# zbMATH — the first resource for mathematics

## Lawvere, Francis William

Compute Distance To:
 Author ID: lawvere.f-william Published as: Lawvere, F. W.; Lawvere, F. William; Lawvere, William External Links: MGP · Wikidata · dblp · GND
 Documents Indexed: 64 Publications since 1963, including 8 Books Biographic References: 3 Publications
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#### Co-Authors

 50 single-authored 4 Schanuel, Stephen Hoel 3 Adámek, Jiří 3 Rosický, Jiří 2 Menni, Matías 1 Betti, Renato 1 Kelly, Gregory Maxwell 1 Mäurer, Christoph 1 Rosebrugh, Robert D. 1 Seely, Robert A. G. 1 Wraith, Gavin C.
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#### Serials

 8 Reprints in Theory and Applications of Categories 7 Theory and Applications of Categories 3 Journal of Pure and Applied Algebra 3 Lecture Notes in Mathematics 2 Cahiers de Topologie et Géométrie Différentielle Catégoriques 2 Revista Colombiana de Matemáticas 2 Proceedings of the National Academy of Sciences of the United States of America 2 Categories and General Algebraic Structures with Applications 1 Algebra Universalis 1 Dialectica 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Theoretical Computer Science 1 Bulletin de la Société Mathématique de Belgique. Série A 1 Applied Categorical Structures 1 Philosophia Mathematica. Series III 1 The Bulletin of Symbolic Logic 1 Scientiae Mathematicae Japonicae 1 Supplemento ai Rendiconti del Circolo Matemàtico di Palermo. Serie II
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#### Fields

 54 Category theory; homological algebra (18-XX) 24 Mathematical logic and foundations (03-XX) 10 General and overarching topics; collections (00-XX) 6 Mechanics of deformable solids (74-XX) 5 Algebraic geometry (14-XX) 4 History and biography (01-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Combinatorics (05-XX) 3 General topology (54-XX) 2 General algebraic systems (08-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Differential geometry (53-XX) 2 Mechanics of particles and systems (70-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH

57 Publications have been cited 1,283 times in 984 Documents Cited by Year
Functorial semantics of algebraic theories. Zbl 0119.25901
Lawvere, F. W.
1963
Metric spaces, generalized logic, and closed categories. Zbl 0335.18006
Lawvere, F. William
1974
Lawvere, F. William
1969
An elementary theory of the category of sets. Zbl 0141.00603
Lawvere, F. W.
1964
Equality in hyperdoctrines and comprehension schema as an adjoint functor. Zbl 0234.18002
Lawvere, William
1970
Metric spaces, generalized logic and closed categories. Reprint. Zbl 1078.18501
Lawvere, F. William
2002
Some algebraic problems in the context of functorial semantics of algebraic theories. Zbl 0204.33802
Lawvere, F. William
1968
Functorial semantics of algebraic theories and some algebraic problems in the context of functorial semantics of algebraic theories. Zbl 1062.18004
Lawvere, F. William
2004
Conceptual mathematics. A first introduction to categories. Zbl 0889.18001
Lawvere, F. William; Schanuel, Stephen H.
1997
Diagonal arguments and cartesian closed categories. Zbl 0218.18002
Lawvere, F. William
1969
Quantifiers and sheaves. Zbl 0261.18010
Lawvere, F. W.
1971
Ordinal sums and equational doctrines. Zbl 0165.03204
Lawvere, F. W.
1969
The category of categories as a foundation for mathematics. Zbl 0192.09702
Lawvere, F. W.
1966
Sets for mathematics. Zbl 1031.18001
Lawvere, F. William; Rosebrugh, Robert
2003
Some thoughts on the future of category theory. Zbl 0779.18001
Lawvere, F. William
1991
Taking categories seriously. Zbl 0648.18001
Lawvere, F. W.
1986
Categorical dynamics. Zbl 0403.18005
Lawvere, F. William
1979
Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body. Zbl 0472.18009
Lawvere, F. William
1980
Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes. Zbl 0745.18002
Lawvere, F. William
1991
Conceptual mathematics. A first introduction to categories. 2nd ed. Zbl 1179.18001
Lawvere, F. William; Schanuel, Stephen H.
2009
Cohesive toposes and Cantor’s ‘lauter Einsen’. Zbl 0801.18005
Lawvere, F. W.
1994
On the complete lattice of essential localizations. Zbl 0686.18005
Kelly, G. M.; Lawvere, F. W.
1989
Continuously variable sets: algebraic geometry = geometric logic. Zbl 0364.18002
Lawvere, F. William
1975
The Hopf algebra of Möbius intervals. Zbl 1236.18001
Lawvere, F. W.; Menni, M.
2010
Axiomatic cohesion. Zbl 1123.18001
Lawvere, F. William
2007
Algebraic theories, algebraic categories, and algebraic functors. Zbl 0158.26401
Lawvere, F. W.
1965
Categories of space and of quantity. Zbl 0846.18001
Lawvere, F. William
1992
Qualitative distinctions between some toposes of generalized graphs. Zbl 0675.18003
Lawvere, F. William
1989
Variable quantities and variable structures in topoi. Zbl 0353.02043
Lawvere, F. William
1976
On the duality between varieties and algebraic theories. Zbl 1090.18004
Adámek, J.; Lawvere, F. W.; Rosický, J.
2003
Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness. Zbl 1375.18017
Lawvere, F. W.; Menni, M.
2015
Continuous categories revisited. Zbl 1018.18003
Adámek, J.; Lawvere, F. W.; Rosický, J.
2003
How algebraic is algebra? Zbl 0978.18006
Adámek, Jiří; Lawvere, F. W.; Rosický, Jiří
2001
Diagonal arguments and Cartesian closed categories (with author commentary). Zbl 1089.18004
Lawvere, F. William
2006
Adjoints in and among bicategories. Zbl 0862.18002
Lawvere, F. William
1996
Introduction. Zbl 0249.18015
Lawvere, F. William
1972
Toposes, algebraic geometry and logic. Dalhousie University, Halifax, January 16-19, 1971. Zbl 0233.00005
Lawvere, F. W. (ed.)
1972
Unity and identity of opposites in calculus and physics. Zbl 0858.18002
Lawvere, F. William
1996
Categories of spaces may not be generalized spaces as exemplified by directed graphs. Zbl 0648.18004
