Edit Profile Foiaş, Ciprian Ilie Compute Distance To: Compute Author ID: foias.ciprian Published as: Foias, C.; Foias, Ciprian; Foias, Cyprian; Foiaş, C; Foiaş, C.; Foiaş, Ciprian; Foiaš, Ciprian External Links: MGP · Wikidata · GND Documents Indexed: 498 Publications since 1954, including 20 Books Biographic References: 5 Publications all top 5 Co-Authors 79 single-authored 59 Temam, Roger Meyer 57 Szőkefalvi-Nagy, Béla 44 Bercovici, Hari 43 Tannenbaum, Allen Robert 41 Pearcy, Carl Mark Jr. 28 Frazho, Arthur E. 26 Jolly, Michael S. 23 Manley, Oscar P. 21 Apostol, Constantin Gelu 16 Nicolaenko, Basil 15 Constantin, Peter 15 Titi, Edriss Saleh 14 Rosa, Ricardo M. S. 13 Saut, Jean-Claude 13 Voiculescu, Dan-Virgil 12 Douglas, Ronald George 12 Gussi, Gheorghe 10 Jung, Il Bong 10 Ko, Eungil 10 Poénaru, Valentin 9 Becker, Robert A. 9 Eden, Alp 9 Kaashoek, Marinus Adriaan 8 Biswas, Animikh 8 Ceausescu, Zoia 8 Dinculeanu, Nicolae 7 Gohberg, Israel 6 Hoang, Luan Thach 6 Olson, Eric J. 6 Sell, George Roger 6 Zames, George 5 Colojoară, Ion 5 Dascaliuc, Radu 5 Gu, Caixing 5 Holm, Darryl D. 4 Kukavica, Igor 4 Singer, Ivan 3 Arsene, Grigore 3 Ball, Joseph Anthony 3 Chen, Shiyi 3 Guillopé, Colette 3 Hamid, Sami M. 3 Helton, John William 3 Kérchy, László 3 Nicolescu, Miron 3 Onica, Constantin 3 Sarkar, Jaydeb 3 Zhang, Bingsheng 2 Balci, Nusret 2 Cheskidov, Alexey 2 Gehér, László 2 Kevrekidis, Ioannis George 2 Kravchenko, Rostyslav V. 2 Li, Weishun 2 Marinescu, Georges 2 Marinescu, Gheorghe 2 Mondaini, Cecilia F. 2 Prodi, Giovanni 2 Sherman, Peter J. 2 Smith, Lidia 2 Suciu, Ion 2 Teman, Roger 2 Vasilescu, Florian-Horia 2 Williams, Jonathan P. 2 Wynne, Shannon 2 Yang, Yong 2 Ziane, Mohammed 2 Zsidó, Lászlo 1 Anastasio, Sal 1 Anderson, Joel 1 Ando, Takahisa 1 Ben-Artzi, Asher 1 Boyd, John H. III 1 Brown, Lawrence Gerald 1 Carlson, Jon Frederick 1 Chae, Dongho 1 Chevreau, Bernard 1 Ching, Wai-Mee 1 Choquet, Gustave 1 Clark, Douglas Napier 1 Cuculescu, Ion 1 Davis, Chandler 1 Davis, Martin David 1 Deckard, Don 1 Dixmier, Jacques 1 Doering, Charles R. 1 Fisher, Joseph A. 1 Frisch, Uriel 1 Georgiou, Tryphon T. 1 Gibbon, John D. 1 Gologan, Radu-Nicolae 1 Kalantarov, Varga K. 1 Katok, Anatole B. 1 Khargonekar, Pramod P. 1 Kovács, István A. 1 Lan, Ruomeng 1 Langer, Heinz 1 Langsam, J. 1 Larios, Adam 1 Lax, Peter David ...and 32 more Co-Authors all top 5 Serials 60 Acta Scientiarum Mathematicarum 30 Revue Roumaine de Mathématiques Pures et Appliquées 18 Indiana University Mathematics Journal 15 Integral Equations and Operator Theory 15 Comptes Rendus de l’Académie des Sciences. Série I 14 Journal of Functional Analysis 13 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 11 Physica D 11 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 10 Journal of Dynamics and Differential Equations 10 Académie de la République Populaire Roumaine, Revue de Mathématiques Pures et Appliquées 9 Journal of Mathematical Analysis and Applications 8 Michigan Mathematical Journal 8 Journal of Operator Theory 7 Nonlinearity 7 Proceedings of the American Mathematical Society 6 Journal of Differential Equations 6 Transactions of the American Mathematical Society 5 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 5 Comunicările Academiei Republicii Populare Române 5 Operator Theory: Advances and Applications 4 Journal of Statistical Physics 4 Rendiconti del Seminario Matematico della Università di Padova 4 SIAM Journal on Control and Optimization 4 Libertas Mathematica 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Discrete and Continuous Dynamical Systems 3 Communications in Mathematical Physics 3 Communications on Pure and Applied Mathematics 3 Journal of Mathematical Physics 3 Studia Mathematica 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Pacific Journal of Mathematics 3 Studii şi Cercetări Matematice 3 Systems & Control Letters 3 Linear Algebra and its Applications 3 SIAM Journal on Mathematical Analysis 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Doklady Akademii Nauk SSSR 2 Israel Journal of Mathematics 2 Journal of Fluid Mechanics 2 Physics of Fluids 2 Russian Mathematical Surveys 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 Physics of Fluids, A 2 Annales de l’Institut Fourier 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Bulletin de la Société Mathématique de France 2 Canadian Journal of Mathematics 2 Journal of Mathematical Economics 2 Mathematische Nachrichten 2 Mathematische Zeitschrift 2 Physics of Fluids 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques 2 Journal of Mathematics and Mechanics 2 Encyclopedia of Mathematics and Its Applications 1 IEEE Transactions on Information Theory 1 IMA Journal of Applied Mathematics 1 International Journal of Control 1 Journal of Mathematical Biology 1 Physics Letters. A 1 Mathematics of Computation 1 Analele Universităţii din Timişoara. Ştiinţe Matematice 1 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 1 