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## Aris, Rutherford

Compute Distance To:
 Author ID: aris.rutherford Published as: Aris, Rutherford; Aris, R.
 Documents Indexed: 60 Publications since 1958, including 16 Books
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#### Co-Authors

 23 single-authored 6 Amundson, Neal R. 6 Rhee, Hyun-Ku 4 Stephanopoulos, George 3 Kennedy, Clinton R. 2 Alhumaizi, Khalid 2 Derby, Jeffrey J. 2 Lauffenburger, Douglas A. 2 Mehta, B. N. 2 Morari, Manfred 2 Salinger, Andrew G. 2 Svoronos, Spyros A. 1 Aronson, Donald G. 1 Astarita, Gianni 1 Brandon, Simon 1 Bunow, Barry 1 Cho, B. K. 1 Denn, Morton M. 1 Farr, William W. 1 Fredrickson, A. G. 1 Kevrekidis, Ioannis George 1 McKarnin, M. A. 1 Pelikan, Stephan 1 Penn, Mischa 1 Petroulas, T. 1 Stephanopoulos, Gregory 1 Swinney, Harry L. 1 Viswanathan, Subbaraman 1 Vlachos, Dionisios G. 1 Yesberg, D. 1 Zygourakis, Kyriacos
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#### Serials

 6 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 4 International Journal of Control 4 Mathematical Biosciences 3 Journal of Mathematical Analysis and Applications 2 Bulletin of Mathematical Biology 2 Chaos, Solitons and Fractals 2 Philosophical Transactions of the Royal Society of London. Ser. A 2 Physica D 2 Mathematical and Computer Modelling 2 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 1 Archive for Rational Mechanics and Analysis 1 Computers & Mathematics with Applications 1 International Journal for Numerical Methods in Fluids 1 Journal of the Institute of Mathematics and its Applications 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematical Modelling 1 Annals of the New York Academy of Sciences 1 The IMA Volumes in Mathematics and its Applications 1 Mathematics in Science and Engineering 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Fields

 20 Biology and other natural sciences (92-XX) 14 Classical thermodynamics, heat transfer (80-XX) 12 Partial differential equations (35-XX) 11 Ordinary differential equations (34-XX) 11 Fluid mechanics (76-XX) 7 Numerical analysis (65-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Systems theory; control (93-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 General and overarching topics; collections (00-XX) 2 Probability theory and stochastic processes (60-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH Open

42 Publications have been cited 728 times in 561 Documents Cited by Year
The mathematical theory of diffusion and reaction in permeable catalysts. Vol. I: The theory of the steady state. Zbl 0315.76051
Aris, Rutherford
1975
Vectors, tensors, and the basic equations of fluid mechanics. Zbl 0123.41502
Aris, Rutherford
1962
Vectors, tensors and the basic equations of fluid mechanics. Reprint of the 1962 original. Zbl 1158.76300
Aris, Rutherford
1989
On the dispersion of a solute in pulsating flow through a tube. Zbl 0094.40201
Aris, R.
1960
The mathematical theory of diffusion and reaction in permeable catalysts. Vol. II: Questions of uniqueness, stability, and transient behaviour. Zbl 0315.76052
Aris, Rutherford
1975
Finite element formulations for large-scale, coupled flows in adjacent porous and open fluid domains. Zbl 0807.76039
Salinger, A. G.; Aris, R.; Derby, J. J.
1994
On the theory of multicomponent chromatography. Zbl 0233.76157
Rhee, Hyun-Ku; Aris, R.; Amundson, N. R.
1970
Discrete dynamic programming. An introduction to the optimization of staged processes. Zbl 0122.37503
Aris, Rutherford
1964
A stochastic analysis of the growth of competing microbial populations in a continuous biochemical reactor. Zbl 0449.92018
Stephanopoulos, Gregory; Aris, R.; Fredrickson, A. G.
1979
On the dispersion of a solute by diffusion, convection and exchange between phases. Zbl 0092.19404
Aris, R.
1959
Traveling waves in a simple population model involving growth and death. Zbl 0431.92021
Kennedy, C. R.; Aris, R.
1980
Mathematical modelling techniques. Zbl 0392.93003
Aris, R.
1978
Bilinear approximation of general non-linear dynamic systems with linear inputs. Zbl 0432.93028
Svoronos, Spyros; Stephanopoulos, George; Aris, Rutherford
1980
Traveling bands of chemotactic bacteria in the context of population growth. Zbl 0525.92018
Lauffenburger, D.; Kennedy, C. R.; Aris, R.
