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Lieb, Elliott H.

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Author ID: lieb.elliott-h Recent zbMATH articles by "Lieb, Elliott H."
Published as: Lieb, E.; Lieb, E. H.; Lieb, Eliott H.; Lieb, Elliot H.; Lieb, Elliott; Lieb, Elliott H.
External Links: MGP · Wikidata · GND
Documents Indexed: 250 Publications since 1957, including 12 Books
Biographic References: 8 Publications
all top 5

Co-Authors

58 single-authored
37 Seiringer, Robert
30 Frank, Rupert L.
27 Yngvason, Jakob
23 Loss, Michael
21 Carlen, Eric Anders
20 Solovej, Jan Philip
12 Almgren, Frederick Justin jun.
7 Brézis, Haïm
7 Siedentop, Heinz Karl Heinrich
6 Brascamp, Herm Jan
5 Thomas, Lawrence E.
4 Giuliani, Alessandro
4 Lebowitz, Joel Louis
4 Lewin, Mathieu
3 Aizenman, Michael
3 Bach, Volker
3 Heilmann, Ole J.
3 Mattis, Daniel Charles
3 Simon, Barry
3 Yau, Horng-Tzer
2 Benguria, Rafael D.
2 Coron, Jean-Michel
2 Daubechies, Ingrid Chantal
2 Jauslin, Ian
2 Liniger, Werner
2 McCann, Robert J.
2 Rougerie, Nicolas
2 Wightman, Arthur Strong
1 Ball, Keith Martin
1 Barnes, John F.
1 Bellazzini, Jacopo
1 Beyer, William A.
1 Browder, William
1 Caffarelli, Luis Ángel
1 Chayes, Jennifer Tour
1 Chayes, Lincoln
1 Conlon, Joseph G.
1 Cordero-Erausquin, Dario
1 Davies, Edward Brian
1 Decker, Colin
1 Fellbaum, Christiane
1 Freericks, James K.
1 Fröhlich, Jürg Martin
1 Griesemer, Marcel
1 Hundertmark, Dirk
1 Iantchenko, Alexei
1 Jansen, Sabine
1 Jerison, David S.
1 Kennedy, Tom
1 Kleitman, Daniel J.
1 Koppe, Heinz
1 Kulkarni, Sanjeev R.
1 Laptev, Ari
1 Lazarev, Oleg
1 Lewis, Roger T.
1 Luttinger, Joaquin M.
1 Nachtergaele, Bruno
1 Narnhofer, Heide
1 Osherson, Daniel N.
1 Ostrover, Yaron
1 Pedersen, Gert Kjærgård
1 Poor, Harold Vincent
1 Predd, Joel B.
1 Reuvers, Robin
1 Ruskai, Mary Beth
1 Sabin, Julien
1 Sakakura, A. Y.
1 Schultz, Theodore
1 Seiler, Ruedi
1 Sherman, Seymour
1 Stein, Elias Menachem
1 Stephens, Benjamin K.
1 Temperley, H. V. N.
1 Thirring, Walter E.
1 Travaglia, Marcos Vinicio
1 Ueltschi, Daniel
1 Wu, Fuyuan
1 Yamazaki, Kazuo
1 Yang, Yisong
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Serials

44 Communications in Mathematical Physics
11 Journal of Mathematical Physics
11 Journal of Statistical Physics
8 Advances in Mathematics
7 Letters in Mathematical Physics
7 Physical Review, II. Series
4 Inventiones Mathematicae
4 Journal of Functional Analysis
4 Annals of Mathematics. Second Series
3 Physica A
3 Reviews in Mathematical Physics
3 Bulletin of the American Mathematical Society. New Series
3 Physical Review Letters
2 Reviews of Modern Physics
2 Duke Mathematical Journal
2 Indiana University Mathematics Journal
2 Studies in Applied Mathematics
2 Journal of the American Mathematical Society
2 Geometric and Functional Analysis. GAFA
2 Linear Algebra and its Applications
2 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
2 Notices of the American Mathematical Society
2 Advances in Theoretical and Mathematical Physics
2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
2 Bulletin of the American Mathematical Society
2 Journal of Combinatorial Theory
2 Graduate Studies in Mathematics
2 Journal of Physics A: Mathematical and Theoretical
1 International Journal of Modern Physics B
1 Communications on Pure and Applied Mathematics
1 Discrete Mathematics
1 Helvetica Physica Acta
1 IEEE Transactions on Information Theory
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Physics Reports
1 Reports on Mathematical Physics
1 Arkiv för Matematik
1 Acta Mathematica
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Bulletin of the London Mathematical Society
1 Publications Mathématiques
1 Journal of Economic Theory
1 Journal für die Reine und Angewandte Mathematik
1 Mathematische Zeitschrift
1 Proceedings of the American Mathematical Society
1 Advances in Applied Mathematics
1 The Journal of Geometric Analysis
1 Annals of Physics
1 Proceedings of the National Academy of Sciences of the United States of America
1 SIAM Journal on Mathematical Analysis
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Calculus of Variations and Partial Differential Equations
1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts)
1 Mathematical Research Letters
1 Methods and Applications of Analysis
1 Documenta Mathematica
1 ELA. The Electronic Journal of Linear Algebra
1 Journal of the European Mathematical Society (JEMS)
1 Annales Henri Poincaré
1 Journal of Mathematics and Mechanics
1 Oberwolfach Seminars
1 Physical Review A, Third Series
1 Journal de l’École Polytechnique – Mathématiques
