Phase transitions (general) in equilibrium statistical mechanics", "description": "Phase transitions (general) in equilibrium statistical mechanics", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B27", "originalCode": "82B27", "name": "Critical phenomena in equilibrium statistical mechanics", "description": "Critical phenomena in equilibrium statistical mechanics", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B28", "originalCode": "82B28", "name": "Renormalization group methods in equilibrium statistical mechanics", "description": "Renormalization group methods in equilibrium statistical mechanics [See also 81T17]", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B30", "originalCode": "82B30", "name": "Statistical thermodynamics", "description": "Statistical thermodynamics [See also 80-XX]", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B31", "originalCode": "82B31", "name": "Stochastic methods applied to problems in equilibrium statistical mechanics", "description": "Stochastic methods applied to problems in equilibrium statistical mechanics", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B35", "originalCode": "82B35", "name": "Irreversible thermodynamics, including Onsager-Machlup theory", "description": "Irreversible thermodynamics, including Onsager-Machlup theory [See also 92E20]", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B40", "originalCode": "82B40", "name": "Kinetic theory of gases in equilibrium statistical mechanics", "description": "Kinetic theory of gases in equilibrium statistical mechanics", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B41", "originalCode": "82B41", "name": "Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics", "description": "Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics [See also 60G50, 82C41]", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B43", "originalCode": "82B43", "name": "Percolation", "description": "Percolation [See also 60K35]", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B44", "originalCode": "82B44", "name": "Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics", "description": "Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82B99", "originalCode": "82B99", "name": "Equilibrium statistical mechanics", "description": "None of the above, but in this section", "kind": "subject", "parent": "82B", "page": 201 }, { "code": "82C", "originalCode": "82Cxx", "name": "Time-dependent statistical mechanics (dynamic and nonequilibrium)", "description": "Time-dependent statistical mechanics (dynamic and nonequilibrium)", "kind": "section", "parent": "82", "page": 201 }, { "code": "82C03", "originalCode": "82C03", "name": "Foundations of time-dependent statistical mechanics", "description": "Foundations of time-dependent statistical mechanics", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C05", "originalCode": "82C05", "name": "Classical dynamic and nonequilibrium statistical mechanics (general)", "description": "Classical dynamic and nonequilibrium statistical mechanics (general)", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C10", "originalCode": "82C10", "name": "Quantum dynamics and nonequilibrium statistical mechanics (general)", "description": "Quantum dynamics and nonequilibrium statistical mechanics (general)", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C20", "originalCode": "82C20", "name": "Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics", "description": "Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics [See also 05Cxx]", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C21", "originalCode": "82C21", "name": "Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics", "description": "Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C22", "originalCode": "82C22", "name": "Interacting particle systems in time-dependent statistical mechanics", "description": "Interacting particle systems in time-dependent statistical mechanics [See also 60K35]", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C23", "originalCode": "82C23", "name": "Exactly solvable dynamic models in time-dependent statistical mechanics", "description": "Exactly solvable dynamic models in time-dependent statistical mechanics [See also 37K60]", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C24", "originalCode": "82C24", "name": "Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics", "description": "Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C26", "originalCode": "82C26", "name": "Dynamic and nonequilibrium phase transitions (general) in statistical mechanics", "description": "Dynamic and nonequilibrium phase transitions (general) in statistical mechanics", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C27", "originalCode": "82C27", "name": "Dynamic critical phenomena in statistical mechanics", "description": "Dynamic critical phenomena in statistical mechanics", "kind": "subject", "parent": "82C", "page": 201 }, { "code": "82C28", "originalCode": "82C28", "name": "Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics", "description": "Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics [See also 81T17]", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C31", "originalCode": "82C31", "name": "Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics", "description": "Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics [See also 60H10]", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C32", "originalCode": "82C32", "name": "Neural nets applied to problems in time-dependent statistical mechanics", "description": "Neural nets applied to problems in time-dependent statistical mechanics [See also 68T05, 91E40, 92B20]", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C35", "originalCode": "82C35", "name": "Irreversible thermodynamics, including Onsager-Machlup theory", "description": "Irreversible thermodynamics, including Onsager-Machlup theory", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C40", "originalCode": "82C40", "name": "Kinetic theory of gases in time-dependent statistical mechanics", "description": "Kinetic theory of gases in time-dependent statistical mechanics", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C41", "originalCode": "82C41", "name": "Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics", "description": "Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics [See also 60G50]", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C43", "originalCode": "82C43", "name": "Time-dependent percolation in statistical mechanics", "description": "Time-dependent percolation in statistical mechanics [See also 60K35]", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C44", "originalCode": "82C44", "name": "Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics", "description": "Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C70", "originalCode": "82C70", "name": "Transport processes in time-dependent statistical mechanics", "description": "Transport processes in time-dependent statistical mechanics", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82C99", "originalCode": "82C99", "name": "Time-dependent statistical mechanics (dynamic and nonequilibrium)", "description": "None of the above, but in this section", "kind": "subject", "parent": "82C", "page": 202 }, { "code": "82D", "originalCode": "82Dxx", "name": "Applications 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"parent": "86A", "page": 206 }, { "code": "86A30", "originalCode": "86A30", "name": "Geodesy, mapping problems", "description": "Geodesy, mapping problems", "kind": "subject", "parent": "86A", "page": 206 }, { "code": "86A32", "originalCode": "86A32", "name": "Geostatistics", "description": "Geostatistics", "kind": "subject", "parent": "86A", "page": 206 }, { "code": "86A40", "originalCode": "86A40", "name": "Glaciology", "description": "Glaciology", "kind": "subject", "parent": "86A", "page": 206 }, { "code": "86A60", "originalCode": "86A60", "name": "Geological problems", "description": "Geological problems", "kind": "subject", "parent": "86A", "page": 206 }, { "code": "86A70", "originalCode": "86A70", "name": "Vulcanology; magma and lava flow", "description": "Vulcanology; magma and lava flow", "kind": "subject", "parent": "86A", "page": 206 }, { "code": "86A99", "originalCode": "86A99", "name": "Geophysics", "description": "None of the above, but in this section", "kind": 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"91A12", "name": "Cooperative games", "description": "Cooperative games", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A14", "originalCode": "91A14", "name": "Potential and congestion games", "description": "Potential and congestion games", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A15", "originalCode": "91A15", "name": "Stochastic games, stochastic differential games", "description": "Stochastic games, stochastic differential games", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A16", "originalCode": "91A16", "name": "Mean field games (aspects of game theory)", "description": "Mean field games (aspects of game theory) \\{For partial differential equations, see 35Q89; for calculus of variations and optimal control, see 49N80\\}", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A18", "originalCode": "91A18", "name": "Games