% 
%
%     The following skeleton TeX header can be adapted
%     to produce output in a desired layout or used
%     "as is"
%
%
\vsize=9in
\hsize=4in
\vbadness=10000

% Special definitions 
 
\def\cprime{$'$}
\def\mod{\rm mod}
\def\scr{\rm }

% Baseline definitions

\rightskip=0pt plus 1in
\hyphenpenalty=10000 
\interlinepenalty=10000
\overfullrule=0pt
\parskip=0pt

\catcode`\@=11
\chardef\gtr=`> 	
\chardef\less=`<
\def \SbjD@shKern{\kern.025em }
%	Suppress ordinary kerning around level 2 character.
\def \SbjNo #1#2#3#4#5{#1#2{}%
	\if #3-\SbjD@shKern--\SbjD@shKern \else #3\fi
	{}\if #4+\if #3-XX\else xx\fi
	  \else #4#5\fi }
%	Note -- #3 tested twice instead of setting a switch and testing that;


\def\fixedspaceskip{\spaceskip.3333em \xspaceskip.5em }

% Special macros

\def \CMPonly #1{\unskip}
\def \ExtraText{}
\def \FullScheme{\unskip\ }
\def \See #1{[See~#1\unskip.]}
\def \SeeAlso #1{\Se@Also{#1}}
\def \Se@Also #1{[See~also~#1\unskip]}
\def \SeeFor #1{\Se@For{#1}}
% \def \Se@For #1{$\{$#1\unskip.$\}$}
\def \lbr@ce{$\delimiter"4266308 $}
\def \rbr@ce{$\delimiter"5267309 $}
\def \Se@For #1{\lbr@ce#1\unskip\rbr@ce}
\def \SeeMainly #1{[See~mainly~#1\unskip]}


%			`boiler-plate' text

%	sub-level -01
\def \Handbooks{Handbooks, dictionaries, and other reference works}

%	sub-level -01
\def \ElementaryExposition{Elementary exposition; textbooks}

%	sub-level -02
\def \AdvancedExposition{Advanced exposition
		(research surveys, monographs,~etc.)}

%	sub-level -03
\def \Historical{Historical (must also be assigned at least
		one classification number from Section 01)}

%	sub-level -04
\def \ExplicitComputation{Explicit machine computation and programs
		(not~the~theory of computation or programming)}

%	sub-level -06
\def \Proceedings{Proceedings, conferences, etc.}

%	sub-level x99
\def \NoneOfAbove{None of the above, but in this section}
\def \Miscellaneous{Miscellaneous topics }

\newtoks\SbjT@ks		% current subject code
\SbjT@ks={00-XX}

% Example macros for setting major headings

\newdimen\lowlevelindent \lowlevelindent=8pt
\newdimen\leftcolwd \leftcolwd=60pt

\def\MajorSub#1\SubText#2\endx{\vskip 8pt plus 3pt minus 2pt
  \begingroup\bf
  \hangindent=\leftcolwd
  \noindent\hbox to \leftcolwd{#1\hss}%
  #2\par
  \endgroup
}

\def\SecndLvl#1\SubText#2\endx{\vskip 5pt plus 2pt minus 1pt
  \begingroup\bf
  \hangindent=\leftcolwd
  \noindent\hbox to \leftcolwd{\kern\lowlevelindent #1\hss}%
  #2\par
  \endgroup
}

\def\ThirdLvl#1\SubText#2\endx{\par
  \hangindent=\leftcolwd
  \noindent\hbox to \leftcolwd{\kern\lowlevelindent #1\hss}%
  #2\par
}

%
%
% 
%
%
 
\MajorSub 00-++\SubText General\endx
% 
%
%     The following skeleton TeX header can be adapted
%     to produce output in a desired layout or used
%     "as is"
%
%
\vsize=9in
\hsize=4in
\vbadness=10000

% Special definitions 
 
\def\cprime{$'$}
\def\mod{\rm mod}
\def\scr{\rm }

% Baseline definitions

\rightskip=0pt plus 1in
\hyphenpenalty=10000 
\interlinepenalty=10000
\overfullrule=0pt
\parskip=0pt

\catcode`\@=11
\chardef\gtr=`> 	
\chardef\less=`<
\def \SbjD@shKern{\kern.025em }
%	Suppress ordinary kerning around level 2 character.
\def \SbjNo #1#2#3#4#5{#1#2{}%
	\if #3-\SbjD@shKern--\SbjD@shKern \else #3\fi
	{}\if #4+\if #3-XX\else xx\fi
	  \else #4#5\fi }
%	Note -- #3 tested twice instead of setting a switch and testing that;


\def\fixedspaceskip{\spaceskip.3333em \xspaceskip.5em }

% Special macros

\def \CMPonly #1{\unskip}
\def \ExtraText{}
\def \FullScheme{\unskip\ }
\def \See #1{[See~#1\unskip.]}
\def \SeeAlso #1{\Se@Also{#1}}
\def \Se@Also #1{[See~also~#1\unskip]}
\def \SeeFor #1{\Se@For{#1}}
% \def \Se@For #1{$\{$#1\unskip.$\}$}
\def \lbr@ce{$\delimiter"4266308 $}
\def \rbr@ce{$\delimiter"5267309 $}
\def \Se@For #1{\lbr@ce#1\unskip\rbr@ce}
\def \SeeMainly #1{[See~mainly~#1\unskip]}


%			`boiler-plate' text

%	sub-level -01
\def \Handbooks{Handbooks, dictionaries, and other reference works}

%	sub-level -01
\def \ElementaryExposition{Elementary exposition; textbooks}

%	sub-level -02
\def \AdvancedExposition{Advanced exposition
		(research surveys, monographs,~etc.)}

%	sub-level -03
\def \Historical{Historical (must also be assigned at least
		one classification number from Section 01)}

%	sub-level -04
\def \ExplicitComputation{Explicit machine computation and programs
		(not~the~theory of computation or programming)}

%	sub-level -06
\def \Proceedings{Proceedings, conferences, etc.}

%	sub-level x99
\def \NoneOfAbove{None of the above, but in this section}
\def \Miscellaneous{Miscellaneous topics }

\newtoks\SbjT@ks		% current subject code
\SbjT@ks={00-XX}

% Example macros for setting major headings

\newdimen\lowlevelindent \lowlevelindent=8pt
\newdimen\leftcolwd \leftcolwd=60pt

\def\MajorSub#1\SubText#2\endx{\vskip 8pt plus 3pt minus 2pt
  \begingroup\bf
  \hangindent=\leftcolwd
  \noindent\hbox to \leftcolwd{#1\hss}%
  #2\par
  \endgroup
}

\def\SecndLvl#1\SubText#2\endx{\vskip 5pt plus 2pt minus 1pt
  \begingroup\bf
  \hangindent=\leftcolwd
  \noindent\hbox to \leftcolwd{\kern\lowlevelindent #1\hss}%
  #2\par
  \endgroup
}

\def\ThirdLvl#1\SubText#2\endx{\par
  \hangindent=\leftcolwd
  \noindent\hbox to \leftcolwd{\kern\lowlevelindent #1\hss}%
  #2\par
}