Archiv der Mathematik 1 Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle Série 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Compositio Mathematica 1 Czechoslovak Mathematical Journal 1 Econometrica 1 IEEE Transactions on Automatic Control 1 Illinois Journal of Mathematics 1 Journal of Economic Theory 1 Journal für die Reine und Angewandte Mathematik 1 Memoirs of the American Mathematical Society 1 Portugaliae Mathematica 1 Proceedings of the London Mathematical Society. Third Series 1 SIAM Journal on Numerical Analysis 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 MCSS. Mathematics of Control, Signals, and Systems 1 Economics Letters 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Proceedings of the National Academy of Sciences of the United States of America 1 Notices of the American Mathematical Society 1 Indagationes Mathematicae. New Series 1 Journal of Nonlinear Science 1 Economic Theory 1 The New York Journal of Mathematics 1 Analele Universităţii din Timişoara. Seria Matematică-Informatică 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Physical Review Letters 1 Journal of the Australian Mathematical Society 1 SIAM Journal on Applied Dynamical Systems 1 Academia Republicii Populare Romîne, Studii Şi Cercetări Matematice 1 Academia Republicii Populare Romîne. Buletin Ştiinţific. Secţiunea de Ştiinţe Matematice şi Fizike 1 Analele Universitaţii din Timişoara. Seria Ştiinţe Matematice-Fizice ...and 15 more Serials all top 5 Fields 204 Operator theory (47-XX) 123 Partial differential equations (35-XX) 98 Fluid mechanics (76-XX) 43 Dynamical systems and ergodic theory (37-XX) 41 Functional analysis (46-XX) 33 Systems theory; control (93-XX) 17 Functions of a complex variable (30-XX) 15 Ordinary differential equations (34-XX) 11 Global analysis, analysis on manifolds (58-XX) 9 Numerical analysis (65-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Probability theory and stochastic processes (60-XX) 6 General and overarching topics; collections (00-XX) 6 Approximations and expansions (41-XX) 5 History and biography (01-XX) 4 Geophysics (86-XX) 2 Number theory (11-XX) 2 Measure and integration (28-XX) 2 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 385 Publications have been cited 8,216 times in 4,702 Documents Cited by ▼ Year ▼ Harmonic analysis of operators on Hilbert space. Zbl 0201.45003Sz.-Nagy, Béla; Foiaş, Ciprian 669 1970 Navier-Stokes equations. Zbl 0687.35071Constantin, Peter; Foias, Ciprian 562 1988 Navier-Stokes equations and turbulence. Zbl 0994.35002Foias, C.; Rosa, R.; Manley, O.; Temam, R. 266 2001 Inertial manifolds for nonlinear evolutionary equations. Zbl 0643.58004Foias, Ciprian; Sell, George R.; Temam, Roger 254 1988 Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. Zbl 0454.35073Foiaş, Ciprian; Temam, R. 247 1979 Gevrey class regularity for the solutions of the Navier-Stokes equations. Zbl 0702.35203Foias, C.; Temam, R. 233 1989 Exponential attractors for dissipative evolution equations. Zbl 0842.58056Eden, A.; Foias, C.; Nicolaenko, B.; Temam, R. 207 1994 Integral manifolds and inertial manifolds for dissipative partial differential equations. Zbl 0683.58002Constantin, P.; Foias, C.; Nicolaenko, B.; Temam, R. 188 1989 Structure of the set of stationary solutions of the Navier Stokes equations. Zbl 0335.35077Foiaş, Ciprian; Temam, R. 186 1977 Harmonic analysis of operators on Hilbert space. 2nd revised and enlarged ed. Zbl 1234.47001Sz.-Nagy, Béla; Foias, Ciprian; Bercovici, Hari; Kérchy, László 175 2010 The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. Zbl 0995.35051Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. 174 2002 The Navier-Stokes-alpha model of fluid turbulence. Zbl 1037.76022Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. 161 2001 The commutant lifting approach to interpolation problems. Zbl 0718.47010Foias, Ciprian; Frazho, Arthur E. 160 1990 Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Zbl 1042.76525Chen, Shiyi; Foias, Ciprian; Holm, Darryl D.; Olson, Eric; Titi, Edriss S. 133 1998 Modelling of the interaction of small and large eddies in two dimensional turbulent flows. Zbl 0663.76054Foias, C.; Manley, O.; Temam, R. 122 1988 Theory of generalized spectral operators. Zbl 0189.44201Colojoară, Ion; Foiaş, Ciprian 117 1968 Attractors representing turbulent flows. Zbl 0567.35070Constantin, P.; Foiaş, Ciprian; Temam, R. 109 1985 Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2. Zbl 0176.54103Foiaš, Ciprian; Prodi, G. 105 1968 Analyse harmonique des opérateurs de l’espace de Hilbert. Zbl 0157.43201Sz.