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## Grushin, V. V.

Compute Distance To:
 Author ID: grushin.v-v Published as: Grushin, V. V. External Links: MGP
 Documents Indexed: 75 Publications since 1959
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#### Co-Authors

 41 single-authored 9 Vishik, Marko Iosifovich 8 Dobrokhotov, Sergei Yurievich 6 Gorin, Evgeniĭ Alekseevich 4 Sergeev, Sergeĭ Alekseevich 3 Brüning, Jochen 3 Palamodov, Victor Pavlovitch 3 Shananin, N. A. 3 Vaĭnberg, Boris Rufimovich 2 Aleksandrov, Pavel Sergeevich 2 Fomin, Sergeĭ Vasil’evich 2 Gel’fand, Israil’ Moiseevich 2 Kolmogorov, Andreĭ Nikolaevich 2 Oleĭnik, Ol’ga Arsen’evna 2 Savsan, M. A. 1 Gorin, A. E. 1 Tirozzi, Brunello 1 Tudorovskii, T. Ya.
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#### Serials

 11 Mathematical Notes 10 Matematicheskiĭ Sbornik. Novaya Seriya 9 Soviet Mathematics. Doklady 8 Uspekhi Matematicheskikh Nauk [N. S.] 7 Mathematics of the USSR, Sbornik 4 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 4 Russian Journal of Mathematical Physics 3 Functional Analysis and its Applications 2 Russian Mathematical Surveys 2 Transactions of the Moscow Mathematical Society 2 Trudy Moskovskogo Matematicheskogo Obshchestva 2 Proceedings of the Steklov Institute of Mathematics 2 Translations. Series 2. American Mathematical Society 1 Matematicheskie Zametki 1 Moscow University Mathematics Bulletin 1 Theoretical and Mathematical Physics 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Nauchnye Doklady Vyssheĭ Shkoly. Fiziko-Matematicheskie Nauki
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#### Fields

 37 Partial differential equations (35-XX) 9 Operator theory (47-XX) 5 Fluid mechanics (76-XX) 5 Quantum theory (81-XX) 3 Numerical analysis (65-XX) 2 History and biography (01-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Geophysics (86-XX)