1 Pure and Applied Analysis
1 Princeton Series in Physics
all top 5

Fields

106 Quantum theory (81-XX)
77 Statistical mechanics, structure of matter (82-XX)
50 Partial differential equations (35-XX)
40 Functional analysis (46-XX)
23 Operator theory (47-XX)
21 Real functions (26-XX)
16 Calculus of variations and optimal control; optimization (49-XX)
14 Linear and multilinear algebra; matrix theory (15-XX)
14 Information and communication theory, circuits (94-XX)
12 Global analysis, analysis on manifolds (58-XX)
12 Probability theory and stochastic processes (60-XX)
11 History and biography (01-XX)
9 Harmonic analysis on Euclidean spaces (42-XX)
9 Classical thermodynamics, heat transfer (80-XX)
8 Measure and integration (28-XX)
6 Combinatorics (05-XX)
5 General and overarching topics; collections (00-XX)
5 Potential theory (31-XX)
5 Astronomy and astrophysics (85-XX)
4 Difference and functional equations (39-XX)
3 Fluid mechanics (76-XX)
2 Optics, electromagnetic theory (78-XX)
1 Number theory (11-XX)
1 Group theory and generalizations (20-XX)
1 Ordinary differential equations (34-XX)
1 Dynamical systems and ergodic theory (37-XX)
1 Approximations and expansions (41-XX)
1 Abstract harmonic analysis (43-XX)
1 Integral transforms, operational calculus (44-XX)
1 Integral equations (45-XX)
1 Convex and discrete geometry (52-XX)
1 Differential geometry (53-XX)
1 Mechanics of deformable solids (74-XX)
1 Relativity and gravitational theory (83-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

Publications by Year

Citations contained in zbMATH

213 Publications have been cited 8,742 times in 6,286 Documents Cited by Year
A relation between pointwise convergence of functions and convergence of functionals. Zbl 0526.46037
Brézis, Haïm; Lieb, Elliott H.
890
1983
Analysis. 2nd ed. Zbl 0966.26002
Lieb, Elliott H.; Loss, Michael
734
2001
Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Zbl 0527.42011
Lieb, Elliott H.
482
1983
Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation. Zbl 0369.35022
Lieb, Elliott H.
333
1977
On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. Zbl 0334.26009
Brascamp, Herm Jan; Lieb, Elliott H.
311
1976
Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ’percolation’ problem. Zbl 0211.56703
Temperley, H. V. N.; Lieb, Elliott H.
238
1971
Two soluble models of an antiferromagnetic chain. Zbl 0129.46401
Lieb, Elliott H.; Schultz, Theodore; Mattis, D.
227
1961
Exact analysis of an interaction Bose gas. I: The general solution and the ground state. Zbl 0138.23001
Lieb, Elliott H.; Liniger, Werner
198
1963
Theory of monomer-dimer systems. Zbl 0228.05131
Heilmann, Ole J.; Lieb, Elliott H.
197
1972
Harmonic maps with defects. Zbl 0608.58016
Brézis, Haïm; Coron, Jean-Michel; Lieb, Elliott H.
177
1986
Convex trace functions and the Wigner-Yanase-Dyson conjecture. Zbl 0267.46055
Lieb, Elliott H.
177
1973
The Thomas-Fermi theory of atoms, molecules and solids. Zbl 0938.81568
Lieb, Elliott H.; Simon, Barry
162
1977
The mathematics of the Bose gas and its condensation. Zbl 1104.82012
Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob
159
2005
Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. Zbl 0342.35044
Lieb, Elliott H.; Thirring, Walter E.
145
1976
The Chandrasekhar theory of stellar collapse as the limit quantum mechanics. Zbl 0641.35065
Lieb, Elliott H.; Yau, Horng-Tzer
131
1987
Sharp uniform convexity and smoothness inequalities for trace norms. Zbl 0803.47037
Ball, Keith; Carlen, Eric A.; Lieb, Elliott H.
118
1994
Best constants in Young’s inequality, its converse, and its generalization to more than three functions. Zbl 0339.26020
Brascamp, Herm Jan; Lieb, Elliott H.
118
1976
A general rearrangement inequality for multiple integrals. Zbl 0286.26005
Brascamp, H. J.; Lieb, Elliott H.; Luttinger, J. M.
115
1974
The Thomas-Fermi-von Weizsäcker theory of atoms and molecules. Zbl 0478.49035
Benguria, Rafael; Brézis, Haïm; Lieb, Elliott H.
111
1981
Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
110
2008
Symmetric decreasing rearrangement is sometimes continuous. Zbl 0688.46014
Almgren, Frederick J. jun.; Lieb, Elliott H.
99
1989
Bounds on the eigenvalues of the Laplace and Schrödinger operators. Zbl 0329.35018
Lieb, Elliott H.
97
1976
Analysis. Zbl 0873.26002
Lieb, Elliott H.; Loss, Michael
95
1996
Ground states in non-relativistic quantum electrodynamics. Zbl 1044.81133
Griesemer, Marcel; Lieb, Elliott H.; Loss, Michael
93
2001
On the lowest eigenvalue of the Laplacian for the intersection of two domains. Zbl 0538.35058
Lieb, Elliott H.