Lawvere, F. William
1986
Lawvere, F. William
2006
An elementary theory of the category of sets (long version) with commentary. Zbl 1072.18005
Lawvere, F. William
2005
Core varieties, extensivity, and rig geometry. Zbl 1210.18012
Lawvere, F. William
2008
Linearization of graphic toposes via Coxeter groups. Zbl 0992.18002
Lawvere, F. William
2002
More on graphic toposes. Zbl 0759.18004
Lawvere, F. William
1991
Introduction to part I. Zbl 0353.18006
Lawvere, F. William
1975
Taking categories seriously. Zbl 1072.18001
Lawvere, F. William
2005
Volterra’s functionals and covariant cohesion of space. Zbl 0979.01014
Lawvere, F. William
2000
Conceptual mathematics. A first introduction to categories. With the assistance of Emilio Faro, Fatima Fenaroli and Danilo Lawvere. Zbl 0889.18002
Lawvere, F. William; Schanuel, Stephen H.
1991
Categories of spaces may not be generalized spaces as exemplified by directed graphs. Zbl 1177.18003
Lawvere, F. William
2005
Everyday physics of extended bodies or why functionals need analyzing. Zbl 1388.18008
Lawvere, F. William
2017
Functorial concepts of complexity for finite automata. Zbl 1062.18001
Lawvere, F. William
2004
Left and right adjoint operations on spaces and data types. Zbl 1046.18001
Lawvere, F. William
2004
Foundations and applications: axiomatization and education. Zbl 1058.03080
Lawvere, F. William
2003
Categorical algebra for continuum micro physics. Zbl 1014.18002
Lawvere, F. William
2002
Comments on the development of topos theory. Zbl 0969.18003
Lawvere, F. William
2000
Categories in continuum physics. Lectures given at a Workshop held at SUNY, Buffalo (New York) 1982. Zbl 0581.00020
Lawvere, F. W. (ed.); Schanuel, S. H. (ed.)
1986
Model theory and topoi. A collection of lectures by various authors. Zbl 0299.00014
Lawvere, F. W. (ed.); Maurer, C. (ed.); Wraith, G. C. (ed.)
1975
Everyday physics of extended bodies or why functionals need analyzing. Zbl 1388.18008
Lawvere, F. William
2017
Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness. Zbl 1375.18017
Lawvere, F. W.; Menni, M.
2015
The Hopf algebra of Möbius intervals. Zbl 1236.18001
Lawvere, F. W.; Menni, M.
2010
Conceptual mathematics. A first introduction to categories. 2nd ed. Zbl 1179.18001
Lawvere, F. William; Schanuel, Stephen H.
2009
Core varieties, extensivity, and rig geometry. Zbl 1210.18012
Lawvere, F. William
2008
Axiomatic cohesion. Zbl 1123.18001
Lawvere, F. William
2007
Diagonal arguments and Cartesian closed categories (with author commentary). Zbl 1089.18004
Lawvere, F. William
2006
Lawvere, F. William
2006
An elementary theory of the category of sets (long version) with commentary. Zbl 1072.18005
Lawvere, F. William
2005
Taking categories seriously. Zbl 1072.18001
Lawvere, F. William
2005
Categories of spaces may not be generalized spaces as exemplified by directed graphs. Zbl 1177.18003
Lawvere, F. William
2005
Functorial semantics of algebraic theories and some algebraic problems in the context of functorial semantics of algebraic theories. Zbl 1062.18004
Lawvere, F. William
2004
Functorial concepts of complexity for finite automata. Zbl 1062.18001
Lawvere, F. William
2004
Left and right adjoint operations on spaces and data types. Zbl 1046.18001
Lawvere, F. William
2004
Sets for mathematics. Zbl 1031.18001
Lawvere, F. William; Rosebrugh, Robert
2003
On the duality between varieties and algebraic theories. Zbl 1090.18004
Adámek, J.; Lawvere, F. W.; Rosický, J.
2003
Continuous categories revisited. Zbl 1018.18003
Adámek, J.; Lawvere, F. W.; Rosický, J.
2003
Foundations and applications: axiomatization and education. Zbl 1058.03080
Lawvere, F. William
2003