-Nagy, Béla; Foiaş, Ciprian 105 1967 Attractors for the Bénard problem: Existence and physical bounds on their fractal dimension. Zbl 0646.76098Foias, C.; Manley, O.; Temam, R. 102 1987 A connection between the Camassa-Holm equations and turbulent flows in channels and pipes. Zbl 1147.76357Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S. 100 1999 The Camassa-Holm equations and turbulence. Zbl 1194.76069Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S. 87 1999 Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension. Zbl 0694.35028Foias, C.; Nicolaenko, B.; Sell, G. R.; Temam, R. 87 1988 Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations. Zbl 0692.35053Foias, Ciprian; Sell, George R.; Titi, Edriss S. 84 1989 Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. I. Zbl 0608.47005Apostol, C.; Bercovici, H.; Foias, C.; Pearcy, C. 83 1985 Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations. Zbl 0582.35092Constantin, P.; Foiaş, Ciprian 79 1985 Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation. Zbl 0384.35047Foiaş, Ciprian; Temam, R. 79 1978 On the dimension of the attractors in two-dimensional turbulence. Zbl 0658.58030Constantin, P.; Foias, C.; Temam, R. 74 1988 Determining modes and fractal dimension of turbulent flows. Zbl 0607.76054Constantin, P.; Foias, C.; Manley, O. P.; Temam, R. 73 1985 Asymptotic analysis of the Navier-Stokes equations. Zbl 0584.35007Foiaş, Ciprian; Manley, O. P.; Temam, R.; Treve, Y. M. 72 1983 Determining nodes, finite differences schemes and inertial manifolds. Zbl 0714.34078Foias, Ciprian; Titi, Edriss S. 68 1991 Determination of the solutions of the Navier-Stokes equations by a set of nodal values. Zbl 0563.35058Foiaş, Ciprian; Temam, Roger 58 1984 Solutions statistiques homogenes des équations de Navier-Stokes. Zbl 0406.35053Foiaş, Ciprian; Teman, R. 55 1979 Spectral barriers and inertial manifolds for dissipative partial differential equations. Zbl 0701.35024Constantin, P.; Foias, C.; Nicolaenko, B.; Témam, R. 53 1989 Energy dissipation in body-forced turbulence. Zbl 1029.76025Doering, Charles R.; Foias, Ciprian 51 2002 Dilatation des commutants d’opérateurs. Zbl 0173.16503Sz.-Nagy, Béla; Foiaš, Ciprian 50 1968 Asymptotic behavior, as \(t\to +\infty\) of solutions of Navier-Stokes equations and nonlinear spectral manifolds. Zbl 0565.35087Foiaş, Ciprian; Saut, J. C. 46 1984 Statistical study of Navier-Stokes equations. II. Zbl 0283.76018Foiaş, Ciprian 43 1973 Metric constrained interpolation, commutant lifting and systems. Zbl 0923.47009Foias, C.; Frazho, A. E.; Gohberg, I.; Kaashoek, M. A. 40 1998 Dual algebras with applications to invariant subspaces and dilation theory. Zbl 0569.47007Bercovici, Hari; Foiaş, Ciprian; Pearcy, Carl 40 1985 Statistical study of Navier-Stokes equations. I. Zbl 0283.76017Foiaş, Ciprian 40 1973 Spectral maximal spaces and decomposable operators in Banach space. Zbl 0176.43802Foiaş, Ciprian 37 1963 On global attractors of the 3D Navier–Stokes equations. Zbl 1113.35140Cheskidov, A.; Foias, C. 36 2006 Robust control of infinite dimensional systems. Frequency domain methods. Zbl 0839.93003Foias, Ciprian; Özbay, Hitay; Tannenbaum, Allen 36 1996 Some results on non-quasitriangular operators. IV. Zbl 0264.47007Apostol, Constantin; Foiaş, Ciprian; Voiculescu, Dan 32 1973 Finite fractal dimension and Hölder-Lipschitz parametrization. Zbl 0887.54034Foias, C.; Olson, E. 31 1996 On the \(H^{\infty}\)-optimal sensitivity problem for systems with delays. Zbl 0631.93020Foias, Ciprian; Tannenbaum, Allen; Zames, George 30 1987 A characterization of Ramsey equilibrium. Zbl 0612.90015Becker, Robert A.; Foias, Ciprian 30 1987 Weighted sensitivity minimization for delay systems. Zbl 0631.93019Foias, Ciprian; Tannenbaum, Allen; Zames, George 30 1986 Asymptotic numerical analysis for the Navier-Stokes equations. Zbl 0555.76030Foiaş, Ciprian; Temam, R. 30 1983 New a priori estimates for Navier-Stokes equations in dimension 3. Zbl 0472.35070Foiaş, Ciprian; Guillopé, Colette; Témam, Roger 30 1981 Statistical estimates for the Navier-Stokes equations and the Kraichnan theory of 2-D fully developed turbulence. Zbl 1158.76327Foias, C.; Jolly, M. S.; Manley, O. P.; Rosa, R. 29 2002 Dissipativity of numerical schemes. Zbl 0734.65080Foias, C.; Jolly, M. S.; Kevrekidis, I. G.; Titi, E. S. 27 1991 What do the Navier-Stokes equations tell us about turbulence? Zbl 0890.76030Foias, Ciprian 26 1997 Some remarks on the representation of linear operators in spaces of vector-valued continuous functions. Zbl 0102.32302Foiaš, Ciprian; Singer, Ivan 26 1960 A discrete data assimilation scheme for the solutions of the two-dimensional Navier-Stokes equations and their statistics. Zbl 1362.35208Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. 