1984
Mathematical modeling. A chemical engineer’s perspective. Zbl 0960.34001
Aris, Rutherford
1999
The optimal design of chemical reactors. A study in dynamic programming. Zbl 0095.14605
Aris, Rutherford
1961
Numerical computation of invariant circles of maps. Zbl 0581.58030
Kevrekidis, I. G.; Aris, R.; Schmidt, L. D.; Pelikan, S.
1985
First-order partial differential equations. Vol. 2: Theory and application of hyperbolic systems of quasilinear equations. Reprint of the 1989 original. Zbl 0982.35002
Rhee, Hyun Ku; Aris, Rutherford; Amundson, Neal R.
2001
Variational methods applied to problems of diffusion and reaction. Zbl 0273.49067
Strieder, W.; Aris, R.
1973
First-order partial differential equations. Volume I: Theory and application of single equations. Zbl 0699.35001
Rhee, Hyun Ku; Aris, Rutherford; Amundson, Neal R.
1986
Weakly coupled systems of nonlinear elliptic boundary value problems. Zbl 0504.35041
Zygourakis, Kyriacos; Aris, Rutherford
1982
First-order partial differential equations. Vol. 1: Theory and application of single equations. Reprint of the 1986 original. Zbl 0982.35001
Rhee, Hyun-Ku; Aris, Rutherford; Amundson, Neal R.
2001
Surveying a dynamical system: a study of the Gray-Scott reaction in a two-phase reactor. Zbl 0854.92024
Alhumaizi, Khalid; Aris, Rutherford
1995
On bilinear estimation and control. Zbl 0474.93079
Svoronos, S.; Stephanopoulos, G.; Aris, R.
1981
Measurement of leukocyte motility and chemotaxis parameters using a quantitative analysis of the under-agarose migration assay. Zbl 0407.92004
Lauffenburger, Douglas; Aris, Rutherford
1979
Diffusion and first order reaction in a general multilayered membrane. Zbl 0307.92004
Bunow, B.; Aris, R.
1975
Buoyancy-driven flows of a radiatively participating fluid in a vertical cylinder heated from below. Zbl 0802.76077
Salinger, A. G.; Brandon, S.; Aris, R.; Derby, J. J.
1993
On the dispersion of linear kinematic waves. Zbl 0083.21401
Aris, R.
1958
First-order partial differential equations. Volume II. Theory and application of hyperbolic systems of quasilinear equations. Zbl 0699.35002
Rhee, Hyun-Ku; Aris, Rutherford; Amundson, Neal R.
1989
A note on a form of the Emden-Fowler equation. Zbl 0219.34002
Mehta, B. N.; Aris, R.
1971
Chaos in a simple two-phase reactor. Zbl 0812.34041
Alhumaizi, Khalid; Aris, Rutherford
1994
Bifurcations of a model diffusion-reaction system. Zbl 0474.35011
Kennedy, C. R.; Aris, R.
1980
Diffusion and reaction in a Mandelbrot lung. Zbl 0749.92001
Aris, Rutherford
1991
Dynamic programming in counter-current systems. Zbl 0118.35504
Yesberg, D.; Aris, R.
1963
Multicomponent adsorption in continuous countercurrent exchangers. Zbl 0233.76158
Rhee, Hyun-Ku; Aris, R.; Amundson, N. R.
1971
The mathematical theory of a countercurrent catalytic reactor. Zbl 0559.76093
Cho, B. K.; Aris, R.; Carr, R. W.
1982
Some characteristic nonlinearities of chemical reaction engineering. Zbl 0494.92026
Aris, Rutherford
1982
The mere notion of a model. Zbl 0522.00019
Aris, Rutherford; Penn, Mischa
1980
An analysis of the counter-current moving bed reactor. Zbl 0301.35014
Viswanathan, Subbaraman; Aris, Rutherford
1974
Autonomous bifurcations of a simple bimolecular surface-reaction model. Zbl 0669.34043
McKarnin, M. A.; Aris, R.; Schmidt, L. D.
1988
Forced oscillations of chemical reactors. Zbl 0722.92021
Aris, R.
1990
Degenerate Hopf bifurcations in the CSTR with reactions A$$\to B\to C$$. Zbl 0636.58027
Farr, W. W.; Aris, R.
1987
First-order partial differential equations. Vol. 2: Theory and application of hyperbolic systems of quasilinear equations. Reprint of the 1989 original. Zbl 0982.35002
Rhee, Hyun Ku; Aris, Rutherford; Amundson, Neal R.
2001
First-order partial differential equations. Vol. 1: Theory and application of single equations. Reprint of the 1986 original. Zbl 0982.35001
Rhee, Hyun-Ku; Aris, Rutherford; Amundson, Neal R.