#### Citations contained in zbMATH Open

40 Publications have been cited 301 times in 229 Documents Cited by Year
On a class of hypoelliptic operators. Zbl 0252.35057
Grushin, V. V.
1971
On a class of elliptic pseudodifferential operators degenerate on a submanifold. Zbl 0238.47038
Grushin, V. V.
1971
On the eigenvalues of finitely perturbed Laplace operators in infinite cylindrical domains. Zbl 1111.35022
Grushin, V. V.
2004
Pseudodifferential operators on $$R^ n$$ with bounded symbols. Zbl 0223.35084
Grushin, V. V.
1970
On Sommerfeld-type conditions for a certain class of partial differential equations. Zbl 0174.14802
Grushin, V. V.
1963
On a class of higher order degenerate elliptic equations. Zbl 0191.11703
Vishik, M. I.; Grushin, V. V.
1970
Boundary value problems for elliptic equations degenerate on the boundary of a domain. Zbl 0202.11402
Vishik, M. I.; Grushin, V. V.
1970
Elliptic pseudodifferential operators on a closed manifold which degenerate on a submanifold. Zbl 0238.35078
Vishik, M. I.; Grushin, V. V.
1969
Hypoelliptic differential equations and pseudodifferential operators with operator-valued symbols. Zbl 0255.35022
Grushin, V. V.
1973
Multiparameter perturbation theory of Fredholm operators applied to Bloch functions. Zbl 1197.47025
Grushin, V. V.
2009
Asymptotic behavior of the eigenvalues of the Schrödinger operator with transversal potential in a weakly curved infinite cylinder. Zbl 1082.35113
Grushin, V. V.
2005
Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. Zbl 1282.47079
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.
2012
Asymptotic behavior of eigenvalues of the Laplace operator in thin infinite tubes. Zbl 1181.35150
Grushin, V. V.
2009
Asymptotic behavior of the eigenvalues of the Schrödinger operator in thin closed tubes. Zbl 1152.35452
Grushin, V. V.
2008
Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source. Zbl 1293.35279
Grushin, V. V.; Dobrokhotov, S. Yu.; Sergeev, S. A.
2013
Peierls substitution and the Maslov operator method. Zbl 1197.35086
Grushin, V. V.; Dobrokhotov, S. Yu.
2010
Uniformly nonelliptic problems. I, II. Zbl 0179.43304
Vajnberg, B. R.; Grushin, V. V.
1968
Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. Zbl 1274.81069
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya.
2011
Elliptic boundary value problems degenerating on a submanifold of the boundary. Zbl 0238.35032
Vishik, M. I.; Grushin, V. V.
1970
On solutions with isolated singularities for partial differential equations with constant coefficients. Zbl 0162.14701
Grushin, V. V.
1966
Some theorems on the singularities of solutions of differential equations with weighted principal symbols. Zbl 0386.35012
Grushin, V. V.; Shananin, N. A.
1977
Approximate formulas for eigenvalues of the Laplace operator on a torus arising in linear problems with oscillating coefficients. Zbl 1257.35135
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.
2012
Randwertprobleme für elliptische Gleichungen, die auf dem Rand des Gebietes entartet sind. Zbl 0186.17101
Vishik, M. I.; Grushin, V. V.
1969
Entartende elliptische Differential- und Pseudodifferentialoperatoren. Zbl 0209.40901
Vishik, M. I.; Grushin, V. V.
1970
On the proof of the discreteness of the spectrum of one class of differential operators in $$R^ n$$. Zbl 0227.35074
Grushin, V. V.
1971
Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057
Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B.
2016
Smoothness of solutions of boundary value problems for a certain class of elliptic equations of arbitrary order which degenerate on the boundary of the domain. Zbl 0318.35029
Grushin, V. V.; Savsan, M. A.
1975
Homogenization in the problem of long water waves over a bottom site with fast oscillations. Zbl 1315.35165
Grushin, V. V.; Dobrokhotov, S. Yu.
2014
Über eine Klasse hypoelliptischer Operatoren. Zbl 0211.40503
Grushin, V. V.
1970
Hypoelliptische Differentialgleichungen und Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Zbl 0243.35020
Grushin, V. V.
1972
Les problèmes aux limites dégénérées et les opérateurs pseudo- différentiels. Zbl 0244.35075
Grushin, V. V.
1971
Asymptotic behavior of eigenvalues of the Laplace operator in infinite cylinders perturbed by transverse extensions. Zbl 1136.35057
Grushin, V. V.
2007
Generalized method of stationary phase for the Fourier transform of a rapidly oscillating function. Zbl 1384.42002
Grushin, V. V.
2017
Uniformly noncoercive problems for elliptic equations. Zbl 0179.43303
Vajnberg, B. R.; Grushin, V. V.
1967
Degenerating elliptic differential and pseudo-differential operators. Zbl 0222.35024
Vishik, M. I.; Grushin, V. V.
1970
A differential equation without a solution. Zbl 0223.35011
Grushin, V. V.
1971
Zur Definition der hypoelliptischen Gleichungen. Zbl 0104.07301
Gorin, E. A.; Grushin, V. V.
1961
Über die maximale Anzahl von paarweise fremden zueinander homöomorphen Figuren, die sich im dreidimensionalen Raum unterbringen lassen. Zbl 0109.41003
Grushin, V. V.; Palamodov, V. P.
1962
Local theorem for partial differential equations with constant coefficients. Zbl 0162.14702
Gorin, E. A.; Grushin, V. V.
1965
Asymptotics of the propagation problem for linear waves on a two-dimensional lattice and modified Maslov’s canonical operator. Zbl 1435.81082
Grushin, V. V.; Sergeev, S. A.
2020