25 2016 Local and global Lyapunov exponents. Zbl 0718.34080Eden, A.; Foias, C.; Temam, R. 25 1991 Variétés inertielles des équations différentielles dissipatives. (Inertial manifolds for dissipative differential equations). Zbl 0591.35062Foiaş, Ciprian; Sell, George R.; Témam, Roger 25 1985 On the large time Galerkin approximation of the Navier-Stokes equations. Zbl 0551.76021Constantin, P.; Foiaş, Ciprian; Temam, R. 24 1984 Sur les solutions statistiques des équations de Navier-Stokes. Zbl 0344.76015Foiaş, Ciprian; Prodi, G. 24 1976 The algebraic approximation of attractors: The finite dimensional case. Zbl 0671.58024Foias, C.; Temam, R. 23 1988 On intertwining dilations. VIII. Zbl 0454.47005Arsene, Gr.; Ceausescu, Zoia; Foiaş, Ciprian 22 1980 Invariant para-closed subspaces. Zbl 0259.47005Foiaş, Ciprian 22 1972 Estimates for the energy cascade in three-dimensional turbulent flows. Zbl 1172.76319Foias, Ciprian; Manley, Oscar P.; Rosa, Ricardo M. S.; Temam, Roger 21 2001 Determining nodes for the Kuramoto-Sivashinsky equation. Zbl 0835.35067Foias, Ciprian; Kukavica, Igor 21 1995 Approximate inertial manifolds and effective viscosity in turbulent flows. Zbl 0732.76001Foias, Ciprian; Manley, Oscar P.; Temam, Roger 21 1991 A spectral commutant lifting theorem. Zbl 0738.47006Bercovici, Hari; Foias, Ciprian; Tannenbaum, Allen 21 1991 Ensembles inertiels pour des équations d’évolution dissipatives. (Inertial sets for dissipative evolution equations). Zbl 0707.35017Eden, Alp; Foias, Ciprian; Nicolaenko, Basil; Temam, Roger 21 1990 Linearization and normal form of the Navier-Stokes equations with potential forces. Zbl 0635.35075Foias, C.; Saut, J. C. 21 1987 Sur l’interaction des petits et grands tourbillons dans des écoulements turbulents. (On the interaction of small and large eddies in turbulent flows). Zbl 0624.76072Foias, Ciprian; Manley, Oscar; Temam, Roger 21 1987 Some explicit formulae for the singular values of certain Hankel operators with factorizable symbol. Zbl 0659.47029Foias, Ciprian; Tannenbaum, Allen; Zames, George 20 1988 On certain classes of power-bounded operators in Hilbert spaces. Zbl 0141.32201Sz.-Nagy, Béla; Foiaş, Ciprian 20 1966 Sur certains théoremes d’interpolation. Zbl 0127.06803Foiaš, Ciprian; Lions, J. L. 20 1961 Une remarque sur l’unicité des solutions des équations de Navier-Stokes en dimension \(n\). Zbl 0107.07602Foiaš, Ciprian 20 1961 Une application des distributions vectorielles à la théorie spectrale. Zbl 0095.09905Foiaş, Ciprian 20 1960 Relations between energy and enstrophy on the global attractor of the 2-D Navier-Stokes equations. Zbl 1100.35078Dascaliuc, R.; Foias, C.; Jolly, M. S. 19 2005 Effects of the forcing function spectrum on the energy spectrum in 2-D turbulence. Zbl 0827.76033Constantin, Peter; Foias, Ciprian; Manley, Oscar P. 19 1994 Properties which normal operators share with normal derivations and related operators. Zbl 0324.47018Anderson, Joel; Foiaş, Ciprian 19 1975 The local bifurcation of Ramsey equilibrium. Zbl 0829.90025Becker, Robert A.; Foias, Ciprian 18 1994 On the Nehari problem for a certain class of \(L^{\infty}\)-functions appearing in control theory. Zbl 0635.47027Foiaş, Ciprian; Tannenbaum, Allen 18 1987 Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations. Zbl 1304.35486Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger 17 2013 A determining form for the two-dimensional Navier-Stokes equations: the Fourier modes case. Zbl 1426.76103Foias, Ciprian; Jolly, Michael S.; Kravchenko, Rostyslav; Titi, Edriss S. 17 2012 Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence. Zbl 1185.35161Dascaliuc, R.; Foias, C.; Jolly, M. S. 17 2010 Complete contractivity of maps associated with the Aluthge and Duggal transforms. Zbl 1066.47037Foiaş, Ciprian; Jung, Il Bong; Ko, Eungil; Pearcy, Carl 17 2003 On the numerical algebraic approximation of global attractors. Zbl 0837.34052Foias, C.; Jolly, M. S. 17 1995 Asymptotic integrations of Navier-Stokes equations with potential forces. I. Zbl 0739.35066Foias, C.; Saut, J. C. 17 1991 Analyse harmonique des opérateurs de l’espace de Hilbert. Zbl 0202.13102Sz.-Nagy, Béla; Foiaş, C. 17 1970 Sur les contractions de l’espace de Hilbert. IV. Zbl 0097.31703Sz.-Nagy, Béla; Foiaş, Ciprian 17 1960 A remark on two constructions of exponential attractors for \(\alpha\)-contractions. Zbl 0898.58035Eden, A.; Foias, C.; Kalantarov, V. 16 1998 Exponential decay of the power spectrum of turbulence. Zbl 1081.35505Bercovici, H.; Constantin, P.; Foias, C.; Manley, O. P. 16 1995 On the structure of intertwining operators. Zbl 0272.47010Sz.-Nagy, Béla; Foiaş, Ciprian 16 1973 Dirichlet quotients and 2D periodic Navier-Stokes equations. Zbl 0874.35085Constantin, Peter; Foias, Ciprian; Kukavica, Igor; Majda, Andrew J. 15 1997 Hölder continuity for the inverse of Mañé’s projection. Zbl 0815.46016Ben-Artzi, A.; Eden, A.; Foiaş, C.; Nicolaenko, B. 15 1993 Dilation theory and systems of simultaneous equations in the predual of an operator algebra. I. Zbl 0541.47007Bercovici, H.; Foiaş, Ciprian; Pearcy, C. 15 1983 Spectral capacities and decomposable operators. Zbl 0176.43801Foiaş, Ciprian 15 1968 A unified approach to determining forms for the 2D Navier-Stokes equations – the general interpolants case. Zbl 1301.35108Foias, C.; Jolly, M. S.; Kravchenko, R.; Titi, E. S. 14 2014 Topological properties of the weak global attractor of the three-dimensional Navier-Stokes equations. Zbl 1191.35204Foias, Ciprian; Rosa, Ricardo; Temam, Roger 