%
%
% 
%
%
 
\MajorSub 00-++\SubText General\endx
\ThirdLvl 00-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 00-02\SubText Research exposition (monographs, survey
 articles)\endx
\SecndLvl 00A++\SubText General and miscellaneous specific topics\endx 
\ThirdLvl 00A05\SubText General mathematics\endx
\ThirdLvl 00A06\SubText Mathematics for nonmathematicians
 (engineering, social sciences, etc.)\endx
\ThirdLvl 00A07\SubText Problem books\endx
\ThirdLvl 00A08\SubText Recreational mathematics\endx
\ThirdLvl 00A15\SubText Bibliographies\endx
\ThirdLvl 00A20\SubText Dictionaries and other general reference
 works\endx
\ThirdLvl 00A22\SubText Formularies\endx
\ThirdLvl 00A30\SubText Philosophy of mathematics \SeeAlso{\SbjNo
 03A05}\endx
\ThirdLvl 00A35\SubText Methodology of mathematics, didactics\endx
\ThirdLvl 00A69\SubText General applied mathematics \SeeFor{For
 physics, see \SbjNo 00A79 and Sections 70 through 86}\endx
\ThirdLvl 00A71\SubText Theory of mathematical modeling\endx
\ThirdLvl 00A72\SubText General methods of simulation\endx
\ThirdLvl 00A73\SubText Dimensional analysis\endx
\ThirdLvl 00A79\SubText Physics (use more specific entries from
 Sections 70 through 86 when possible)\endx
\ThirdLvl 00A99\SubText \Miscellaneous\endx
\SecndLvl 00B++\SubText Conference proceedings and collections of
 papers\endx
\ThirdLvl 00B05\SubText Collections of abstracts of lectures\endx
\ThirdLvl 00B10\SubText Collections of articles of general
 interest\endx
\ThirdLvl 00B15\SubText Collections of articles of miscellaneous
 specific content\endx
\ThirdLvl 00B20\SubText Proceedings of conferences of general
 interest\endx
\ThirdLvl 00B25\SubText Proceedings of conferences of miscellaneous
 specific interest\endx
\ThirdLvl 00B30\SubText Festschriften\endx
\ThirdLvl 00B50\SubText Volumes of selected translations\endx
\ThirdLvl 00B55\SubText Miscellaneous volumes of translations\endx
\ThirdLvl 00B60\SubText Collections of reprinted articles
 \SeeAlso{\SbjNo 01A75}\endx
\MajorSub 01-++\SubText History and biography \FullScheme{\SeeAlso{the
 classification number --03 in the other sections}}\endx
\ThirdLvl 01-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 01-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 01-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 01-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 01-08\SubText Computational methods\endx
\SecndLvl 01A++\SubText History of mathematics and mathematicians\endx
\ThirdLvl 01A05\SubText General histories, source books\endx
\ThirdLvl 01A07\SubText Ethnomathematics, general\endx
\ThirdLvl 01A10\SubText Paleolithic, Neolithic\endx
\ThirdLvl 01A12\SubText Indigenous cultures of the Americas\endx
\ThirdLvl 01A13\SubText Other indigenous cultures (non-European)\endx
\ThirdLvl 01A15\SubText Indigenous European cultures (pre-Greek,
 etc.)\endx
\ThirdLvl 01A16\SubText Egyptian\endx
\ThirdLvl 01A17\SubText Babylonian\endx
\ThirdLvl 01A20\SubText Greek, Roman\endx
\ThirdLvl 01A25\SubText China\endx
\ThirdLvl 01A27\SubText Japan\endx
\ThirdLvl 01A29\SubText Southeast Asia\endx
\ThirdLvl 01A30\SubText Islam (Medieval)\endx
\ThirdLvl 01A32\SubText India\endx
\ThirdLvl 01A35\SubText Medieval\endx
\ThirdLvl 01A40\SubText 15th and 16th centuries, Renaissance\endx
\ThirdLvl 01A45\SubText 17th century\endx
\ThirdLvl 01A50\SubText 18th century\endx
\ThirdLvl 01A55\SubText 19th century\endx
\ThirdLvl 01A60\SubText 20th century\endx
\ThirdLvl 01A65\SubText Contemporary\endx
\ThirdLvl 01A67\SubText Future prospectives\endx
\ThirdLvl 01A70\SubText Biographies, obituaries, personalia,
 bibliographies\endx
\ThirdLvl 01A72\SubText Schools of mathematics\endx
\ThirdLvl 01A73\SubText Universities\endx
\ThirdLvl 01A74\SubText Other institutions and academies\endx
\ThirdLvl 01A75\SubText Collected or selected works; reprintings or
 translations of classics \SeeAlso{\SbjNo 00B60}\endx
\ThirdLvl 01A80\SubText Sociology (and profession) of mathematics\endx
\ThirdLvl 01A99\SubText \Miscellaneous\endx
\MajorSub 03-++\SubText Mathematical logic and foundations\endx
\ThirdLvl 03-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 03-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 03-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 03-03\SubText \Historical\endx
\ThirdLvl 03-04\SubText \ExplicitComputation\endx
\ThirdLvl 03-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 03A05\SubText Philosophical and critical \SeeFor{For
 philosophy of mathematics, see \SbjNo 00A30}\endx
\SecndLvl 03B++\SubText General logic\endx
\ThirdLvl 03B05\SubText Classical propositional logic\endx
\ThirdLvl 03B10\SubText Classical first-order logic\endx
\ThirdLvl 03B15\SubText Higher-order logic and type-theory\endx
\ThirdLvl 03B20\SubText Subsystems of classical logic (including
 intuitionistic logic)\endx
\ThirdLvl 03B22\SubText Abstract deductive systems\endx
\ThirdLvl 03B25\SubText Decidability of theories and sets of sentences
 \SeeAlso{\SbjNo 11U05, \SbjNo 12L05, \SbjNo 20F10}\endx
\ThirdLvl 03B30\SubText Foundations and axiomatics of classical
 theories\endx
\ThirdLvl 03B35\SubText Mechanization of proofs and logical operations
 \SeeAlso{\SbjNo 68T15}\endx
\ThirdLvl 03B40\SubText Combinatory logic and $\lambda$-calculus\endx
\ThirdLvl 03B45\SubText Modal and tense logic \SeeFor{For provability
 logics, see also \SbjNo 03F40}\endx
\ThirdLvl 03B46\SubText Relevance and entailment\endx
\ThirdLvl 03B48\SubText Probability and inductive logic
 \SeeAlso{\SbjNo 60A05}\endx
\ThirdLvl 03B50\SubText Many-valued logic\endx
\ThirdLvl 03B52\SubText Fuzzy logic \SeeAlso{\SbjNo 94D05}\endx
\ThirdLvl 03B53\SubText Paraconsistent logic\endx
\ThirdLvl 03B55\SubText Intermediate logics\endx
\ThirdLvl 03B60\SubText Other nonclassical logic\endx
\ThirdLvl 03B65\SubText Logic of natural languages \SeeAlso{\SbjNo
 68S05, \SbjNo 92K20}\endx
\ThirdLvl 03B70\SubText Logic of programming \SeeAlso{\SbjNo 68Q55,
 \SbjNo 68Q60}\endx
\ThirdLvl 03B80\SubText Other applications of logic\endx
\ThirdLvl 03B99\SubText \NoneOfAbove\endx
\SecndLvl 03C++\SubText Model theory\endx
\ThirdLvl 03C05\SubText Equational classes, universal algebra
 \SeeAlso{\SbjNo 08Axx}\endx
\ThirdLvl 03C07\SubText Basic properties of first-order languages and
 structures\endx
\ThirdLvl 03C10\SubText Quantifier elimination and related topics\endx
\ThirdLvl 03C13\SubText Finite structures\endx
\ThirdLvl 03C15\SubText Denumerable structures\endx
\ThirdLvl 03C20\SubText Ultraproducts and related constructions\endx
\ThirdLvl 03C25\SubText Model-theoretic forcing\endx
\ThirdLvl 03C30\SubText Other model constructions\endx
\ThirdLvl 03C35\SubText Categoricity and completeness of theories\endx
\ThirdLvl 03C40\SubText Interpolation, preservation, definability\endx
\ThirdLvl 03C45\SubText Stability and related concepts\endx
\ThirdLvl 03C50\SubText Models with special properties (saturated,
 rigid, etc.)\endx
\ThirdLvl 03C52\SubText Properties of classes of models\endx
\ThirdLvl 03C55\SubText Set-theoretic model theory\endx
\ThirdLvl 03C57\SubText Recursion-theoretic model theory
 \SeeAlso{\SbjNo 03D45}\endx
\ThirdLvl 03C60\SubText Model-theoretic algebra \SeeAlso{\SbjNo 08C10,
 \SbjNo 12Lxx, \SbjNo 13L05}\endx
\ThirdLvl 03C62\SubText Models of arithmetic and set theory
 \SeeAlso{\SbjNo 03Hxx}\endx
\ThirdLvl 03C65\SubText Models of other mathematical theories\endx
\ThirdLvl 03C68\SubText Other classical first-order model theory\endx
\ThirdLvl 03C70\SubText Logic on admissible sets\endx
\ThirdLvl 03C75\SubText Other infinitary logic\endx
\ThirdLvl 03C80\SubText Logic with extra quantifiers and operators
 \SeeAlso{\SbjNo 03B45}\endx
\ThirdLvl 03C85\SubText Second- and higher-order model theory\endx
\ThirdLvl 03C90\SubText Nonclassical models (Boolean-valued, sheaf,
 etc.)\endx
\ThirdLvl 03C95\SubText Abstract model theory\endx
\ThirdLvl 03C99\SubText \NoneOfAbove\endx
\SecndLvl 03D++\SubText Recursion theory\endx
\ThirdLvl 03D03\SubText Thue and Post systems, etc.\endx
\ThirdLvl 03D05\SubText Automata and formal grammars in connection
 with logical questions \SeeAlso{\SbjNo 68Qxx}\endx
\ThirdLvl 03D10\SubText Turing machines and related notions
 \SeeAlso{\SbjNo 68Q05}\endx
\ThirdLvl 03D15\SubText Complexity of computation \SeeAlso{\SbjNo
 68Q15}\endx
\ThirdLvl 03D20\SubText Recursive functions and relations,
 subrecursive hierarchies\endx
\ThirdLvl 03D25\SubText Recursively enumerable sets and degrees\endx
\ThirdLvl 03D30\SubText Other degrees; reducibilities\endx
\ThirdLvl 03D35\SubText Undecidability and degrees of sets of
 sentences\endx
\ThirdLvl 03D40\SubText Word problems, etc. \SeeAlso{\SbjNo 06B25,
 \SbjNo 08A50, \SbjNo 20F10}\endx
\ThirdLvl 03D45\SubText Theory of numerations, effectively presented
 structures \SeeAlso{\SbjNo 03C57}\endx
\ThirdLvl 03D50\SubText Recursive equivalence types of sets and
 structures, isols\endx
\ThirdLvl 03D55\SubText Hierarchies\endx
\ThirdLvl 03D60\SubText Recursion theory on ordinals, admissible sets,
 etc.\endx
\ThirdLvl 03D65\SubText Higher-type and set recursion theory\endx
\ThirdLvl 03D70\SubText Inductive definability\endx
\ThirdLvl 03D75\SubText Abstract and axiomatic recursion theory\endx
\ThirdLvl 03D80\SubText Applications of recursion theory\endx
\ThirdLvl 03D99\SubText \NoneOfAbove\endx
\SecndLvl 03E++\SubText Set theory \SeeAlso{\SbjNo 04-XX}\endx
\ThirdLvl 03E05\SubText Combinatorial set theory \SeeAlso{\SbjNo
 04A20}\endx
\ThirdLvl 03E10\SubText Ordinal and cardinal numbers \SeeAlso{\SbjNo
 04A10}\endx
\ThirdLvl 03E15\SubText Descriptive set theory \SeeAlso{\SbjNo 04A15,
 \SbjNo 28A05, \SbjNo 54H05}\endx
\ThirdLvl 03E20\SubText Other classical set theory\endx
\ThirdLvl 03E25\SubText Axiom of choice and related propositions
 \SeeAlso{\SbjNo 04A25}\endx
\ThirdLvl 03E30\SubText Axiomatics of classical set theory and its
 fragments\endx
\ThirdLvl 03E35\SubText Consistency and independence results\endx
\ThirdLvl 03E40\SubText Other aspects of forcing and Boolean-valued
 models\endx
\ThirdLvl 03E45\SubText Constructibility, ordinal definability, and
 related notions\endx
\ThirdLvl 03E47\SubText Other notions of set-theoretic
 definability\endx
\ThirdLvl 03E50\SubText Continuum hypothesis and Martin's axiom
 \SeeAlso{\SbjNo 04A30, \SbjNo 54A25}\endx
\ThirdLvl 03E55\SubText Large cardinals\endx
\ThirdLvl 03E60\SubText Determinacy and related principles which
 contradict the axiom of choice\endx
\ThirdLvl 03E65\SubText Other hypotheses and axioms\endx
\ThirdLvl 03E70\SubText Nonclassical and second-order set
 theories\endx
\ThirdLvl 03E72\SubText Fuzzy sets \SeeMainly{\SbjNo 04A72}\endx
\ThirdLvl 03E75\SubText Applications\endx
\ThirdLvl 03E99\SubText \NoneOfAbove\endx
\SecndLvl 03F++\SubText Proof theory and constructive mathematics\endx
\ThirdLvl 03F03\SubText Proof theory, general\endx
\ThirdLvl 03F05\SubText Cut-elimination and normal-form theorems\endx
\ThirdLvl 03F07\SubText Structure of proofs\endx
\ThirdLvl 03F10\SubText Functionals in proof theory\endx
\ThirdLvl 03F15\SubText Recursive ordinals and ordinal notations\endx
\ThirdLvl 03F20\SubText Complexity of proofs\endx
\ThirdLvl 03F25\SubText Relative consistency and interpretations\endx
\ThirdLvl 03F30\SubText First-order arithmetic and fragments\endx
\ThirdLvl 03F35\SubText Second- and higher-order arithmetic and
 fragments \SeeAlso{\SbjNo 03E30, \SbjNo 03E70}\endx
\ThirdLvl 03F40\SubText G\"odel numberings in proof theory\endx
\ThirdLvl 03F50\SubText Metamathematics of constructive systems\endx
\ThirdLvl 03F55\SubText Intuitionistic mathematics\endx
\ThirdLvl 03F60\SubText Constructive and recursive analysis
 \SeeAlso{\SbjNo 26E40, \SbjNo 46S30, \SbjNo 47S30}\endx
\ThirdLvl 03F65\SubText Other constructive mathematics \SeeAlso{\SbjNo
 26E40, \SbjNo 46S30, \SbjNo 47S30}\endx
\ThirdLvl 03F99\SubText \NoneOfAbove\endx
\SecndLvl 03G++\SubText Algebraic logic\endx
\ThirdLvl 03G05\SubText Boolean algebras \SeeAlso{\SbjNo 06Exx}\endx
\ThirdLvl 03G10\SubText Lattices and related structures
 \SeeAlso{\SbjNo 06Bxx}\endx
\ThirdLvl 03G12\SubText Quantum logic \SeeAlso{\SbjNo 81P10}\endx
\ThirdLvl 03G15\SubText Cylindric and polyadic algebras; relation
 algebras\endx
\ThirdLvl 03G20\SubText \L ukasiewicz and Post algebras
 \SeeAlso{\SbjNo 06D25, \SbjNo 06D30}\endx
\ThirdLvl 03G25\SubText Other algebras related to logic
 \SeeAlso{\SbjNo 06F35}\endx
\ThirdLvl 03G30\SubText Categorical logic, topoi \SeeAlso{\SbjNo
 18B25}\endx
\ThirdLvl 03G99\SubText \NoneOfAbove\endx
\SecndLvl 03H++\SubText Nonstandard models \SeeAlso{\SbjNo 03C62}\endx
\ThirdLvl 03H05\SubText Nonstandard models in mathematics
 \SeeAlso{\SbjNo 26E35, \SbjNo 28E05, \SbjNo 30G06, \SbjNo 46S20,
 \SbjNo 47S20, \SbjNo 54J05}\endx
\ThirdLvl 03H10\SubText Other applications of nonstandard models
 (economics, physics, etc.)\endx
\ThirdLvl 03H15\SubText Nonstandard models of arithmetic
 \SeeAlso{\SbjNo 11U10, \SbjNo 12L15, \SbjNo 13L05}\endx
\ThirdLvl 03H99\SubText \NoneOfAbove\endx
\MajorSub 04-++\SubText Set theory \SeeAlso{\SbjNo 03Exx}\endx
\ThirdLvl 04-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 04-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 04-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 04-03\SubText \Historical\endx
\ThirdLvl 04-04\SubText \ExplicitComputation\endx
\ThirdLvl 04-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 04A03\SubText Set algebra\endx
\ThirdLvl 04A05\SubText Relations, functions \SeeAlso{\SbjNo
 08A02}\endx
\ThirdLvl 04A10\SubText Ordinal and cardinal numbers; generalizations
 \SeeAlso {\SbjNo 03E10}\endx
\ThirdLvl 04A15\SubText Descriptive set theory; Borel classifications,
 Suslin schemes, etc. \SeeAlso{\SbjNo 03E15, \SbjNo 26A21, \SbjNo
 28A05, \SbjNo 54H05}\endx
\ThirdLvl 04A20\SubText Combinatorial set theory \SeeAlso{\SbjNo
 03E05, \SbjNo 05A05}; filters\endx
\ThirdLvl 04A25\SubText Axiom of choice and equivalent propositions
 (Zorn's lemma, etc.) \SeeAlso{\SbjNo 03E25}\endx
\ThirdLvl 04A30\SubText Continuum hypothesis, generalized continuum
 hypothesis \SeeAlso{\SbjNo 03E50, \SbjNo 54A25}\endx
\ThirdLvl 04A72\SubText Fuzzy sets, fuzzy relations \SeeAlso{\SbjNo
 03E72, \SbjNo 94D05} \SeeFor{For fuzzy versions, see specific
 sections}\endx
\ThirdLvl 04A99\SubText \Miscellaneous\endx
\MajorSub 05-++\SubText Combinatorics \SeeFor{For finite fields,
 see~\SbjNo 11Txx}\endx
\ThirdLvl 05-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 05-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 05-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 05-03\SubText \Historical\endx
\ThirdLvl 05-04\SubText \ExplicitComputation\endx
\ThirdLvl 05-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 05A++\SubText Classical combinatorial problems\endx
\ThirdLvl 05A05\SubText Combinatorial choice problems (subsets,
 representatives, permutations)\endx
\ThirdLvl 05A10\SubText Factorials, binomial coefficients,
 combinatorial functions \SeeAlso{\SbjNo 11B65, \SbjNo 33Cxx}\endx
\ThirdLvl 05A15\SubText Exact enumeration problems, generating
 functions \SeeAlso{\SbjNo 33Cxx, \SbjNo 33Dxx}\endx
\ThirdLvl 05A16\SubText Asymptotic enumeration\endx
\ThirdLvl 05A17\SubText Partitions of integers \SeeAlso{\SbjNo 11P81,
 \SbjNo 11P82, \SbjNo 11P83}\endx
\ThirdLvl 05A18\SubText Partitions of sets\endx
\ThirdLvl 05A19\SubText Combinatorial identities\endx
\ThirdLvl 05A20\SubText Combinatorial inequalities\endx
\ThirdLvl 05A30\SubText $q$-calculus and related topics
 \SeeAlso{\SbjNo 03Dxx}\endx
\ThirdLvl 05A40\SubText Umbral calculus\endx
\ThirdLvl 05A99\SubText \NoneOfAbove\endx
\SecndLvl 05B++\SubText Designs and configurations \SeeFor{For
 applications of design theory, see \SbjNo 94C30}\endx
\ThirdLvl 05B05\SubText Block designs \SeeAlso{\SbjNo 51E05, \SbjNo
 62K10}\endx
\ThirdLvl 05B07\SubText Triple systems\endx
\ThirdLvl 05B10\SubText Difference sets (number-theoretic,
 group-theoretic, etc.) \SeeAlso{\SbjNo 11B13}\endx
\ThirdLvl 05B15\SubText Orthogonal arrays, Latin squares, Room
 squares\endx
\ThirdLvl 05B20\SubText Matrices (incidence, Hadamard, etc.)\endx
\ThirdLvl 05B25\SubText Finite geometries \SeeAlso{\SbjNo 51D20,
 \SbjNo 51Exx}\endx
\ThirdLvl 05B30\SubText Other designs, configurations \SeeAlso{\SbjNo
 51E30}\endx
\ThirdLvl 05B35\SubText Matroids, geometric lattices \SeeAlso{\SbjNo
 52B40, \SbjNo 90C27}\endx
\ThirdLvl 05B40\SubText Packing and covering \SeeAlso{\SbjNo 11H31,
 \SbjNo 52C15, \SbjNo 52C17}\endx
\ThirdLvl 05B45\SubText Tessellation and tiling problems
 \SeeAlso{\SbjNo 52C20, \SbjNo 52C22}\endx
\ThirdLvl 05B50\SubText Polyominoes\endx
\ThirdLvl 05B99\SubText \NoneOfAbove\endx
\SecndLvl 05C++\SubText Graph theory \SeeFor{For applications of
 graphs, see \SbjNo 68Q90, \SbjNo 68R10, \SbjNo 90C35, \SbjNo
 94C15}\endx
\ThirdLvl 05C05\SubText Trees\endx
\ThirdLvl 05C10\SubText Topological graph theory, imbedding
 \SeeAlso{\SbjNo 57M15, \SbjNo 57M25}\endx
\ThirdLvl 05C12\SubText Distance in graphs\endx
\ThirdLvl 05C15\SubText Chromatic theory of graphs and maps\endx
\ThirdLvl 05C20\SubText Directed graphs (digraphs), tournaments\endx
\ThirdLvl 05C25\SubText Graphs and groups \SeeAlso{\SbjNo 20F32}\endx
\ThirdLvl 05C30\SubText Enumeration of graphs and maps\endx
\ThirdLvl 05C35\SubText Extremal problems \SeeAlso{\SbjNo 90C35}\endx
\ThirdLvl 05C38\SubText Paths and cycles \SeeAlso{\SbjNo 90B10}\endx
\ThirdLvl 05C40\SubText Connectivity\endx
\ThirdLvl 05C45\SubText Eulerian and Hamiltonian graphs\endx
\ThirdLvl 05C50\SubText Graphs and matrices\endx
\ThirdLvl 05C55\SubText Generalized Ramsey theory\endx
\ThirdLvl 05C60\SubText Isomorphism problems (reconstruction
 conjecture, perfect graphs, etc.)\endx
\ThirdLvl 05C65\SubText Hypergraphs\endx
\ThirdLvl 05C70\SubText Factorization, matching, covering and
 packing\endx
\ThirdLvl 05C75\SubText Structural characterization of types of
 graphs\endx
\ThirdLvl 05C78\SubText Graph labelling (graceful graphs, bandwidth,
 etc.)\endx
\ThirdLvl 05C80\SubText Random graphs\endx
\ThirdLvl 05C85\SubText Graph algorithms \SeeAlso{\SbjNo 68Q20, \SbjNo
 68R10}\endx
\ThirdLvl 05C90\SubText Applications\endx
\ThirdLvl 05C99\SubText \NoneOfAbove\endx
\SecndLvl 05D++\SubText Extremal combinatorics\endx
\ThirdLvl 05D05\SubText Extremal set theory\endx
\ThirdLvl 05D10\SubText Ramsey theory\endx
\ThirdLvl 05D15\SubText Transversal (matching) theory\endx
\ThirdLvl 05D99\SubText \NoneOfAbove\endx
\SecndLvl 05E++\SubText Algebraic combinatorics\endx
\ThirdLvl 05E05\SubText Symmetric functions\endx
\ThirdLvl 05E10\SubText Tableaux, representations of the symmetric
 group \SeeAlso{\SbjNo 20C30}\endx
\ThirdLvl 05E15\SubText Combinatorial problems concerning the
 classical groups \SeeAlso{\SbjNo 22E45, \SbjNo 33C80}\endx
\ThirdLvl 05E20\SubText Group actions on designs, geometries and
 codes\endx
\ThirdLvl 05E25\SubText Group actions on posets and homology groups of
 posets \SeeAlso{\SbjNo 06A09}\endx
\ThirdLvl 05E30\SubText Association schemes, strongly regular
 graphs\endx
\ThirdLvl 05E35\SubText Orthogonal polynomials \SeeAlso{\SbjNo 33C45,
 \SbjNo 33C50, \SbjNo 33D45}\endx
\ThirdLvl 05E99\SubText \NoneOfAbove\endx
\MajorSub 06-++\SubText Order, lattices, ordered algebraic structures
 \SeeAlso{\SbjNo 18B35}\endx
\ThirdLvl 06-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 06-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 06-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 06-03\SubText \Historical\endx
\ThirdLvl 06-04\SubText \ExplicitComputation\endx
\ThirdLvl 06-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 06A++\SubText Ordered sets\endx
\ThirdLvl 06A05\SubText Total order\endx
\ThirdLvl 06A06\SubText Partial order, general\endx
\ThirdLvl 06A07\SubText Combinatorics of partially ordered sets\endx
\ThirdLvl 06A08\SubText Shellable posets, Cohen-Macaulay posets
 \SeeAlso{\SbjNo 52B20}\endx
\ThirdLvl 06A09\SubText Cohomology of posets \SeeAlso{\SbjNo
 05E25}\endx
\ThirdLvl 06A12\SubText Semilattices \SeeAlso{\SbjNo 20M10}\endx
\ThirdLvl 06A15\SubText Galois correspondences, closure operators\endx
\ThirdLvl 06A23\SubText Complete lattices, completions\endx
\ThirdLvl 06A99\SubText \NoneOfAbove\endx
\SecndLvl 06B++\SubText Lattices \SeeAlso{\SbjNo 03G10}\endx
\ThirdLvl 06B05\SubText Structure theory\endx
\ThirdLvl 06B10\SubText Ideals, congruence relations\endx
\ThirdLvl 06B15\SubText Representation theory\endx
\ThirdLvl 06B20\SubText Varieties of lattices\endx
\ThirdLvl 06B25\SubText Free lattices, projective lattices, word
 problems \SeeAlso{\SbjNo 03D40, \SbjNo 08A50, \SbjNo 20F10}\endx
\ThirdLvl 06B30\SubText Topological lattices, order topologies
 \SeeAlso{\SbjNo 06F30, \SbjNo 22A26, \SbjNo 54F05, \SbjNo 54H12}\endx
\ThirdLvl 06B35\SubText Continuous lattices, generalizations,
 applications \SeeAlso{\SbjNo 06B30, \SbjNo 06D10, \SbjNo 06F30,
 \SbjNo 18B35, \SbjNo 22A26, \SbjNo 68Q55}\endx
\ThirdLvl 06B99\SubText \NoneOfAbove\endx
\SecndLvl 06C++\SubText Modular lattices, complemented lattices\endx
\ThirdLvl 06C05\SubText Modular lattices, Desarguesian lattices\endx
\ThirdLvl 06C10\SubText Semimodular lattices, geometric lattices\endx
\ThirdLvl 06C15\SubText Complemented lattices, orthocomplemented
 lattices\endx
\ThirdLvl 06C20\SubText Complemented modular lattices, continuous
 geometries\endx
\ThirdLvl 06C99\SubText \NoneOfAbove\endx
\SecndLvl 06D++\SubText Distributive lattices\endx
\ThirdLvl 06D05\SubText Structure and representation theory\endx
\ThirdLvl 06D10\SubText Complete distributivity\endx
\ThirdLvl 06D15\SubText Pseudocomplemented lattices\endx
\ThirdLvl 06D20\SubText Heyting algebras \SeeAlso{\SbjNo 03Gxx}\endx
\ThirdLvl 06D25\SubText Post algebras \SeeAlso{\SbjNo 03G20}\endx
\ThirdLvl 06D30\SubText De Morgan algebras, \L ukasiewicz algebras
 \SeeAlso{\SbjNo 03G20}\endx
\ThirdLvl 06D99\SubText \NoneOfAbove\endx
\SecndLvl 06E++\SubText Boolean algebras (Boolean rings)
 \SeeAlso{\SbjNo 03G05}\endx
\ThirdLvl 06E05\SubText Structure theory\endx
\ThirdLvl 06E10\SubText Chain conditions, complete algebras\endx
\ThirdLvl 06E15\SubText Stone space and related constructions \endx
\ThirdLvl 06E20\SubText Ring-theoretic properties \SeeAlso{\SbjNo
 16E50, \SbjNo 16G30}\endx
\ThirdLvl 06E25\SubText Boolean algebras with additional operations
 (diagonalizable algebras, etc.)\endx
\ThirdLvl 06E30\SubText Boolean functions \SeeAlso{\SbjNo 94C10}\endx
\ThirdLvl 06E99\SubText \NoneOfAbove\endx
\SecndLvl 06F++\SubText Ordered structures\endx
\ThirdLvl 06F05\SubText Ordered semigroups \SeeAlso{\SbjNo 20Mxx}\endx
\ThirdLvl 06F10\SubText Noether lattices\endx
\ThirdLvl 06F15\SubText Ordered groups \SeeAlso{\SbjNo 20F60}\endx
\ThirdLvl 06F20\SubText Ordered abelian groups, Riesz groups, ordered
 linear spaces \SeeAlso{\SbjNo 46A40}\endx
\ThirdLvl 06F25\SubText Ordered rings, algebras, modules \SeeFor{For
 ordered fields, see \SbjNo 12J15; see also \SbjNo 13J25, \SbjNo
 16W80}\endx
\ThirdLvl 06F30\SubText Topological lattices, order topologies
 \SeeAlso{\SbjNo 06B30, \SbjNo 22A26, \SbjNo 54F05, \SbjNo 54H12}\endx
\ThirdLvl 06F35\SubText BCK-algebras, BCI-algebras \SeeAlso{\SbjNo
 03G25}\endx
\ThirdLvl 06F99\SubText \NoneOfAbove\endx
\MajorSub 08-++\SubText General algebraic systems\endx
\ThirdLvl 08-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 08-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 08-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 08-03\SubText \Historical\endx
\ThirdLvl 08-04\SubText \ExplicitComputation\endx
\ThirdLvl 08-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 08A++\SubText Algebraic structures \SeeAlso{\SbjNo
 03C05}\endx
\ThirdLvl 08A02\SubText Relational systems, laws of composition\endx
\ThirdLvl 08A05\SubText Structure theory\endx
\ThirdLvl 08A30\SubText Subalgebras, congruence relations\endx
\ThirdLvl 08A35\SubText Automorphisms, endomorphisms\endx
\ThirdLvl 08A40\SubText Operations, polynomials, primal algebras\endx
\ThirdLvl 08A45\SubText Equational compactness\endx
\ThirdLvl 08A50\SubText Word problems \SeeAlso{\SbjNo 03D40, \SbjNo
 06B25, \SbjNo 20F10, \SbjNo 68R15}\endx
\ThirdLvl 08A55\SubText Partial algebras\endx
\ThirdLvl 08A60\SubText Unary algebras\endx
\ThirdLvl 08A62\SubText Finitary algebras\endx
\ThirdLvl 08A65\SubText Infinitary algebras\endx
\ThirdLvl 08A70\SubText Applications of universal algebra in computer
 science\endx
\ThirdLvl 08A99\SubText \NoneOfAbove\endx
\SecndLvl 08B++\SubText Varieties\endx
\ThirdLvl 08B05\SubText Equational logic, Mal\cprime cev (Mal\cprime
 tsev) conditions\endx
\ThirdLvl 08B10\SubText Congruence modularity, congruence
 distributivity\endx
\ThirdLvl 08B15\SubText Lattices of varieties\endx
\ThirdLvl 08B20\SubText Free algebras\endx
\ThirdLvl 08B25\SubText Products, amalgamated products, and other
 kinds of limits and colimits \SeeAlso{\SbjNo 18A30}\endx
\ThirdLvl 08B26\SubText Subdirect products and subdirect
 irreducibility\endx
\ThirdLvl 08B30\SubText Injectives, projectives\endx
\ThirdLvl 08B99\SubText \NoneOfAbove\endx
\SecndLvl 08C++\SubText Other classes of algebras\endx
\ThirdLvl 08C05\SubText Categories of algebras \SeeAlso{\SbjNo
 18C05}\endx
\ThirdLvl 08C10\SubText Axiomatic model classes \SeeAlso{\SbjNo 03Cxx,
 in particular \SbjNo 03C60}\endx
\ThirdLvl 08C15\SubText Quasivarieties\endx
\ThirdLvl 08C99\SubText \NoneOfAbove\endx
\MajorSub 11-++\SubText Number theory\endx
\ThirdLvl 11-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 11-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 11-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 11-03\SubText \Historical\endx
\ThirdLvl 11-04\SubText \ExplicitComputation\endx
\ThirdLvl 11-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 11A++\SubText Elementary number theory \SeeFor{For analogues
 in number fields, see \SbjNo 11R04}\endx
\ThirdLvl 11A05\SubText Multiplicative structure; Euclidean algorithm;
 greatest common divisors\endx
\ThirdLvl 11A07\SubText Congruences; primitive roots; residue
 systems\endx
\ThirdLvl 11A15\SubText Power residues, reciprocity\endx
\ThirdLvl 11A25\SubText Arithmetic functions; related numbers;
 inversion formulas\endx
\ThirdLvl 11A41\SubText Primes\endx
\ThirdLvl 11A51\SubText Factorization; primality\endx
\ThirdLvl 11A55\SubText Continued fractions \SeeFor{For approximation
 results, see \SbjNo 11J70; see also \SbjNo 11K50, \SbjNo 30B70,
 \SbjNo 40A15}\endx
\ThirdLvl 11A63\SubText Radix representation; digital problems
 \SeeFor{For metric results, see \SbjNo 11K16}\endx
\ThirdLvl 11A67\SubText Other representations\endx
\ThirdLvl 11A99\SubText \NoneOfAbove\endx
\SecndLvl 11B++\SubText Sequences and sets\endx
\ThirdLvl 11B05\SubText Density, gaps, topology\endx
\ThirdLvl 11B13\SubText Additive bases \SeeAlso{\SbjNo 05B10}\endx
\ThirdLvl 11B25\SubText Arithmetic progressions \SeeAlso{\SbjNo
 11N13}\endx
\ThirdLvl 11B34\SubText Representation functions\endx
\ThirdLvl 11B37\SubText Recurrences \SeeFor{For applications to
 special functions, see \SbjNo 33-XX}\endx
\ThirdLvl 11B39\SubText Fibonacci and Lucas numbers and polynomials
 and generalizations\endx
\ThirdLvl 11B50\SubText Sequences ($\mod m$)\endx
\ThirdLvl 11B57\SubText Farey sequences; the sequences $\{1\sp k, 2\sp
 k, \cdots \}$\endx
\ThirdLvl 11B65\SubText Binomial coefficients; factorials;
 $q$-identities \SeeAlso{\SbjNo 05A10, \SbjNo 05A30}\endx
\ThirdLvl 11B68\SubText Bernoulli and Euler numbers and
 polynomials\endx
\ThirdLvl 11B73\SubText Bell and Stirling numbers\endx
\ThirdLvl 11B75\SubText Other combinatorial number theory\endx
\ThirdLvl 11B83\SubText Special sequences and polynomials\endx
\ThirdLvl 11B85\SubText Automata sequences\endx
\ThirdLvl 11B99\SubText \NoneOfAbove\endx
\SecndLvl 11C++\SubText Polynomials and matrices\endx
\ThirdLvl 11C08\SubText Polynomials \SeeAlso{\SbjNo 13F20}\endx
\ThirdLvl 11C20\SubText Matrices, determinants \SeeAlso{\SbjNo
 15A36}\endx
\ThirdLvl 11C99\SubText \NoneOfAbove\endx
\SecndLvl 11D++\SubText Diophantine equations \SeeAlso{\SbjNo 11Gxx,
 \SbjNo 14Gxx}\endx
\ThirdLvl 11D04\SubText Linear equations\endx
\ThirdLvl 11D09\SubText Quadratic and bilinear equations\endx
\ThirdLvl 11D25\SubText Cubic and quartic equations\endx
\ThirdLvl 11D41\SubText Higher degree equations; Fermat's
 equation\endx
\ThirdLvl 11D57\SubText Multiplicative and norm form equations\endx
\ThirdLvl 11D61\SubText Exponential equations\endx
\ThirdLvl 11D68\SubText Rational numbers as sums of fractions\endx
\ThirdLvl 11D72\SubText Equations in many variables \SeeAlso{\SbjNo
 11P55}\endx
\ThirdLvl 11D75\SubText Diophantine inequalities \SeeAlso{\SbjNo
 11J25}\endx
\ThirdLvl 11D79\SubText Congruences in many variables\endx
\ThirdLvl 11D85\SubText Representation problems \SeeAlso{\SbjNo
 11P55}\endx
\ThirdLvl 11D88\SubText $p$-adic and power series fields\endx
\ThirdLvl 11D99\SubText \NoneOfAbove\endx
\SecndLvl 11E++\SubText Forms and linear algebraic groups
 \SeeAlso{\SbjNo 19Gxx} \SeeFor{For quadratic forms in linear algebra,
 see \SbjNo 15A63}\endx
\ThirdLvl 11E04\SubText Quadratic forms over general fields\endx
\ThirdLvl 11E08\SubText Quadratic forms over local rings and
 fields\endx
\ThirdLvl 11E10\SubText Forms over real fields\endx
\ThirdLvl 11E12\SubText Quadratic forms over global rings and
 fields\endx
\ThirdLvl 11E16\SubText General binary quadratic forms\endx
\ThirdLvl 11E20\SubText General ternary and quaternary quadratic
 forms; forms of more than two variables\endx
\ThirdLvl 11E25\SubText Sums of squares and representations by other
 particular quadratic forms\endx
\ThirdLvl 11E39\SubText Bilinear and Hermitian forms\endx
\ThirdLvl 11E41\SubText Class numbers of quadratic and Hermitian
 forms\endx
\ThirdLvl 11E45\SubText Analytic theory (Epstein zeta functions;
 relations with automorphic forms and functions)\endx
\ThirdLvl 11E57\SubText Classical groups \SeeAlso{\SbjNo 14Lxx, \SbjNo
 20Gxx}\endx
\ThirdLvl 11E70\SubText $K$-theory of quadratic and Hermitian
 forms\endx
\ThirdLvl 11E72\SubText Galois cohomology of linear algebraic groups
 \SeeAlso{\SbjNo 20G10}\endx
\ThirdLvl 11E76\SubText Forms of degree higher than two\endx
\ThirdLvl 11E81\SubText Algebraic theory of quadratic forms; Witt
 groups and rings \SeeAlso{\SbjNo 19G12, \SbjNo 19G24}\endx
\ThirdLvl 11E88\SubText Quadratic spaces; Clifford algebras
 \SeeAlso{\SbjNo 15A63, \SbjNo 15A66}\endx
\ThirdLvl 11E95\SubText $p$-adic theory\endx
\ThirdLvl 11E99\SubText \NoneOfAbove\endx
\SecndLvl 11F++\SubText Discontinuous groups and automorphic forms
 \SeeAlso{\SbjNo 11R39, \SbjNo 11S37, \CMPonly{\SbjNo 14-XX, \SbjNo
 22Exx}\FullScheme{\SbjNo 14Gxx, \SbjNo 14Kxx, \SbjNo 22E50, \SbjNo
 22E55}, \SbjNo 30F35, \SbjNo 32Nxx; for relations with quadratic
 forms, see \SbjNo 11E45}\endx
\ThirdLvl 11F03\SubText Modular and automorphic functions\endx
\ThirdLvl 11F06\SubText Structure of modular groups and
 generalizations; arithmetic groups \SeeAlso{\SbjNo 20H05, \SbjNo
 20H10, \SbjNo 22E40}\endx
\ThirdLvl 11F11\SubText Modular forms, one variable\endx
\ThirdLvl 11F12\SubText Automorphic forms, one variable\endx
\ThirdLvl 11F20\SubText Dedekind eta function, Dedekind sums\endx
\ThirdLvl 11F22\SubText Relationship to Lie algebras and finite simple
 groups\endx
\ThirdLvl 11F25\SubText Hecke-Petersson operators, differential
 operators (one variable)\endx
\ThirdLvl 11F27\SubText Theta series; Weil representation\endx
\ThirdLvl 11F30\SubText Fourier coefficients of automorphic forms\endx
\ThirdLvl 11F32\SubText Modular correspondences, etc.\endx
\ThirdLvl 11F33\SubText Congruences for modular and $p$-adic modular
 forms \SeeAlso{\SbjNo 14G20, \SbjNo 22E50}\endx
\ThirdLvl 11F37\SubText Forms of half-integer weight; nonholomorphic
 modular forms\endx
\ThirdLvl 11F41\SubText Hilbert and Hilbert-Siegel modular groups and
 their modular and automorphic forms; Hilbert modular surfaces
 \SeeAlso{\SbjNo 14J20}\endx
\ThirdLvl 11F46\SubText Siegel modular groups and their modular and
 automorphic forms\endx
\ThirdLvl 11F55\SubText Other groups and their modular and automorphic
 forms (several variables)\endx
\ThirdLvl 11F60\SubText Hecke-Petersson operators, differential
 operators (several variables)\endx
\ThirdLvl 11F66\SubText Dirichlet series and functional equations in
 connection with modular forms\endx
\ThirdLvl 11F67\SubText Special values of automorphic $L$-series,
 periods of modular forms, cohomology, modular symbols\endx
\ThirdLvl 11F70\SubText Representation-theoretic methods; automorphic
 representations over local and global fields\endx
\ThirdLvl 11F72\SubText Spectral theory; Selberg trace formula\endx
\ThirdLvl 11F75\SubText Cohomology of arithmetic groups\endx
\ThirdLvl 11F80\SubText Galois properties\endx
\ThirdLvl 11F85\SubText $p$-adic theory, local fields \SeeAlso{\SbjNo
 14G20, 22E50}\endx
\ThirdLvl 11F99\SubText \NoneOfAbove\endx
\SecndLvl 11G++\SubText Arithmetic algebraic geometry (Diophantine
 geometry) \SeeAlso{\SbjNo 11Dxx, \CMPonly{\SbjNo
 14-XX}\FullScheme{\SbjNo 14Gxx, \SbjNo 14Kxx}}\endx
\ThirdLvl 11G05\SubText Elliptic curves over global fields
 \SeeAlso{\SbjNo 14H52}\endx
\ThirdLvl 11G07\SubText Elliptic curves over local fields
 \SeeAlso{\SbjNo 14G20, \SbjNo 14H52}\endx
\ThirdLvl 11G09\SubText Drinfel\cprime d modules; higher-dimensional
 motives, etc. \SeeAlso{\SbjNo 14L05}\endx
\ThirdLvl 11G10\SubText Abelian varieties of dimension $\gtr \! 1$
 \SeeAlso{\SbjNo 14Kxx}\endx
\ThirdLvl 11G15\SubText Complex multiplication and moduli of abelian
 varieties \SeeAlso{\SbjNo 14K22}\endx
\ThirdLvl 11G16\SubText Elliptic and modular units \SeeAlso{\SbjNo
 11R27}\endx
\ThirdLvl 11G18\SubText Arithmetic aspects of modular and Shimura
 varieties \SeeAlso{\SbjNo 14G35}\endx
\ThirdLvl 11G20\SubText Curves over finite and local fields
 \SeeAlso{\SbjNo 14H25}\endx
\ThirdLvl 11G25\SubText Varieties over finite and local fields
 \SeeAlso{\SbjNo 14G15, \SbjNo 14G20}\endx
\ThirdLvl 11G30\SubText Curves of arbitrary genus or genus $\ne 1$
 over global fields \SeeAlso{\SbjNo 14H25}\endx
\ThirdLvl 11G35\SubText Varieties over global fields \SeeAlso{\SbjNo
 14G25}\endx
\ThirdLvl 11G40\SubText $L$-functions of varieties over global fields;
 Birch-Swinnerton-Dyer conjecture \SeeAlso{\SbjNo 14G10}\endx
\ThirdLvl 11G45\SubText Geometric class field theory \SeeAlso{\SbjNo
 11R37, \SbjNo 14C35, \SbjNo 19F05}\endx
\ThirdLvl 11G99\SubText \NoneOfAbove\endx
\SecndLvl 11H++\SubText Geometry of numbers \SeeFor{For applications
 in coding theory, see \SbjNo 94B75}\endx
\ThirdLvl 11H06\SubText Lattices and convex bodies \SeeAlso{\SbjNo
 11P21, \SbjNo 52C05, \SbjNo 52C07}\endx
\ThirdLvl 11H16\SubText Nonconvex bodies\endx
\ThirdLvl 11H31\SubText Lattice packing and covering \SeeAlso{\SbjNo
 05B40, \SbjNo 52C15, \SbjNo 52C17}\endx
\ThirdLvl 11H46\SubText Products of linear forms\endx
\ThirdLvl 11H50\SubText Minima of forms\endx
\ThirdLvl 11H55\SubText Quadratic forms (reduction theory, extreme
 forms, etc.)\endx
\ThirdLvl 11H56\SubText Automorphism groups of lattices\endx
\ThirdLvl 11H60\SubText Mean value and transfer theorems\endx
\ThirdLvl 11H99\SubText \NoneOfAbove\endx
\SecndLvl 11J++\SubText Diophantine approximation, transcendental
 number theory \SeeAlso{\SbjNo 11K60}\endx
\ThirdLvl 11J04\SubText Homogeneous approximation to one number\endx
\ThirdLvl 11J06\SubText Markov and Lagrange spectra and
 generalizations\endx
\ThirdLvl 11J13\SubText Simultaneous homogeneous approximation, linear
 forms\endx
\ThirdLvl 11J17\SubText Approximation by numbers from a fixed
 field\endx
\ThirdLvl 11J20\SubText Inhomogeneous linear forms\endx
\ThirdLvl 11J25\SubText Diophantine inequalities \SeeAlso{\SbjNo
 11D75}\endx
\ThirdLvl 11J54\SubText Small fractional parts of polynomials and
 generalizations\endx
\ThirdLvl 11J61\SubText Approximation in non-Archimedean
 valuations\endx
\ThirdLvl 11J68\SubText Approximation to algebraic numbers\endx
\ThirdLvl 11J70\SubText Continued fractions and generalizations
 \SeeAlso{\SbjNo 11A55, \SbjNo 11K50}\endx
\ThirdLvl 11J71\SubText Distribution modulo one \SeeAlso{\SbjNo
 11K06}\endx
\ThirdLvl 11J72\SubText Irrationality; linear independence over a
 field\endx
\ThirdLvl 11J81\SubText Transcendence (general theory)\endx
\ThirdLvl 11J82\SubText Measures of irrationality and of transcendence
 \endx
\ThirdLvl 11J83\SubText Metric theory\endx
\ThirdLvl 11J85\SubText Algebraic independence; Gel\cprime fond's
 method\endx
\ThirdLvl 11J86\SubText Linear forms in logarithms; Baker's
 method\endx
\ThirdLvl 11J89\SubText Transcendence theory of elliptic and abelian
 functions\endx
\ThirdLvl 11J91\SubText Transcendence theory of other special
 functions\endx
\ThirdLvl 11J99\SubText \NoneOfAbove\endx
\SecndLvl 11K++\SubText Probabilistic theory: distribution modulo $1$;
 metric theory of algorithms\endx
\ThirdLvl 11K06\SubText General theory of distribution modulo $1$
 \SeeAlso{\SbjNo 11J71}\endx
\ThirdLvl 11K16\SubText Normal numbers, radix expansions, etc.
 \SeeAlso{\SbjNo 11A63}\endx
\ThirdLvl 11K31\SubText Special sequences\endx
\ThirdLvl 11K36\SubText Well-distributed sequences and other
 variations\endx
\ThirdLvl 11K38\SubText Irregularities of distribution, discrepancy
 \SeeAlso{\SbjNo 11Nxx}\endx
\ThirdLvl 11K41\SubText Continuous, $p$-adic and abstract
 analogues\endx
\ThirdLvl 11K45\SubText Pseudo-random numbers; Monte Carlo
 methods\endx
\ThirdLvl 11K50\SubText Metric theory of continued fractions
 \SeeAlso{\SbjNo 11A55, \SbjNo 11J70}\endx
\ThirdLvl 11K55\SubText Metric theory of other algorithms and
 expansions; measure and Hausdorff dimension \SeeAlso{\SbjNo 11N99,
 \SbjNo 28Dxx}\endx
\ThirdLvl 11K60\SubText Diophantine approximation \SeeAlso{\SbjNo
 11Jxx}\endx
\ThirdLvl 11K65\SubText Arithmetic functions \SeeAlso{\SbjNo
 11Nxx}\endx
\ThirdLvl 11K70\SubText Harmonic analysis and almost periodicity\endx
\ThirdLvl 11K99\SubText \NoneOfAbove\endx
\SecndLvl 11L++\SubText Exponential sums and character sums
 \SeeFor{For finite fields, see \SbjNo 11Txx}\endx
\ThirdLvl 11L03\SubText Trigonometric and exponential sums,
 general\endx
\ThirdLvl 11L05\SubText Gauss and Kloosterman sums;
 generalizations\endx
\ThirdLvl 11L07\SubText Estimates on exponential sums\endx
\ThirdLvl 11L10\SubText Jacobsthal and Brewer sums; other complete
 character sums\endx
\ThirdLvl 11L15\SubText Weyl sums\endx
\ThirdLvl 11L20\SubText Sums over primes\endx
\ThirdLvl 11L26\SubText Sums over arbitrary intervals\endx
\ThirdLvl 11L40\SubText Estimates on character sums\endx
\ThirdLvl 11L99\SubText \NoneOfAbove\endx
\SecndLvl 11M++\SubText Zeta and $L$-functions: analytic theory\endx
\ThirdLvl 11M06\SubText $\zeta (s)$ and $L(s, \chi)$\endx
\ThirdLvl 11M20\SubText Real zeros of $L(s, \chi)$; results on $L(1,
 \chi)$\endx
\ThirdLvl 11M26\SubText Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$;
 Riemann and other hypotheses\endx
\ThirdLvl 11M35\SubText Hurwitz and Lerch zeta functions\endx
\ThirdLvl 11M41\SubText Other Dirichlet series and zeta functions
 \SeeFor{For local and global ground fields, see \SbjNo 11R42, \SbjNo
 11R52, \SbjNo 11S40, \SbjNo 11S45; for algebro-geometric methods, see
 \SbjNo 14G10; %\endx
see also \SbjNo 11E45, \SbjNo 11F66, \SbjNo 11F70, \SbjNo 11F72}\endx
\ThirdLvl 11M45\SubText Tauberian theorems \SeeAlso{\SbjNo 40E05}\endx
\ThirdLvl 11M99\SubText \NoneOfAbove\endx
\SecndLvl 11N++\SubText Multiplicative number theory\endx
\ThirdLvl 11N05\SubText Distribution of primes\endx
\ThirdLvl 11N13\SubText Primes in progressions \SeeAlso{\SbjNo
 11B25}\endx
\ThirdLvl 11N25\SubText Distribution of integers with specified
 multiplicative constraints\endx
\ThirdLvl 11N30\SubText Tur\'an theory \SeeAlso{\SbjNo 30Bxx}\endx
\ThirdLvl 11N32\SubText Primes represented by polynomials; other
 multiplicative structure of polynomial values\endx
\ThirdLvl 11N35\SubText Sieves\endx
\ThirdLvl 11N36\SubText Applications of sieve methods\endx
\ThirdLvl 11N37\SubText Asymptotic results on arithmetic
 functions\endx
\ThirdLvl 11N45\SubText Asymptotic results on counting functions for
 algebraic and topological structures\endx
\ThirdLvl 11N56\SubText Rate of growth of arithmetic functions\endx
\ThirdLvl 11N60\SubText Distribution functions associated with
 additive and positive multiplicative functions\endx
\ThirdLvl 11N64\SubText Other results on the distribution of values or
 the characterization of arithmetic functions\endx
\ThirdLvl 11N69\SubText Distribution of integers in special residue
 classes\endx
\ThirdLvl 11N75\SubText Applications of automorphic functions and
 forms to multiplicative problems \SeeAlso{\SbjNo 11Fxx}\endx
\ThirdLvl 11N80\SubText Generalized primes and integers\endx
\ThirdLvl 11N99\SubText \NoneOfAbove\endx
\SecndLvl 11P++\SubText Additive number theory; partitions\endx
\ThirdLvl 11P05\SubText Waring's problem and variants\endx
\ThirdLvl 11P21\SubText Lattice points in specified regions\endx
\ThirdLvl 11P32\SubText Goldbach-type theorems; other additive
 questions involving primes\endx
\ThirdLvl 11P55\SubText Applications of the Hardy\_Littlewood method
 \SeeAlso{\SbjNo 11D85}\endx
\ThirdLvl 11P81\SubText Elementary theory of partitions
 \SeeAlso{\SbjNo 05A17}\endx
\ThirdLvl 11P82\SubText Analytic theory of partitions\endx
\ThirdLvl 11P83\SubText Partitions; congruences and congruential
 restrictions\endx
\ThirdLvl 11P99\SubText \NoneOfAbove\endx
\SecndLvl 11R++\SubText Algebraic number theory: global fields
 \SeeFor{For complex multiplication, see \SbjNo 11G15}\endx
\ThirdLvl 11R04\SubText Algebraic numbers; rings of algebraic
 integers\endx
\ThirdLvl 11R06\SubText PV-numbers and generalizations; other special
 algebraic numbers\endx
\ThirdLvl 11R09\SubText Polynomials (irreducibility, etc.)\endx
\ThirdLvl 11R11\SubText Quadratic extensions\endx
\ThirdLvl 11R16\SubText Cubic and quartic extensions\endx
\ThirdLvl 11R18\SubText Cyclotomic extensions\endx
\ThirdLvl 11R20\SubText Other abelian and metabelian extensions\endx
\ThirdLvl 11R21\SubText Other number fields\endx
\ThirdLvl 11R23\SubText Iwasawa theory\endx
\ThirdLvl 11R27\SubText Units and factorization\endx
\ThirdLvl 11R29\SubText Class numbers, class groups,
 discriminants\endx
\ThirdLvl 11R32\SubText Galois theory\endx
\ThirdLvl 11R33\SubText Integral representations related to algebraic
 numbers; Galois module structure of rings of integers \SeeAlso{\SbjNo
 20C10}\endx
\ThirdLvl 11R34\SubText Galois cohomology \SeeAlso{\SbjNo 12Gxx,
 \SbjNo 16H05, \SbjNo 19A31}\endx
\ThirdLvl 11R37\SubText Class field theory\endx
\ThirdLvl 11R39\SubText Langlands-Weil conjectures, nonabelian class
 field theory \SeeAlso{\SbjNo 11Fxx, \SbjNo 22E55}\endx
\ThirdLvl 11R42\SubText Zeta functions and $L$-functions of number
 fields \SeeAlso{\SbjNo 11M41, \SbjNo 19F27}\endx
\ThirdLvl 11R44\SubText Distribution of prime ideals \SeeAlso{\SbjNo
 11N05}\endx
\ThirdLvl 11R45\SubText Density theorems\endx
\ThirdLvl 11R47\SubText Other analytic theory \SeeAlso{\SbjNo
 11Nxx}\endx
\ThirdLvl 11R52\SubText Quaternion and other division algebras:
 arithmetic, zeta functions\endx
\ThirdLvl 11R54\SubText Other algebras and orders, and their zeta and
 $L$-functions \SeeAlso{\SbjNo 11S45, \SbjNo 16H05, \SbjNo 16Kxx}\endx
\ThirdLvl 11R56\SubText Ad\`ele rings and groups\endx
\ThirdLvl 11R58\SubText Arithmetic theory of algebraic function fields
 \SeeAlso{\SbjNo 14-XX}\endx
\ThirdLvl 11R65\SubText Class groups and Picard groups of orders\endx
\ThirdLvl 11R70\SubText $K$-theory of global fields \SeeAlso{\SbjNo
 19Fxx}\endx
\ThirdLvl 11R80\SubText Totally real and totally positive fields
 \SeeAlso{\SbjNo 12J15}\endx
\ThirdLvl 11R99\SubText \NoneOfAbove\endx
\SecndLvl 11S++\SubText Algebraic number theory: local and $p$-adic
 fields\endx
\ThirdLvl 11S05\SubText Polynomials\endx
\ThirdLvl 11S15\SubText Ramification and extension theory\endx
\ThirdLvl 11S20\SubText Galois theory\endx
\ThirdLvl 11S23\SubText Integral representations\endx
\ThirdLvl 11S25\SubText Galois cohomology \SeeAlso{\SbjNo 12Gxx,
 \SbjNo 16H05}\endx
\ThirdLvl 11S31\SubText Class field theory; $p$-adic formal groups
 \SeeAlso{\SbjNo 14L05}\endx
\ThirdLvl 11S37\SubText Langlands-Weil conjectures, nonabelian class
 field theory \SeeAlso{\SbjNo 11Fxx, \SbjNo 22E50}\endx
\ThirdLvl 11S40\SubText Zeta functions and $L$-functions
 \SeeAlso{\SbjNo 11M41, \SbjNo 19F27}\endx
\ThirdLvl 11S45\SubText Algebras and orders, and their zeta functions
 \SeeAlso{\SbjNo 11R52, \SbjNo 11R54, \SbjNo 16H05, \SbjNo 16Kxx}\endx
\ThirdLvl 11S70\SubText $K$-theory of local fields \SeeAlso{\SbjNo
 19Fxx}\endx
\ThirdLvl 11S80\SubText Other analytic theory (analogues of beta and
 gamma functions, $p$-adic integration, etc.)\endx
\ThirdLvl 11S85\SubText Other nonanalytic theory\endx
\ThirdLvl 11S99\SubText \NoneOfAbove\endx
\SecndLvl 11T++\SubText Finite fields and commutative rings
 (number-theoretic aspects)\endx
\ThirdLvl 11T06\SubText Polynomials\endx
\ThirdLvl 11T22\SubText Cyclotomy\endx
\ThirdLvl 11T23\SubText Exponential sums\endx
\ThirdLvl 11T24\SubText Other character sums and Gauss sums\endx
\ThirdLvl 11T30\SubText Structure theory\endx
\ThirdLvl 11T55\SubText Arithmetic theory of polynomial rings over
 finite fields\endx
\ThirdLvl 11T71\SubText Algebraic coding theory; cryptography\endx
\ThirdLvl 11T99\SubText \NoneOfAbove\endx
\SecndLvl 11U++\SubText Connections with logic\endx
\ThirdLvl 11U05\SubText Decidability \SeeAlso{\SbjNo 03B25}\endx
\ThirdLvl 11U07\SubText Ultraproducts \SeeAlso{\SbjNo 03C20}\endx
\ThirdLvl 11U09\SubText Model theory \SeeAlso{\SbjNo 03Cxx}\endx
\ThirdLvl 11U10\SubText Nonstandard arithmetic \SeeAlso{\SbjNo
 03H15}\endx
\ThirdLvl 11U99\SubText \NoneOfAbove\endx
\SecndLvl 11Y++\SubText Computational number theory \SeeAlso{\SbjNo
 11-04}\endx
\ThirdLvl 11Y05\SubText Factorization\endx
\ThirdLvl 11Y11\SubText Primality\endx
\ThirdLvl 11Y16\SubText Algorithms; complexity \SeeAlso{\SbjNo
 68Q25}\endx
\ThirdLvl 11Y35\SubText Analytic computations\endx
\ThirdLvl 11Y40\SubText Algebraic number theory computations\endx
\ThirdLvl 11Y50\SubText Computer solution of Diophantine
 equations\endx
\ThirdLvl 11Y55\SubText Calculation of integer sequences\endx
\ThirdLvl 11Y60\SubText Evaluation of constants\endx
\ThirdLvl 11Y65\SubText Continued fraction calculations\endx
\ThirdLvl 11Y70\SubText Values of arithmetic functions; tables\endx
\ThirdLvl 11Y99\SubText \NoneOfAbove\endx
\SecndLvl 11Z50\SubText Miscellaneous applications of number
 theory\endx
\MajorSub 12-++\SubText Field theory and polynomials\endx
\ThirdLvl 12-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 12-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 12-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 12-03\SubText \Historical\endx
\ThirdLvl 12-04\SubText \ExplicitComputation\endx
\ThirdLvl 12-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 12D++\SubText Real and complex fields\endx
\ThirdLvl 12D05\SubText Polynomials: factorization\endx
\ThirdLvl 12D10\SubText Polynomials: location of zeros (algebraic
 theorems) \SeeFor{For the analytic theory, see \SbjNo 26C10, \SbjNo
 30C15}\endx
\ThirdLvl 12D15\SubText Fields related with sums of squares (formally
 real fields, Pythagorean fields, etc.) \SeeAlso{\SbjNo 11Exx}\endx
\ThirdLvl 12D99\SubText \NoneOfAbove\endx
\SecndLvl 12E++\SubText General field theory\endx
\ThirdLvl 12E05\SubText Polynomials (irreducibility, etc.)\endx
\ThirdLvl 12E10\SubText Special polynomials\endx
\ThirdLvl 12E12\SubText Equations\endx
\ThirdLvl 12E15\SubText Skew fields, division rings \SeeAlso{\SbjNo
 11R52, \SbjNo 11R54, \SbjNo 11S45, \SbjNo 16Kxx}\endx
\ThirdLvl 12E20\SubText Finite fields (field-theoretic aspects)\endx
\ThirdLvl 12E25\SubText Hilbertian fields; Hilbert's irreducibility
 theorem\endx
\ThirdLvl 12E99\SubText \NoneOfAbove\endx
\SecndLvl 12F++\SubText Field extensions\endx
\ThirdLvl 12F05\SubText Algebraic extensions\endx
\ThirdLvl 12F10\SubText Separable extensions, Galois theory\endx
\ThirdLvl 12F12\SubText Inverse Galois theory\endx
\ThirdLvl 12F15\SubText Inseparable extensions\endx
\ThirdLvl 12F20\SubText Transcendental extensions\endx
\ThirdLvl 12F99\SubText \NoneOfAbove\endx
\SecndLvl 12G++\SubText Homological methods (field theory)\endx
\ThirdLvl 12G05\SubText Galois cohomology \SeeAlso{\SbjNo 13A20,
 \SbjNo 16H05}\endx
\ThirdLvl 12G10\SubText Cohomological dimension\endx
\ThirdLvl 12G99\SubText \NoneOfAbove\endx
\SecndLvl 12H++\SubText Differential and difference algebra\endx
\ThirdLvl 12H05\SubText Differential algebra \SeeAlso{\SbjNo
 13Nxx}\endx
\ThirdLvl 12H10\SubText Difference algebra \SeeAlso{\SbjNo 39Axx}\endx
\ThirdLvl 12H20\SubText Abstract differential equations
 \SeeAlso{\SbjNo 34Gxx}\endx
\ThirdLvl 12H25\SubText $p$-adic differential equations
 \SeeAlso{\SbjNo 11S80, \SbjNo 14G20, \SbjNo 34Gxx}\endx
\ThirdLvl 12H99\SubText \NoneOfAbove\endx
\SecndLvl 12J++\SubText Topological fields\endx
\ThirdLvl 12J05\SubText Normed fields\endx
\ThirdLvl 12J10\SubText Valued fields \endx
\ThirdLvl 12J12\SubText Formally $p$-adic fields\endx
\ThirdLvl 12J15\SubText Ordered fields\endx
\ThirdLvl 12J17\SubText Topological semifields\endx
\ThirdLvl 12J20\SubText General valuation theory\endx
\ThirdLvl 12J25\SubText Non-Archimedean valued fields \SeeAlso{\SbjNo
 30G06, \SbjNo 32P05, \SbjNo 46S10, \SbjNo 47S10}\endx
\ThirdLvl 12J27\SubText Krasner-Tate algebras \SeeMainly{\SbjNo 32P05;
 see also \SbjNo 46S10, \SbjNo 47S10}\endx
\ThirdLvl 12J99\SubText \NoneOfAbove\endx
\SecndLvl 12K++\SubText Generalizations of fields\endx
\ThirdLvl 12K05\SubText Near-fields \SeeAlso{\SbjNo 16Y30}\endx
\ThirdLvl 12K10\SubText Semifields \SeeAlso{\SbjNo 16Y60}\endx
\ThirdLvl 12K99\SubText \NoneOfAbove\endx
\SecndLvl 12L++\SubText Connections with logic\endx
\ThirdLvl 12L05\SubText Decidability \SeeAlso{\SbjNo 03B25}\endx
\ThirdLvl 12L10\SubText Ultraproducts \SeeAlso{\SbjNo 03C20}\endx
\ThirdLvl 12L12\SubText Model theory \SeeAlso{\SbjNo 03C60}\endx
\ThirdLvl 12L15\SubText Nonstandard arithmetic \SeeAlso{\SbjNo
 03H15}\endx
\ThirdLvl 12L99\SubText \NoneOfAbove\endx
\SecndLvl 12Y05\SubText Computational aspects of field theory and
 polynomials\endx
\MajorSub 13-++\SubText Commutative rings and algebras\endx
\ThirdLvl 13-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 13-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 13-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 13-03\SubText \Historical\endx
\ThirdLvl 13-04\SubText \ExplicitComputation\endx