Asymptotics of the propagation problem for linear waves on a two-dimensional lattice and modified Maslov’s canonical operator. Zbl 1435.81082
Grushin, V. V.; Sergeev, S. A.
2020
Generalized method of stationary phase for the Fourier transform of a rapidly oscillating function. Zbl 1384.42002
Grushin, V. V.
2017
Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections. Zbl 1359.76057
Dobrokhotov, S. Yu.; Grushin, V. V.; Sergeev, S. A.; Tirozzi, B.
2016
Homogenization in the problem of long water waves over a bottom site with fast oscillations. Zbl 1315.35165
Grushin, V. V.; Dobrokhotov, S. Yu.
2014
Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source. Zbl 1293.35279
Grushin, V. V.; Dobrokhotov, S. Yu.; Sergeev, S. A.
2013
Averaging of linear operators, adiabatic approximation, and pseudodifferential operators. Zbl 1282.47079
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.
2012
Approximate formulas for eigenvalues of the Laplace operator on a torus arising in linear problems with oscillating coefficients. Zbl 1257.35135
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.
2012
Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. Zbl 1274.81069
Brüning, J.; Grushin, V. V.; Dobrokhotov, S. Yu.; Tudorovskii, T. Ya.
2011
Peierls substitution and the Maslov operator method. Zbl 1197.35086
Grushin, V. V.; Dobrokhotov, S. Yu.
2010
Multiparameter perturbation theory of Fredholm operators applied to Bloch functions. Zbl 1197.47025
Grushin, V. V.
2009
Asymptotic behavior of eigenvalues of the Laplace operator in thin infinite tubes. Zbl 1181.35150
Grushin, V. V.
2009
Asymptotic behavior of the eigenvalues of the Schrödinger operator in thin closed tubes. Zbl 1152.35452
Grushin, V. V.
2008
Asymptotic behavior of eigenvalues of the Laplace operator in infinite cylinders perturbed by transverse extensions. Zbl 1136.35057
Grushin, V. V.
2007
Asymptotic behavior of the eigenvalues of the Schrödinger operator with transversal potential in a weakly curved infinite cylinder. Zbl 1082.35113
Grushin, V. V.
2005
On the eigenvalues of finitely perturbed Laplace operators in infinite cylindrical domains. Zbl 1111.35022
Grushin, V. V.
2004
Some theorems on the singularities of solutions of differential equations with weighted principal symbols. Zbl 0386.35012
Grushin, V. V.; Shananin, N. A.
1977
Smoothness of solutions of boundary value problems for a certain class of elliptic equations of arbitrary order which degenerate on the boundary of the domain. Zbl 0318.35029
Grushin, V. V.; Savsan, M. A.
1975
Hypoelliptic differential equations and pseudodifferential operators with operator-valued symbols. Zbl 0255.35022
Grushin, V. V.
1973
Hypoelliptische Differentialgleichungen und Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Zbl 0243.35020
Grushin, V. V.
1972
On a class of hypoelliptic operators. Zbl 0252.35057
Grushin, V. V.
1971
On a class of elliptic pseudodifferential operators degenerate on a submanifold. Zbl 0238.47038
Grushin, V. V.
1971
On the proof of the discreteness of the spectrum of one class of differential operators in $$R^ n$$. Zbl 0227.35074
Grushin, V. V.
1971
Les problèmes aux limites dégénérées et les opérateurs pseudo- différentiels. Zbl 0244.35075
Grushin, V. V.
1971
A differential equation without a solution. Zbl 0223.35011
Grushin, V. V.
1971
Pseudodifferential operators on $$R^ n$$ with bounded symbols. Zbl 0223.35084
Grushin, V. V.
1970
On a class of higher order degenerate elliptic equations. Zbl 0191.11703
Vishik, M. I.; Grushin, V. V.
1970
Boundary value problems for elliptic equations degenerate on the boundary of a domain. Zbl 0202.11402
Vishik, M. I.; Grushin, V. V.
1970
Elliptic boundary value problems degenerating on a submanifold of the boundary. Zbl 0238.35032
Vishik, M. I.; Grushin, V. V.
1970
Entartende elliptische Differential- und Pseudodifferentialoperatoren. Zbl 0209.40901
Vishik, M. I.; Grushin, V. V.
1970
Über eine Klasse hypoelliptischer Operatoren. Zbl 0211.40503
Grushin, V. V.
1970
Degenerating elliptic differential and pseudo-differential operators. Zbl 0222.35024
Vishik, M. I.; Grushin, V. V.
1970
Elliptic pseudodifferential operators on a closed manifold which degenerate on a submanifold. Zbl 0238.35078
Vishik, M. I.; Grushin, V. V.
1969
Randwertprobleme für elliptische Gleichungen, die auf dem Rand des Gebietes entartet sind. Zbl 0186.17101
Vishik, M. I.; Grushin, V. V.
1969
Uniformly nonelliptic problems. I, II. Zbl 0179.43304
Vajnberg, B. R.; Grushin, V. V.
1968
Uniformly noncoercive problems for elliptic equations. Zbl 0179.43303
Vajnberg, B. R.; Grushin, V. V.
1967
On solutions with isolated singularities for partial differential equations with constant coefficients. Zbl 0162.14701
Grushin, V. V.
1966
Local theorem for partial differential equations with constant coefficients. Zbl 0162.14702
Gorin, E. A.; Grushin, V. V.
1965
On Sommerfeld-type conditions for a certain class of partial differential equations. Zbl 0174.14802
Grushin, V. V.
1963
Über die maximale Anzahl von paarweise fremden zueinander homöomorphen Figuren, die sich im dreidimensionalen Raum unterbringen lassen. Zbl 0109.41003
Grushin, V. V.; Palamodov, V. P.
1962
Zur Definition der hypoelliptischen Gleichungen. Zbl 0104.07301
Gorin, E. A.; Grushin, V. V.
1961
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#### Cited by 237 Authors