2001
Mathematical modeling. A chemical engineer’s perspective. Zbl 0960.34001
Aris, Rutherford
1999
Surveying a dynamical system: a study of the Gray-Scott reaction in a two-phase reactor. Zbl 0854.92024
Alhumaizi, Khalid; Aris, Rutherford
1995
Finite element formulations for large-scale, coupled flows in adjacent porous and open fluid domains. Zbl 0807.76039
Salinger, A. G.; Aris, R.; Derby, J. J.
1994
Chaos in a simple two-phase reactor. Zbl 0812.34041
Alhumaizi, Khalid; Aris, Rutherford
1994
Buoyancy-driven flows of a radiatively participating fluid in a vertical cylinder heated from below. Zbl 0802.76077
Salinger, A. G.; Brandon, S.; Aris, R.; Derby, J. J.
1993
Diffusion and reaction in a Mandelbrot lung. Zbl 0749.92001
Aris, Rutherford
1991
Forced oscillations of chemical reactors. Zbl 0722.92021
Aris, R.
1990
Vectors, tensors and the basic equations of fluid mechanics. Reprint of the 1962 original. Zbl 1158.76300
Aris, Rutherford
1989
First-order partial differential equations. Volume II. Theory and application of hyperbolic systems of quasilinear equations. Zbl 0699.35002
Rhee, Hyun-Ku; Aris, Rutherford; Amundson, Neal R.
1989
Autonomous bifurcations of a simple bimolecular surface-reaction model. Zbl 0669.34043
McKarnin, M. A.; Aris, R.; Schmidt, L. D.
1988
Degenerate Hopf bifurcations in the CSTR with reactions A$$\to B\to C$$. Zbl 0636.58027
Farr, W. W.; Aris, R.
1987
First-order partial differential equations. Volume I: Theory and application of single equations. Zbl 0699.35001
Rhee, Hyun Ku; Aris, Rutherford; Amundson, Neal R.
1986
Numerical computation of invariant circles of maps. Zbl 0581.58030
Kevrekidis, I. G.; Aris, R.; Schmidt, L. D.; Pelikan, S.
1985
Traveling bands of chemotactic bacteria in the context of population growth. Zbl 0525.92018
Lauffenburger, D.; Kennedy, C. R.; Aris, R.
1984
Weakly coupled systems of nonlinear elliptic boundary value problems. Zbl 0504.35041
Zygourakis, Kyriacos; Aris, Rutherford
1982
The mathematical theory of a countercurrent catalytic reactor. Zbl 0559.76093
Cho, B. K.; Aris, R.; Carr, R. W.
1982
Some characteristic nonlinearities of chemical reaction engineering. Zbl 0494.92026
Aris, Rutherford
1982
On bilinear estimation and control. Zbl 0474.93079
Svoronos, S.; Stephanopoulos, G.; Aris, R.
1981
Traveling waves in a simple population model involving growth and death. Zbl 0431.92021
Kennedy, C. R.; Aris, R.
1980
Bilinear approximation of general non-linear dynamic systems with linear inputs. Zbl 0432.93028
Svoronos, Spyros; Stephanopoulos, George; Aris, Rutherford
1980
Bifurcations of a model diffusion-reaction system. Zbl 0474.35011
Kennedy, C. R.; Aris, R.
1980
The mere notion of a model. Zbl 0522.00019
Aris, Rutherford; Penn, Mischa
1980
A stochastic analysis of the growth of competing microbial populations in a continuous biochemical reactor. Zbl 0449.92018
Stephanopoulos, Gregory; Aris, R.; Fredrickson, A. G.
1979
Measurement of leukocyte motility and chemotaxis parameters using a quantitative analysis of the under-agarose migration assay. Zbl 0407.92004
Lauffenburger, Douglas; Aris, Rutherford
1979
Mathematical modelling techniques. Zbl 0392.93003
Aris, R.
1978
The mathematical theory of diffusion and reaction in permeable catalysts. Vol. I: The theory of the steady state. Zbl 0315.76051
Aris, Rutherford
1975
The mathematical theory of diffusion and reaction in permeable catalysts. Vol. II: Questions of uniqueness, stability, and transient behaviour. Zbl 0315.76052
Aris, Rutherford
1975
Diffusion and first order reaction in a general multilayered membrane. Zbl 0307.92004
Bunow, B.; Aris, R.
1975
An analysis of the counter-current moving bed reactor. Zbl 0301.35014
Viswanathan, Subbaraman; Aris, Rutherford
1974
Variational methods applied to problems of diffusion and reaction. Zbl 0273.49067
Strieder, W.; Aris, R.