93
1983
The classical limit of quantum spin systems. Zbl 1125.82305
Lieb, Elliott H.
91
1973
Thomas-Fermi and related theories of atoms and molecules. Zbl 1114.81336
Lieb, Elliott H.
83
1981
The stability of matter in quantum mechanics. Zbl 1179.81004
Lieb, Elliott H.; Seiringer, Robert
80
2009
Gaussian kernels have only Gaussian maximizers. Zbl 0726.42005
Lieb, Elliott H.
77
1990
The stability and instability of relativistic matter. Zbl 0686.35099
Lieb, Elliott H.; Yau, Horng-Tzer
77
1988
Minimum action solutions of some vector field equations. Zbl 0579.35025
Brézis, Haïm; Lieb, Elliott H.
77
1984
Thomas-Fermi and related theories of atoms and molecules. Zbl 1049.81679
Lieb, Elliott H.
70
1981
Generalized Hartree-Fock theory and the Hubbard model. Zbl 0839.60095
Bach, Volker; Lieb, Elliott H.; Solovej, Jan Philip
67
1994
Stability of Coulomb systems with magnetic fields. I: The one-electron atom. Zbl 0595.35098
Fröhlich, Jürg; Lieb, Elliott H.; Loss, Michael
63
1986
Proof of an entropy conjecture of Wehrl. Zbl 0385.60089
Lieb, Elliott H.
63
1978
Exact analysis of an interacting Bose gas. II: The excitation spectrum. Zbl 0138.23002
Lieb, Elliott H.
63
1963
A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Zbl 0996.82010
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
62
2001
Sobolev inequalities with remainder terms. Zbl 0577.46031
Brézis, Haïm; Lieb, Elliott H.
62
1985
Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Zbl 1233.82004
Lieb, Elliott H.; Seiringer, Robert
61
2006
Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023
Frank, Rupert L.; Lieb, Elliott H.
58
2012
The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei. Zbl 1049.82501
Lieb, Eliott H.; Lebowitz, Joel L.
54
1972
The ground state energy and density of interacting bosons in a trap. Zbl 1043.82515
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
49
2000
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024
Frank, Rupert L.; Lieb, Elliott H.
46
2010
Monotonicity of a relative Rényi entropy. Zbl 1350.94020
Frank, Rupert L.; Lieb, Elliott H.
45
2013
Integral bounds for radar ambiguity functions and Wigner distributions. Zbl 0704.46050
Lieb, Elliott H.
45
1990
Some operator inequalities of the Schwarz type. Zbl 0274.46045
Lieb, Elliott H.; Ruskai, Mary Beth
43
1974
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382
Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert
39
2006
A sharp analog of Young’s inequality on \(S^N\) and related entropy inequalities. Zbl 1056.43002
Carlen, E. A.; Lieb, E. H.; Loss, M.
39
2004
Asymptotics of heavy atoms in high magnetic fields. II: Semiclassical regions. Zbl 0807.47058
Lieb, Elliott H.; Solovej, Jan Philip; Yngvason, Jakob
37
1994
Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma. Zbl 0348.26011
Brascamp, H. J.; Lieb, Elliott H.
37
1975
Existence of atoms and molecules in non-relativistic quantum electrodynamics. Zbl 1058.81080
Lieb, Elliott H.; Loss, Michael
36
2003
Bose-Einstein condensation of dilute gases in traps. Zbl 1041.81107
Lieb, Elliott H.; Seiringer, Robert
34
2003
The physics and mathematics of the second law of thermodynamics. Zbl 1027.80504
Lieb, Elliott H.; Yngvason, Jakob
34
1999
Some convexity and subadditivity properties of entropy. Zbl 0308.94020
Lieb, Elliott H.
34
1975
Optimal hypercontractivity for Fermi fields and related non-commutative integration inequalities. Zbl 0796.46054
Carlen, Eric A.; Lieb, Elliott H.
33
1993
The stability of matter: From atoms to stars. Zbl 0698.35135
Lieb, Elliott H.
33
1990
On characteristic exponents in turbulence. Zbl 0598.76054
Lieb, Elliott H.
33
1984
Proofs of some conjectures on permanents. Zbl 0144.26802
Lieb, Elliott H.
33
1966
Ordering energy levels of interacting spin systems. Zbl 0101.45302
Lieb, Elliott H.; Mattis, Daniel
33
1962
On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005
Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H.
31
1996
A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity. Zbl 1171.47015
Carlen, Eric A.; Lieb, Elliott H.
30
2008
Ground state energy of the one-component charged Bose gas. Zbl 1042.82004
Lieb, Elliott H.; Solovej, Jan Philip
30
2002
The ground state energy of a dilute two-dimensional Bose gas. Zbl 1115.82306
Lieb, Elliott H.; Yngvason, Jakob
30
2001
Concavity properties and a generating function for Stirling numbers. Zbl 0164.33002
Lieb, Elliott H.
30
1968
A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator. Zbl 0929.34076
Hundertmark, Dirk; Lieb, Elliott H.; Thomas, Lawrence E.
29
1998
Exact ground state energy of the strong-coupling polaron. Zbl 0874.60095
Lieb, Elliott H.; Thomas, Lawrence E.
29
1997
Long range atomic potentials in Thomas-Fermi theory. Zbl 0416.35066
Brézis, Haïm; Lieb, Elliott H.