 13 Grushin, V. V. 13 Nazarov, Sergeĭ Aleksandrovich 12 Dobrokhotov, Sergei Yurievich 7 Baev, Aleksandr Dmitrievich 6 Sergeev, Sergeĭ Alekseevich 6 Weinstein, Michael I. 5 Helffer, Bernard 5 Nguyễn Minh Trí 4 Garofalo, Nicola 4 Liu, Hairong 4 Mughetti, Marco 4 Nazaikinskii, Vladimir E. 4 Rădulescu, Vicenţiu D. 4 Rothschild, Linda Preiss 3 Bagirov, Lev A. 3 Bahrouni, Anouar 3 Borisov, Denis Ivanovich 3 Brüning, Jochen 3 Cardone, Giuseppe 3 Fefferman, Charles Louis 3 Kaneko, Akira 3 Matsuzawa, Tadato 3 Nicola, Fabio 3 Rabinovich, Vladimir Samuilovich 3 Rodino, Luigi 3 Saks, Romèn Semenovich 3 Tirozzi, Brunello 3 Yang, Xiaoping 2 Bauer, Wolfram 2 Bolley, Pierre 2 Boutet de Monvel, Louis 2 Bove, Antonio 2 Bruneau, Vincent 2 Budaev, V. S. 2 Camus, Jacques 2 Chang, Der-Chen E. 2 D’Ambrosio, Lorenzo 2 Debbaj, Omar 2 Drouot, Alexis 2 Egorov, Yuriĭ Vladimirovich 2 Furutani, Kenro 2 Gadyl’shin, Rustem R. 2 Hashimoto, Yoshiaki 2 Iwasaki, Chisato 2 Kachmar, Ayman 2 Karlovich, Alexeĭ Yur’evich 2 Kim, KyeongHun 2 Kobylinskii, P. A. 2 Kovalevskĭ, Rostislav A. 2 Kovařík, Hynek 2 Krejčiřík, David 2 Kuchment, Peter A. 2 Kumano-go, Hitoshi 2 Lampart, Jonas 2 Lee-Thorp, James P. 2 Li, Yutian 2 Luyen, Duong Trong 2 Miranda, Pablo L. 2 Mishchenko, Aleksandr Sergeevich 2 Natroshvili, David 2 Oaku, Toshinori 2 Popoff, Nicolas 2 Radkevich, Evgeniĭ Vladimirovich 2 Repovš, Dušan D. 2 Robert, Didier 2 Samet, Bessem 2 Samoĭlenko, Yuliya Ivanivna 2 Sekerzh-Zen’kovich, Sergeĭ Yakovlevich 2 Shananin, N. A. 2 Shen, Zhongwei 2 Shimakura, Norio 2 Taniguchi, Kazuo 2 Tartakoff, David S. 2 Teufel, Stefan 2 Tian, Long 2 Trèves, François 2 Tsutsumi, Akira 2 Verri, Alessandra A. 2 Wong, Man Wah 2 Yener, Abdullah 1 Agarwal, Ravi P. 1 Ahmad, Bashir 1 Alimohammady, Mohsen 1 Al-saedi, Ahmed Eid Salem 1 Arutyunov, Andronick Aramovich 1 Babaytsev, A. A. 1 Barseghyan, Diana 1 Bazaliĭ, Boris V. 1 Beals, Richard W. 1 Beckner, William 1 Bellaïche, André 1 Berestovskiĭ, Valeriĭ Nikolaevich 1 Berkhin, P. E. 1 Bikmetov, Aĭdar Renatovich 1 Briet, Philippe 1 Brudnyi, Yuri A. 1 Buneev, S. S. 1 Burskii, Vladimir Petrovich 1 Calin, Ovidiu L. 1 Cardoso, Fernando ...and 137 more Authors
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#### Cited in 92 Serials