\ThirdLvl 13-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 13A++\SubText General commutative ring theory\endx
\ThirdLvl 13A02\SubText Graded rings \SeeAlso{\SbjNo 16W50}\endx
\ThirdLvl 13A05\SubText Divisibility\endx
\ThirdLvl 13A10\SubText Radical theory\endx
\ThirdLvl 13A15\SubText Ideals; multiplicative ideal theory\endx
\ThirdLvl 13A18\SubText Valuations and their generalizations\endx
\ThirdLvl 13A20\SubText Brauer groups \SeeAlso{\SbjNo 12Gxx, \SbjNo
 16H05}\endx
\ThirdLvl 13A30\SubText Associated graded rings of ideals (Rees ring,
 form ring) and related topics\endx
\ThirdLvl 13A35\SubText Characteristic $p$ methods (Frobenius
 endomorphism) and reduction to characteristic $p$ \SeeAlso{\SbjNo
 13Mxx}\endx
\ThirdLvl 13A50\SubText Invariant theory \SeeAlso{\SbjNo 14D25}\endx
\ThirdLvl 13A99\SubText \NoneOfAbove\endx
\SecndLvl 13B++\SubText Ring extensions and related topics\endx
\ThirdLvl 13B02\SubText Extension theory\endx
\ThirdLvl 13B05\SubText Galois theory (commutative rings)\endx
\ThirdLvl 13B10\SubText Morphisms and derivations\endx
\ThirdLvl 13B15\SubText Ramification theory\endx
\ThirdLvl 13B21\SubText Integral dependence\endx
\ThirdLvl 13B22\SubText Integral closure; integrally closed rings,
 related rings (Japanese, etc.)\endx
\ThirdLvl 13B24\SubText Going up; going down; going between\endx
\ThirdLvl 13B25\SubText Polynomials over commutative rings\endx
\ThirdLvl 13B30\SubText Quotients and localization\endx
\ThirdLvl 13B35\SubText Completion \SeeAlso{\SbjNo 13J10}\endx
\ThirdLvl 13B40\SubText \'Etale extensions and Henselization; Artin
 approximation \SeeAlso{\SbjNo 13J15, \SbjNo 14B12}\endx
\ThirdLvl 13B99\SubText \NoneOfAbove\endx
\SecndLvl 13C++\SubText Theory of modules and ideals\endx
\ThirdLvl 13C05\SubText Structure, classification theorems\endx
\ThirdLvl 13C10\SubText Projective and free modules and ideals
 \SeeAlso{\SbjNo 18G05, \SbjNo 19A13}\endx
\ThirdLvl 13C11\SubText Injective and flat modules and ideals
 \SeeAlso{\SbjNo 18G05}\endx
\ThirdLvl 13C12\SubText Torsion modules and ideals\endx
\ThirdLvl 13C13\SubText Other special types\endx
\ThirdLvl 13C14\SubText Cohen-Macaulay modules \SeeAlso{\SbjNo
 13H10}\endx
\ThirdLvl 13C15\SubText Dimension theory, depth, related rings
 (catenary, etc.)\endx
\ThirdLvl 13C20\SubText Class groups\endx
\ThirdLvl 13C40\SubText Linkage, complete intersections and
 determinantal ideals \SeeAlso{\SbjNo 14M12}\endx
\ThirdLvl 13C99\SubText \NoneOfAbove\endx
\SecndLvl 13D++\SubText (Co)homological methods\endx
\ThirdLvl 13D02\SubText Syzygies\endx
\ThirdLvl 13D03\SubText (Co)homology of commutative rings and
 algebras\endx
\ThirdLvl 13D05\SubText (Co)homological dimension \SeeAlso{\SbjNo
 18G20}\endx
\ThirdLvl 13D10\SubText Deformations and infinitesimal methods
 \SeeAlso{\SbjNo 14B12, \SbjNo 14D15, \SbjNo 16S80, \SbjNo 32Gxx}\endx
\ThirdLvl 13D15\SubText Grothendieck groups, $K$-theory
 \SeeAlso{\SbjNo 14C35, \SbjNo 18F30, \SbjNo 19-XX}\endx
\ThirdLvl 13D25\SubText Complexes\endx
\ThirdLvl 13D30\SubText Torsion theory \SeeAlso{\SbjNo 13C12, \SbjNo
 18E40}\endx
\ThirdLvl 13D40\SubText Hilbert-Samuel functions and Poincar\'e
 series\endx
\ThirdLvl 13D45\SubText Local cohomology \SeeAlso{\SbjNo 14B15}\endx
\ThirdLvl 13D99\SubText \NoneOfAbove\endx
\SecndLvl 13E++\SubText Chain conditions, finiteness conditions\endx
\ThirdLvl 13E05\SubText Noetherian rings and modules\endx
\ThirdLvl 13E10\SubText Artinian rings and modules, finite-dimensional
 algebras\endx
\ThirdLvl 13E15\SubText Rings and modules of finite generation or
 presentation\endx
\ThirdLvl 13E99\SubText \NoneOfAbove\endx
\SecndLvl 13F++\SubText Arithmetic rings and other special rings
 \SeeAlso{\SbjNo 12-XX}\endx
\ThirdLvl 13F05\SubText Dedekind and Pr\"ufer rings and their
 generalizations\endx
\ThirdLvl 13F07\SubText Euclidean rings and generalizations\endx
\ThirdLvl 13F10\SubText Principal ideal rings\endx
\ThirdLvl 13F15\SubText Factorial rings, unique factorization domains
 \SeeAlso{\SbjNo 14M05}\endx
\ThirdLvl 13F20\SubText Polynomial rings and ideals \SeeAlso{\SbjNo
 11C08}\endx
\ThirdLvl 13F25\SubText Formal power series rings \SeeAlso{\SbjNo
 13J05}\endx
\ThirdLvl 13F30\SubText Valuation rings\endx
\ThirdLvl 13F40\SubText Excellent rings\endx
\ThirdLvl 13F45\SubText Seminormal rings\endx
\ThirdLvl 13F50\SubText Rings with straightening laws, Hodge
 algebras\endx
\ThirdLvl 13F99\SubText \NoneOfAbove\endx
\SecndLvl 13G05\SubText Integral domains\endx
\SecndLvl 13H++\SubText Local rings and semilocal rings\endx
\ThirdLvl 13H05\SubText Regular local rings\endx
\ThirdLvl 13H10\SubText Special types (Cohen-Macaulay, Gorenstein,
 Buchsbaum, etc.) \SeeAlso{\SbjNo 14M05}\endx
\ThirdLvl 13H15\SubText Multiplicity theory and related topies\endx
\ThirdLvl 13H99\SubText \NoneOfAbove\endx
\SecndLvl 13J++\SubText Topological rings and modules \SeeAlso{\SbjNo
 16W60, \SbjNo 16W80}\endx
\ThirdLvl 13J05\SubText Power series rings \SeeAlso{\SbjNo 13F25}\endx
\ThirdLvl 13J07\SubText Analytical algebras and rings \SeeAlso{\SbjNo
 32B05}\endx
\ThirdLvl 13J10\SubText Complete rings, completion \SeeAlso{\SbjNo
 13B35}\endx
\ThirdLvl 13J15\SubText Henselian rings \SeeAlso{\SbjNo 13B40}\endx
\ThirdLvl 13J20\SubText Global topological rings\endx
\ThirdLvl 13J25\SubText Ordered rings \SeeAlso{\SbjNo 06F25}\endx
\ThirdLvl 13J99\SubText \NoneOfAbove\endx
\SecndLvl 13K05\SubText Witt vectors and related rings\endx
\SecndLvl 13L05\SubText Applications of logic to commutative algebra
 \SeeAlso {\SbjNo 03Cxx, \SbjNo 03Hxx}\endx
\SecndLvl 13M++\SubText Finite commutative rings \SeeFor{For
 number-theoretic aspects, see \SbjNo 11Txx}\endx
\ThirdLvl 13M05\SubText Structure\endx
\ThirdLvl 13M10\SubText	Polynomials (commutative rings)\endx
\ThirdLvl 13M99\SubText \NoneOfAbove\endx
\SecndLvl 13N++\SubText Differential algebra \SeeAlso{\SbjNo 12H05,
 \SbjNo 14F10}\endx
\ThirdLvl 13N05\SubText Modules of differentials \SeeAlso{\SbjNo
 16S32}\endx
\ThirdLvl 13N10\SubText Rings of differential operators
 \SeeAlso{\SbjNo 16S32, \SbjNo 32C38}\endx
\ThirdLvl 13N99\SubText \NoneOfAbove\endx
\SecndLvl 13P++\SubText Computational aspects of commutative algebra
 \SeeAlso{\SbjNo 68Q40}\endx
\ThirdLvl 13P05\SubText Polynomials, factorization \SeeAlso{\SbjNo
 12Y05}\endx
\ThirdLvl 13P10\SubText Polynomial ideals, Gr\"obner bases\endx
\ThirdLvl 13P99\SubText \NoneOfAbove\endx
\MajorSub 14-++\SubText Algebraic geometry\endx
\ThirdLvl 14-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 14-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 14-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 14-03\SubText \Historical\endx
\ThirdLvl 14-04\SubText \ExplicitComputation\endx
\ThirdLvl 14-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 14A++\SubText Foundations\endx
\ThirdLvl 14A05\SubText Relevant commutative algebra \SeeAlso{\SbjNo
 13-XX}\endx
\ThirdLvl 14A10\SubText Varieties\endx
\ThirdLvl 14A15\SubText Schemes\endx
\ThirdLvl 14A20\SubText Generalizations (algebraic spaces,
 motifs)\endx
\ThirdLvl 14A22\SubText Noncommutative algebraic geometry; algebraic
 supervarieties \SeeAlso{\SbjNo 14M30, \SbjNo 32C11, \SbjNo
 58A50}\endx
\ThirdLvl 14A25\SubText Elementary questions\endx
\ThirdLvl 14A99\SubText \NoneOfAbove\endx
\SecndLvl 14B++\SubText Local theory \SeeAlso{\SbjNo 32Sxx}\endx
\ThirdLvl 14B05\SubText Singularities \SeeAlso{\SbjNo 14E15, \SbjNo
 14H20, \SbjNo 32Sxx, \SbjNo 58C27}\endx
\ThirdLvl 14B07\SubText Deformations of singularities \SeeAlso{\SbjNo
 14D15, \SbjNo 32Sxx}\endx
\ThirdLvl 14B10\SubText Infinitesimal methods \SeeAlso{\SbjNo
 13D10}\endx
\ThirdLvl 14B12\SubText Local deformation theory, Artin approximation,
 etc. \SeeAlso{\SbjNo 13B40, \SbjNo 13D10}\endx
\ThirdLvl 14B15\SubText Local cohomology \SeeAlso{\SbjNo 13D45, \SbjNo
 32C36}\endx
\ThirdLvl 14B20\SubText Formal neighborhoods\endx
\ThirdLvl 14B99\SubText \NoneOfAbove\endx
\SecndLvl 14C++\SubText Cycles and subschemes\endx
\ThirdLvl 14C05\SubText Parametrization (Chow and Hilbert
 schemes)\endx
\ThirdLvl 14C10\SubText Equivalence relations\endx
\ThirdLvl 14C15\SubText Rational equivalence rings\endx
\ThirdLvl 14C17\SubText Intersection theory\endx
\ThirdLvl 14C20\SubText Divisors, linear systems, invertible
 sheaves\endx
\ThirdLvl 14C21\SubText Pencils, nets, webs \SeeAlso{\SbjNo
 53A60}\endx
\ThirdLvl 14C22\SubText Picard groups\endx
\ThirdLvl 14C25\SubText Algebraic cycles\endx
\ThirdLvl 14C30\SubText Transcendental methods, Hodge theory
 \SeeAlso{\SbjNo 14D07, \SbjNo 32G20, \SbjNo 32J25, \SbjNo 32S35},
 Hodge conjecture\endx
\ThirdLvl 14C34\SubText Torelli problem \SeeAlso{\SbjNo 32G20}\endx
\ThirdLvl 14C35\SubText Applications of methods of algebraic
 $K$-theory \SeeAlso{\SbjNo 14F05, \SbjNo 19Exx}\endx
\ThirdLvl 14C40\SubText Riemann-Roch theorems \SeeAlso{\SbjNo 19E20,
 \SbjNo 19L10}\endx
\ThirdLvl 14C99\SubText \NoneOfAbove\endx
\SecndLvl 14D++\SubText Families, fibrations\endx
\ThirdLvl 14D05\SubText Structure of families (Picard-Lefschetz,
 Picard-Fuchs theory, etc.)\endx
\ThirdLvl 14D07\SubText Variation of Hodge structures\endx
\ThirdLvl 14D10\SubText Arithmetic ground fields (finite, local,
 global)\endx
\ThirdLvl 14D15\SubText Formal methods; deformations \SeeAlso{\SbjNo
 13D10, \SbjNo 14B07, \SbjNo 16S80 \SbjNo 32Gxx}\endx
\ThirdLvl 14D20\SubText Algebraic moduli problems, moduli of vector
 bundles \SeeFor{For analytic moduli problems, see \SbjNo 32G13}\endx
\ThirdLvl 14D22\SubText Fine and coarse moduli spaces\endx
\ThirdLvl 14D25\SubText Geometric invariants \SeeAlso{\SbjNo
 14L30}\endx
\ThirdLvl 14D99\SubText \NoneOfAbove\endx
\SecndLvl 14E++\SubText Mappings and correspondences\endx
\ThirdLvl 14E05\SubText Rational maps, birational correspondences\endx
\ThirdLvl 14E07\SubText Birational automorphisms, Cremona group and
 generalizations \SeeAlso{\SbjNo 32G20}\endx
\ThirdLvl 14E09\SubText Automorphisms \SeeAlso{\SbjNo 14J50, \SbjNo
 14L27}\endx
\ThirdLvl 14E10\SubText General correspondences\endx
\ThirdLvl 14E15\SubText Global theory of singularities, resolution
 \SeeAlso{\SbjNo 14B05, \SbjNo 32S20, \SbjNo 32S45}\endx
\ThirdLvl 14E20\SubText Coverings, fundamental group (mappings)\endx
\ThirdLvl 14E22\SubText Ramification problems \SeeAlso{\SbjNo
 11S15}\endx
\ThirdLvl 14E25\SubText Imbeddings\endx
\ThirdLvl 14E30\SubText Minimal models\endx
\ThirdLvl 14E35\SubText Results in dimension $\leq 3$\endx
\ThirdLvl 14E40\SubText Local structure of maps: \'etale, flat, etc.
 \SeeAlso{\SbjNo 13-XX, \SbjNo 14F20}\endx
\ThirdLvl 14E99\SubText \NoneOfAbove\endx
\SecndLvl 14F++\SubText (Co)homology theory \SeeAlso{\SbjNo
 13Dxx}\endx
\ThirdLvl 14F05\SubText Vector bundles, sheaves, related construction
 \SeeAlso{\SbjNo 18F20, \SbjNo 32Lxx, \SbjNo 46M20}\endx
\ThirdLvl 14F10\SubText Differentials and other special sheaves
 \SeeAlso{\SbjNo 32C38}\endx
\ThirdLvl 14F17\SubText Vanishing theorems \SeeAlso{\SbjNo 32L20}\endx
\ThirdLvl 14F20\SubText \'Etale and other Grothendieck topologies and
 cohomologies\endx
\ThirdLvl 14F25\SubText Classical real and complex cohomology\endx
\ThirdLvl 14F30\SubText $p$-adic cohomology, crystalline
 cohomology\endx
\ThirdLvl 14F32\SubText Intersection (co)homology \SeeAlso{\SbjNo
 32S60}\endx
\ThirdLvl 14F35\SubText Homotopy theory; fundamental groups
 \SeeAlso{\SbjNo 14E20, \SbjNo 14H30}\endx
\ThirdLvl 14F40\SubText de Rham cohomology \SeeAlso{\SbjNo 14C30,
 \SbjNo 32C35, \SbjNo 32L10}\endx
\ThirdLvl 14F45\SubText Topological properties\endx
\ThirdLvl 14F99\SubText \NoneOfAbove\endx
\SecndLvl 14G++\SubText Arithmetic problems. Diophantine geometry
 \SeeAlso{\SbjNo 11Dxx, \SbjNo 11Gxx}\endx
\ThirdLvl 14G05\SubText Rationality questions, rational points\endx
\ThirdLvl 14G10\SubText Zeta-functions and related questions
 \SeeAlso{\SbjNo 11G40} (Birch-Swinnerton-Dyer conjecture)\endx
\ThirdLvl 14G15\SubText Finite ground fields\endx
\ThirdLvl 14G20\SubText $p$-adic ground fields\endx
\ThirdLvl 14G25\SubText Global ground fields\endx
\ThirdLvl 14G27\SubText Nonalgebraically closed ground fields\endx
\ThirdLvl 14G35\SubText Modular and Shimura varieties \SeeAlso{\SbjNo
 11F41, \SbjNo 11F46, \SbjNo 11G18}\endx
\ThirdLvl 14G40\SubText Arithmetic varieties and schemes; Arakelov
 theory\endx
\ThirdLvl 14G99\SubText \NoneOfAbove\endx
\SecndLvl 14H++\SubText Curves\endx
\ThirdLvl 14H05\SubText Algebraic functions; function fields
 \SeeAlso{\SbjNo 11R58}\endx
\ThirdLvl 14H10\SubText Families, moduli (algebraic)\endx
\ThirdLvl 14H15\SubText Families, moduli (analytic) \SeeAlso{\SbjNo
 30F10, \SbjNo 32Gxx}\endx
\ThirdLvl 14H20\SubText Singularities, local rings \SeeAlso{\SbjNo
 13Hxx}\endx
\ThirdLvl 14H25\SubText Arithmetic ground fields \SeeAlso{\SbjNo
 11Dxx, \SbjNo 11G05, \SbjNo 14Gxx}\endx
\ThirdLvl 14H30\SubText Coverings, fundamental group \SeeAlso{\SbjNo
 14E20, \SbjNo 14F35}\endx
\ThirdLvl 14H35\SubText Correspondences \SeeAlso{\SbjNo 14Exx}\endx
\ThirdLvl 14H40\SubText Jacobians \SeeAlso{\SbjNo 32G20}\endx
\ThirdLvl 14H42\SubText Theta functions; Schottky problem
 \SeeAlso{\SbjNo 14K25, \SbjNo 32G20}\endx
\ThirdLvl 14H45\SubText Special curves and curves of low genus\endx
\ThirdLvl 14H50\SubText Space curves\endx
\ThirdLvl 14H52\SubText Elliptic curves \SeeAlso{\SbjNo 11G05, \SbjNo
 11G07, \SbjNo 14Kxx}\endx
\ThirdLvl 14H55\SubText Riemann surfaces; Weierstrass points; gap
 sequences \SeeAlso{\SbjNo 30Fxx}\endx
\ThirdLvl 14H60\SubText Vector bundles on curves \SeeAlso{\SbjNo
 14F05}\endx
\ThirdLvl 14H99\SubText \NoneOfAbove\endx
\SecndLvl 14J++\SubText Surfaces and higher-dimensional varieties
 \SeeFor{For analytic theory, see \SbjNo 32Jxx}\endx
\ThirdLvl 14J05\SubText Picard group \SeeAlso{\SbjNo 14C22, \SbjNo
 19A49, \SbjNo 32L05}\endx
\ThirdLvl 14J10\SubText Families, moduli, classification: algebraic
 theory\endx
\ThirdLvl 14J15\SubText Moduli, classification: analytic theory
 \SeeAlso{\SbjNo 32G13, \SbjNo 32J15}\endx
\ThirdLvl 14J17\SubText Singularities of surfaces\endx
\ThirdLvl 14J20\SubText Arithmetic ground fields \SeeAlso{\SbjNo
 11Dxx, \SbjNo 11G25, \SbjNo 11G35, \SbjNo 14Gxx}\endx
\ThirdLvl 14J25\SubText Special surfaces \SeeFor{For Hilbert modular
 surfaces, see \SbjNo 14G35}\endx
\ThirdLvl 14J26\SubText Rational and ruled surfaces\endx
\ThirdLvl 14J27\SubText Elliptic surfaces\endx
\ThirdLvl 14J28\SubText $K3$ surfaces and Enriques surfaces\endx
\ThirdLvl 14J29\SubText Surfaces of general type\endx
\ThirdLvl 14J30\SubText Special $3$-folds \SeeAlso{\SbjNo 14E05}\endx
\ThirdLvl 14J35\SubText Special $4$-folds \SeeAlso{\SbjNo 14E05}\endx
\ThirdLvl 14J40\SubText Special $n$-folds\endx
\ThirdLvl 14J45\SubText Fano varieties\endx
\ThirdLvl 14J50\SubText Automorphisms of surfaces and
 higher-dimensional varieties \SeeAlso{\SbjNo 14E09}\endx
\ThirdLvl 14J60\SubText Vector bundles on surfaces and
 higher-dimensional varieties \SeeAlso{\SbjNo 14F05, \SbjNo
 32Lxx}\endx
\ThirdLvl 14J70\SubText Hypersurfaces\endx
\ThirdLvl 14J99\SubText \NoneOfAbove\endx
\SecndLvl 14K++\SubText Abelian varieties and schemes\endx
\ThirdLvl 14K02\SubText Isogeny\endx
\ThirdLvl 14K05\SubText Algebraic theory\endx
\ThirdLvl 14K10\SubText Algebraic moduli, classification\endx
\ThirdLvl 14K15\SubText Arithmetic ground fields \SeeAlso{\SbjNo
 11Dxx, \SbjNo 11Fxx, \SbjNo 11Gxx, \SbjNo 14Gxx}\endx
\ThirdLvl 14K20\SubText Analytic theory; abelian integrals and
 differentials\endx
\ThirdLvl 14K22\SubText Complex multiplication \SeeAlso{\SbjNo
 11G15}\endx
\ThirdLvl 14K25\SubText Theta functions\endx
\ThirdLvl 14K30\SubText Picard schemes, higher Jacobians
 \SeeAlso{\SbjNo 14H40, \SbjNo 32G20}\endx
\ThirdLvl 14K99\SubText \NoneOfAbove\endx
\SecndLvl 14L++\SubText Group schemes \SeeFor{For linear algebraic
 groups, see \SbjNo 20Gxx. For Lie algebras, see \SbjNo 17B45}\endx
\ThirdLvl 14L05\SubText Formal groups, $p$-divisible groups
 \SeeAlso{\SbjNo 55N22}\endx
\ThirdLvl 14L10\SubText Group varieties\endx
\ThirdLvl 14L15\SubText Group schemes\endx
\ThirdLvl 14L17\SubText Affine algebraic groups, hyperalgebra
 constructions \SeeAlso{\SbjNo 17B45, \SbjNo 18D35}\endx
\ThirdLvl 14L27\SubText Automorphism groups \SeeAlso{\SbjNo
 14E09}\endx
\ThirdLvl 14L30\SubText Group actions on varieties or schemes
 (quotients) \SeeAlso{\SbjNo 14D25}\endx
\ThirdLvl 14L35\SubText Classical groups (geometric aspects)
 \SeeAlso{\SbjNo 20Gxx, \SbjNo 51N30}\endx
\ThirdLvl 14L40\SubText Other algebraic groups (geometric
 aspects)\endx
\ThirdLvl 14L99\SubText \NoneOfAbove\endx
\SecndLvl 14M++\SubText Special varieties\endx
\ThirdLvl 14M05\SubText Varieties defined by ring conditions
 (factorial, Cohen-Macaulay, seminormal) \SeeAlso{\SbjNo 13C14, \SbjNo
 13F45, \SbjNo 13H10}\endx
\ThirdLvl 14M06\SubText Linkage \SeeAlso{\SbjNo 13C40}\endx
\ThirdLvl 14M07\SubText Low codimension problems \SeeAlso{\SbjNo
 14Cxx}\endx
\ThirdLvl 14M10\SubText Complete intersections \SeeAlso{\SbjNo
 13C40}\endx
\ThirdLvl 14M12\SubText Determinantal varieties \SeeAlso{\SbjNo
 13C40}\endx
\ThirdLvl 14M15\SubText Grassmannians, Schubert varieties, flag
 manifolds \SeeAlso{\SbjNo 32M10, \SbjNo 51M35}\endx
\ThirdLvl 14M17\SubText Homogeneous spaces and generalizations
 \SeeAlso{\SbjNo 32M10, \SbjNo 53C30, \SbjNo 57T15}\endx
\ThirdLvl 14M20\SubText Rational varieties\endx
\ThirdLvl 14M25\SubText Toric varieties, Newton polyhedra\endx
\ThirdLvl 14M30\SubText Supervarieties \SeeAlso{\SbjNo 14A22, \SbjNo
 32C11, \SbjNo 58A50}\endx
\ThirdLvl 14M99\SubText \NoneOfAbove\endx
\SecndLvl 14N++\SubText Classical methods and problems \SeeAlso{\SbjNo
 51-XX}\endx
\ThirdLvl 14N05\SubText Projective techniques \SeeAlso{\SbjNo
 51N35}\endx
\ThirdLvl 14N10\SubText Enumerative problems (combinatorial
 problems)\endx
\ThirdLvl 14N99\SubText \NoneOfAbove\endx
\SecndLvl 14P++\SubText Real algebraic and real analytic geometry\endx
\ThirdLvl 14P05\SubText Real algebraic sets \SeeAlso{\SbjNo
 12Dxx}\endx
\ThirdLvl 14P10\SubText Semialgebraic sets and related spaces\endx
\ThirdLvl 14P15\SubText Real analytic and semianalytic sets
 \SeeAlso{\SbjNo 32B20, \SbjNo 32C05}\endx
\ThirdLvl 14P20\SubText Nash functions and manifolds \SeeAlso{\SbjNo
 32C07, \SbjNo 58A07}\endx
\ThirdLvl 14P25\SubText Topology of real algebraic varieties\endx
\ThirdLvl 14P99\SubText \NoneOfAbove\endx
\SecndLvl 14Q++\SubText Computational aspects in algebraic geometry
 \SeeAlso{\SbjNo 12-04, \SbjNo 68Q40}\endx
\ThirdLvl 14Q05\SubText Curves\endx
\ThirdLvl 14Q10\SubText Surfaces, hypersurfaces\endx
\ThirdLvl 14Q15\SubText Higher-dimensional varieties\endx
\ThirdLvl 14Q20\SubText Effectivity\endx
\ThirdLvl 14Q99\SubText \NoneOfAbove\endx
\MajorSub 15-++\SubText Linear and multilinear algebra; matrix theory
 \ExtraText{(finite and infinite)}\endx
\ThirdLvl 15-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 15-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 15-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 15-03\SubText \Historical\endx
\ThirdLvl 15-04\SubText \ExplicitComputation\endx
\ThirdLvl 15-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 15A03\SubText Vector spaces, linear dependence, rank\endx
\ThirdLvl 15A04\SubText Linear transformations, semilinear
 transformations\endx
\ThirdLvl 15A06\SubText Linear equations\endx
\ThirdLvl 15A09\SubText Matrix inversion, generalized inverses\endx
\ThirdLvl 15A12\SubText Conditioning of matrices \SeeAlso{\SbjNo
 65F35}\endx
\ThirdLvl 15A15\SubText Determinants, permanents, other special matrix
 functions \SeeAlso{\SbjNo 19B10, \SbjNo 19B14}\endx
\ThirdLvl 15A18\SubText Eigenvalues, singular values, and
 eigenvectors\endx
\ThirdLvl 15A21\SubText Canonical forms, reductions,
 classification\endx
\ThirdLvl 15A22\SubText Matrix pencils \SeeAlso{\SbjNo 47A56}\endx
\ThirdLvl 15A23\SubText Factorization of matrices\endx
\ThirdLvl 15A24\SubText Matrix equations and identities\endx
\ThirdLvl 15A27\SubText Commutativity\endx
\ThirdLvl 15A30\SubText Algebraic systems of matrices \SeeAlso{\SbjNo
 16S50, \SbjNo 20Gxx, \SbjNo 20Hxx}\endx
\ThirdLvl 15A33\SubText Matrices over special rings (quaternions,
 finite fields, etc.)\endx
\ThirdLvl 15A36\SubText Matrices of integers \SeeAlso{\SbjNo
 11C20}\endx
\ThirdLvl 15A39\SubText Linear inequalities\endx
\ThirdLvl 15A42\SubText Inequalities involving eigenvalues and
 eigenvectors\endx
\ThirdLvl 15A45\SubText Miscellaneous inequalities involving
 matrices\endx
\ThirdLvl 15A48\SubText Positive matrices and their generalizations;
 cones of matrices\endx
\ThirdLvl 15A51\SubText Stochastic matrices\endx
\ThirdLvl 15A52\SubText Random matrices\endx
\ThirdLvl 15A54\SubText Matrices over function rings in one or more
 variables\endx
\ThirdLvl 15A57\SubText Other types of matrices (Hermitian,
 skew-Hermitian, etc.)\endx
\ThirdLvl 15A60\SubText Norms of matrices, numerical range,
 applications of functional analysis to matrix theory \SeeAlso{\SbjNo
 65F35, \SbjNo 65J05}\endx
\ThirdLvl 15A63\SubText Quadratic and bilinear forms, inner products
 \SeeMainly{\SbjNo 11Exx}\endx
\ThirdLvl 15A66\SubText Clifford algebras, spinors\endx
\ThirdLvl 15A69\SubText Multilinear algebra, tensor products\endx
\ThirdLvl 15A72\SubText Vector and tensor algebra, theory of
 invariants \SeeAlso{\SbjNo 13A50, \SbjNo 14D25}\endx
\ThirdLvl 15A75\SubText Exterior algebra, Grassmann algebras\endx
\ThirdLvl 15A78\SubText Other algebras built from modules\endx
\ThirdLvl 15A90\SubText Applications of matrix theory to physics\endx
\ThirdLvl 15A99\SubText \Miscellaneous\endx
\MajorSub 16-++\SubText Associative rings and algebras \SeeFor{For the
 commutative case, see~\SbjNo 13-XX}\endx
\ThirdLvl 16-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 16-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 16-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 16-03\SubText \Historical\endx
\ThirdLvl 16-04\SubText \ExplicitComputation\endx
\ThirdLvl 16-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 16B++\SubText General and miscellaneous\endx
\ThirdLvl 16B50\SubText Category-theoretic methods and results (except
 as in \SbjNo 16D90, \SbjNo 16E10) \SeeAlso{\SbjNo 18-++}\endx
\ThirdLvl 16B70\SubText Applications of logic \SeeAlso{\SbjNo
 03Cxx}\endx
\ThirdLvl 16B99\SubText \NoneOfAbove\endx
\SecndLvl 16D++\SubText Modules, bimodules and ideals\endx
\ThirdLvl 16D10\SubText General module theory\endx
\ThirdLvl 16D15\SubText 1-sided ideals\endx
\ThirdLvl 16D20\SubText Bimodules\endx
\ThirdLvl 16D25\SubText 2-sided ideals\endx
\ThirdLvl 16D30\SubText Maximal and prime 2-sided ideals
 \SeeAlso{\SbjNo 16N60, \SbjNo 16D60}, simple rings (except as in
 \SbjNo 16Kxx)\endx
\ThirdLvl 16D40\SubText Free, projective, and flat modules and ideals
 \SeeAlso{\SbjNo 18G05, \SbjNo 19A13}\endx
\ThirdLvl 16D50\SubText Injective modules, self-injective rings
 \SeeAlso{\SbjNo 16L60, \SbjNo 18G05}\endx
\ThirdLvl 16D60\SubText Simple and semisimple modules, primitive rings
 and ideals\endx
\ThirdLvl 16D70\SubText Structure and classification (except as in
 \SbjNo 16Gxx), direct sum decomposition, cancellation\endx
\ThirdLvl 16D80\SubText Other classes of modules and ideals
 \SeeAlso{\SbjNo 16G60}\endx
\ThirdLvl 16D90\SubText Module categories \SeeAlso{\SbjNo 16Exx,
 \SbjNo 16Gxx, \SbjNo 16S90}; module theory in a category-theoretic
 context; Morita equivalence and duality\endx
\ThirdLvl 16D99\SubText \NoneOfAbove\endx
\SecndLvl 16E++\SubText Homological methods and results
 \SeeAlso{\SbjNo 18Gxx}\endx
\ThirdLvl 16E10\SubText Homological dimension \endx
\ThirdLvl 16E20\SubText Grothendieck groups, $K$-theory, etc.
 \SeeAlso{\SbjNo 18F30, \SbjNo 19-XX}\endx
\ThirdLvl 16E30\SubText Homological functors on modules\endx
\ThirdLvl 16E40\SubText Hochschild and other homology and cohomology
 theories for rings\endx
\ThirdLvl 16E50\SubText von Neumann regular rings and
 generalizations\endx
\ThirdLvl 16E60\SubText Semihereditary and hereditary rings, free
 ideal rings, Sylvester rings, etc.\endx
\ThirdLvl 16E70\SubText Other rings of low global or flat
 dimension\endx
\ThirdLvl 16E99\SubText \NoneOfAbove\endx
\SecndLvl 16G++\SubText Representation theory of rings and
 algebras\endx
\ThirdLvl 16G10\SubText Representations of Artinian rings\endx
\ThirdLvl 16G20\SubText Representations of quivers and partially
 ordered sets\endx
\ThirdLvl 16G30\SubText Representations of orders, lattices, algebras
 over commutative rings \SeeAlso{\SbjNo 16H05}\endx
\ThirdLvl 16G50\SubText Cohen-Macaulay modules\endx
\ThirdLvl 16G60\SubText Representation type (finite, tame, wild,
 etc.)\endx
\ThirdLvl 16G70\SubText Auslander-Reiten sequences (almost split
 sequences) and Auslander-Reiten quivers\endx
\ThirdLvl 16G99\SubText \NoneOfAbove\endx
\SecndLvl 16H05\SubText Orders and arithmetic, separable algebras,
 Azumaya algebras \SeeAlso{\SbjNo 11R52, \SbjNo 11R54, \SbjNo 11S45,
 \SbjNo 13A20}\endx
\SecndLvl 16K++\SubText Division rings and semisimple Artin rings
 \SeeAlso{\SbjNo 12E15, \SbjNo 15A30}\endx
\ThirdLvl 16K20\SubText Finite-dimensional \SeeFor{For Brauer group
 theory, see \SbjNo 12Gxx, \SbjNo 13A20; for crossed products, see
 \SbjNo 16S35}\endx
\ThirdLvl 16K40\SubText Infinite-dimensional and general\endx
\ThirdLvl 16K99\SubText \NoneOfAbove\endx
\SecndLvl 16L++\SubText Local rings and generalizations\endx
\ThirdLvl 16L30\SubText Noncommutative local and semilocal rings,
 perfect rings\endx
\ThirdLvl 16L60\SubText Quasi-Frobenius rings \SeeAlso{\SbjNo
 16D50}\endx
\ThirdLvl 16L99\SubText \NoneOfAbove\endx
\SecndLvl 16N++\SubText Radicals and radical properties of rings\endx
\ThirdLvl 16N20\SubText Jacobson radical, quasimultiplication\endx
\ThirdLvl 16N40\SubText Nil and nilpotent radicals, sets, ideals,
 rings\endx
\ThirdLvl 16N60\SubText Prime and semiprime rings \SeeAlso{\SbjNo
 16D30, \SbjNo 16D60, \SbjNo 16U10}\endx
\ThirdLvl 16N80\SubText General radicals and rings \SeeFor{For
 radicals in module categories, see \SbjNo 16S90}\endx
\ThirdLvl 16N99\SubText \NoneOfAbove\endx
\SecndLvl 16P++\SubText Chain conditions, growth conditions, and other
 forms of finiteness\endx
\ThirdLvl 16P10\SubText Finite rings and finite-dimensional algebras
 \SeeFor{For semisimple, see \SbjNo 16K20; for commutative, see \SbjNo
 11Txx, \SbjNo 13Mxx}\endx
\ThirdLvl 16P20\SubText Artinian rings and modules\endx
\ThirdLvl 16P40\SubText Noetherian rings and modules\endx
\ThirdLvl 16P50\SubText Localization and Noetherian rings
 \SeeAlso{\SbjNo 16U20}\endx
\ThirdLvl 16P60\SubText Chain conditions on annihilators and summands:
 Goldie type conditions \SeeAlso{\SbjNo 16U20}, Krull dimension\endx
\ThirdLvl 16P70\SubText Chain conditions on other classes of
 submodules, ideals, subrings, etc.; coherence\endx
\ThirdLvl 16P90\SubText Growth rate, Gel\cprime fand-Kirillov
 dimension\endx
\ThirdLvl 16P99\SubText \NoneOfAbove\endx
\SecndLvl 16R++\SubText Rings with polynomial identity\endx
\ThirdLvl 16R10\SubText $T$-ideals, identities, varieties of rings and
 algebras\endx
\ThirdLvl 16R20\SubText Semiprime p.i.\ rings, rings embeddable in
 matrices over commutative rings\endx
\ThirdLvl 16R30\SubText Trace rings and invariant theory\endx
\ThirdLvl 16R40\SubText Identities other than those of matrices over
 commutative rings\endx
\ThirdLvl 16R50\SubText Other kinds of identities (generalized
 polynomial, rational, involution)\endx
\ThirdLvl 16R99\SubText \NoneOfAbove\endx
\SecndLvl 16S++\SubText Rings and algebras arising under various
 constructions\endx
\ThirdLvl 16S10\SubText Rings determined by universal properties (free
 algebras, coproducts, adjunction of inverses, etc.)\endx
\ThirdLvl 16S15\SubText Finite generation, finite presentability,
 normal forms (diamond lemma, term-rewriting)\endx
\ThirdLvl 16S20\SubText Centralizing and normalizing extensions\endx
\ThirdLvl 16S30\SubText Universal enveloping algebras of Lie algebras
 \SeeMainly{\SbjNo 17B35}\endx
\ThirdLvl 16S32\SubText Rings of differential operators
 \SeeAlso{\SbjNo 13N10, \SbjNo 32C38}\endx
\ThirdLvl 16S34\SubText Group rings \SeeAlso{\SbjNo 20C05, \SbjNo
 20C07}, Laurent polynomial rings\endx
\ThirdLvl 16S35\SubText Twisted and skew group rings, crossed
 products\endx
\ThirdLvl 16S36\SubText Ordinary and skew polynomial rings and
 semigroup rings \SeeAlso{\SbjNo 20M25}\endx
\ThirdLvl 16S40\SubText Smash products of general Hopf actions
 \SeeAlso{\SbjNo 16W30}\endx
\ThirdLvl 16S50\SubText Endomorphism rings: matrix rings
 \SeeAlso{\SbjNo 15-XX}\endx
\ThirdLvl 16S60\SubText Rings of functions, subdirect products,
 sheaves of rings\endx
\ThirdLvl 16S70\SubText Extensions of rings by ideals\endx
\ThirdLvl 16S80\SubText Deformations of rings \SeeAlso{\SbjNo
 14D15}\endx
\ThirdLvl 16S90\SubText Maximal ring of quotients, torsion theories,
 radicals on module categories \SeeAlso{\SbjNo 13D30, \SbjNo 18E40}
 \SeeFor{For radicals of rings see~{\SbjNo 16Nxx}}\endx
\ThirdLvl 16S99\SubText \NoneOfAbove\endx
\SecndLvl 16U++\SubText Conditions on elements (including elements of
 matrix rings, etc.)\endx
\ThirdLvl 16U10\SubText Integral domains\endx
\ThirdLvl 16U20\SubText Ore rings, multiplicative sets, Ore
 localization\endx
\ThirdLvl 16U30\SubText Divisibility, noncommutative UFDs\endx
\ThirdLvl 16U50\SubText Algebraicity and local finiteness
 \SeeAlso{\SbjNo 16N40}\endx
\ThirdLvl 16U60\SubText Units, groups of units, general linear
 groups\endx
\ThirdLvl 16U70\SubText Center, normalizer (invariant elements)\endx
\ThirdLvl 16U80\SubText Generalizations of commutativity\endx
\ThirdLvl 16U99\SubText \NoneOfAbove\endx
\SecndLvl 16W++\SubText Rings and algebras with additional
 structure\endx
\ThirdLvl 16W10\SubText Rings with involution: Lie, Jordan and other
 nonassociative structures \SeeAlso{\SbjNo 17B60, \SbjNo 17C50, \SbjNo
 46Kxx}\endx
\ThirdLvl 16W20\SubText Automorphisms and endomorphisms, actions of
 groups and semigroups and their fixed rings\endx
\ThirdLvl 16W25\SubText Derivations, actions of Lie algebras\endx
\ThirdLvl 16W30\SubText Coalgebras, bialgebras, Hopf algebras
 \SeeAlso{\SbjNo 57T05, \SbjNo 16S30--\SbjNo 16S40}; rings, modules,
 etc. on which these act\endx
\ThirdLvl 16W50\SubText Graded rings and modules\endx
\ThirdLvl 16W55\SubText ``Super'' (or ``skew'') structure
 \SeeAlso{\SbjNo 17A70, \SbjNo 17B70, \SbjNo 17C70} \SeeFor{For
 exterior algebras, see {\SbjNo 15A75}; for Clifford algebras, see
 \SbjNo 11E88, \SbjNo 15A66}\endx
\ThirdLvl 16W60\SubText Filtrations and valuations, generalizations of
 Euclidean algorithm, completions, formal power series and related
 constructions \SeeAlso{\SbjNo 13Jxx}\endx
\ThirdLvl 16W80\SubText Topological and ordered rings and modules
 \SeeAlso{\SbjNo 13Jxx}\endx
\ThirdLvl 16W99\SubText \NoneOfAbove\endx
\SecndLvl 16Y++\SubText Generalizations \SeeFor{For nonassociative
 rings, see \SbjNo 17-xx}\endx
\ThirdLvl 16Y30\SubText Near-rings \SeeAlso{\SbjNo 12K05}\endx
\ThirdLvl 16Y60\SubText Semirings \SeeAlso{\SbjNo 12K10}\endx
\ThirdLvl 16Y99\SubText \NoneOfAbove\endx
\MajorSub 17-++\SubText Nonassociative rings and algebras\endx
\ThirdLvl 17-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 17-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 17-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 17-03\SubText \Historical\endx
\ThirdLvl 17-04\SubText \ExplicitComputation\endx
\ThirdLvl 17-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 17-08\SubText Computational methods\endx
\SecndLvl 17A++\SubText General nonassociative rings\endx
\ThirdLvl 17A01\SubText General theory\endx
\ThirdLvl 17A05\SubText Power-associative\endx
\ThirdLvl 17A10\SubText Commutative power-associative\endx
\ThirdLvl 17A15\SubText Noncommutative Jordan algebras\endx
\ThirdLvl 17A20\SubText Flexible algebras\endx
\ThirdLvl 17A25\SubText Nodal algebras\endx
\ThirdLvl 17A30\SubText Algebras satisfying other identities\endx
\ThirdLvl 17A35\SubText Division algebras\endx
\ThirdLvl 17A36\SubText Automorphisms, derivatives, other
 operators\endx
\ThirdLvl 17A40\SubText Ternary compositions\endx
\ThirdLvl 17A42\SubText Other $n$-ary compositions\endx
\ThirdLvl 17A45\SubText Quadratic algebras (but not quadratic Jordan
 algebras)\endx
\ThirdLvl 17A50\SubText Free algebras\endx
\ThirdLvl 17A60\SubText Structure theory\endx
\ThirdLvl 17A65\SubText Radical theory\endx
\ThirdLvl 17A70\SubText Superalgebras\endx
\ThirdLvl 17A75\SubText Composition algebras\endx
\ThirdLvl 17A80\SubText Valued algebras\endx
\ThirdLvl 17A99\SubText \NoneOfAbove\endx
\SecndLvl 17B++\SubText Lie algebras \SeeFor{For Lie groups, see
 \SbjNo 22Exx}\endx
\ThirdLvl 17B01\SubText Identities, free Lie algebras\endx
\ThirdLvl 17B05\SubText Structure theory\endx
\ThirdLvl 17B10\SubText Representations, algebraic theory
 (weights)\endx
\ThirdLvl 17B15\SubText Representations, analytic theory\endx
\ThirdLvl 17B20\SubText Simple, semisimple, reductive algebras
 (roots)\endx
\ThirdLvl 17B25\SubText Exceptional algebras\endx
\ThirdLvl 17B30\SubText Solvable, nilpotent algebras\endx
\ThirdLvl 17B35\SubText Universal enveloping algebras \SeeAlso{\SbjNo
 16S30}\endx
\ThirdLvl 17B37\SubText Quantum groups and related deformations
 \SeeAlso{\SbjNo 16W30, \SbjNo 81R50, \SbjNo 82B23}\endx
\ThirdLvl 17B40\SubText Automorphisms, derivations, other
 operators\endx
\ThirdLvl 17B45\SubText Lie algebras of linear algebraic groups
 \SeeAlso{\SbjNo 14Lxx and \SbjNo 20Gxx}\endx
\ThirdLvl 17B50\SubText Modular Lie algebras\endx
\ThirdLvl 17B55\SubText Homological methods in Lie algebras\endx
\ThirdLvl 17B56\SubText Cohomology of Lie algebras\endx
\ThirdLvl 17B60\SubText Lie rings associated with other structures
 (associative, Jordan, etc.) \SeeAlso{\SbjNo 15A30, \SbjNo 16W10,
 \SbjNo 17C40, \SbjNo 17C50}\endx
\ThirdLvl 17B65\SubText Infinite-dimensional Lie algebras
 \SeeAlso{\SbjNo 22E65}\endx
\ThirdLvl 17B66\SubText Lie algebras of vector fields and related
 algebras\endx
\ThirdLvl 17B67\SubText Kac-Moody algebras (structure and
 representation theory)\endx
\ThirdLvl 17B68\SubText Virasoro and related algebras\endx
\ThirdLvl 17B70\SubText Graded Lie algebras\endx
\ThirdLvl 17B81\SubText Applications to physics\endx
\ThirdLvl 17B99\SubText \NoneOfAbove\endx
\SecndLvl 17C++\SubText Jordan algebras (algebras, triples and
 pairs)\endx
\ThirdLvl 17C05\SubText Identities and free Jordan structures\endx
\ThirdLvl 17C10\SubText Structure theory\endx
\ThirdLvl 17C17\SubText Radicals\endx
\ThirdLvl 17C20\SubText Simple, semisimple algebras\endx
\ThirdLvl 17C27\SubText Idempotents, Peirce decompositions\endx
\ThirdLvl 17C30\SubText Associated groups, automorphisms\endx
\ThirdLvl 17C36\SubText Associated manifolds\endx
\ThirdLvl 17C37\SubText Associated geometries\endx
\ThirdLvl 17C40\SubText Exceptional Jordan structures\endx
\ThirdLvl 17C50\SubText Jordan structures associated with other
 structures \SeeAlso{\SbjNo 16W10}\endx
\ThirdLvl 17C55\SubText Finite-dimensional structures\endx
\ThirdLvl 17C60\SubText Division algebras\endx
\ThirdLvl 17C65\SubText Jordan structures on Banach spaces and
 algebras \SeeAlso{\SbjNo 46H70, \SbjNo 46L70}\endx
\ThirdLvl 17C70\SubText Super structures\endx
\ThirdLvl 17C90\SubText Applications to physics\endx
\ThirdLvl 17C99\SubText \NoneOfAbove\endx
\SecndLvl 17D++\SubText Other nonassociative rings and algebras\endx
\ThirdLvl 17D05\SubText Alternative rings\endx
\ThirdLvl 17D10\SubText Mal\cprime cev (Mal\cprime tsev) rings and
 algebras\endx
\ThirdLvl 17D15\SubText Right alternative rings\endx
\ThirdLvl 17D20\SubText $(\gamma, \delta)$-rings, including
 $(1,-1)$-rings\endx
\ThirdLvl 17D25\SubText Lie-admissible algebras\endx
\ThirdLvl 17D92\SubText Genetic algebras\endx
\ThirdLvl 17D99\SubText \NoneOfAbove\endx
\MajorSub 18-++\SubText Category theory, homological algebra\endx
\ThirdLvl 18-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 18-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 18-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 18-03\SubText \Historical\endx
\ThirdLvl 18-04\SubText \ExplicitComputation\endx
\ThirdLvl 18-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 18A++\SubText General theory of categories and functors\endx
\ThirdLvl 18A05\SubText Definitions, generalizations\endx
\ThirdLvl 18A10\SubText Graphs, diagram schemes, precategories,
 neocategories \SeeAlso{\SbjNo 20Lxx}\endx
\ThirdLvl 18A15\SubText Foundations, relations to logic and deductive
 systems \SeeAlso{\hbox{\SbjNo 03-XX}}\endx
\ThirdLvl 18A20\SubText Epimorphisms, monomorphisms, special classes
 of morphisms, null morphisms, factorization (bicategories)\endx
\ThirdLvl 18A22\SubText Special properties of functors (faithful,
 full, etc.)\endx
\ThirdLvl 18A23\SubText Natural morphisms, dinatural morphisms\endx
\ThirdLvl 18A25\SubText Functor categories, comma categories\endx
\ThirdLvl 18A30\SubText Limits and colimits (products, sums, directed
 limits, pushouts, fiber products, equalizers, kernels, ends and
 coends, etc.)\endx
\ThirdLvl 18A32\SubText Factorization of morphisms (via images,
 coimages, dominions, codominions), substructures, quotient
 structures, congruences, amalgams\endx
\ThirdLvl 18A35\SubText Categories admitting limits (complete
 categories), functors commuting with limits, continuous functors,
 completions\endx
\ThirdLvl 18A40\SubText Adjoint functors (representable functors,
 universal constructions, reflective subcategories, reflections,
 etc.), constructions of adjoints (Kan extensions, etc.)\endx
\ThirdLvl 18A99\SubText \NoneOfAbove\endx
\SecndLvl 18B++\SubText Special categories\endx
\ThirdLvl 18B05\SubText Category of sets, characterizations
 \SeeAlso{\SbjNo 03-XX}\endx
\ThirdLvl 18B10\SubText Category of relations, additive relations\endx
\ThirdLvl 18B15\SubText Embedding theorems, universal categories
 \SeeAlso{\SbjNo 18E20}\endx
\ThirdLvl 18B20\SubText Categories of machines, automata, operative
 categories \SeeAlso{\SbjNo 03D05, \SbjNo 68Qxx}\endx
\ThirdLvl 18B25\SubText Topoi \SeeAlso{\SbjNo 03G30}\endx
\ThirdLvl 18B30\SubText Categories of topological spaces and
 continuous mappings \SeeAlso{\SbjNo 54-XX}\endx
\ThirdLvl 18B35\SubText Preorders, orders and lattices (viewed as
 categories) \SeeAlso{\SbjNo 06-XX}\endx
\ThirdLvl 18B40\SubText Groupoids, semigroupoids, semigroups, groups
 (viewed as categories) \SeeAlso{\SbjNo 20Axx, \SbjNo 20Lxx, \SbjNo
 20Mxx}\endx
\ThirdLvl 18B99\SubText \NoneOfAbove\endx
\SecndLvl 18C++\SubText Categories and algebraic theories\endx
\ThirdLvl 18C05\SubText Equational categories \SeeAlso{\SbjNo 03C05,
 \SbjNo 08C05}\endx
\ThirdLvl 18C10\SubText Theories (e.g.\ algebraic theories),
 structure, and semantics \SeeAlso{\SbjNo 03G30}\endx
\ThirdLvl 18C15\SubText Triples (= standard construction, monad or
 triad), algebras for a triple, homology and derived functors for
 triples \SeeAlso{\SbjNo 18Gxx}\endx
\ThirdLvl 18C20\SubText Algebras and Kleisli categories associated
 with monads\endx
\ThirdLvl 18C99\SubText \NoneOfAbove\endx
\SecndLvl 18D++\SubText Categories with structure\endx
\ThirdLvl 18D05\SubText Double categories, $2$-categories,
 bicategories, hypercategories\endx
\ThirdLvl 18D10\SubText Monoidal categories (= multiplicative
 categories) \SeeAlso{\SbjNo 19D23}\endx
\ThirdLvl 18D15\SubText Closed categories (closed monoidal and
 Cartesian closed categories, etc.)\endx
\ThirdLvl 18D20\SubText Enriched categories (over closed or monoidal
 categories)\endx
\ThirdLvl 18D25\SubText Strong functors, strong adjunctions\endx
\ThirdLvl 18D30\SubText Fibered categories\endx
\ThirdLvl 18D35\SubText Structured objects in a category (group
 objects, etc.)\endx
\ThirdLvl 18D99\SubText \NoneOfAbove\endx
\SecndLvl 18E++\SubText Abelian categories\endx
\ThirdLvl 18E05\SubText Preadditive, additive categories\endx
\ThirdLvl 18E10\SubText Exact categories, abelian categories\endx
\ThirdLvl 18E15\SubText Grothendieck categories\endx
\ThirdLvl 18E20\SubText Embedding theorems \SeeAlso{\SbjNo 18B15}\endx
\ThirdLvl 18E25\SubText Derived functors and satellites\endx
\ThirdLvl 18E30\SubText Derived categories, triangulated
 categories\endx
\ThirdLvl 18E35\SubText Localization of categories\endx
\ThirdLvl 18E40\SubText Torsion theories, radicals \SeeAlso{\SbjNo
 13D30, \SbjNo 16S90}\endx
\ThirdLvl 18E99\SubText \NoneOfAbove\endx
\SecndLvl 18F++\SubText Categories and geometry\endx
\ThirdLvl 18F05\SubText Local categories and functors\endx
\ThirdLvl 18F10\SubText Grothendieck topologies \SeeAlso{\SbjNo
 14F20}\endx
\ThirdLvl 18F15\SubText Abstract manifolds and fiber bundles
 \SeeAlso{\SbjNo 55Rxx, \SbjNo 57Pxx}\endx
\ThirdLvl 18F20\SubText Presheaves and sheaves \SeeAlso{\SbjNo 14F05,
 \SbjNo 32C35, \SbjNo 32L10, \SbjNo 54B40, \SbjNo 55N30}\endx
\ThirdLvl 18F25\SubText Algebraic $K$-theory and $L$-theory
 \SeeAlso{\SbjNo 11Exx, \SbjNo 11R70, \SbjNo 11S70, % \endx
\hbox{\SbjNo 12-XX}, \SbjNo 13D15, \SbjNo 14Cxx, \SbjNo 16E20, \SbjNo
 19-XX, \SbjNo 46L80, \SbjNo 57R65, \SbjNo 57R67}\endx
\ThirdLvl 18F30\SubText Grothendieck groups \SeeAlso{\SbjNo 13D15,
 \SbjNo 16E20, \SbjNo 19Axx}\endx
\ThirdLvl 18F99\SubText \NoneOfAbove\endx
\SecndLvl 18G++\SubText Homological algebra \SeeAlso{\SbjNo 13Dxx,
 \SbjNo 16Exx, \SbjNo 55Uxx}\endx
\ThirdLvl 18G05\SubText Projectives and injectives \SeeAlso{\SbjNo
 13C10, \SbjNo 13C11, \SbjNo 16D40, \SbjNo 16D50}\endx
\ThirdLvl 18G10\SubText Resolutions; derived functors \SeeAlso{\SbjNo
 18E25}\endx
\ThirdLvl 18G15\SubText Ext and Tor, generalizations, K\"unneth
 formula \SeeAlso{\SbjNo 55U25}\endx
\ThirdLvl 18G20\SubText Homological dimension \SeeAlso{\SbjNo 13D05,
 \SbjNo 16E10}\endx
\ThirdLvl 18G25\SubText Relative homological algebra, projective
 classes\endx
\ThirdLvl 18G30\SubText Simplicial sets, simplicial objects (in a
 category) \SeeAlso{\SbjNo 55U10}\endx
\ThirdLvl 18G35\SubText Chain complexes \SeeAlso{\SbjNo 18E30, \SbjNo
 55U15}\endx
\ThirdLvl 18G40\SubText Spectral sequences, hypercohomology
 \SeeAlso{\SbjNo 55Txx}\endx
\ThirdLvl 18G50\SubText Nonabelian homological algebra \endx
\ThirdLvl 18G55\SubText Nonabelian homotopical algebra\endx
\ThirdLvl 18G60\SubText Other (co)homology theories (cyclic, dihedral,
 etc.) \SeeAlso{\SbjNo 19D55, \SbjNo 46L80, \SbjNo 58B30, \SbjNo
 58G12}\endx
\ThirdLvl 18G99\SubText \NoneOfAbove\endx
\MajorSub 19-++\SubText $K$-theory \SeeAlso{\SbjNo 16E20, \SbjNo
 18F25}\endx
\ThirdLvl 19-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 19-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 19-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 19-03\SubText \Historical\endx
\ThirdLvl 19-04\SubText \ExplicitComputation\endx
\ThirdLvl 19-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 19A++\SubText Grothendieck groups and $K\sb 0$
 \SeeAlso{\SbjNo 13D15, \SbjNo 18F30}\endx
\ThirdLvl 19A13\SubText Stability for projective modules
 \SeeAlso{\SbjNo 13C10}\endx
\ThirdLvl 19A15\SubText Efficient generation\endx
\ThirdLvl 19A22\SubText Frobenius induction, Burnside and
 representation rings\endx
\ThirdLvl 19A31\SubText $K\sb 0$ of group rings and orders\endx
\ThirdLvl 19A49\SubText $K\sb 0$ of other rings\endx
\ThirdLvl 19A99\SubText \NoneOfAbove\endx
\SecndLvl 19B++\SubText Whitehead groups and $K\sb 1$\endx
\ThirdLvl 19B10\SubText Stable range conditions\endx
\ThirdLvl 19B14\SubText Stability for linear groups\endx
\ThirdLvl 19B28\SubText $K\sb 1$ of group rings and orders
 \SeeAlso{\SbjNo 57Q10}\endx
\ThirdLvl 19B37\SubText Congruence subgroup problems \SeeAlso{\SbjNo
 20H05}\endx
\ThirdLvl 19B99\SubText \NoneOfAbove\endx
\SecndLvl 19C++\SubText Steinberg groups and $K\sb 2$\endx
\ThirdLvl 19C09\SubText Central extensions and Schur multipliers\endx
\ThirdLvl 19C20\SubText Symbols, presentations and stability of $K\sb
 2$\endx
\ThirdLvl 19C30\SubText $K\sb 2$ and the Brauer group\endx
\ThirdLvl 19C40\SubText Excision for $K\sb 2$\endx
\ThirdLvl 19C99\SubText \NoneOfAbove\endx
\SecndLvl 19D++\SubText Higher algebraic $K$-theory\endx
\ThirdLvl 19D06\SubText $Q$- and plus-constructions\endx
\ThirdLvl 19D10\SubText Algebraic $K$-theory of spaces\endx
\ThirdLvl 19D23\SubText Symmetric monoidal categories \SeeAlso{\SbjNo
 18D10}\endx
\ThirdLvl 19D25\SubText Karoubi-Villamayor-Gersten $K$-theory\endx
\ThirdLvl 19D35\SubText Negative $K$-theory, NK and Nil\endx
\ThirdLvl 19D45\SubText Higher symbols, Milnor $K$-theory\endx
\ThirdLvl 19D50\SubText Computations of higher $K$-theory of rings
 \SeeAlso{\SbjNo 13D15, \SbjNo 16E20}\endx
\ThirdLvl 19D55\SubText $K$-theory and homology; cyclic homology and
 cohomology \SeeAlso{\SbjNo 18G60}\endx
\ThirdLvl 19D99\SubText \NoneOfAbove\endx
\SecndLvl 19E++\SubText $K$-theory in geometry\endx
\ThirdLvl 19E08\SubText $K$-theory of schemes \SeeAlso{\SbjNo
 14C35}\endx
\ThirdLvl 19E15\SubText Algebraic cycles \SeeAlso{\SbjNo 14C25, \SbjNo
 14C35}\endx
\ThirdLvl 19E20\SubText Relations with cohomology theories
 \SeeAlso{\SbjNo 14Fxx}\endx
\ThirdLvl 19E99\SubText \NoneOfAbove\endx
\SecndLvl 19F++\SubText $K$-theory in number theory \SeeAlso{\SbjNo
 11R70, \SbjNo 11S70}\endx
\ThirdLvl 19F05\SubText Generalized class field theory \SeeAlso{\SbjNo
 11G45}\endx
\ThirdLvl 19F15\SubText Symbols and arithmetic \SeeAlso{\SbjNo
 11R37}\endx
\ThirdLvl 19F27\SubText \'Etale cohomology, higher regulators, zeta
 and $L$-functions \SeeAlso{\SbjNo 11G40, \SbjNo 11R42, \SbjNo 11S40,
 \SbjNo 14F20, \SbjNo 14G10}\endx
\ThirdLvl 19F99\SubText \NoneOfAbove\endx
\SecndLvl 19G++\SubText $K$-theory of forms \SeeAlso{\SbjNo
 11E++}\endx
\ThirdLvl 19G05\SubText Stability for quadratic modules\endx
\ThirdLvl 19G12\SubText Witt groups of rings \SeeAlso{\SbjNo
 11E81}\endx
\ThirdLvl 19G24\SubText $L$-theory of group rings \SeeAlso{\SbjNo
 11E81}\endx
\ThirdLvl 19G38\SubText Hermitian $K$-theory, relations with
 $K$-theory of rings\endx
\ThirdLvl 19G99\SubText \NoneOfAbove\endx
\SecndLvl 19J++\SubText Obstructions from topology\endx
\ThirdLvl 19J05\SubText Finiteness and other obstructions in $K\sb
 0$\endx
\ThirdLvl 19J10\SubText Whitehead (and related) torsion\endx
\ThirdLvl 19J25\SubText Surgery obstructions \SeeAlso{\SbjNo
 57R67}\endx
\ThirdLvl 19J35\SubText Obstructions to group actions\endx
\ThirdLvl 19J99\SubText \NoneOfAbove\endx
\SecndLvl 19K++\SubText $K$-theory and operator algebras
 \SeeMainly{\SbjNo 46L80, and also \SbjNo 46M20}\endx
\ThirdLvl 19K14\SubText $K\sb 0$ as an ordered group, traces\endx
\ThirdLvl 19K33\SubText EXT and $K$-homology \SeeAlso{\SbjNo
 55N22}\endx
\ThirdLvl 19K35\SubText Kasparov theory ($KK$-theory) \SeeAlso{\SbjNo
 58G12}\endx
\ThirdLvl 19K56\SubText Index theory \SeeAlso{\SbjNo 58G12}\endx
\ThirdLvl 19K99\SubText \NoneOfAbove\endx
\SecndLvl 19L++\SubText Topological $K$-theory \SeeAlso{\SbjNo 55N15,
 \SbjNo 55R50, \SbjNo 55S25}\endx
\ThirdLvl 19L10\SubText Riemann-Roch theorems, Chern characters\endx
\ThirdLvl 19L20\SubText $J$-homomorphism, Adams operations
 \SeeAlso{\SbjNo 55Q50}\endx
\ThirdLvl 19L41\SubText Connective $K$-theory, cobordism
 \SeeAlso{\SbjNo 55N22}\endx
\ThirdLvl 19L47\SubText Equivariant $K$-theory \SeeAlso{\SbjNo 55N91,
 \SbjNo 55P91, \SbjNo 55Q91, \SbjNo 55R91, \SbjNo 55S91}\endx
\ThirdLvl 19L64\SubText Computations, geometric applications\endx
\ThirdLvl 19L99\SubText \NoneOfAbove\endx
\SecndLvl 19M05\SubText Miscellaneous applications of $K$-theory\endx
\MajorSub 20-++\SubText Group theory and generalizations\endx
\ThirdLvl 20-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 20-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 20-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 20-03\SubText \Historical\endx
\ThirdLvl 20-04\SubText \ExplicitComputation\endx
\ThirdLvl 20-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 20A++\SubText Foundations\endx
\ThirdLvl 20A05\SubText Axiomatics and elementary properties\endx
\ThirdLvl 20A10\SubText Metamathematical considerations \SeeFor{For
 word problems, see \SbjNo 20F10}\endx
\ThirdLvl 20A15\SubText Applications of logic to group theory\endx
\ThirdLvl 20A99\SubText \NoneOfAbove\endx
\SecndLvl 20B++\SubText Permutation groups\endx
\ThirdLvl 20B05\SubText General theory for finite groups\endx
\ThirdLvl 20B07\SubText General theory for infinite groups\endx
\ThirdLvl 20B10\SubText Characterization theorems\endx
\ThirdLvl 20B15\SubText Primitive groups\endx
\ThirdLvl 20B20\SubText Multiply transitive finite groups\endx
\ThirdLvl 20B22\SubText Multiply transitive infinite groups\endx
\ThirdLvl 20B25\SubText Finite automorphism groups of algebraic,
 geometric, or combinatorial structures \SeeAlso{\SbjNo 05Bxx, \SbjNo
 12F10, \SbjNo 20G40, \SbjNo 20H30, \SbjNo 51-XX}\endx
\ThirdLvl 20B27\SubText Infinite automorphism groups \SeeAlso{\SbjNo
 12F10}\endx
\ThirdLvl 20B30\SubText Symmetric groups \endx
\ThirdLvl 20B35\SubText Subgroups of symmetric groups\endx
\ThirdLvl 20B40\SubText Computational methods\endx
\ThirdLvl 20B99\SubText \NoneOfAbove\endx
\SecndLvl 20C++\SubText Representation theory of groups
 \SeeAlso{\SbjNo 19A22 (for representation rings and Burnside
 rings)}\endx
\ThirdLvl 20C05\SubText Group rings of finite groups and their modules
 \SeeAlso{\SbjNo 16S34}\endx
\ThirdLvl 20C07\SubText Group rings of infinite groups and their
 modules \SeeAlso{\SbjNo 16S34}\endx
\ThirdLvl 20C10\SubText Integral representations of finite groups\endx
\ThirdLvl 20C11\SubText $p$-adic representations of finite groups\endx
\ThirdLvl 20C12\SubText Integral representations of infinite
 groups\endx
\ThirdLvl 20C15\SubText Ordinary representations and characters\endx
\ThirdLvl 20C20\SubText Modular representations and characters\endx
\ThirdLvl 20C25\SubText Projective representations and
 multipliers\endx
\ThirdLvl 20C30\SubText Representations of finite symmetric
 groups\endx
\ThirdLvl 20C32\SubText Representations of infinite symmetric
 groups\endx
\ThirdLvl 20C33\SubText Representations of finite groups of Lie
 type\endx
\ThirdLvl 20C34\SubText Representations of sporadic groups\endx
\ThirdLvl 20C35\SubText Applications of group representations to
 physics\endx
\ThirdLvl 20C40\SubText Computational methods\endx
\ThirdLvl 20C99\SubText \NoneOfAbove\endx
\SecndLvl 20D++\SubText Abstract finite groups\endx
\ThirdLvl 20D05\SubText Classification of simple and nonsolvable
 groups\endx
\ThirdLvl 20D06\SubText Simple groups: alternating groups and groups
 of Lie type \SeeAlso{\SbjNo 20Gxx, \SbjNo 22Exx}\endx
\ThirdLvl 20D08\SubText Simple groups: sporadic groups\endx
\ThirdLvl 20D10\SubText Solvable groups, theory of formations, Schunck
 classes, Fitting classes, $\pi$-length, ranks \SeeAlso{\SbjNo