in extensive form", "description": "Games in extensive form", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A20", "originalCode": "91A20", "name": "Multistage and repeated games", "description": "Multistage and repeated games", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A22", "originalCode": "91A22", "name": "Evolutionary games", "description": "Evolutionary games", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A23", "originalCode": "91A23", "name": "Differential games (aspects of game theory)", "description": "Differential games (aspects of game theory) [See also 49N70]", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A24", "originalCode": "91A24", "name": "Positional games (pursuit and evasion, etc.)", "description": "Positional games (pursuit and evasion, etc.) [See also 49N75]", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A25", "originalCode": "91A25", "name": "Dynamic games", "description": "Dynamic games", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A26", "originalCode": "91A26", "name": "Rationality and learning in game theory", "description": "Rationality and learning in game theory", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A27", "originalCode": "91A27", "name": "Games with incomplete information, Bayesian games", "description": "Games with incomplete information, Bayesian games", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A28", "originalCode": "91A28", "name": "Signaling and communication in game theory", "description": "Signaling and communication in game theory", "kind": "subject", "parent": "91A", "page": 209 }, { "code": "91A30", "originalCode": "91A30", "name": "Utility theory for games", "description": "Utility theory for games [See also 91B16]", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A35", "originalCode": "91A35", "name": "Decision theory for games", "description": "Decision theory for games [See also 62Cxx, 90B50, 91B06]", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A40", "originalCode": "91A40", "name": "Other game-theoretic models", "description": "Other game-theoretic models", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A43", "originalCode": "91A43", "name": "Games involving graphs", "description": "Games involving graphs \\{For games on graphs, see also 05C57\\}", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A44", "originalCode": "91A44", "name": "Games involving topology, set theory, or logic", "description": "Games involving topology, set theory, or logic", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A46", "originalCode": "91A46", "name": "Combinatorial games", "description": "Combinatorial games", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A50", "originalCode": "91A50", "name": "Discrete-time games", "description": "Discrete-time games", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A55", "originalCode": "91A55", "name": "Games of timing", "description": "Games of timing", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A60", "originalCode": "91A60", "name": "Probabilistic games; gambling", "description": "Probabilistic games; gambling [See also 60G40]", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A65", "originalCode": "91A65", "name": "Hierarchical games (including Stackelberg games)", "description": "Hierarchical games (including Stackelberg games)", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A68", "originalCode": "91A68", "name": "Algorithmic game theory and complexity", "description": "Algorithmic game theory and complexity [See also 68Qxx, 68Wxx]", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A70", "originalCode": "91A70", "name": "Spaces of games", "description": "Spaces of games", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A80", "originalCode": "91A80", "name": "Applications of game theory", "description": "Applications of game theory", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A81", "originalCode": "91A81", "name": "Quantum games", "description": "Quantum games", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A86", "originalCode": "91A86", "name": "Game theory and fuzziness", "description": "Game theory and fuzziness", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A90", "originalCode": "91A90", "name": "Experimental studies", "description": "Experimental studies", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91A99", "originalCode": "91A99", "name": "Game theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "91A", "page": 210 }, { "code": "91B", "originalCode": "91Bxx", "name": "Mathematical economics", "description": "Mathematical economics \\{For econometrics, see 62P20\\}", "kind": "section", "parent": "91", "page": 210 }, { "code": "91B02", "originalCode": "91B02", "name": "Fundamental topics (basic mathematics, methodology; applicable to economics in general)", "description": "Fundamental topics (basic mathematics, methodology; applicable to economics in general)", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B03", "originalCode": "91B03", "name": "Mechanism design theory", "description": "Mechanism design theory", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B05", "originalCode": "91B05", "name": "Risk models (general)", "description": "Risk models (general) \\{For actuarial and financial risk, see 91Gxx\\}", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B06", "originalCode": "91B06", "name": "Decision theory", "description": "Decision theory [See also 62Cxx, 90B50, 91A35]", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B08", "originalCode": "91B08", "name": "Individual preferences", "description": "Individual preferences", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B10", "originalCode": "91B10", "name": "Group preferences", "description": "Group preferences", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B12", "originalCode": "91B12", "name": "Voting theory", "description": "Voting theory", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B14", "originalCode": "91B14", "name": "Social choice", "description": "Social choice", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B15", "originalCode": "91B15", "name": "Welfare economics", "description": "Welfare economics", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B16", "originalCode": "91B16", "name": "Utility theory", "description": "Utility theory [See also 91A30]", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B18", "originalCode": "91B18", "name": "Public goods", "description": "Public goods", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B24", "originalCode": "91B24", "name": "Microeconomic theory (price theory and economic markets)", "description": "Microeconomic theory (price theory and economic markets)", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B26", "originalCode": "91B26", "name": "Auctions, bargaining, bidding and selling, and other market models", "description": "Auctions, bargaining, bidding and selling, and other market models", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B32", "originalCode": "91B32", "name": "Resource and cost allocation (including fair division, apportionment, etc.)", "description": "Resource and cost allocation (including fair division, apportionment, etc.)", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B38", "originalCode": "91B38", "name": "Production theory, theory of the firm", "description": "Production theory, theory of the firm", "kind": "subject", "parent": "91B", "page": 210 }, { "code": "91B39", "originalCode": "91B39", "name": "Labor markets", "description": "Labor markets", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B41", "originalCode": "91B41", "name": "Contract theory (moral hazard, adverse selection)", "description": "Contract theory (moral hazard, adverse selection)", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B42", "originalCode": "91B42", "name": "Consumer behavior, demand theory", "description": "Consumer behavior, demand theory", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B43", "originalCode": "91B43", "name": "Principal-agent models", "description": "Principal-agent models", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B44", "originalCode": "91B44", "name": "Economics of information", "description": "Economics of information", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B50", "originalCode": "91B50", "name": "General equilibrium theory", "description": "General equilibrium theory", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B51", "originalCode": "91B51", "name": "Dynamic stochastic general equilibrium theory", "description": "Dynamic stochastic general equilibrium theory", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B52", "originalCode": "91B52", "name": "Special types of economic equilibria", "description": "Special types of economic equilibria", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B54", "originalCode": "91B54", "name": "Special types of economic markets (including Cournot, Bertrand)", "description": "Special types of economic markets (including Cournot, Bertrand)", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B55", "originalCode": "91B55", "name": "Economic dynamics", "description": "Economic