14 2010 The existence of Ramsey equilibrium. Zbl 0745.90017Becker, Robert A.; Boyd, John H. III; Foias, Ciprian 14 1991 Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. II. Zbl 0608.47006Apostol, C.; Bercovici, H.; Foias, C.; Pearcy, C. 14 1985 Navier-Stokes equations and turbulence. Paperback reprint of the hardback edition 2001. Zbl 1139.35001Foias, C.; Rosa, R.; Manley, O.; Temam, R. 13 2008 Properties of stationary statistical solutions of the three-dimensional Navier-Stokes equations. Zbl 1421.35243Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger M. 6 2019 Downscaling data assimilation algorithm with applications to statistical solutions of the Navier-Stokes equations. Zbl 1420.35181Biswas, Animikh; Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. 6 2019 Navier and Stokes meet Poincaré and Dulac. Zbl 1457.35024Foias, Ciprian; Hoang, Luan; Saut, Jean-Claude 1 2018 Existence time for the 3D Navier-Stokes equations in a generalized Gevrey class. Zbl 1398.76032Biswas, Animikh; Foias, Ciprian; Nicolaenko, Basil 1 2018 On the attractor for the semi-dissipative Boussinesq equations. Zbl 1361.35138Biswas, Animikh; Foias, Ciprian; Larios, Adam 10 2017 One-dimensional parametric determining form for the two-dimensional Navier-Stokes equations. Zbl 1379.35211Foias, Ciprian; Jolly, Michael S.; Lithio, Dan; Titi, Edriss S. 3 2017 A discrete data assimilation scheme for the solutions of the two-dimensional Navier-Stokes equations and their statistics. Zbl 1362.35208Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. 25 2016 Convergence of time averages of weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1357.35246Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger M. 9 2015 Time analyticity with higher norm estimates for the 2D Navier-Stokes equations. Zbl 1339.35211Foias, Ciprian; Jolly, Michael S.; Lan, Ruomeng; Rupam, Rishika; Yang, Yong; Zhang, Bingsheng 6 2015 A unified approach to determining forms for the 2D Navier-Stokes equations – the general interpolants case. Zbl 1301.35108Foias, C.; Jolly, M. S.; Kravchenko, R.; Titi, E. S. 14 2014 On the maximal space analyticity radius for the 3D Navier-Stokes equations and energy cascades. Zbl 1298.35133Biswas, Animikh; Foias, Ciprian 6 2014 On whether zero is in the global attractor of the 2D Navier-Stokes equations. Zbl 1304.35485Foias, Ciprian; Jolly, Michael S.; Yang, Yong; Zhang, Bingsheng 1 2014 Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations. Zbl 1304.35486Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger 17 2013 On single mode forcing of the 2D-NSE. Zbl 1285.35067Foias, C.; Jolly, M. S.; Yang, M. 4 2013 A determining form for the two-dimensional Navier-Stokes equations: the Fourier modes case. Zbl 1426.76103Foias, Ciprian; Jolly, Michael S.; Kravchenko, Rostyslav; Titi, Edriss S. 17 2012 Canonical models for bi-isometries. Zbl 1266.47025Bercovici, H.; Douglas, R. G.; Foias, C. 7 2012 Contractions with polynomial characteristic functions. I: Geometric approach. Zbl 1284.47008Foias, Ciprian; Sarkar, Jaydeb 4 2012 Resolutions of Hilbert modules and similarity. Zbl 1260.46018Douglas, Ronald G.; Foias, Ciprian; Sarkar, Jaydeb 2 2012 Asymptotic integration of Navier-Stokes equations with potential forces. II: An explicit Poincaré-Dulac normal form. Zbl 1232.35115Foias, Ciprian; Hoang, Luan; Saut, Jean-Claude 8 2011 Spectral decomposability of rank-one perturbations of normal operators. Zbl 1203.47012Foias, C.; Jung, I. B.; Ko, E.; Pearcy, C. 5 2011 Harmonic analysis of operators on Hilbert space. 2nd revised and enlarged ed. Zbl 1234.47001Sz.-Nagy, Béla; Foias, Ciprian; Bercovici, Hari; Kérchy, László 175 2010 Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence. Zbl 1185.35161Dascaliuc, R.; Foias, C.; Jolly, M. S. 17 2010 Topological properties of the weak global attractor of the three-dimensional Navier-Stokes equations. Zbl 1191.35204Foias, Ciprian; Rosa, Ricardo; Temam, Roger 14 2010 A note on statistical solutions of the three-dimensional Navier-Stokes equations: the time-dependent case. Zbl 1186.35141Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger 11 2010 A note on statistical solutions of the three-dimensional Navier-Stokes equations: The stationary case. Zbl 1186.35142Foias, Ciprian; Rosa, Ricardo M. S.; Temam, Roger 10 2010 Confluent operator algebras and the closability property. Zbl 1190.47086Bercovici, H.; Douglas, R. G.; Foias, C.; Pearcy, C. 5 2010 2-D turbulence for forcing in all scales. Zbl 1193.35123Balci, N.; Foias, C.; Jolly, M. S. 3 2010 On universal relations in 2-D turbulence. Zbl 1193.35124Balci, Nusret; Foias, Ciprian; Jolly, M. S.; Rosa, Ricardo 3 2010 Bi-isometries and commutant lifting. Zbl 1207.47009Bercovici, Hari; Douglas, Ronald G.; Foias, Ciprian 1 2010 The normal form of the Navier-Stokes equations in suitable normed spaces. Zbl 1179.35212Foias, Ciprian; Hoang, Luan; Olson, Eric; Ziane, Mohammed 8 2009 On the helicity in 3D-periodic