Econometrica, ISSN 0012-9682, 11/2016, Volume 84, Issue 6, pp. 2071 - 2111

The past forty years have seen a rapid rise in top income inequality in the United States...

spectral methods | Pareto distribution | speed of transition | operator methods | superstars | Inequality | UNITED-STATES | EARNINGS INEQUALITY | PARETO | STATISTICS & PROBABILITY | MODEL | TOP INCOME | WEALTH | RISE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | GROWTH | ECONOMIES | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | ZIPFS LAW | Income distribution | Analysis | Equality

spectral methods | Pareto distribution | speed of transition | operator methods | superstars | Inequality | UNITED-STATES | EARNINGS INEQUALITY | PARETO | STATISTICS & PROBABILITY | MODEL | TOP INCOME | WEALTH | RISE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | GROWTH | ECONOMIES | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | ZIPFS LAW | Income distribution | Analysis | Equality

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 01/2019, Volume 266, Issue 2-3, pp. 1051 - 1072

The Adimurthi–Druet [1] inequality is an improvement of the standard Moser–Trudinger inequality by adding a L2-type perturbation, quantified by α∈[0,λ1...

EXISTENCE | MATHEMATICS | MOSER-TRUDINGER INEQUALITY | SHARP FORM | POSITIVE SOLUTIONS | CRITICAL-POINTS | Analysis | Equality | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

EXISTENCE | MATHEMATICS | MOSER-TRUDINGER INEQUALITY | SHARP FORM | POSITIVE SOLUTIONS | CRITICAL-POINTS | Analysis | Equality | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 5/2017, Volume 352, Issue 1, pp. 37 - 58

We prove several trace inequalities that extend the Golden–Thompson and the Araki...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | RELATIVE ENTROPY | LIEB | QUANTUM-MECHANICAL ENTROPY | GOLDEN-THOMPSON INEQUALITY | PHYSICS, MATHEMATICAL | ALGEBRA | Atoms

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | RELATIVE ENTROPY | LIEB | QUANTUM-MECHANICAL ENTROPY | GOLDEN-THOMPSON INEQUALITY | PHYSICS, MATHEMATICAL | ALGEBRA | Atoms

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 25

We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive...

Jensen’s inequality | 26A51 | 26A24 | Mathematics | Hermite-Hadamard’s inequality | Green function | Giaccardi’s inequality | Analysis | converse Jensen’s inequality | Levinson’s inequality | Mathematics, general | Applications of Mathematics | 26D15 | mean-value theorems | MATHEMATICS | MATHEMATICS, APPLIED | Jensen's inequality | Hermite-Hadamard's inequality | Giaccardi's inequality | HADAMARD INEQUALITY | converse Jensen's inequality | Levinson's inequality | Theorems | Inequalities | Research

Jensen’s inequality | 26A51 | 26A24 | Mathematics | Hermite-Hadamard’s inequality | Green function | Giaccardi’s inequality | Analysis | converse Jensen’s inequality | Levinson’s inequality | Mathematics, general | Applications of Mathematics | 26D15 | mean-value theorems | MATHEMATICS | MATHEMATICS, APPLIED | Jensen's inequality | Hermite-Hadamard's inequality | Giaccardi's inequality | HADAMARD INEQUALITY | converse Jensen's inequality | Levinson's inequality | Theorems | Inequalities | Research

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 8/2016, Volume 165, Issue 3, pp. 1025 - 1049

.... The method is based on Grothendieck’s inequality. Unlike the previous uses of this inequality that lead to constant relative accuracy, we achieve any given relative accuracy by leveraging randomness...

Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Operation Research/Decision Theory | Quantitative Finance | MAXIMUM-LIKELIHOOD | CUT | SPECTRAL TECHNIQUES | APPROXIMATION | EIGENVECTORS | STOCHASTIC BLOCKMODELS | NORM | STATISTICS & PROBABILITY | ALGORITHMS | Analysis | Equality | Studies | Semidefinite programming | Graph theory | Mathematical analysis | Optimization | Networks | Accuracy | Communities | Inequalities | Consistency | Constants | Graphs | Functional Analysis

Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Operation Research/Decision Theory | Quantitative Finance | MAXIMUM-LIKELIHOOD | CUT | SPECTRAL TECHNIQUES | APPROXIMATION | EIGENVECTORS | STOCHASTIC BLOCKMODELS | NORM | STATISTICS & PROBABILITY | ALGORITHMS | Analysis | Equality | Studies | Semidefinite programming | Graph theory | Mathematical analysis | Optimization | Networks | Accuracy | Communities | Inequalities | Consistency | Constants | Graphs | Functional Analysis

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 2/2015, Volume 334, Issue 1, pp. 473 - 505

... on $${\ell^{2}(\mathbb{Z})}$$ ℓ 2 ( Z ) to provide new proofs of sharp Lieb–Thirring inequalities for the powers $${\gamma = \frac{1}{2}}$$ γ = 1 2 and $${\gamma = \frac{3}{2}}$$ γ = 3 2...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EIGENVALUES | PHYSICS, MATHEMATICAL | BOUNDS | SIMPLE PROOF

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EIGENVALUES | PHYSICS, MATHEMATICAL | BOUNDS | SIMPLE PROOF

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 01/2014, Volume 266, Issue 1, pp. 55 - 66

The paper gives the following improvement of the Trudinger–Moser inequality:(0.1)sup∫Ω|∇u|2dx−ψ(u)⩽1,u∈C0∞(Ω)∫Ωe4πu2dx<∞,Ω∈R2, related to the Hardy...

Spectral gap | Virtual bound state | Singular elliptic operators | Trudinger–Moser inequality | Borderline Sobolev imbeddings | Hardy–Sobolev–Mazya inequality | Remainder terms | Trudinger-Moser inequality | Hardy-Sobolev-Mazya inequality | MATHEMATICS | Equality

Spectral gap | Virtual bound state | Singular elliptic operators | Trudinger–Moser inequality | Borderline Sobolev imbeddings | Hardy–Sobolev–Mazya inequality | Remainder terms | Trudinger-Moser inequality | Hardy-Sobolev-Mazya inequality | MATHEMATICS | Equality

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2018, Volume 274, Issue 6, pp. 1739 - 1746

In 1975, Lieb and Thirring derived a semiclassical lower bound on the kinetic energy for fermions, which agrees with the Thomas–Fermi approximation up to a...

Lieb–Thirring inequality | Sharp constant | Gradient error | Semiclassical approximation | DENSITY | MATHEMATICS | MATTER | ENERGY | STABILITY | Lieb-Thirring inequality | ATOMS | HARDY | MOLECULES | Force and energy | Equality

Lieb–Thirring inequality | Sharp constant | Gradient error | Semiclassical approximation | DENSITY | MATHEMATICS | MATTER | ENERGY | STABILITY | Lieb-Thirring inequality | ATOMS | HARDY | MOLECULES | Force and energy | Equality

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2015, Volume 485, pp. 153 - 193

.... This lemma relates the positive semi-definiteness of the Popov function on the imaginary axis to the solvability of a linear matrix inequality on a certain subspace...

Even matrix pencils | Kalman–Yakubovich–Popov lemma | Lur'e equations | Algebraic Riccati equations | Differential-algebraic equations | Linear-quadratic optimal control | KalmanYakubovichPopov lemma | Lure equations | LURE EQUATIONS | MATHEMATICS, APPLIED | Kalman-Yakubovich-Popov lemma | TIME DESCRIPTOR SYSTEMS | DISSIPATIVITY | FORM | LEMMA | MATHEMATICS | MATRIX PENCILS | AUTOMATIC CONTROL | SPECTRAL FACTORIZATION | RICCATI EQUATION | Equality | Control systems | Rankings