dynamics", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B60", "originalCode": "91B60", "name": "Trade models", "description": "Trade models", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B62", "originalCode": "91B62", "name": "Economic growth models", "description": "Economic growth models", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B64", "originalCode": "91B64", "name": "Macroeconomic theory (monetary models, models of taxation)", "description": "Macroeconomic theory (monetary models, models of taxation)", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B66", "originalCode": "91B66", "name": "Multisectoral models in economics", "description": "Multisectoral models in economics", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B68", "originalCode": "91B68", "name": "Matching models", "description": "Matching models", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B69", "originalCode": "91B69", "name": "Heterogeneous agent models", "description": "Heterogeneous agent models", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B70", "originalCode": "91B70", "name": "Stochastic models in economics", "description": "Stochastic models in economics", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B72", "originalCode": "91B72", "name": "Spatial models in economics", "description": "Spatial models in economics [See also 91D25]", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B74", "originalCode": "91B74", "name": "Economic models of real-world systems (e.g., electricity markets, etc.)", "description": "Economic models of real-world systems (e.g., electricity markets, etc.)", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B76", "originalCode": "91B76", "name": "Environmental economics (natural resource models, harvesting, pollution, etc.)", "description": "Environmental economics (natural resource models, harvesting, pollution, etc.)", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B80", "originalCode": "91B80", "name": "Applications of statistical and quantum mechanics to economics (econophysics)", "description": "Applications of statistical and quantum mechanics to economics (econophysics)", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B82", "originalCode": "91B82", "name": "Statistical methods; economic indices and measures", "description": "Statistical methods; economic indices and measures [See also 62P20]", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B84", "originalCode": "91B84", "name": "Economic time series analysis", "description": "Economic time series analysis \\{For statistical theory of time series, see 62M10\\}", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B86", "originalCode": "91B86", "name": "Mathematical economics and fuzziness", "description": "Mathematical economics and fuzziness", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91B99", "originalCode": "91B99", "name": "Mathematical economics", "description": "None of the above, but in this section", "kind": "subject", "parent": "91B", "page": 211 }, { "code": "91C", "originalCode": "91Cxx", "name": "Social and behavioral sciences: general topics", "description": "Social and behavioral sciences: general topics \\{For statistics, see 62P25\\}", "kind": "section", "parent": "91", "page": 211 }, { "code": "91C05", "originalCode": "91C05", "name": "Measurement theory in the social and behavioral sciences", "description": "Measurement theory in the social and behavioral sciences", "kind": "subject", "parent": "91C", "page": 211 }, { "code": "91C15", "originalCode": "91C15", "name": "One- and multidimensional scaling in the social and behavioral sciences", "description": "One- and multidimensional scaling in the social and behavioral sciences", "kind": "subject", "parent": "91C", "page": 211 }, { "code": "91C20", "originalCode": "91C20", "name": "Clustering in the social and behavioral sciences", "description": "Clustering in the social and behavioral sciences [See also 62H30]", "kind": "subject", "parent": "91C", "page": 211 }, { "code": "91C99", "originalCode": "91C99", "name": "Social and behavioral sciences: general topics", "description": "None of the above, but in this section", "kind": "subject", "parent": "91C", "page": 211 }, { "code": "91D", "originalCode": "91Dxx", "name": "Mathematical sociology (including anthropology)", "description": "Mathematical sociology (including anthropology)", "kind": "section", "parent": "91", "page": 212 }, { "code": "91D10", "originalCode": "91D10", "name": "Models of societies, social and urban evolution", "description": "Models of societies, social and urban evolution", "kind": "subject", "parent": "91D", "page": 212 }, { "code": "91D15", "originalCode": "91D15", "name": "Social learning", "description": "Social learning", "kind": "subject", "parent": "91D", "page": 212 }, { "code": "91D20", "originalCode": "91D20", "name": "Mathematical geography and demography", "description": "Mathematical geography and demography", "kind": "subject", "parent": "91D", "page": 212 }, { "code": "91D25", "originalCode": "91D25", "name": "Spatial models in sociology", "description": "Spatial models in sociology [See also 91B72]", "kind": "subject", "parent": "91D", "page": 212 }, { "code": "91D30", "originalCode": "91D30", "name": "Social networks; opinion dynamics", "description": "Social networks; opinion dynamics", "kind": "subject", "parent": "91D", "page": 212 }, { "code": "91D35", "originalCode": "91D35", "name": "Manpower systems in sociology", "description": "Manpower systems in sociology [See also 90B70, 91B39]", "kind": "subject", "parent": "91D", "page": 212 }, { "code": "91D99", "originalCode": "91D99", "name": "Mathematical sociology (including anthropology)", "description": "None of the above, but in this section", "kind": "subject", "parent": "91D", "page": 212 }, { "code": "91E", "originalCode": "91Exx", "name": "Mathematical psychology", "description": "Mathematical psychology \\{For psychometrics, see 62P15\\}", "kind": "section", "parent": "91", "page": 212 }, { "code": "91E10", "originalCode": "91E10", "name": "Cognitive psychology", "description": "Cognitive psychology", "kind": "subject", "parent": "91E", "page": 212 }, { "code": "91E30", "originalCode": "91E30", "name": "Psychophysics and psychophysiology; perception", "description": "Psychophysics and psychophysiology; perception", "kind": "subject", "parent": "91E", "page": 212 }, { "code": "91E40", "originalCode": "91E40", "name": "Memory and learning in psychology", "description": "Memory and learning in psychology [See also 68T05]", "kind": "subject", "parent": "91E", "page": 212 }, { "code": "91E45", "originalCode": "91E45", "name": "Measurement and performance in psychology", "description": "Measurement and performance in psychology", "kind": "subject", "parent": "91E", "page": 212 }, { "code": "91E99", "originalCode": "91E99", "name": "Mathematical psychology", "description": "None of the above, but in this section", "kind": "subject", "parent": "91E", "page": 212 }, { "code": "91F", "originalCode": "91Fxx", "name": "Other social and behavioral sciences (mathematical treatment)", "description": "Other social and behavioral sciences (mathematical treatment)", "kind": "section", "parent": "91", "page": 212 }, { "code": "91F10", "originalCode": "91F10", "name": "History, political science", "description": "History, political science", "kind": "subject", "parent": "91F", "page": 212 }, { "code": "91F20", "originalCode": "91F20", "name": "Linguistics", "description": "Linguistics [See also 03B65, 68T50]", "kind": "subject", "parent": "91F", "page": 212 }, { "code": "91F99", "originalCode": "91F99", "name": "Other social and behavioral sciences (mathematical treatment)", "description": "None of the above, but in this section", "kind": "subject", "parent": "91F", "page": 212 }, { "code": "91G", "originalCode": "91Gxx", "name": "Actuarial science and mathematical finance", "description": "Actuarial science and mathematical finance \\{For statistics, see 62P05\\}", "kind": "section", "parent": "91", "page": 212 }, { "code": "91G05", "originalCode": "91G05", "name": "Actuarial mathematics", "description": "Actuarial mathematics", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G10", "originalCode": "91G10", "name": "Portfolio theory", "description": "Portfolio theory", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G15", "originalCode": "91G15", "name": "Financial markets", "description": "Financial markets", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G20", "originalCode": "91G20", "name": "Derivative securities (option pricing, hedging, etc.)", "description": "Derivative securities (option pricing, hedging, etc.)", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G30", "originalCode": "91G30", "name": "Interest rates, asset pricing, etc. (stochastic models)", "description": "Interest rates, asset pricing, etc. (stochastic models)", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G40", "originalCode": "91G40", "name": "Credit risk", "description": "Credit risk", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G45", "originalCode": "91G45", "name": "Financial networks (including contagion, systemic risk, regulation)", "description": "Financial networks (including contagion, systemic risk, regulation)", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G50", "originalCode": "91G50", "name": "Corporate finance (dividends, real options, etc.)", "description": "Corporate finance (dividends, real options, etc.)", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G60", "originalCode": "91G60", "name": "Numerical methods (including Monte Carlo methods)", "description": "Numerical methods (including Monte Carlo methods)", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G70", "originalCode": "91G70", "name": "Statistical methods; risk measures", "description": "Statistical methods; risk measures [See also 62P05, 62P20]", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G80", "originalCode": "91G80", "name": "Financial applications of other theories", "description": "Financial applications of other theories [See also 35Q91, 37N40, 49N90, 60J70, 60K10, 60H30, 93E20]", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "91G99", "originalCode": "91G99", "name": "Actuarial science and mathematical finance", "description": "None of the above, but in this section", "kind": "subject", "parent": "91G", "page": 212 }, { "code": "92", "originalCode": "92-XX", "name": "Biology and other natural sciences", "description": "Biology and other natural sciences", "kind": "class", "parent": null, "page": 213 }, { "code": "92-00", "originalCode": "92-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to biology", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-01", "originalCode": "92-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-02", "originalCode": "92-02", "name": "Research exposition (monographs, survey articles) pertaining to biology", "description": "Research exposition (monographs, survey articles) pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-03", "originalCode": "92-03", "name": "History of biology", "description": "History of biology [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-04", "originalCode": "92-04", "name": "Software, source code, etc. for problems pertaining to biology", "description": "Software, source code, etc. for problems pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-05", "originalCode": "92-05", "name": "Experimental work for problems pertaining to biology", "description": "Experimental work for problems pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-06", "originalCode": "92-06", "name": "Proceedings, conferences, collections, etc. pertaining to biology", "description": "Proceedings, conferences, collections, etc. pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-08", "originalCode": "92-08", "name": "Computational methods for problems pertaining to biology", "description": "Computational methods for problems pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-10", "originalCode": "92-10", "name": "Mathematical modeling or simulation for problems pertaining to biology", "description": "Mathematical modeling or simulation for problems pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92-11", "originalCode": "92-11", "name": "Research data for problems pertaining to biology", "description": "Research data for problems pertaining to biology", "kind": "subject", "parent": "92", "page": 213 }, { "code": "92B", "originalCode": "92Bxx", "name": "Mathematical biology in general", "description": "Mathematical biology in general", "kind": "section", "parent": "92", "page": 213 }, { "code": "92B05", "originalCode": "92B05", "name": "General biology and biomathematics", "description": "General biology and biomathematics", "kind": "subject", "parent": "92B", "page": 213 }, { "code": "92B10", "originalCode": "92B10", "name": "Taxonomy, cladistics, statistics in mathematical biology", "description": "Taxonomy, cladistics, statistics in mathematical biology", "kind": "subject", "parent": "92B", "page": 213 }, { "code": "92B15", "originalCode": "92B15", "name": "General biostatistics", "description": "General biostatistics [See also 62P10]", "kind": "subject", "parent": "92B", "page": 213 }, { "code": "92B20", "originalCode": "92B20", "name": "Neural networks for/in biological studies, artificial life and related topics", "description": "Neural networks for/in biological studies, artificial life and related topics [See also 68T05, 82C32, 94Cxx]", "kind": "subject", "parent": "92B", "page": 213 }, { "code": "92B25", "originalCode": "92B25", "name": "Biological rhythms and synchronization", "description": "Biological rhythms and synchronization", "kind": "subject", "parent": "92B", "page": 213 }, { "code": "92B99", "originalCode": "92B99", "name": "Mathematical biology in general", "description": "None of the above, but in this section", "kind": "subject", "parent": "92B", "page": 213 }, { "code": "92C", "originalCode": "92Cxx", "name": "Physiological, cellular and medical topics", "description": "Physiological, cellular and medical topics", "kind": "section", "parent": "92", "page": 213 }, { "code": "92C05", "originalCode": "92C05", "name": "Biophysics", "description": "Biophysics", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C10", "originalCode": "92C10", "name": "Biomechanics", "description": "Biomechanics [See also 74L15]", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C15", "originalCode": "92C15", "name": "Developmental biology, pattern formation", "description": "Developmental biology, pattern formation", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C17", "originalCode": "92C17", "name": "Cell movement (chemotaxis, etc.)", "description": "Cell movement (chemotaxis, etc.)", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C20", "originalCode": "92C20", "name": "Neural biology", "description": "Neural biology", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C30", "originalCode": "92C30", "name": "Physiology (general)", "description": "Physiology (general)", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C32", "originalCode": "92C32", "name": "Pathology, pathophysiology", "description": "Pathology, pathophysiology", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C35", "originalCode": "92C35", "name": "Physiological flow", "description": "Physiological flow [See also 76Z05]", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C37", "originalCode": "92C37", "name": "Cell biology", "description": "Cell biology", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C40", "originalCode": "92C40", "name": "Biochemistry, molecular biology", "description": "Biochemistry, molecular biology", "kind": "subject", "parent": "92C", "page": 213 }, { "code": "92C42", "originalCode": "92C42", "name": "Systems biology, networks", "description": "Systems biology, networks", "kind": "subject", "parent": "92C", "page": 213 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"code": "92D10", "originalCode": "92D10", "name": "Genetics and epigenetics", "description": "Genetics and epigenetics \\{For genetic algebras, see 17D92\\}", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92D15", "originalCode": "92D15", "name": "Problems related to evolution", "description": "Problems related to evolution", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92D20", "originalCode": "92D20", "name": "Protein sequences, DNA sequences", "description": "Protein sequences, DNA sequences", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92D25", "originalCode": "92D25", "name": "Population dynamics (general)", "description": "Population dynamics (general)", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92D30", "originalCode": "92D30", "name": "Epidemiology", "description": "Epidemiology \\{For medical applications, see 92C60\\}", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92D40", "originalCode": "92D40", "name": "Ecology", "description": "Ecology", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92D45", "originalCode": "92D45", "name": "Pest management", "description": "Pest management", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92D50", "originalCode": "92D50", "name": "Animal behavior", "description": "Animal behavior", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92D99", "originalCode": "92D99", "name": "Genetics and population dynamics", "description": "None of the above, but in this section", "kind": "subject", "parent": "92D", "page": 214 }, { "code": "92E", "originalCode": "92Exx", "name": "Chemistry", "description": "Chemistry \\{For biochemistry, see 92C40\\}", "kind": "section", "parent": "92", "page": 214 }, { "code": "92E10", "originalCode": "92E10", "name": "Molecular structure (graph-theoretic methods, methods of differential topology, etc.)", "description": "Molecular structure (graph-theoretic methods, methods of differential topology, etc.) [See also 05C92]", "kind": "subject", "parent": "92E", "page": 214 }, { "code": "92E20", "originalCode": "92E20", "name": "Classical flows, reactions, etc. in chemistry", "description": "Classical flows, reactions, etc. in chemistry [See also 80A30, 80A32]", "kind": "subject", "parent": "92E", "page": 214 }, { "code": "92E99", "originalCode": "92E99", "name": "Chemistry", "description": "None of the above, but in this section", "kind": "subject", "parent": "92E", "page": 214 }, { "code": "92F", "originalCode": "92Fxx", "name": "Other