Navier-Stokes equations. II: The statistical case. Zbl 1184.35239Foias, Ciprian; Hoang, Luan; Nicolaenko, Basil 6 2009 On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows. Zbl 1160.37419Dascaliuc, R.; Foias, C.; Jolly, M. S. 5 2009 Operators with a compact imaginary part. Zbl 1230.47014Foias, C.; Hamid, S.; Onica, C.; Pearcy, C. 1 2009 Navier-Stokes equations and turbulence. Paperback reprint of the hardback edition 2001. Zbl 1139.35001Foias, C.; Rosa, R.; Manley, O.; Temam, R. 13 2008 On rank-one perturbations of normal operators. II. Zbl 1166.47013Foias, C.; Jung, I. B.; Ko, E.; Pearcy, C. 8 2008 Some specific mathematical constraints on 2D turbulence. Zbl 1158.76016Dascaliuc, R.; Foias, C.; Jolly, M. S. 6 2008 On the hyperinvariant subspace problem. IV. Zbl 1153.47004Bercovici, H.; Foias, C.; Pearcy, C. 3 2008 On the helicity in 3D-periodic Navier-Stokes equations. I: The non-statistical case. Zbl 1109.76015Foias, Ciprian; Hoang, Luan; Nicolaenko, Basil 13 2007 On rank-one perturbations of normal operators. Zbl 1134.47004Foias, C.; Jung, I. B.; Ko, E.; Pearcy, C. 10 2007 Universal bounds on the attractor of the Navier-Stokes equation in the energy, enstrophy plane. Zbl 1144.81335Dascaliuc, R.; Foias, C.; Jolly, M. S. 7 2007 Strategic Ramsey equilibrium dynamics. Zbl 1151.91629Becker, Robert A.; Foias, Ciprian 6 2007 Hyperinvariant subspaces for some subnormal operators. Zbl 1115.47003Foias, C.; Jung, I. B.; Ko, E.; Pearcy, C. 2 2007 On global attractors of the 3D Navier–Stokes equations. Zbl 1113.35140Cheskidov, A.; Foias, C. 36 2006 On the solutions to the normal form of the Navier-Stokes equations. Zbl 1246.76019Foias, Ciprian; Hoang, Luan; Olson, Eric; Ziane, Mohammed 12 2006 On the classification of multi-isometries. Zbl 1164.47301Bercovici, H.; Douglas, R. G.; Foias, C. 9 2006 On the structure of the square of a \(C_0(1)\) operator. Zbl 1119.47010Douglas, Ronald G.; Foias, Ciprian 3 2006 Relations between energy and enstrophy on the global attractor of the 2-D Navier-Stokes equations. Zbl 1100.35078Dascaliuc, R.; Foias, C.; Jolly, M. S. 19 2005 Kolmogorov theory via finite-time averages. Zbl 1083.35091Foias, C.; Jolly, M. S.; Manley, O. P.; Rosa, R.; Temam, R. 10 2005 Kraichnan turbulence via finite time averages. Zbl 1065.76101Foias, C.; Jolly, M. S.; Manley, O. P. 9 2005 On quasinilpotent operators. III. Zbl 1106.47008Foiaş, Ciprian; Jung, Il Bong; Ko, Eungil; Pearcy, Carl 7 2005 On the hyperinvariant subspace problem. Zbl 1066.47004Foias, Ciprian; Pearcy, Carl 3 2005 On the hyperinvariant subspace problem. III. Zbl 1068.47008Foias, C.; Hamid, S.; Onica, C.; Pearcy, C. 2 2005 On the behavior of the Lorenz equation backward in time. Zbl 1068.34044Foias, C.; Jolly, M. S. 2 2005 Operators that admit a moment sequence. Zbl 1079.47023Foias, Ciprian; Jung, Il Bong; Ko, Eungil; Pearcy, Carl 1 2005 On quasinilpotent operators. II. Zbl 1096.47008Foiaş, Ciprian; Jung, Il Bong; Ko, Eungil; Pearcy, Carl 6 2004 Complete contractivity of maps associated with the Aluthge and Duggal transforms. Zbl 1066.47037Foiaş, Ciprian; Jung, Il Bong; Ko, Eungil; Pearcy, Carl 17 2003 On the Landau–Lifschitz degrees of freedom in 2-D turbulence. Zbl 1028.76014Foias, C.; Jolly, M. S.; Manley, O. P.; Rosa, R. 6 2003 The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. Zbl 0995.35051Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. 174 2002 Energy dissipation in body-forced turbulence. Zbl 1029.76025Doering, Charles R.; Foias, Ciprian 51 2002 Statistical estimates for the Navier-Stokes equations and the Kraichnan theory of 2-D fully developed turbulence. Zbl 1158.76327Foias, C.; Jolly, M. S.; Manley, O. P.; Rosa, R. 29 2002 Relaxation of metric constrained interpolation and a new lifting theorem. Zbl 1060.47021Foias, C.; Frazho, A. E.; Kaashoek, M. A. 7 2002 Nevanlinna-Pick interpolation of attractors. Zbl 1015.37046Foias, C.; Jolly, M. S.; Li, W.-S. 4 2002 Navier-Stokes equations and turbulence. Zbl 0994.35002Foias, C.; Rosa, R.; Manley, O.; Temam, R. 266 2001 The Navier-Stokes-alpha model of fluid turbulence. Zbl 1037.76022Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. 161 2001 Estimates for the energy cascade in three-dimensional turbulent flows. Zbl 1172.76319Foias, Ciprian; Manley, Oscar P.; Rosa, Ricardo M. S.; Temam, Roger 21 2001 Cascade of energy in turbulent flows. Zbl 0986.35089Foias, Ciprian; Manley, Oscar P.; Rosa, Ricardo M. S.; Temam, Roger 11 2001 The Lorenz equation as a metaphor for the Navier-Stokes equations. Zbl 1052.76012Foias, C.; Jolly, M. S.; Kukavica, I.; Titi, E. S. 8 2001 On the non-homogeneous stationary Kuramoto-Sivashinsky equation. Zbl 0976.35062Cheskidov, A.; Foias, C. 5 2001 The general commutant extension problem. Zbl 1239.47012Foias, Ciprian 2 2001 A weighted version of almost commutant lifting. Zbl 1030.47005Foias, C.; Frazho, A. E.; Kaashoek, M. A. 1 2001 A connection between the Camassa-Holm equations and turbulent flows in