Even matrix pencils | Kalman–Yakubovich–Popov lemma | Lur'e equations | Algebraic Riccati equations | Differential-algebraic equations | Linear-quadratic optimal control | KalmanYakubovichPopov lemma | Lure equations | LURE EQUATIONS | MATHEMATICS, APPLIED | Kalman-Yakubovich-Popov lemma | TIME DESCRIPTOR SYSTEMS | DISSIPATIVITY | FORM | LEMMA | MATHEMATICS | MATRIX PENCILS | AUTOMATIC CONTROL | SPECTRAL FACTORIZATION | RICCATI EQUATION | Equality | Control systems | Rankings

Journal Article

Studia Mathematica, ISSN 0039-3223, 2018, Volume 242, Issue 3, pp. 303 - 319

The aim of this paper is twofold. In the first part, we present a refinement of the Renyi Entropy Power Inequality (EPI...

(reverse) entropy power inequality | Pth mean bodies | MATHEMATICS | CONVEX-BODIES | PROOF | SPECTRAL GAP | BRUNN-MINKOWSKI | pth mean bodies | COMMUNICATION | MATHEMATICAL-THEORY | JUMPS

(reverse) entropy power inequality | Pth mean bodies | MATHEMATICS | CONVEX-BODIES | PROOF | SPECTRAL GAP | BRUNN-MINKOWSKI | pth mean bodies | COMMUNICATION | MATHEMATICAL-THEORY | JUMPS

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 9/2015, Volume 217, Issue 3, pp. 873 - 898

The equivalence between the inequalities of Babuška–Aziz and Friedrichs for sufficiently smooth bounded domains in the plane was shown by Horgan and Payne 30 years ago...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | Functional Analysis | Numerical Analysis | Mathematics

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | Functional Analysis | Numerical Analysis | Mathematics

Journal Article

Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 2016, Volume 92, Issue 10, pp. 125 - 130

We extend the Hardy inequalities to the classical Hardy spaces and the rearrangement-invariant Hardy spaces.

Interpolation | Rearrangement-invariant | Hardy's inequality | Atomic decomposition | Hardy space | MATHEMATICS | atomic decomposition | interpolation | rearrangement-invariant | HAUSDORFF OPERATORS | BANACH FUNCTION-SPACES | Inequalities (Mathematics) | Analysis | Mathematics | Decomposition | Inequality | Series (mathematics) | Mathematical analysis | Inequalities

Interpolation | Rearrangement-invariant | Hardy's inequality | Atomic decomposition | Hardy space | MATHEMATICS | atomic decomposition | interpolation | rearrangement-invariant | HAUSDORFF OPERATORS | BANACH FUNCTION-SPACES | Inequalities (Mathematics) | Analysis | Mathematics | Decomposition | Inequality | Series (mathematics) | Mathematical analysis | Inequalities

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 4/2017, Volume 107, Issue 4, pp. 717 - 732

...–Krahn-type inequality for the principal eigenvalue of these operators. The proofs rely on the Birman-Schwinger principle and on the fact that circles are unique minimizers for a class of energy functionals...

Conical surface | Theoretical, Mathematical and Computational Physics | Complex Systems | Isoperimetric inequality | Existence of bound states | 35Q40 | Physics | Secondary 35J10 | Geometry | 81Q37 | 46F10 | Schrödinger operator | Group Theory and Generalizations | delta $$ δ -interaction | 81Q10 | Primary 35P15 | δ-interaction | EIGENVALUE | BOUND-STATES | CHORDS | Schrodinger operator | delta-interaction | PHYSICS, MATHEMATICAL | DOMAINS | SCHRODINGER-OPERATORS | PARAMETER | Nuclear physics | Equality

Conical surface | Theoretical, Mathematical and Computational Physics | Complex Systems | Isoperimetric inequality | Existence of bound states | 35Q40 | Physics | Secondary 35J10 | Geometry | 81Q37 | 46F10 | Schrödinger operator | Group Theory and Generalizations | delta $$ δ -interaction | 81Q10 | Primary 35P15 | δ-interaction | EIGENVALUE | BOUND-STATES | CHORDS | Schrodinger operator | delta-interaction | PHYSICS, MATHEMATICAL | DOMAINS | SCHRODINGER-OPERATORS | PARAMETER | Nuclear physics | Equality

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2016, Volume 18, Issue 6, p. 1650020

In this paper, we are dealing with quantitative Rellich inequalities on Finsler–Hadamard manifolds where the remainder terms are expressed by means of the flag curvature...