natural sciences (mathematical treatment)", "description": "Other natural sciences (mathematical treatment)", "kind": "section", "parent": "92", "page": 214 }, { "code": "92F05", "originalCode": "92F05", "name": "Other natural sciences (mathematical treatment)", "description": "Other natural sciences (mathematical treatment)", "kind": "subject", "parent": "92F", "page": 214 }, { "code": "92F99", "originalCode": "92F99", 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"subject", "parent": "93", "page": 214 }, { "code": "93-02", "originalCode": "93-02", "name": "Research exposition (monographs, survey articles) pertaining to systems and control theory", "description": "Research exposition (monographs, survey articles) pertaining to systems and control theory", "kind": "subject", "parent": "93", "page": 214 }, { "code": "93-03", "originalCode": "93-03", "name": "History of systems and control theory", "description": "History of systems and control theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "93", "page": 214 }, { "code": "93-04", "originalCode": "93-04", "name": "Software, source code, etc. for problems pertaining to systems and control theory", "description": "Software, source code, etc. for problems pertaining to systems and control theory", "kind": "subject", "parent": "93", "page": 214 }, { "code": "93-05", "originalCode": "93-05", "name": "Experimental work for problems pertaining to systems and 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"name": "Decentralized systems", "description": "Decentralized systems", "kind": "subject", "parent": "93A", "page": 215 }, { "code": "93A15", "originalCode": "93A15", "name": "Large-scale systems", "description": "Large-scale systems", "kind": "subject", "parent": "93A", "page": 215 }, { "code": "93A16", "originalCode": "93A16", "name": "Multi-agent systems", "description": "Multi-agent systems", "kind": "subject", "parent": "93A", "page": 215 }, { "code": "93A99", "originalCode": "93A99", "name": "General systems theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "93A", "page": 215 }, { "code": "93B", "originalCode": "93Bxx", "name": "Controllability, observability, and system structure", "description": "Controllability, observability, and system structure", "kind": "section", "parent": "93", "page": 215 }, { "code": "93B03", "originalCode": "93B03", "name": "Attainable sets, reachability", "description": "Attainable sets, reachability", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B05", "originalCode": "93B05", "name": "Controllability", "description": "Controllability", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B07", "originalCode": "93B07", "name": "Observability", "description": "Observability", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B10", "originalCode": "93B10", "name": "Canonical structure", "description": "Canonical structure", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B11", "originalCode": "93B11", "name": "System structure simplification", "description": "System structure simplification", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B12", "originalCode": "93B12", "name": "Variable structure systems", "description": "Variable structure systems", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B15", "originalCode": "93B15", "name": "Realizations from input-output data", "description": "Realizations from input-output data", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B17", "originalCode": "93B17", "name": "Transformations", "description": "Transformations", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B18", "originalCode": "93B18", "name": "Linearizations", "description": "Linearizations", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B20", "originalCode": "93B20", "name": "Minimal systems representations", "description": "Minimal systems representations", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B24", "originalCode": "93B24", "name": "Topological methods", "description": "Topological methods", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B25", "originalCode": "93B25", "name": "Algebraic methods", "description": "Algebraic methods", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B27", "originalCode": "93B27", "name": "Geometric methods", "description": 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"originalCode": "93B47", "name": "Iterative learning control", "description": "Iterative learning control", "kind": "subject", "parent": "93B", "page": 215 }, { "code": "93B50", "originalCode": "93B50", "name": "Synthesis problems", "description": "Synthesis problems", "kind": "subject", "parent": "93B", "page": 216 }, { "code": "93B51", "originalCode": "93B51", "name": "Design techniques (robust design, computer-aided design, etc.)", "description": "Design techniques (robust design, computer-aided design, etc.)", "kind": "subject", "parent": "93B", "page": 216 }, { "code": "93B52", "originalCode": "93B52", "name": "Feedback control", "description": "Feedback control", "kind": "subject", "parent": "93B", "page": 216 }, { "code": "93B53", "originalCode": "93B53", "name": "Observers", "description": "Observers", "kind": "subject", "parent": "93B", "page": 216 }, { "code": "93B55", "originalCode": "93B55", "name": "Pole and zero placement problems", "description": "Pole and zero placement problems", "kind": "subject", "parent": "93B", "page": 216 }, { "code": "93B60", "originalCode": "93B60", "name": "Eigenvalue problems", "description": "Eigenvalue problems", "kind": "subject", "parent": "93B", "page": 216 }, { "code": "93B70", "originalCode": "93B70", "name": "Networked control", "description": "Networked control", "kind": "subject", "parent": "93B", "page": 216 }, { "code": "93B99", "originalCode": "93B99", "name": "Controllability, observability, and system structure", "description": "None of the above, but in this section", "kind": "subject", "parent": "93B", "page": 216 }, { "code": "93C", "originalCode": "93Cxx", "name": "Model systems in control theory", "description": "Model systems in control theory", "kind": "section", "parent": "93", "page": 216 }, { "code": "93C05", "originalCode": "93C05", "name": "Linear systems in control theory", "description": "Linear systems in control theory", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C10", "originalCode": "93C10", "name": "Nonlinear systems in control theory", "description": "Nonlinear systems in control theory", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C15", "originalCode": "93C15", "name": "Control/observation systems governed by ordinary differential equations", "description": "Control/observation systems governed by ordinary differential equations [See also 34Hxx]", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C20", "originalCode": "93C20", "name": "Control/observation systems governed by partial differential equations", "description": "Control/observation systems governed by partial differential equations", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C23", "originalCode": "93C23", "name": "Control/observation systems governed by functional-differential equations", "description": "Control/observation systems governed by functional-differential equations [See also 34K35]", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C25", "originalCode": "93C25", "name": "Control/observation systems in abstract spaces", "description": "Control/observation systems in abstract spaces", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C27", "originalCode": "93C27", "name": "Impulsive control/observation systems", "description": "Impulsive control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C28", "originalCode": "93C28", "name": "Positive control/observation systems", "description": "Positive control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C29", "originalCode": "93C29", "name": "Boolean control/observation systems", "description": "Boolean control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C30", "originalCode": "93C30", "name": "Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)", "description": "Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C35", "originalCode": "93C35", "name": "Multivariable systems, multidimensional control systems", "description": "Multivariable systems, multidimensional control systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C40", "originalCode": "93C40", "name": "Adaptive control/observation systems", "description": "Adaptive control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C41", "originalCode": "93C41", "name": "Control/observation systems with incomplete information", "description": "Control/observation systems with incomplete information", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C42", "originalCode": "93C42", "name": "Fuzzy control/observation systems", "description": "Fuzzy control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C43", "originalCode": "93C43", "name": "Delay control/observation systems", "description": "Delay control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C55", "originalCode": "93C55", "name": "Discrete-time control/observation systems", "description": "Discrete-time control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C57", "originalCode": "93C57", "name": "Sampled-data