Metric spaces, generalized logic and closed categories. Reprint. Zbl 1078.18501
Lawvere, F. William
2002
Linearization of graphic toposes via Coxeter groups. Zbl 0992.18002
Lawvere, F. William
2002
Categorical algebra for continuum micro physics. Zbl 1014.18002
Lawvere, F. William
2002
How algebraic is algebra? Zbl 0978.18006
Adámek, Jiří; Lawvere, F. W.; Rosický, Jiří
2001
Volterra’s functionals and covariant cohesion of space. Zbl 0979.01014
Lawvere, F. William
2000
Comments on the development of topos theory. Zbl 0969.18003
Lawvere, F. William
2000
Conceptual mathematics. A first introduction to categories. Zbl 0889.18001
Lawvere, F. William; Schanuel, Stephen H.
1997
Adjoints in and among bicategories. Zbl 0862.18002
Lawvere, F. William
1996
Unity and identity of opposites in calculus and physics. Zbl 0858.18002
Lawvere, F. William
1996
Cohesive toposes and Cantor’s ‘lauter Einsen’. Zbl 0801.18005
Lawvere, F. W.
1994
Categories of space and of quantity. Zbl 0846.18001
Lawvere, F. William
1992
Some thoughts on the future of category theory. Zbl 0779.18001
Lawvere, F. William
1991
Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes. Zbl 0745.18002
Lawvere, F. William
1991
More on graphic toposes. Zbl 0759.18004
Lawvere, F. William
1991
Conceptual mathematics. A first introduction to categories. With the assistance of Emilio Faro, Fatima Fenaroli and Danilo Lawvere. Zbl 0889.18002
Lawvere, F. William; Schanuel, Stephen H.
1991
On the complete lattice of essential localizations. Zbl 0686.18005
Kelly, G. M.; Lawvere, F. W.
1989
Qualitative distinctions between some toposes of generalized graphs. Zbl 0675.18003
Lawvere, F. William
1989
Taking categories seriously. Zbl 0648.18001
Lawvere, F. W.
1986
Categories of spaces may not be generalized spaces as exemplified by directed graphs. Zbl 0648.18004
Lawvere, F. William
1986
Categories in continuum physics. Lectures given at a Workshop held at SUNY, Buffalo (New York) 1982. Zbl 0581.00020
Lawvere, F. W. (ed.); Schanuel, S. H. (ed.)
1986
Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body. Zbl 0472.18009
Lawvere, F. William
1980
Categorical dynamics. Zbl 0403.18005
Lawvere, F. William
1979
Variable quantities and variable structures in topoi. Zbl 0353.02043
Lawvere, F. William
1976
Continuously variable sets: algebraic geometry = geometric logic. Zbl 0364.18002
Lawvere, F. William
1975
Introduction to part I. Zbl 0353.18006
Lawvere, F. William
1975
Model theory and topoi. A collection of lectures by various authors. Zbl 0299.00014
Lawvere, F. W. (ed.); Maurer, C. (ed.); Wraith, G. C. (ed.)
1975
Metric spaces, generalized logic, and closed categories. Zbl 0335.18006
Lawvere, F. William
1974
Introduction. Zbl 0249.18015
Lawvere, F. William
1972
Toposes, algebraic geometry and logic. Dalhousie University, Halifax, January 16-19, 1971. Zbl 0233.00005
Lawvere, F. W. (ed.)
1972
Quantifiers and sheaves. Zbl 0261.18010
Lawvere, F. W.
1971
Equality in hyperdoctrines and comprehension schema as an adjoint functor. Zbl 0234.18002
Lawvere, William
1970
Lawvere, F. William
1969
Diagonal arguments and cartesian closed categories. Zbl 0218.18002
Lawvere, F. William
1969
Ordinal sums and equational doctrines. Zbl 0165.03204
Lawvere, F. W.
1969
Some algebraic problems in the context of functorial semantics of algebraic theories. Zbl 0204.33802
Lawvere, F. William
1968
The category of categories as a foundation for mathematics. Zbl 0192.09702
Lawvere, F. W.
1966
Algebraic theories, algebraic categories, and algebraic functors. Zbl 0158.26401
Lawvere, F. W.
1965
An elementary theory of the category of sets. Zbl 0141.00603
Lawvere, F. W.
1964
Functorial semantics of algebraic theories. Zbl 0119.25901
Lawvere, F. W.
1963
all top 5