 20F17}\endx
\ThirdLvl 20D15\SubText Nilpotent groups, $p$-groups\endx
\ThirdLvl 20D20\SubText Sylow subgroups, Sylow properties,
 $\pi$-groups, $\pi$-structure\endx
\ThirdLvl 20D25\SubText Special subgroups (Frattini, Fitting,
 etc.)\endx
\ThirdLvl 20D30\SubText Series and lattices of subgroups\endx
\ThirdLvl 20D35\SubText Subnormal subgroups\endx
\ThirdLvl 20D40\SubText Products of subgroups\endx
\ThirdLvl 20D45\SubText Automorphisms\endx
\ThirdLvl 20D50\SubText Covering of subgroups\endx
\ThirdLvl 20D60\SubText Arithmetic and combinatorial problems\endx
\ThirdLvl 20D99\SubText \NoneOfAbove\endx
\SecndLvl 20E++\SubText Structure and classification of infinite or
 finite groups\endx
\ThirdLvl 20E05\SubText Free nonabelian groups\endx
\ThirdLvl 20E06\SubText Free products, free products with
 amalgamation, Higman-Neumann-Neumann extensions, and
 generalizations\endx
\ThirdLvl 20E07\SubText Subgroup theorems\endx
\ThirdLvl 20E08\SubText Groups acting on trees\endx
\ThirdLvl 20E10\SubText Quasivarieties and varieties of groups\endx
\ThirdLvl 20E15\SubText Chains and lattices of subgroups, subnormal
 subgroups \SeeAlso{\SbjNo 20F22}\endx
\ThirdLvl 20E18\SubText Limits, profinite groups\endx
\ThirdLvl 20E22\SubText Extensions, wreath products, and other
 compositions \SeeAlso{\SbjNo 20J05}\endx
\ThirdLvl 20E25\SubText Local properties\endx
\ThirdLvl 20E26\SubText Residual properties and generalizations\endx
\ThirdLvl 20E28\SubText Maximal subgroups\endx
\ThirdLvl 20E32\SubText Simple groups \SeeAlso{\SbjNo 20D05}\endx
\ThirdLvl 20E34\SubText General structure theorems\endx
\ThirdLvl 20E36\SubText General theorems concerning automorphisms of
 groups\endx
\ThirdLvl 20E42\SubText Groups with a $BN$-pair; buildings
 \SeeAlso{\SbjNo 51E24}\endx
\ThirdLvl 20E99\SubText \NoneOfAbove\endx
\SecndLvl 20F++\SubText Special aspects of infinite or finite
 groups\endx
\ThirdLvl 20F05\SubText Generators, relations, and presentations\endx
\ThirdLvl 20F06\SubText Cancellation theory; application of van Kampen
 diagrams \SeeAlso{\SbjNo 57M05}\endx
\ThirdLvl 20F10\SubText Word problems, other decision problems,
 connections with logic and automata \SeeAlso{\SbjNo 03B25, \SbjNo
 03D05, \SbjNo 03D40, \SbjNo 06B25, \SbjNo 08A50, \SbjNo 68Qxx}\endx
\ThirdLvl 20F12\SubText Commutator calculus\endx
\ThirdLvl 20F14\SubText Derived series, central series, and
 generalizations\endx
\ThirdLvl 20F16\SubText Solvable groups, supersolvable groups\endx
\ThirdLvl 20F17\SubText Formations of groups, Fitting classes
 \SeeAlso{\SbjNo 20D10}\endx
\ThirdLvl 20F18\SubText Nilpotent groups\endx
\ThirdLvl 20F19\SubText Generalizations of solvable and nilpotent
 groups\endx
\ThirdLvl 20F22\SubText Other classes of groups defined by subgroup
 chains\endx
\ThirdLvl 20F24\SubText FC-groups and their generalizations\endx
\ThirdLvl 20F28\SubText Automorphism groups of groups \SeeAlso{\SbjNo
 20E36}\endx
\ThirdLvl 20F29\SubText Representations of groups as automorphism
 groups of algebraic systems\endx
\ThirdLvl 20F32\SubText Geometric group theory \SeeAlso{\SbjNo 05C25,
 \SbjNo 20Exx, \SbjNo 20Gxx}\endx
\ThirdLvl 20F34\SubText Fundamental groups and their automorphisms
 \SeeAlso{\SbjNo 57M05, \SbjNo 57Sxx, \SbjNo 22E40}\endx
\ThirdLvl 20F36\SubText Braid groups; Artin groups\endx
\ThirdLvl 20F38\SubText Other groups related to topology or
 analysis\endx
\ThirdLvl 20F40\SubText Associated Lie structures\endx
\ThirdLvl 20F45\SubText Engel conditions\endx
\ThirdLvl 20F50\SubText Periodic groups; locally finite groups\endx
\ThirdLvl 20F55\SubText Coxeter groups \SeeAlso{\SbjNo 22E40}\endx
\ThirdLvl 20F60\SubText Ordered groups \SeeMainly{\SbjNo 06F15}\endx
\ThirdLvl 20F99\SubText \NoneOfAbove\endx
\SecndLvl 20G++\SubText Linear algebraic groups (classical groups)
 \SeeFor{For arithmetic theory, see \SbjNo 11E57, \SbjNo 11H06; for
 geometric theory, see \SbjNo 14Lxx, \SbjNo 22Exx; for other methods
 in representation theory, see \CMPonly{\SbjNo 15AQ30, \SbjNo
 22Exx}\FullScheme{\SbjNo 15A30, \SbjNo 22E45, \SbjNo 22E46, \SbjNo
 22E47, \SbjNo 22E50, \SbjNo 22E55}}\endx
\ThirdLvl 20G05\SubText Representation theory\endx
\ThirdLvl 20G10\SubText Cohomology theory\endx
\ThirdLvl 20G15\SubText Linear algebraic groups over arbitrary
 fields\endx
\ThirdLvl 20G20\SubText Linear algebraic groups over the reals, the
 complexes, the quaternions\endx
\ThirdLvl 20G25\SubText Linear algebraic groups over local fields and
 their integers\endx
\ThirdLvl 20G30\SubText Linear algebraic groups over global fields and
 their integers\endx
\ThirdLvl 20G35\SubText Linear algebraic groups over ad\`eles and
 other rings and schemes\endx
\ThirdLvl 20G40\SubText Linear algebraic groups over finite
 fields\endx
\ThirdLvl 20G45\SubText Applications to physics; explicit
 representations\endx
\ThirdLvl 20G99\SubText \NoneOfAbove\endx
\SecndLvl 20H++\SubText Other groups of matrices \SeeAlso{\SbjNo
 15A30}\endx
\ThirdLvl 20H05\SubText Unimodular groups, congruence subgroups
 \SeeAlso{\SbjNo 11F06, \SbjNo 19B37, \SbjNo 22E40, \SbjNo 51F20}\endx
\ThirdLvl 20H10\SubText Fuchsian groups and their generalizations
 \SeeAlso{\SbjNo 11F06, \SbjNo 22E40, \SbjNo 30F35, \SbjNo 32Nxx}\endx
\ThirdLvl 20H15\SubText Other geometric groups, including
 crystallographic groups \SeeAlso{\SbjNo 51-XX, especially \SbjNo
 51F15, and \SbjNo 82D25}\endx
\ThirdLvl 20H20\SubText Other matrix groups over fields\endx
\ThirdLvl 20H25\SubText Other matrix groups over rings\endx
\ThirdLvl 20H30\SubText Other matrix groups over finite fields\endx
\ThirdLvl 20H99\SubText \NoneOfAbove\endx
\SecndLvl 20J++\SubText Connections with homological algebra and
 category theory\endx
\ThirdLvl 20J05\SubText Homological methods in group theory\endx
\ThirdLvl 20J06\SubText Cohomology of finite groups\endx
\ThirdLvl 20J10\SubText Groups arising as cohomology groups\endx
\ThirdLvl 20J15\SubText Category of groups\endx
\ThirdLvl 20J99\SubText \NoneOfAbove\endx
\SecndLvl 20K++\SubText Abelian groups\endx
\ThirdLvl 20K01\SubText Finite abelian groups\endx
\ThirdLvl 20K05\SubText Finitely generated groups\endx
\ThirdLvl 20K10\SubText Torsion groups, primary groups and generalized
 primary groups\endx
\ThirdLvl 20K12\SubText Ulm sequences\endx
\ThirdLvl 20K15\SubText Torsion free groups, finite rank\endx
\ThirdLvl 20K20\SubText Torsion free groups, infinite rank\endx
\ThirdLvl 20K21\SubText Mixed groups\endx
\ThirdLvl 20K25\SubText Direct sums, direct products, etc.\endx
\ThirdLvl 20K26\SubText Indecomposable groups\endx
\ThirdLvl 20K27\SubText Subgroups\endx
\ThirdLvl 20K30\SubText Automorphisms, homomorphisms, endomorphisms,
 etc.\endx
\ThirdLvl 20K35\SubText Extensions\endx
\ThirdLvl 20K40\SubText Homological and categorical methods\endx
\ThirdLvl 20K45\SubText Topological methods \SeeAlso{\SbjNo 22A05,
 \SbjNo 22B05}\endx
\ThirdLvl 20K99\SubText \NoneOfAbove\endx
\SecndLvl 20L++\SubText Groupoids (i.e.\ small categories in which all
 morphisms are isomorphisms) \SeeFor{For sets with a single binary
 operation, see \SbjNo 20N02; for topological groupoids, see \SbjNo
 22A22, \SbjNo 58H05}\endx
\ThirdLvl 20L05\SubText General theory\endx
\ThirdLvl 20L10\SubText Connections with group theory\endx
\ThirdLvl 20L13\SubText Mappings of groupoids\endx
\ThirdLvl 20L15\SubText Connections with topology\endx
\ThirdLvl 20L17\SubText Connections with category theory\endx
\ThirdLvl 20L99\SubText \NoneOfAbove\endx
\SecndLvl 20M++\SubText Semigroups\endx
\ThirdLvl 20M05\SubText Free semigroups, generators and relations,
 word problems\endx
\ThirdLvl 20M07\SubText Varieties of semigroups\endx
\ThirdLvl 20M10\SubText General structure theory\endx
\ThirdLvl 20M11\SubText Radical theory\endx
\ThirdLvl 20M12\SubText Ideal theory\endx
\ThirdLvl 20M14\SubText Commutative semigroups\endx
\ThirdLvl 20M15\SubText Mappings of semigroups\endx
\ThirdLvl 20M17\SubText Regular semigroups \endx
\ThirdLvl 20M18\SubText Inverse semigroups\endx
\ThirdLvl 20M19\SubText Orthodox semigroups\endx
\ThirdLvl 20M20\SubText Semigroups of transformations, etc.
 \SeeAlso{\SbjNo 47D03, \SbjNo 47H20, \SbjNo 54H15}\endx
\ThirdLvl 20M25\SubText Semigroup rings, multiplicative semigroups of
 rings \SeeAlso{\SbjNo 16S36, \SbjNo 16Y60}\endx
\ThirdLvl 20M30\SubText Representation of semigroups\endx
\ThirdLvl 20M35\SubText Semigroups in automata theory, linguistics,
 etc. \SeeAlso{\SbjNo 03D05, \SbjNo 68Qxx, \SbjNo 68S05}\endx
\ThirdLvl 20M50\SubText Connections of semigroups with homological
 algebra and category theory\endx
\ThirdLvl 20M99\SubText \NoneOfAbove\endx
\SecndLvl 20N++\SubText Other generalizations of groups\endx
\ThirdLvl 20N02\SubText Sets with a single binary operation
 (groupoids)\endx
\ThirdLvl 20N05\SubText Loops, quasigroups \SeeAlso{\SbjNo 05Bxx}\endx
\ThirdLvl 20N07\SubText Mappings of loops\endx
\ThirdLvl 20N10\SubText Ternary systems (heaps, semiheaps, heapoids,
 etc.)\endx
\ThirdLvl 20N15\SubText $n$-ary systems\endx
\ThirdLvl 20N20\SubText Hypergroups\endx
\ThirdLvl 20N25\SubText Fuzzy groups \SeeAlso{\SbjNo 04A72}\endx
\ThirdLvl 20N99\SubText \NoneOfAbove\endx
\SecndLvl 20P05\SubText Probabilistic methods in group theory\endx
\MajorSub 22-++\SubText Topological groups, Lie groups \SeeFor{For
 transformation groups, see~\SbjNo 54H15, \SbjNo 57Sxx, \SbjNo 58-XX.
 For abstract harmonic analysis, see~\SbjNo 43-XX}\endx
\ThirdLvl 22-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 22-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 22-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 22-03\SubText \Historical\endx
\ThirdLvl 22-04\SubText \ExplicitComputation\endx
\ThirdLvl 22-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 22A++\SubText Topological and differentiable algebraic
 systems \SeeFor{For topological rings and fields, see \SbjNo 12Jxx,
 \SbjNo 13Jxx, \SbjNo 16W80; for dual spaces of operator algebras and
 topological groups, see \SbjNo 47D35}\endx
\ThirdLvl 22A05\SubText Structure of general topological groups\endx
\ThirdLvl 22A10\SubText Analysis on general topological groups\endx
\ThirdLvl 22A15\SubText Structure of topological semigroups\endx
\ThirdLvl 22A20\SubText Analysis on topological semigroups\endx
\ThirdLvl 22A22\SubText Topological groupoids (including
 differentiable and Lie groupoids)\endx
\ThirdLvl 22A25\SubText Representations of general topological groups
 and semigroups\endx
\ThirdLvl 22A26\SubText Topological semilattices, lattices and
 applications \SeeAlso{\SbjNo 06B30, \SbjNo 06B35, \SbjNo 06F30}\endx
\ThirdLvl 22A30\SubText Other topological algebraic systems and their
 representations\endx
\ThirdLvl 22A99\SubText \NoneOfAbove\endx
\SecndLvl 22B++\SubText Locally compact abelian groups (LCA
 groups)\endx
\ThirdLvl 22B05\SubText General properties and structure of LCA
 groups\endx
\ThirdLvl 22B10\SubText Structure of group algebras of LCA groups\endx
\ThirdLvl 22B99\SubText \NoneOfAbove\endx
\SecndLvl 22C05\SubText Compact groups\endx
\SecndLvl 22D++\SubText Locally compact groups and their algebras\endx
\ThirdLvl 22D05\SubText General properties and structure of locally
 compact groups\endx
\ThirdLvl 22D10\SubText Unitary representations of locally compact
 groups\endx
\ThirdLvl 22D12\SubText Other representations of locally compact
 groups\endx
\ThirdLvl 22D15\SubText Group algebras of locally compact groups\endx
\ThirdLvl 22D20\SubText Representations of group algebras\endx
\ThirdLvl 22D25\SubText $C$*-algebras and $W$*-algebras arising from
 group representations \SeeAlso{\SbjNo 46Lxx}\endx
\ThirdLvl 22D30\SubText Induced representations\endx
\ThirdLvl 22D35\SubText Duality theorems\endx
\ThirdLvl 22D40\SubText Ergodic theory on groups \SeeAlso{\SbjNo
 28Dxx, \SbjNo 43A60}\endx
\ThirdLvl 22D45\SubText Automorphism groups of locally compact
 groups\endx
\ThirdLvl 22D99\SubText \NoneOfAbove\endx
\SecndLvl 22E++\SubText Lie groups \SeeFor{For the topology of Lie
 groups and homogeneous spaces, see \CMPonly{\SbjNo
 57-XX}\FullScheme{\SbjNo 57Sxx, \SbjNo 57Txx}; for analysis thereon,
 see \CMPonly{\SbjNo 43-XX}\FullScheme{\SbjNo 43A80, \SbjNo 43A85,
 \SbjNo 43A90}}\endx
\ThirdLvl 22E05\SubText Local Lie groups \SeeAlso{\SbjNo 34-XX, \SbjNo
 35-XX, \SbjNo 58H05}\endx
\ThirdLvl 22E10\SubText General properties and structure of complex
 Lie groups \SeeAlso{\SbjNo 32M05}\endx
\ThirdLvl 22E15\SubText General properties and structure of real Lie
 groups\endx
\ThirdLvl 22E20\SubText General properties and structure of other Lie
 groups\endx
\ThirdLvl 22E25\SubText Nilpotent and solvable Lie groups\endx
\ThirdLvl 22E27\SubText Representations of nilpotent and solvable Lie
 groups (special orbital integrals, non-type I representations,
 etc.)\endx
\ThirdLvl 22E30\SubText Analysis on real and complex Lie groups
 \SeeAlso{\SbjNo 33C80, \SbjNo 43-XX}\endx
\ThirdLvl 22E35\SubText Analysis on $p$-adic Lie groups
 \SeeAlso{\SbjNo 11R56}\endx
\ThirdLvl 22E40\SubText Discrete subgroups of Lie groups
 \SeeAlso{\SbjNo 20Hxx, \SbjNo 32Nxx}\endx
\ThirdLvl 22E41\SubText Continuous cohomology \SeeAlso{\SbjNo 57R32,
 \SbjNo 57Txx, \SbjNo 58H10}\endx
\ThirdLvl 22E43\SubText Structure and representation of the Lorentz
 group\endx
\ThirdLvl 22E45\SubText Representations of Lie and linear algebraic
 groups over real fields: analytic methods \SeeFor{For the purely
 algebraic theory, see \SbjNo 20G05}\endx
\ThirdLvl 22E46\SubText Semisimple Lie groups and their
 representations\endx
\ThirdLvl 22E47\SubText Representations of Lie and real algebraic
 groups: algebraic methods (Verma modules, etc.) \SeeAlso{\SbjNo
 17B35}\endx
\ThirdLvl 22E50\SubText Representations of Lie and linear algebraic
 groups over local fields\endx
\ThirdLvl 22E55\SubText Representations of Lie and linear algebraic
 groups over global fields and ad\`ele rings \SeeAlso{\SbjNo
 20G05}\endx
\ThirdLvl 22E60\SubText Lie algebras of Lie groups \SeeFor{For the
 algebraic theory of Lie algebras, see \SbjNo 17Bxx}\endx
\ThirdLvl 22E65\SubText Infinite-dimensional Lie groups and their Lie
 algebras \SeeAlso{\SbjNo 17B65, \SbjNo 58B25, \SbjNo 58H05}\endx
\ThirdLvl 22E67\SubText Loop groups and related constructions,
 group-theoretic treatment \SeeAlso{\SbjNo 58D05}\endx
\ThirdLvl 22E70\SubText Applications of Lie groups to physics;
 explicit representations \SeeAlso{\SbjNo 81R05, \SbjNo 81R10}\endx
\ThirdLvl 22E99\SubText \NoneOfAbove\endx
\MajorSub 26-++\SubText Real functions \SeeAlso{\SbjNo 54C30}\endx
\ThirdLvl 26-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 26-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 26-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 26-03\SubText \Historical\endx
\ThirdLvl 26-04\SubText \ExplicitComputation\endx
\ThirdLvl 26-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 26A++\SubText Functions of one variable\endx
\ThirdLvl 26A03\SubText Foundations: limits and generalizations,
 elementary topology of the line\endx
\ThirdLvl 26A06\SubText One-variable calculus\endx
\ThirdLvl 26A09\SubText Elementary functions\endx
\ThirdLvl 26A12\SubText Rate of growth of functions, orders of
 infinity, slowly varying functions \SeeAlso{\SbjNo 26A48}\endx
\ThirdLvl 26A15\SubText Continuity and related questions (modulus of
 continuity, semicontinuity, discontinuities, etc.) \SeeFor{For
 properties determined by Fourier coefficients, see \SbjNo 42A16; for
 those determined by approximation properties, see \SbjNo 41A25,
 \SbjNo 41A27}\endx
\ThirdLvl 26A16\SubText Lipschitz (H\"older) classes\endx
\ThirdLvl 26A18\SubText Iteration \SeeAlso{\SbjNo 39B12, \SbjNo 47H10,
 \SbjNo 54H25, \SbjNo 58F08, \SbjNo 58F13}\endx
\ThirdLvl 26A21\SubText Classification of real functions; Baire
 classification of sets and functions \SeeAlso{\SbjNo 04A15, \SbjNo
 28A05, \SbjNo 54C50}\endx
\ThirdLvl 26A24\SubText Differentiation (functions of one variable):
 general theory, generalized derivatives, mean-value theorems
 \SeeAlso{\SbjNo 28A15}\endx
\ThirdLvl 26A27\SubText Nondifferentiability (nondifferentiable
 functions, points of nondifferentiability), discontinuous
 derivatives\endx
\ThirdLvl 26A30\SubText Singular functions, Cantor functions,
 functions with other special properties\endx
\ThirdLvl 26A33\SubText Fractional derivatives and integrals\endx
\ThirdLvl 26A36\SubText Antidifferentiation\endx
\ThirdLvl 26A39\SubText Denjoy and Perron integrals, other special
 integrals\endx
\ThirdLvl 26A42\SubText Integrals of Riemann, Stieltjes and Lebesgue
 type \SeeAlso{\SbjNo 28-XX}\endx
\ThirdLvl 26A45\SubText Functions of bounded variation,
 generalizations\endx
\ThirdLvl 26A46\SubText Absolutely continuous functions\endx
\ThirdLvl 26A48\SubText Monotonic functions, generalizations\endx
\ThirdLvl 26A51\SubText Convexity, generalizations\endx
\ThirdLvl 26A99\SubText \NoneOfAbove\endx
\SecndLvl 26B++\SubText Functions of several variables\endx
\ThirdLvl 26B05\SubText Continuity and differentiation questions\endx
\ThirdLvl 26B10\SubText Implicit function theorems, Jacobians,
 transformations with several variables\endx
\ThirdLvl 26B12\SubText Calculus of vector functions\endx
\ThirdLvl 26B15\SubText Integration: length, area, volume
 \SeeAlso{\SbjNo 28A75, \SbjNo 51M25}\endx
\ThirdLvl 26B20\SubText Integral formulas (Stokes, Gauss, Green,
 etc.)\endx
\ThirdLvl 26B25\SubText Convexity, generalizations\endx
\ThirdLvl 26B30\SubText Absolutely continuous functions, functions of
 bounded variation\endx
\ThirdLvl 26B35\SubText Special properties of functions of several
 variables, H\"older conditions, etc.\endx
\ThirdLvl 26B40\SubText Representation and superposition of
 functions\endx
\ThirdLvl 26B99\SubText \NoneOfAbove\endx
\SecndLvl 26C++\SubText Polynomials, rational functions\endx
\ThirdLvl 26C05\SubText Polynomials: analytic properties, etc.
 \SeeAlso{\SbjNo 12Dxx, \SbjNo 12Exx}\endx
\ThirdLvl 26C10\SubText Polynomials: location of zeros \SeeAlso{\SbjNo
 12D10, \SbjNo 30C15, \SbjNo 65H05}\endx
\ThirdLvl 26C15\SubText Rational functions \SeeAlso{\SbjNo 14Pxx}\endx
\ThirdLvl 26C99\SubText \NoneOfAbove\endx
\SecndLvl 26D++\SubText Inequalities \SeeFor{For maximal function
 inequalities, see \SbjNo 42B25; for functional inequalities, see
 \SbjNo 39B72; for probabilistic inequalities, see \SbjNo 60E15}\endx
\ThirdLvl 26D05\SubText Inequalities for trigonometric functions and
 polynomials\endx
\ThirdLvl 26D07\SubText Inequalities involving other types of
 functions\endx
\ThirdLvl 26D10\SubText Inequalities involving derivatives and
 differential and integral operators\endx
\ThirdLvl 26D15\SubText Inequalities for sums, series and
 integrals\endx
\ThirdLvl 26D20\SubText Other analytical inequalities\endx
\ThirdLvl 26D99\SubText \NoneOfAbove\endx
\SecndLvl 26E++\SubText Miscellaneous topics \SeeAlso{\SbjNo
 58Cxx}\endx
\ThirdLvl 26E05\SubText Real-analytic functions \SeeAlso{\SbjNo 32B05,
 \SbjNo 32C05}\endx
\ThirdLvl 26E10\SubText $C\sp\infty$-functions, quasi-analytic
 functions \SeeAlso{\SbjNo 58C25}\endx
\ThirdLvl 26E15\SubText Calculus of functions on infinite-dimensional
 spaces \SeeAlso{\SbjNo 46G05, \SbjNo 58Cxx}\endx
\ThirdLvl 26E20\SubText Calculus of functions taking values in
 infinite-dimensional spaces \SeeAlso{\SbjNo 46E40, \SbjNo 46G10,
 \SbjNo 58Cxx}\endx
\ThirdLvl 26E25\SubText Set-valued functions \SeeAlso{\SbjNo 28B20,
 \SbjNo 54C60} \SeeFor{For nonsmooth analysis, see~\SbjNo 49J52,
 \SbjNo 58Cxx, \SbjNo 90Cxx}\endx
\ThirdLvl 26E30\SubText Non-Archimedean analysis \SeeAlso{\SbjNo
 12J25}\endx
\ThirdLvl 26E35\SubText Nonstandard analysis \SeeAlso{\SbjNo 03H05,
 \SbjNo 28E05, \SbjNo 54J05}\endx
\ThirdLvl 26E40\SubText Constructive real analysis \SeeAlso{\SbjNo
 03F60, \SbjNo 03F65}\endx
\ThirdLvl 26E50\SubText Fuzzy real analysis \SeeAlso{\SbjNo 04A72,
 \SbjNo 28E10}\endx
\ThirdLvl 26E99\SubText \NoneOfAbove\endx
\MajorSub 28-++\SubText Measure and integration \SeeFor{For analysis
 on manifolds, see~\SbjNo 58-XX}\endx
\ThirdLvl 28-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 28-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 28-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 28-03\SubText \Historical\endx
\ThirdLvl 28-04\SubText \ExplicitComputation\endx
\ThirdLvl 28-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 28A++\SubText Classical measure theory\endx
\ThirdLvl 28A05\SubText Classes of sets (Borel fields, $\sigma$-rings,
 etc.), measurable sets, Suslin sets, analytic sets \SeeAlso{\SbjNo
 03E15, \SbjNo 04A15, \SbjNo 26A21, \SbjNo 54H05}\endx
\ThirdLvl 28A10\SubText Real- or complex-valued set functions\endx
\ThirdLvl 28A12\SubText Contents, measures, outer measures,
 capacities\endx
\ThirdLvl 28A15\SubText Abstract differentiation theory,
 differentiation of set functions \SeeAlso{\SbjNo 26A24}\endx
\ThirdLvl 28A20\SubText Measurable and nonmeasurable functions,
 sequences of measurable functions, modes of convergence\endx
\ThirdLvl 28A25\SubText Integration with respect to measures and other
 set functions\endx
\ThirdLvl 28A33\SubText Spaces of measures, convergence of measures
 \SeeAlso{\SbjNo 46E27, \SbjNo 60Bxx}\endx
\ThirdLvl 28A35\SubText Measures and integrals in product spaces\endx
\ThirdLvl 28A50\SubText Integration and disintegration of
 measures\endx
\ThirdLvl 28A51\SubText Lifting theory \SeeAlso{\SbjNo 46G15}\endx
\ThirdLvl 28A60\SubText Measures on Boolean rings, measure algebras
 \SeeAlso{\SbjNo 54H10}\endx
\ThirdLvl 28A75\SubText Length, area, volume, other geometric measure
 theory \SeeAlso{\SbjNo 26B15, \SbjNo 49Q15}\endx
\ThirdLvl 28A78\SubText Hausdorff measures\endx
\ThirdLvl 28A80\SubText Fractals \SeeAlso{\SbjNo 58Fxx}\endx
\ThirdLvl 28A99\SubText \NoneOfAbove\endx
\SecndLvl 28B++\SubText Set functions, measures and integrals with
 values in abstract spaces\endx
\ThirdLvl 28B05\SubText Vector-valued set functions, measures and
 integrals \SeeAlso{\SbjNo 46G10}\endx
\ThirdLvl 28B10\SubText Group- or semigroup-valued set functions,
 measures and integrals\endx
\ThirdLvl 28B15\SubText Set functions, measures and integrals with
 values in ordered spaces\endx
\ThirdLvl 28B20\SubText Set-valued set functions and measures;
 integration of set-valued functions; measurable selections
 \SeeAlso{\SbjNo 26E25, \SbjNo 54C60, \SbjNo 54C65, \SbjNo 90A14}\endx
\ThirdLvl 28B99\SubText \NoneOfAbove\endx
\SecndLvl 28C++\SubText Set functions and measures on spaces with
 additional structure \SeeAlso{\SbjNo 46G12, \SbjNo 58C35, \SbjNo
 58D20}\endx
\ThirdLvl 28C05\SubText Integration theory via linear functionals
 (Radon measures, Daniell integrals, etc.), representing set functions
 and measures\endx
\ThirdLvl 28C10\SubText Set functions and measures on topological
 groups, Haar measures, invariant measures \SeeAlso{\SbjNo 22Axx,
 \SbjNo 43A05}\endx
\ThirdLvl 28C15\SubText Set functions and measures on topological
 spaces (regularity of measures, etc.)\endx
\ThirdLvl 28C20\SubText Set functions and measures and integrals in
 infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
 \SeeAlso{\SbjNo 46G12, \SbjNo 58C35, \SbjNo 58D20, \SbjNo 60B11}\endx
\ThirdLvl 28C99\SubText \NoneOfAbove\endx
\SecndLvl 28D++\SubText Measure-theoretic ergodic theory
 \SeeAlso{\SbjNo 11K50, \SbjNo 11K55, \SbjNo 22D40, \SbjNo 47A35,
 \SbjNo 54H20, \SbjNo 58Fxx, \SbjNo 60Fxx, \SbjNo 60G10}\endx
\ThirdLvl 28D05\SubText Measure-preserving transformations\endx
\ThirdLvl 28D10\SubText One-parameter continuous families of
 measure-preserving transformations\endx
\ThirdLvl 28D15\SubText General groups of measure-preserving
 transformations\endx
\ThirdLvl 28D20\SubText Entropy and other invariants\endx
\ThirdLvl 28D99\SubText \NoneOfAbove\endx
\SecndLvl 28E++\SubText Miscellaneous topics in measure theory\endx
\ThirdLvl 28E05\SubText Nonstandard measure theory \SeeAlso{\SbjNo
 03H05, \SbjNo 26E35}\endx
\ThirdLvl 28E10\SubText Fuzzy measure theory \SeeAlso{\SbjNo 04A72,
 \SbjNo 26E50, \SbjNo 94D05}\endx
\ThirdLvl 28E15\SubText Other connections with logic and set
 theory\endx
\ThirdLvl 28E99\SubText \NoneOfAbove\endx
\MajorSub 30-++\SubText Functions of a complex variable \SeeFor{For
 analysis on manifolds, see~\SbjNo 58-XX}\endx
\ThirdLvl 30-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 30-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 30-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 30-03\SubText \Historical\endx
\ThirdLvl 30-04\SubText \ExplicitComputation\endx
\ThirdLvl 30-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 30A++\SubText General properties\endx
\ThirdLvl 30A05\SubText Monogenic properties of complex functions
 (including polygenic and areolar monogenic functions)\endx
\ThirdLvl 30A10\SubText Inequalities in the complex domain\endx
\ThirdLvl 30A99\SubText \NoneOfAbove\endx
\SecndLvl 30B++\SubText Series expansions\endx
\ThirdLvl 30B10\SubText Power series (including lacunary series)\endx
\ThirdLvl 30B20\SubText Random power series\endx
\ThirdLvl 30B30\SubText Boundary behavior of power series,
 over-convergence\endx
\ThirdLvl 30B40\SubText Analytic continuation\endx
\ThirdLvl 30B50\SubText Dirichlet series and other series expansions,
 exponential series \SeeAlso{\SbjNo 11M41, \SbjNo 42-XX}\endx
\ThirdLvl 30B60\SubText Completeness problems, closure of a system of
 functions\endx
\ThirdLvl 30B70\SubText Continued fractions \SeeAlso{\SbjNo 11A55,
 \SbjNo 40A15}\endx
\ThirdLvl 30B99\SubText \NoneOfAbove\endx
\SecndLvl 30C++\SubText Geometric function theory\endx
\ThirdLvl 30C10\SubText Polynomials\endx
\ThirdLvl 30C15\SubText Zeros of polynomials, rational functions, and
 other analytic functions (e.g.\ zeros of functions with bounded
 Dirichlet integral) \SeeFor{For algebraic theory, see \SbjNo 12D10;
 for real methods, see \SbjNo 26C10}\endx
\ThirdLvl 30C20\SubText Conformal mappings of special domains\endx
\ThirdLvl 30C25\SubText Covering theorems in conformal mapping
 theory\endx
\ThirdLvl 30C30\SubText Numerical methods in conformal mapping theory
 \SeeAlso{\SbjNo 65E05}\endx
\ThirdLvl 30C35\SubText General theory of conformal mappings\endx
\ThirdLvl 30C40\SubText Kernel functions and applications\endx
\ThirdLvl 30C45\SubText Special classes of univalent and multivalent
 functions (starlike, convex, bounded rotation, etc.)\endx
\ThirdLvl 30C50\SubText Coefficient problems for univalent and
 multivalent functions \endx
\ThirdLvl 30C55\SubText General theory of univalent and multivalent
 functions\endx
\ThirdLvl 30C62\SubText Quasiconformal mappings in the plane\endx
\ThirdLvl 30C65\SubText Quasiconformal mappings in ${\bf R}^n$, other
 generalizations\endx
\ThirdLvl 30C70\SubText Extremal problems for conformal and
 quasiconformal mappings, variational methods\endx
\ThirdLvl 30C75\SubText Extremal problems for conformal and
 quasiconformal mappings, other methods\endx
\ThirdLvl 30C80\SubText Maximum principle; Schwarz's lemma, Lindel\"of
 principle, analogues and generalizations; subordination\endx
\ThirdLvl 30C85\SubText Capacity and harmonic measure in the complex
 plane \SeeAlso{\SbjNo 31A15}\endx
\ThirdLvl 30C99\SubText \NoneOfAbove\endx
\SecndLvl 30D++\SubText Entire and meromorphic functions, and related
 topics\endx
\ThirdLvl 30D05\SubText Functional equations in the complex domain,
 iteration and composition of analytic functions \SeeAlso{\SbjNo
 34A20, \SbjNo 39-XX, \SbjNo 58F05, \SbjNo 58F23}\endx
\ThirdLvl 30D10\SubText Representations of entire functions by series
 and integrals\endx
\ThirdLvl 30D15\SubText Special classes of entire functions and growth
 estimates\endx
\ThirdLvl 30D20\SubText Entire functions, general theory\endx
\ThirdLvl 30D30\SubText Meromorphic functions, general theory\endx
\ThirdLvl 30D35\SubText Distribution of values, Nevanlinna theory\endx
\ThirdLvl 30D40\SubText Cluster sets, prime ends, boundary
 behavior\endx
\ThirdLvl 30D45\SubText Bloch functions, normal functions, normal
 families\endx
\ThirdLvl 30D50\SubText Blashke products, bounded mean oscillation,
 bounded characteristic, bounded functions, functions with positive
 real part\endx
\ThirdLvl 30D55\SubText ${\it H}\sp p$-classes\endx
\ThirdLvl 30D60\SubText Quasi-analytic and other classes of
 functions\endx
\ThirdLvl 30D99\SubText \NoneOfAbove\endx
\SecndLvl 30E++\SubText Miscellaneous topics of analysis in the
 complex domain\endx
\ThirdLvl 30E05\SubText Moment problems, interpolation problems\endx
\ThirdLvl 30E10\SubText Approximation in the complex domain\endx
\ThirdLvl 30E15\SubText Asymptotic representations in the complex
 domain\endx
\ThirdLvl 30E20\SubText Integration, integrals of Cauchy type,
 integral representations of analytic functions \SeeAlso{\SbjNo
 45Exx}\endx
\ThirdLvl 30E25\SubText Boundary value problems \SeeAlso{\SbjNo
 45Exx}\endx
\ThirdLvl 30E99\SubText \NoneOfAbove\endx
\SecndLvl 30F++\SubText Riemann surfaces\endx
\ThirdLvl 30F10\SubText Compact Riemann surfaces and uniformization
 \SeeAlso{\SbjNo 14H15, \SbjNo 32G15}\endx
\ThirdLvl 30F15\SubText Harmonic functions on Riemann surfaces\endx
\ThirdLvl 30F20\SubText Classification theory of Riemann surfaces\endx
\ThirdLvl 30F25\SubText Ideal boundary theory\endx
\ThirdLvl 30F30\SubText Differentials on Riemann surfaces\endx
\ThirdLvl 30F35\SubText Fuchsian groups and automorphic functions
 \SeeAlso{\SbjNo 11Fxx, \SbjNo 20H10, \SbjNo 22E40, \SbjNo 32Gxx,
 \SbjNo 32Nxx}\endx
\ThirdLvl 30F40\SubText Kleinian groups \SeeAlso{\SbjNo 20H10}\endx
\ThirdLvl 30F45\SubText Conformal metrics (hyperbolic, Poincar\'e,
 distance functions)\endx
\ThirdLvl 30F50\SubText Klein surfaces\endx
\ThirdLvl 30F60\SubText Teichm\"uller theory \SeeAlso{\SbjNo
 32G15}\endx
\ThirdLvl 30F99\SubText \NoneOfAbove\endx
\SecndLvl 30G++\SubText Generalized function theory\endx
\ThirdLvl 30G06\SubText Non-Archimedean function theory
 \SeeAlso{\SbjNo 12J25}; nonstandard function theory \SeeAlso{\SbjNo
 03H05}\endx
\ThirdLvl 30G12\SubText Finely holomorphic functions and topological
 function theory\endx
\ThirdLvl 30G15\SubText Topological function theory\endx
\ThirdLvl 30G20\SubText Generalizations of Bers or Vekua type
 (pseudoanalytic, $p$-analytic, etc.)\endx
\ThirdLvl 30G25\SubText Discrete analytic functions\endx
\ThirdLvl 30G30\SubText Other generalizations of analytic functions
 (including abstract-valued functions)\endx
\ThirdLvl 30G35\SubText Functions of hypercomplex variables and
 generalized variables\endx
\ThirdLvl 30G99\SubText \NoneOfAbove\endx
\SecndLvl 30H05\SubText Spaces and algebras of analytic functions
 \SeeAlso{\SbjNo 32E25, \SbjNo 46Exx, \SbjNo 46J15}\endx
\MajorSub 31-++\SubText Potential theory \SeeFor{For probabilistic
 potential theory, see~\SbjNo 60J45}\endx
\ThirdLvl 31-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 31-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 31-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 31-03\SubText \Historical\endx
\ThirdLvl 31-04\SubText \ExplicitComputation\endx
\ThirdLvl 31-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 31A++\SubText Two-dimensional theory\endx
\ThirdLvl 31A05\SubText Harmonic, subharmonic, superharmonic
 functions\endx
\ThirdLvl 31A10\SubText Integral representations, integral operators,
 integral equations methods\endx
\ThirdLvl 31A15\SubText Potentials and capacity, harmonic measure,
 extremal length \SeeAlso{\SbjNo 30C85}\endx
\ThirdLvl 31A20\SubText Boundary behavior (theorems of Fatou type,
 etc.)\endx
\ThirdLvl 31A25\SubText Boundary value and inverse problems\endx
\ThirdLvl 31A30\SubText Biharmonic, polyharmonic functions and
 equations, Poisson's equation\endx
\ThirdLvl 31A35\SubText Connections with differential equations\endx
\ThirdLvl 31A99\SubText \NoneOfAbove\endx
\SecndLvl 31B++\SubText Higher-dimensional theory\endx
\ThirdLvl 31B05\SubText Harmonic, subharmonic, superharmonic
 functions\endx
\ThirdLvl 31B10\SubText Integral representations, integral operators,
 integral equations methods\endx
\ThirdLvl 31B15\SubText Potentials and capacities, extremal
 length\endx
\ThirdLvl 31B20\SubText Boundary value and inverse problems\endx
\ThirdLvl 31B25\SubText Boundary behavior\endx
\ThirdLvl 31B30\SubText Biharmonic and polyharmonic equations and
 functions\endx
\ThirdLvl 31B35\SubText Connections with differential equations\endx
\ThirdLvl 31B99\SubText \NoneOfAbove\endx
\SecndLvl 31C++\SubText Other generalizations\endx
\ThirdLvl 31C05\SubText Harmonic, subharmonic, superharmonic
 functions\endx
\ThirdLvl 31C10\SubText Pluriharmonic and plurisubharmonic functions
 \SeeAlso{\SbjNo 32F05}\endx
\ThirdLvl 31C12\SubText Potential theory on Riemannian manifolds
 \SeeAlso{\SbjNo 53C20; for Hodge theory, see \SbjNo 58A14}\endx
\ThirdLvl 31C15\SubText Potentials and capacities\endx
\ThirdLvl 31C20\SubText Discrete potential theory and numerical
 methods\endx
\ThirdLvl 31C25\SubText Dirichlet spaces\endx
\ThirdLvl 31C35\SubText Martin boundary theory \SeeAlso{\SbjNo
 60J50}\endx
\ThirdLvl 31C40\SubText Fine potential theory\endx
\ThirdLvl 31C45\SubText Other generalizations (nonlinear potential
 theory, etc.)\endx
\ThirdLvl 31C99\SubText \NoneOfAbove\endx
\SecndLvl 31D05\SubText Axiomatic potential theory\endx
\MajorSub 32-++\SubText Several complex variables and analytic spaces
 \SeeFor{For infinite-dimensional holomorphy, see~also~\SbjNo 46G20,
 \SbjNo 58B12}\endx
\ThirdLvl 32-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 32-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 32-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 32-03\SubText \Historical\endx
\ThirdLvl 32-04\SubText \ExplicitComputation\endx
\ThirdLvl 32-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 32A++\SubText Holomorphic functions of several complex
 variables\endx
\ThirdLvl 32A05\SubText Power series, series of functions\endx
\ThirdLvl 32A07\SubText Special domains (Reinhardt, Hartogs, tube
 domains, etc.)\endx
\ThirdLvl 32A10\SubText Holomorphic functions\endx
\ThirdLvl 32A15\SubText Entire functions\endx
\ThirdLvl 32A17\SubText Special families of functions (e.g.\ normal
 families)\endx
\ThirdLvl 32A20\SubText Meromorphic functions\endx
\ThirdLvl 32A22\SubText Nevanlinna theory (local); growth estimates;
 other inequalities \SeeFor{For geometric theory, see \SbjNo 32H25,
 \SbjNo 32H30}\endx
\ThirdLvl 32A25\SubText Integral representation\endx
\ThirdLvl 32A27\SubText Local theory of residues \SeeAlso{\SbjNo
 32C30}\endx
\ThirdLvl 32A30\SubText Other generalizations of function theory of
 one complex variable (should also be assigned at least one
 classification number from Section 30) \SeeFor{For functions of
 several hypercomplex variables, see \SbjNo 30G35}\endx
\ThirdLvl 32A35\SubText ${\it H}\sp p$-spaces \SeeAlso{\SbjNo 32M15,
 \SbjNo 42B30, \SbjNo 43A85, \SbjNo 46J15}\endx
\ThirdLvl 32A37\SubText Other spaces of holomorphic functions (e.g.\
 bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA) in
 $n$ dimensions) \SeeAlso{\SbjNo 46Exx}\endx
\ThirdLvl 32A40\SubText Boundary behavior\endx
\ThirdLvl 32A45\SubText Hyperfunctions \SeeAlso{\SbjNo 46F15}\endx
\ThirdLvl 32A99\SubText \NoneOfAbove\endx
\SecndLvl 32B++\SubText Local analytic geometry \SeeAlso{\SbjNo 13-XX
 and \SbjNo 14-XX}\endx
\ThirdLvl 32B05\SubText Analytic algebras and generalizations,
 preparation theorems\endx
\ThirdLvl 32B10\SubText Germs of analytic sets\endx
\ThirdLvl 32B15\SubText Analytic subsets of affine space\endx
\ThirdLvl 32B20\SubText Semi-analytic sets and subanalytic sets
 \SeeAlso{\SbjNo 14P15}\endx
\ThirdLvl 32B25\SubText Triangulation and related questions\endx
\ThirdLvl 32B99\SubText \NoneOfAbove\endx
\SecndLvl 32C++\SubText General theory of analytic spaces\endx
\ThirdLvl 32C05\SubText Real-analytic manifolds, real-analytic spaces
 \SeeAlso{\SbjNo 14Pxx, \SbjNo 58A07}\endx
\ThirdLvl 32C07\SubText Real-analytic sets, complex Nash functions
 \SeeAlso{\SbjNo 14P15, \SbjNo 14P20}\endx
\ThirdLvl 32C10\SubText Complex manifolds \SeeFor{For almost complex
 manifolds, see \SbjNo 53C15}\endx
\ThirdLvl 32C11\SubText Complex supergeometry \SeeAlso{\SbjNo 14A22,
 \SbjNo 14M30, \SbjNo 58A50}\endx
\ThirdLvl 32C15\SubText Complex spaces\endx
\ThirdLvl 32C16\SubText CR-manifolds\endx
\ThirdLvl 32C17\SubText K\"ahler geometry \SeeFor{For
 differential-geometric methods see \SbjNo 53C55}\endx
\ThirdLvl 32C18\SubText Topology of analytic spaces\endx
\ThirdLvl 32C20\SubText Normal analytic spaces\endx
\ThirdLvl 32C25\SubText Analytic subsets and submanifolds\endx
\ThirdLvl 32C30\SubText Integration on analytic sets and spaces,
 currents \SeeFor{For local theory, see \SbjNo 32A25 or \SbjNo
 32A27}\endx
\ThirdLvl 32C35\SubText Analytic sheaves and cohomology groups
 \SeeAlso{\SbjNo 14Fxx, \SbjNo 18F20, \SbjNo 55N30}\endx
\ThirdLvl 32C36\SubText Local cohomology of analytic spaces\endx
\ThirdLvl 32C37\SubText Duality theorems\endx
\ThirdLvl 32C38\SubText Sheaves of differential operators and their
 modules \SeeAlso{\SbjNo 14F10, \SbjNo 16S32, \SbjNo 35A27, \SbjNo
 58G07}\endx
\ThirdLvl 32C81\SubText Applications to physics\endx
\ThirdLvl 32C99\SubText \NoneOfAbove\endx
\SecndLvl 32D++\SubText Analytic continuation\endx
\ThirdLvl 32D05\SubText Domains of holomorphy\endx
\ThirdLvl 32D10\SubText Envelopes of holomorphy\endx
\ThirdLvl 32D15\SubText Continuation of analytic objects\endx
\ThirdLvl 32D20\SubText Removable singularities\endx
\ThirdLvl 32D99\SubText \NoneOfAbove\endx
\SecndLvl 32E++\SubText Holomorphic convexity\endx
\ThirdLvl 32E05\SubText Holomorphically convex complex spaces,
 reduction theory\endx
\ThirdLvl 32E10\SubText Stein spaces, Stein manifolds\endx
\ThirdLvl 32E20\SubText Polynomial convexity\endx
\ThirdLvl 32E25\SubText Algebras of holomorphic functions
 \SeeAlso{\SbjNo 30H05, \SbjNo 46J10, \SbjNo 46J15}\endx
\ThirdLvl 32E30\SubText Holomorphic and polynomial approximation,
 Runge pairs, interpolation\endx
\ThirdLvl 32E35\SubText Global boundary behavior of holomorphic
 functions\endx
\ThirdLvl 32E99\SubText \NoneOfAbove\endx
\SecndLvl 32F++\SubText Geometric convexity, partial differential
 operators\endx
\ThirdLvl 32F05\SubText Plurisubharmonic functions and generalizations
 \SeeAlso{\SbjNo 31C10}\endx
\ThirdLvl 32F07\SubText Complex Monge-Amp\`ere operator\endx
\ThirdLvl 32F10\SubText $q$-convexity, $q$-concavity\endx
\ThirdLvl 32F15\SubText Pseudoconvex domains\endx
\ThirdLvl 32F20\SubText $\overline\partial$- and
 $\overline\partial_b$-Neumann problems \SeeAlso{\SbjNo 35N15}\endx
\ThirdLvl 32F25\SubText Real submanifolds in complex manifolds\endx
\ThirdLvl 32F30\SubText Pseudoconvex manifolds\endx
\ThirdLvl 32F40\SubText CR structures, (tangential) CR operators and
 generalizations\endx
\ThirdLvl 32F99\SubText \NoneOfAbove\endx
\SecndLvl 32G++\SubText Deformations of analytic structures\endx
\ThirdLvl 32G05\SubText Deformations of complex structures
 \SeeAlso{\SbjNo 13D10, \SbjNo 16S80, \SbjNo 58H10, \SbjNo 58H15}\endx
\ThirdLvl 32G07\SubText Deformations of special (e.g.\ CR)
 structures\endx
\ThirdLvl 32G08\SubText Deformations of fiber bundles\endx
\ThirdLvl 32G10\SubText Deformations of submanifolds and
 subspaces\endx
\ThirdLvl 32G13\SubText Analytic moduli problems \SeeFor{For algebraic
 moduli problems, see \SbjNo 14D20, \SbjNo 14D22, \SbjNo 14H10, \SbjNo
 14J10} \SeeAlso{\SbjNo 14H15, \SbjNo 14J15}\endx
\ThirdLvl 32G15\SubText Moduli of Riemann surfaces, Teichm\"uller
 theory \SeeAlso{\SbjNo 14H15, \SbjNo 30Fxx}\endx
\ThirdLvl 32G20\SubText Period matrices, variation of Hodge structure;
 degenerations \SeeAlso{\SbjNo 14D05, \SbjNo 14D07, \SbjNo 14K30}\endx
\ThirdLvl 32G34\SubText Moduli and deformations for ordinary
 differential equations \SeeAlso{\SbjNo 34A20}\endx
\ThirdLvl 32G81\SubText Applications to physics\endx
\ThirdLvl 32G99\SubText \NoneOfAbove\endx
\SecndLvl 32H++\SubText Holomorphic mappings and correspondences\endx
\ThirdLvl 32H02\SubText Holomorphic mappings, (holomorphic) embeddings
 and related questions\endx
\ThirdLvl 32H04\SubText Meromorphic mappings\endx
\ThirdLvl 32H10\SubText Bergman kernel function, representative
 domains\endx
\ThirdLvl 32H15\SubText Invariant metrics and pseudodistances\endx
\ThirdLvl 32H20\SubText Hyperbolic complex manifolds\endx
\ThirdLvl 32H25\SubText Picard-type theorems and generalizations
 \SeeFor{For function-theoretic properties, see \SbjNo 32A22}\endx
\ThirdLvl 32H30\SubText Value distribution theory in higher dimensions
 \SeeFor{For function-theoretic properties, see \SbjNo 32A22}\endx
\ThirdLvl 32H35\SubText Proper mappings, finiteness theorems\endx
\ThirdLvl 32H40\SubText Boundary regularity of holomorphic maps\endx
\ThirdLvl 32H50\SubText Iteration problems\endx
\ThirdLvl 32H99\SubText \NoneOfAbove\endx
\SecndLvl 32J++\SubText Compact analytic spaces \SeeFor{For Riemann
 surfaces, see \SbjNo 14Hxx, \SbjNo 30Fxx; for algebraic theory, see
 \SbjNo 14Jxx}\endx
\ThirdLvl 32J05\SubText Compactification of analytic spaces\endx
\ThirdLvl 32J10\SubText Algebraic dependence theorems\endx
\ThirdLvl 32J15\SubText Compact surfaces\endx
\ThirdLvl 32J17\SubText Compact $3$-folds\endx
\ThirdLvl 32J18\SubText Compact $n$-folds $(n \ge 4)$\endx
\ThirdLvl 32J20\SubText Algebraicity criteria\endx
\ThirdLvl 32J25\SubText Transcendental methods of algebraic geometry
 \SeeAlso{\SbjNo 14C30}\endx
\ThirdLvl 32J27\SubText Compact K\"ahler manifolds: generalizations,
 classification\endx
\ThirdLvl 32J81\SubText Applications to physics\endx
\ThirdLvl 32J99\SubText \NoneOfAbove\endx
\SecndLvl 32K++\SubText Generalizations of analytic spaces
 \ExtraText{(should also be assigned at least one other classification
 number in this section)}\endx
\ThirdLvl 32K05\SubText Banach analytic spaces \SeeAlso{\SbjNo
 58Bxx}\endx
\ThirdLvl 32K07\SubText Formal and graded complex spaces
 \SeeAlso{\SbjNo 58C50}\endx
\ThirdLvl 32K15\SubText Differentiable functions on analytic spaces,
 differentiable spaces \SeeAlso{\SbjNo 58C25}\endx
\ThirdLvl 32K99\SubText \NoneOfAbove\endx
\SecndLvl 32L++\SubText Holomorphic fiber spaces \SeeAlso{\SbjNo
 55Rxx}\endx
\ThirdLvl 32L05\SubText Holomorphic fiber bundles and
 generalizations\endx
\ThirdLvl 32L07\SubText Hermite-Einstein bundles; K\"ahler-Einstein
 bundles \SeeAlso{\SbjNo 53C07}\endx
\ThirdLvl 32L10\SubText Sheaves and cohomology of sections of
 holomorphic vector bundles, general results \SeeAlso{\SbjNo 14F05,
 \SbjNo 18F20, \SbjNo 55N30}\endx
\ThirdLvl 32L15\SubText Bundle convexity \SeeAlso{\SbjNo 32F10}\endx
\ThirdLvl 32L20\SubText Vanishing theorems\endx
\ThirdLvl 32L25\SubText Twistor theory, double fibrations\endx
\ThirdLvl 32L30\SubText Holomorphic foliations \SeeAlso{\SbjNo
 58F18}\endx
\ThirdLvl 32L81\SubText Applications to physics\endx
\ThirdLvl 32L99\SubText \NoneOfAbove\endx
\SecndLvl 32M++\SubText Complex spaces with a group of
 automorphisms\endx
\ThirdLvl 32M05\SubText Complex Lie groups, automorphism groups of
 complex spaces \SeeAlso{\SbjNo 22E10}\endx
\ThirdLvl 32M10\SubText Homogeneous complex manifolds \SeeAlso{\SbjNo
 14M17, \SbjNo 57T15}\endx
\ThirdLvl 32M12\SubText Almost homogeneous manifolds and spaces
 \SeeAlso{\SbjNo 14M17}\endx
\ThirdLvl 32M15\SubText Hermitian symmetric spaces, bounded symmetric
 domains \SeeAlso{\SbjNo 22E10, \SbjNo 22E40, \SbjNo 53C35, \SbjNo
 57T15}\endx
\ThirdLvl 32M99\SubText \NoneOfAbove\endx
\SecndLvl 32N++\SubText Automorphic functions \SeeAlso{\SbjNo 11Fxx,
 \SbjNo 20H10, \SbjNo 22E40, \SbjNo 30F35}\endx
\ThirdLvl 32N05\SubText General theory of automorphic functions of
 several complex variables\endx
\ThirdLvl 32N10\SubText Automorphic forms\endx
\ThirdLvl 32N15\SubText Automorphic functions in symmetric
 domains\endx
\ThirdLvl 32N99\SubText \NoneOfAbove\endx
\SecndLvl 32P05\SubText Non-Archimedean complex analysis (should also
 be assigned at least one other classification number from Section
 $32$ describing the type of problem)\endx
\SecndLvl 32S++\SubText Singularities\endx
\ThirdLvl 32S05\SubText Local singularities \SeeAlso{\SbjNo
 14B05}\endx
\ThirdLvl 32S10\SubText Invariants of analytic local rings \endx
\ThirdLvl 32S15\SubText Equisingularity (topological and analytic)
 \SeeAlso{\SbjNo 14E15}\endx
\ThirdLvl 32S20\SubText Global theory of singularities; cohomological
 properties \SeeAlso{\SbjNo 14E15}\endx
\ThirdLvl 32S25\SubText (Hyper-) surface singularities \SeeAlso{\SbjNo
 14J17}\endx
\ThirdLvl 32S30\SubText Deformations of singularities; vanishing
 cycles \SeeAlso{\SbjNo 14B07}\endx
\ThirdLvl 32S35\SubText Mixed Hodge theory of singular varieties
 \SeeAlso{\SbjNo 14C30, \SbjNo 14D07}\endx
\ThirdLvl 32S40\SubText Monodromy; relations with differential
 equations and $D$-modules\endx
\ThirdLvl 32S45\SubText Modifications; resolution of singularities
 \SeeAlso{\SbjNo 14E15}\endx
\ThirdLvl 32S50\SubText Topological aspects: Lefschetz theorems,
 topological classification, invariants\endx
\ThirdLvl 32S55\SubText Milnor fibration; relations with knot theory
 \SeeAlso{\SbjNo 57M25, \SbjNo 57Q45}\endx
\ThirdLvl 32S60\SubText Stratifications; constructible sheaves;
 intersection cohomology \SeeAlso{\SbjNo 58C27}\endx
\ThirdLvl 32S65\SubText Singularities of holomorphic vector
 fields\endx
\ThirdLvl 32S70\SubText Other operations on singularities\endx
\MajorSub 33-++\SubText Special functions \SeeFor{\SbjNo 33-XX deals
 with the properties of functions as functions.  For orthogonal
 functions, see also~\SbjNo 42Cxx; for aspects of combinatorics, see
 \SbjNo 05Axx; for number-theoretic aspects, see \SbjNo 11-XX; for
 representation theory, see \SbjNo 22Exx}\endx
\ThirdLvl 33-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 33-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 33-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 33-03\SubText \Historical\endx
\ThirdLvl 33-04\SubText \ExplicitComputation\endx
\ThirdLvl 33-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 33B++\SubText Elementary classical functions\endx
\ThirdLvl 33B10\SubText Exponential and trigonometric functions\endx
\ThirdLvl 33B15\SubText Gamma, beta and polygamma functions\endx
\ThirdLvl 33B20\SubText Incomplete beta and gamma functions (error
 functions, probability integral, Fresnel integrals)\endx
\ThirdLvl 33B99\SubText \NoneOfAbove\endx
\SecndLvl 33C++\SubText Hypergeometric functions\endx
\ThirdLvl 33C05\SubText Classical hypergeometric functions,
 $_2F_1$\endx
\ThirdLvl 33C10\SubText Bessel and Airy functions, cylinder functions,
 $_0F_1$ \endx
\ThirdLvl 33C15\SubText Confluent hypergeometric functions, Whittaker
 functions, $_1F_1$ \endx
\ThirdLvl 33C20\SubText Generalized hypergeometric series, $_pF_q$
 \endx
\ThirdLvl 33C45\SubText Orthogonal polynomials and functions
 (Chebyshev, Legendre, Gegenbauer, Jacobi, Laguerre, Hermite, Hahn,
 etc.)\endx
\ThirdLvl 33C50\SubText Orthogonal polynomials and functions in
 several variables\endx
\ThirdLvl 33C55\SubText Spherical functions, spherical harmonics,
 ultraspherical polynomials\endx
\ThirdLvl 33C60\SubText Hypergeometric integrals and functions defined
 by them ($E$, $G$ and ${\it H}$ functions)\endx
\ThirdLvl 33C65\SubText Appell, Horn and Lauricella functions\endx
\ThirdLvl 33C70\SubText Other hypergeometric functions and integrals
 in several variables\endx
\ThirdLvl 33C75\SubText Elliptic integrals as hypergeometric
 functions\endx
\ThirdLvl 33C80\SubText Connections with groups, algebras, root
 systems and related topics\endx
\ThirdLvl 33C90\SubText Applications\endx
\ThirdLvl 33C99\SubText \NoneOfAbove\endx
\SecndLvl 33D++\SubText Basic hypergeometric functions\endx
\ThirdLvl 33D05\SubText $q$-gamma functions, $q$-beta functions and
 integrals\endx
\ThirdLvl 33D10\SubText Basic theta functions\endx
\ThirdLvl 33D15\SubText Basic hypergeometric functions in one
 variable\endx
\ThirdLvl 33D20\SubText Generalized basic hypergeometric series \endx
\ThirdLvl 33D45\SubText Basic orthogonal polynomials and functions in
 one and several variables\endx
\ThirdLvl 33D55\SubText Basic spherical functions, spherical harmonics
 (continuous and discrete)\endx
\ThirdLvl 33D60\SubText Basic hypergeometric integrals and functions
 defined by them \endx
\ThirdLvl 33D65\SubText Bibasic functions and multiple bases\endx
\ThirdLvl 33D70\SubText Other basic hypergeometric functions and
 integrals in several variables\endx
\ThirdLvl 33D80\SubText Connections with groups, algebras, and related
 topics\endx
\ThirdLvl 33D90\SubText Applications\endx
\ThirdLvl 33D99\SubText \NoneOfAbove\endx
\SecndLvl 33E++\SubText Other special functions\endx
\ThirdLvl 33E05\SubText Elliptic functions and integrals\endx
\ThirdLvl 33E10\SubText Lam\'e, Mathieu, and spheroidal wave
 functions\endx
\ThirdLvl 33E15\SubText Other wave functions\endx
\ThirdLvl 33E20\SubText Other functions defined by series and
 integrals\endx
\ThirdLvl 33E30\SubText Other functions coming from differential,
 difference and integral equations\endx
\ThirdLvl 33E99\SubText \NoneOfAbove\endx
\MajorSub 34-++\SubText Ordinary differential equations\endx
\ThirdLvl 34-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 34-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 34-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 34-03\SubText \Historical\endx
\ThirdLvl 34-04\SubText \ExplicitComputation\endx
\ThirdLvl 34-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 34A++\SubText General theory\endx
\ThirdLvl 34A05\SubText Explicit solutions and reductions\endx
\ThirdLvl 34A09\SubText Implicit equations\endx
\ThirdLvl 34A12\SubText Initial value problems, existence, uniqueness,
 continuous dependence and continuation of solutions\endx
\ThirdLvl 34A20\SubText Differential equations in the complex domain
 \SeeAlso{\SbjNo 30D05, \SbjNo 32G34}\endx
\ThirdLvl 34A25\SubText Analytical theory: series, transformations,
 transforms, operational calculus, etc. \SeeAlso{\SbjNo 44-XX, \SbjNo
 47E05}\endx
\ThirdLvl 34A26\SubText Geometric methods in differential
 equations\endx
\ThirdLvl 34A30\SubText Linear equations and systems\endx
\ThirdLvl 34A34\SubText Nonlinear equations and systems, general\endx
\ThirdLvl 34A35\SubText Differential equations of infinite order\endx
\ThirdLvl 34A37\SubText Differential equations with impulses\endx
\ThirdLvl 34A40\SubText Differential inequalities\endx
\ThirdLvl 34A45\SubText Theoretical approximation of solutions\endx
\ThirdLvl 34A46\SubText Theoretical solution methods other than
 approximations\endx
\ThirdLvl 34A47\SubText Bifurcation\endx
\ThirdLvl 34A50\SubText Numerical approximation of solutions
 \SeeFor{For numerical analysis, see \SbjNo 65Lxx}\endx