1973
A note on a form of the Emden-Fowler equation. Zbl 0219.34002
Mehta, B. N.; Aris, R.
1971
Multicomponent adsorption in continuous countercurrent exchangers. Zbl 0233.76158
Rhee, Hyun-Ku; Aris, R.; Amundson, N. R.
1971
On the theory of multicomponent chromatography. Zbl 0233.76157
Rhee, Hyun-Ku; Aris, R.; Amundson, N. R.
1970
Discrete dynamic programming. An introduction to the optimization of staged processes. Zbl 0122.37503
Aris, Rutherford
1964
Dynamic programming in counter-current systems. Zbl 0118.35504
Yesberg, D.; Aris, R.
1963
Vectors, tensors, and the basic equations of fluid mechanics. Zbl 0123.41502
Aris, Rutherford
1962
The optimal design of chemical reactors. A study in dynamic programming. Zbl 0095.14605
Aris, Rutherford
1961
On the dispersion of a solute in pulsating flow through a tube. Zbl 0094.40201
Aris, R.
1960
On the dispersion of a solute by diffusion, convection and exchange between phases. Zbl 0092.19404
Aris, R.
1959
On the dispersion of linear kinematic waves. Zbl 0083.21401
Aris, R.
1958
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#### Cited by 834 Authors

 8 Andrei, Neculai 8 Zhan, Huashui 7 Baronas, Romas 7 Howes, Frederick A. 7 O’Regan, Donal 6 Bobisud, Larry E. 6 Staněk, Svatoslav 5 Diaz Diaz, Jesus Ildefonso 5 Kulys, Juozas 5 da Silva Montenegro, Marcelo 5 Rosen, Gerald 4 Ajbar, Abdelhamid 4 Al-Refai, Mohammed 4 Basaran, Osman A. 4 Carl, Siegfried 4 Feng, Zhaosheng 4 Gutlyanskiĭ, Vladimir Ya. 4 Merkin, John H. 4 Ryazanov, Vladimir Il’ich 4 Venturi, Daniele 4 Wang, Yuanming 4 Wu, Jianhua 3 Agarwal, Ravi P. 3 Aris, Rutherford 3 Beale, J. Thomas 3 Bohl, Erich 3 Bourdarias, Christian 3 Cherniha, Roman M. 3 De, Sirshendu 3 Friedman, Avner 3 Herrera, Blas 3 Ivanauskas, Feliksas 3 Jia, Huabing 3 Kennedy, Clinton R. 3 Lauffenburger, Douglas A. 3 Lu, Yunguang 3 McCartin, Brian J. 3 Nesmelova, Ol’ga Vladimirovna 3 Peletier, Lambertus Adrianus 3 Petkevičius, Linas 3 Phillips, Daniel R. 3 Pintér, János D. 3 Prakash, Jai 3 Qu, Changzheng 3 Ramachandran, Palghat A. 3 Sekhar, G. P. Raja 3 Serov, Mykola I. 3 Shaker, Hamid Reza 3 Sniedovich, Moshe 3 Stakgold, Ivar 3 Wendroff, Burton 3 Yin, Jingxue 2 Alhumaizi, Khalid 2 Amann, Herbert 2 Anderson, Daniel M. 2 Bandle, Catherine 2 Bedrikovetsky, Pavel G. 2 Bellman, Richard Ernest 2 Bertele, Umberto 2 Betti, Raimondo 2 Böhm, Michael C. 2 Bonorino, Leonardo Prange 2 Borazjani, S. 2 Bradshaw-Hajek, Bronwyn H. 2 Brioschi, Francesco 2 Bürger, Raimund 2 Cannata, Giovanni 2 Canon, Éric 2 Chen, Kangping 2 Cohen, Donald Sussman 2 da Silva, João Vítor 2 Dávila, Juan 2 De Graaf, J. M. 2 de Queiroz, Olivâine Santana 2 Djebali, Smail 2 Dopazo, César 2 Duduchava, Roland 2 Dyson, Rosemary J. 2 Elghobashi, Said E. 2 Fan, Liang-Tseng 2 Ferrante, Antonino 2 Fiedler, Bernold 2 Forbes, Lawrence K. 2 Formaggia, Luca 2 Gallerano, Francesco 2 Galligani, Emanuele 2 Gerolymos, G. A. 2 Giacomoni, Jacques 2 Gisclon, Marguerite 2 Huang, Wenzhang 2 Iwamoto, Seiichi 2 Jeffrey, Alan P. 2 Ji, Lina 2 Johansen, Thormod E. 2 Jones, Andrew D. jun. 2 Juang, Jer-Nan 2 Junca, Stéphane 2 Kamat, Pritish M. 2 Kotta, Ulle 2 Lee, Cheh-Han ...and 734 more Authors
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#### Cited in 178 Serials

 44 Journal of Mathematical Analysis and Applications 27 Journal of Fluid Mechanics 25 Journal of Computational Physics 20 Journal of Differential Equations 15 Nonlinear Analysis. Theory, Methods & Applications 14 Bulletin of Mathematical Biology 11 Computers & Mathematics with Applications 10 Applicable Analysis 10 Journal of Computational and Applied Mathematics 9 International Journal of Control 9 International Journal of Engineering Science 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Studies in Applied Mathematics 8 Applied Mathematical Modelling 8 Physics of Fluids 7 Journal of Engineering Mathematics 7 Applied Mathematics and Computation 7 Physica D 7 Mathematical and Computer Modelling 7 Journal of Mathematical Chemistry 7 Nonlinear