#### Cited by 796 Authors

 20 Hofmann, Dirk 20 Zhang, Dexue 18 Street, Ross H. 16 Lai, Hongliang 16 Tholen, Walter 15 Bunge, Marta C. 15 Ésik, Zoltán 13 Carboni, Aurelio 13 Clementino, Maria Manuel 13 Rosický, Jiří 12 Borceux, Francis 12 Lack, Stephen 12 Menni, Matías 12 Rosenthal, Kimmo I. 11 Bloom, Stephen L. 11 Došen, Kosta 11 Lambek, Joachim 10 Adámek, Jiří 10 Meseguer Guaita, José 10 Power, John 10 Trnková, Věra 10 Walters, Robert F. C. 9 Kelly, Gregory Maxwell 9 Montanari, Ugo G. 9 Reyes, Gonzalo E. 9 Shen, Lili 9 Zafiris, Elias 8 Fiore, Marcelo P. 8 Grandis, Marco 8 Kock, Anders 7 Diers, Yves 7 Garner, Richard 7 Goguen, Joseph Amadee 7 Höhle, Ulrich 7 Kock, Joachim 7 Stubbe, Isar 7 Vitale, Enrico Maria 6 Abramsky, Samson 6 Awodey, Steve 6 Hyland, J. Martin E. 6 Jacobs, Bart 6 Kasangian, Stefano 6 Kerkhoff, Sebastian 6 Lawvere, Francis William 6 Petrić, Zoran 6 Solovyov, Sergey A. 5 Gunji, Yukio-Pegio 5 Isbell, John Rolfe 5 Johnstone, Peter T. 5 Kurz, Alexander 5 Labella, Anna 5 Manes, Ernest G. 5 Niefield, Susan B. 5 Pavlović, Duško 5 Rosebrugh, Robert D. 5 Rosolini, Giuseppe 5 Schröder, Lutz 5 Shulman, Michael A. 5 Stout, Lawrence Neff 5 Wood, Robert James 4 Barr, Michael 4 Berger, Clemens 4 Betti, Renato 4 Blanc, David Abraham 4 Bruni, Roberto 4 Denecke, Klaus Dieter 4 Elgot, Calvin C. 4 Ellerman, David P. 4 Funk, Jonathon R. 4 Gadducci, Fabio 4 Gálvez-Carrillo, Imma 4 Gambino, Nicola 4 Ghani, Neil 4 Hermida, Claudio 4 Heymans, Hans 4 Leinster, Tom 4 Lindner, Harald 4 Lucyshyn-Wright, Rory B. B. 4 Maietti, Maria Emilia 4 Mulry, Philip S. 4 Nishimura, Hirokazu 4 Oriat, C. 4 Paré, Robert 4 Pasquali, Fabio 4 Rabe, Florian 4 Riehl, Emily 4 Santocanale, Luigi 4 Sassone, Vladimiro 4 Sichler, Jiří Jan 4 Sobociński, Paweł 4 Sousa, Lurdes 4 Tonks, Andrew 4 Wagner, Eric G. 4 Waszkiewicz, Paweł 4 Wright, Jesse B. 3 Appel, Andrea 3 Bauer, Andrej 3 Bergman, George M. 3 Blanc, Georges 3 Bourn, Dominique ...and 696 more Authors
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#### Cited in 141 Serials