29
1979
Fluxes, Laplacians, and Kasteleyn’s theorem. Zbl 0787.05083
Lieb, Elliott H.; Loss, Michael
28
1993
Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds. Zbl 0673.58013
Almgren, Frederick J. jun.; Lieb, Elliot H.
28
1988
A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023
Frank, Rupert L.; Lieb, Elliott H.
27
2012
Ground state energy of the two-component charged Bose gas. Zbl 1124.82303
Lieb, Elliott H.; Solovej, Jan Philip
26
2004
One-electron relativistic molecules with Coulomb interaction. Zbl 0946.81522
Daubechies, Ingrid; Lieb, Elliott H.
26
1983
Asymptotics of heavy atoms in high magnetic fields. I: Lowest Landau band regions. Zbl 0800.49041
Lieb, Elliott H.; Solovej, Jan Philip; Yngvason, Jakob
25
1994
Stability of matter in magnetic fields. Zbl 1020.81957
Lieb, Elliott H.; Loss, Michael; Solovej, Jan Philip
24
1995
An itinerant electron model with crystalline or magnetic long range order. Zbl 1002.82508
Kennedy, Tom; Lieb, Elliott H.
24
1986
Co-area, liquid crystals, and minimal surfaces. Zbl 0645.58015
Almgren, F.; Browder, W.; Lieb, E. H.
23
1988
The number of bound states of one-body Schrödinger operators and the Weyl problem. Zbl 0445.58029
Lieb, Elliott H.
23
1980
The thermodynamic limit for jellium. Zbl 0973.82500
Lieb, Elliott H.; Narnhofer, Heide
23
1975
Stability of Coulomb systems with magnetic fields. II. The many-electron atom and the one-electron molecule. Zbl 0607.35082
Lieb, Elliott H.; Loss, Michael
22
1986
Equivalent forms of the Bessis-Moussa-Villani conjecture. Zbl 1157.81313
Lieb, Elliott H.; Seiringer, Robert
21
2004
Studies in mathematical physics. Essays in honor of Valentine Bargmann. Zbl 0326.00007
Lieb, Elliott H. (ed.); Simon, Barry (ed.); Wightman, Arthur S. (ed.)
21
1976
A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042
Frank, Rupert L.; Lieb, Elliott H.
20
2015
Theory of ferromagnetism and the ordering of electronic energy levels. Zbl 0118.46202
Lieb, Elliott H.; Mattis, D.
18
1962
A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
17
2013
One-dimensional behavior of dilute, trapped Bose gases. Zbl 1075.82002
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
17
2004
A bound on binding energies and mass renormalization in models of quantum electrodynamics. Zbl 1027.81040
Lieb, Elliott H.; Loss, Michael
17
2002
Strichartz inequality for orthonormal functions. Zbl 1307.35245
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
16
2014
Bose-Einstein condensation as a quantum phase transition in an optical lattice. Zbl 1170.82325
Aizenman, M.; Lieb, E. H.; Seiringer, R.; Solovej, J. P.; Yngvason, J.
16
2006
Non-abelian vortices in supersymmetric gauge field theory via direct methods. Zbl 1255.81216
Lieb, Elliott H.; Yang, Yisong
15
2012
An inequality of Hadamard type for permanents. Zbl 1116.15015
Carlen, Eric; Lieb, Elliott H.; Loss, Michael
14
2006
A note on polarization vectors in quantum electrodynamics. Zbl 1102.81070
Lieb, Elliott H.; Loss, Michael
14
2004
The one-dimensional Hubbard model: a reminiscence. Zbl 1037.82009
Lieb, Elliott H.; Wu, F. Y.
14
2003
A guide to entropy and second law of thermodynamics. Zbl 1038.80504
Lieb, Elliott H.; Yngvason, Jakob
14
1998
Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
13
2014
Stability and absence of binding for multi-polaron systems. Zbl 1227.82083
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E.
13
2011
Poincaré inequalities in punctured domains. Zbl 1048.26012
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
13
2003
A Minkowski type trace inequality and strong subadditivity of quantum entropy. Zbl 0933.47014
Carlen, Eric A.; Lieb, Elliott H.
13
1999
Symmetry of the Ginzburg-Landau minimizer in a disc. Zbl 0842.49014
Lieb, Elliott H.; Loss, Michael
13
1994
Ground-state energy and effective mass of the polaron. Zbl 0100.42504
Lieb, Elliott H.; Yamazaki, Kazuo
13
1958
Remainder terms for some quantum entropy inequalities. Zbl 1292.81021
Carlen, Eric A.; Lieb, Elliott H.
12
2014
Divergence of the effective mass of a polaron in the strong coupling limit. Zbl 1446.81045
Lieb, Elliott H.; Seiringer, Robert
1
2020
The local density approximation in density functional theory. Zbl 1435.35320
Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
1
2020
Local incompressibility estimates for the Laughlin phase. Zbl 1410.82009
Lieb, Elliott H.; Rougerie, Nicolas; Yngvason, Jakob
3
2019
Periodic energy minimizers for a one-dimensional liquid drop model. Zbl 1428.82062
Frank, Rupert L.; Lieb, Elliott H.
1
2019
Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
8
2018
Statistical mechanics of the uniform electron gas. Zbl 1404.82003
Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
6
2018
A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040
Frank, Rupert; Lieb, Elliott H.