channels and pipes. Zbl 1147.76357Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S. 100 1999 The Camassa-Holm equations and turbulence. Zbl 1194.76069Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S. 87 1999 Weighted commutant lifting. Zbl 0954.47018Biswas, A.; Foias, C.; Frazho, A. E. 11 1999 Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Zbl 1042.76525Chen, Shiyi; Foias, Ciprian; Holm, Darryl D.; Olson, Eric; Titi, Edriss S. 133 1998 Metric constrained interpolation, commutant lifting and systems. Zbl 0923.47009Foias, C.; Frazho, A. E.; Gohberg, I.; Kaashoek, M. A. 40 1998 A remark on two constructions of exponential attractors for \(\alpha\)-contractions. Zbl 0898.58035Eden, A.; Foias, C.; Kalantarov, V. 16 1998 Implicit programming and the invariant manifold for Ramsey equilibria. Zbl 0907.90053Becker, Robert A.; Foias, Ciprian 5 1998 On skew Toeplitz operators. II. Zbl 0915.47021Bercovici, H.; Foias, C.; Tannenbaum, A. 4 1998 On the Zorn spaces in Beurling’s approach to the Riemann hypothesis. Zbl 0958.11062Bercovici, H.; Foias, C. 1 1998 The maximum principle for the three chains completion problem. Zbl 0901.47008Foias, C.; Frazho, A. E.; Gohberg, I.; Kaashoek, M. A. 1 1998 What do the Navier-Stokes equations tell us about turbulence? Zbl 0890.76030Foias, Ciprian 26 1997 Dirichlet quotients and 2D periodic Navier-Stokes equations. Zbl 0874.35085Constantin, Peter; Foias, Ciprian; Kukavica, Igor; Majda, Andrew J. 15 1997 A time-variant version of the commutant lifting theorem and nonstationary interpolation problems. Zbl 0897.47010Foias, C.; Frazho, A. E.; Gohberg, I.; Kaashoek, M. A. 5 1997 Parametrization of all solutions of the three chains completion problem. Zbl 0896.47011Foias, C.; Frazho, A. E.; Gohberg, I.; Kaashoek, M. A. 4 1997 Robust control of infinite dimensional systems. Frequency domain methods. Zbl 0839.93003Foias, Ciprian; Özbay, Hitay; Tannenbaum, Allen 36 1996 Finite fractal dimension and Hölder-Lipschitz parametrization. Zbl 0887.54034Foias, C.; Olson, E. 31 1996 Discrete time-variant interpolation as classical interpolation with an operator argument. Zbl 0861.47011Foias, C.; Frazho, A. E.; Gohberg, I.; Kaashoek, M. A. 8 1996 The structured singular value for linear input/output operators. Zbl 0864.93040Bercovici, Hari; Foias, Ciprian; Tannenbaum, Allen 7 1996 Localization of attractors by their analytic properties. Zbl 0905.34048Foias, C.; Jolly, M. S.; Kukavica, I. 5 1996 Determining nodes for the Kuramoto-Sivashinsky equation. Zbl 0835.35067Foias, Ciprian; Kukavica, Igor 21 1995 On the numerical algebraic approximation of global attractors. Zbl 0837.34052Foias, C.; Jolly, M. S. 17 1995 Exponential decay of the power spectrum of turbulence. Zbl 1081.35505Bercovici, H.; Constantin, P.; Foias, C.; Manley, O. P. 16 1995 Constructing the Schur contraction in the commutant lifting theorem. Zbl 0846.47003Foias, Ciprian; Frazho, Arthur E. 2 1995 On \(H^ 2\) minimization for the Carathéodory-Schur interpolation problem. Zbl 0829.30023Foias, C.; Frazho, A. E.; Li, W. S. 2 1995 On the extension of intertwining operators. Zbl 0843.47003Foias, Ciprian 1 1995 On the structured singular value for operators on Hilbert space. Zbl 0821.93027Bercovici, Hari; Foias, Ciprian; Tannenbaum, Allen 1 1995 Exponential attractors for dissipative evolution equations. Zbl 0842.58056Eden, A.; Foias, C.; Nicolaenko, B.; Temam, R. 207 1994 Effects of the forcing function spectrum on the energy spectrum in 2-D turbulence. Zbl 0827.76033Constantin, Peter; Foias, Ciprian; Manley, Oscar P. 19 1994 The local bifurcation of Ramsey equilibrium. Zbl 0829.90025Becker, Robert A.; Foias, Ciprian 18 1994 On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation. Zbl 0941.65526Foias, C.; Jolly, M. S.; Kevrekidis, I. G.; Titi, E. S. 10 1994 ...and 285 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,430 Authors 126 Foiaş, Ciprian Ilie 96 Titi, Edriss Saleh 70 Temam, Roger Meyer 44 Popescu, Gelu 37 Robinson, James Cooper 36 Jolly, Michael S. 34 Ko, Eungil 31 Miranville, Alain M. 30 Ball, Joseph Anthony 28 He, Yinnian 28 Kukavica, Igor 27 Bercovici, Hari 27 Constantin, Peter 27 Frazho, Arthur E. 27 Holm, Darryl D. 26 Rebholz, Leo G. 26 Tannenbaum, Allen Robert 25 Sarkar, Jaydeb 23 Guo, Boling 23 Pearcy, Carl Mark Jr. 22 Chueshov, Igor’ Dmitrievich 21 Caraballo Garrido, Tomás 21 Jung, Il Bong 21 Wu, Peiyuan 19 Gibbon, John D. 18 Doering, Charles R. 18 Grujić, Zoran 18 Wang, Xiaoming 18 Zelik, Sergey V. 17 Berselli, Luigi Carlo 17 Layton, William J. 17 Timotin, Dan 16 Agler, Jim 16 Biswas, Animikh 16 Helton, John William 16 Hoang, Luan Thach 16 Hou, Yanren 16 Kaashoek, Marinus Adriaan 16 Li, Kaitai 16 Nicolaenko, Basil 16 Vicol, Vlad C. 15 Allahverdiev, Bilender Paşaoğlu 15 Cheskidov, Alexey 15 Duan, Jinqiao 15 Özbay, Hitay 14 Danca, Marius-Florin 14 Jørgensen, Palle E. T. 14 Levan, Nhan 14 Łukaszewicz, Grzegorz 14 Olson, Eric J. 14 Tian, Lixin 14 Young, Nicholas John 14 