 159 Journal of Pure and Applied Algebra 59 Theoretical Computer Science 52 Cahiers de Topologie et Géométrie Différentielle Catégoriques 50 Fuzzy Sets and Systems 47 Applied Categorical Structures 36 Advances in Mathematics 30 MSCS. Mathematical Structures in Computer Science 28 Topology and its Applications 28 Annals of Pure and Applied Logic 25 Journal of Algebra 22 Theory and Applications of Categories 20 Algebra Universalis 15 Journal of Computer and System Sciences 15 Synthese 14 Information and Computation 10 The Journal of Symbolic Logic 10 Studia Logica 10 The Review of Symbolic Logic 9 Diagrammes 9 Tbilisi Mathematical Journal 8 Mathematische Zeitschrift 8 Transactions of the American Mathematical Society 8 Logica Universalis 7 Applied Mathematics and Computation 7 Journal of Philosophical Logic 7 Cahiers de Topologie et Géométrie Différentielle Catégoriques 6 Communications in Algebra 6 International Journal of General Systems 6 International Journal of Theoretical Physics 6 Archiv der Mathematik 6 The Bulletin of Symbolic Logic 5 Manuscripta Mathematica 5 Logical Methods in Computer Science 4 Journal of Mathematical Physics 4 Proceedings of the American Mathematical Society 4 Siberian Mathematical Journal 4 History and Philosophy of Logic 4 Algebraic & Geometric Topology 4 Bulletin of the American Mathematical Society 3 Mathematische Annalen 3 Mathematical Systems Theory 3 Semigroup Forum 3 Journal of Symbolic Computation 3 Archive for Mathematical Logic 3 Journal of Mathematical Sciences (New York) 3 Selecta Mathematica. New Series 3 Foundations of Science 3 The Journal of Logic and Algebraic Programming 3 Central European Journal of Mathematics 3 Journal of Homotopy and Related Structures 3 Journal of Logical and Algebraic Methods in Programming 2 Communications in Mathematical Physics 2 Discrete Mathematics 2 Journal of Mathematical Analysis and Applications 2 Periodica Mathematica Hungarica 2 Bulletin of Mathematical Biology 2 Journal of Geometry and Physics 2 The Mathematical Intelligencer 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Information Sciences 2 Journal of Geometry 2 Kybernetika 2 Mathematica Slovaca 2 Quaestiones Mathematicae 2 Rendiconti del Seminario Matemàtico e Fisico di Milano 2 Advances in Applied Mathematics 2 Physica D 2 Bulletin of the American Mathematical Society. New Series 2 Indagationes Mathematicae. New Series 2 Journal of Applied Non-Classical Logics 2 Topology Proceedings 2 St. Petersburg Mathematical Journal 2 Annals of Mathematics and Artificial Intelligence 2 Logic and Logical Philosophy 2 Journal of Applied Logic 2 Foundations of Physics 2 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 2 Armenian Journal of Mathematics 2 Formalized Mathematics 2 Axiomathes 2 Higher Structures 1 International Journal of Modern Physics A 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Archive for History of Exact Sciences 1 Archiv für Mathematische Logik und Grundlagenforschung 1 Bulletin of the Australian Mathematical Society 1 Discrete Applied Mathematics 1 Letters in Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Chaos, Solitons and Fractals 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Automatica 1 Commentationes Mathematicae Universitatis Carolinae 1 Computing 1 Czechoslovak Mathematical Journal 1 Duke Mathematical Journal 1 Geometriae Dedicata 1 Glasgow Mathematical Journal 1 Inventiones Mathematicae 1 Memoirs of the American Mathematical Society ...and 41 more Serials
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#### Cited in 48 Fields

 675 Category theory; homological algebra (18-XX) 312 Mathematical logic and foundations (03-XX) 209 Computer science (68-XX) 130 Order, lattices, ordered algebraic structures (06-XX) 101 General topology (54-XX) 97 General algebraic systems (08-XX) 52 Algebraic topology (55-XX) 40 Associative rings and algebras (16-XX) 33 Quantum theory (81-XX) 32 Group theory and generalizations (20-XX) 29 General and overarching topics; collections (00-XX) 19 Combinatorics (05-XX) 18 Algebraic geometry (14-XX) 18 Functional analysis (46-XX) 16 Geometry (51-XX) 14 History and biography (01-XX) 13 Commutative algebra (13-XX) 11 Nonassociative rings and algebras (17-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Biology and other natural sciences (92-XX) 10 Manifolds and cell complexes (57-XX) 9 Differential geometry (53-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Systems theory; control (93-XX) 6 Field theory and polynomials (12-XX) 6 Real functions (26-XX) 6 Measure and integration (28-XX) 6 Convex and discrete geometry (52-XX) 6 Information and communication theory, circuits (94-XX) 5 Dynamical systems and ergodic theory (37-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Probability theory and stochastic processes (60-XX) 3 Relativity and gravitational theory (83-XX) 2 Number theory (11-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Mechanics of deformable solids (74-XX) 1 $$K$$-theory (19-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX)

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