6
2018
Rigidity of the Laughlin liquid. Zbl 1398.81326
Lieb, Elliott H.; Rougerie, Nicolas; Yngvason, Jakob
5
2018
Nematic liquid crystal phase in a system of interacting dimers and monomers. Zbl 1400.82320
Jauslin, Ian; Lieb, Elliott H.
2
2018
Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091
Frank, Rupert L.; Lieb, Elliott H.
7
2017
Maximizers for the Stein-Tomas inequality. Zbl 1357.42023
Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien
11
2016
Some operator and trace function convexity theorems. Zbl 1342.47024
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
9
2016
A Pfaffian formula for monomer-dimer partition functions. Zbl 1342.82161
Giuliani, Alessandro; Jauslin, Ian; Lieb, Elliott H.
5
2016
Entropy and entanglement bounds for reduced density matrices of fermionic states. Zbl 1342.81031
Carlen, Eric A.; Lieb, Elliott H.; Reuvers, Robin
3
2016
On a quantum entropy power inequality of Audenaert, Datta, and Ozols. Zbl 1341.81015
Carlen, Eric A.; Lieb, Elliott H.; Loss, Michael
3
2016
A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042
Frank, Rupert L.; Lieb, Elliott H.
20
2015
Columnar phase in quantum dimer models. Zbl 1320.82011
Giuliani, Alessandro; Lieb, Elliott H.
2
2015
Strichartz inequality for orthonormal functions. Zbl 1307.35245
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
16
2014
Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
13
2014
Remainder terms for some quantum entropy inequalities. Zbl 1292.81021
Carlen, Eric A.; Lieb, Elliott H.
12
2014
Proof of an entropy conjecture for Bloch coherent spin states and its generalizations. Zbl 1298.81116
Lieb, Elliott H.; Solovej, Jan Philip
12
2014
Formation of stripes and slabs near the ferromagnetic transition. Zbl 1302.82018
Giuliani, Alessandro; Lieb, Elliott H.; Seiringer, Robert
4
2014
Equivalence of two definitions of the effective mass of a polaron. Zbl 1295.81055
Lieb, Elliott H.; Seiringer, Robert
2
2014
Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099
Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
2
2014
Entropy meters and the entropy of non-extensive systems. Zbl 1371.80005
Lieb, Elliott H.; Yngvason, Jakob
1
2014
Ground state properties of multi-polaron systems. Zbl 1304.82075
Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E.
1
2014
Monotonicity of a relative Rényi entropy. Zbl 1350.94020
Frank, Rupert L.; Lieb, Elliott H.
45
2013
A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
17
2013
Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022
Frank, Rupert L.; Lieb, Elliott H.
6
2013
Asymmetric covariance estimates of Brascamp-Lieb type and related inequalities for log-concave measures. Zbl 1270.26016
Carlen, Eric A.; Cordero-Erausquin, Dario; Lieb, Elliott H.
5
2013
The entropy concept for non-equilibrium states. Zbl 1371.80004
Lieb, Elliott H.; Yngvason, Jakob
3
2013
On an extension problem for density matrices. Zbl 1282.81020
Carlen, Eric A.; Lebowitz, Joel L.; Lieb, Elliott H.
3
2013
A smooth complex generalization of the Hobby-Rice theorem. Zbl 1295.41025
Lazarev, Oleg; Lieb, Elliott H.
2
2013
Unique equilibria and substitution effects in a stochastic model of the marriage market. Zbl 1275.91098
Decker, Colin; Lieb, Elliott H.; McCann, Robert J.; Stephens, Benjamin K.
2
2013
Symmetry of bipolaron bound states for small Coulomb repulsion. Zbl 1269.82064
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
1
2013
Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023
Frank, Rupert L.; Lieb, Elliott H.
58
2012
A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023
Frank, Rupert L.; Lieb, Elliott H.
27
2012
Non-abelian vortices in supersymmetric gauge field theory via direct methods. Zbl 1255.81216
Lieb, Elliott H.; Yang, Yisong
15
2012
Bounds for entanglement via an extension of strong subadditivity of entropy. Zbl 1254.81019
Carlen, Eric A.; Lieb, Elliott H.
7
2012
Binding of polarons and atoms at threshold. Zbl 1250.82046
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
7
2012
Entropy and the uncertainty principle. Zbl 1256.81022
Frank, Rupert L.; Lieb, Elliott H.
4
2012
Further implications of the Bessis-Moussa-Villani conjecture. Zbl 1257.82009
Lieb, Elliott H.; Seiringer, Robert
1
2012
Stability and absence of binding for multi-polaron systems. Zbl 1227.82083
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E.
13
2011
Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013
Frank, Rupert L.; Lieb, Elliott H.
4
2011
Binding, stability, and non-binding of multi-polaron systems. Zbl 1245.82073
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E.
1
2011
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024
Frank, Rupert L.; Lieb, Elliott H.
46
2010
Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
9
2010
Localization of multidimensional Wigner distributions. Zbl 1314.81129
Lieb, Elliott H.; Ostrover, Yaron
4
2010
The stability of matter in quantum mechanics. Zbl 1179.81004
Lieb, Elliott H.; Seiringer, Robert
80
2009
Periodic minimizers in 1D local mean field theory. Zbl 1173.82008
Giuliani, Alessandro; Lebowitz, Joel L.; Lieb, Elliott H.