Analysis. Real World Applications 6 Archive for Rational Mechanics and Analysis 6 Journal of Mathematical Biology 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Journal of Optimization Theory and Applications 6 Acta Applicandae Mathematicae 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Mathematical Biosciences 5 Transactions of the American Mathematical Society 5 Journal of Non-Newtonian Fluid Mechanics 5 Continuum Mechanics and Thermodynamics 5 The ANZIAM Journal 4 Computer Methods in Applied Mechanics and Engineering 4 International Journal for Numerical Methods in Fluids 4 Journal of the Mechanics and Physics of Solids 4 Physica A 4 Numerische Mathematik 4 Quarterly of Applied Mathematics 4 Applied Numerical Mathematics 4 Applied Mathematics Letters 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Communications in Partial Differential Equations 4 Journal of Theoretical Biology 3 Computers and Fluids 3 Reports on Mathematical Physics 3 Chaos, Solitons and Fractals 3 Applied Mathematics and Optimization 3 Automatica 3 International Journal of Computer Mathematics 3 Nonlinear Dynamics 3 Optimization Methods & Software 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 European Journal of Mechanics. B. Fluids 3 Advances in Difference Equations 2 Acta Mechanica 2 International Journal of Heat and Mass Transfer 2 Journal of Statistical Physics 2 Mathematical Methods in the Applied Sciences 2 Physics of Fluids 2 Rocky Mountain Journal of Mathematics 2 Theoretical and Computational Fluid Dynamics 2 Mathematics and Computers in Simulation 2 Mathematische Nachrichten 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 2 Applied Mathematics and Mechanics. (English Edition) 2 Computational Mechanics 2 Numerical Algorithms 2 Annals of Physics 2 Linear Algebra and its Applications 2 SIAM Journal on Scientific Computing 2 Journal of Mathematical Sciences (New York) 2 Computational and Applied Mathematics 2 Advances in Differential Equations 2 Engineering Analysis with Boundary Elements 2 Journal of Inequalities and Applications 2 Interfaces and Free Boundaries 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Function Spaces 1 International Journal of Modern Physics B 1 Bulletin of the Australian Mathematical Society 1 Classical and Quantum Gravity 1 Computer Physics Communications 1 Fluid Dynamics 1 General Relativity and Gravitation 1 International Journal of Mathematical Education in Science and Technology 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Applied Mathematics and Mechanics 1 Journal of the Franklin Institute 1 Journal of Mathematical Physics 1 Letters in Mathematical Physics 1 Nonlinearity 1 Physics Reports 1 Rheologica Acta 1 Wave Motion 1 Prikladnaya Matematika i Mekhanika 1 Soviet Applied Mechanics 1 Annali di Matematica Pura ed Applicata. Serie Quarta ...and 78 more Serials
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#### Cited in 38 Fields

 254 Partial differential equations (35-XX) 170 Fluid mechanics (76-XX) 94 Biology and other natural sciences (92-XX) 90 Numerical analysis (65-XX) 71 Ordinary differential equations (34-XX) 42 Classical thermodynamics, heat transfer (80-XX) 29 Operations research, mathematical programming (90-XX) 28 Systems theory; control (93-XX) 27 Mechanics of deformable solids (74-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 20 Dynamical systems and ergodic theory (37-XX) 17 Operator theory (47-XX) 12 Global analysis, analysis on manifolds (58-XX) 11 Statistical mechanics, structure of matter (82-XX) 7 Optics, electromagnetic theory (78-XX) 6 Differential geometry (53-XX) 5 Real functions (26-XX) 5 Approximations and expansions (41-XX) 4 Functional analysis (46-XX) 4 Statistics (62-XX) 4 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Integral transforms, operational calculus (44-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Difference and functional equations (39-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)