control/observation systems", "description": "Sampled-data control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C62", "originalCode": "93C62", "name": "Digital control/observation systems", "description": "Digital control/observation systems", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C65", "originalCode": "93C65", "name": "Discrete event control/observation 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involving computers (process control, etc.)", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C85", "originalCode": "93C85", "name": "Automated systems (robots, etc.) in control theory", "description": "Automated systems (robots, etc.) in control theory [See also 68T40, 70B15, 70Q05]", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C95", "originalCode": "93C95", "name": "Application models in control theory", "description": "Application models in control theory", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93C99", "originalCode": "93C99", "name": "Model systems in control theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "93C", "page": 216 }, { "code": "93D", "originalCode": "93Dxx", "name": "Stability of control systems", "description": "Stability of control systems", "kind": "section", "parent": "93", "page": 217 }, { "code": "93D05", "originalCode": "93D05", "name": "Lyapunov and other 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"93D", "page": 217 }, { "code": "93D21", "originalCode": "93D21", "name": "Adaptive or robust stabilization", "description": "Adaptive or robust stabilization", "kind": "subject", "parent": "93D", "page": 217 }, { "code": "93D23", "originalCode": "93D23", "name": "Exponential stability", "description": "Exponential stability", "kind": "subject", "parent": "93D", "page": 217 }, { "code": "93D25", "originalCode": "93D25", "name": "Input-output approaches in control theory", "description": "Input-output approaches in control theory", "kind": "subject", "parent": "93D", "page": 217 }, { "code": "93D30", "originalCode": "93D30", "name": "Lyapunov and storage functions", "description": "Lyapunov and storage functions", "kind": "subject", "parent": "93D", "page": 217 }, { "code": "93D40", "originalCode": "93D40", "name": "Finite-time stability", "description": "Finite-time stability", "kind": "subject", "parent": "93D", "page": 217 }, { "code": "93D50", "originalCode": "93D50", "name": "Consensus", "description": "Consensus", "kind": "subject", "parent": "93D", "page": 217 }, { "code": "93D99", "originalCode": "93D99", "name": "Stability of control systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "93D", "page": 217 }, { "code": "93E", "originalCode": "93Exx", "name": "Stochastic systems and control", "description": "Stochastic systems and control", "kind": "section", "parent": "93", "page": 217 }, { "code": "93E03", "originalCode": "93E03", "name": "Stochastic systems in control theory (general)", "description": "Stochastic systems in control theory (general)", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E10", "originalCode": "93E10", "name": "Estimation and detection in stochastic control theory", "description": "Estimation and detection in stochastic control theory [See also 60G35]", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E11", "originalCode": "93E11", "name": "Filtering in stochastic control theory", "description": "Filtering in stochastic control theory [See also 60G35]", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E12", "originalCode": "93E12", "name": "Identification in stochastic control theory", "description": "Identification in stochastic control theory", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E14", "originalCode": "93E14", "name": "Data smoothing in stochastic control theory", "description": "Data smoothing in stochastic control theory", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E15", "originalCode": "93E15", "name": "Stochastic stability in control theory", "description": "Stochastic stability in control theory", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E20", "originalCode": "93E20", "name": "Optimal stochastic control", "description": "Optimal stochastic control [See also 49J55, 49K45]", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E24", "originalCode": "93E24", "name": "Least squares and related methods for stochastic control systems", "description": "Least squares and related methods for stochastic control systems", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E35", "originalCode": "93E35", "name": "Stochastic learning and adaptive control", "description": "Stochastic learning and adaptive control", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "93E99", "originalCode": "93E99", "name": "Stochastic systems and control", "description": "None of the above, but in this section", "kind": "subject", "parent": "93E", "page": 217 }, { "code": "94", "originalCode": "94-XX", "name": "Information and communication theory, circuits", "description": "Information and communication theory, circuits", "kind": "class", "parent": null, "page": 217 }, { "code": "94-00", "originalCode": "94-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to information and communication theory", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 217 }, { "code": "94-01", "originalCode": "94-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 217 }, { "code": "94-02", "originalCode": "94-02", "name": "Research exposition (monographs, survey articles) pertaining to information and communication theory", "description": "Research exposition (monographs, survey articles) pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 217 }, { "code": "94-03", "originalCode": "94-03", "name": "History of information and communication theory", "description": "History of information and communication theory [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "94", "page": 217 }, { "code": "94-04", "originalCode": "94-04", "name": "Software, source code, etc. for problems pertaining to information and communication theory", "description": "Software, source code, etc. for problems pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 217 }, { "code": "94-05", "originalCode": "94-05", "name": "Experimental work for problems pertaining to information and communication theory", "description": "Experimental work for problems pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 217 }, { "code": "94-06", "originalCode": "94-06", "name": "Proceedings, conferences, collections, etc. pertaining to information and communication theory", "description": "Proceedings, conferences, collections, etc. pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 218 }, { "code": "94-08", "originalCode": "94-08", "name": "Computational methods for problems pertaining to information and communication theory", "description": "Computational methods for problems pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 218 }, { "code": "94-10", "originalCode": "94-10", "name": "Mathematical modeling or simulation for problems pertaining to information and communication theory", "description": "Mathematical modeling or simulation for problems pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 218 }, { "code": "94-11", "originalCode": "94-11", "name": "Research data for problems pertaining to information and communication theory", "description": "Research data for problems pertaining to information and communication theory", "kind": "subject", "parent": "94", "page": 218 }, { "code": "94A", "originalCode": "94Axx", "name": "Communication, information", "description": "Communication, information", "kind": "section", "parent": "94", "page": 218 }, { "code": "94A05", "originalCode": "94A05", "name": "Communication theory", "description": "Communication theory [See also 60G35, 90B18]", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A08", "originalCode": "94A08", "name": "Image processing (compression, reconstruction, etc.) in information and communication theory", "description": "Image processing (compression, reconstruction, etc.) in information and communication theory [See also 68U10]", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A11", "originalCode": "94A11", "name": "Application of orthogonal and other special functions", "description": "Application of orthogonal and other special functions", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A12", "originalCode": "94A12", "name": "Signal theory (characterization, reconstruction, filtering, etc.)", "description": "Signal theory (characterization, reconstruction, filtering, etc.)", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A13", "originalCode": "94A13", "name": "Detection theory in information and communication theory", "description": "Detection theory in information and communication theory", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A14", "originalCode": "94A14", "name": "Modulation and demodulation in information and communication theory", "description": "Modulation and demodulation in information and communication theory", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A15", "originalCode": "94A15", "name": "Information theory (general)", "description": "Information theory (general) [See