Zhao, Caidi 13 Bolotnikov, Vladimir 13 Dascaliuc, Radu 13 Duggal, Bhagwati Prashad 13 Gunzburger, Max D. 13 Herrero, Domingo Antonio 13 Langa, Jose’ Antonio 13 Razafimandimby, Paul André 13 Rosa, Ricardo M. S. 13 Sell, George Roger 13 Suciu, Laurian 13 Wang, Shouhong 12 Fuhrmann, Paul A. 12 Kalantarov, Varga K. 12 Lee, Jieun 12 Manley, Oscar P. 12 Real Anguas, José 12 Stochel, Jan 12 Valero, José 11 Chae, Dongho 11 Eden, Alp 11 Gau, Hwa-Long 11 Ghidaglia, Jean-Michel 11 Gohberg, Israel 11 Grasselli, Maurizio 11 Ilyin, Alexei A. 11 Mbekhta, Mostafa 11 Peller, Vladimir Vsevolodovich 11 Tachim Medjo, Theodore 11 Yakubovich, Dmitry V. 10 Arov, Damir Zyamovich 10 Becker, Robert A. 10 Debussche, Arnaud 10 Farhat, Aseel 10 Glatt-Holtz, Nathan E. 10 Gu, Caixing 10 Hadwin, Donald W. 10 Jung, Sungeun 10 Kubrusly, Carlos S. 10 Lunasin, Evelyn M. 10 Malamud, Mark M. 10 Müller, Vladimír 10 Neidhardt, Hagen 10 Pata, Vittorino 10 Pražák, Dalibor 10 Wu, Jiahong 10 Yao, Zhengan 10 Zhong, Chengkui ...and 4,330 more Authors all top 5 Cited in 459 Serials 376 Journal of Mathematical Analysis and Applications 253 Journal of Functional Analysis 179 Integral Equations and Operator Theory 177 Journal of Differential Equations 170 Proceedings of the American Mathematical Society 131 Physica D 121 Linear Algebra and its Applications 103 Nonlinear Analysis. 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Modélisation Mathématique et Analyse Numérique 12 Applications of Mathematics 12 Stochastic Processes and their Applications 12 Bulletin of the American Mathematical Society. New Series 12 Acta Mathematica Sinica. English Series 12 Communications in Nonlinear Science and Numerical Simulation 12 Banach Journal of Mathematical Analysis 11 Physics Letters. A 11 Acta Mathematicae Applicatae Sinica. English Series 11 Numerical Methods for Partial Differential Equations 11 St. Petersburg Mathematical Journal 11 Stochastics and Dynamics 11 SIAM Journal on Applied Dynamical Systems 11 Science China. Mathematics 10 Rocky Mountain Journal of Mathematics 10 Archiv der Mathematik 10 Chinese Annals of Mathematics. Series B 10 MCSS. Mathematics of Control, Signals, and Systems 10 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 10 Bulletin des Sciences Mathématiques 10 Nonlinear Dynamics 9 Bulletin of the Australian Mathematical Society 9 International Journal of Control 9 Reports on Mathematical Physics ...and 359 more Serials all top 5 Cited in 61 Fields 1,965 Partial differential equations (35-XX) 1,499 Fluid mechanics (76-XX) 1,484 Operator theory (47-XX) 578 Dynamical systems and ergodic theory (37-XX) 477 Functional analysis (46-XX) 409 Numerical analysis (65-XX) 321 Systems theory; control (93-XX) 262 Ordinary differential equations (34-XX) 228 Probability theory and stochastic processes (60-XX) 168 Functions of a complex variable (30-XX) 104 Calculus of variations and optimal control; optimization (49-XX) 98 Geophysics (86-XX) 94 Linear and multilinear algebra; matrix theory (15-XX) 90 Mechanics of deformable solids (74-XX) 87 Harmonic analysis on Euclidean spaces (42-XX) 75 Statistical mechanics, structure of matter (82-XX) 69 Quantum theory (81-XX) 66 Several complex variables and analytic spaces (32-XX) 53 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 51 Classical thermodynamics, heat transfer (80-XX) 50 Measure and integration (28-XX) 50 Biology and other natural sciences (92-XX) 45 Global analysis, analysis on manifolds (58-XX) 32 Approximations and expansions (41-XX) 30 Abstract harmonic analysis (43-XX) 28 Mechanics of particles and systems (70-XX) 26 Real functions (26-XX) 25 Difference and functional equations (39-XX) 23 Integral equations (45-XX) 21 Optics, electromagnetic theory (78-XX) 19 Integral transforms, operational calculus (44-XX) 19 General topology (54-XX) 18 Statistics (62-XX) 17 Number theory (11-XX) 15 Information and communication theory, circuits (94-XX) 14 Operations research, mathematical programming (90-XX) 13 Associative rings and algebras (16-XX) 12 Combinatorics (05-XX) 12 Manifolds and cell complexes (57-XX) 11 History and biography (01-XX) 11 Nonassociative rings and algebras (17-XX) 11 Topological groups, Lie groups (22-XX) 11 Differential geometry (53-XX) 10 Group theory and generalizations (20-XX) 9 Algebraic geometry (14-XX) 7 General and overarching topics; collections (00-XX) 7 Astronomy and astrophysics (85-XX) 6 Special functions (33-XX) 6 Sequences, series, summability (40-XX) 6 Relativity and gravitational theory (83-XX) 5 Potential theory (31-XX) 5 Computer science (68-XX) 4 Mathematical logic and foundations (03-XX) 3 Convex and discrete geometry (52-XX) 3 Algebraic topology (55-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 2 Mathematics education (97-XX) 1 Field theory and polynomials (12-XX) 1 \(K\)-theory (19-XX) 1 Geometry (51-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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