12
2009
Probabilistic coherence and proper scoring rules. Zbl 1367.94139
Predd, Joel B.; Seiringer, Robert; Lieb, Elliott H.; Osherson, Daniel N.; Poor, H. Vincent; Kulkarni, Sanjeev R.
8
2009
Symmetry breaking in Laughlin’s state on a cylinder. Zbl 1155.81032
Jansen, S.; Lieb, E. H.; Seiler, R.
4
2009
Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices. Zbl 1190.15009
Carlen, Eric A.; Lieb, Elliott H.
2
2009
Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
110
2008
A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity. Zbl 1171.47015
Carlen, Eric A.; Lieb, Elliott H.
30
2008
Brascamp–Lieb inequalities for non-commutative integration. Zbl 1173.46045
Carlen, Eric A.; Lieb, Elliott H.
2
2008
Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Zbl 1135.81030
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
10
2007
Bose-Einstein condensation and spontaneous symmetry breaking. Zbl 1160.82308
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
4
2007
Number of bound states of Schrödinger operators with matrix-valued potentials. Zbl 1135.35052
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
4
2007
Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Zbl 1233.82004
Lieb, Elliott H.; Seiringer, Robert
61
2006
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382
Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert
39
2006
Bose-Einstein condensation as a quantum phase transition in an optical lattice. Zbl 1170.82325
Aizenman, M.; Lieb, E. H.; Seiringer, R.; Solovej, J. P.; Yngvason, J.
16
2006
An inequality of Hadamard type for permanents. Zbl 1116.15015
Carlen, Eric; Lieb, Elliott H.; Loss, Michael
14
2006
Ground-state energy of a dilute Fermi gas. Zbl 1114.82004
Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip
2
2006
Ferromagnetism of the Hubbard model at strong coupling in the Hartree-Fock approximation. Zbl 1125.82031
Bach, Volker; Lieb, Elliott H.; Travaglia, Marcos V.
2
2006
Some matrix rearrangement inequalities. Zbl 1197.15011
Carlen, Eric; Lieb, Elliott H.
1
2006
The mathematics of the Bose gas and its condensation. Zbl 1104.82012
Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob
159
2005
Stronger subadditivity of entropy. Zbl 1227.82012
Lieb, Elliott H.; Seiringer, Robert
6
2005
One-dimensional behavior of dilute Bose gases in traps. Zbl 1106.82004
Seiringer, Robert; Lieb, Elliott H.; Yngvason, Jakob
6
2005
The quantum-mechanical many-body problem: the Bose gas. Zbl 1113.82007
Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob
6
2005
The stability of matter: From atoms to stars. Selecta of Elliott H. Lieb. 4th ed. Zbl 1165.01331
Lieb, Elliott H.
5
2005
The thermodynamic limit for matter interacting with Coulomb forces and with the quantized electromagnetic field. I: The lower bound. Zbl 1115.81064
Lieb, Elliott H.; Loss, Michael
5
2005
A sharp analog of Young’s inequality on \(S^N\) and related entropy inequalities. Zbl 1056.43002
Carlen, E. A.; Lieb, E. H.; Loss, M.
39
2004
Ground state energy of the two-component charged Bose gas. Zbl 1124.82303
Lieb, Elliott H.; Solovej, Jan Philip
26
2004
Equivalent forms of the Bessis-Moussa-Villani conjecture. Zbl 1157.81313
Lieb, Elliott H.; Seiringer, Robert
21
2004
One-dimensional behavior of dilute, trapped Bose gases. Zbl 1075.82002
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
17
2004
A note on polarization vectors in quantum electrodynamics. Zbl 1102.81070
Lieb, Elliott H.; Loss, Michael
14
2004
The stability of matter and quantum electrodynamics. Zbl 1081.81566
Lieb, Elliott H.
4
2004
Quantum mechanics, the stability of matter and quantum electrodynamics. Zbl 1255.81002
Lieb, Elliott H.
2
2004
A short appreciation of Freeman Dyson’s long career in mathematical physics. Zbl 1101.01315
Lieb, Elliott
1
2004
Existence of atoms and molecules in non-relativistic quantum electrodynamics. Zbl 1058.81080
Lieb, Elliott H.; Loss, Michael
36
2003
Bose-Einstein condensation of dilute gases in traps. Zbl 1041.81107
Lieb, Elliott H.; Seiringer, Robert
34
2003
The one-dimensional Hubbard model: a reminiscence. Zbl 1037.82009
Lieb, Elliott H.; Wu, F. Y.
14
2003
Poincaré inequalities in punctured domains. Zbl 1048.26012
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
13
2003
The entropy of classical thermodynamics. Zbl 1163.80300
Lieb, Elliott H.; Yngvason, Jakob
2
2003
Ground state energy of the one-component charged Bose gas. Zbl 1042.82004
Lieb, Elliott H.; Solovej, Jan Philip
30
2002
A bound on binding energies and mass renormalization in models of quantum electrodynamics. Zbl 1027.81040
Lieb, Elliott H.; Loss, Michael
17
2002
Stability of a model of relativistic quantum electrodynamics. Zbl 1005.81091
Lieb, Elliott H.; Loss, Michael
11
2002
Segregation in the Falicov-Kimball model. Zbl 1004.82009
Freericks, James K.; Lieb, Elliott H.; Ueltschi, Daniel
8
2002
Convex multivariable trace functions. Zbl 1034.46050
Lieb, Elliott H.; Pedersen, Gert K.