 17 Mathematical Notes 12 Proceedings of the Japan Academy 11 Communications in Partial Differential Equations 9 Annales de l’Institut Fourier 9 Russian Journal of Mathematical Physics 8 Journal of Differential Equations 8 Doklady Mathematics 7 Siberian Mathematical Journal 7 Journal of Mathematical Sciences (New York) 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 5 Proceedings of the American Mathematical Society 4 Journal of Mathematical Analysis and Applications 4 Advances in Mathematics 4 Mathematische Annalen 3 Communications on Pure and Applied Mathematics 3 Journal of Applied Mathematics and Mechanics 3 Journal of Mathematical Physics 3 Theoretical and Mathematical Physics 3 Journal of Functional Analysis 3 Proceedings of the Japan Academy. Series A 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Complex Variables and Elliptic Equations 3 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 2 Archive for Rational Mechanics and Analysis 2 Journal d’Analyse Mathématique 2 Rocky Mountain Journal of Mathematics 2 Russian Mathematical Surveys 2 Ukrainian Mathematical Journal 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Arkiv för Matematik 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Functional Analysis and its Applications 2 Journal of Soviet Mathematics 2 Nagoya Mathematical Journal 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Transactions of the American Mathematical Society 2 The Journal of Geometric Analysis 2 Computational Mathematics and Mathematical Physics 2 Russian Mathematics 2 Sbornik: Mathematics 2 Annales Henri Poincaré 2 Bulletin de la Société Mathématique de France. Supplément. Mémoires 2 Proceedings of the Steklov Institute of Mathematics 2 Journal of Pseudo-Differential Operators and Applications 1 Applicable Analysis 1 Communications in Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Nonlinearity 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Reviews in Mathematical Physics 1 Acta Mathematica 1 Boletim da Sociedade Brasileira de Matemática 1 Bulletin de la Société Mathématique de France 1 Compositio Mathematica 1 Duke Mathematical Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Inventiones Mathematicae 1 Zeitschrift für Analysis und ihre Anwendungen 1 Annals of Global Analysis and Geometry 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 Journal of the American Mathematical Society 1 Aequationes Mathematicae 1 Historia Mathematica 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Knot Theory and its Ramifications 1 St. Petersburg Mathematical Journal 1 Kyushu Journal of Mathematics 1 Turkish Journal of Mathematics 1 Georgian Mathematical Journal 1 NoDEA. Nonlinear Differential Equations and Applications 1 Integral Transforms and Special Functions 1 Izvestiya: Mathematics 1 Abstract and Applied Analysis 1 Acta Mathematica Sinica. English Series 1 Differential Equations 1 Journal of Evolution Equations 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Multiscale Modeling & Simulation 1 Journal of Mathematical Physics, Analysis, Geometry 1 Journal of Physics A: Mathematical and Theoretical 1 Operators and Matrices 1 Banach Journal of Mathematical Analysis 1 Science China. Mathematics 1 Bulletin of Mathematical Sciences 1 Publications of the Research Institute for Mathematical Sciences, Series A 1 Arabian Journal of Mathematics 1 Annals of PDE 1 Pure and Applied Analysis
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#### Cited in 35 Fields

 194 Partial differential equations (35-XX) 45 Operator theory (47-XX) 29 Quantum theory (81-XX) 20 Functional analysis (46-XX) 16 Global analysis, analysis on manifolds (58-XX) 16 Fluid mechanics (76-XX) 12 Optics, electromagnetic theory (78-XX) 12 Statistical mechanics, structure of matter (82-XX) 7 Differential geometry (53-XX) 5 Numerical analysis (65-XX) 5 Mechanics of deformable solids (74-XX) 4 Real functions (26-XX) 4 Special functions (33-XX) 3 History and biography (01-XX) 3 Topological groups, Lie groups (22-XX) 3 Functions of a complex variable (30-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Probability theory and stochastic processes (60-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Ordinary differential equations (34-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Information and communication theory, circuits (94-XX)