also 62B10] \\{For quantum-theoretic aspects, see also 81P45\\}", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A16", "originalCode": "94A16", "name": "Informational aspects of data analysis and big data", "description": "Informational aspects of data analysis and big data [See also 62R07, 68T09] \\{For homological aspects, see 55N31\\}", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A17", "originalCode": "94A17", "name": "Measures of information, entropy", "description": "Measures of information, entropy [See also 62B10]", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A20", "originalCode": "94A20", "name": "Sampling theory in information and communication theory", "description": "Sampling theory in information and communication theory", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A24", "originalCode": "94A24", "name": "Coding theorems (Shannon theory)", "description": "Coding theorems (Shannon theory)", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A29", "originalCode": "94A29", "name": "Source coding", "description": "Source coding [See also 68P30]", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A34", "originalCode": "94A34", "name": "Rate-distortion theory in information and communication theory", "description": "Rate-distortion theory in information and communication theory", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A40", "originalCode": "94A40", "name": "Channel models (including quantum) in information and communication theory", "description": "Channel models (including quantum) in information and communication theory [See also 81P47]", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A45", "originalCode": "94A45", "name": "Prefix, length-variable, comma-free codes", "description": "Prefix, length-variable, comma-free codes [See also 20M35, 68Q45]", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A50", "originalCode": "94A50", "name": "Theory of questionnaires", "description": "Theory of questionnaires", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A55", "originalCode": "94A55", "name": "Shift register sequences and sequences over finite alphabets in information and communication theory", "description": "Shift register sequences and sequences over finite alphabets in information and communication theory", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A60", "originalCode": "94A60", "name": "Cryptography", "description": "Cryptography [See also 11T71, 14G50, 68P25, 81P94]", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A62", "originalCode": "94A62", "name": "Authentication, digital signatures and secret sharing", "description": "Authentication, digital signatures and secret sharing", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94A99", "originalCode": "94A99", "name": "Communication, information", "description": "None of the above, but in this section", "kind": "subject", "parent": "94A", "page": 218 }, { "code": "94B", "originalCode": "94Bxx", "name": "Theory of error-correcting codes and error-detecting codes", "description": "Theory of error-correcting codes and error-detecting codes", "kind": "section", "parent": "94", "page": 218 }, { "code": "94B05", "originalCode": "94B05", "name": "Linear codes (general theory)", "description": "Linear codes (general theory)", "kind": "subject", "parent": "94B", "page": 218 }, { "code": "94B10", "originalCode": "94B10", "name": "Convolutional codes", "description": "Convolutional codes", "kind": "subject", "parent": "94B", "page": 218 }, { "code": "94B12", "originalCode": "94B12", "name": "Combined modulation schemes (including trellis codes) in coding theory", "description": "Combined modulation schemes (including trellis codes) in coding theory", "kind": "subject", "parent": "94B", "page": 218 }, { "code": "94B15", "originalCode": "94B15", "name": "Cyclic codes", "description": "Cyclic codes", "kind": "subject", "parent": "94B", "page": 218 }, { "code": "94B20", "originalCode": "94B20", "name": "Burst-correcting codes", "description": "Burst-correcting codes", "kind": "subject", "parent": "94B", "page": 218 }, { "code": "94B25", "originalCode": "94B25", "name": "Combinatorial codes", "description": "Combinatorial codes", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B27", "originalCode": "94B27", "name": "Geometric methods (including applications of algebraic geometry) applied to coding theory", "description": "Geometric methods (including applications of algebraic geometry) applied to coding theory [See also 11T71, 14G50]", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B30", "originalCode": "94B30", "name": "Majority codes", "description": "Majority codes", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B35", "originalCode": "94B35", "name": "Decoding", "description": "Decoding", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B40", "originalCode": "94B40", "name": "Arithmetic codes", "description": "Arithmetic codes [See also 11T71, 14G50]", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B50", "originalCode": "94B50", "name": "Synchronization error-correcting codes", "description": "Synchronization error-correcting codes", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B60", "originalCode": "94B60", "name": "Other types of codes", "description": "Other types of codes", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B65", "originalCode": "94B65", "name": "Bounds on codes", "description": "Bounds on codes", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B70", "originalCode": "94B70", "name": "Error probability in coding theory", "description": "Error probability in coding theory", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B75", "originalCode": "94B75", "name": "Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory", "description": "Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory [See also 11H31, 11H71]", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94B99", "originalCode": "94B99", "name": "Theory of error-correcting codes and error-detecting codes", "description": "None of the above, but in this section", "kind": "subject", "parent": "94B", "page": 219 }, { "code": "94C", "originalCode": "94Cxx", "name": "Circuits, networks", "description": "Circuits, networks [See also 68Q06]", "kind": "section", "parent": "94", "page": 219 }, { "code": "94C05", "originalCode": "94C05", "name": "Analytic circuit theory", "description": "Analytic circuit theory", "kind": "subject", "parent": "94C", "page": 219 }, { "code": "94C11", "originalCode": "94C11", "name": "Switching theory, applications of Boolean algebras to circuits and networks", "description": "Switching theory, applications of Boolean algebras to circuits and networks", "kind": "subject", "parent": "94C", "page": 219 }, { "code": "94C12", "originalCode": "94C12", "name": "Fault detection; testing in circuits and networks", "description": "Fault detection; testing in circuits and networks", "kind": "subject", "parent": "94C", "page": 219 }, { "code": "94C15", "originalCode": "94C15", "name": "Applications of graph theory to circuits and networks", "description": "Applications of graph theory to circuits and networks [See also 05Cxx, 68R10]", "kind": "subject", "parent": "94C", "page": 219 }, { "code": "94C30", "originalCode": "94C30", "name": "Applications of design theory to circuits and networks", "description": "Applications of design theory to circuits and networks [See also 05Bxx]", "kind": "subject", "parent": "94C", "page": 219 }, { "code": "94C60", "originalCode": "94C60", "name": "Circuits in qualitative investigation and simulation of models", "description": "Circuits in qualitative investigation and simulation of models", "kind": "subject", "parent": "94C", "page": 219 }, { "code": "94C99", "originalCode": "94C99", "name": "Circuits, networks", "description": "None of the above, but in this section", "kind": "subject", "parent": "94C", "page": 219 }, { "code": "94D", "originalCode": "94Dxx", "name": "Miscellaneous topics in information and communication theory", "description": "Miscellaneous topics in information and communication theory", "kind": "section", "parent": "94", "page": 219 }, { "code": "94D05", "originalCode": "94D05", "name": "Fuzzy sets and logic (in connection with information, communication, or circuits theory)", "description": "Fuzzy sets and logic (in connection with information, communication, or circuits theory) [See also 03B52, 03E72, 28E10]", "kind": "subject", "parent": "94D", "page": 219 }, { "code": "94D10", "originalCode": "94D10", "name": "Boolean functions", "description": "Boolean functions [See also 06E30] \\{For connections with circuits and networks, see 94C11\\}", "kind": "subject", "parent": "94D", "page": 219 }, { "code": "94D99", "originalCode": "94D99", "name": "Miscellaneous topics in information and communication theory", "description": "None of the above, but in this section", "kind": "subject", "parent": "94D", "page": 219 }, { "code": "97", "originalCode": "97-XX", "name": "Mathematics education", "description": "Mathematics education", "kind": "class", "parent": null, "page": 219 }, { "code": "97-00", "originalCode": "97-00", "name": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematics education", "description": "General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematics education", "kind": "subject", "parent": "97", "page": 219 }, { "code": "97-01", "originalCode": "97-01", "name": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education", "description": "Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education", "kind": "subject", "parent": "97", "page": 219 }, { "code": "97-02", "originalCode": "97-02", "name": "Research exposition (monographs, survey articles) pertaining to mathematics education", "description": "Research exposition (monographs, survey articles) pertaining to mathematics education", "kind": "subject", "parent": "97", "page": 219 }, { "code": "97-03", "originalCode": "97-03", "name": "History of mathematics education", "description": "History of mathematics education [Consider also classification numbers from Section 01-XX]", "kind": "subject", "parent": "97", "page": 219 }, { "code": "97-06", "originalCode": "97-06", "name": "Proceedings, conferences, collections, etc. pertaining to mathematics education", "description": "Proceedings, conferences, collections, etc. pertaining to mathematics education", "kind": "subject", "parent": "97", "page": 219 }, { "code": "97-11", "originalCode": "97-11", "name": "Research data for problems pertaining to mathematics education", "description": "Research data for problems pertaining to mathematics education", "kind": "subject", "parent": "97", "page": 219 }, { "code": "97A", "originalCode": "97Axx", "name": "History and society (aspects of mathematics education)", "description": "History and society (aspects of mathematics education)", "kind": "section", "parent": "97", "page": 220 }, { "code": "97A30", "originalCode": "97A30", "name": "History in mathematics education", "description": "History in mathematics education \\{For mathematics history, see 01-XX; for biographies, see 01A70; for history of mathematics education, see 97-03\\}", "kind": "subject", "parent": "97A", "page": 220 }, { "code": "97A40", "originalCode": "97A40", "name": "Mathematics education and society", "description": "Mathematics education and society \\{For sociology (and profession) of mathematics, see 01A80\\}", "kind": "subject", "parent": "97A", "page": 220 }, { "code": "97A99", "originalCode": "97A99", "name": "History and society (aspects of mathematics education)", "description": "None of the above, but in this section", "kind": "subject", "parent": "97A", "page": 220 }, { "code": "97B", "originalCode": "97Bxx", "name": "Educational policy and systems", "description": "Educational policy and systems", "kind": "section", "parent": "97", "page": 220 }, { "code": "97B10", "originalCode": "97B10", "name": "Mathematics educational research and planning", "description": "Mathematics educational research and planning", "kind": "subject", "parent": "97B", "page": 220 }, { "code": "97B20", "originalCode": "97B20", "name": "Educational policy for general education", "description": "Educational policy for general education", "kind": "subject", "parent": "97B", "page": 220 }, { "code": "97B30", "originalCode": "97B30", "name": "Educational policy for vocational education", "description": "Educational policy for vocational education", "kind": "subject", "parent": "97B", "page": 220 }, { "code": "97B40", "originalCode": "97B40", "name": "Educational policy for higher education", "description": "Educational policy for higher education", "kind": "subject", "parent": "97B", "page": 220 }, { "code": "97B50", "originalCode": "97B50", "name": "Mathematics teacher education", "description": "Mathematics teacher education", "kind": "subject", "parent": "97B", "page": 220 }, { "code": "97B60", "originalCode": "97B60", "name": "Educational policy for adult and further education", "description": "Educational policy for adult and further education", "kind": "subject", "parent": "97B", "page": 220 }, { "code": "97B70", "originalCode": "97B70", "name": "Syllabuses, educational standards", "description": "Syllabuses, educational standards", "kind": "subject", "parent": "97B", "page": 220 }, { "code": "97B99", "originalCode": "97B99", "name": "Educational policy and systems", "description": "None of the above, but in this section", "kind": "subject", "parent": "97B", "page": 220 }, { "code": "97C", "originalCode": "97Cxx", "name": "Psychology of mathematics education, research in mathematics education", "description": "Psychology of mathematics education, research in mathematics education", "kind": "section", "parent": "97", "page": 220 }, { "code": "97C10", "originalCode": "97C10", "name": "Comprehensive works on psychology of mathematics education", "description": "Comprehensive works on psychology of mathematics education", "kind": "subject", "parent": "97C", "page": 220 }, { "code": "97C20", "originalCode": "97C20", "name": "Affective behavior and mathematics education", "description": "Affective behavior and mathematics education", "kind": "subject", "parent": "97C", "page": 220 }, { "code": "97C30", "originalCode": "97C30", "name": "Cognitive processes, learning theories (aspects of mathematics education)", "description": "Cognitive processes, learning theories (aspects of mathematics education)", "kind": "subject", "parent": "97C", "page": 220 }, { "code": "97C40", "originalCode": "97C40", "name": "Intelligence and aptitudes (aspects of mathematics education)", "description": "Intelligence and aptitudes (aspects of mathematics education)", "kind": "subject", "parent": "97C", "page": 220 }, { "code": "97C50", "originalCode": "97C50", "name": "Language and verbal communities (aspects of mathematics education)", "description": "Language and verbal communities (aspects of mathematics education)", "kind": "subject", "parent": "97C", "page": 220 }, { "code": "97C60", "originalCode": "97C60", "name": "Sociological aspects of learning (aspects of mathematics education)", "description": "Sociological aspects of learning (aspects of mathematics education)", "kind": "subject", "parent": "97C", "page": 220 }, { "code": "97C70", "originalCode": "97C70", "name": "Teaching-learning processes in mathematics education", "description": "Teaching-learning processes in mathematics education", "kind": "subject", "parent": "97C", "page": 220 }, { "code": "97C99", "originalCode": "97C99", "name": "Psychology of mathematics education, research in mathematics education", "description": "None of the above, but in this section", "kind": "subject", "parent": "97C", "page": 220 }, { "code": "97D", "originalCode": "97Dxx", "name": "Education and instruction in mathematics", "description": "Education and instruction in mathematics", "kind": "section", "parent": "97", "page": 220 }, { "code": "97D10", "originalCode": "97D10", "name": "Comprehensive works and comparative studies on education and instruction in mathematics", "description": "Comprehensive works and comparative studies on education and instruction in mathematics", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97D20", "originalCode": "97D20", "name": "Philosophical and theoretical contributions (didactics of mathematics)", "description": "Philosophical and theoretical contributions (didactics of mathematics)", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97D30", "originalCode": "97D30", "name": "Objectives and goals of mathematics teaching", "description": "Objectives and goals of mathematics teaching", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97D40", "originalCode": "97D40", "name": "Mathematics teaching methods and classroom techniques", "description": "Mathematics teaching methods and classroom techniques", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97D50", "originalCode": "97D50", "name": "Teaching mathematical problem solving and heuristic strategies", "description": "Teaching mathematical problem solving and heuristic strategies", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97D60", "originalCode": "97D60", "name": "Student assessment, achievement control, and rating (aspects of mathematics education)", "description": "Student assessment, achievement control, and rating (aspects of mathematics education)", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97D70", "originalCode": "97D70", "name": "Learning difficulties and student errors (aspects of mathematics education)", "description": "Learning difficulties and student errors (aspects of mathematics education)", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97D80", "originalCode": "97D80", "name": "Mathematics teaching units and draft lessons", "description": "Mathematics teaching units and draft lessons", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97D99", "originalCode": "97D99", "name": "Education and instruction in mathematics", "description": "None of the above, but in this section", "kind": "subject", "parent": "97D", "page": 220 }, { "code": "97E", "originalCode": "97Exx", "name": "Education of foundations of mathematics", "description": "Education of foundations of mathematics", "kind": "section", "parent": "97", "page": 221 }, { "code": "97E10", "originalCode": "97E10", "name": "Comprehensive works on education of foundations of mathematics", "description": "Comprehensive works on education of foundations of 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