7
2002
Inequalities. Selecta of Elliott H. Lieb. Edited, with a preface and commentaries by M. Loss and M. B. Ruskai. Zbl 1159.01356
Lieb, Elliott H.
3
2002
Analysis. 2nd ed. Zbl 0966.26002
Lieb, Elliott H.; Loss, Michael
734
2001
Ground states in non-relativistic quantum electrodynamics. Zbl 1044.81133
Griesemer, Marcel; Lieb, Elliott H.; Loss, Michael
93
2001
A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Zbl 0996.82010
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
62
2001
The ground state energy of a dilute two-dimensional Bose gas. Zbl 1115.82306
Lieb, Elliott H.; Yngvason, Jakob
30
2001
The ground state of the Bose gas. Zbl 1111.82300
Lieb, Elliot H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob
4
2001
The mathematical structure of the second law of thermodynamics. Zbl 1027.80002
Lieb, Elliott H.; Yngvason, Jakob
4
2001
The stability of matter: from atoms to stars. Selecta of Elliott H. Lieb. Edited by W. Thirring. With a preface by F. Dyson. 3rd ed. Zbl 1052.01016
Lieb, Elliott H.
1
2001
The ground state energy and density of interacting bosons in a trap. Zbl 1043.82515
Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob
49
2000
Renormalization of the regularized relativistic electron-positron field. Zbl 0982.81037
Lieb, Elliott H.; Siedentop, Heinz
9
2000
...and 113 more Documents
all top 5

Cited by 5,876 Authors