\ThirdLvl 34A55\SubText Inverse problems\endx
\ThirdLvl 34A60\SubText Equations with multivalued right-hand sides
 \SeeAlso{\SbjNo 49J24, \SbjNo 49K24}\endx
\ThirdLvl 34A65\SubText Stiff equations\endx
\ThirdLvl 34A99\SubText \NoneOfAbove\endx
\SecndLvl 34B++\SubText Boundary value problems \SeeFor{For ordinary
 differential operators, see \SbjNo 34Lxx}\endx
\ThirdLvl 34B05\SubText Linear equations\endx
\ThirdLvl 34B10\SubText Multipoint boundary value problems\endx
\ThirdLvl 34B15\SubText Nonlinear boundary value problems\endx
\ThirdLvl 34B20\SubText Weyl theory and its generalizations\endx
\ThirdLvl 34B24\SubText Sturm-Liouville theory \SeeAlso{\SbjNo
 34Lxx}\endx
\ThirdLvl 34B27\SubText Green functions\endx
\ThirdLvl 34B30\SubText Special equations (Mathieu, Hill, Bessel,
 etc.) \endx
\ThirdLvl 34B99\SubText \NoneOfAbove\endx
\SecndLvl 34C++\SubText Qualitative theory \SeeAlso{\SbjNo 58Fxx}\endx
\ThirdLvl 34C05\SubText Location of integral curves, singular points,
 limit cycles\endx
\ThirdLvl 34C10\SubText Oscillation theory, zeros, disconjugacy and
 comparison theory\endx
\ThirdLvl 34C11\SubText Growth, boundedness, comparison of
 solutions\endx
\ThirdLvl 34C15\SubText Nonlinear oscillations\endx
\ThirdLvl 34C20\SubText Transformation and reduction of equations and
 systems, normal forms\endx
\ThirdLvl 34C23\SubText Bifurcation \SeeMainly{\SbjNo 58F14}\endx
\ThirdLvl 34C25\SubText Periodic solutions\endx
\ThirdLvl 34C27\SubText Almost-periodic solutions\endx
\ThirdLvl 34C28\SubText Other types of ``recurrent'' solutions\endx
\ThirdLvl 34C29\SubText Averaging method\endx
\ThirdLvl 34C30\SubText Manifolds of solutions\endx
\ThirdLvl 34C35\SubText Dynamical systems \SeeAlso{\SbjNo 54H20,
 \SbjNo 58Fxx, \SbjNo 70-XX}\endx
\ThirdLvl 34C37\SubText Homoclinic and heteroclinic solutions
 \SeeAlso{\SbjNo 58F15}\endx
\ThirdLvl 34C40\SubText Equations and systems on manifolds
 \SeeMainly{\SbjNo 58Fxx, \SbjNo 58Gxx}\endx
\ThirdLvl 34C45\SubText Method of integral manifolds\endx
\ThirdLvl 34C50\SubText Method of accelerated convergence\endx
\ThirdLvl 34C99\SubText \NoneOfAbove\endx
\SecndLvl 34D++\SubText Stability theory \SeeAlso{\SbjNo 58F10, \SbjNo
 93Dxx}\endx
\ThirdLvl 34D05\SubText Asymptotic properties\endx
\ThirdLvl 34D08\SubText Lyapunov exponents\endx
\ThirdLvl 34D10\SubText Perturbations\endx
\ThirdLvl 34D15\SubText Singular perturbations\endx
\ThirdLvl 34D20\SubText Lyapunov stability\endx
\ThirdLvl 34D25\SubText Popov-type stability\endx
\ThirdLvl 34D30\SubText Structural stability and analogous concepts
 \SeeAlso{\SbjNo 58F10, \SbjNo 58F12}\endx
\ThirdLvl 34D35\SubText Stability of manifolds of solutions\endx
\ThirdLvl 34D40\SubText Ultimate boundedness\endx
\ThirdLvl 34D45\SubText Attractors\endx
\ThirdLvl 34D99\SubText \NoneOfAbove\endx
\SecndLvl 34E++\SubText Asymptotic theory\endx
\ThirdLvl 34E05\SubText Asymptotic expansions\endx
\ThirdLvl 34E10\SubText Perturbations, asymptotics\endx
\ThirdLvl 34E15\SubText Singular perturbations, general theory\endx
\ThirdLvl 34E20\SubText Singular perturbations, turning point theory,
 WKB methods\endx
\ThirdLvl 34E99\SubText \NoneOfAbove\endx
\SecndLvl 34F05\SubText Equations and systems with randomness
 \SeeAlso{\SbjNo 34K50, \SbjNo 60H10, \SbjNo 93E03}\endx
\SecndLvl 34G++\SubText Differential equations in abstract spaces
 \SeeAlso{\SbjNo 58D25}\endx
\ThirdLvl 34G10\SubText Linear equations \SeeAlso{\SbjNo 47Axx, \SbjNo
 47Bxx, \SbjNo 47D06, \SbjNo 47D09}\endx
\ThirdLvl 34G20\SubText Nonlinear equations \SeeAlso{\SbjNo
 47Hxx}\endx
\ThirdLvl 34G99\SubText \NoneOfAbove\endx
\SecndLvl 34H05\SubText Control problems \SeeAlso{\SbjNo 49J25, \SbjNo
 49K25, \SbjNo 93C15}\endx
\SecndLvl 34K++\SubText Functional-differential and
 differential-difference equations\FullScheme{\unskip, with or without
 deviating arguments}\endx
\ThirdLvl 34K05\SubText General theory\endx
\ThirdLvl 34K10\SubText Boundary value problems\endx
\ThirdLvl 34K15\SubText Qualitative theory\endx
\ThirdLvl 34K20\SubText Stability theory\endx
\ThirdLvl 34K25\SubText Asymptotic theory\endx
\ThirdLvl 34K30\SubText Equations in abstract spaces \SeeAlso{\SbjNo
 34Gxx}\endx
\ThirdLvl 34K35\SubText Control problems \SeeAlso{\SbjNo 49J25, \SbjNo
 49K25, \SbjNo 93C15}\endx
\ThirdLvl 34K40\SubText Neutral equations\endx
\ThirdLvl 34K50\SubText Stochastic delay equations \SeeAlso{\SbjNo
 34F05, \SbjNo 60Hxx}\endx
\ThirdLvl 34K99\SubText \NoneOfAbove\endx
\SecndLvl 34L++\SubText Ordinary differential operators
 \SeeAlso{\SbjNo 47E05}\endx
\ThirdLvl 34L05\SubText General spectral theory\endx
\ThirdLvl 34L10\SubText Eigenfunction expansions, completeness of
 eigenfunctions\endx
\ThirdLvl 34L15\SubText Estimation of eigenvalues, upper and lower
 bounds\endx
\ThirdLvl 34L20\SubText Asymptotic distribution of eigenvalues,
 asymptotic theory of eigenfunctions\endx
\ThirdLvl 34L25\SubText Scattering theory\endx
\ThirdLvl 34L30\SubText Nonlinear ordinary differential operators\endx
\ThirdLvl 34L40\SubText Particular operators (Dirac, one-dimensional
 Schr\"odinger, etc.)\endx
\ThirdLvl 34L99\SubText \NoneOfAbove\endx
\MajorSub 35-++\SubText Partial differential equations\endx
\ThirdLvl 35-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 35-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 35-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 35-03\SubText \Historical\endx
\ThirdLvl 35-04\SubText \ExplicitComputation\endx
\ThirdLvl 35-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 35A++\SubText General theory\endx
\ThirdLvl 35A05\SubText General existence and uniqueness theorems\endx
\ThirdLvl 35A07\SubText Local existence and uniqueness theorems
 \SeeAlso{\SbjNo 35H05, \SbjNo 35Sxx}\endx
\ThirdLvl 35A08\SubText Fundamental solutions\endx
\ThirdLvl 35A10\SubText Cauchy-Kovalevskaya theorems\endx
\ThirdLvl 35A15\SubText Variational methods\endx
\ThirdLvl 35A20\SubText Analytic methods, singularities\endx
\ThirdLvl 35A22\SubText Transform methods (e.g.\ integral
 transforms)\endx
\ThirdLvl 35A25\SubText Other special methods\endx
\ThirdLvl 35A27\SubText Microlocal methods; methods of sheaf theory
 and homological algebra in PDE \SeeAlso{\SbjNo 32C38, \SbjNo
 58G07}\endx
\ThirdLvl 35A30\SubText Geometric theory, characteristics,
 transformations \SeeAlso{\SbjNo 58G35, \SbjNo 58G37}\endx
\ThirdLvl 35A35\SubText Theoretical approximation to solutions\endx
\ThirdLvl 35A40\SubText Numerical approximation to solutions
 \SeeFor{For numerical analysis, see \SbjNo 65Mxx, \SbjNo 65Nxx,
 \SbjNo 65P05}\endx
\ThirdLvl 35A99\SubText \NoneOfAbove\endx
\SecndLvl 35B++\SubText Qualitative properties of solutions\endx
\ThirdLvl 35B05\SubText General behavior of solutions of PDE
 (comparison theorems; oscillation, zeros and growth of solutions;
 mean value theorems)\endx
\ThirdLvl 35B10\SubText Periodic solutions\endx
\ThirdLvl 35B15\SubText Almost periodic solutions\endx
\ThirdLvl 35B20\SubText Perturbations\endx
\ThirdLvl 35B25\SubText Singular perturbations\endx
\ThirdLvl 35B27\SubText Homogenization; partial differential equations
 in media with periodic structure \SeeAlso{\SbjNo 73B27, \SbjNo
 76D30}\endx
\ThirdLvl 35B30\SubText Dependence of solutions of PDE on initial and
 boundary data, parameters \SeeAlso{\SbjNo 58F14}\endx
\ThirdLvl 35B32\SubText Bifurcation \SeeAlso{\SbjNo 58F14}\endx
\ThirdLvl 35B35\SubText Stability, boundedness\endx
\ThirdLvl 35B37\SubText PDE in connection with control problems
 \SeeAlso{\SbjNo 49J20, \SbjNo 49K20, \SbjNo 93C20}\endx
\ThirdLvl 35B40\SubText Asymptotic behavior of solutions\endx
\ThirdLvl 35B45\SubText A priori estimates\endx
\ThirdLvl 35B50\SubText Maximum principles\endx
\ThirdLvl 35B60\SubText Continuation and prolongation of solutions of
 PDE \SeeAlso{\SbjNo 58A15, \SbjNo 58A17, \SbjNo 58Hxx}\endx
\ThirdLvl 35B65\SubText Smoothness/regularity of solutions of PDE\endx
\ThirdLvl 35B99\SubText \NoneOfAbove\endx
\SecndLvl 35C++\SubText Representations of solutions\endx
\ThirdLvl 35C05\SubText Solutions in closed form\endx
\ThirdLvl 35C10\SubText Series solutions, expansion theorems\endx
\ThirdLvl 35C15\SubText Integral representations of solutions of
 PDE\endx
\ThirdLvl 35C20\SubText Asymptotic expansions\endx
\ThirdLvl 35C99\SubText \NoneOfAbove\endx
\SecndLvl 35D++\SubText Generalized solutions of partial differential
 equations\endx
\ThirdLvl 35D05\SubText Existence of generalized solutions\endx
\ThirdLvl 35D10\SubText Regularity of generalized solutions\endx
\ThirdLvl 35D99\SubText \NoneOfAbove\endx
\SecndLvl 35E++\SubText Equations and systems with constant
 coefficients \SeeAlso{\SbjNo 35N05}\endx
\ThirdLvl 35E05\SubText Fundamental solutions\endx
\ThirdLvl 35E10\SubText Convexity properties\endx
\ThirdLvl 35E15\SubText Initial value problems\endx
\ThirdLvl 35E20\SubText General theory\endx
\ThirdLvl 35E99\SubText \NoneOfAbove\endx
\SecndLvl 35F++\SubText General first-order equations and systems\endx
\ThirdLvl 35F05\SubText General theory of linear first-order PDE\endx
\ThirdLvl 35F10\SubText Initial value problems for linear first-order
 PDE, linear evolution equations\endx
\ThirdLvl 35F15\SubText Boundary value problems for linear first-order
 PDE\endx
\ThirdLvl 35F20\SubText General theory of nonlinear first-order
 PDE\endx
\ThirdLvl 35F25\SubText Initial value problems for nonlinear
 first-order PDE, nonlinear evolution equations\endx
\ThirdLvl 35F30\SubText Boundary value problems for nonlinear
 first-order PDE\endx
\ThirdLvl 35F99\SubText \NoneOfAbove\endx
\SecndLvl 35G++\SubText General higher-order equations and
 systems\endx
\ThirdLvl 35G05\SubText General theory of linear higher-order PDE\endx
\ThirdLvl 35G10\SubText Initial value problems for linear higher-order
 PDE, linear evolution equations\endx
\ThirdLvl 35G15\SubText Boundary value problems for linear
 higher-order PDE\endx
\ThirdLvl 35G20\SubText General theory of nonlinear higher-order
 PDE\endx
\ThirdLvl 35G25\SubText Initial value problems for nonlinear
 higher-order PDE, nonlinear evolution equations\endx
\ThirdLvl 35G30\SubText Boundary value problems for nonlinear
 higher-order PDE\endx
\ThirdLvl 35G99\SubText \NoneOfAbove\endx
\SecndLvl 35H05\SubText Hypoelliptic equations and systems
 \SeeAlso{\SbjNo 58Gxx}\endx
\SecndLvl 35J++\SubText Partial differential equations of elliptic
 type \SeeAlso{\CMPonly{\SbjNo 58Gxx}\FullScheme{\SbjNo 58G05, \SbjNo
 58G10}}\endx
\ThirdLvl 35J05\SubText Laplace equation, reduced wave equation
 (Helmholtz), Poisson equation \SeeAlso{\SbjNo 31Axx, \SbjNo
 31Bxx}\endx
\ThirdLvl 35J10\SubText Schr\"odinger operator \SeeAlso{\SbjNo
 35Pxx}\endx
\ThirdLvl 35J15\SubText General theory of second-order, elliptic
 equations\endx
\ThirdLvl 35J20\SubText Variational methods for second-order, elliptic
 equations\endx
\ThirdLvl 35J25\SubText Boundary value problems for second-order,
 elliptic equations\endx
\ThirdLvl 35J30\SubText General theory of higher-order, elliptic
 equations \SeeAlso{\SbjNo 31A30, \SbjNo 31B30}\endx
\ThirdLvl 35J35\SubText Variational methods for higher-order, elliptic
 equations\endx
\ThirdLvl 35J40\SubText Boundary value problems for higher-order,
 elliptic equations\endx
\ThirdLvl 35J45\SubText General theory of elliptic systems of PDE\endx
\ThirdLvl 35J50\SubText Variational methods for elliptic systems\endx
\ThirdLvl 35J55\SubText Boundary value problems for elliptic
 systems\endx
\ThirdLvl 35J60\SubText Nonlinear PDE of elliptic type\endx
\ThirdLvl 35J65\SubText Nonlinear boundary value problems for linear
 elliptic PDE; boundary value problems for nonlinear elliptic PDE\endx
\ThirdLvl 35J67\SubText Boundary values of solutions to elliptic
 PDE\endx
\ThirdLvl 35J70\SubText Elliptic partial differential equations of
 degenerate type\endx
\ThirdLvl 35J85\SubText Unilateral problems and variational
 inequalities for elliptic PDE \SeeAlso{\SbjNo 35R35, \SbjNo
 49J40}\endx
\ThirdLvl 35J99\SubText \NoneOfAbove\endx
\SecndLvl 35K++\SubText Parabolic equations and systems
 \SeeAlso{\SbjNo 35Bxx, \SbjNo 35Dxx, \SbjNo 35R30, \SbjNo 35R35,
 \SbjNo 58G11}\endx
\ThirdLvl 35K05\SubText Heat equation\endx
\ThirdLvl 35K10\SubText General theory of second-order, parabolic
 equations\endx
\ThirdLvl 35K15\SubText Initial value problems for second-order,
 parabolic equations\endx
\ThirdLvl 35K20\SubText Boundary value problems for second-order,
 parabolic equations\endx
\ThirdLvl 35K22\SubText Evolution equations (any order in the spatial
 derivatives) \SeeAlso{\SbjNo 58D25}\endx
\ThirdLvl 35K25\SubText General theory of higher-order, parabolic
 equations\endx
\ThirdLvl 35K30\SubText Initial value problems for higher-order,
 parabolic equations\endx
\ThirdLvl 35K35\SubText Boundary value problems for higher-order,
 parabolic equations\endx
\ThirdLvl 35K40\SubText General theory of parabolic systems of
 PDE\endx
\ThirdLvl 35K45\SubText Initial value problems for pararabolic
 systems\endx
\ThirdLvl 35K50\SubText Boundary value problems for parabolic
 systems\endx
\ThirdLvl 35K55\SubText Nonlinear PDE of parabolic type\endx
\ThirdLvl 35K57\SubText Reaction-diffusion equations\endx
\ThirdLvl 35K60\SubText Nonlinear boundary value problems for linear
 parabolic PDE; boundary value problems for nonlinear parabolic
 PDE\endx
\ThirdLvl 35K65\SubText Parabolic partial differential equations of
 degenerate type\endx
\ThirdLvl 35K70\SubText Ultraparabolic, pseudoparabolic PDE, etc.\endx
\ThirdLvl 35K85\SubText Unilateral problems and variational
 inequalities for parabolic PDE \SeeAlso{\SbjNo 35R35, \SbjNo
 49J40}\endx
\ThirdLvl 35K99\SubText \NoneOfAbove\endx
\SecndLvl 35L++\SubText Partial differential equations of hyperbolic
 type \SeeAlso{\SbjNo 58G16}\endx
\ThirdLvl 35L05\SubText Wave equation\endx
\ThirdLvl 35L10\SubText General theory of second-order, hyperbolic
 equations\endx
\ThirdLvl 35L15\SubText Initial value problems for second-order,
 hyperbolic equations\endx
\ThirdLvl 35L20\SubText Boundary value problems for second-order,
 hyperbolic equations\endx
\ThirdLvl 35L25\SubText General theory of higher-order, hyperbolic
 equations\endx
\ThirdLvl 35L30\SubText Initial value problems for higher-order,
 hyperbolic equations\endx
\ThirdLvl 35L35\SubText Boundary value problems for higher-order,
 hyperbolic equations\endx
\ThirdLvl 35L40\SubText General theory of hyperbolic systems of
 first-order PDE\endx
\ThirdLvl 35L45\SubText Initial value problems for hyperbolic systems
 of first-order PDE\endx
\ThirdLvl 35L50\SubText Boundary value problems for hyperbolic systems
 of first-order PDE\endx
\ThirdLvl 35L55\SubText Hyperbolic systems of higher-order PDE\endx
\ThirdLvl 35L60\SubText Nonlinear first-order PDE of hyperbolic
 type\endx
\ThirdLvl 35L65\SubText Conservation laws \endx
\ThirdLvl 35L67\SubText Shocks and singularities \SeeAlso{\SbjNo
 58C27, \SbjNo 76L05}\endx
\ThirdLvl 35L70\SubText Nonlinear second-order PDE of hyperbolic
 type\endx
\ThirdLvl 35L75\SubText Nonlinear hyperabolic PDE of higher ($\gtr 2$)
 order \endx
\ThirdLvl 35L80\SubText Hyperbolic PDE of degenerate type\endx
\ThirdLvl 35L85\SubText Unilateral problems; variational inequalities
 for hyperbolic PDE \SeeAlso{\SbjNo 35R35, \SbjNo 49J40}\endx
\ThirdLvl 35L99\SubText \NoneOfAbove\endx
\SecndLvl 35M++\SubText Partial differential equations of special type
 (mixed, composite, etc.) \SeeFor{For degenerate types, see~\SbjNo
 35J70, \SbjNo 35K65, \SbjNo 35L80}\endx
\ThirdLvl 35M10\SubText PDE of mixed type\endx
\ThirdLvl 35M20\SubText PDE of composite type\endx
\ThirdLvl 35M99\SubText \NoneOfAbove\endx
\SecndLvl 35N++\SubText Overdetermined systems
 \SeeAlso{\CMPonly{\SbjNo 58Gxx}\FullScheme{\SbjNo 58G05, \SbjNo
 58G07, \SbjNo 58Hxx}}\endx
\ThirdLvl 35N05\SubText Overdetermined systems with constant
 coefficients\endx
\ThirdLvl 35N10\SubText Overdetermined systems with variable
 coefficients (general)\endx
\ThirdLvl 35N15\SubText $\overline\partial$-Neumann problem and
 generalizations; formal complexes \SeeAlso{\SbjNo 32F20 and \SbjNo
 58G05}\endx
\ThirdLvl 35N99\SubText \NoneOfAbove\endx
\SecndLvl 35P++\SubText Spectral theory and eigenvalue problems for
 partial differential operators \SeeAlso{\SbjNo 47Axx, \SbjNo 47Bxx,
 \SbjNo 47F05}\endx
\ThirdLvl 35P05\SubText General spectral theory of PDE\endx
\ThirdLvl 35P10\SubText Completeness of eigenfunctions, eigenfunction
 expansions for PDO\endx
\ThirdLvl 35P15\SubText Estimation of eigenvalues, upper and lower
 bounds\endx
\ThirdLvl 35P20\SubText Asymptotic distribution of eigenvalues and
 eigenfunctions for PDO\endx
\ThirdLvl 35P25\SubText Scattering theory for PDE \SeeAlso{\SbjNo
 47A40}\endx
\ThirdLvl 35P30\SubText Nonlinear eigenvalue problems, nonlinear
 spectral theory for PDO\endx
\ThirdLvl 35P99\SubText \NoneOfAbove\endx
\SecndLvl 35Q++\SubText Equations of mathematical physics and other
 areas of application \SeeAlso{\SbjNo 35J05, \SbjNo 35J10, \SbjNo
 35K05, \SbjNo 35L05}\endx
\ThirdLvl 35Q05\SubText Euler-Poisson-Darboux equation and
 generalizations\endx
\ThirdLvl 35Q15\SubText Riemann-Hilbert problems \SeeAlso{\SbjNo
 30E25, \SbjNo 31A25, \SbjNo 31B20}\endx
\ThirdLvl 35Q30\SubText Stokes and Navier-Stokes equations
 \SeeAlso{\SbjNo 76D05, \SbjNo 76D07, \SbjNo 76N10}\endx
\ThirdLvl 35Q35\SubText Other equations arising in fluid
 mechanics\endx
\ThirdLvl 35Q40\SubText Equations from quantum mechanics\endx
\ThirdLvl 35Q51\SubText Solitons \SeeAlso{\SbjNo 58F07}\endx
\ThirdLvl 35Q53\SubText KdV-like equations (Korteweg-de Vries,
 Burgers, sine-Gordon, sinh-Gordon, etc.) \SeeAlso{\SbjNo 58F07}\endx
\ThirdLvl 35Q55\SubText NLS-like (nonlinear Schr\"odinger) equations
 \SeeAlso{\SbjNo 58F07}\endx
\ThirdLvl 35Q58\SubText Other completely integrable equations
 \SeeAlso{\SbjNo 58F07}\endx
\ThirdLvl 35Q60\SubText Equations of electromagnetic theory and
 optics\endx
\ThirdLvl 35Q72\SubText Other equations from mechanics\endx
\ThirdLvl 35Q75\SubText PDE in relativity\endx
\ThirdLvl 35Q80\SubText Applications of PDE in areas other than
 physics\endx
\ThirdLvl 35Q99\SubText \NoneOfAbove\endx
\SecndLvl 35R++\SubText Miscellaneous topics involving partial
 differential equations \SeeFor{For equations on manifolds, see \SbjNo
 58Gxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs,
 see also \SbjNo 60H15}\endx
\ThirdLvl 35R05\SubText PDE with discontinuous coefficients or
 data\endx
\ThirdLvl 35R10\SubText Partial functional-differential or
 differential-difference equations, with or without deviating
 arguments\endx
\ThirdLvl 35R15\SubText Partial differential equations on
 infinite-dimensional (e.g.\ function) spaces (= PDE in infinitely
 many variables) \SeeAlso{\SbjNo 46Gxx, \SbjNo 58D25}\endx
\ThirdLvl 35R20\SubText Partial operator-differential equations (i.e.\
 PDE on finite-dimensional spaces for abstract space valued functions)
 \SeeAlso{ \SbjNo 34Gxx, \SbjNo 47A50, \SbjNo 47D03, \SbjNo 47D06,
 \SbjNo 47D09, \SbjNo 47H15, \SbjNo 47H20}\endx
\ThirdLvl 35R25\SubText Improperly posed problems for PDE\endx
\ThirdLvl 35R30\SubText Inverse problems (undetermined coefficients,
 etc.) for PDE\endx
\ThirdLvl 35R35\SubText Free boundary problems for PDE\endx
\ThirdLvl 35R45\SubText Partial differential inequalities\endx
\ThirdLvl 35R50\SubText Partial differential equations of infinite
 order\endx
\ThirdLvl 35R60\SubText Partial differential equations with randomness
 \SeeAlso{ \SbjNo 60H15}\endx
\ThirdLvl 35R70\SubText PDE with multivalued right-hand sides\endx
\ThirdLvl 35R99\SubText \NoneOfAbove\endx
\SecndLvl 35S++\SubText Pseudodifferential operators and other
 generalizations of partial differential operators \SeeAlso{\SbjNo
 47G30, \SbjNo 58G15}\endx
\ThirdLvl 35S05\SubText General theory of $\Psi$DO\endx
\ThirdLvl 35S10\SubText Initial value problems for $\Psi$DO\endx
\ThirdLvl 35S15\SubText Boundary value problems for $\Psi$DO\endx
\ThirdLvl 35S30\SubText Fourier integral operators\endx
\ThirdLvl 35S35\SubText Topological aspects: intersection cohomology,
 stratified sets, etc. \SeeAlso{\SbjNo 32C38, \SbjNo 32S40, \SbjNo
 32S60, \SbjNo 58G07}\endx
\ThirdLvl 35S50\SubText Paradifferential operators\endx
\ThirdLvl 35S99\SubText \NoneOfAbove\endx
\MajorSub 39-++\SubText Finite differences and functional
 equations\endx
\ThirdLvl 39-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 39-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 39-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 39-03\SubText \Historical\endx
\ThirdLvl 39-04\SubText \ExplicitComputation\endx
\ThirdLvl 39-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 39A++\SubText Difference equations \SeeFor{For dynamical
 systems, see \SbjNo 58Fxx}\endx
\ThirdLvl 39A05\SubText General\endx
\ThirdLvl 39A10\SubText Difference equations \SeeAlso{\SbjNo
 33Dxx}\endx
\ThirdLvl 39A11\SubText Stability of difference equations\endx
\ThirdLvl 39A12\SubText Discrete version of topics in analysis\endx
\ThirdLvl 39A70\SubText Difference operators \SeeAlso{\SbjNo
 47B39}\endx
\ThirdLvl 39A99\SubText \NoneOfAbove\endx
\SecndLvl 39B++\SubText Functional equations \SeeAlso{\SbjNo
 30D05}\endx
\ThirdLvl 39B05\SubText General\endx
\ThirdLvl 39B12\SubText Iteration theory, iterative and composite
 equations \SeeAlso{\SbjNo 26A18, \SbjNo 30D05, \SbjNo 58F08}\endx
\ThirdLvl 39B22\SubText Equations for real functions\endx
\ThirdLvl 39B32\SubText Equations for complex functions
 \SeeAlso{\SbjNo 30D05}\endx
\ThirdLvl 39B42\SubText Matrix and operator equations\endx
\ThirdLvl 39B52\SubText Equations for functions with more general
 domains and/or ranges\endx
\ThirdLvl 39B62\SubText Systems of functional equations\endx
\ThirdLvl 39B72\SubText Inequalities involving unknown functions
 \SeeAlso{\SbjNo 26A51, \SbjNo 26Dxx}\endx
\ThirdLvl 39B99\SubText \NoneOfAbove\endx
\MajorSub 40-++\SubText Sequences, series, summability\endx
\ThirdLvl 40-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 40-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 40-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 40-03\SubText \Historical\endx
\ThirdLvl 40-04\SubText \ExplicitComputation\endx
\ThirdLvl 40-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 40A++\SubText Convergence and divergence of infinite
 limiting processes\endx
\ThirdLvl 40A05\SubText Convergence and divergence of series and
 sequences\endx
\ThirdLvl 40A10\SubText Convergence and divergence of integrals\endx
\ThirdLvl 40A15\SubText Convergence and divergence of continued
 fractions \SeeAlso{\SbjNo 30B70}\endx
\ThirdLvl 40A20\SubText Convergence and divergence of infinite
 products\endx
\ThirdLvl 40A25\SubText Approximation to limiting values (summation of
 series, etc.) \SeeFor{For the Euler-Maclaurin summation formula, see
 \SbjNo 65B15}\endx
\ThirdLvl 40A30\SubText Convergence and divergence of series and
 sequences of functions\endx
\ThirdLvl 40A99\SubText \NoneOfAbove\endx
\SecndLvl 40B05\SubText Multiple sequences and series
 \ExtraText{(should also be assigned at least one other classification
 number in this section)}\endx
\SecndLvl 40C++\SubText General summability methods\endx
\ThirdLvl 40C05\SubText Matrix methods\endx
\ThirdLvl 40C10\SubText Integral methods\endx
\ThirdLvl 40C15\SubText Function-theoretic methods (including power
 series methods and semicontinuous methods)\endx
\ThirdLvl 40C99\SubText \NoneOfAbove\endx
\SecndLvl 40D++\SubText Direct theorems on summability\endx
\ThirdLvl 40D05\SubText General theorems\endx
\ThirdLvl 40D09\SubText Structure of summability fields\endx
\ThirdLvl 40D10\SubText Tauberian constants and oscillation
 limits\endx
\ThirdLvl 40D15\SubText Convergence factors and summability
 factors\endx
\ThirdLvl 40D20\SubText Summability and bounded fields of methods\endx
\ThirdLvl 40D25\SubText Inclusion and equivalence theorems\endx
\ThirdLvl 40D99\SubText \NoneOfAbove\endx
\SecndLvl 40E++\SubText Inversion theorems\endx
\ThirdLvl 40E05\SubText Tauberian theorems, general\endx
\ThirdLvl 40E10\SubText Growth estimates\endx
\ThirdLvl 40E15\SubText Lacunary inversion theorems\endx
\ThirdLvl 40E20\SubText Tauberian constants\endx
\ThirdLvl 40E99\SubText \NoneOfAbove\endx
\SecndLvl 40F05\SubText Absolute and strong summability\endx
\SecndLvl 40G++\SubText Special methods of summability\endx
\ThirdLvl 40G05\SubText Ces\`aro, Euler, N\"orlund and Hausdorff
 methods\endx
\ThirdLvl 40G10\SubText Abel, Borel and power series methods\endx
\ThirdLvl 40G99\SubText \NoneOfAbove\endx
\SecndLvl 40H05\SubText Functional analytic methods in
 summability\endx
\SecndLvl 40J05\SubText Summability in abstract structures
 \SeeAlso{\SbjNo 43A55, \SbjNo 46A35, \SbjNo 46B15}\endx
\MajorSub 41-++\SubText Approximations and expansions \SeeFor{For all
 approximation theory in the complex domain, see~\CMPonly{\SbjNo
 30Exx}\FullScheme{\SbjNo 30E05 and \SbjNo 30E10}; for all
 trigonometric approximation and interpolation, see~\CMPonly{\SbjNo
 42Axx}\FullScheme{\SbjNo 42A10 and \SbjNo 42A15}; for numerical
 approximation, see~\SbjNo 65Dxx}\endx
\ThirdLvl 41-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 41-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 41-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 41-03\SubText \Historical\endx
\ThirdLvl 41-04\SubText \ExplicitComputation\endx
\ThirdLvl 41-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 41A05\SubText Interpolation \SeeAlso{\SbjNo 42A15 and \SbjNo
 65D05}\endx
\ThirdLvl 41A10\SubText Approximation by polynomials \SeeFor{For
 approximation by trigonometric polynomials, see \SbjNo 42A10}\endx
\ThirdLvl 41A15\SubText Spline approximation\endx
\ThirdLvl 41A17\SubText Inequalities in approximation (Bernstein,
 Jackson, Nikol\cprime ski\u\i\ type inequalities)\endx
\ThirdLvl 41A20\SubText Approximation by rational functions\endx
\ThirdLvl 41A21\SubText Pad\'e approximation\endx
\ThirdLvl 41A25\SubText Rate of convergence, degree of
 approximation\endx
\ThirdLvl 41A27\SubText Inverse theorems\endx
\ThirdLvl 41A28\SubText Simultaneous approximation\endx
\ThirdLvl 41A29\SubText Approximation with constraints\endx
\ThirdLvl 41A30\SubText Approximation by other special function
 classes\endx
\ThirdLvl 41A35\SubText Approximation by operators (in particular, by
 integral operators)\endx
\ThirdLvl 41A36\SubText Approximation by positive operators\endx
\ThirdLvl 41A40\SubText Saturation\endx
\ThirdLvl 41A44\SubText Best constants\endx
\ThirdLvl 41A45\SubText Approximation by arbitrary linear
 expressions\endx
\ThirdLvl 41A46\SubText Approximation by arbitrary nonlinear
 expressions; widths and entropy\endx
\ThirdLvl 41A50\SubText Best approximation, Chebyshev systems\endx
\ThirdLvl 41A52\SubText Uniqueness of best approximation\endx
\ThirdLvl 41A55\SubText Approximate quadratures\endx
\ThirdLvl 41A58\SubText Series expansions (e.g.\ Taylor, Lidstone
 series, but not Fourier series)\endx
\ThirdLvl 41A60\SubText Asymptotic approximations, asymptotic
 expansions (steepest descent, etc.) \SeeAlso{\SbjNo 30E15}\endx
\ThirdLvl 41A63\SubText Multidimensional problems (should also be
 assigned at least one other classification number in this
 section)\endx
\ThirdLvl 41A65\SubText Abstract approximation theory (approximation
 in normed linear spaces and other abstract spaces)\endx
\ThirdLvl 41A80\SubText Remainders in approximation formulas\endx
\ThirdLvl 41A99\SubText \Miscellaneous\endx
\MajorSub 42-++\SubText Fourier analysis\endx
\ThirdLvl 42-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 42-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 42-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 42-03\SubText \Historical\endx
\ThirdLvl 42-04\SubText \ExplicitComputation\endx
\ThirdLvl 42-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 42A++\SubText Fourier analysis in one variable\endx
\ThirdLvl 42A05\SubText Trigonometric polynomials, inequalities,
 extremal problems\endx
\ThirdLvl 42A10\SubText Trigonometric approximation\endx
\ThirdLvl 42A15\SubText Trigonometric interpolation\endx
\ThirdLvl 42A16\SubText Fourier coefficients, Fourier series of
 functions with special properties, special Fourier series \SeeFor{For
 automorphic theory, see mainly \SbjNo 11F30}\endx
\ThirdLvl 42A20\SubText Convergence of Fourier and trigonometric
 series\endx
\ThirdLvl 42A24\SubText Summability of Fourier and trigonometric
 series\endx
\ThirdLvl 42A28\SubText Absolute convergence, absolute
 summability\endx
\ThirdLvl 42A32\SubText Trigonometric series of special types
 (positive coefficients, monotonic coefficients, etc.)\endx
\ThirdLvl 42A38\SubText Fourier and Fourier-Stieltjes transforms and
 other transforms of Fourier type\endx
\ThirdLvl 42A45\SubText Multipliers\endx
\ThirdLvl 42A50\SubText Conjugate functions, conjugate series,
 singular integrals\endx
\ThirdLvl 42A55\SubText Lacunary series of trigonometric and other
 functions; Riesz products\endx
\ThirdLvl 42A61\SubText Probabilistic methods\endx
\ThirdLvl 42A63\SubText Uniqueness of trigonometric expansions,
 uniqueness of Fourier expansions, Riemann theory, localization\endx
\ThirdLvl 42A65\SubText Completeness of sets of functions\endx
\ThirdLvl 42A70\SubText Trigonometric moment problems\endx
\ThirdLvl 42A75\SubText Classical almost periodic functions, mean
 periodic functions \SeeAlso{\SbjNo 43A60}\endx
\ThirdLvl 42A82\SubText Positive definite functions\endx
\ThirdLvl 42A85\SubText Convolution, factorization\endx
\ThirdLvl 42A99\SubText \NoneOfAbove\endx
\SecndLvl 42B++\SubText Fourier analysis in several variables
 \SeeFor{For automorphic theory, see mainly \SbjNo 11F30}\endx
\ThirdLvl 42B05\SubText Fourier series and coefficients\endx
\ThirdLvl 42B08\SubText Summability\endx
\ThirdLvl 42B10\SubText Fourier and Fourier-Stieltjes transforms and
 other transforms of Fourier type\endx
\ThirdLvl 42B15\SubText Multipliers\endx
\ThirdLvl 42B20\SubText Singular integrals (Calder\'on-Zygmund,
 etc.)\endx
\ThirdLvl 42B25\SubText Maximal functions, Littlewood-Paley
 theory\endx
\ThirdLvl 42B30\SubText $H\sp p$-spaces\endx
\ThirdLvl 42B99\SubText \NoneOfAbove\endx
\SecndLvl 42C++\SubText Nontrigonometric Fourier analysis\endx
\ThirdLvl 42C05\SubText Orthogonal functions and polynomials, general
 theory \SeeAlso{\SbjNo 33A65, \SbjNo 33C45, \SbjNo 33C50, \SbjNo
 33D45}\endx
\ThirdLvl 42C10\SubText Fourier series in special orthogonal functions
 (Legendre polynomials, Walsh functions, etc.)\endx
\ThirdLvl 42C15\SubText Series of general orthogonal functions,
 generalized Fourier expansions, nonorthogonal expansions\endx
\ThirdLvl 42C20\SubText Rearrangements and other transformations of
 Fourier and other orthogonal series\endx
\ThirdLvl 42C25\SubText Uniqueness and localization for orthogonal
 series\endx
\ThirdLvl 42C30\SubText Completeness of sets of functions\endx
\ThirdLvl 42C99\SubText \NoneOfAbove\endx
\MajorSub 43-++\SubText Abstract harmonic analysis \SeeFor{For other
 analysis on topological and Lie groups, see~\SbjNo 22Exx}\endx
\ThirdLvl 43-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 43-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 43-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 43-03\SubText \Historical\endx
\ThirdLvl 43-04\SubText \ExplicitComputation\endx
\ThirdLvl 43-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 43A05\SubText Measures on groups and semigroups, etc.\endx
\ThirdLvl 43A07\SubText Means on groups, semigroups, etc.; amenable
 groups\endx
\ThirdLvl 43A10\SubText Measure algebras on groups, semigroups,
 etc.\endx
\ThirdLvl 43A15\SubText $L\sp p$-spaces and other function spaces on
 groups, semigroups, etc.\endx
\ThirdLvl 43A17\SubText Analysis on ordered groups, ${\it H}\sp
 p$-theory\endx
\ThirdLvl 43A20\SubText $L\sp 1$-algebras on groups, semigroups,
 etc.\endx
\ThirdLvl 43A22\SubText Homomorphisms and multipliers of function
 spaces on groups, semigroups, etc.\endx
\ThirdLvl 43A25\SubText Fourier and Fourier-Stieltjes transforms on
 locally compact abelian groups\endx
\ThirdLvl 43A30\SubText Fourier and Fourier-Stieltjes transforms on
 nonabelian groups and on semigroups, etc.\endx
\ThirdLvl 43A32\SubText Other transforms and operators of Fourier
 type\endx
\ThirdLvl 43A35\SubText Positive definite functions on groups,
 semigroups, etc.\endx
\ThirdLvl 43A40\SubText Character groups and dual objects\endx
\ThirdLvl 43A45\SubText Spectral synthesis on groups, semigroups,
 etc.\endx
\ThirdLvl 43A46\SubText Special sets (thin sets, Kronecker sets,
 Helson sets, Ditkin sets, Sidon sets, etc.)\endx
\ThirdLvl 43A50\SubText Convergence of Fourier series and of inverse
 transforms\endx
\ThirdLvl 43A55\SubText Summability methods on groups, semigroups,
 etc. \SeeAlso{\SbjNo 40J05}\endx
\ThirdLvl 43A60\SubText Almost periodic functions on groups and
 semigroups and their generalizations (recurrent functions, distal
 functions, etc.); almost automorphic functions\endx
\ThirdLvl 43A62\SubText Hypergroups\endx
\ThirdLvl 43A65\SubText Representations of groups, semigroups, etc.
 \SeeAlso{\SbjNo 22A10, \SbjNo 22A20, \SbjNo 22Dxx, \SbjNo 22E45}\endx
\ThirdLvl 43A70\SubText Analysis on specific locally compact abelian
 groups \SeeAlso{\SbjNo 11R56, \SbjNo 22B05}\endx
\ThirdLvl 43A75\SubText Analysis on specific compact groups\endx
\ThirdLvl 43A77\SubText Analysis on general compact groups\endx
\ThirdLvl 43A80\SubText Analysis on other specific Lie groups
 \SeeAlso{\SbjNo 22Exx}\endx
\ThirdLvl 43A85\SubText Analysis on homogeneous spaces\endx
\ThirdLvl 43A90\SubText Spherical functions \SeeAlso{\SbjNo 22E45,
 \SbjNo 22E46, \SbjNo 33C65, \SbjNo 33D55}\endx
\ThirdLvl 43A95\SubText Categorical methods \SeeAlso{\SbjNo
 46Mxx}\endx
\ThirdLvl 43A99\SubText \Miscellaneous\endx
\MajorSub 44-++\SubText Integral transforms, operational calculus
 \SeeFor{For fractional derivatives and integrals, see~\SbjNo 26A33.
 For Fourier transforms, see \SbjNo 42A38, \SbjNo 42B10. %\endx
For integral transforms in distribution spaces, see \SbjNo 46F12.  For
 numerical methods, see~\SbjNo 65R10}\endx
\ThirdLvl 44-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 44-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 44-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 44-03\SubText \Historical\endx
\ThirdLvl 44-04\SubText \ExplicitComputation\endx
\ThirdLvl 44-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 44A05\SubText General transforms \SeeAlso{\SbjNo 42A38}\endx
\ThirdLvl 44A10\SubText Laplace transform\endx
\ThirdLvl 44A12\SubText Radon transform \SeeAlso{\SbjNo 92C55}\endx
\ThirdLvl 44A15\SubText Special transforms (Legendre, Hilbert,
 etc.)\endx
\ThirdLvl 44A20\SubText Transforms of special functions\endx
\ThirdLvl 44A30\SubText Multiple transforms\endx
\ThirdLvl 44A35\SubText Convolution\endx
\ThirdLvl 44A40\SubText Calculus of Mikusi\'nski and other operational
 calculi\endx
\ThirdLvl 44A45\SubText Classical operational calculus\endx
\ThirdLvl 44A55\SubText Discrete operational calculus\endx
\ThirdLvl 44A60\SubText Moment problems\endx
\ThirdLvl 44A99\SubText \Miscellaneous\endx
\MajorSub 45-++\SubText Integral equations\endx
\ThirdLvl 45-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 45-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 45-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 45-03\SubText \Historical\endx
\ThirdLvl 45-04\SubText \ExplicitComputation\endx
\ThirdLvl 45-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 45A05\SubText Linear integral equations\endx
\SecndLvl 45B05\SubText Fredholm integral equations\endx
\SecndLvl 45C05\SubText Eigenvalue problems \SeeAlso{\SbjNo 34Lxx,
 \SbjNo 35Pxx, \SbjNo 45P05, \SbjNo 47A75}\endx
\SecndLvl 45D05\SubText Volterra integral equations \SeeAlso{\SbjNo
 34A12}\endx
\SecndLvl 45E++\SubText Singular integral equations
 \SeeAlso{\CMPonly{\SbjNo 30Exx, \SbjNo 44-XX}\FullScheme{\SbjNo
 30E20, \SbjNo 30E25, \SbjNo 44A15, \SbjNo 44A35}}\endx
\ThirdLvl 45E05\SubText Integral equations with kernels of Cauchy type
 \SeeAlso{\SbjNo 35J15}\endx
\ThirdLvl 45E10\SubText Integral equations of the convolution type
 (Abel, Picard, Toeplitz and Wiener-Hopf type) \SeeAlso{\SbjNo
 47B35}\endx
\ThirdLvl 45E99\SubText \NoneOfAbove\endx
\SecndLvl 45F++\SubText Systems of linear integral equations\endx
\ThirdLvl 45F05\SubText Systems of nonsingular linear integral
 equations\endx
\ThirdLvl 45F10\SubText Dual, triple, etc., integral and series
 equations\endx
\ThirdLvl 45F15\SubText Systems of singular linear integral
 equations\endx
\ThirdLvl 45F99\SubText \NoneOfAbove\endx
\SecndLvl 45G++\SubText Nonlinear integral equations \SeeAlso{\SbjNo
 47H15}\endx
\ThirdLvl 45G05\SubText Singular nonlinear integral equations\endx
\ThirdLvl 45G10\SubText Other nonlinear integral equations\endx
\ThirdLvl 45G15\SubText Systems of nonlinear integral equations\endx
\SecndLvl 45H05\SubText Miscellaneous special kernels \SeeAlso{\SbjNo
 44A15}\endx
\SecndLvl 45J05\SubText Integro-ordinary differential equations\endx
\SecndLvl 45K05\SubText Integro-partial differential equations\endx
\SecndLvl 45L++\SubText Approximation of solutions\endx
\ThirdLvl 45L05\SubText Theoretical approximation of solutions\endx
\ThirdLvl 45L10\SubText Numerical approximation of solutions
 \SeeFor{For numerical analysis, see \SbjNo 65R20}\endx
\ThirdLvl 45L99\SubText \NoneOfAbove\endx
\SecndLvl 45M++\SubText Qualitative behavior\endx
\ThirdLvl 45M05\SubText Asymptotics\endx
\ThirdLvl 45M10\SubText Stability theory\endx
\ThirdLvl 45M15\SubText Periodic solutions\endx
\ThirdLvl 45M20\SubText Positive solutions\endx
\ThirdLvl 45M99\SubText \NoneOfAbove\endx
\SecndLvl 45N05\SubText Abstract integral equations, integral
 equations in abstract spaces\endx
\SecndLvl 45P05\SubText Integral operators \SeeAlso{\SbjNo 47B38,
 \SbjNo 47G10}\endx
\MajorSub 46-++\SubText Functional analysis \SeeFor{For manifolds
 modeled on topological linear spaces, see~\SbjNo 57N20, \SbjNo
 58Bxx}\endx
\ThirdLvl 46-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 46-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 46-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 46-03\SubText \Historical\endx
\ThirdLvl 46-04\SubText \ExplicitComputation\endx
\ThirdLvl 46-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 46A++\SubText Topological linear spaces and related
 structures \SeeFor{For function spaces, see~\SbjNo 46Exx}\endx
\ThirdLvl 46A03\SubText General theory of locally convex spaces\endx
\ThirdLvl 46A04\SubText Locally convex Fr\'echet spaces and
 (DF)-spaces\endx
\ThirdLvl 46A08\SubText Barrelled spaces, bornological spaces\endx
\ThirdLvl 46A11\SubText Spaces determined by compactness or
 summability properties (nuclear spaces, Schwartz spaces, Montel
 spaces, etc.)\endx
\ThirdLvl 46A13\SubText Spaces defined by inductive or projective
 limits (LB, LF, etc.) \SeeAlso{\SbjNo 46M40}\endx
\ThirdLvl 46A16\SubText Not locally convex spaces (metrizable
 topological linear spaces, locally bounded spaces, quasi-Banach
 spaces, etc.)\endx
\ThirdLvl 46A17\SubText Bornologies and related structures; Mackey
 convergence, etc.\endx
\ThirdLvl 46A19\SubText Other ``topological'' linear spaces
 (convergence spaces, ranked spaces, spaces with a metric taking
 values in an ordered structure more general than ${\bf R}$,
 etc.)\endx
\ThirdLvl 46A20\SubText Duality theory\endx
\ThirdLvl 46A22\SubText Theorems of Hahn-Banach type; extension and
 lifting of functionals and operators \SeeAlso{\SbjNo 46M10}\endx
\ThirdLvl 46A25\SubText Reflexivity and semi-reflexivity
 \SeeAlso{\SbjNo 46B10}\endx
\ThirdLvl 46A30\SubText Open mapping and closed graph theorems;
 completeness (including $B$-, $B\sb r$-completeness)\endx
\ThirdLvl 46A32\SubText Spaces of linear operators; topological tensor
 products; approximation properties \SeeAlso{\SbjNo 46B28, \SbjNo
 46M05, \SbjNo 47D15, \SbjNo 47D50}\endx
\ThirdLvl 46A35\SubText Summability and bases \SeeAlso{\SbjNo
 46B15}\endx
\ThirdLvl 46A40\SubText Ordered topological linear spaces, vector
 lattices \SeeAlso{\SbjNo 06F20, \SbjNo 46B40, \SbjNo 46B42}\endx
\ThirdLvl 46A45\SubText Sequence spaces (including K\"othe sequence
 spaces) \SeeAlso{\SbjNo 46B45}\endx
\ThirdLvl 46A50\SubText Compactness in topological linear spaces;
 angelic spaces, etc.\endx
\ThirdLvl 46A55\SubText Convex sets in topological linear spaces;
 Choquet theory \SeeAlso{\SbjNo 52A07}\endx
\ThirdLvl 46A70\SubText Saks spaces and their duals (strict
 topologies, mixed topologies, two-norm spaces, co-Saks spaces,
 etc.)\endx
\ThirdLvl 46A80\SubText Modular spaces\endx
\ThirdLvl 46A99\SubText \NoneOfAbove\endx
\SecndLvl 46B++\SubText Normed linear spaces and Banach spaces; Banach
 lattices \SeeFor{For function spaces, see \SbjNo 46Exx}\endx
\ThirdLvl 46B03\SubText Isomorphic theory (including renorming) of
 Banach spaces\endx
\ThirdLvl 46B04\SubText Isometric theory of Banach spaces\endx
\ThirdLvl 46B07\SubText Local theory of Banach spaces\endx
\ThirdLvl 46B08\SubText Ultraproduct techniques in Banach space theory
 \SeeAlso{\SbjNo 46M07}\endx
\ThirdLvl 46B09\SubText Probabilistic methods in Banach space theory
 \SeeAlso{\SbjNo 60Bxx}\endx
\ThirdLvl 46B10\SubText Duality and reflexivity \SeeAlso{\SbjNo
 46A25}\endx
\ThirdLvl 46B15\SubText Summability and bases \SeeAlso{\SbjNo
 46A35}\endx
\ThirdLvl 46B20\SubText Geometry and structure of normed linear
 spaces\endx
\ThirdLvl 46B22\SubText Radon-Nikod\'ym, Kre\u\i n-Mil\cprime man and
 related properties \SeeAlso{\SbjNo 46G10}\endx
\ThirdLvl 46B25\SubText Classical Banach spaces in the general
 theory\endx
\ThirdLvl 46B26\SubText Nonseparable Banach spaces\endx
\ThirdLvl 46B28\SubText Spaces of operators; tensor products;
 approximation properties \SeeAlso{\SbjNo 46A32, \SbjNo 46M05, \SbjNo
 47D15, \SbjNo 47D50}\endx
\ThirdLvl 46B40\SubText Ordered normed spaces \SeeAlso{\SbjNo 46A40,
 \SbjNo 46B42}\endx
\ThirdLvl 46B42\SubText Banach lattices \SeeAlso{\SbjNo 46A40, \SbjNo
 46B40}\endx
\ThirdLvl 46B45\SubText Banach sequence spaces \SeeAlso{\SbjNo
 46A45}\endx
\ThirdLvl 46B70\SubText Interpolation between normed linear spaces
 \SeeAlso{\SbjNo 46M35}\endx
\ThirdLvl 46B99\SubText \NoneOfAbove\endx
\SecndLvl 46C++\SubText Inner product spaces and their
 generalizations, Hilbert spaces \SeeFor{For function spaces, see
 \SbjNo 46Exx}\endx
\ThirdLvl 46C05\SubText Hilbert and pre-Hilbert spaces: geometry and
 topology (including spaces with semidefinite inner product)\endx
\ThirdLvl 46C15\SubText Characterizations of Hilbert spaces\endx
\ThirdLvl 46C20\SubText Spaces with indefinite inner product\endx
\ThirdLvl 46C50\SubText Generalizations of inner products (semi-inner
 products, partial inner products, etc.)\endx
\ThirdLvl 46C99\SubText \NoneOfAbove\endx
\SecndLvl 46E++\SubText Linear function spaces and their duals
 \SeeAlso{\SbjNo 30H05, \SbjNo 32E25, \SbjNo 46F05; for function
 algebras, see \SbjNo 46J10}\endx
\ThirdLvl 46E05\SubText Lattices of continuous, differentiable or
 analytic functions\endx
\ThirdLvl 46E10\SubText Topological linear spaces of continuous,
 differentiable or analytic functions\endx
\ThirdLvl 46E15\SubText Banach spaces of continuous, differentiable or
 analytic functions\endx
\ThirdLvl 46E20\SubText Hilbert spaces of continuous, differentiable
 or analytic functions\endx
\ThirdLvl 46E22\SubText Hilbert spaces with reproducing kernels (=
 [proper] functional Hilbert spaces)\endx
\ThirdLvl 46E25\SubText Rings and algebras of continuous,
 differentiable or analytic functions \SeeFor{For Banach function
 algebras, see \SbjNo 46J10, \SbjNo 46J15}\endx
\ThirdLvl 46E27\SubText Spaces of measures \SeeAlso{\SbjNo 28A33,
 \SbjNo 46Gxx}\endx
\ThirdLvl 46E30\SubText Spaces of measurable functions ($L\sp
 p$-spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces,
 rearrangement invariant spaces, ideal spaces, etc.)\endx
\ThirdLvl 46E35\SubText Sobolev spaces and other spaces of ``smooth''
 functions, embedding theorems, trace theorems\endx
\ThirdLvl 46E39\SubText Sobolev (and similar kinds of) spaces of
 functions of discrete variables\endx
\ThirdLvl 46E40\SubText Spaces of vector- and operator-valued
 functions\endx
\ThirdLvl 46E50\SubText Spaces of differentiable or holomorphic
 functions on infinite-dimensional spaces \SeeAlso{\SbjNo 46G20}\endx
\ThirdLvl 46E99\SubText \NoneOfAbove\endx
\SecndLvl 46F++\SubText Distributions, generalized functions,
 distribution spaces \SeeFor{For distribution theory on nonlinear
 spaces, see \SbjNo 58Cxx}\endx
\ThirdLvl 46F05\SubText Topological linear spaces of test functions,
 distributions and ultradistributions \SeeAlso{\SbjNo 46E10, \SbjNo
 46E35}\endx
\ThirdLvl 46F10\SubText Operations with distributions\endx
\ThirdLvl 46F12\SubText Integral transforms in distribution spaces
 \SeeAlso{\SbjNo 42-XX, \SbjNo 44-XX}\endx
\ThirdLvl 46F15\SubText Hyperfunctions, analytic functionals
 \SeeAlso{\SbjNo 32A25, \SbjNo 32A45, \SbjNo 32C35, \SbjNo 58G07}\endx
\ThirdLvl 46F20\SubText Distributions and ultradistributions as
 boundary values of analytic functions \SeeAlso{\SbjNo 30D40, \SbjNo
 30E25, \SbjNo 32A40}\endx
\ThirdLvl 46F25\SubText Distributions on infinite-dimensional spaces
 \SeeAlso{\SbjNo 58C35}\endx
\ThirdLvl 46F99\SubText \NoneOfAbove\endx
\SecndLvl 46G++\SubText Measures, integration, derivative, holomorphy
 (all involving infinite-dimensional spaces) \SeeAlso{\SbjNo
 28-XX}\SeeFor{For nonlinear functional analysis, see \SbjNo 47Hxx,
 \SbjNo 58-XX, especially \SbjNo 58Cxx}\endx
\ThirdLvl 46G05\SubText Derivatives \SeeAlso{\SbjNo 58C20, \SbjNo
 58C25}\endx
\ThirdLvl 46G10\SubText Vector-valued measures and integration
 \SeeAlso{\SbjNo 28Bxx, \SbjNo 46B22}\endx
\ThirdLvl 46G12\SubText Measures and integration on abstract linear
 spaces \SeeAlso{\SbjNo 28C20}\endx
\ThirdLvl 46G15\SubText Functional analytic lifting theory
 \SeeAlso{\SbjNo 28A51}\endx
\ThirdLvl 46G20\SubText Infinite-dimensional holomorphy
 \SeeAlso{\SbjNo 32-XX, \SbjNo 46E50, \SbjNo 58B12, \SbjNo 58C10}\endx
\ThirdLvl 46G99\SubText \NoneOfAbove\endx
\SecndLvl 46H++\SubText Topological algebras, normed rings and
 algebras, Banach algebras \SeeFor{For group algebras, convolution
 algebras and measure algebras, see \SbjNo 43A10, \SbjNo 43A20}\endx
\ThirdLvl 46H05\SubText General theory of topological algebras\endx
\ThirdLvl 46H10\SubText Ideals and subalgebras\endx
\ThirdLvl 46H15\SubText Representations of topological algebras\endx
\ThirdLvl 46H20\SubText Structure, classification of topological
 algebras\endx
\ThirdLvl 46H25\SubText Normed modules and Banach modules, topological
 modules (if not placed in \SbjNo 13-XX or \SbjNo 16-XX)\endx
\ThirdLvl 46H30\SubText Functional calculus in topological algebras
 \SeeAlso{\SbjNo 47A60}\endx
\ThirdLvl 46H35\SubText Topological algebras of operators [See mainly
 \SbjNo 47D30, and also \SbjNo 47D25, \SbjNo 47D50]\endx
\ThirdLvl 46H40\SubText Automatic continuity\endx
\ThirdLvl 46H70\SubText Nonassociative topological algebras
 \SeeAlso{\SbjNo 46K70, \SbjNo 46L70}\endx
\ThirdLvl 46H99\SubText \NoneOfAbove\endx
\SecndLvl 46J++\SubText Commutative Banach algebras and commutative
 topological algebras \SeeAlso{\SbjNo 46E25}\endx
\ThirdLvl 46J05\SubText General theory of commutative topological
 algebras\endx
\ThirdLvl 46J10\SubText Banach algebras of continuous functions,
 function algebras \SeeAlso{\SbjNo 46E25}\endx
\ThirdLvl 46J15\SubText Banach algebras of differentiable or analytic
 functions, ${\it H}\sp p$-spaces \SeeAlso{\SbjNo 30D55, \SbjNo 30H05,
 \SbjNo 32A35, \SbjNo 32A37, \SbjNo 32E25, \SbjNo 42B30}\endx
\ThirdLvl 46J20\SubText Ideals, maximal ideals, boundaries\endx
\ThirdLvl 46J25\SubText Representations of commutative topological
 algebras\endx
\ThirdLvl 46J30\SubText Subalgebras\endx
\ThirdLvl 46J40\SubText Structure, classification of commutative
 topological algebras\endx
\ThirdLvl 46J45\SubText Radical Banach algebras\endx
\ThirdLvl 46J99\SubText \NoneOfAbove\endx
\SecndLvl 46K++\SubText Topological (rings and) algebras with an
 involution \SeeAlso{\SbjNo 16W10}\endx
\ThirdLvl 46K05\SubText General theory of topological algebras with
 involution\endx
\ThirdLvl 46K10\SubText Representations of topological algebras with
 involution\endx
\ThirdLvl 46K15\SubText Hilbert algebras\endx
\ThirdLvl 46K50\SubText Nonselfadjoint (sub)algebras in algebras with
 involution\endx
\ThirdLvl 46K70\SubText Nonassociative topological algebras with an
 involution \SeeAlso{\SbjNo 46H70, \SbjNo 46L70}\endx
\ThirdLvl 46K99\SubText \NoneOfAbove\endx
\SecndLvl 46L++\SubText Selfadjoint operator algebras ($C$*-algebras,
 von Neumann ($W$*-) algebras, etc.) \SeeAlso{\SbjNo 22D25}\endx
\ThirdLvl 46L05\SubText General theory of $C$*-algebras\endx
\ThirdLvl 46L10\SubText General theory of von Neumann algebras\endx
\ThirdLvl 46L30\SubText States\endx
\ThirdLvl 46L35\SubText Classifications of $C^*$-algebras,
 factors\endx
\ThirdLvl 46L37\SubText Subfactors and their classification\endx
\ThirdLvl 46L40\SubText Automorphisms\endx
\ThirdLvl 46L45\SubText Decomposition theory for $C^*$-algebras\endx
\ThirdLvl 46L50\SubText Noncommutative measure, integration and
 probability\endx
\ThirdLvl 46L55\SubText Noncommutative dynamical systems
 \SeeAlso{\SbjNo 28Dxx, \SbjNo 54H20, \SbjNo 58Fxx}\endx
\ThirdLvl 46L57\SubText Derivations, dissipations and positive
 semigroups in $C^*$-algebras\endx
\ThirdLvl 46L60\SubText Applications of selfadjoint operator algebras
 to physics \SeeAlso{\SbjNo 46N50, \SbjNo 46N55, \SbjNo 47D45, \SbjNo
 81T05, \SbjNo 82B10, \SbjNo 82C10}\endx
\ThirdLvl 46L70\SubText Nonassociative selfadjoint operator algebras
 \SeeAlso{\SbjNo 46H70, \SbjNo 46K70}\endx
\ThirdLvl 46L80\SubText $K$-theory and operator algebras (including
 cyclic theory) \SeeAlso{\SbjNo 18F25, \SbjNo 19Kxx, \SbjNo 46M20,
 \SbjNo 55Rxx, \SbjNo 58G12}\endx
\ThirdLvl 46L85\SubText Noncommutative topology \SeeAlso{\SbjNo 58B30,
 \SbjNo 58G12}\endx
\ThirdLvl 46L87\SubText Noncommutative differential geometry
 \SeeAlso{\SbjNo 58B30, \SbjNo 58G12}\endx
\ThirdLvl 46L89\SubText Other ``noncommutative'' mathematics based on
 $C^*$-algebra theory \SeeAlso{\SbjNo 58B30, \SbjNo 58G12}\endx
\ThirdLvl 46L99\SubText \NoneOfAbove\endx
\SecndLvl 46M++\SubText Methods of category theory in functional
 analysis \SeeAlso{\SbjNo 18-XX}\endx
\ThirdLvl 46M05\SubText Tensor products \SeeAlso{\SbjNo 46A32, \SbjNo
 46B28, \SbjNo 47A80}\endx
\ThirdLvl 46M07\SubText Ultraproducts \SeeAlso{\SbjNo 46B08, \SbjNo
 46S20}\endx
\ThirdLvl 46M10\SubText Projective and injective objects
 \SeeAlso{\SbjNo 46A22}\endx
\ThirdLvl 46M15\SubText Functors \SeeFor{For $K$-theory and EXT, see
 \SbjNo 19K33, \SbjNo 46L80, \SbjNo 46M20}\endx
\ThirdLvl 46M20\SubText Methods of algebraic topology (cohomology,
 sheaf and bundle theory, etc.) \SeeAlso{\SbjNo 14F05, \SbjNo 18Fxx,
 \SbjNo 19Kxx, \SbjNo 32Cxx, \SbjNo 32Lxx, \SbjNo 46L80, \SbjNo
 55Rxx}\endx
\ThirdLvl 46M35\SubText Abstract interpolation of topological vector
 spaces \SeeAlso{\SbjNo 46B70}\endx
\ThirdLvl 46M40\SubText Inductive and projective limits
 \SeeAlso{\SbjNo 46A13}\endx
\ThirdLvl 46M99\SubText \NoneOfAbove\endx
\SecndLvl 46N++\SubText Miscellaneous applications of functional
 analysis \SeeAlso{\SbjNo 47Nxx}\endx
\ThirdLvl 46N10\SubText Applications in optimization, convex analysis,
 mathematical programming, economics\endx
\ThirdLvl 46N20\SubText Applications to differential and integral
 equations\endx
\ThirdLvl 46N30\SubText Applications in probability theory and
 statistics\endx
\ThirdLvl 46N40\SubText Applications in numerical analysis
 \SeeAlso{\SbjNo 65Jxx}\endx
\ThirdLvl 46N50\SubText Applications in quantum physics\endx
\ThirdLvl 46N55\SubText Applications in statistical physics\endx
\ThirdLvl 46N60\SubText Applications in biology and other
 sciences\endx
\ThirdLvl 46N99\SubText \NoneOfAbove\endx
\SecndLvl 46S++\SubText Other (nonclassical) types of functional
 analysis \SeeAlso{\SbjNo 47Sxx}\endx
\ThirdLvl 46S10\SubText Functional analysis over fields other than
 ${\bf R}$ or ${\bf C}$ or the quaternions; non-Archimedean functional
 analysis \SeeAlso{\SbjNo 12J25, \SbjNo 32P05}\endx
\ThirdLvl 46S20\SubText Nonstandard functional analysis
 \SeeAlso{\SbjNo 03H05}\endx
\ThirdLvl 46S30\SubText Constructive functional analysis
 \SeeAlso{\SbjNo 03F65}\endx
\ThirdLvl 46S40\SubText Fuzzy functional analysis \SeeAlso{\SbjNo
 04A72}\endx
\ThirdLvl 46S50\SubText Functional analysis in probabilistic metric
 linear spaces\endx
\ThirdLvl 46S99\SubText \NoneOfAbove\endx
\MajorSub 47-++\SubText Operator theory\endx
\ThirdLvl 47-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 47-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 47-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 47-03\SubText \Historical\endx
\ThirdLvl 47-04\SubText \ExplicitComputation\endx
\ThirdLvl 47-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 47A++\SubText General theory of linear operators\endx
\ThirdLvl 47A05\SubText General (adjoints, conjugates, products,
 inverses, domains, ranges, etc.)\endx
\ThirdLvl 47A10\SubText Spectrum, resolvent\endx
\ThirdLvl 47A11\SubText Local spectral properties\endx
\ThirdLvl 47A12\SubText Numerical range\endx
\ThirdLvl 47A13\SubText Several-variable spectral theory\endx
\ThirdLvl 47A15\SubText Invariant subspaces\endx
\ThirdLvl 47A20\SubText Dilations, extensions, compressions\endx
\ThirdLvl 47A25\SubText Spectral sets\endx
\ThirdLvl 47A30\SubText Norms (inequalities, more than one norm,
 etc.)\endx
\ThirdLvl 47A35\SubText Ergodic theory \SeeAlso{\SbjNo 28Dxx}\endx
\ThirdLvl 47A40\SubText Scattering theory \SeeAlso{\SbjNo 34L25,
 \SbjNo 35P25, \SbjNo 81Uxx}\endx
\ThirdLvl 47A45\SubText Canonical models for contractions and
 nonselfadjoint operators\endx
\ThirdLvl 47A48\SubText Operator colligations (=\ nodes)\endx
\ThirdLvl 47A50\SubText Equations and inequalities involving linear
 operators, with vector unknowns\endx
\ThirdLvl 47A53\SubText (Semi-) Fredholm operators; index theories
 \SeeAlso{\SbjNo 58B10, \SbjNo 58G12}\endx
\ThirdLvl 47A55\SubText Perturbation theory\endx
\ThirdLvl 47A56\SubText Functions whose values are linear operators
 (operator and matrix pencils, etc.)\endx
\ThirdLvl 47A57\SubText Operator methods in interpolation, moment and
 extension problems \SeeAlso{\SbjNo 30E05, \SbjNo 42A70, \SbjNo
 42A82}\endx
\ThirdLvl 47A58\SubText Operator approximation theory\endx
\ThirdLvl 47A60\SubText Functional calculus\endx
\ThirdLvl 47A62\SubText Equations involving linear operators, with
 operator unknowns\endx
\ThirdLvl 47A63\SubText Operator inequalities, operator means, shorted
 operators, etc.\endx
\ThirdLvl 47A65\SubText Structure theory\endx
\ThirdLvl 47A66\SubText (Non)quasitriangular, (non)quasidiagonal
 operators\endx
\ThirdLvl 47A67\SubText Representation theory\endx
\ThirdLvl 47A68\SubText Factorization theory (including Wiener-Hopf
 and spectral factorizations)\endx
\ThirdLvl 47A70\SubText (Generalized) eigenfunction expansions; rigged
 Hilbert spaces\endx
\ThirdLvl 47A75\SubText Eigenvalue problems \SeeAlso{\SbjNo
 49Rxx}\endx
\ThirdLvl 47A80\SubText Tensor products of operators \SeeAlso{\SbjNo
 46M05}\endx
\ThirdLvl 47A99\SubText \NoneOfAbove\endx
\SecndLvl 47B++\SubText Special classes of linear operators\endx
\ThirdLvl 47B06\SubText Riesz operators; eigenvalue distributions;
 approximation numbers, $s$-numbers, Kolmogorov numbers, entropy
 numbers, etc.\ of operators\endx
\ThirdLvl 47B07\SubText Operators defined by compactness
 properties\endx
\ThirdLvl 47B10\SubText Operators belonging to operator ideals
 (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
 \SeeAlso{\SbjNo 47D50}\endx
\ThirdLvl 47B15\SubText Hermitian and normal operators (spectral
 measures, functional calculus, etc.)\endx
\ThirdLvl 47B20\SubText Subnormal operators, hyponormal operators,
 etc.\endx
\ThirdLvl 47B25\SubText Symmetric and selfadjoint operators
 (unbounded)\endx
\ThirdLvl 47B35\SubText Toeplitz operators, Hankel operators,
 Wiener-Hopf operators \SeeAlso{\SbjNo 45P05, \SbjNo 47G10 for other
 integral operators; see also \SbjNo 32H10, \SbjNo 32M15}\endx
\ThirdLvl 47B37\SubText Operators on special spaces (weighted shifts,
 operators on sequence spaces, etc.)\endx
\ThirdLvl 47B38\SubText Operators on function spaces (including
 composition operators, kernel operators)\endx
\ThirdLvl 47B39\SubText Difference operators \SeeAlso{\SbjNo
 39A70}\endx
\ThirdLvl 47B40\SubText Spectral operators, decomposable operators,
 well-bounded operators, etc.\endx
\ThirdLvl 47B44\SubText Accretive operators, dissipative operators,
 etc.\endx
\ThirdLvl 47B47\SubText Commutators, derivations, elementary
 operators, etc.\endx
\ThirdLvl 47B48\SubText Operators on Banach algebras\endx
\ThirdLvl 47B49\SubText Transformers (= operators on spaces of
 operators)\endx
\ThirdLvl 47B50\SubText Operators on spaces with an indefinite
 metric\endx
\ThirdLvl 47B60\SubText Operators on ordered spaces\endx
\ThirdLvl 47B65\SubText Positive operators and order-bounded
 operators\endx
\ThirdLvl 47B80\SubText Random operators \SeeAlso{\SbjNo 60H25}\endx
\ThirdLvl 47B99\SubText \NoneOfAbove\endx
\SecndLvl 47C++\SubText Individual linear operators as elements of
 algebraic systems\endx
\ThirdLvl 47C05\SubText Operators in algebras\endx
\ThirdLvl 47C10\SubText Operators in $\ast$-algebras\endx
\ThirdLvl 47C15\SubText Operators in $C$*- or von Neumann
 algebras\endx
\ThirdLvl 47C99\SubText \NoneOfAbove\endx
\SecndLvl 47D++\SubText Algebraic systems of linear operators
 \SeeAlso{\SbjNo 46Lxx}\endx
\ThirdLvl 47D03\SubText (Semi)groups of linear operators \SeeFor{For
 nonlinear operators, see \SbjNo 47H20; see also \SbjNo 20M20}\endx
\ThirdLvl 47D06\SubText One-parameter semigroups and linear evolution
 equations\endx
\ThirdLvl 47D07\SubText Markov semigroups \SeeFor{For Markov
 processes, see \SbjNo 60Jxx}\endx
\ThirdLvl 47D09\SubText Operator cosine functions and higher-order
 Cauchy problems\endx
\ThirdLvl 47D15\SubText Linear spaces of operators \SeeAlso{\SbjNo
 46A32, \SbjNo 46B28}\endx
\ThirdLvl 47D20\SubText Convex sets and cones of operators
 \SeeAlso{\SbjNo 90C25, \SbjNo 90C31}\endx
\ThirdLvl 47D25\SubText Operator algebras on Hilbert space \endx
\ThirdLvl 47D27\SubText Dual operator algebras\endx
\ThirdLvl 47D30\SubText Operator algebras on Banach spaces and other
 linear topological spaces\endx
\ThirdLvl 47D35\SubText Dual spaces of operator algebras and
 topological groups\endx
\ThirdLvl 47D40\SubText Algebras of unbounded operators\endx
\ThirdLvl 47D45\SubText Applications of operator algebras to physics
 \SeeAlso{\SbjNo 46L60, \SbjNo 46N50, \SbjNo 46N55, \SbjNo 47N50,
 \SbjNo 47N55}\endx
\ThirdLvl 47D50\SubText Operator ideals\endx
\ThirdLvl 47D99\SubText \NoneOfAbove\endx
\SecndLvl 47E05\SubText Ordinary differential operators
 \SeeAlso{\SbjNo 34Bxx, \SbjNo 34Lxx, \SbjNo 58F19}\endx
\SecndLvl 47F05\SubText Partial differential operators \SeeAlso{\SbjNo
 35Pxx, \SbjNo 58G05}\endx
\SecndLvl 47G++\SubText Integral, integro-differential, and
 pseudodifferential operators \endx
\ThirdLvl 47G10\SubText Integral operators \SeeAlso{\SbjNo 45P05}\endx
\ThirdLvl 47G20\SubText Integro-differential operators \SeeAlso{\SbjNo
 45J05, \SbjNo 45K05}\endx
\ThirdLvl 47G30\SubText Pseudodifferential operators \SeeAlso{\SbjNo
 35Sxx, \SbjNo 58G15}\endx
\ThirdLvl 47G99\SubText \NoneOfAbove\endx
\SecndLvl 47H++\SubText Nonlinear operators \SeeFor{For global and
 geometric aspects, see \SbjNo 58-XX, especially \SbjNo 58Cxx}\endx
\ThirdLvl 47H04\SubText Set-valued operators \SeeAlso{\SbjNo 28B20,
 \SbjNo 54C60, \SbjNo 58C06}\endx
\ThirdLvl 47H05\SubText Monotone operators (with respect to
 duality)\endx
\ThirdLvl 47H06\SubText Accretive operators, dissipative operators,
 etc.\endx
\ThirdLvl 47H07\SubText Monotone and positive operators on ordered
 Banach spaces or other ordered topological vector spaces\endx
\ThirdLvl 47H09\SubText Nonexpansive mappings, and their
 generalizations (ultimately compact mappings, measures of
 noncompactness, $A$-proper mappings, $K$-set contractions, etc.)\endx
\ThirdLvl 47H10\SubText Fixed-point theorems \SeeAlso{\SbjNo 54H25,
 \SbjNo 55M20, \SbjNo 58C30}\endx
\ThirdLvl 47H11\SubText Degree theory \SeeAlso{\SbjNo 55M25, \SbjNo
 58C30}\endx
\ThirdLvl 47H12\SubText Spectral theory of nonlinear operators
 \SeeAlso{\SbjNo 58C40}\endx
\ThirdLvl 47H15\SubText Equations involving nonlinear operators
 \SeeAlso{\SbjNo 58E07 for abstract bifurcation theory}\endx
\ThirdLvl 47H17\SubText Methods for solving equations involving
 nonlinear operators \SeeAlso{\SbjNo 58C15} \SeeFor{For numerical
 analysis, see \SbjNo 65J15}\endx
\ThirdLvl 47H19\SubText Inequalities involving nonlinear operators
 \SeeAlso{\SbjNo 49J27, \SbjNo 49J40, \SbjNo 49K27}\endx
\ThirdLvl 47H20\SubText Semigroups of nonlinear operators and
 nonlinear evolution equations \SeeAlso{\SbjNo 58D07}\endx
\ThirdLvl 47H30\SubText Particular nonlinear operators (superposition,
 Hammerstein, Nemytski\u\i, Uryson, hysteresis operators, etc.)
 \SeeAlso{\SbjNo 45P05}\endx
\ThirdLvl 47H40\SubText Random operators \SeeAlso{\SbjNo 60H25}\endx
\ThirdLvl 47H99\SubText \NoneOfAbove\endx
\SecndLvl 47N++\SubText Miscellaneous applications of operator theory
 \SeeAlso{\SbjNo 46Nxx}\endx
\ThirdLvl 47N10\SubText Applications in optimization, convex analysis,
 mathematical programming, economics\endx
\ThirdLvl 47N20\SubText Applications to differential and integral
 equations\endx
\ThirdLvl 47N30\SubText Applications in probability theory and
 statistics\endx
\ThirdLvl 47N40\SubText Applications in numerical analysis
 \SeeAlso{\SbjNo 65Jxx}\endx
\ThirdLvl 47N50\SubText Applications in quantum physics\endx
\ThirdLvl 47N55\SubText Applications in statistical physics\endx
\ThirdLvl 47N60\SubText Applications in biology and other
 sciences\endx
\ThirdLvl 47N70\SubText Applications in systems theory, circuits,
 etc.\endx
\ThirdLvl 47N99\SubText \NoneOfAbove\endx
\SecndLvl 47S++\SubText Other (nonclassical) types of operator theory
 \SeeAlso{\SbjNo 46Sxx}\endx
\ThirdLvl 47S10\SubText Operator theory over fields other than ${\bf
 R}$, ${\bf C}$ or the quaternions; non-Archimedean operator theory
 \endx
\ThirdLvl 47S20\SubText Nonstandard operator theory \SeeAlso{\SbjNo
 03H05}\endx
\ThirdLvl 47S30\SubText Constructive operator theory \SeeAlso{\SbjNo
 03F65}\endx
\ThirdLvl 47S40\SubText Fuzzy operator theory \SeeAlso{\SbjNo
 04A72}\endx
\ThirdLvl 47S50\SubText Operator theory in probabilistic metric linear
 spaces \endx
\ThirdLvl 47S99\SubText \NoneOfAbove\endx
\MajorSub 49-++\SubText Calculus of variations and optimal control;
 optimization \SeeAlso{\SbjNo 34H05, \SbjNo 65Kxx, \SbjNo 90Cxx,
 \SbjNo 93-XX}\endx
\ThirdLvl 49-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 49-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 49-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 49-03\SubText \Historical\endx
\ThirdLvl 49-04\SubText \ExplicitComputation\endx
\ThirdLvl 49-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 49J++\SubText Existence theory for optimal solutions \endx
\ThirdLvl 49J05\SubText Free problems in one independent variable\endx
\ThirdLvl 49J10\SubText Free problems in two or more independent
 variables\endx
\ThirdLvl 49J15\SubText Optimal control problems involving ordinary
 differential equations\endx
\ThirdLvl 49J20\SubText Optimal control problems involving partial
 differential equations\endx
\ThirdLvl 49J22\SubText Optimal control problems involving integral
 equations\endx
\ThirdLvl 49J24\SubText Optimal control problems involving
 differential inclusions\endx
\ThirdLvl 49J25\SubText Optimal control problems involving equations
 with retarded arguments \SeeAlso{\SbjNo 34K35}\endx
\ThirdLvl 49J27\SubText Problems in abstract spaces [see~\SbjNo
 90C48]\endx
\ThirdLvl 49J30\SubText Optimal solutions belonging to restricted
 classes (Lipschitz controls, bang-bang controls, etc.)\endx
\ThirdLvl 49J35\SubText Minimax problems\endx
\ThirdLvl 49J40\SubText Variational methods including variational
 inequalities\endx
\ThirdLvl 49J45\SubText Problems involving semicontinuity and
 convergence\endx
\ThirdLvl 49J50\SubText Fr\'echet and Gateaux differentiability
 \SeeAlso{\SbjNo 46G05, \SbjNo 58C20}\endx
\ThirdLvl 49J52\SubText Nonsmooth analysis (other weak concepts of
 optimality) \SeeAlso{\SbjNo 58C20, \SbjNo 90C48}\endx
\ThirdLvl 49J55\SubText Problems involving randomness \SeeAlso{\SbjNo
 93E20}\endx
\ThirdLvl 49J99\SubText \NoneOfAbove\endx
\SecndLvl 49K++\SubText Necessary conditions and sufficient conditions
 for optimality\endx
\ThirdLvl 49K05\SubText Free problems in one independent variable\endx
\ThirdLvl 49K10\SubText Free problems in two or more independent
 variables\endx
\ThirdLvl 49K15\SubText Problems involving ordinary differential
 equations\endx
\ThirdLvl 49K20\SubText Problems involving partial differential
 equations\endx
\ThirdLvl 49K22\SubText Problems involving integral equations\endx
\ThirdLvl 49K24\SubText Problems involving differential
 inclusions\endx
\ThirdLvl 49K25\SubText Problems involving equations with retarded
 arguments \SeeAlso{\SbjNo 34K35}\endx
\ThirdLvl 49K27\SubText Problems in abstract spaces [See~\SbjNo 90C48,
 \SbjNo 93C25]\endx
\ThirdLvl 49K30\SubText Optimal solutions belonging to restricted
 classes\endx
\ThirdLvl 49K35\SubText Minimax problems\endx
\ThirdLvl 49K40\SubText Sensitivity of optimal solutions in the
 presence of perturbations\endx
\ThirdLvl 49K45\SubText Problems involving randomness \SeeAlso{\SbjNo
 93E20}\endx
\ThirdLvl 49K99\SubText \NoneOfAbove\endx
\SecndLvl 49L++\SubText Carath\'eodory, Hamilton-Jacobi theories,
 including dynamic programming\endx
\ThirdLvl 49L05\SubText Free problems and problems involving ordinary
 differential equations\endx
\ThirdLvl 49L10\SubText Free problems and problems involving partial
 differential equations\endx
\ThirdLvl 49L15\SubText Problems in abstract spaces or problems
 involving functional relations other than differential equations\endx
\ThirdLvl 49L20\SubText Dynamic programming method\endx
\ThirdLvl 49L25\SubText Viscosity solutions\endx
\ThirdLvl 49L99\SubText \NoneOfAbove\endx
\SecndLvl 49M++\SubText Methods of successive approximations
 \SeeFor{For discrete problems, see \SbjNo 90Cxx; see also \SbjNo
 65Kxx}\endx
\ThirdLvl 49M05\SubText Methods based on necessary conditions\endx
\ThirdLvl 49M07\SubText Gradient methods\endx
\ThirdLvl 49M10\SubText Methods of steepest descent type\endx
\ThirdLvl 49M15\SubText Methods of Newton-Raphson, Galerkin and Ritz
 types\endx
\ThirdLvl 49M20\SubText Methods of relaxation type\endx
\ThirdLvl 49M25\SubText Finite difference methods\endx
\ThirdLvl 49M27\SubText Decomposition methods\endx
\ThirdLvl 49M29\SubText Multiplier methods\endx
\ThirdLvl 49M30\SubText Other methods, not based on necessary
 conditions (penalty function, etc.)\endx
\ThirdLvl 49M35\SubText Methods of linear programming type
 \SeeAlso{\SbjNo 90C05}\endx
\ThirdLvl 49M37\SubText Nonlinear programming \SeeAlso{\SbjNo
 90C30}\endx
\ThirdLvl 49M39\SubText Semi-infinite programming \SeeAlso{\SbjNo
 90C34}\endx
\ThirdLvl 49M40\SubText Methods of quadratic programming type
 \SeeAlso{\SbjNo 90C20}\endx
\ThirdLvl 49M45\SubText Methods of convex programming type
 \SeeAlso{\SbjNo 90C25}\endx
\ThirdLvl 49M49\SubText Geometric programming \SeeAlso{\SbjNo
 90C28}\endx
\ThirdLvl 49M99\SubText \NoneOfAbove\endx
\SecndLvl 49N++\SubText Miscellaneous topics \endx
\ThirdLvl 49N05\SubText Linear optimal control problems
 \SeeAlso{\SbjNo 93C05}\endx
\ThirdLvl 49N10\SubText Linear-quadratic problems\endx
\ThirdLvl 49N15\SubText Duality theory\endx
\ThirdLvl 49N20\SubText Periodic optimization\endx
\ThirdLvl 49N25\SubText Impulsive optimal control problems
 \SeeAlso{\SbjNo 93C57}\endx
\ThirdLvl 49N30\SubText Problems with incomplete information
 \SeeAlso{\SbjNo 93C41}\endx
\ThirdLvl 49N35\SubText Closed-loop controls\endx
\ThirdLvl 49N40\SubText Open-loop controls\endx
\ThirdLvl 49N45\SubText Inverse problems in calculus of
 variations\endx
\ThirdLvl 49N50\SubText Inverse problems in optimal control
 theory\endx
\ThirdLvl 49N55\SubText Noneconomic applications of optimal control
 theory and differential games \SeeAlso{\SbjNo 90D25}\endx
\ThirdLvl 49N60\SubText Regularity of solutions in the calculus of
 variations\endx
\ThirdLvl 49N65\SubText Applications of measurable selections to
 control theory \SeeAlso{\SbjNo 28B20, \SbjNo 26E25}\endx
\ThirdLvl 49N99\SubText \NoneOfAbove\endx
\SecndLvl 49Q++\SubText Manifolds \SeeAlso{\SbjNo 58Fxx}\endx
\ThirdLvl 49Q05\SubText Minimal surfaces \SeeAlso{\SbjNo 53A10, \SbjNo
 58E12}\endx
\ThirdLvl 49Q10\SubText Optimization of the shape other than minimal
 surfaces \SeeAlso{\SbjNo 73K40, \SbjNo 90C90}\endx
\ThirdLvl 49Q12\SubText Sensitivity analysis\endx
\ThirdLvl 49Q15\SubText Geometric measure and integration theory,
 integral and normal currents \SeeAlso{\SbjNo 28A75, \SbjNo 32C30,
 \SbjNo 58A25, \SbjNo 58C35}\endx
\ThirdLvl 49Q20\SubText Variational problems in a geometric
 measure-theoretic setting\endx
\ThirdLvl 49Q25\SubText Surface area \endx
\ThirdLvl 49Q99\SubText \NoneOfAbove\endx
\SecndLvl 49R++\SubText Variational methods \SeeFor{For eigenvalues of
 operators, see~\SbjNo 47A75}\endx
\ThirdLvl 49R05\SubText Variational approach to eigenvalues\endx
\ThirdLvl 49R10\SubText Rayleigh-Ritz methods\endx
\ThirdLvl 49R15\SubText Weinstein and Aronszajn methods, intermediate
 problems\endx
\ThirdLvl 49R20\SubText Linear operators in Hilbert spaces\endx
\ThirdLvl 49R99\SubText \NoneOfAbove\endx
\SecndLvl 49S05\SubText Variational principles of physics\endx
\MajorSub 51-++\SubText Geometry \SeeFor{For algebraic geometry,
 see~\SbjNo 14-XX}\endx
\ThirdLvl 51-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 51-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 51-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 51-03\SubText \Historical\endx
\ThirdLvl 51-04\SubText \ExplicitComputation\endx
\ThirdLvl 51-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 51A++\SubText Linear incidence geometry\endx
\ThirdLvl 51A05\SubText General theory and projective geometries\endx
\ThirdLvl 51A10\SubText Homomorphism, automorphism and dualities\endx
\ThirdLvl 51A15\SubText Structures with parallelism\endx
\ThirdLvl 51A20\SubText Configuration theorems\endx
\ThirdLvl 51A25\SubText Algebraization \SeeAlso{\SbjNo 12Kxx, \SbjNo
 20N05}\endx
\ThirdLvl 51A30\SubText Desarguesian and Pappian geometries\endx
\ThirdLvl 51A35\SubText Non-Desarguesian affine and projective
 planes\endx
\ThirdLvl 51A40\SubText Translation planes and spreads\endx
\ThirdLvl 51A45\SubText Incidence structures imbeddable into
 projective geometries\endx
\ThirdLvl 51A50\SubText Polar geometry, symplectic spaces, orthogonal
 spaces\endx
\ThirdLvl 51A99\SubText \NoneOfAbove\endx
\SecndLvl 51B++\SubText Nonlinear incidence geometry\endx
\ThirdLvl 51B05\SubText General theory\endx
\ThirdLvl 51B10\SubText M\"obius geometries\endx
\ThirdLvl 51B15\SubText Laguerre geometries\endx
\ThirdLvl 51B20\SubText Minkowski geometries\endx
\ThirdLvl 51B25\SubText Lie geometries\endx
\ThirdLvl 51B99\SubText \NoneOfAbove\endx
\SecndLvl 51C05\SubText Ring geometry (Hjelmslev, Barbilian,
 etc.)\endx
\SecndLvl 51D++\SubText Geometric closure systems\endx
\ThirdLvl 51D05\SubText Abstract (Maeda) geometries\endx
\ThirdLvl 51D10\SubText Abstract geometries with exchange axiom\endx
\ThirdLvl 51D15\SubText Abstract geometries with parallelism\endx
\ThirdLvl 51D20\SubText Combinatorial geometries \SeeAlso{\SbjNo
 05B25, \SbjNo 05B35}\endx
\ThirdLvl 51D25\SubText Lattices of subspaces \SeeAlso{\SbjNo
 05B35}\endx
\ThirdLvl 51D30\SubText Continuous geometries and related topics
 \SeeAlso{\SbjNo 06Cxx}\endx
\ThirdLvl 51D99\SubText \NoneOfAbove\endx
\SecndLvl 51E++\SubText Finite geometry and special incidence
 structures\endx
\ThirdLvl 51E05\SubText General block designs \SeeAlso{\SbjNo
 05B05}\endx
\ThirdLvl 51E10\SubText Steiner systems\endx
\ThirdLvl 51E12\SubText Generalized quadrangles, generalized
 polygons\endx
\ThirdLvl 51E14\SubText Finite partial geometries (general), nets,
 partial spreads\endx
\ThirdLvl 51E15\SubText Affine and projective planes\endx
\ThirdLvl 51E20\SubText Combinatorial structures in finite projective
 spaces \SeeAlso{\SbjNo 05Bxx}\endx
\ThirdLvl 51E21\SubText Blocking sets, ovals, $k$-arcs\endx
\ThirdLvl 51E22\SubText Linear codes and caps in Galois spaces
 \SeeAlso{\SbjNo 94B05}\endx
\ThirdLvl 51E23\SubText Spreads and packing problems\endx
\ThirdLvl 51E24\SubText Buildings and the geometry of diagrams\endx
\ThirdLvl 51E25\SubText Other finite nonlinear geometries\endx
\ThirdLvl 51E26\SubText Other finite linear geometries\endx
\ThirdLvl 51E30\SubText Other finite incidence structures
 \SeeAlso{\SbjNo 05B30}\endx
\ThirdLvl 51E99\SubText \NoneOfAbove\endx
\SecndLvl 51F++\SubText Metric geometry\endx
\ThirdLvl 51F05\SubText Absolute planes\endx
\ThirdLvl 51F10\SubText Absolute spaces\endx
\ThirdLvl 51F15\SubText Reflection groups, reflection geometries
 \SeeAlso{\SbjNo 20H10, \SbjNo 20H15; for Coxeter groups, see \SbjNo
 20F55}\endx
\ThirdLvl 51F20\SubText Congruence and orthogonality \SeeAlso{\SbjNo
 20H05}\endx
\ThirdLvl 51F25\SubText Orthogonal and unitary groups \SeeAlso{\SbjNo
 20H05}\endx
\ThirdLvl 51F99\SubText \NoneOfAbove\endx
\SecndLvl 51G05\SubText Ordered geometries (ordered incidence
 structures, etc.)\endx
\SecndLvl 51H++\SubText Topological geometry\endx
\ThirdLvl 51H05\SubText General theory\endx
\ThirdLvl 51H10\SubText Topological linear incidence structures\endx
\ThirdLvl 51H15\SubText Topological nonlinear incidence
 structures\endx
\ThirdLvl 51H20\SubText Topological geometries on manifolds
 \SeeAlso{\SbjNo 57-XX}\endx
\ThirdLvl 51H25\SubText Geometries with differentiable structure
 \SeeAlso{\SbjNo 53Cxx, \SbjNo 53C70}\endx
\ThirdLvl 51H30\SubText Geometries with algebraic manifold structure
 \SeeAlso{\SbjNo 14-XX}\endx
\ThirdLvl 51H99\SubText \NoneOfAbove\endx
\SecndLvl 51J++\SubText Incidence groups\endx
\ThirdLvl 51J05\SubText General theory\endx
\ThirdLvl 51J10\SubText Projective incidence groups\endx
\ThirdLvl 51J15\SubText Kinematic spaces\endx
\ThirdLvl 51J20\SubText Representation by near-fields and
 near-algebras \SeeAlso{\SbjNo 12K05, \SbjNo 16Y30}\endx
\ThirdLvl 51J99\SubText \NoneOfAbove\endx
\SecndLvl 51K++\SubText Distance geometry\endx
\ThirdLvl 51K05\SubText General theory\endx
\ThirdLvl 51K10\SubText Synthetic differential geometry\endx
\ThirdLvl 51K99\SubText \NoneOfAbove\endx
\SecndLvl 51L++\SubText Geometric order structures \SeeAlso{\SbjNo
 53C75}\endx
\ThirdLvl 51L05\SubText Geometry of orders of nondifferentiable
 curves\endx
\ThirdLvl 51L10\SubText Directly differentiable curves\endx
\ThirdLvl 51L15\SubText $n$-vertex theorems via direct methods\endx
\ThirdLvl 51L20\SubText Geometry of orders of surfaces\endx
\ThirdLvl 51L99\SubText \NoneOfAbove\endx
\SecndLvl 51M++\SubText Real and complex geometry\endx
\ThirdLvl 51M04\SubText Elementary problems in Euclidean
 geometries\endx
\ThirdLvl 51M05\SubText Euclidean geometries (general) and
 generalizations\endx
\ThirdLvl 51M09\SubText Elementary problems in hyperbolic and elliptic
 geometries\endx
\ThirdLvl 51M10\SubText Hyperbolic and elliptic geometries (general)
 and generalizations\endx
\ThirdLvl 51M15\SubText Geometric constructions\endx
\ThirdLvl 51M16\SubText Inequalities and extremum problems \SeeFor{For
 convex problems see \SbjNo 52A40}\endx
\ThirdLvl 51M20\SubText Polyhedra and polytopes; regular figures,
 division of spaces \SeeAlso{\SbjNo 51F15}\endx
\ThirdLvl 51M25\SubText Length, area and volume \SeeAlso{\SbjNo
 26B15}\endx
\ThirdLvl 51M30\SubText Line geometries and their generalizations
 \SeeAlso{\SbjNo 53A25}\endx
\ThirdLvl 51M35\SubText Synthetic treatment of fundamental manifolds
 in projective geometries (Grassmannians, Veronesians and their
 generalizations) \SeeAlso{\SbjNo 14M15}\endx
\ThirdLvl 51M99\SubText \NoneOfAbove\endx
\SecndLvl 51N++\SubText Analytic and descriptive geometry \endx
\ThirdLvl 51N05\SubText Descriptive geometry \SeeAlso{\SbjNo 65D17,
 \SbjNo 68U07}\endx
\ThirdLvl 51N10\SubText Affine analytic geometry\endx
\ThirdLvl 51N15\SubText Projective analytic geometry\endx
\ThirdLvl 51N20\SubText Euclidean analytic geometry\endx
\ThirdLvl 51N25\SubText Analytic geometry with other transformation
 groups\endx
\ThirdLvl 51N30\SubText Geometry of classical groups \SeeAlso{\SbjNo
 20Gxx, \SbjNo 14L35}\endx
\ThirdLvl 51N35\SubText Questions of classical algebraic geometry
 \SeeAlso{\SbjNo 14Nxx}\endx
\ThirdLvl 51N99\SubText \NoneOfAbove\endx
\SecndLvl 51P05\SubText Geometry and physics (should also be assigned
 at least one other classification number from Sections 70--86)\endx
\MajorSub 52-++\SubText Convex and discrete geometry\endx
\ThirdLvl 52-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 52-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 52-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 52-03\SubText \Historical\endx
\ThirdLvl 52-04\SubText \ExplicitComputation\endx
\ThirdLvl 52-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 52A++\SubText General convexity\endx
\ThirdLvl 52A01\SubText Axiomatic and generalized convexity\endx
\ThirdLvl 52A05\SubText Convex sets without dimension
 restrictions\endx
\ThirdLvl 52A07\SubText Convex sets in topological vector spaces
 \SeeAlso{\SbjNo 46A55}\endx
\ThirdLvl 52A10\SubText Convex sets in $2$ dimensions (including
 convex curves) \SeeAlso{\SbjNo 53A04}\endx
\ThirdLvl 52A15\SubText Convex sets in $3$ dimensions (including
 convex surfaces) \SeeAlso{\SbjNo 53A05, \SbjNo 53C45}\endx
\ThirdLvl 52A20\SubText Convex sets in $n$ dimensions (including
 convex hypersurfaces) \SeeAlso{\SbjNo 53A07, \SbjNo 53C45}\endx
\ThirdLvl 52A21\SubText Finite-dimensional Banach spaces (including
 special norms, zonoids, etc.) \SeeAlso{\SbjNo 46Bxx}\endx
\ThirdLvl 52A22\SubText Random convex sets and integral geometry
 \SeeAlso{\SbjNo 53C65, \SbjNo 60D05}\endx
\ThirdLvl 52A27\SubText Approximation by convex sets\endx
\ThirdLvl 52A30\SubText Variants of convex sets (star-shaped, ($m,
 n$)-convex, etc.)\endx
\ThirdLvl 52A35\SubText Helly-type theorems\endx
\ThirdLvl 52A37\SubText Other problems of combinatorial convexity\endx
\ThirdLvl 52A38\SubText Length, area, volume \SeeAlso{\SbjNo 26B15,
 \SbjNo 28A75, \SbjNo 49Q20}\endx
\ThirdLvl 52A39\SubText Mixed volumes and related topics\endx
\ThirdLvl 52A40\SubText Inequalities and extremum problems\endx
\ThirdLvl 52A41\SubText Convex functions and convex programs
 \SeeAlso{\SbjNo 26B25, \SbjNo 90C25}\endx
\ThirdLvl 52A55\SubText Spherical and hyperbolic convexity\endx
\ThirdLvl 52A99\SubText \NoneOfAbove\endx
\SecndLvl 52B++\SubText Polytopes and polyhedra\endx
\ThirdLvl 52B05\SubText Combinatorial properties (number of faces,
 shortest paths, etc.) \SeeAlso{\SbjNo 05Cxx}\endx
\ThirdLvl 52B10\SubText Three-dimensional polytopes\endx
\ThirdLvl 52B11\SubText $n$-dimensional polytopes\endx
\ThirdLvl 52B12\SubText Special polytopes (linear programming,
 centrally symmetric, etc.)\endx
\ThirdLvl 52B15\SubText Symmetry properties of polytopes\endx
\ThirdLvl 52B20\SubText Lattice polytopes (including relations with
 commutative algebra and algebraic geometry) \SeeAlso{\SbjNo 06A08,
 \SbjNo 13F20, \SbjNo 13Hxx}\endx
\ThirdLvl 52B30\SubText Arrangements of hyperplanes\endx
\ThirdLvl 52B35\SubText Gale and other diagrams\endx
\ThirdLvl 52B40\SubText Matroids (realizations in the context of
 convex polytopes, convexity in combinatorial structures, etc.)
 \SeeAlso{\SbjNo 05B35}\endx
\ThirdLvl 52B45\SubText Dissections and valuations (Hilbert's third
 problem, etc.)\endx
\ThirdLvl 52B55\SubText Computational aspects related to convexity
 \SeeFor{For computational geometry and algorithms, see \SbjNo 68Q20,
 \SbjNo 68Q25, \SbjNo 68U05; for numerical algorithms, see \SbjNo
 65Yxx}\endx
\ThirdLvl 52B60\SubText Isoperimetric problems for polytopes\endx
\ThirdLvl 52B70\SubText Polyhedral manifolds\endx
\ThirdLvl 52B99\SubText \NoneOfAbove\endx
\SecndLvl 52C++\SubText Discrete geometry\endx
\ThirdLvl 52C05\SubText Lattices and convex bodies in $2$ dimensions
 \SeeAlso{\SbjNo 11H06, \SbjNo 11H31, \SbjNo 11P21}\endx
\ThirdLvl 52C07\SubText Lattices and convex bodies in $n$ dimensions
 \SeeAlso{\SbjNo 11H06, \SbjNo 11H31, \SbjNo 11P21}\endx
\ThirdLvl 52C10\SubText Erd\H os problems and related topics of
 discrete geometry \SeeAlso{\SbjNo 11Hxx}\endx
\ThirdLvl 52C15\SubText Packing and covering in $2$ dimensions
 \SeeAlso{\SbjNo 05B40, \SbjNo 11H31}\endx
\ThirdLvl 52C17\SubText Packing and covering in $n$ dimensions
 \SeeAlso{\SbjNo 05B40, \SbjNo 11H31}\endx
\ThirdLvl 52C20\SubText Tilings in $2$ dimensions \SeeAlso{\SbjNo
 05B45, \SbjNo 51M20}\endx
\ThirdLvl 52C22\SubText Tilings in $n$ dimensions \SeeAlso{\SbjNo
 05B45, \SbjNo 51M20} \endx
\ThirdLvl 52C25\SubText Rigidity and flexibility of structures
 \SeeAlso{\SbjNo 70B15}\endx
\ThirdLvl 52C99\SubText \NoneOfAbove\endx
\MajorSub 53-++\SubText Differential geometry \SeeFor{For differential
 topology, see~\SbjNo 57Rxx. For foundational questions of
 differentiable manifolds, see~\SbjNo 58Axx}\endx
\ThirdLvl 53-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 53-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 53-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 53-03\SubText \Historical\endx
\ThirdLvl 53-04\SubText \ExplicitComputation\endx
\ThirdLvl 53-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 53A++\SubText Classical differential geometry\endx
\ThirdLvl 53A04\SubText Curves in Euclidean space\endx
\ThirdLvl 53A05\SubText Surfaces in Euclidean space\endx
\ThirdLvl 53A07\SubText Higher-dimension and -codimension surfaces in
 Euclidean $n$-space\endx
\ThirdLvl 53A10\SubText Minimal surfaces, surfaces with prescribed
 mean curvature \SeeAlso{\SbjNo 49Q05, \SbjNo 49Q10, \SbjNo
 53C42}\endx
\ThirdLvl 53A15\SubText Affine differential geometry\endx
\ThirdLvl 53A17\SubText Kinematics\endx
\ThirdLvl 53A20\SubText Projective differential geometry\endx
\ThirdLvl 53A25\SubText Differential line geometry\endx
\ThirdLvl 53A30\SubText Conformal differential geometry\endx
\ThirdLvl 53A35\SubText Non-Euclidean differential geometry\endx
\ThirdLvl 53A40\SubText Other special differential geometries\endx
\ThirdLvl 53A45\SubText Vector and tensor analysis\endx
\ThirdLvl 53A50\SubText Spinor analysis\endx
\ThirdLvl 53A55\SubText Differential invariants (local theory),
 geometric objects\endx
\ThirdLvl 53A60\SubText Geometry of webs \SeeAlso{\SbjNo 14C21, \SbjNo
 20N05}\endx
\ThirdLvl 53A99\SubText \NoneOfAbove\endx
\SecndLvl 53B++\SubText Local differential geometry\endx
\ThirdLvl 53B05\SubText Linear and affine connections\endx
\ThirdLvl 53B10\SubText Projective connections\endx
\ThirdLvl 53B15\SubText Other connections\endx
\ThirdLvl 53B20\SubText Local Riemannian geometry\endx
\ThirdLvl 53B21\SubText Methods of Riemannian geometry\endx
\ThirdLvl 53B25\SubText Local submanifolds \SeeAlso{\SbjNo 53C40}\endx
\ThirdLvl 53B30\SubText Lorentz metrics, indefinite metrics\endx
\ThirdLvl 53B35\SubText Hermitian and K\"ahlerian structures
 \SeeAlso{\SbjNo 32Cxx}\endx
\ThirdLvl 53B40\SubText Finsler spaces and generalizations (areal
 metrics)\endx
\ThirdLvl 53B50\SubText Applications to physics\endx
\ThirdLvl 53B99\SubText \NoneOfAbove\endx
\SecndLvl 53C++\SubText Global differential geometry \SeeAlso{\SbjNo
 51H25, \SbjNo 58-XX; for related bundle theory, see \SbjNo 55Rxx,
 \SbjNo 57Rxx}\endx
\ThirdLvl 53C05\SubText Connections, general theory\endx
\ThirdLvl 53C07\SubText Special connections and metrics on vector
 bundles (Hermite-Einstein-Yang-Mills) \SeeAlso{\SbjNo 32L07}\endx
\ThirdLvl 53C10\SubText $G$-structures\endx
\ThirdLvl 53C12\SubText Foliations (differential geometric aspects)
 \SeeAlso{\SbjNo 57R30, \SbjNo 57R32}\endx
\ThirdLvl 53C15\SubText General geometric structures on manifolds
 (almost complex, contact, symplectic, almost product structures,
 etc.)\endx
\ThirdLvl 53C20\SubText Global Riemannian geometry, including pinching
 \SeeAlso{\SbjNo 31C12, \SbjNo 58B20}\endx
\ThirdLvl 53C21\SubText Methods of Riemannian geometry, including PDE
 methods; curvature restrictions \SeeAlso{\SbjNo 58G30}\endx
\ThirdLvl 53C22\SubText Geodesics \SeeAlso{\SbjNo 58E10}\endx
\ThirdLvl 53C23\SubText Global topological methods (\`a la
 Gromov)\endx
\ThirdLvl 53C25\SubText Special Riemannian manifolds (Einstein,
 Sasakian, etc.)\endx
\ThirdLvl 53C30\SubText Homogeneous manifolds \SeeAlso{\SbjNo 14M15,
 \SbjNo 14M17, \SbjNo 32M10, \SbjNo 57T15}\endx
\ThirdLvl 53C35\SubText Symmetric spaces \SeeAlso{\SbjNo 32M15, \SbjNo
 57T15}\endx
\ThirdLvl 53C40\SubText Global submanifolds \SeeAlso{\SbjNo
 53B25}\endx
\ThirdLvl 53C42\SubText Immersions (minimal, prescribed curvature,
 tight, etc.) \SeeAlso{\SbjNo 49Q05, \SbjNo 49Q10, \SbjNo 53A10,
 \SbjNo 57R40, \SbjNo 57R42}\endx
\ThirdLvl 53C45\SubText Global surface theory (convex surfaces \`a la
 A. D. Aleksandrov)\endx
\ThirdLvl 53C50\SubText Lorentz manifolds, manifolds with indefinite
 metrics\endx
\ThirdLvl 53C55\SubText Hermitian and K\"ahlerian manifolds
 \SeeAlso{\SbjNo 32Cxx}\endx
\ThirdLvl 53C56\SubText Other complex differential geometry
 \SeeAlso{\SbjNo 32Cxx}\endx
\ThirdLvl 53C60\SubText Finsler spaces and generalizations (areal
 metrics) \SeeAlso{\SbjNo 58B20}\endx
\ThirdLvl 53C65\SubText Integral geometry \SeeAlso{\SbjNo 52A22,
 \SbjNo 60D05}; differential forms, currents, etc. \SeeMainly{\SbjNo
 58Axx}\endx
\ThirdLvl 53C70\SubText Direct methods ($G$-spaces of Busemann,
 etc.)\endx
\ThirdLvl 53C75\SubText Geometric orders, order geometry
 \SeeAlso{\SbjNo 51Lxx}\endx
\ThirdLvl 53C80\SubText Applications to physics\endx
\ThirdLvl 53C99\SubText \NoneOfAbove\endx
\MajorSub 54-++\SubText General topology \SeeFor{For the topology of
 manifolds of all dimensions, see~\SbjNo 57Nxx}\endx
\ThirdLvl 54-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 54-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 54-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 54-03\SubText \Historical\endx
\ThirdLvl 54-04\SubText \ExplicitComputation\endx
\ThirdLvl 54-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 54A++\SubText Generalities\endx
\ThirdLvl 54A05\SubText Topological spaces and generalizations
 (closure spaces, etc.)\endx
\ThirdLvl 54A10\SubText Several topologies on one set (change of
 topology, comparison of topologies, lattices of topologies)\endx
\ThirdLvl 54A15\SubText Syntopogeneous structures\endx
\ThirdLvl 54A20\SubText Convergence in general topology (sequences,
 filters, limits, convergence spaces, etc.)\endx
\ThirdLvl 54A25\SubText Cardinality properties (cardinal functions and
 inequalities, discrete subsets) \SeeAlso{\SbjNo 03Exx, \SbjNo 04A30}
 \SeeFor{For ultrafilters, see~\SbjNo 54D80}\endx
\ThirdLvl 54A35\SubText Consistency and independence results
 \SeeAlso{\SbjNo 03E35}\endx
\ThirdLvl 54A40\SubText Fuzzy topology \SeeAlso{\SbjNo 04A72}\endx
\ThirdLvl 54A99\SubText \NoneOfAbove\endx
\SecndLvl 54B++\SubText Basic constructions\endx
\ThirdLvl 54B05\SubText Subspaces\endx
\ThirdLvl 54B10\SubText Product spaces\endx
\ThirdLvl 54B15\SubText Quotient spaces, decompositions\endx
\ThirdLvl 54B17\SubText Adjunction spaces and similar
 constructions\endx
\ThirdLvl 54B20\SubText Hyperspaces\endx
\ThirdLvl 54B30\SubText Categorical methods \SeeAlso{\SbjNo
 18B30}\endx
\ThirdLvl 54B35\SubText Spectra\endx
\ThirdLvl 54B40\SubText Presheaves and sheaves \SeeAlso{\SbjNo
 18F20}\endx
\ThirdLvl 54B99\SubText \NoneOfAbove\endx
\SecndLvl 54C++\SubText Maps and general types of spaces defined by
 maps\endx
\ThirdLvl 54C05\SubText Continuous maps\endx
\ThirdLvl 54C08\SubText Weak and generalized continuity\endx
\ThirdLvl 54C10\SubText Special maps on topological spaces (open,
 closed, perfect, etc.)\endx
\ThirdLvl 54C15\SubText Retraction\endx
\ThirdLvl 54C20\SubText Extension of maps\endx
\ThirdLvl 54C25\SubText Embedding\endx
\ThirdLvl 54C30\SubText Real-valued functions \SeeAlso{\SbjNo
 26-XX}\endx
\ThirdLvl 54C35\SubText Function spaces \SeeAlso{\SbjNo 46Exx, \SbjNo
 58D15}\endx
\ThirdLvl 54C40\SubText Algebraic properties of function spaces
 \SeeAlso{\SbjNo 46J10}\endx
\ThirdLvl 54C45\SubText $C$- and $C$*-embedding\endx
\ThirdLvl 54C50\SubText Special sets defined by functions
 \SeeAlso{\SbjNo 26A21}\endx
\ThirdLvl 54C55\SubText Absolute neighborhood extensor, absolute
 extensor, absolute neighborhood retract (ANR), absolute retract
 spaces (general properties) \SeeAlso{\SbjNo 55M15}\endx
\ThirdLvl 54C56\SubText Shape theory \SeeAlso{\SbjNo 55P55, \SbjNo
 57N25}\endx
\ThirdLvl 54C60\SubText Set-valued maps \SeeAlso{\SbjNo 26E25, \SbjNo
 28B20, \SbjNo 47H04, \SbjNo 58C06}\endx
\ThirdLvl 54C65\SubText Selections \SeeAlso{\SbjNo 28B20}\endx
\ThirdLvl 54C70\SubText Entropy\endx
\ThirdLvl 54C99\SubText \NoneOfAbove\endx
\SecndLvl 54D++\SubText Fairly general properties\endx
\ThirdLvl 54D05\SubText Connected and locally connected spaces
 (general aspects)\endx
\ThirdLvl 54D10\SubText Lower separation axioms, ($T\sb 0$--$T\sb 3$,
 etc.)\endx
\ThirdLvl 54D15\SubText Higher separation axioms (completely regular,
 normal, perfectly or collectionwise normal, etc.)\endx
\ThirdLvl 54D20\SubText Noncompact covering properties (paracompact,
 Lindel\"of, etc.)\endx
\ThirdLvl 54D25\SubText ``$P$-minimal'' and ``$P$-closed'' spaces\endx
\ThirdLvl 54D30\SubText Compactness\endx
\ThirdLvl 54D35\SubText Extensions of spaces (compactifications,
 supercompactifications, completions, etc.)\endx
\ThirdLvl 54D40\SubText Remainders\endx
\ThirdLvl 54D45\SubText Local compactness, $\sigma$-compactness\endx
\ThirdLvl 54D50\SubText $k$-spaces\endx
\ThirdLvl 54D55\SubText Sequential spaces\endx
\ThirdLvl 54D60\SubText Realcompactness and realcompactification\endx
\ThirdLvl 54D65\SubText Separability\endx
\ThirdLvl 54D70\SubText Base properties\endx
\ThirdLvl 54D80\SubText Special constructions of spaces (spaces of
 ultrafilters, etc.)\endx
\ThirdLvl 54D99\SubText \NoneOfAbove\endx
\SecndLvl 54E++\SubText Spaces with richer structures\endx
\ThirdLvl 54E05\SubText Proximity structures and generalizations\endx
\ThirdLvl 54E15\SubText Uniform structures and generalizations\endx
\ThirdLvl 54E17\SubText Nearness spaces\endx
\ThirdLvl 54E18\SubText $p$-spaces, $M$-spaces, $\sigma$-spaces,
 etc.\endx
\ThirdLvl 54E20\SubText Stratifiable spaces, cosmic spaces, etc.\endx
\ThirdLvl 54E25\SubText Semimetric spaces\endx
\ThirdLvl 54E30\SubText Moore spaces\endx
\ThirdLvl 54E35\SubText Metric spaces, metrizability\endx
\ThirdLvl 54E40\SubText Special maps on metric spaces\endx
\ThirdLvl 54E45\SubText Compact (locally compact) metric spaces\endx
\ThirdLvl 54E50\SubText Complete metric spaces\endx
\ThirdLvl 54E52\SubText Baire category, Baire spaces\endx
\ThirdLvl 54E55\SubText Bitopologies\endx
\ThirdLvl 54E70\SubText Probabilistic metric spaces\endx
\ThirdLvl 54E99\SubText \NoneOfAbove\endx
\SecndLvl 54F++\SubText Special properties\endx
\ThirdLvl 54F05\SubText Ordered topological spaces, partially ordered
 spaces \SeeAlso{\SbjNo 06B30, \SbjNo 06F30}\endx
\ThirdLvl 54F15\SubText Continua and generalizations\endx
\ThirdLvl 54F35\SubText Higher-dimensional local connectedness
 \SeeAlso{\SbjNo 55Mxx, \SbjNo 55Nxx}\endx
\ThirdLvl 54F45\SubText Dimension theory \SeeAlso{\SbjNo 55M10}\endx
\ThirdLvl 54F50\SubText Spaces of dimension $\leq 1$; curves,
 dendrites \SeeAlso{\SbjNo 26A03}\endx
\ThirdLvl 54F55\SubText Unicoherence, multicoherence\endx
\ThirdLvl 54F65\SubText Topological characterizations of particular
 spaces\endx
\ThirdLvl 54F99\SubText \NoneOfAbove\endx
\SecndLvl 54G++\SubText Peculiar spaces\endx
\ThirdLvl 54G05\SubText Extremally disconnected spaces, $F$-spaces,
 etc.\endx
\ThirdLvl 54G10\SubText $P$-spaces\endx
\ThirdLvl 54G12\SubText Scattered spaces\endx
\ThirdLvl 54G15\SubText Pathological spaces\endx
\ThirdLvl 54G20\SubText Counterexamples\endx
\ThirdLvl 54G99\SubText \NoneOfAbove\endx
\SecndLvl 54H++\SubText Connections with other structures,
 applications\endx
\ThirdLvl 54H05\SubText Descriptive set theory (topological aspects of
 Borel, analytic, projective, etc.\ sets) \SeeAlso{\SbjNo 03E15,
 \SbjNo 04A15, \SbjNo 26A21, \SbjNo 28A05}\endx
\ThirdLvl 54H10\SubText Topological representations of algebraic
 systems \SeeAlso{\SbjNo 22-XX}\endx
\ThirdLvl 54H11\SubText Topological groups \SeeAlso{\SbjNo 22A05}\endx
\ThirdLvl 54H12\SubText Topological lattices, etc. \SeeAlso{\SbjNo
 06B30, \SbjNo 06F30}\endx
\ThirdLvl 54H13\SubText Topological fields, rings, etc.
 \SeeAlso{\SbjNo 12Jxx} \SeeFor{For algebraic aspects, see \SbjNo
 13Jxx, \SbjNo 16W80}\endx
\ThirdLvl 54H15\SubText Transformation groups and semigroups
 \SeeAlso{\SbjNo 20M20, \SbjNo 22-XX, \SbjNo 57Sxx}\endx
\ThirdLvl 54H20\SubText Topological dynamics \SeeAlso{\SbjNo 28Dxx,
 \SbjNo 34C35, \SbjNo 58Fxx}\endx
\ThirdLvl 54H25\SubText Fixed-point and coincidence theorems
 \SeeAlso{\SbjNo 47H10, \SbjNo 55M20}\endx
\ThirdLvl 54H99\SubText \NoneOfAbove\endx
\SecndLvl 54J05\SubText Nonstandard topology \SeeAlso{\SbjNo
 03H05}\endx
\MajorSub 55-++\SubText Algebraic topology\endx
\ThirdLvl 55-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 55-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 55-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 55-03\SubText \Historical\endx
\ThirdLvl 55-04\SubText \ExplicitComputation\endx
\ThirdLvl 55-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 55M++\SubText Classical topics \SeeFor{For the topology of
 Euclidean spaces and manifolds, see \CMPonly{\SbjNo
 57Nxx}\FullScheme{\SbjNo 57Nxx}}\endx
\ThirdLvl 55M05\SubText Duality\endx
\ThirdLvl 55M10\SubText Dimension theory \SeeAlso{\SbjNo 54F45}\endx
\ThirdLvl 55M15\SubText Absolute neighborhood retracts \SeeAlso{\SbjNo
 54C55}\endx
\ThirdLvl 55M20\SubText Fixed points and coincidences \SeeAlso{\SbjNo
 54H25}\endx
\ThirdLvl 55M25\SubText Degree, winding number\endx
\ThirdLvl 55M30\SubText Ljusternik-Schnirelman
 (Lyusternik-Shnirel\cprime man) category of a space\endx
\ThirdLvl 55M35\SubText Finite groups of transformations (including
 Smith theory) \SeeAlso{\SbjNo 57S17}\endx
\ThirdLvl 55M99\SubText \NoneOfAbove\endx
\SecndLvl 55N++\SubText Homology and cohomology theories
 \SeeAlso{\SbjNo 57Txx}\endx
\ThirdLvl 55N05\SubText \v Cech types\endx
\ThirdLvl 55N07\SubText Steenrod-Sitnikov homologies\endx
\ThirdLvl 55N10\SubText Singular theory\endx
\ThirdLvl 55N15\SubText $K$-theory \SeeAlso{\SbjNo 19Lxx} \SeeFor{For
 algebraic $K$-theory, see \SbjNo 18F25, \SbjNo 19-XX} \endx
\ThirdLvl 55N20\SubText Generalized (extraordinary) homology and
 cohomology theories\endx
\ThirdLvl 55N22\SubText Bordism and cobordism theories, formal group
 laws \SeeAlso{\SbjNo 14L05, \SbjNo 19L41, \SbjNo 57R75, \SbjNo 57R77,
 \SbjNo 57R85, \SbjNo 57R90}\endx
\ThirdLvl 55N25\SubText Homology with local coefficients, equivariant
 cohomology\endx
\ThirdLvl 55N30\SubText Sheaf cohomology \SeeAlso{\SbjNo 18F20, \SbjNo
 32C35, \SbjNo 32L10}\endx
\ThirdLvl 55N33\SubText Intersection homology and cohomology\endx
\ThirdLvl 55N35\SubText Other homology theories\endx
\ThirdLvl 55N40\SubText Axioms for homology theory and uniqueness
 theorems\endx
\ThirdLvl 55N45\SubText Products and intersections\endx
\ThirdLvl 55N91\SubText Equivariant homology and cohomology
 \SeeAlso{\SbjNo 19L47}\endx
\ThirdLvl 55N99\SubText \NoneOfAbove\endx
\SecndLvl 55P++\SubText Homotopy theory \SeeFor{For simple homotopy
 type, see \SbjNo 57Q10}\endx
\ThirdLvl 55P05\SubText Homotopy extension properties,
 cofibrations\endx
\ThirdLvl 55P10\SubText Homotopy equivalences\endx
\ThirdLvl 55P15\SubText Classification of homotopy type\endx
\ThirdLvl 55P20\SubText Eilenberg-Mac~Lane spaces\endx
\ThirdLvl 55P25\SubText Spanier-Whitehead duality\endx
\ThirdLvl 55P30\SubText Eckmann-Hilton duality\endx
\ThirdLvl 55P35\SubText Loop spaces\endx
\ThirdLvl 55P40\SubText Suspensions\endx
\ThirdLvl 55P42\SubText Stable homotopy theory, spectra\endx
\ThirdLvl 55P45\SubText ${\it H}$-spaces and duals\endx
\ThirdLvl 55P47\SubText Infinite loop spaces\endx
\ThirdLvl 55P50\SubText Category and cocategory, etc.\endx
\ThirdLvl 55P55\SubText Shape theory \SeeAlso{\SbjNo 54C56, \SbjNo
 55Q07}\endx
\ThirdLvl 55P60\SubText Localization and completion\endx
\ThirdLvl 55P62\SubText Rational homotopy theory\endx
\ThirdLvl 55P65\SubText Homotopy functors\endx
\ThirdLvl 55P91\SubText Equivariant homotopy theory \SeeAlso{\SbjNo
 19L47}\endx
\ThirdLvl 55P99\SubText \NoneOfAbove\endx
\SecndLvl 55Q++\SubText Homotopy groups\endx
\ThirdLvl 55Q05\SubText Homotopy groups, general; sets of homotopy
 classes\endx
\ThirdLvl 55Q07\SubText Shape groups\endx
\ThirdLvl 55Q10\SubText Stable homotopy groups\endx
\ThirdLvl 55Q15\SubText Whitehead products and generalizations\endx
\ThirdLvl 55Q20\SubText Homotopy groups of wedges, joins, and simple
 spaces\endx
\ThirdLvl 55Q25\SubText Hopf invariants\endx
\ThirdLvl 55Q30\SubText Homotopy groups of triads, $n$-ads\endx
\ThirdLvl 55Q35\SubText Operations in homotopy groups\endx
\ThirdLvl 55Q40\SubText Homotopy groups of spheres\endx
\ThirdLvl 55Q45\SubText Stable homotopy of spheres\endx
\ThirdLvl 55Q50\SubText $J$-morphism \SeeAlso{\SbjNo 19L20}\endx
\ThirdLvl 55Q52\SubText Homotopy groups of special spaces\endx
\ThirdLvl 55Q55\SubText Cohomotopy groups\endx
\ThirdLvl 55Q70\SubText Homotopy groups of special types
 \SeeAlso{\SbjNo 55N05, \SbjNo 55N07}\endx
\ThirdLvl 55Q91\SubText Equivariant homotopy groups \SeeAlso{\SbjNo
 19L47}\endx
\ThirdLvl 55Q99\SubText \NoneOfAbove\endx
\SecndLvl 55R++\SubText Fiber spaces and bundles \SeeAlso{\SbjNo
 18F15, \SbjNo 32Lxx, \SbjNo 46M20, \CMPonly{\SbjNo
 57Rxx}\FullScheme{\SbjNo 57R20, \SbjNo 57R22, \SbjNo 57R25}}\endx
\ThirdLvl 55R05\SubText Fiber spaces\endx
\ThirdLvl 55R10\SubText Fiber bundles\endx
\ThirdLvl 55R12\SubText Transfer\endx
\ThirdLvl 55R15\SubText Classification\endx
\ThirdLvl 55R20\SubText Spectral sequences and homology of fiber
 spaces \SeeAlso{\SbjNo 55Txx}\endx
\ThirdLvl 55R25\SubText Sphere bundles and vector space bundles\endx
\ThirdLvl 55R35\SubText Classifying spaces of groups and ${\it
 H}$-spaces\endx
\ThirdLvl 55R40\SubText Homology of classifying spaces, characteristic
 classes \SeeAlso{\SbjNo 57Txx, \SbjNo 57R20}\endx
\ThirdLvl 55R45\SubText Homology and homotopy of $B\rm O$ and $B\rm
 U$; Bott periodicity \endx
\ThirdLvl 55R50\SubText Stable classes of vector space bundles,
 $K$-theory \SeeAlso{\SbjNo 19Lxx} \SeeFor{For algebraic $K$-theory,
 see \SbjNo 18F25, \SbjNo 19-XX}\endx
\ThirdLvl 55R55\SubText Fiberings with singularities\endx
\ThirdLvl 55R60\SubText Microbundles and block bundles \SeeAlso{\SbjNo
 57N55, \SbjNo 57Q50}\endx
\ThirdLvl 55R65\SubText Generalizations of fiber spaces and
 bundles\endx
\ThirdLvl 55R91\SubText Equivariant fiber spaces and bundles
 \SeeAlso{\SbjNo 19L47}\endx
\ThirdLvl 55R99\SubText \NoneOfAbove\endx
\SecndLvl 55S++\SubText Operations and obstructions\endx
\ThirdLvl 55S05\SubText Primary cohomology operations\endx
\ThirdLvl 55S10\SubText Steenrod algebra\endx
\ThirdLvl 55S12\SubText Dyer-Lashof operations\endx
\ThirdLvl 55S15\SubText Symmetric products, cyclic products\endx
\ThirdLvl 55S20\SubText Secondary and higher cohomology
 operations\endx
\ThirdLvl 55S25\SubText $K$-theory operations and generalized
 cohomology operations \SeeAlso{\SbjNo 19D55, \SbjNo 19Lxx}\endx
\ThirdLvl 55S30\SubText Massey products\endx
\ThirdLvl 55S35\SubText Obstruction theory\endx
\ThirdLvl 55S36\SubText Extension and compression of mappings\endx
\ThirdLvl 55S37\SubText Classification of mappings\endx
\ThirdLvl 55S40\SubText Sectioning fiber spaces and bundles\endx
\ThirdLvl 55S45\SubText Postnikov systems, $k$-invariants\endx
\ThirdLvl 55S91\SubText Equivariant operations and obstructions
 \SeeAlso{\SbjNo 19L47}\endx
\ThirdLvl 55S99\SubText \NoneOfAbove\endx
\SecndLvl 55T++\SubText Spectral sequences \SeeAlso{\SbjNo 18G40,
 \SbjNo 55R20}\endx
\ThirdLvl 55T05\SubText General\endx
\ThirdLvl 55T10\SubText Serre spectral sequences\endx
\ThirdLvl 55T15\SubText Adams spectral sequences\endx
\ThirdLvl 55T20\SubText Eilenberg-Moore spectral sequences
 \SeeAlso{\SbjNo 57T35}\endx
\ThirdLvl 55T25\SubText Generalized cohomology\endx
\ThirdLvl 55T99\SubText \NoneOfAbove\endx
\SecndLvl 55U++\SubText Applied homological algebra and category
 theory \SeeAlso{\SbjNo 18Gxx}\endx
\ThirdLvl 55U05\SubText Abstract complexes\endx
\ThirdLvl 55U10\SubText Semisimplicial complexes\endx
\ThirdLvl 55U15\SubText Chain complexes\endx
\ThirdLvl 55U20\SubText Universal coefficient theorems, Bockstein
 operator\endx
\ThirdLvl 55U25\SubText Homology of a product, K\"unneth formula\endx
\ThirdLvl 55U30\SubText Duality\endx