105 Lieb, Elliott H.
68 Frank, Rupert L.
60 Seiringer, Robert
51 Solovej, Jan Philip
45 Lewin, Mathieu
36 Fröhlich, Jürg Martin
36 Loss, Michael
32 Alves, Claudianor Oliveira
32 Tang, Xianhua
32 Yang, Minbo
30 Carlen, Eric Anders
30 Wu, Tsungfang
28 Dolbeault, Jean
28 Laptev, Ari
27 Hainzl, Christian
27 Schlein, Benjamin
27 Van Schaftingen, Jean
26 Peng, Shuangjie
26 Rougerie, Nicolas
25 Chen, Sitong
25 Deng, Yinbin
25 Siedentop, Heinz Karl Heinrich
24 Squassina, Marco
23 Brézis, Haïm
23 Phan Thanh Nam
23 Zou, Wenming
22 Ambrosio, Vincenzo
22 Erdős, László
22 Fournais, Søren
22 Simon, Barry
21 Lions, Pierre-Louis
20 Miyagaki, Olimpio Hiroshi
19 Lei, Yutian
19 Lu, Guozhen
19 Naor, Assaf
19 Petz, Dénes
19 Ruskai, Mary Beth
19 Yau, Horng-Tzer
19 Yngvason, Jakob
18 Bach, Volker
18 Chen, Jianqing
18 Chen, Thomas M.
18 Hiai, Fumio
18 Miyao, Tadahiro
18 Salani, Paolo
18 Wang, Zhi-Qiang
18 Xue, Kang
17 Benguria, Rafael D.
17 Figueiredo, Giovany Malcher
17 Rădulescu, Vicenţiu D.
17 Xiao, Jie
16 Chen, Caisheng
16 Hiroshima, Fumio
16 Li, Congming
16 Nachtergaele, Bruno
16 Spohn, Herbert
16 Sreenadh, Konijeti
15 Cao, Daomin
15 Carrillo de la Plata, José Antonio
15 Faupin, Jérémy
15 Griesemer, Marcel
15 Hansen, Frank-Peter
15 Pucci, Patrizia
15 Serfaty, Sylvia
15 Sigal, Israel Michael
15 Tang, Chun-Lei
15 Yang, Jianfu
14 Bez, Neal
14 Esteban, Maria J.
14 Hsu, TsingSan
14 Nguyễn Văn Hoàng
14 Slavnov, Nikita A.
14 Sun, Juntao
14 Tintarev, Kyril
13 Fiscella, Alessio
13 Guo, Yujin
13 Helffer, Bernard
13 Lü, Dengfeng
13 Mironescu, Petru
13 Suragan, Durvudkhan
13 Valdinoci, Enrico
13 Vazquez, Juan Luis
12 Bobkov, Sergey Germanovich
12 Chen, Haibo
12 Hajaiej, Hichem
12 Kovařík, Hynek
12 Lenzmann, Enno
12 Li, Gongbao
12 Li, YanYan
12 Peral Alonso, Ireneo
12 Ruzhansky, Michael V.
12 Safronov, Oleg
12 Sun, Chunfang
12 Tasaki, Hal
11 Bao, Weizhu
11 Barbaroux, Jean-Marie
11 Byeon, Jaeyoung
11 Choi, Woocheol
11 Cianchi, Andrea
11 Correggi, Michele
...and 5,776 more Authors
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Cited in 521 Serials

387 Journal of Mathematical Physics
365 Communications in Mathematical Physics
255 Journal of Mathematical Analysis and Applications
253 Journal of Functional Analysis
235 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
189 Journal of Statistical Physics
185 Journal of Differential Equations
165 Calculus of Variations and Partial Differential Equations
102 Advances in Mathematics
99 Archive for Rational Mechanics and Analysis
97 Letters in Mathematical Physics
93 Journal of Statistical Mechanics: Theory and Experiment
87 Linear Algebra and its Applications
84 Annales Henri Poincaré
81 Proceedings of the American Mathematical Society
76 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
74 Transactions of the American Mathematical Society
69 Communications in Partial Differential Equations
64 Communications in Contemporary Mathematics
59 Discrete and Continuous Dynamical Systems
54 Reviews in Mathematical Physics
54 Communications on Pure and Applied Analysis
44 Advanced Nonlinear Studies
40 Journal de Mathématiques Pures et Appliquées. Neuvième Série
40 Potential Analysis
40 Journal of Physics A: Mathematical and Theoretical
38 The Journal of Geometric Analysis
38 Nonlinear Analysis. Theory, Methods & Applications
37 ZAMP. Zeitschrift für angewandte Mathematik und Physik
36 Annali di Matematica Pura ed Applicata. Serie Quarta
35 International Journal of Modern Physics B
35 Comptes Rendus. Mathématique. Académie des Sciences, Paris
34 Mathematische Annalen
34 Applied Mathematics Letters
33 Duke Mathematical Journal
31 Theoretical and Mathematical Physics
31 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
29 The Annals of Probability
29 SIAM Journal on Mathematical Analysis
29 Quantum Information Processing
29 Science China. Mathematics
28 Computers & Mathematics with Applications
28 Discrete Mathematics
27 Journal of Computational Physics
26 Journal of the European Mathematical Society (JEMS)
26 Journal of High Energy Physics
25 Applicable Analysis
25 International Journal of Theoretical Physics
25 Manuscripta Mathematica
25 Bulletin of the American Mathematical Society. New Series
25 Journal of Mathematical Sciences (New York)
25 NoDEA. Nonlinear Differential Equations and Applications
24 Communications on Pure and Applied Mathematics
24 Inventiones Mathematicae
24 Probability Theory and Related Fields
23 Journal d’Analyse Mathématique
23 Mathematische Zeitschrift
23 Boundary Value Problems
23 Complex Variables and Elliptic Equations
23 Advances in Nonlinear Analysis
22 Nuclear Physics. B
22 Journal of Combinatorial Theory. Series A
22 Abstract and Applied Analysis
21 Mathematical Methods in the Applied Sciences
21 New Journal of Physics
19 Applied Mathematics and Computation
19 Stochastic Processes and their Applications
18 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
18 Physical Review Letters
17 Reports on Mathematical Physics
17 Annales de l’Institut Henri Poincaré. Physique Théorique
17 Acta Mathematica Sinica. English Series
16 Discrete Applied Mathematics
16 Monatshefte für Mathematik
16 Physica D
16 Journal of the American Mathematical Society
16 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
16 International Journal of Quantum Information
16 Mediterranean Journal of Mathematics
15 Nonlinearity
15 Annales de l’Institut Fourier
15 Mathematische Nachrichten
15 Acta Applicandae Mathematicae
15 Revista Matemática Iberoamericana
15 Topological Methods in Nonlinear Analysis
15 St. Petersburg Mathematical Journal
15 The Journal of Fourier Analysis and Applications
15 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
15 Mathematical Physics, Analysis and Geometry
15 Infinite Dimensional Analysis, Quantum Probability and Related Topics
15 Nonlinear Analysis. Real World Applications
14 Physics Letters. A
14 Acta Mathematica
14 Journal of Algebra
14 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics
13 Integral Equations and Operator Theory
13 Advances in Applied Mathematics
13 Journal of Fixed Point Theory and Applications
13 Journal of Function Spaces
12 Linear and Multilinear Algebra
...and 421 more Serials
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Cited in 62 Fields

2,943 Partial differential equations (35-XX)
1,446 Quantum theory (81-XX)
1,191 Statistical mechanics, structure of matter (82-XX)
691 Functional analysis (46-XX)
653 Operator theory (47-XX)
469 Probability theory and stochastic processes (60-XX)
391 Calculus of variations and optimal control; optimization (49-XX)
382 Global analysis, analysis on manifolds (58-XX)
368 Real functions (26-XX)
266 Combinatorics (05-XX)
220 Information and communication theory, circuits (94-XX)
198 Linear and multilinear algebra; matrix theory (15-XX)
187 Differential geometry (53-XX)
181 Harmonic analysis on Euclidean spaces (42-XX)
180 Fluid mechanics (76-XX)
168 Convex and discrete geometry (52-XX)
133 Integral equations (45-XX)
119 Numerical analysis (65-XX)
108 Dynamical systems and ergodic theory (37-XX)
103 Ordinary differential equations (34-XX)
97 Group theory and generalizations (20-XX)
88 Potential theory (31-XX)
76 Optics, electromagnetic theory (78-XX)
73 Measure and integration (28-XX)
65 Statistics (62-XX)
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43 Number theory (11-XX)
40 Special functions (33-XX)
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38 Functions of a complex variable (30-XX)
36 Integral transforms, operational calculus (44-XX)
36 Classical thermodynamics, heat transfer (80-XX)
32 Several complex variables and analytic spaces (32-XX)
31 Computer science (68-XX)
22 Approximations and expansions (41-XX)
18 Geometry (51-XX)
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15 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
14 General and overarching topics; collections (00-XX)
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14 Systems theory; control (93-XX)
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3 Mathematics education (97-XX)

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