\ThirdLvl 55U35\SubText Abstract homotopy theory\endx
\ThirdLvl 55U40\SubText Topological categories\endx
\ThirdLvl 55U99\SubText \NoneOfAbove\endx
\MajorSub 57-++\SubText Manifolds and cell complexes \SeeFor{For
 complex manifolds, see~\SbjNo 32C10}\endx
\ThirdLvl 57-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 57-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 57-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 57-03\SubText \Historical\endx
\ThirdLvl 57-04\SubText \ExplicitComputation\endx
\ThirdLvl 57-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 57M++\SubText Low-dimensional topology \endx
\ThirdLvl 57M05\SubText Fundamental group, presentations, free
 differential calculus\endx
\ThirdLvl 57M07\SubText Topological methods in group theory\endx
\ThirdLvl 57M10\SubText Covering spaces\endx
\ThirdLvl 57M12\SubText Special coverings, e.g.\ branched\endx
\ThirdLvl 57M15\SubText Relations with graph theory \SeeAlso{\SbjNo
 05Cxx}\endx
\ThirdLvl 57M20\SubText Two-dimensional complexes\endx
\ThirdLvl 57M25\SubText Knots and links in $S\sp 3$ \SeeFor{For higher
 dimensions, see \SbjNo 57Q45}\endx
\ThirdLvl 57M30\SubText Wild knots and surfaces, etc., wild
 embeddings\endx
\ThirdLvl 57M35\SubText Dehn's lemma, sphere theorem, loop theorem,
 asphericity\endx
\ThirdLvl 57M40\SubText Characterizations of $E\sp 3$ and $S\sp 3$
 (Poincar\'e conjecture) \SeeAlso{\SbjNo 57N12}\endx
\ThirdLvl 57M50\SubText Geometric structures on low-dimensional
 manifolds\endx
\ThirdLvl 57M60\SubText Group actions in low dimensions\endx
\ThirdLvl 57M99\SubText \NoneOfAbove\endx
\SecndLvl 57N++\SubText Topological manifolds\endx
\ThirdLvl 57N05\SubText Topology of $E\sp 2$, $2$-manifolds\endx
\ThirdLvl 57N10\SubText Topology of general $3$-manifolds
 \SeeAlso{\SbjNo 57Mxx}\endx
\ThirdLvl 57N12\SubText Topology of $E\sp 3$ and $S\sp 3$
 \SeeAlso{\SbjNo 57M40}\endx
\ThirdLvl 57N13\SubText Topology of $E\sp 4$, $4$-manifolds
 \SeeAlso{\SbjNo 14Jxx, \SbjNo 32Jxx}\endx
\ThirdLvl 57N15\SubText Topology of $E\sp n$, $n$-manifolds ($4 \less
 n \less \infty$)\endx
\ThirdLvl 57N17\SubText Topology of topological vector spaces\endx
\ThirdLvl 57N20\SubText Topology of infinite-dimensional manifolds
 \SeeAlso{\SbjNo 58Bxx}\endx
\ThirdLvl 57N25\SubText Shapes \SeeAlso{\SbjNo 54C56, \SbjNo 55P55,
 \SbjNo 55Q07}\endx
\ThirdLvl 57N30\SubText Engulfing\endx
\ThirdLvl 57N35\SubText Embeddings and immersions\endx
\ThirdLvl 57N37\SubText Isotopy and pseudo-isotopy\endx
\ThirdLvl 57N40\SubText Neighborhoods of submanifolds\endx
\ThirdLvl 57N45\SubText Flatness and tameness\endx
\ThirdLvl 57N50\SubText $S\sp{n-1}\subset E\sp n$, Schoenflies
 problem\endx
\ThirdLvl 57N55\SubText Microbundles and block bundles \SeeAlso{\SbjNo
 55R60, \SbjNo 57Q50}\endx
\ThirdLvl 57N60\SubText Cellularity\endx
\ThirdLvl 57N65\SubText Algebraic topology of manifolds\endx
\ThirdLvl 57N70\SubText Cobordism and concordance\endx
\ThirdLvl 57N75\SubText General position and transversality\endx
\ThirdLvl 57N80\SubText Stratifications\endx
\ThirdLvl 57N99\SubText \NoneOfAbove\endx
\SecndLvl 57P++\SubText Generalized manifolds \SeeAlso{\SbjNo
 18F15}\endx
\ThirdLvl 57P05\SubText Local properties of generalized manifolds\endx
\ThirdLvl 57P10\SubText Poincar\'e duality spaces\endx
\ThirdLvl 57P99\SubText \NoneOfAbove\endx
\SecndLvl 57Q++\SubText PL-topology\endx
\ThirdLvl 57Q05\SubText General topology of complexes\endx
\ThirdLvl 57Q10\SubText Simple homotopy type, Whitehead torsion,
 Reidemeister-Franz torsion, etc. \SeeAlso{\SbjNo 19B28}\endx
\ThirdLvl 57Q12\SubText Wall finiteness obstruction for
 CW-complexes\endx
\ThirdLvl 57Q15\SubText Triangulating manifolds\endx
\ThirdLvl 57Q20\SubText Cobordism\endx
\ThirdLvl 57Q25\SubText Comparison of PL-structures: classification,
 Hauptvermutung\endx
\ThirdLvl 57Q30\SubText Engulfing\endx
\ThirdLvl 57Q35\SubText Embeddings and immersions\endx
\ThirdLvl 57Q37\SubText Isotopy\endx
\ThirdLvl 57Q40\SubText Regular neighborhoods\endx
\ThirdLvl 57Q45\SubText Knots and links (in high dimensions)
 \SeeFor{For the low-dimensional case, see \SbjNo 57M25}\endx
\ThirdLvl 57Q50\SubText Microbundles and block bundles \SeeAlso{\SbjNo
 55R60, \SbjNo 57N55}\endx
\ThirdLvl 57Q55\SubText Approximations\endx
\ThirdLvl 57Q60\SubText Cobordism and concordance\endx
\ThirdLvl 57Q65\SubText General position and transversality\endx
\ThirdLvl 57Q91\SubText Equivariant PL-topology\endx
\ThirdLvl 57Q99\SubText \NoneOfAbove\endx
\SecndLvl 57R++\SubText Differential topology \SeeFor{For foundational
 questions of differentiable manifolds, see \SbjNo 58Axx; for
 infinite-dimensional manifolds, see \SbjNo 58Bxx}\endx
\ThirdLvl 57R05\SubText Triangulating\endx
\ThirdLvl 57R10\SubText Smoothing\endx
\ThirdLvl 57R12\SubText Smooth approximations\endx
\ThirdLvl 57R15\SubText Specialized structures on manifolds (spin
 manifolds, framed manifolds, etc.)\endx
\ThirdLvl 57R19\SubText Algebraic topology on manifolds\endx
\ThirdLvl 57R20\SubText Characteristic classes and numbers\endx
\ThirdLvl 57R22\SubText Topology of vector bundles and fiber bundles
 \SeeAlso{\SbjNo 55Rxx}\endx
\ThirdLvl 57R25\SubText Vector fields, frame fields\endx
\ThirdLvl 57R27\SubText Controllability of vector fields on
 $C\sp\infty$ and real-analytic manifolds \SeeAlso{\SbjNo 49Qxx,
 \SbjNo 58F40, \SbjNo 93B05}\endx
\ThirdLvl 57R30\SubText Foliations; geometric theory\endx
\ThirdLvl 57R32\SubText Classifying spaces for foliations; Gel\cprime
 fand-Fuks cohomology \SeeAlso{\SbjNo 58H10}\endx
\ThirdLvl 57R35\SubText Differentiable mappings\endx
\ThirdLvl 57R40\SubText Embeddings\endx
\ThirdLvl 57R42\SubText Immersions\endx
\ThirdLvl 57R45\SubText Singularities of differentiable mappings\endx
\ThirdLvl 57R50\SubText Diffeomorphisms\endx
\ThirdLvl 57R52\SubText Isotopy\endx
\ThirdLvl 57R55\SubText Differentiable structures\endx
\ThirdLvl 57R57\SubText Applications of global analysis to structures
 on manifolds \SeeAlso{\SbjNo 58-XX}\endx
\ThirdLvl 57R60\SubText Homotopy spheres, Poincar\'e conjecture\endx
\ThirdLvl 57R65\SubText Surgery and handlebodies\endx
\ThirdLvl 57R67\SubText Surgery obstructions, Wall groups
 \SeeAlso{\SbjNo 19J25}\endx
\ThirdLvl 57R70\SubText Critical points and critical submanifolds\endx
\ThirdLvl 57R75\SubText O- and SO-cobordism\endx
\ThirdLvl 57R77\SubText Complex cobordism (U- and SU-cobordism)
 \SeeAlso{\SbjNo 55N22}\endx
\ThirdLvl 57R80\SubText $h$- and $s$-cobordism\endx
\ThirdLvl 57R85\SubText Equivariant cobordism\endx
\ThirdLvl 57R90\SubText Other types of cobordism \See{\SbjNo
 55N22}\endx
\ThirdLvl 57R91\SubText Equivariant algebraic topology of
 manifolds\endx
\ThirdLvl 57R95\SubText Realizing cycles by submanifolds\endx
\ThirdLvl 57R99\SubText \NoneOfAbove\endx
\SecndLvl 57S++\SubText Topological transformation groups
 \SeeAlso{\SbjNo 20F34, \SbjNo 22-XX, \SbjNo 54H15, \SbjNo 58D05}\endx
\ThirdLvl 57S05\SubText Topological properties of groups of
 homeomorphisms or diffeomorphisms\endx
\ThirdLvl 57S10\SubText Compact groups of homeomorphisms\endx
\ThirdLvl 57S15\SubText Compact Lie groups of differentiable
 transformations\endx
\ThirdLvl 57S17\SubText Finite transformation groups\endx
\ThirdLvl 57S20\SubText Noncompact Lie groups of transformations\endx
\ThirdLvl 57S25\SubText Groups acting on specific manifolds\endx
\ThirdLvl 57S30\SubText Discontinuous groups of transformations\endx
\ThirdLvl 57S99\SubText \NoneOfAbove\endx
\SecndLvl 57T++\SubText Homology and homotopy of topological groups
 and related structures\endx
\ThirdLvl 57T05\SubText Hopf algebras \SeeAlso{\SbjNo 16W30}\endx
\ThirdLvl 57T10\SubText Homology and cohomology of Lie groups\endx
\ThirdLvl 57T15\SubText Homology and cohomology of homogeneous spaces
 of Lie groups\endx
\ThirdLvl 57T20\SubText Homotopy groups of topological groups and
 homogeneous spaces\endx
\ThirdLvl 57T25\SubText Homology and cohomology of ${\it
 H}$-spaces\endx
\ThirdLvl 57T30\SubText Bar and cobar constructions \SeeAlso{\SbjNo
 18G55, \SbjNo 55Uxx}\endx
\ThirdLvl 57T35\SubText Applications of Eilenberg-Moore spectral
 sequences \SeeAlso{\SbjNo 55R20, \SbjNo 55T20}\endx
\ThirdLvl 57T99\SubText \NoneOfAbove\endx
\MajorSub 58-++\SubText Global analysis, analysis on manifolds
 \SeeAlso{\CMPonly{\SbjNo 32-XX}\FullScheme{\SbjNo 32Cxx, \SbjNo
 32Fxx}, \SbjNo 46-XX, \SbjNo 47Hxx, \SbjNo 53Cxx; for geometric
 integration theory, see~\CMPonly{\SbjNo 49Fxx}\FullScheme{\SbjNo
 49Q15}}\endx
\ThirdLvl 58-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 58-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 58-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 58-03\SubText \Historical\endx
\ThirdLvl 58-04\SubText \ExplicitComputation\endx
\ThirdLvl 58-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 58A++\SubText General theory of differentiable
 manifolds\endx
\ThirdLvl 58A03\SubText Topos-theoretic approach to differentiable
 manifolds\endx
\ThirdLvl 58A05\SubText Differentiable manifolds, foundations \endx
\ThirdLvl 58A07\SubText Real-analytic and Nash manifolds
 \SeeAlso{\SbjNo 14P20, \SbjNo 32C07}\endx
\ThirdLvl 58A10\SubText Differential forms\endx
\ThirdLvl 58A12\SubText de Rham theory \SeeAlso{\SbjNo 14Fxx}\endx
\ThirdLvl 58A14\SubText Hodge theory \SeeAlso{\SbjNo 14C30, \SbjNo
 14Fxx, \SbjNo 32J25, \SbjNo 32S35}\endx
\ThirdLvl 58A15\SubText Exterior differential systems (Cartan
 theory)\endx
\ThirdLvl 58A17\SubText Pfaffian systems\endx
\ThirdLvl 58A20\SubText Jets\endx
\ThirdLvl 58A25\SubText Currents \SeeAlso{\SbjNo 32C30, \SbjNo
 53C65}\endx
\ThirdLvl 58A30\SubText Vector distributions (subbundles of the
 tangent bundles)\endx
\ThirdLvl 58A35\SubText Stratified sets \SeeAlso{\SbjNo 32S60, \SbjNo
 58C27}\endx
\ThirdLvl 58A40\SubText Differential spaces\endx
\ThirdLvl 58A50\SubText Supermanifolds and graded manifolds
 \SeeAlso{\SbjNo 14A22, \SbjNo 32C11}\endx
\ThirdLvl 58A99\SubText \NoneOfAbove\endx
\SecndLvl 58B++\SubText Infinite-dimensional manifolds\endx
\ThirdLvl 58B05\SubText Homotopy and topological questions\endx
\ThirdLvl 58B10\SubText Differentiability questions\endx
\ThirdLvl 58B12\SubText Questions of holomorphy \SeeAlso{\SbjNo 32-XX,
 \SbjNo 46G20}\endx
\ThirdLvl 58B15\SubText Fredholm structures \SeeAlso{\SbjNo
 47A53}\endx
\ThirdLvl 58B20\SubText Riemannian, Finsler and other geometric
 structures \SeeAlso{\SbjNo 53C20, \SbjNo 53C60}\endx
\ThirdLvl 58B25\SubText Group structures and generalizations on
 infinite-dimensional manifolds \SeeAlso{\SbjNo 22E65, \SbjNo
 58D05}\endx
\ThirdLvl 58B30\SubText Noncommutative differential geometry and
 topology \SeeAlso{\SbjNo 46L30, \SbjNo 46L87, \SbjNo 46L89}\endx
\ThirdLvl 58B99\SubText \NoneOfAbove\endx
\SecndLvl 58C++\SubText Calculus on manifolds; nonlinear operators
 \SeeAlso{\SbjNo 47Hxx}\endx
\ThirdLvl 58C05\SubText Real-valued functions\endx
\ThirdLvl 58C06\SubText Set valued and function-space valued mappings
 \SeeAlso{\SbjNo 47H04, \SbjNo 54C60}\endx
\ThirdLvl 58C07\SubText Continuity properties of mappings\endx
\ThirdLvl 58C10\SubText Holomorphic maps \SeeAlso{\SbjNo 32-XX}\endx
\ThirdLvl 58C15\SubText Implicit function theorems; global Newton
 methods\endx
\ThirdLvl 58C20\SubText Differentiation theory (Gateaux, Fr\'echet,
 etc.) \SeeAlso{\SbjNo 26Exx, \SbjNo 46G05}\endx
\ThirdLvl 58C25\SubText Differentiable maps\endx
\ThirdLvl 58C27\SubText Singularities of differentiable maps
 \SeeAlso{\SbjNo 14B05, \SbjNo 14E15, \SbjNo 32Sxx}\endx
\ThirdLvl 58C28\SubText Catastrophes \SeeAlso{\SbjNo 57R70, \SbjNo
 58Exx}\endx
\ThirdLvl 58C30\SubText Fixed point theorems on
 manifolds\SeeAlso{\SbjNo 47H10}\endx
\ThirdLvl 58C35\SubText Integration on manifolds; measures on
 manifolds \SeeAlso{\SbjNo 28Cxx}\endx
\ThirdLvl 58C40\SubText Spectral theory; eigenvalue problems
 \SeeAlso{\SbjNo 47H12, \SbjNo 58E07}\endx
\ThirdLvl 58C50\SubText Analysis on supermanifolds or graded
 manifolds\endx
\ThirdLvl 58C99\SubText \NoneOfAbove\endx
\SecndLvl 58D++\SubText Spaces and manifolds of mappings
 \ExtraText{(including nonlinear versions of \SbjNo 46Exx)}\endx
\ThirdLvl 58D05\SubText Groups of diffeomorphisms and homeomorphisms
 as manifolds \SeeAlso{\SbjNo 22E65, \SbjNo 57S05}\endx
\ThirdLvl 58D07\SubText Groups and semigroups of nonlinear operators
 \SeeAlso{\SbjNo 17B65, \SbjNo 47D03, \SbjNo 47D06, \SbjNo 47H20}\endx
\ThirdLvl 58D10\SubText Spaces of imbeddings and immersions\endx
\ThirdLvl 58D15\SubText Manifolds of mappings \SeeAlso{\SbjNo
 54C35}\endx
\ThirdLvl 58D17\SubText Manifolds of metrics (esp.\ Riemannian)\endx
\ThirdLvl 58D19\SubText Group actions and symmetry properties\endx
\ThirdLvl 58D20\SubText Measures (Gaussian, cylindrical, etc.) on
 manifolds of maps \See{\SbjNo 28Cxx}\endx
\ThirdLvl 58D25\SubText Equations in function spaces; evolution
 equations \SeeAlso{\SbjNo 34Gxx, \SbjNo 35K22, \SbjNo 35R15, \SbjNo
 47H15}\endx
\ThirdLvl 58D27\SubText Moduli problems for differential geometric
 structures\endx
\ThirdLvl 58D29\SubText Moduli problems for topological
 structures\endx
\ThirdLvl 58D30\SubText Applications (in quantum mechanics (Feynman
 path integrals), relativity, fluid dynamics, etc.)\endx
\ThirdLvl 58D99\SubText \NoneOfAbove\endx
\SecndLvl 58E++\SubText Variational problems in infinite-dimensional
 spaces\endx
\ThirdLvl 58E05\SubText Abstract critical point theory (Morse theory,
 Ljusternik-Schnirelman (Lyusternik-Shnirel\cprime man) theory,
 etc.)\endx
\ThirdLvl 58E07\SubText Abstract bifurcation theory\endx
\ThirdLvl 58E09\SubText Group-invariant bifurcation theory\endx
\ThirdLvl 58E10\SubText Applications to the theory of geodesics
 (problems in one independent variable)\endx
\ThirdLvl 58E11\SubText Critical metrics\endx
\ThirdLvl 58E12\SubText Applications to minimal surfaces (problems in
 two independent variables)\endx
\ThirdLvl 58E15\SubText Application to extremal problems in several
 variables; Yang-Mills functionals \SeeAlso{\SbjNo 81T13}, etc.\endx
\ThirdLvl 58E17\SubText Pareto optimality, etc., applications to
 economics\endx
\ThirdLvl 58E20\SubText Harmonic maps\endx
\ThirdLvl 58E25\SubText Applications to control theory (optimal and
 nonoptimal)\endx
\ThirdLvl 58E30\SubText Variational principles\endx
\ThirdLvl 58E35\SubText Variational inequalities (global
 problems)\endx
\ThirdLvl 58E40\SubText Group actions\endx
\ThirdLvl 58E50\SubText Applications\endx
\ThirdLvl 58E99\SubText \NoneOfAbove\endx
\SecndLvl 58F++\SubText Ordinary differential equations on manifolds;
 dynamical systems \SeeAlso{\SbjNo 28D10, \SbjNo 34Cxx,
 \CMPonly{\SbjNo 34Cxx}\FullScheme{\SbjNo 54H20}}\endx
\ThirdLvl 58F03\SubText One-dimensional dynamics, general symbolic
 dynamics \SeeAlso{\SbjNo 26A18}\endx
\ThirdLvl 58F05\SubText Hamiltonian and Lagrangian systems; symplectic
 geometry \SeeAlso{\SbjNo 70Hxx, \SbjNo 81S10}\endx
\ThirdLvl 58F06\SubText Geometric quantization (applications of
 representation theory) \SeeAlso{\SbjNo 22E45, \SbjNo 81S10}\endx
\ThirdLvl 58F07\SubText Completely integrable systems (including
 systems with an infinite number of degrees of freedom) \endx
\ThirdLvl 58F08\SubText Point-mapping properties, iterations,
 completeness; dynamics of cellular automata \SeeAlso{\SbjNo 26A18,
 \SbjNo 30D05}\endx
\ThirdLvl 58F09\SubText Morse-Smale systems\endx
\ThirdLvl 58F10\SubText Stability theory\endx
\ThirdLvl 58F11\SubText Ergodic theory; invariant measures
 \SeeAlso{\SbjNo 28Dxx}\endx
\ThirdLvl 58F12\SubText Structure of attractors (and repellors)\endx
\ThirdLvl 58F13\SubText Strange attractors; chaos and other
 pathologies \SeeAlso{\SbjNo 70K50}\endx
\ThirdLvl 58F14\SubText Bifurcation theory and singularities\endx
\ThirdLvl 58F15\SubText Hyperbolic structures (expanding maps, Anosov
 systems, etc.)\endx
\ThirdLvl 58F17\SubText Geodesic and horocycle flows\endx
\ThirdLvl 58F18\SubText Relations with foliations\endx
\ThirdLvl 58F19\SubText Eigenvalue and spectral problems\endx
\ThirdLvl 58F20\SubText Periodic points and zeta functions\endx
\ThirdLvl 58F21\SubText Limit cycles, singular points, etc.\endx
\ThirdLvl 58F22\SubText Periodic solutions\endx
\ThirdLvl 58F23\SubText Holomorphic dynamics \SeeAlso{\SbjNo
 30D05}\endx
\ThirdLvl 58F25\SubText Flows\endx
\ThirdLvl 58F27\SubText Quasiperiodic flows\endx
\ThirdLvl 58F30\SubText Perturbations\endx
\ThirdLvl 58F32\SubText Functional-differential equations on
 manifolds\endx
\ThirdLvl 58F35\SubText Invariance properties\endx
\ThirdLvl 58F36\SubText Normal forms\endx
\ThirdLvl 58F37\SubText Correspondences and other transformation
 methods (e.g.\ Lie-B\"acklund)\endx
\ThirdLvl 58F39\SubText Dynamical systems treatment of PDE (should be
 assigned another number from 58F) \SeeAlso{\SbjNo 35B32, \SbjNo
 35K57}\endx
\ThirdLvl 58F40\SubText Applications\endx
\ThirdLvl 58F99\SubText \NoneOfAbove\endx
\SecndLvl 58G++\SubText Partial differential equations on manifolds;
 differential operators \SeeAlso{\SbjNo 35-XX}\endx
\ThirdLvl 58G03\SubText Elliptic equations on manifolds, general
 theory\endx
\ThirdLvl 58G05\SubText Differential complexes \SeeAlso{\SbjNo 35Nxx};
 elliptic complexes\endx
\ThirdLvl 58G07\SubText Relations with hyperfunctions \endx
\ThirdLvl 58G10\SubText Index theory and related fixed point theorems
 \SeeAlso{\SbjNo 19K56, \SbjNo 46L80}\endx
\ThirdLvl 58G11\SubText Heat and other parabolic equation methods\endx
\ThirdLvl 58G12\SubText Exotic index theories \SeeAlso{\SbjNo 19K56,
 \SbjNo 46L05, \SbjNo 46L10, \SbjNo 46L80, \SbjNo 46M20}\endx
\ThirdLvl 58G15\SubText Pseudodifferential and Fourier integral
 operators on manifolds \SeeAlso{\SbjNo 35Sxx}\endx
\ThirdLvl 58G16\SubText Hyperbolic equations\endx
\ThirdLvl 58G17\SubText Propagation of singularities; initial value
 problems\endx
\ThirdLvl 58G18\SubText Perturbations; asymptotics\endx
\ThirdLvl 58G20\SubText Boundary value problems on manifolds\endx
\ThirdLvl 58G25\SubText Spectral problems; spectral geometry;
 scattering theory \SeeAlso{\SbjNo 35Pxx}\endx
\ThirdLvl 58G26\SubText Determinants and determinant bundles\endx
\ThirdLvl 58G28\SubText Bifurcations \SeeAlso{\SbjNo 35B32}\endx
\ThirdLvl 58G30\SubText Relations with special manifold structures
 (Riemannian, Finsler, etc.)\endx
\ThirdLvl 58G32\SubText Diffusion processes and stochastic analysis on
 manifolds\endx
\ThirdLvl 58G35\SubText Invariance and symmetry properties
 \SeeAlso{\SbjNo 35A30}\endx
\ThirdLvl 58G37\SubText Correspondences and other transformation
 methods (e.g.\ Lie-B\"acklund) \SeeAlso{\SbjNo 35A22}\endx
\ThirdLvl 58G40\SubText Applications\endx
\ThirdLvl 58G99\SubText \NoneOfAbove\endx
\SecndLvl 58H++\SubText Pseudogroups, differentiable groupoids and
 general structures on manifolds\endx
\ThirdLvl 58H05\SubText Pseudogroups and differentiable groupoids
 \SeeAlso{\SbjNo 22A22, \SbjNo 22E65}\endx
\ThirdLvl 58H10\SubText Cohomology of classifying spaces for
 pseudogroup structures (Spencer, Gel\cprime fand-Fuks, etc.)
 \SeeAlso{\SbjNo 57R32}\endx
\ThirdLvl 58H15\SubText Deformations of structures \SeeAlso{\SbjNo
 32Gxx, \SbjNo 58G05}\endx
\ThirdLvl 58H99\SubText \NoneOfAbove\endx
\SecndLvl 58Z05\SubText Applications to physics\endx
\MajorSub 60-++\SubText Probability theory and stochastic processes
 \SeeFor{For additional applications, see~\SbjNo 11Kxx, \SbjNo 62-XX,
 \SbjNo 90-XX, \SbjNo 92-XX, \SbjNo 93-XX, \SbjNo 94-XX. For numerical
 results, see~\SbjNo 65U05}\endx
\ThirdLvl 60-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 60-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 60-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 60-03\SubText \Historical\endx
\ThirdLvl 60-04\SubText \ExplicitComputation\endx
\ThirdLvl 60-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 60A++\SubText Foundations of probability theory\endx
\ThirdLvl 60A05\SubText Axioms; other general questions\endx
\ThirdLvl 60A10\SubText Probabilistic measure theory \SeeFor{For
 ergodic theory, see \SbjNo 28Dxx and \SbjNo 60Fxx}\endx
\ThirdLvl 60A99\SubText \NoneOfAbove\endx
\SecndLvl 60B++\SubText Probability theory on algebraic and
 topological structures\endx
\ThirdLvl 60B05\SubText Probability measures on topological
 spaces\endx
\ThirdLvl 60B10\SubText Convergence of probability measures\endx
\ThirdLvl 60B11\SubText Probability theory on linear topological
 spaces \SeeAlso{\SbjNo 28C20}\endx
\ThirdLvl 60B12\SubText Limit theorems for vector-valued random
 variables (infinite-dimensional case)\endx
\ThirdLvl 60B15\SubText Probability measures on groups, Fourier
 transforms, factorization\endx
\ThirdLvl 60B99\SubText \NoneOfAbove\endx
\SecndLvl 60C05\SubText Combinatorial probability\endx
\SecndLvl 60D05\SubText Geometric probability, stochastic geometry,
 random sets \SeeAlso{\SbjNo 52A22, \SbjNo 53C65}\endx
\SecndLvl 60E++\SubText Distribution theory \SeeAlso{\SbjNo 62Exx,
 \SbjNo 62Hxx}\endx
\ThirdLvl 60E05\SubText Distributions: general theory\endx
\ThirdLvl 60E07\SubText Infinitely divisible distributions; stable
 distributions\endx
\ThirdLvl 60E10\SubText Characteristic functions; other
 transforms\endx
\ThirdLvl 60E15\SubText Inequalities (Chebyshev, Kolmogorov,
 etc.)\endx
\ThirdLvl 60E99\SubText \NoneOfAbove\endx
\SecndLvl 60F++\SubText Limit theorems \SeeAlso{\SbjNo 28Dxx, \SbjNo
 60B12}\endx
\ThirdLvl 60F05\SubText Central limit and other weak theorems\endx
\ThirdLvl 60F10\SubText Large deviations\endx
\ThirdLvl 60F15\SubText Strong theorems\endx
\ThirdLvl 60F17\SubText Functional limit theorems; invariance
 principles\endx
\ThirdLvl 60F20\SubText Zero-one laws\endx
\ThirdLvl 60F25\SubText $L\sp p$-limit theorems\endx
\ThirdLvl 60F99\SubText \NoneOfAbove\endx
\SecndLvl 60G++\SubText Stochastic processes\endx
\ThirdLvl 60G05\SubText Foundations of stochastic processes\endx
\ThirdLvl 60G07\SubText General theory of processes\endx
\ThirdLvl 60G09\SubText Exchangeability\endx
\ThirdLvl 60G10\SubText Stationary processes\endx
\ThirdLvl 60G12\SubText General second-order processes\endx
\ThirdLvl 60G15\SubText Gaussian processes\endx
\ThirdLvl 60G17\SubText Sample path properties\endx
\ThirdLvl 60G18\SubText Self-similar processes\endx
\ThirdLvl 60G20\SubText Generalized stochastic processes\endx
\ThirdLvl 60G25\SubText Prediction theory \SeeAlso{\SbjNo 62M20}\endx
\ThirdLvl 60G30\SubText Continuity and singularity of induced
 measures\endx
\ThirdLvl 60G35\SubText Applications (signal detection, filtering,
 etc.) \SeeAlso{\SbjNo 62M20, \SbjNo 93E10, \SbjNo 93E11, \SbjNo
 94Axx}\endx
\ThirdLvl 60G40\SubText Stopping times; optimal stopping problems;
 gambling theory \SeeAlso{\SbjNo 62L15, \SbjNo 90D60}\endx
\ThirdLvl 60G42\SubText Martingales with discrete parameter\endx
\ThirdLvl 60G44\SubText Martingales with continuous parameter\endx
\ThirdLvl 60G46\SubText Martingales and classical analysis\endx
\ThirdLvl 60G48\SubText Generalizations of martingales\endx
\ThirdLvl 60G50\SubText Sums of independent random variables\endx
\ThirdLvl 60G55\SubText Point processes\endx
\ThirdLvl 60G57\SubText Random measures\endx
\ThirdLvl 60G60\SubText Random fields\endx
\ThirdLvl 60G70\SubText Extreme value theory; extremal processes\endx
\ThirdLvl 60G99\SubText \NoneOfAbove\endx
\SecndLvl 60H++\SubText Stochastic analysis \SeeAlso{\SbjNo
 58G32}\endx
\ThirdLvl 60H05\SubText Stochastic integrals\endx
\ThirdLvl 60H07\SubText Stochastic calculus of variations and the
 Malliavin calculus\endx
\ThirdLvl 60H10\SubText Stochastic ordinary differential equations
 \SeeAlso{\SbjNo 34F05}\endx
\ThirdLvl 60H15\SubText Stochastic partial differential equations
 \SeeAlso{\SbjNo 35R60}\endx
\ThirdLvl 60H20\SubText Stochastic integral equations\endx
\ThirdLvl 60H25\SubText Random operators and equations \SeeAlso{\SbjNo
 47B80}\endx
\ThirdLvl 60H30\SubText Applications of stochastic analysis (to PDE,
 etc.)\endx
\ThirdLvl 60H99\SubText \NoneOfAbove\endx
\SecndLvl 60J++\SubText Markov processes\endx
\ThirdLvl 60J05\SubText Markov processes with discrete parameter\endx
\ThirdLvl 60J10\SubText Markov chains with discrete parameter\endx
\ThirdLvl 60J15\SubText Random walks\endx
\ThirdLvl 60J20\SubText Applications of discrete Markov processes
 (social mobility, learning theory, industrial processes, etc.)
 \SeeAlso{\SbjNo 90B30, \SbjNo 92H10, \SbjNo 92H35, \SbjNo 92J40}\endx
\ThirdLvl 60J25\SubText Markov processes with continuous
 parameter\endx
\ThirdLvl 60J27\SubText Markov chains with continuous parameter\endx
\ThirdLvl 60J30\SubText Processes with independent increments \endx
\ThirdLvl 60J35\SubText Transition functions, generators and
 resolvents \SeeAlso{\SbjNo 47D03, \SbjNo 47D07}\endx
\ThirdLvl 60J40\SubText Right processes\endx
\ThirdLvl 60J45\SubText Probabilistic potential theory \SeeAlso{\SbjNo
 31Cxx, \SbjNo 31D05}\endx
\ThirdLvl 60J50\SubText Boundary theory\endx
\ThirdLvl 60J55\SubText Local time and additive functionals\endx
\ThirdLvl 60J57\SubText Multiplicative functionals\endx
\ThirdLvl 60J60\SubText Diffusion processes \SeeAlso{\SbjNo
 58G32}\endx
\ThirdLvl 60J65\SubText Brownian motion \SeeAlso{\SbjNo 58G32}\endx
\ThirdLvl 60J70\SubText Applications of diffusion theory (population
 genetics, absorption problems, etc.) \SeeAlso{\SbjNo 92Dxx}\endx
\ThirdLvl 60J75\SubText Jump processes\endx
\ThirdLvl 60J80\SubText Branching processes (Galton-Watson,
 birth-and-death, etc.)\endx
\ThirdLvl 60J85\SubText Applications of branching processes
 \SeeAlso{\SbjNo 92Dxx}\endx
\ThirdLvl 60J99\SubText \NoneOfAbove\endx
\SecndLvl 60K++\SubText Special processes\endx
\ThirdLvl 60K05\SubText Renewal theory\endx
\ThirdLvl 60K10\SubText Applications (reliability, demand theory,
 etc.)\endx
\ThirdLvl 60K15\SubText Markov renewal processes, semi-Markov
 processes\endx
\ThirdLvl 60K20\SubText Applications of Markov renewal processes
 (reliability, queueing networks, etc.) \SeeAlso{\SbjNo 90Bxx}\endx
\ThirdLvl 60K25\SubText Queueing theory \SeeAlso{\SbjNo 68M20, \SbjNo
 90B22}\endx
\ThirdLvl 60K30\SubText Applications (congestion, allocation, storage,
 traffic, etc.) \SeeAlso{\SbjNo 90Bxx}\endx
\ThirdLvl 60K35\SubText Interacting random processes; statistical
 mechanics type models; percolation theory \SeeAlso{\SbjNo 82B43,
 \SbjNo 82C43}\endx
\ThirdLvl 60K40\SubText Other physical applications of random
 processes\endx
\ThirdLvl 60K99\SubText \NoneOfAbove\endx
\MajorSub 62-++\SubText Statistics \SeeFor{For numerical methods,
 see~\SbjNo 65U05}\endx
\ThirdLvl 62-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 62-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 62-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 62-03\SubText \Historical\endx
\ThirdLvl 62-04\SubText \ExplicitComputation\endx
\ThirdLvl 62-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 62-07\SubText Data analysis\endx
\ThirdLvl 62-09\SubText Graphical methods\endx
\SecndLvl 62A++\SubText Foundations\endx
\ThirdLvl 62A05\SubText Invariance and group considerations\endx
\ThirdLvl 62A10\SubText The likelihood approach\endx
\ThirdLvl 62A15\SubText The Bayesian approach\endx
\ThirdLvl 62A20\SubText The classical approach\endx
\ThirdLvl 62A25\SubText The structural approach\endx
\ThirdLvl 62A30\SubText The fiducial approach\endx
\ThirdLvl 62A99\SubText \NoneOfAbove\endx
\SecndLvl 62B++\SubText Sufficiency and information\endx
\ThirdLvl 62B05\SubText Sufficient statistics and fields\endx
\ThirdLvl 62B10\SubText Statistical information theory \SeeAlso{\SbjNo
 94A17}\endx
\ThirdLvl 62B15\SubText Theory of statistical experiments\endx
\ThirdLvl 62B20\SubText Measure-theoretic results, etc.\endx
\ThirdLvl 62B99\SubText \NoneOfAbove\endx
\SecndLvl 62C++\SubText Decision theory \SeeAlso{\SbjNo 90A05, \SbjNo
 90B50; for game theory, see \SbjNo 90D35}\endx
\ThirdLvl 62C05\SubText General considerations\endx
\ThirdLvl 62C07\SubText Complete class results\endx
\ThirdLvl 62C10\SubText Bayesian problems; characterization of Bayes
 procedures\endx
\ThirdLvl 62C12\SubText Empirical decision procedures; empirical Bayes
 procedures\endx
\ThirdLvl 62C15\SubText Admissibility\endx
\ThirdLvl 62C20\SubText Minimax procedures\endx
\ThirdLvl 62C25\SubText Compound decision problems\endx
\ThirdLvl 62C99\SubText \NoneOfAbove\endx
\SecndLvl 62D05\SubText Sampling theory, sample surveys\endx
\SecndLvl 62E++\SubText Distribution theory \SeeAlso{\SbjNo
 60Exx}\endx
\ThirdLvl 62E10\SubText Characterization and structure theory\endx
\ThirdLvl 62E15\SubText Exact distribution theory\endx
\ThirdLvl 62E17\SubText Approximations to distributions
 (nonasymptotic)\endx
\ThirdLvl 62E20\SubText Asymptotic distribution theory\endx
\ThirdLvl 62E25\SubText Monte Carlo studies\endx
\ThirdLvl 62E30\SubText Formal computational methods (polykays,
 etc.)\endx
\ThirdLvl 62E99\SubText \NoneOfAbove\endx
\SecndLvl 62F++\SubText Parametric inference\endx
\ThirdLvl 62F03\SubText Hypothesis testing\endx
\ThirdLvl 62F04\SubText Small sample properties of tests\endx
\ThirdLvl 62F05\SubText Asymptotic properties of tests\endx
\ThirdLvl 62F07\SubText Ranking and selection\endx
\ThirdLvl 62F10\SubText Point estimation\endx
\ThirdLvl 62F11\SubText Small sample properties of estimators\endx
\ThirdLvl 62F12\SubText Asymptotic properties of estimators\endx
\ThirdLvl 62F15\SubText Bayesian inference\endx
\ThirdLvl 62F25\SubText Tolerance and confidence regions\endx
\ThirdLvl 62F30\SubText Inference under constraints\endx
\ThirdLvl 62F35\SubText Robustness and adaptive procedures\endx
\ThirdLvl 62F99\SubText \NoneOfAbove\endx
\SecndLvl 62G++\SubText Nonparametric inference\endx
\ThirdLvl 62G05\SubText Estimation\endx
\ThirdLvl 62G07\SubText Curve estimation (nonparametric regression,
 density estimation, etc.)\endx
\ThirdLvl 62G09\SubText Resampling methods\endx
\ThirdLvl 62G10\SubText Hypothesis testing\endx
\ThirdLvl 62G15\SubText Tolerance and confidence regions\endx
\ThirdLvl 62G20\SubText Asymptotic properties\endx
\ThirdLvl 62G30\SubText Order statistics; empirical distribution
 functions\endx
\ThirdLvl 62G35\SubText Robustness\endx
\ThirdLvl 62G99\SubText \NoneOfAbove\endx
\SecndLvl 62H++\SubText Multivariate analysis \SeeAlso{\SbjNo
 60Exx}\endx
\ThirdLvl 62H05\SubText Characterization and structure theory\endx
\ThirdLvl 62H10\SubText Distribution of statistics\endx
\ThirdLvl 62H11\SubText Directional data; spatial statistics\endx
\ThirdLvl 62H12\SubText Estimation\endx
\ThirdLvl 62H15\SubText Hypothesis testing\endx
\ThirdLvl 62H17\SubText Contingency\endx
\ThirdLvl 62H20\SubText Measures of association (correlation,
 canonical correlation, etc.)\endx
\ThirdLvl 62H25\SubText Factor analysis and principal components;
 correspondence analysis\endx
\ThirdLvl 62H30\SubText Classification and discrimination; cluster
 analysis \SeeAlso{\SbjNo 68T10}\endx
\ThirdLvl 62H40\SubText Projection pursuit\endx
\ThirdLvl 62H99\SubText \NoneOfAbove\endx
\SecndLvl 62J++\SubText Linear inference, regression\endx
\ThirdLvl 62J02\SubText General nonlinear regression\endx
\ThirdLvl 62J05\SubText Linear regression\endx
\ThirdLvl 62J07\SubText Ridge regression; James-Stein estimators\endx
\ThirdLvl 62J10\SubText Analysis of variance and covariance\endx
\ThirdLvl 62J12\SubText Generalized linear models\endx
\ThirdLvl 62J15\SubText Paired and multiple comparisons\endx
\ThirdLvl 62J20\SubText Diagnostics\endx
\ThirdLvl 62J99\SubText \NoneOfAbove\endx
\SecndLvl 62K++\SubText Experimental design \SeeAlso{\SbjNo
 05Bxx}\endx
\ThirdLvl 62K05\SubText Optimal designs\endx
\ThirdLvl 62K10\SubText Block designs\endx
\ThirdLvl 62K15\SubText Factorial designs\endx
\ThirdLvl 62K99\SubText \NoneOfAbove\endx
\SecndLvl 62L++\SubText Sequential methods\endx
\ThirdLvl 62L05\SubText Sequential design\endx
\ThirdLvl 62L10\SubText Sequential analysis\endx
\ThirdLvl 62L12\SubText Sequential estimation\endx
\ThirdLvl 62L15\SubText Optimal stopping \SeeAlso{\SbjNo 60G40, \SbjNo
 90D60}\endx
\ThirdLvl 62L20\SubText Stochastic approximation\endx
\ThirdLvl 62L99\SubText \NoneOfAbove\endx
\SecndLvl 62M++\SubText Inference from stochastic processes\endx
\ThirdLvl 62M02\SubText Markov processes: hypothesis testing\endx
\ThirdLvl 62M05\SubText Markov processes: estimation\endx
\ThirdLvl 62M07\SubText Non-Markovian processes: hypothesis
 testing\endx
\ThirdLvl 62M09\SubText Non-Markovian processes: estimation\endx
\ThirdLvl 62M10\SubText Time series, auto-correlation, regression,
 etc. \SeeAlso{\SbjNo 90A20}\endx
\ThirdLvl 62M15\SubText Spectral analysis\endx
\ThirdLvl 62M20\SubText Prediction \SeeAlso{\SbjNo 60G25}; filtering
 \SeeAlso{\SbjNo 60G35, \SbjNo 93E10, \SbjNo 93E11}\endx
\ThirdLvl 62M30\SubText Spatial processes\endx
\ThirdLvl 62M40\SubText Random fields\endx
\ThirdLvl 62M99\SubText \NoneOfAbove\endx
\SecndLvl 62N++\SubText Engineering statistics\endx
\ThirdLvl 62N05\SubText Reliability and life testing \SeeAlso{\SbjNo
 90B25}\endx
\ThirdLvl 62N10\SubText Quality control\endx
\ThirdLvl 62N99\SubText \NoneOfAbove\endx
\SecndLvl 62P++\SubText Applications \SeeAlso{\SbjNo 90-XX, \SbjNo
 92-XX}\endx
\ThirdLvl 62P05\SubText Applications to actuarial sciences and
 financial mathematics\endx
\ThirdLvl 62P10\SubText Applications to biology\endx
\ThirdLvl 62P15\SubText Applications to psychology\endx
\ThirdLvl 62P20\SubText Applications to economics \SeeAlso{\SbjNo
 90Axx}\endx
\ThirdLvl 62P25\SubText Applications to social sciences\endx
\ThirdLvl 62P99\SubText \NoneOfAbove\endx
\SecndLvl 62Q05\SubText Statistical tables\endx
\MajorSub 65-++\SubText Numerical analysis\endx
\ThirdLvl 65-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 65-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 65-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 65-03\SubText \Historical\endx
\ThirdLvl 65-04\SubText \ExplicitComputation\endx
\ThirdLvl 65-05\SubText Experimental papers\endx
\ThirdLvl 65-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 65A05\SubText Tables\endx
\SecndLvl 65B++\SubText Acceleration of convergence\endx
\ThirdLvl 65B05\SubText Extrapolation to the limit, deferred
 corrections\endx
\ThirdLvl 65B10\SubText Summation of series\endx
\ThirdLvl 65B15\SubText Euler-Maclaurin formula\endx
\ThirdLvl 65B99\SubText \NoneOfAbove\endx
\SecndLvl 65C++\SubText Numerical simulation \SeeFor{For theoretical
 aspects, see \SbjNo 68U20}\endx
\ThirdLvl 65C05\SubText Monte Carlo methods\endx
\ThirdLvl 65C10\SubText Random number generation\endx
\ThirdLvl 65C20\SubText Models, numerical methods\endx
\ThirdLvl 65C99\SubText \NoneOfAbove\endx
\SecndLvl 65D++\SubText Numerical approximation \SeeFor{Primarily
 algorithms; for theory, see \SbjNo 41-XX}\endx
\ThirdLvl 65D05\SubText Interpolation\endx
\ThirdLvl 65D07\SubText Splines\endx
\ThirdLvl 65D10\SubText Smoothing, curve fitting\endx
\ThirdLvl 65D15\SubText Algorithms for functional approximation\endx
\ThirdLvl 65D17\SubText Computer aided design (modeling of curves and
 surfaces) \SeeAlso{\SbjNo 68U05}\endx
\ThirdLvl 65D20\SubText Computation of special functions, construction
 of tables\endx
\ThirdLvl 65D25\SubText Numerical differentiation\endx
\ThirdLvl 65D30\SubText Numerical integration\endx
\ThirdLvl 65D32\SubText Quadrature and cubature formulas\endx
\ThirdLvl 65D99\SubText \NoneOfAbove\endx
\SecndLvl 65E05\SubText Numerical methods in complex analysis
 (potential theory, etc.) \SeeFor{For numerical methods in conformal
 mapping, see \SbjNo 30C30}\endx
\SecndLvl 65F++\SubText Numerical linear algebra\endx
\ThirdLvl 65F05\SubText Direct methods for linear systems and matrix
 inversion\endx
\ThirdLvl 65F10\SubText Iterative methods for linear systems
 \SeeAlso{\SbjNo 65N22}\endx
\ThirdLvl 65F15\SubText Eigenvalues, eigenvectors\endx
\ThirdLvl 65F20\SubText Overdetermined systems, pseudoinverses\endx
\ThirdLvl 65F25\SubText Orthogonalization\endx
\ThirdLvl 65F30\SubText Other matrix algorithms\endx
\ThirdLvl 65F35\SubText Matrix norms, conditioning, scaling
 \SeeAlso{\SbjNo 15A12, \SbjNo 15A60}\endx
\ThirdLvl 65F40\SubText Determinants\endx
\ThirdLvl 65F50\SubText Sparse matrices\endx
\ThirdLvl 65F99\SubText \NoneOfAbove\endx
\SecndLvl 65G++\SubText Error analysis\endx
\ThirdLvl 65G05\SubText Roundoff error\endx
\ThirdLvl 65G10\SubText Interval and finite arithmetic\endx
\ThirdLvl 65G99\SubText \NoneOfAbove\endx
\SecndLvl 65H++\SubText Nonlinear algebraic or transcendental
 equations\endx
\ThirdLvl 65H05\SubText Single equations\endx
\ThirdLvl 65H10\SubText Systems of equations\endx
\ThirdLvl 65H17\SubText Eigenvalues, eigenvectors and bifurcation
 problems \SeeAlso{\SbjNo 58C40, \SbjNo 58E07, \SbjNo 58F14, \SbjNo
 90C30}\endx
\ThirdLvl 65H20\SubText Global methods, including homotopy approaches
 \SeeAlso{\SbjNo 58C30, \SbjNo 90C30}\endx
\ThirdLvl 65H99\SubText \NoneOfAbove\endx
\SecndLvl 65J++\SubText Numerical analysis in abstract spaces\endx
\ThirdLvl 65J05\SubText General theory\endx
\ThirdLvl 65J10\SubText Equations with linear operators (do not use
 \SbjNo 65Fxx)\endx
\ThirdLvl 65J15\SubText Equations with nonlinear operators (do not use
 \SbjNo 65Hxx)\endx
\ThirdLvl 65J20\SubText Improperly posed problems\endx
\ThirdLvl 65J99\SubText \NoneOfAbove\endx
\SecndLvl 65K++\SubText Mathematical programming, optimization and
 variational techniques \endx
\ThirdLvl 65K05\SubText Mathematical programming \SeeAlso{\SbjNo
 90Cxx}\endx
\ThirdLvl 65K10\SubText Optimization and variational techniques
 \SeeAlso{\SbjNo 49Mxx, \SbjNo 93B40}\endx
\ThirdLvl 65K99\SubText \NoneOfAbove\endx
\SecndLvl 65L++\SubText Ordinary differential equations\endx
\ThirdLvl 65L05\SubText Initial value problems\endx
\ThirdLvl 65L06\SubText Multistep, Runge-Kutta and extrapolation
 methods\endx
\ThirdLvl 65L07\SubText Numerical investigation of stability of
 solutions\endx
\ThirdLvl 65L08\SubText Improperly posed problems\endx
\ThirdLvl 65L10\SubText Boundary value problems\endx
\ThirdLvl 65L12\SubText Finite difference methods\endx
\ThirdLvl 65L15\SubText Eigenvalue problems\endx
\ThirdLvl 65L20\SubText Stability of numerical methods\endx
\ThirdLvl 65L50\SubText Mesh generation and refinement\endx
\ThirdLvl 65L60\SubText Finite elements, Rayleigh-Ritz, Galerkin and
 collocation methods\endx
\ThirdLvl 65L70\SubText Error bounds\endx
\ThirdLvl 65L99\SubText \NoneOfAbove\endx
\SecndLvl 65M++\SubText Partial differential equations, initial value
 and time-dependent initial-boundary value problems\endx
\ThirdLvl 65M06\SubText Finite difference methods\endx
\ThirdLvl 65M12\SubText Stability and convergence of numerical
 methods\endx
\ThirdLvl 65M15\SubText Error bounds\endx
\ThirdLvl 65M20\SubText Method of lines\endx
\ThirdLvl 65M25\SubText Method of characteristics\endx
\ThirdLvl 65M30\SubText Improperly posed problems\endx
\ThirdLvl 65M50\SubText Mesh generation and refinement\endx
\ThirdLvl 65M55\SubText Multigrid methods; domain decomposition\endx
\ThirdLvl 65M60\SubText Finite elements, Rayleigh-Ritz and Galerkin
 methods, finite methods\endx
\ThirdLvl 65M70\SubText Spectral, collocation and related methods\endx
\ThirdLvl 65M99\SubText \NoneOfAbove\endx
\SecndLvl 65N++\SubText Partial differential equations, boundary value
 problems\endx
\ThirdLvl 65N06\SubText Finite difference methods\endx
\ThirdLvl 65N12\SubText Stability and convergence of numerical
 methods\endx
\ThirdLvl 65N15\SubText Error bounds\endx
\ThirdLvl 65N22\SubText Solution of discretized equations
 \SeeAlso{\SbjNo 65Fxx, \SbjNo 65Hxx}\endx
\ThirdLvl 65N25\SubText Eigenvalue problems\endx
\ThirdLvl 65N30\SubText Finite elements, Rayleigh-Ritz and Galerkin
 methods, finite methods\endx
\ThirdLvl 65N35\SubText Spectral, collocation and related methods\endx
\ThirdLvl 65N38\SubText Boundary element methods\endx
\ThirdLvl 65N40\SubText Method of lines\endx
\ThirdLvl 65N45\SubText Method of contraction of the boundary\endx
\ThirdLvl 65N50\SubText Mesh generation and refinement\endx
\ThirdLvl 65N55\SubText Multigrid methods; domain decomposition\endx
\ThirdLvl 65N99\SubText \NoneOfAbove\endx
\SecndLvl 65P05\SubText Partial differential equations, miscellaneous
 problems\endx
\SecndLvl 65Q05\SubText Difference and functional equations,
 recurrence relations\endx
\SecndLvl 65R++\SubText Integral equations, integral transforms
 \SeeAlso{\SbjNo 45Lxx}\endx
\ThirdLvl 65R10\SubText Integral transforms\endx
\ThirdLvl 65R20\SubText Integral equations\endx
\ThirdLvl 65R30\SubText Improperly posed problems\endx
\ThirdLvl 65R99\SubText \NoneOfAbove\endx
\SecndLvl 65S05\SubText Graphical methods\endx
\SecndLvl 65T++\SubText Numerical methods in Fourier analysis\endx
\ThirdLvl 65T10\SubText Trigonometric approximation and
 interpolation\endx
\ThirdLvl 65T20\SubText Discrete and fast Fourier transforms\endx
\ThirdLvl 65T99\SubText \NoneOfAbove\endx
\SecndLvl 65U05\SubText Numerical methods in probability and
 statistics\endx
\SecndLvl 65Y++\SubText Computer aspects of numerical algorithms\endx
\ThirdLvl 65Y05\SubText Parallel computation\endx
\ThirdLvl 65Y10\SubText Algorithms for specific classes of
 architectures\endx
\ThirdLvl 65Y15\SubText Packaged methods\endx
\ThirdLvl 65Y20\SubText Complexity and performance of numerical
 algorithms \SeeAlso{\SbjNo 68Q25}\endx
\ThirdLvl 65Y25\SubText Computer graphics and computational geometry
 \SeeAlso{\SbjNo 51N05, \SbjNo 68U05}\endx
\ThirdLvl 65Y99\SubText \NoneOfAbove\endx
\MajorSub 68-++\SubText Computer science \SeeFor{For papers involving
 machine computations and programs in a specific mathematical area,
 see \FullScheme{Section --04 in} that area}\endx
\ThirdLvl 68-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 68-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 68-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 68-03\SubText \Historical\endx
\ThirdLvl 68-04\SubText \ExplicitComputation\endx
\ThirdLvl 68-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 68M++\SubText Computer system organization\endx
\ThirdLvl 68M05\SubText General\endx
\ThirdLvl 68M07\SubText Mathematical problems of computer
 architecture\endx
\ThirdLvl 68M10\SubText Computer networks \SeeAlso{\SbjNo 90B12}\endx
\ThirdLvl 68M15\SubText Reliability and testing\endx
\ThirdLvl 68M20\SubText Performance evaluation; queueing; scheduling
 \SeeAlso{\SbjNo 60K25, \SbjNo 90Bxx}\endx
\ThirdLvl 68M99\SubText \NoneOfAbove\endx
\SecndLvl 68N++\SubText Software\endx
\ThirdLvl 68N05\SubText General theory of programming\endx
\ThirdLvl 68N15\SubText Programming languages\endx
\ThirdLvl 68N17\SubText Logic programming\endx
\ThirdLvl 68N20\SubText Compilers and generators \SeeAlso{\SbjNo
 68Q52}\endx
\ThirdLvl 68N25\SubText Monitors and operating systems\endx
\ThirdLvl 68N99\SubText	\NoneOfAbove\endx
\SecndLvl 68P++\SubText Theory of data\endx
\ThirdLvl 68P05\SubText Data structures\endx
\ThirdLvl 68P10\SubText Searching and sorting\endx
\ThirdLvl 68P15\SubText Database theory\endx
\ThirdLvl 68P20\SubText Information storage and retrieval\endx
\ThirdLvl 68P25\SubText Data encryption \SeeAlso{\SbjNo 94A60}\endx
\ThirdLvl 68P99\SubText \NoneOfAbove\endx
\SecndLvl 68Q++\SubText Theory of computing\endx
\ThirdLvl 68Q05\SubText Models of computation (abstract processors,
 Turing machines, etc.) \SeeAlso{\SbjNo 03D10}\endx
\ThirdLvl 68Q10\SubText Modes of computation (concurrent, parallel,
 nondeterministic, etc.) \SeeAlso{\SbjNo 68Q90}\endx
\ThirdLvl 68Q15\SubText Complexity classes \SeeAlso{\SbjNo 03D15}\endx
\ThirdLvl 68Q20\SubText Nonnumerical algorithms \SeeFor{For numerical
 algorithms, see \SbjNo 65-XX; for combinatorics and graph theory, see
 \SbjNo 68Rxx}\endx
\ThirdLvl 68Q22\SubText Parallel and distributed algorithms
 \SeeFor{For numerical algorithms, see \SbjNo 65Y05, \SbjNo
 68Y10}\endx
\ThirdLvl 68Q25\SubText Analysis of algorithms and problem
 complexity\endx
\ThirdLvl 68Q30\SubText Algorithmic information theory (Kolmogorov
 complexity, etc.)\endx
\ThirdLvl 68Q35\SubText VLSI algorithms\endx
\ThirdLvl 68Q40\SubText Symbolic computation, algebraic computation
 \SeeAlso{\SbjNo 11Yxx, \SbjNo 12Y05, \SbjNo 13Pxx, \SbjNo 14Qxx,
 \SbjNo 16-08, \SbjNo 17-08}\endx
\ThirdLvl 68Q42\SubText Rewriting systems \endx
\ThirdLvl 68Q45\SubText Formal languages \SeeAlso{\SbjNo 03D05, \SbjNo
 20M35, \SbjNo 94A45}\endx
\ThirdLvl 68Q50\SubText Grammars \SeeAlso{\SbjNo 03D05}\endx
\ThirdLvl 68Q52\SubText Parsing \SeeAlso{\SbjNo 68N20}\endx
\ThirdLvl 68Q55\SubText Semantics \SeeAlso{\SbjNo 03B70, \SbjNo
 06B35}\endx
\ThirdLvl 68Q60\SubText Specification and verification of programs
 \SeeAlso{\SbjNo 03B70}\endx
\ThirdLvl 68Q65\SubText Abstract data types; algebraic
 specification\endx
\ThirdLvl 68Q68\SubText Automata theory, general \SeeAlso{\SbjNo
 03D05}\endx
\ThirdLvl 68Q70\SubText Algebraic theory of automata \SeeAlso{\SbjNo
 18B20, \SbjNo 20M35}\endx
\ThirdLvl 68Q75\SubText Stochastic and nondeterministic automata\endx
\ThirdLvl 68Q80\SubText Tessellation automata, iterative arrays,
 cellular structures\endx
\ThirdLvl 68Q90\SubText Transition nets\endx
\ThirdLvl 68Q99\SubText \NoneOfAbove\endx
\SecndLvl 68R++\SubText Discrete mathematics in relation to computer
 science\endx
\ThirdLvl 68R05\SubText Combinatorics\endx
\ThirdLvl 68R10\SubText Graph theory \SeeAlso{\SbjNo 05Cxx, \SbjNo
 90B10, \SbjNo 90B35, \SbjNo 90C35}\endx
\ThirdLvl 68R15\SubText Combinatorics on words\endx
\ThirdLvl 68R99\SubText \NoneOfAbove\endx
\SecndLvl 68S05\SubText Mathematical linguistics \SeeAlso{\SbjNo
 03B65, \SbjNo 92K20}\endx
\SecndLvl 68T++\SubText Artificial intelligence \SeeAlso{\SbjNo
 92J40}\endx
\ThirdLvl 68T01\SubText General\endx
\ThirdLvl 68T05\SubText Learning and adaptive systems\endx
\ThirdLvl 68T10\SubText Pattern recognition, speech recognition
 \SeeFor{For cluster analysis, see \SbjNo 62H30}\endx
\ThirdLvl 68T15\SubText Theorem proving \SeeAlso{\SbjNo 03B35}\endx
\ThirdLvl 68T20\SubText Problem solving\endx
\ThirdLvl 68T25\SubText AI languages\endx
\ThirdLvl 68T27\SubText AI logics\endx
\ThirdLvl 68T30\SubText Knowledge representation\endx
\ThirdLvl 68T35\SubText AI software systems (knowledge-based systems,
 expert systems, etc.)\endx
\ThirdLvl 68T99\SubText \NoneOfAbove\endx
\SecndLvl 68U++\SubText Computing methodologies\endx
\ThirdLvl 68U05\SubText Computer graphics; computational geometry
 \SeeAlso{\SbjNo 65Y25}\endx
\ThirdLvl 68U07\SubText Computer-aided design\endx
\ThirdLvl 68U10\SubText Image processing\endx
\ThirdLvl 68U15\SubText Text processing; mathematical typography \endx
\ThirdLvl 68U20\SubText Simulation \SeeAlso{\SbjNo 65Cxx}\endx
\ThirdLvl 68U30\SubText Other applications\endx
\ThirdLvl 68U99\SubText \NoneOfAbove\endx
\MajorSub 70-++\SubText Mechanics of particles and systems \SeeFor{For
 relativistic mechanics, see~\CMPonly{\SbjNo 83-XX}\FullScheme{\SbjNo
 83A05 and \SbjNo 83C10}; for statistical mechanics, see~\SbjNo
 82-XX}\endx
\ThirdLvl 70-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 70-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 70-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 70-03\SubText \Historical\endx
\ThirdLvl 70-04\SubText \ExplicitComputation\endx
\ThirdLvl 70-05\SubText Experimental papers\endx
\ThirdLvl 70-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 70-08\SubText Computational methods\endx
\SecndLvl 70A05\SubText Axiomatics, foundations\endx
\SecndLvl 70B++\SubText Kinematics \SeeAlso{\SbjNo 53A17}\endx
\ThirdLvl 70B05\SubText Kinematics of a particle\endx
\ThirdLvl 70B10\SubText Kinematics of a rigid body\endx
\ThirdLvl 70B15\SubText Mechanisms, robots \SeeAlso{\SbjNo 73K05}\endx
\ThirdLvl 70B99\SubText \NoneOfAbove\endx
\SecndLvl 70C20\SubText Statics\endx
\SecndLvl 70D++\SubText Dynamics of a particle \SeeAlso{\SbjNo
 70Hxx}\endx
\ThirdLvl 70D05\SubText Newtonian dynamics\endx
\ThirdLvl 70D10\SubText Lagrangian dynamics\endx
\ThirdLvl 70D99\SubText \NoneOfAbove\endx
\SecndLvl 70E++\SubText Dynamics of a rigid body\endx
\ThirdLvl 70E05\SubText Motion of the gyroscope\endx
\ThirdLvl 70E10\SubText Motion of projectiles and rockets\endx
\ThirdLvl 70E15\SubText Motion of rigid bodies\endx
\ThirdLvl 70E20\SubText Perturbation methods for Euler's
 equations\endx
\ThirdLvl 70E99\SubText \NoneOfAbove\endx
\SecndLvl 70F++\SubText Dynamics of a system of particles, including
 celestial mechanics\endx
\ThirdLvl 70F05\SubText Two-body problem\endx
\ThirdLvl 70F07\SubText Three-body problem\endx
\ThirdLvl 70F10\SubText $n$-body problem\endx
\ThirdLvl 70F15\SubText Celestial mechanics\endx
\ThirdLvl 70F20\SubText Holonomic systems\endx
\ThirdLvl 70F25\SubText Nonholonomic systems\endx
\ThirdLvl 70F30\SubText Impulsive motion\endx
\ThirdLvl 70F35\SubText Collisions\endx
\ThirdLvl 70F99\SubText \NoneOfAbove\endx
\SecndLvl 70G++\SubText General representations of dynamical systems
 \SeeAlso{\SbjNo 58Fxx}\endx
\ThirdLvl 70G05\SubText Riemannian geometry, tensorial methods
 \SeeAlso{\SbjNo 53A45, \SbjNo 53A50, \SbjNo 53B20}\endx
\ThirdLvl 70G10\SubText Generalized coordinates\endx
\ThirdLvl 70G15\SubText Space of events\endx
\ThirdLvl 70G20\SubText Impulse-energy space\endx
\ThirdLvl 70G25\SubText Configuration space\endx
\ThirdLvl 70G30\SubText State space\endx
\ThirdLvl 70G35\SubText Phase space\endx
\ThirdLvl 70G50\SubText Classical field theories (general)\endx
\ThirdLvl 70G99\SubText \NoneOfAbove\endx
\SecndLvl 70H++\SubText Hamiltonian and Lagrangian mechanics
 \SeeAlso{\SbjNo 58F05}\endx
\ThirdLvl 70H05\SubText Hamilton's equations\endx
\ThirdLvl 70H10\SubText Liouville's theorem\endx
\ThirdLvl 70H15\SubText Canonical transformations\endx
\ThirdLvl 70H20\SubText Hamilton-Jacobi equations\endx
\ThirdLvl 70H25\SubText Hamilton's principle\endx
\ThirdLvl 70H30\SubText Other variational principles\endx
\ThirdLvl 70H33\SubText Symmetries\endx
\ThirdLvl 70H35\SubText Lagrange's equation of motion\endx
\ThirdLvl 70H40\SubText Relativistic dynamics\endx
\ThirdLvl 70H99\SubText \NoneOfAbove\endx
\SecndLvl 70J++\SubText Linear vibration theory \SeeAlso{\SbjNo
 73D30}\endx
\ThirdLvl 70J05\SubText Finite degree of freedom systems\endx
\ThirdLvl 70J10\SubText Modal analysis\endx
\ThirdLvl 70J25\SubText Stability\endx
\ThirdLvl 70J30\SubText Free motions\endx
\ThirdLvl 70J35\SubText Forced motions\endx
\ThirdLvl 70J40\SubText Parametric resonances\endx
\ThirdLvl 70J99\SubText \NoneOfAbove\endx
\SecndLvl 70K++\SubText Nonlinear motions \SeeAlso{\SbjNo 34Cxx,
 \SbjNo 58Fxx, \SbjNo 73D35, \SbjNo 73K12}\endx
\ThirdLvl 70K05\SubText Phase plane analysis\endx
\ThirdLvl 70K10\SubText Limit cycles\endx
\ThirdLvl 70K15\SubText Lyapunov theorems\endx
\ThirdLvl 70K20\SubText Stability\endx
\ThirdLvl 70K25\SubText Free motions\endx
\ThirdLvl 70K28\SubText Parametric resonances\endx
\ThirdLvl 70K30\SubText Nonlinear resonances\endx
\ThirdLvl 70K40\SubText Forced motions\endx
\ThirdLvl 70K50\SubText Transition to stochasticity (chaotic behavior)
 \SeeAlso{\SbjNo 58F13}\endx
\ThirdLvl 70K99\SubText \NoneOfAbove\endx
\SecndLvl 70L05\SubText Random vibrations \SeeAlso{\SbjNo 73K35,
 \SbjNo 93Exx}\endx
\SecndLvl 70M20\SubText Orbital mechanics\endx
\SecndLvl 70P05\SubText Variable mass, rockets\endx
\SecndLvl 70Q05\SubText Control of mechanical systems \SeeAlso{\SbjNo
 49-XX, \SbjNo 73K50, \SbjNo 93Cxx, \SbjNo 93Dxx}\endx
\MajorSub 73-++\SubText Mechanics of solids\endx
\ThirdLvl 73-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 73-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 73-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 73-03\SubText \Historical\endx
\ThirdLvl 73-04\SubText \ExplicitComputation\endx
\ThirdLvl 73-05\SubText Experimental papers\endx
\ThirdLvl 73-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 73A05\SubText Axiomatics, foundations of solid
 mechanics\endx
\SecndLvl 73B++\SubText Continuum mechanics of solids (constitutive
 description and properties)\endx
\ThirdLvl 73B05\SubText Constitutive equations\endx
\ThirdLvl 73B10\SubText Symmetry groups\endx
\ThirdLvl 73B18\SubText Nonlocal theories\endx
\ThirdLvl 73B25\SubText Polar theories\endx
\ThirdLvl 73B27\SubText Nonhomogeneous materials; homogenization\endx
\ThirdLvl 73B30\SubText Thermodynamics of solids \SeeFor{For gases and
 fluids, see \SbjNo 80-XX}\endx
\ThirdLvl 73B35\SubText Random materials\endx
\ThirdLvl 73B40\SubText Anisotropic materials\endx
\ThirdLvl 73B50\SubText Stress concentrations\endx
\ThirdLvl 73B99\SubText \NoneOfAbove\endx
\SecndLvl 73C++\SubText Elasticity \SeeFor{For the biharmonic
 equation, see~\SbjNo 31A30, \SbjNo 31B30}\endx
\ThirdLvl 73C02\SubText Classical linear elasticity\endx
\ThirdLvl 73C05\SubText Stress functions\endx
\ThirdLvl 73C10\SubText Saint-Venant's principle\endx
\ThirdLvl 73C15\SubText Uniqueness theorems\endx
\ThirdLvl 73C35\SubText Mixed boundary value problems \SeeAlso{\SbjNo
 45F05}\endx
\ThirdLvl 73C50\SubText Nonlinear elasticity\endx
\ThirdLvl 73C99\SubText \NoneOfAbove\endx
\SecndLvl 73D++\SubText Wave propagation in and vibrations of
 solids\endx
\ThirdLvl 73D05\SubText Impact and explosion problems \SeeAlso{\SbjNo
 76L05}\endx
\ThirdLvl 73D10\SubText Integral transforms\endx
\ThirdLvl 73D15\SubText Body waves\endx
\ThirdLvl 73D20\SubText Surface waves\endx
\ThirdLvl 73D25\SubText Wave diffraction and dispersion\endx
\ThirdLvl 73D30\SubText Linear vibrations \SeeAlso{\SbjNo 70Jxx}\endx
\ThirdLvl 73D35\SubText Nonlinear vibrations \SeeAlso{\SbjNo
 70Kxx}\endx
\ThirdLvl 73D40\SubText Singular surfaces\endx
\ThirdLvl 73D50\SubText Inverse problems \SeeAlso{\SbjNo 35Lxx, \SbjNo
 35R30}\endx
\ThirdLvl 73D70\SubText Random waves\endx
\ThirdLvl 73D99\SubText \NoneOfAbove\endx
\SecndLvl 73E++\SubText Plasticity\endx
\ThirdLvl 73E05\SubText Constitutive specifications (yield criteria,
 flow rules, hardening, softening)\endx
\ThirdLvl 73E10\SubText Method of successive approximations\endx
\ThirdLvl 73E20\SubText Limit analysis\endx
\ThirdLvl 73E50\SubText Time-dependent problems\endx
\ThirdLvl 73E60\SubText Viscoplasticity\endx
\ThirdLvl 73E70\SubText Plastic waves\endx
\ThirdLvl 73E99\SubText \NoneOfAbove\endx
\SecndLvl 73F++\SubText Viscoelasticity\endx
\ThirdLvl 73F05\SubText Creep and relaxation functions\endx
\ThirdLvl 73F10\SubText Correspondence principle\endx
\ThirdLvl 73F15\SubText Time-dependent problems\endx
\ThirdLvl 73F20\SubText Aging of materials\endx
\ThirdLvl 73F25\SubText Environmental-dependent materials\endx
\ThirdLvl 73F99\SubText \NoneOfAbove\endx
\SecndLvl 73G++\SubText Finite deformations\endx
\ThirdLvl 73G05\SubText Finite elasticity\endx
\ThirdLvl 73G20\SubText Finite plasticity\endx
\ThirdLvl 73G25\SubText Finite viscoelasticity\endx
\ThirdLvl 73G99\SubText \NoneOfAbove\endx
\SecndLvl 73H++\SubText Stability (linear and nonlinear)\endx
\ThirdLvl 73H05\SubText Buckling\endx
\ThirdLvl 73H10\SubText Dynamic stability\endx
\ThirdLvl 73H99\SubText \NoneOfAbove\endx
\SecndLvl 73K++\SubText Mechanics of structures\endx
\ThirdLvl 73K03\SubText Strings\endx
\ThirdLvl 73K05\SubText Beams, columns, rods\endx
\ThirdLvl 73K10\SubText Plates, discs, membranes\endx
\ThirdLvl 73K12\SubText Dynamics of structures\endx
\ThirdLvl 73K15\SubText Shells\endx
\ThirdLvl 73K20\SubText Composite structures and materials\endx
\ThirdLvl 73K35\SubText Random vibrations\endx
\ThirdLvl 73K40\SubText Optimization \SeeAlso{\SbjNo 90C90}\endx
\ThirdLvl 73K50\SubText Control of structures\endx
\ThirdLvl 73K70\SubText Aero- or hydromechanic structure
 interactions\endx
\ThirdLvl 73K99\SubText \NoneOfAbove\endx
\SecndLvl 73M25\SubText Fracture mechanics\endx
\SecndLvl 73N20\SubText Geophysical solid mechanics \SeeAlso{\SbjNo
 86A15, \SbjNo 86A17}\endx
\SecndLvl 73P05\SubText Biomechanics of solids \SeeAlso{\SbjNo
 92C10}\endx
\SecndLvl 73Q05\SubText Soil and rock mechanics \SeeAlso{\SbjNo
 86A60}\endx
\SecndLvl 73R05\SubText Electromagnetic elasticity\endx
\SecndLvl 73S10\SubText Micromechanics of solids\endx
\SecndLvl 73T05\SubText Contact and surface mechanics\endx
\SecndLvl 73V++\SubText Basic methods in solid mechanics
 \SeeAlso{\SbjNo 65-xx}\endx
\ThirdLvl 73V05\SubText Finite element methods\endx
\ThirdLvl 73V10\SubText Boundary element methods\endx
\ThirdLvl 73V15\SubText Finite difference methods\endx
\ThirdLvl 73V20\SubText Other numerical methods\endx
\ThirdLvl 73V25\SubText Variational methods\endx
\ThirdLvl 73V30\SubText Stochastic analysis\endx
\ThirdLvl 73V35\SubText Complex variable techniques\endx
\ThirdLvl 73V99\SubText \NoneOfAbove\endx
\MajorSub 76-++\SubText Fluid mechanics \SeeFor{For general continuum
 mechanics, see~\SbjNo 73Bxx, or other parts of~\SbjNo 73-XX}\endx
\ThirdLvl 76-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 76-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 76-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 76-03\SubText \Historical\endx
\ThirdLvl 76-04\SubText \ExplicitComputation\endx
\ThirdLvl 76-05\SubText Experimental papers\endx
\ThirdLvl 76-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 76A++\SubText Foundations, constitutive equations, rheology
 \endx
\ThirdLvl 76A02\SubText Foundations of fluid mechanics\endx
\ThirdLvl 76A05\SubText Non-Newtonian fluids\endx
\ThirdLvl 76A10\SubText Viscoelastic fluids\endx
\ThirdLvl 76A15\SubText Liquid crystals \SeeAlso{\SbjNo 82D30}\endx
\ThirdLvl 76A99\SubText \NoneOfAbove\endx
\SecndLvl 76B++\SubText Incompressible inviscid fluids, potential
 theory\endx
\ThirdLvl 76B05\SubText Airfoil theory\endx
\ThirdLvl 76B10\SubText Jets and cavities, cavitation, free-streamline
 theory, water-entry problems, hydrofoil theory, sloshing\endx
\ThirdLvl 76B15\SubText Water waves, gravity waves; dispersion and
 diffraction, nonlinear interaction \SeeAlso{\SbjNo 35Q53}\endx
\ThirdLvl 76B20\SubText Ship waves\endx
\ThirdLvl 76B25\SubText Solitary and cnoidal waves \SeeAlso{\SbjNo
 35Q51}\endx
\ThirdLvl 76B35\SubText Random waves, inviscid fluids\endx
\ThirdLvl 76B40\SubText Added mass computations\endx
\ThirdLvl 76B45\SubText Capillarity\endx
\ThirdLvl 76B99\SubText \NoneOfAbove\endx
\SecndLvl 76C++\SubText Incompressible inviscid fluids, vorticity
 flows\endx
\ThirdLvl 76C05\SubText Vorticity flows\endx
\ThirdLvl 76C10\SubText Internal waves\endx
\ThirdLvl 76C15\SubText Atmospheric waves\endx
\ThirdLvl 76C20\SubText Rossby waves\endx
\ThirdLvl 76C99\SubText \NoneOfAbove\endx
\SecndLvl 76D++\SubText Incompressible viscous fluids\endx
\ThirdLvl 76D05\SubText Navier-Stokes equations \SeeAlso{\SbjNo
 35Q30}\endx
\ThirdLvl 76D07\SubText Stokes flows\endx
\ThirdLvl 76D08\SubText Lubrication theory\endx
\ThirdLvl 76D10\SubText Boundary-layer theory\endx
\ThirdLvl 76D15\SubText Boundary-layer separation and
 reattachment\endx
\ThirdLvl 76D20\SubText Higher-order effects in boundary layers\endx
\ThirdLvl 76D25\SubText Wakes and jets\endx
\ThirdLvl 76D30\SubText Singular perturbation problems\endx
\ThirdLvl 76D33\SubText Waves\endx
\ThirdLvl 76D35\SubText Random waves, viscous fluids\endx
\ThirdLvl 76D45\SubText Capillarity \SeeAlso{\SbjNo 76B45}\endx
\ThirdLvl 76D99\SubText \NoneOfAbove\endx
\SecndLvl 76E++\SubText Hydrodynamic stability\endx
\ThirdLvl 76E05\SubText Stability of parallel flows\endx
\ThirdLvl 76E10\SubText Inertial instability\endx
\ThirdLvl 76E15\SubText Convective instability\endx
\ThirdLvl 76E20\SubText Instability of geophysical and astrophysical
 flows\endx
\ThirdLvl 76E25\SubText Magnetohydrodynamic and electrohydrodynamic
 instabilities\endx
\ThirdLvl 76E30\SubText Nonlinear effects\endx
\ThirdLvl 76E99\SubText \NoneOfAbove\endx
\SecndLvl 76F++\SubText Turbulence \SeeAlso{\CMPonly{\SbjNo
 58Fxx}\FullScheme{\SbjNo 58F13, \SbjNo 58F27}, \SbjNo 60Gxx, \SbjNo
 60Jxx}\endx
\ThirdLvl 76F05\SubText Homogeneous isotropic turbulence\endx
\ThirdLvl 76F10\SubText Shear flows\endx
\ThirdLvl 76F20\SubText Turbulence via chaos techniques\endx
\ThirdLvl 76F99\SubText \NoneOfAbove\endx
\SecndLvl 76G25\SubText General aerodynamics and subsonic flows\endx
\SecndLvl 76H05\SubText Transonic flows\endx
\SecndLvl 76J20\SubText Supersonic flows\endx
\SecndLvl 76K05\SubText Hypersonic flows\endx
\SecndLvl 76L05\SubText Shock waves and blast waves \SeeAlso{\SbjNo
 35L67, \SbjNo 73D05}\endx
\SecndLvl 76M++\SubText Basic methods in fluid mechanics
 \SeeAlso{\SbjNo 65-XX}\endx
\ThirdLvl 76M10\SubText Finite element methods \endx
\ThirdLvl 76M15\SubText Boundary element methods\endx
\ThirdLvl 76M20\SubText Finite difference methods\endx
\ThirdLvl 76M25\SubText Other numerical methods\endx
\ThirdLvl 76M30\SubText Variational methods\endx
\ThirdLvl 76M35\SubText Stochastic analysis\endx
\ThirdLvl 76M99\SubText \NoneOfAbove\endx
\SecndLvl 76N++\SubText Compressible fluids and gas dynamics,
 general\endx
\ThirdLvl 76N10\SubText Compressible fluids, general \SeeAlso{\SbjNo
 35Q30}\endx
\ThirdLvl 76N15\SubText Gas dynamics, general\endx
\ThirdLvl 76N20\SubText Boundary-layer theory\endx
\ThirdLvl 76N99\SubText \NoneOfAbove\endx
\SecndLvl 76P05\SubText Rarefied gas flows, Boltzmann equation
 \SeeAlso{\SbjNo 82B40, \SbjNo 82C40, \SbjNo 82D05}\endx
\SecndLvl 76Q05\SubText Hydrodynamic sound, acoustics\endx
\SecndLvl 76R++\SubText Diffusion and convection \endx
\ThirdLvl 76R05\SubText Forced convection\endx
\ThirdLvl 76R10\SubText Free convection\endx
\ThirdLvl 76R50\SubText Diffusion \SeeAlso{\SbjNo 60J60}\endx
\ThirdLvl 76R99\SubText \NoneOfAbove\endx
\SecndLvl 76S05\SubText Flows in porous media; filtration;
 seepage\endx
\SecndLvl 76T05\SubText Two-phase and multiphase flows\endx
\SecndLvl 76U05\SubText Rotating fluids\endx
\SecndLvl 76V05\SubText Stratified and reacting fluids\endx
\SecndLvl 76W05\SubText Magnetohydrodynamics and
 electrohydrodynamics\endx
\SecndLvl 76X05\SubText Ionized gas flow in electromagnetic fields;
 plasmic flow\endx
\SecndLvl 76Y05\SubText Quantum hydrodynamics and relativistic
 hydrodynamics \SeeAlso{\SbjNo 83C55, \SbjNo 85A30}\endx
\SecndLvl 76Z++\SubText Biological fluid mechanics \SeeAlso{\SbjNo
 92Cxx}\endx
\ThirdLvl 76Z05\SubText Physiological flows \SeeAlso{\SbjNo
 92C35}\endx
\ThirdLvl 76Z10\SubText Biopropulsion in water and in air\endx
\ThirdLvl 76Z99\SubText \NoneOfAbove\endx
\MajorSub 78-++\SubText Optics, electromagnetic theory \SeeFor{For
 quantum optics, see~\SbjNo 81V80}\endx
\ThirdLvl 78-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 78-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 78-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 78-03\SubText \Historical\endx
\ThirdLvl 78-04\SubText \ExplicitComputation\endx
\ThirdLvl 78-05\SubText Experimental papers\endx
\ThirdLvl 78-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 78-08\SubText Computational methods\endx
\ThirdLvl 78A02\SubText Foundations\endx
\ThirdLvl 78A05\SubText Geometric optics\endx
\ThirdLvl 78A10\SubText Physical optics\endx
\ThirdLvl 78A15\SubText Electron optics\endx
\ThirdLvl 78A20\SubText Space charge waves\endx
\ThirdLvl 78A25\SubText Electromagnetic theory, general\endx
\ThirdLvl 78A30\SubText Electro- and magnetostatics\endx
\ThirdLvl 78A35\SubText Motion of charged particles\endx
\ThirdLvl 78A40\SubText Waves and radiation\endx
\ThirdLvl 78A45\SubText Diffraction, scattering \SeeAlso{\SbjNo 34E20
 for WKB methods}\endx
\ThirdLvl 78A50\SubText Antennas, wave-guides\endx
\ThirdLvl 78A55\SubText Technical applications\endx
\ThirdLvl 78A60\SubText Lasers, masers, optical bistability, nonlinear
 optics \SeeAlso{\SbjNo 81V80}\endx
\ThirdLvl 78A70\SubText Biological applications \SeeAlso{\SbjNo 92C30,
 \SbjNo 92J30}\endx
\ThirdLvl 78A97\SubText Mathematically heuristic optics and
 electromagnetic theory (must also be assigned at least one other
 classification number in this section)\endx
\ThirdLvl 78A99\SubText \Miscellaneous\endx
\MajorSub 80-++\SubText Classical thermodynamics, heat transfer
 \SeeFor{For thermodynamics of solids, see~\SbjNo 73B30}\endx
\ThirdLvl 80-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 80-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 80-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 80-03\SubText \Historical\endx
\ThirdLvl 80-04\SubText \ExplicitComputation\endx
\ThirdLvl 80-05\SubText Experimental papers\endx
\ThirdLvl 80-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 80-08\SubText Computational methods\endx
\ThirdLvl 80A05\SubText Foundations\endx
\ThirdLvl 80A10\SubText Classical thermodynamics\endx
\ThirdLvl 80A15\SubText Thermodynamics of mixtures\endx
\ThirdLvl 80A20\SubText Heat and mass transfer, heat flow\endx
\ThirdLvl 80A22\SubText Stefan problems, phase changes, etc.\endx
\ThirdLvl 80A23\SubText Inverse problems\endx
\ThirdLvl 80A25\SubText Combustion, interior ballistics\endx
\ThirdLvl 80A30\SubText Chemical kinetics \SeeAlso{\SbjNo 92C45,
 \SbjNo 92E20}\endx
\ThirdLvl 80A32\SubText Chemically reacting flows \SeeAlso{\SbjNo
 92C45, \SbjNo 92E20}\endx
\ThirdLvl 80A50\SubText Chemistry (general) \SeeMainly{\SbjNo
 92Exx}\endx
\ThirdLvl 80A97\SubText Mathematically heuristic classical
 thermodynamics (must also be assigned at least one other
 classification number in this section)\endx
\ThirdLvl 80A99\SubText \Miscellaneous\endx
\MajorSub 81-++\SubText Quantum Theory\endx
\ThirdLvl 81-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 81-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 81-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 81-03\SubText \Historical\endx
\ThirdLvl 81-04\SubText \ExplicitComputation\endx
\ThirdLvl 81-05\SubText Experimental papers\endx
\ThirdLvl 81-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 81-08\SubText Computational methods\endx
\SecndLvl 81P++\SubText Axiomatics, foundations, philosophy\endx
\ThirdLvl 81P05\SubText General and philosophical\endx
\ThirdLvl 81P10\SubText Logical foundations of quantum mechanics\endx
\ThirdLvl 81P15\SubText Quantum measurement theory\endx
\ThirdLvl 81P20\SubText Stochastic mechanics (including stochastic
 electrodynamics)\endx
\ThirdLvl 81P99\SubText \NoneOfAbove\endx
\SecndLvl 81Q++\SubText General mathematical topics and methods in
 quantum theory\endx
\ThirdLvl 81Q05\SubText Closed and approximate solutions to the
 Schr\"odinger, Dirac, Klein-Gordon and other quantum-mechanical
 equations\endx
\ThirdLvl 81Q10\SubText Selfadjoint operator theory in quantum theory,
 including spectral analysis\endx
\ThirdLvl 81Q15\SubText Perturbation theories for operators and
 differential equations\endx
\ThirdLvl 81Q20\SubText Semiclassical techniques including WKB and
 Maslov methods\endx
\ThirdLvl 81Q30\SubText Feynman integrals and graphs; applications of
 algebraic topology and algebraic geometry \SeeAlso{\SbjNo 14D05,
 \SbjNo 32S40}\endx
\ThirdLvl 81Q40\SubText Bethe-Salpeter and other integral
 equations\endx
\ThirdLvl 81Q50\SubText Quantum chaos \SeeAlso{\SbjNo 58F13}\endx
\ThirdLvl 81Q60\SubText Supersymmetric quantum mechanics\endx
\ThirdLvl 81Q99\SubText \NoneOfAbove\endx
\SecndLvl 81R++\SubText Groups and algebras in quantum theory\endx
\ThirdLvl 81R05\SubText Representations of finite-dimensional groups
 and algebras motivated by physics \SeeAlso{\SbjNo 20C35, \SbjNo
 22E70}\endx
\ThirdLvl 81R10\SubText Representations of infinite-dimensional groups
 and algebras motivated by physics, including Virasoro, Kac-Moody and
 other current algebras \SeeAlso{\SbjNo 17B65, \SbjNo 17B67, \SbjNo
 22E65, \SbjNo 22E67, \SbjNo 22E70}\endx
\ThirdLvl 81R20\SubText Covariant wave equations\endx
\ThirdLvl 81R25\SubText Spinor and twistor methods \SeeAlso{\SbjNo
 32L25}\endx
\ThirdLvl 81R30\SubText Coherent states \SeeAlso{\SbjNo 22E45}\endx
\ThirdLvl 81R40\SubText Symmetry breaking\endx
\ThirdLvl 81R50\SubText Quantum groups and related algebraic methods
 \SeeAlso{\SbjNo 16W30, \SbjNo 17B37}\endx
\ThirdLvl 81R99\SubText \NoneOfAbove\endx
\SecndLvl 81S++\SubText General quantum mechanics and problems of
 quantization\endx
\ThirdLvl 81S05\SubText Commutation relations\endx
\ThirdLvl 81S10\SubText Geometric quantization, symplectic methods
 \SeeAlso{\SbjNo 58F06}\endx
\ThirdLvl 81S20\SubText Stochastic quantization\endx
\ThirdLvl 81S25\SubText Quantum stochastic calculus\endx
\ThirdLvl 81S30\SubText Phase space methods including Wigner
 distributions, etc.\endx
\ThirdLvl 81S40\SubText Path integrals \SeeAlso{\SbjNo 58D30}\endx
\ThirdLvl 81S99\SubText \NoneOfAbove\endx
\SecndLvl 81T++\SubText Quantum field theory; related classical field
 theories\endx
\ThirdLvl 81T05\SubText Axiomatic quantum field theory; operator
 algebras\endx
\ThirdLvl 81T08\SubText Constructive quantum field theory\endx
\ThirdLvl 81T10\SubText Model quantum field theories\endx
\ThirdLvl 81T13\SubText Yang-Mills and other gauge theories
 \SeeAlso{\SbjNo 53C07, \SbjNo 58E15}\endx
\ThirdLvl 81T15\SubText Perturbative methods of renormalization\endx
\ThirdLvl 81T16\SubText Nonperturbative methods of
 renormalization\endx
\ThirdLvl 81T17\SubText Renormalization group methods\endx
\ThirdLvl 81T18\SubText Feynman diagrams\endx
\ThirdLvl 81T20\SubText Quantum field theory on curved space
 backgrounds\endx
\ThirdLvl 81T25\SubText Quantum field theory on lattices\endx
\ThirdLvl 81T27\SubText Continuum limits\endx
\ThirdLvl 81T30\SubText String and superstring theories; other
 extended objects \SeeAlso{\SbjNo 83E30}\endx
\ThirdLvl 81T40\SubText Two-dimensional field theories, conformal
 field theories, etc.\endx
\ThirdLvl 81T50\SubText Anomalies\endx
\ThirdLvl 81T60\SubText Supersymmetric field theories \endx
\ThirdLvl 81T70\SubText Quantization in field theory; cohomological
 methods \SeeAlso{\SbjNo 58F06}\endx
\ThirdLvl 81T80\SubText Simulation and numerical modeling\endx
\ThirdLvl 81T99\SubText \NoneOfAbove\endx
\SecndLvl 81U++\SubText Scattering theory \SeeAlso{\SbjNo 47A40}\endx
\ThirdLvl 81U05\SubText $2$-body potential scattering theory
 \SeeAlso{\SbjNo 34E20 for WKB methods}\endx
\ThirdLvl 81U10\SubText $n$-body potential scattering theory\endx
\ThirdLvl 81U20\SubText $S$-matrix theory, etc.\endx
\ThirdLvl 81U30\SubText Dispersion theory, dispersion relations\endx
\ThirdLvl 81U40\SubText Inverse scattering problems \SeeAlso{\SbjNo
 58F07, \SbjNo 58F19}\endx
\ThirdLvl 81U99\SubText \NoneOfAbove\endx
\SecndLvl 81V++\SubText Applications to specific physical systems\endx
\ThirdLvl 81V05\SubText Strong interaction, including quantum
 chromodynamics\endx
\ThirdLvl 81V10\SubText Electromagnetic interaction; quantum
 electrodynamics\endx
\ThirdLvl 81V15\SubText Weak interaction\endx
\ThirdLvl 81V17\SubText Gravitational interaction\endx
\ThirdLvl 81V19\SubText Other fundamental interactions\endx
\ThirdLvl 81V22\SubText Unified theories\endx
\ThirdLvl 81V25\SubText Other elementary particle theory\endx
\ThirdLvl 81V35\SubText Nuclear physics\endx
\ThirdLvl 81V45\SubText Atomic physics\endx
\ThirdLvl 81V55\SubText Molecular physics \SeeAlso{\SbjNo 92E10}\endx
\ThirdLvl 81V70\SubText Many-body theory\endx
\ThirdLvl 81V80\SubText Quantum optics\endx
\ThirdLvl 81V99\SubText \NoneOfAbove\endx
\MajorSub 82-++\SubText Statistical mechanics, structure of
 matter\endx
\ThirdLvl 82-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 82-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 82-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 82-03\SubText \Historical\endx
\ThirdLvl 82-04\SubText \ExplicitComputation\endx
\ThirdLvl 82-05\SubText Experimental papers\endx
\ThirdLvl 82-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 82-08\SubText Computational methods\endx
\SecndLvl 82B++\SubText Equilibrium statistical mechanics\endx
\ThirdLvl 82B03\SubText Foundations\endx
\ThirdLvl 82B05\SubText Classical equilibrium statistical mechanics
 (general)\endx
\ThirdLvl 82B10\SubText Quantum equilibrium statistical mechanics
 (general)\endx
\ThirdLvl 82B20\SubText Lattice systems (Ising, dimer, Potts,
 etc.)\endx
\ThirdLvl 82B21\SubText Continuum models (systems of particles,
 etc.)\endx
\ThirdLvl 82B23\SubText Exactly solvable models\endx
\ThirdLvl 82B24\SubText Interface problems\endx
\ThirdLvl 82B26\SubText Phase transitions (general)\endx
\ThirdLvl 82B27\SubText Critical phenomena\endx
\ThirdLvl 82B28\SubText Renormalization group methods \SeeAlso{\SbjNo
 81T17}\endx
\ThirdLvl 82B30\SubText Statistical thermodynamics \SeeAlso{\SbjNo
 80-XX}\endx
\ThirdLvl 82B31\SubText Stochastic methods\endx
\ThirdLvl 82B35\SubText Irreversible thermodynamics, including
 Onsager-Machlup theory \SeeAlso{\SbjNo 92E20}\endx
\ThirdLvl 82B40\SubText Kinetic theory of gases\endx
\ThirdLvl 82B41\SubText Random walks, random surfaces, lattice
 animals, etc. \SeeAlso{\SbjNo 60J15, \SbjNo 82C41}\endx
\ThirdLvl 82B43\SubText Percolation \SeeAlso{\SbjNo 60K35}\endx
\ThirdLvl 82B44\SubText Disordered systems (random Ising models,
 random Schr\"odinger operators, etc.)\endx
\ThirdLvl 82B80\SubText Numerical methods (Monte Carlo, series
 resummation, etc.) \SeeAlso{\SbjNo 65-XX, \SbjNo 81T80}\endx
\ThirdLvl 82B99\SubText \Miscellaneous\endx
\SecndLvl 82C++\SubText Time-dependent statistical mechanics (dynamic
 and nonequilibrium)\endx
\ThirdLvl 82C03\SubText Foundations\endx
\ThirdLvl 82C05\SubText Classical dynamic and nonequilibrium
 statistical mechanics (general)\endx
\ThirdLvl 82C10\SubText Quantum dynamics and nonequilibrium
 statistical mechanics (general)\endx
\ThirdLvl 82C20\SubText Dynamic lattice systems (kinetic Ising,
 etc.)\endx
\ThirdLvl 82C21\SubText Dynamic continuum models (systems of
 particles, etc.)\endx
\ThirdLvl 82C22\SubText Interacting particle systems \SeeAlso{\SbjNo
 60K35}\endx
\ThirdLvl 82C23\SubText Exactly solvable dynamic models
 \SeeAlso{\SbjNo 58F07}\endx
\ThirdLvl 82C24\SubText Interface problems\endx
\ThirdLvl 82C26\SubText Dynamic and nonequilibrium phase transitions
 (general)\endx
\ThirdLvl 82C27\SubText Dynamic critical phenomena\endx
\ThirdLvl 82C28\SubText Dynamic renormalization group methods
 \SeeAlso{\SbjNo 81T17}\endx
\ThirdLvl 82C31\SubText Stochastic methods (Fokker-Planck, Langevin,
 etc.) \SeeAlso{\SbjNo 60H10}\endx
\ThirdLvl 82C32\SubText Neural nets \SeeAlso{\SbjNo 68T05, \SbjNo
 92B20, \SbjNo 92J40}\endx
\ThirdLvl 82C35\SubText Irreversible thermodynamics, including
 Onsager-Machlup theory\endx
\ThirdLvl 82C40\SubText Kinetic theory of gases\endx
\ThirdLvl 82C41\SubText Dynamics of random walks, random surfaces,
 lattice animals, etc. \SeeAlso{\SbjNo 60J15}\endx
\ThirdLvl 82C43\SubText Time-dependent percolation \SeeAlso{\SbjNo
 60K35}\endx
\ThirdLvl 82C44\SubText Dynamics of disordered systems (random Ising
 systems, etc.)\endx
\ThirdLvl 82C70\SubText Transport processes\endx
\ThirdLvl 82C80\SubText Numerical methods (Monte Carlo, series
 resummation, etc.)\endx
\ThirdLvl 82C99\SubText \NoneOfAbove\endx
\SecndLvl 82D++\SubText Applications to specific types of physical
 systems\endx
\ThirdLvl 82D05\SubText Gases\endx
\ThirdLvl 82D10\SubText Plasmas\endx
\ThirdLvl 82D15\SubText Liquids\endx
\ThirdLvl 82D20\SubText Solids\endx
\ThirdLvl 82D25\SubText Crystals \SeeFor{For crystallographic group
 theory, see \SbjNo 20H15}\endx
\ThirdLvl 82D30\SubText Random media, disordered materials (including
 liquid crystals and spin glasses)\endx
\ThirdLvl 82D35\SubText Metals\endx
\ThirdLvl 82D40\SubText Magnetic materials\endx
\ThirdLvl 82D45\SubText Ferroelectrics\endx
\ThirdLvl 82D50\SubText Superfluids\endx
\ThirdLvl 82D55\SubText Superconductors\endx
\ThirdLvl 82D60\SubText Polymers\endx
\ThirdLvl 82D75\SubText Nuclear reactor theory\endx
\ThirdLvl 82D99\SubText \NoneOfAbove\endx
\MajorSub 83-++\SubText Relativity and gravitational theory\endx
\ThirdLvl 83-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 83-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 83-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 83-03\SubText \Historical\endx
\ThirdLvl 83-04\SubText \ExplicitComputation\endx
\ThirdLvl 83-05\SubText Experimental papers\endx
\ThirdLvl 83-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 83-08\SubText Computational methods\endx
\SecndLvl 83A05\SubText Special relativity\endx
\SecndLvl 83B05\SubText Observational and experimental questions\endx
\SecndLvl 83C++\SubText General relativity\endx
\ThirdLvl 83C05\SubText Einstein's equations (general structure,
 canonical formalism, Cauchy problems)\endx
\ThirdLvl 83C10\SubText Equations of motion\endx
\ThirdLvl 83C15\SubText Exact solutions\endx
\ThirdLvl 83C20\SubText Classes of solutions; algebraically special
 solutions, metrics with symmetries\endx
\ThirdLvl 83C22\SubText Electromagnetic fields, Einstein-Maxwell
 equations\endx
\ThirdLvl 83C25\SubText Approximation procedures, weak fields\endx
\ThirdLvl 83C27\SubText Lattice gravity, Regge calculus and other
 discrete methods\endx
\ThirdLvl 83C30\SubText Asymptotic procedures (radiation, news
 functions, {\scr H}-spaces, etc.)\endx
\ThirdLvl 83C35\SubText Gravitational waves\endx
\ThirdLvl 83C40\SubText Gravitational energy and conservation laws;
 groups of motions\endx
\ThirdLvl 83C45\SubText Quantization of the gravitational field\endx
\ThirdLvl 83C47\SubText Quantum field theory aspects \SeeAlso{\SbjNo
 81T20}\endx
\ThirdLvl 83C50\SubText Electromagnetic fields\endx
\ThirdLvl 83C55\SubText Macroscopic interaction of the gravitational
 field with matter (hydrodynamics, etc.)\endx
\ThirdLvl 83C57\SubText Black holes\endx
\ThirdLvl 83C60\SubText Spinor and twistor methods \endx
\ThirdLvl 83C75\SubText Space-time singularities, cosmic censorship,
 etc.\endx
\ThirdLvl 83C99\SubText \NoneOfAbove\endx
\SecndLvl 83D05\SubText Relativistic gravitational theories other than
 Einstein's, including asymmetric field theories\endx
\SecndLvl 83E++\SubText Unified, higher-dimensional and super field
 theories\endx
\ThirdLvl 83E05\SubText Geometrodynamics\endx
\ThirdLvl 83E15\SubText Kaluza-Klein and other higher-dimensional
 theories\endx
\ThirdLvl 83E30\SubText String and superstring theories
 \SeeAlso{\SbjNo 81T30}\endx
\ThirdLvl 83E50\SubText Supergravity \endx
\ThirdLvl 83E99\SubText \NoneOfAbove\endx
\SecndLvl 83F05\SubText Cosmology\endx
\MajorSub 85-++\SubText Astronomy and astrophysics \SeeFor{For
 celestial mechanics, see~\SbjNo 70F15}\endx
\ThirdLvl 85-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 85-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 85-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 85-03\SubText \Historical\endx
\ThirdLvl 85-04\SubText \ExplicitComputation\endx
\ThirdLvl 85-05\SubText Experimental papers\endx
\ThirdLvl 85-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 85-08\SubText Computational methods\endx
\ThirdLvl 85A04\SubText General\endx
\ThirdLvl 85A05\SubText Galactic and stellar dynamics\endx
\ThirdLvl 85A15\SubText Galactic and stellar structure\endx
\ThirdLvl 85A20\SubText Stellar atmospheres\endx
\ThirdLvl 85A25\SubText Radiative transfer\endx
\ThirdLvl 85A30\SubText Hydrodynamic and hydromagnetic problems
 \SeeAlso{\SbjNo 76Y05}\endx
\ThirdLvl 85A35\SubText Statistical astronomy\endx
\ThirdLvl 85A40\SubText Cosmology \SeeFor{For relativistic cosmology,
 see \SbjNo 83F05}\endx
\ThirdLvl 85A45\SubText Radio astronomy\endx
\ThirdLvl 85A99\SubText \Miscellaneous\endx
\MajorSub 86-++\SubText Geophysics \SeeAlso{\SbjNo 73N05, \SbjNo
 76U05, \SbjNo 76V05}\endx
\ThirdLvl 86-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 86-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 86-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 86-03\SubText \Historical\endx
\ThirdLvl 86-04\SubText \ExplicitComputation\endx
\ThirdLvl 86-05\SubText Experimental papers\endx
\ThirdLvl 86-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 86-08\SubText Computational methods\endx
\ThirdLvl 86A04\SubText General\endx
\ThirdLvl 86A05\SubText Hydrology, hydrography, oceanography
 \SeeAlso{\SbjNo 76B15, \SbjNo 76B20, \SbjNo 76B25, \SbjNo 76C15,
 \SbjNo 76E20, \SbjNo 76Q05, \SbjNo 76Rxx, \SbjNo 76U05}\endx
\ThirdLvl 86A10\SubText Meteorology and atmospheric physics
 \SeeAlso{\SbjNo 76Bxx, \SbjNo 76C15, \SbjNo 76C20, \SbjNo 76E20,
 \SbjNo 76N15, \SbjNo 76Q05, \SbjNo 76Rxx, \SbjNo 76U05, \SbjNo
 76V05}\endx
\ThirdLvl 86A15\SubText Seismology \SeeAlso{\SbjNo 73Dxx, \SbjNo
 73Fxx, \SbjNo 73M25, \SbjNo 73N20, \SbjNo 73Q05}\endx
\ThirdLvl 86A17\SubText Global dynamics, earthquake problems\endx
\ThirdLvl 86A20\SubText Potentials, prospecting \SeeAlso{\SbjNo 76S05,
 \SbjNo 76W05}\endx
\ThirdLvl 86A22\SubText Inverse problems \SeeAlso{\SbjNo 35R30}\endx
\ThirdLvl 86A25\SubText Geo-electricity and geomagnetism
 \SeeAlso{\SbjNo 78A25}\endx
\ThirdLvl 86A30\SubText Geodesy, mapping problems\endx
\ThirdLvl 86A32\SubText Geostatistics\endx
\ThirdLvl 86A40\SubText Glaciology\endx
\ThirdLvl 86A60\SubText Geological problems\endx
\ThirdLvl 86A99\SubText \Miscellaneous\endx
\MajorSub 90-++\SubText Economics, operations research, programming,
 games\endx
\ThirdLvl 90-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 90-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 90-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 90-03\SubText \Historical\endx
\ThirdLvl 90-04\SubText \ExplicitComputation\endx
\ThirdLvl 90-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 90-08\SubText Computational methods\endx
\SecndLvl 90A++\SubText Mathematical economics \SeeFor{For
 econometrics, see \SbjNo 62P20}\endx
\ThirdLvl 90A05\SubText Decision theory \SeeAlso{\SbjNo 62Cxx, \SbjNo
 90B50, \SbjNo 90D35}\endx
\ThirdLvl 90A06\SubText Individual preferences\endx
\ThirdLvl 90A07\SubText Group preferences\endx
\ThirdLvl 90A08\SubText Social choice\endx
\ThirdLvl 90A09\SubText Finance, portfolios, investment\endx
\ThirdLvl 90A10\SubText Utility theory\endx
\ThirdLvl 90A11\SubText Production theory, theory of the firm\endx
\ThirdLvl 90A12\SubText Price theory and market structure\endx
\ThirdLvl 90A14\SubText Equilibrium: general theory\endx
\ThirdLvl 90A15\SubText General economic models, trade models\endx
\ThirdLvl 90A16\SubText Dynamic economic models, growth models\endx
\ThirdLvl 90A17\SubText Multisectoral models\endx
\ThirdLvl 90A19\SubText Statistical models; economic indexes and
 measures\endx
\ThirdLvl 90A20\SubText Economic time series analysis \SeeAlso{\SbjNo
 62M10}\endx
\ThirdLvl 90A25\SubText Spatial models\endx
\ThirdLvl 90A27\SubText Public goods\endx
\ThirdLvl 90A28\SubText Voting theory\endx
\ThirdLvl 90A30\SubText Environmental economics (natural resource
 models, harvesting, pollution, etc.)\endx
\ThirdLvl 90A35\SubText Informational economics\endx
\ThirdLvl 90A36\SubText Incentives theory\endx
\ThirdLvl 90A40\SubText Consumer behavior, demand theory\endx
\ThirdLvl 90A43\SubText Expected utility; risk-averse utility\endx
\ThirdLvl 90A46\SubText Risk theory\endx
\ThirdLvl 90A50\SubText Labor market\endx
\ThirdLvl 90A53\SubText Special types of economies\endx
\ThirdLvl 90A56\SubText Special types of equilibria\endx
\ThirdLvl 90A58\SubText Models of real-world systems; general
 macro-economic models, etc.\endx
\ThirdLvl 90A60\SubText Market models (auctions, bargaining, bidding,
 selling, etc.)\endx
\ThirdLvl 90A70\SubText Macro-economic policy-making, taxation\endx
\ThirdLvl 90A80\SubText Resource allocation\endx
\ThirdLvl 90A99\SubText \NoneOfAbove\endx
\SecndLvl 90B++\SubText Operations research and management
 science\endx
\ThirdLvl 90B05\SubText Inventory, storage, reservoirs\endx
\ThirdLvl 90B06\SubText Transportation, logistics\endx
\ThirdLvl 90B10\SubText Flows in networks, deterministic\endx
\ThirdLvl 90B12\SubText Communication networks \SeeAlso{\SbjNo 68M10,
 \SbjNo 94A05}\endx
\ThirdLvl 90B15\SubText Flows in networks, probabilistic\endx
\ThirdLvl 90B20\SubText Highway traffic\endx
\ThirdLvl 90B22\SubText Queues and service \SeeAlso{\SbjNo 60K25,
 \SbjNo 68M20}\endx
\ThirdLvl 90B25\SubText Reliability, availability, maintenance,
 inspection \SeeAlso{\SbjNo 60K10, \SbjNo 62N05}\endx
\ThirdLvl 90B30\SubText Production models\endx
\ThirdLvl 90B35\SubText Scheduling theory \SeeAlso{\SbjNo 68M20}\endx
\ThirdLvl 90B40\SubText Search theory\endx
\ThirdLvl 90B50\SubText Management decision-making, including multiple
 objectives \SeeAlso{\SbjNo 90A05, \SbjNo 90C31, \SbjNo 90D35}\endx
\ThirdLvl 90B60\SubText Marketing, advertising \SeeAlso{\SbjNo
 90A60}\endx
\ThirdLvl 90B70\SubText Theory of organizations, industrial and
 manpower planning \SeeAlso{\SbjNo 92H35}\endx
\ThirdLvl 90B80\SubText Discrete location and assignment
 \SeeAlso{\SbjNo 90C10}\endx
\ThirdLvl 90B85\SubText Continuous location\endx
\ThirdLvl 90B90\SubText Case-oriented studies\endx
\ThirdLvl 90B99\SubText \NoneOfAbove\endx
\SecndLvl 90C++\SubText Mathematical programming \SeeAlso{\SbjNo
 49Mxx, \SbjNo 65Kxx}\endx
\ThirdLvl 90C05\SubText Linear programming\endx
\ThirdLvl 90C06\SubText Large-scale problems\endx
\ThirdLvl 90C08\SubText Special problems of linear programming
 (transportation, multi-index, etc.)\endx
\ThirdLvl 90C09\SubText Boolean programming\endx
\ThirdLvl 90C10\SubText Integer programming\endx
\ThirdLvl 90C11\SubText Mixed integer programming\endx
\ThirdLvl 90C15\SubText Stochastic programming\endx
\ThirdLvl 90C20\SubText Quadratic programming\endx
\ThirdLvl 90C25\SubText Convex programming\endx
\ThirdLvl 90C26\SubText Nonconvex programming, quasiconvex
 programming\endx
\ThirdLvl 90C27\SubText Combinatorial optimization\endx
\ThirdLvl 90C28\SubText Geometric programming\endx
\ThirdLvl 90C29\SubText Multi-objective and goal programming; vector
 optimization\endx
\ThirdLvl 90C30\SubText Nonlinear programming\endx
\ThirdLvl 90C31\SubText Sensitivity, stability, parametric
 optimization\endx
\ThirdLvl 90C32\SubText Fractional programming\endx
\ThirdLvl 90C33\SubText Complementarity problems\endx
\ThirdLvl 90C34\SubText Semi-infinite programming\endx
\ThirdLvl 90C35\SubText Programming involving graphs or networks\endx
\ThirdLvl 90C39\SubText Dynamic programming \SeeAlso{\SbjNo
 49L20}\endx
\ThirdLvl 90C40\SubText Markov and semi-Markov decision processes\endx
\ThirdLvl 90C42\SubText Markov programming and Markov renewal
 programming\endx
\ThirdLvl 90C45\SubText Continuous programming\endx
\ThirdLvl 90C48\SubText Programming in abstract spaces\endx
\ThirdLvl 90C60\SubText Abstract computational complexity for
 mathematical programming problems \SeeAlso{\SbjNo 68Q25}\endx
\ThirdLvl 90C70\SubText Fuzzy programming\endx
\ThirdLvl 90C90\SubText Applications of mathematical programming\endx
\ThirdLvl 90C99\SubText \NoneOfAbove\endx
\SecndLvl 90D++\SubText Game theory\endx
\ThirdLvl 90D05\SubText $2$-person games\endx
\ThirdLvl 90D06\SubText $n$-person games, $n>2$\endx
\ThirdLvl 90D10\SubText Noncooperative games\endx
\ThirdLvl 90D12\SubText Cooperative games\endx
\ThirdLvl 90D13\SubText Games with infinitely many players\endx
\ThirdLvl 90D15\SubText Stochastic games \SeeAlso{\SbjNo 93E05}\endx
\ThirdLvl 90D20\SubText Multistage and repeated games\endx
\ThirdLvl 90D25\SubText Differential games \SeeAlso{\SbjNo 49N55}\endx
\ThirdLvl 90D26\SubText Pursuit and evasion games\endx
\ThirdLvl 90D35\SubText Decision theory for games \SeeAlso{\SbjNo
 62Cxx, \SbjNo 90A05, \SbjNo 90B50}\endx
\ThirdLvl 90D40\SubText Game-theoretic models \SeeAlso{\SbjNo
 65Cxx}\endx
\ThirdLvl 90D42\SubText Positional games\endx
\ThirdLvl 90D43\SubText Games involving graphs\endx
\ThirdLvl 90D44\SubText Games involving topology or set theory\endx
\ThirdLvl 90D46\SubText Combinatorial games\endx
\ThirdLvl 90D50\SubText Discrete-time games\endx
\ThirdLvl 90D55\SubText Games of timing\endx
\ThirdLvl 90D60\SubText Probabilistic games; gambling\endx
\ThirdLvl 90D65\SubText Hierarchical games\endx
\ThirdLvl 90D70\SubText Spaces of games\endx
\ThirdLvl 90D80\SubText Applications of game theory\endx
\ThirdLvl 90D99\SubText \NoneOfAbove\endx
\MajorSub 92-++\SubText Biology and other natural sciences, behavioral
 sciences\endx
\ThirdLvl 92-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 92-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 92-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 92-03\SubText \Historical\endx
\ThirdLvl 92-04\SubText \ExplicitComputation\endx
\ThirdLvl 92-06\SubText Proceedings, conferences, collections,
 etc.\endx
\ThirdLvl 92-08\SubText Computational methods\endx
\SecndLvl 92B++\SubText Mathematical biology in general\endx
\ThirdLvl 92B05\SubText General biology and biomathematics\endx
\ThirdLvl 92B10\SubText Taxonomy, statistics\endx
\ThirdLvl 92B15\SubText General biostatistics \SeeAlso{\SbjNo
 62P10}\endx
\ThirdLvl 92B20\SubText Neural networks \SeeAlso{\SbjNo 68T05, \SbjNo
 82C32, \SbjNo 94Cxx}\endx
\ThirdLvl 92B99\SubText \NoneOfAbove\endx
\SecndLvl 92C++\SubText Physiological, cellular and medical
 topics\endx
\ThirdLvl 92C05\SubText Biophysics\endx
\ThirdLvl 92C10\SubText Biomechanics \SeeAlso{\SbjNo 73P05}\endx
\ThirdLvl 92C15\SubText Developmental biology, pattern formation\endx
\ThirdLvl 92C20\SubText Neural biology\endx
\ThirdLvl 92C30\SubText Physiology (general)\endx
\ThirdLvl 92C35\SubText Physiological flow \SeeAlso{\SbjNo 76Z05}\endx
\ThirdLvl 92C40\SubText Biochemistry, molecular biology\endx
\ThirdLvl 92C45\SubText Kinetics in biochemical problems
 (pharmacokinetics, enzyme kinetics, etc.) \SeeAlso{\SbjNo 80A30}\endx
\ThirdLvl 92C50\SubText Medical applications (general)\endx
\ThirdLvl 92C55\SubText Tomography \SeeAlso{\SbjNo 44A12, \SbjNo
 65R10}\endx
\ThirdLvl 92C60\SubText Medical epidemiology\endx
\ThirdLvl 92C99\SubText \NoneOfAbove\endx
\SecndLvl 92D++\SubText Genetics and population dynamics\endx
\ThirdLvl 92D10\SubText Genetics \SeeFor{For genetic algebras, see
 \SbjNo 17D92} \endx
\ThirdLvl 92D15\SubText Problems related to evolution\endx
\ThirdLvl 92D20\SubText Protein sequences, DNA sequences\endx
\ThirdLvl 92D25\SubText Population dynamics (general)\endx
\ThirdLvl 92D30\SubText Epidemiology\endx
\ThirdLvl 92D40\SubText Ecology\endx
\ThirdLvl 92D50\SubText Animal behavior\endx
\ThirdLvl 92D99\SubText \NoneOfAbove\endx
\SecndLvl 92E++\SubText Chemistry \SeeFor{For biochemistry, see \SbjNo
 92C40}\endx
\ThirdLvl 92E10\SubText Molecular structure (graph-theoretic methods,
 methods of differential topology, etc.)\endx
\ThirdLvl 92E20\SubText Classical flows, reactions, etc.
 \SeeAlso{\SbjNo 80A30, \SbjNo 80A32}\endx
\ThirdLvl 92E99\SubText \NoneOfAbove\endx
\SecndLvl 92F05\SubText Other natural sciences\endx
\SecndLvl 92G++\SubText Social and behavioral sciences: methodology
 \SeeFor{For statistics, see \SbjNo 62-XX}\endx
\ThirdLvl 92G05\SubText Measurement theory\endx
\ThirdLvl 92G15\SubText One- and multidimensional scaling\endx
\ThirdLvl 92G20\SubText Test theory\endx
\ThirdLvl 92G25\SubText Questionnaire analysis\endx
\ThirdLvl 92G30\SubText Clustering \SeeAlso{\SbjNo 62H30}\endx
\ThirdLvl 92G40\SubText Q-analysis\endx
\ThirdLvl 92G99\SubText \NoneOfAbove\endx
\SecndLvl 92H++\SubText Mathematical sociology (including
 anthropology)\endx
\ThirdLvl 92H10\SubText Models of societies, social and urban
 evolution\endx
\ThirdLvl 92H20\SubText Mathematical geography and demography\endx
\ThirdLvl 92H25\SubText Spatial models \SeeAlso{\SbjNo 90A25}\endx
\ThirdLvl 92H30\SubText Social networks\endx
\ThirdLvl 92H35\SubText Manpower systems \SeeAlso{\SbjNo 90A50, \SbjNo
 90B70}\endx
\ThirdLvl 92H99\SubText \NoneOfAbove\endx
\SecndLvl 92J++\SubText Mathematical psychology\endx
\ThirdLvl 92J10\SubText Cognitive psychology\endx
\ThirdLvl 92J30\SubText Psychophysics and psychophysiology;
 perception\endx
\ThirdLvl 92J40\SubText Memory and learning \SeeAlso{\SbjNo
 68T05}\endx
\ThirdLvl 92J45\SubText Measurement and performance\endx
\ThirdLvl 92J99\SubText \NoneOfAbove\endx
\SecndLvl 92K++\SubText Other social and behavioral sciences
 (mathematical treatment)\endx
\ThirdLvl 92K10\SubText History, political science \endx
\ThirdLvl 92K20\SubText Linguistics \SeeAlso{\SbjNo 03B65, \SbjNo
 68S05}\endx
\ThirdLvl 92K99\SubText \NoneOfAbove\endx
\MajorSub 93-++\SubText Systems theory; control \SeeFor{For optimal
 control, see~\SbjNo 49-XX}\endx
\ThirdLvl 93-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 93-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 93-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 93-03\SubText \Historical\endx
\ThirdLvl 93-04\SubText \ExplicitComputation\endx
\ThirdLvl 93-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 93A++\SubText General\endx
\ThirdLvl 93A05\SubText Axiomatic system theory\endx
\ThirdLvl 93A10\SubText General systems\endx
\ThirdLvl 93A13\SubText Hierarchical systems\endx
\ThirdLvl 93A14\SubText Decentralized systems\endx
\ThirdLvl 93A15\SubText Large scale systems\endx
\ThirdLvl 93A20\SubText Cascaded systems\endx
\ThirdLvl 93A25\SubText Input-output systems\endx
\ThirdLvl 93A30\SubText Mathematical modeling (models of systems,
 model-matching, etc.)\endx
\ThirdLvl 93A99\SubText \NoneOfAbove\endx
\SecndLvl 93B++\SubText Controllability, observability, and system
 structure\endx
\ThirdLvl 93B03\SubText Attainable sets\endx
\ThirdLvl 93B05\SubText Controllability\endx
\ThirdLvl 93B06\SubText Relations between controllability and optimal
 solutions\endx
\ThirdLvl 93B07\SubText Observability \endx
\ThirdLvl 93B10\SubText Canonical structure\endx
\ThirdLvl 93B11\SubText System structure simplication\endx
\ThirdLvl 93B12\SubText Variable structure systems\endx
\ThirdLvl 93B15\SubText Realizability of systems from input-output
 data\endx
\ThirdLvl 93B17\SubText Transformation\endx
\ThirdLvl 93B18\SubText Linearizability\endx
\ThirdLvl 93B20\SubText Minimal systems representations\endx
\ThirdLvl 93B25\SubText Algebraic methods\endx
\ThirdLvl 93B27\SubText Geometric methods (including
 algebro-geometric)\endx
\ThirdLvl 93B28\SubText Operator-theoretic methods \SeeAlso{\SbjNo
 47A57, \SbjNo 47N70}\endx
\ThirdLvl 93B29\SubText Differential-geometric methods \endx
\ThirdLvl 93B30\SubText System identification\endx
\ThirdLvl 93B35\SubText Sensitivity (robustness)\endx
\ThirdLvl 93B36\SubText ${\it H}^ \infty$-control\endx
\ThirdLvl 93B40\SubText Computational methods \endx
\ThirdLvl 93B50\SubText Synthesis problems\endx
\ThirdLvl 93B51\SubText Design techniques (robust design,
 computer-aided design, etc.)\endx
\ThirdLvl 93B52\SubText Feedback control\endx
\ThirdLvl 93B55\SubText Pole and zero placement problems\endx
\ThirdLvl 93B60\SubText Eigenvalue problems\endx
\ThirdLvl 93B99\SubText \NoneOfAbove\endx
\SecndLvl 93C++\SubText Control systems, guided systems\endx
\ThirdLvl 93C05\SubText Linear\endx
\ThirdLvl 93C10\SubText Nonlinear\endx
\ThirdLvl 93C15\SubText Systems governed by ordinary differential
 equations\endx
\ThirdLvl 93C20\SubText Systems governed by partial differential
 equations\endx
\ThirdLvl 93C22\SubText Systems governed by integral equations\endx
\ThirdLvl 93C25\SubText Systems in abstract spaces\endx
\ThirdLvl 93C30\SubText Systems governed by functional relations other
 than differential or integral equations\endx
\ThirdLvl 93C35\SubText Multivariable, multidimensional systems\endx
\ThirdLvl 93C40\SubText Adaptive control systems\endx
\ThirdLvl 93C41\SubText Problems with incomplete information \endx
\ThirdLvl 93C42\SubText Fuzzy control\endx
\ThirdLvl 93C45\SubText Time-invariant\endx
\ThirdLvl 93C50\SubText Time-dependent\endx
\ThirdLvl 93C55\SubText Discrete-time\endx
\ThirdLvl 93C57\SubText Sampled-data\endx
\ThirdLvl 93C60\SubText Continuous-time\endx
\ThirdLvl 93C62\SubText Digital systems\endx
\ThirdLvl 93C70\SubText Time-scale analysis and related topics\endx
\ThirdLvl 93C73\SubText Perturbations in control systems\endx
\ThirdLvl 93C80\SubText Frequency-response methods\endx
\ThirdLvl 93C83\SubText Control problems involving computers (process
 control, etc.)\endx
\ThirdLvl 93C85\SubText Automated systems (robots, etc.)\endx
\ThirdLvl 93C90\SubText Random disturbances in control systems\endx
\ThirdLvl 93C95\SubText Applications of control theory\endx
\ThirdLvl 93C99\SubText \NoneOfAbove\endx
\SecndLvl 93D++\SubText Stability\endx
\ThirdLvl 93D05\SubText Lyapunov and other classical stabilities
 (Lagrange, Poisson, $L\sp p, l\sp p$, etc.)\endx
\ThirdLvl 93D09\SubText Robust stability\endx
\ThirdLvl 93D10\SubText Popov-type stability of feedback systems\endx
\ThirdLvl 93D15\SubText Stabilization of systems by feedback\endx
\ThirdLvl 93D20\SubText Asymptotic stability\endx
\ThirdLvl 93D21\SubText Adaptive and robust stabilization\endx
\ThirdLvl 93D22\SubText Interrelations between stability problems and
 optimization problems\endx
\ThirdLvl 93D25\SubText Input-output approaches\endx
\ThirdLvl 93D30\SubText Scalar and vector Lyapunov functions\endx
\ThirdLvl 93D99\SubText \NoneOfAbove\endx
\SecndLvl 93E++\SubText Stochastic systems and control\endx
\ThirdLvl 93E03\SubText Stochastic systems, general\endx
\ThirdLvl 93E05\SubText Stochastic games, stochastic differential
 games \SeeAlso{\SbjNo 90D15}\endx
\ThirdLvl 93E10\SubText Estimation and detection \SeeAlso{\SbjNo
 60G35}\endx
\ThirdLvl 93E11\SubText Filtering \SeeAlso{\SbjNo 60G35}\endx
\ThirdLvl 93E12\SubText System identification\endx
\ThirdLvl 93E14\SubText Data smoothing\endx
\ThirdLvl 93E15\SubText Stochastic stability\endx
\ThirdLvl 93E20\SubText Optimal stochastic control\endx
\ThirdLvl 93E23\SubText Stochastic gradient methods\endx
\ThirdLvl 93E24\SubText Least squares and related methods\endx
\ThirdLvl 93E25\SubText Other computational methods\endx
\ThirdLvl 93E30\SubText Computer simulations of stochastic
 systems\endx
\ThirdLvl 93E35\SubText Stochastic learning and adaptive control\endx
\ThirdLvl 93E99\SubText \NoneOfAbove\endx
\MajorSub 94-++\SubText Information and communication, circuits\endx
\ThirdLvl 94-00\SubText General reference works (handbooks,
 dictionaries, bibliographies, etc.)\endx
\ThirdLvl 94-01\SubText Instructional exposition (textbooks, tutorial
 papers, etc.)\endx
\ThirdLvl 94-02\SubText Research exposition (monographs, survey
 articles)\endx
\ThirdLvl 94-03\SubText \Historical\endx
\ThirdLvl 94-04\SubText \ExplicitComputation\endx
\ThirdLvl 94-06\SubText Proceedings, conferences, collections,
 etc.\endx
\SecndLvl 94A++\SubText Communication, information\endx
\ThirdLvl 94A05\SubText Communication theory \SeeAlso{\SbjNo 60G35,
 \SbjNo 90B12}\endx
\ThirdLvl 94A11\SubText Application of orthogonal functions in
 communication\endx
\ThirdLvl 94A12\SubText Signal theory (characterization,
 reconstruction, etc.)\endx
\ThirdLvl 94A13\SubText Detection theory\endx
\ThirdLvl 94A14\SubText Modulation and demodulation\endx
\ThirdLvl 94A15\SubText Information theory, general \SeeAlso{\SbjNo
 62B10}\endx
\ThirdLvl 94A17\SubText Measures of information, entropy\endx
\ThirdLvl 94A24\SubText Coding theorems (Shannon theory)\endx
\ThirdLvl 94A29\SubText Source coding\endx
\ThirdLvl 94A34\SubText Rate-distortion theory\endx
\ThirdLvl 94A40\SubText Channel models\endx
\ThirdLvl 94A45\SubText Prefix, length-variable, comma-free codes
 \SeeAlso{\SbjNo 20M35, \SbjNo 68Q45}\endx
\ThirdLvl 94A50\SubText Theory of questionnaires\endx
\ThirdLvl 94A55\SubText Shift register sequences\endx
\ThirdLvl 94A60\SubText Cryptography \SeeAlso{\SbjNo 11T71, \SbjNo
 68P25}\endx
\ThirdLvl 94A99\SubText \NoneOfAbove\endx
\SecndLvl 94B++\SubText Theory of error-correcting codes\endx
\ThirdLvl 94B05\SubText Linear codes, general\endx
\ThirdLvl 94B10\SubText Convolutional codes\endx
\ThirdLvl 94B12\SubText Combined modulation schemes (including trellis
 codes)\endx
\ThirdLvl 94B15\SubText Cyclic codes\endx
\ThirdLvl 94B20\SubText Burst-correcting codes\endx
\ThirdLvl 94B25\SubText Combinatorial codes\endx
\ThirdLvl 94B27\SubText Geometric methods (including applications of
 algebraic geometry) \SeeAlso{\SbjNo 11T71}\endx
\ThirdLvl 94B30\SubText Majority codes\endx
\ThirdLvl 94B35\SubText Decoding\endx
\ThirdLvl 94B40\SubText Arithmetic codes \SeeAlso{\SbjNo 11T71}\endx
\ThirdLvl 94B50\SubText Synchronization error-correcting codes\endx
\ThirdLvl 94B60\SubText Other types of codes\endx
\ThirdLvl 94B65\SubText Bounds on codes\endx
\ThirdLvl 94B70\SubText Error probability\endx
\ThirdLvl 94B75\SubText Applications of the theory of convex sets and
 geometry of numbers (covering radius, etc.) \SeeAlso{\SbjNo
 11H31}\endx
\ThirdLvl 94B99\SubText \NoneOfAbove\endx
\SecndLvl 94C++\SubText Circuits, networks\endx
\ThirdLvl 94C05\SubText Analytic circuit theory\endx
\ThirdLvl 94C10\SubText Switching theory, application of Boolean
 algebra; Boolean functions \SeeAlso{\SbjNo 06E30}\endx
\ThirdLvl 94C12\SubText Fault detection; testing\endx
\ThirdLvl 94C15\SubText Applications of graph theory \SeeAlso{\SbjNo
 05Cxx, \SbjNo 68R10}\endx
\ThirdLvl 94C30\SubText Applications of design theory \SeeAlso{\SbjNo
 05Bxx}\endx
\ThirdLvl 94C99\SubText \NoneOfAbove\endx
\SecndLvl 94D05\SubText Fuzzy sets and logic \ExtraText{(in connection
 with questions of Section 94)} \SeeAlso{\SbjNo 03B52, \SbjNo 03E72,
 \SbjNo 04A72, \SbjNo 28E10}\endx
% 3/20/85 - (DCL) added \ExtraText to the parenthetical remarks\endx

% after 58D and 94D05\endx
% 5/22/85 - (DCL) added \ExtraText to the parenthetical remark after 40B05 -\endx
% was printing in MR.\endx
% 8/90 Major revision -- plus two new sections added (64 and 91)\endx