Rellich inequality | Finsler-Hadamard manifold | Finsler-Laplace operator | curvature | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | HARDY | RIEMANNIAN-MANIFOLDS | GEOMETRY | Mathematics - Analysis of PDEs

Rellich inequality | Finsler-Hadamard manifold | Finsler-Laplace operator | curvature | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | HARDY | RIEMANNIAN-MANIFOLDS | GEOMETRY | Mathematics - Analysis of PDEs

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 12/2015, Volume 61, Issue 12, pp. 6550 - 6559

We show that Shannon's entropy-power inequality admits a strengthened version in the case in which the densities are log-concave...

Stam's Fisher information inequality | Heating | Entropy | Convex functions | Random variables | information theory | Mathematical model | Covariance matrices | information measure | entropy-power inequality | Entropy-power inequality | Information measure | Information theory | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | SPECTRAL GAP | MATHEMATICAL-THEORY | SIMPLE PROOF | ENGINEERING, ELECTRICAL & ELECTRONIC | SMOOTH DENSITIES | PLANCK-TYPE EQUATIONS | EQUILIBRIUM | CONVERGENCE | COMMUNICATION | CENTRAL-LIMIT-THEOREM | Usage | Mathematical models | Entropy (Information theory)

Stam's Fisher information inequality | Heating | Entropy | Convex functions | Random variables | information theory | Mathematical model | Covariance matrices | information measure | entropy-power inequality | Entropy-power inequality | Information measure | Information theory | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | SPECTRAL GAP | MATHEMATICAL-THEORY | SIMPLE PROOF | ENGINEERING, ELECTRICAL & ELECTRONIC | SMOOTH DENSITIES | PLANCK-TYPE EQUATIONS | EQUILIBRIUM | CONVERGENCE | COMMUNICATION | CENTRAL-LIMIT-THEOREM | Usage | Mathematical models | Entropy (Information theory)

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 9

...He and Huang Journal of Inequalities and Applications 2014, 2014:114 http://www.journaloﬁnequalitiesandapplications.com/content/2014/1/114 R E S E A R C H Open...

eigenvalues | nonnegative tensor | Analysis | Mathematics, general | Mathematics | M -tensors | Applications of Mathematics | spectral radius | M-tensors | Eigenvalues | Nonnegative tensor | Spectral radius | MATHEMATICS | MATHEMATICS, APPLIED | LARGEST EIGENVALUE | PERRON-FROBENIUS THEOREM | Lower bounds | Theorems | Inequalities

eigenvalues | nonnegative tensor | Analysis | Mathematics, general | Mathematics | M -tensors | Applications of Mathematics | spectral radius | M-tensors | Eigenvalues | Nonnegative tensor | Spectral radius | MATHEMATICS | MATHEMATICS, APPLIED | LARGEST EIGENVALUE | PERRON-FROBENIUS THEOREM | Lower bounds | Theorems | Inequalities

Journal Article

Revista Matematica Iberoamericana, ISSN 0213-2230, 2018, Volume 34, Issue 3, pp. 1021 - 1054

.... In particular these formulae entail new functional inequalities of Brascamp-Lieb type for log-concave distributions and beyond...

Log-concave probability measure | Brascamp-Lieb type inequalities | Diffusion operator on vector fields | Spectral gap | Intertwining | LOGARITHMIC SOBOLEV INEQUALITIES | DECAY | BRUNN-MINKOWSKI | CONCAVE PROBABILITY-MEASURES | COMPLETE RIEMANNIAN MANIFOLD | log- concave probability measure | ONE-DIMENSIONAL DIFFUSIONS | MATHEMATICS | POINCARE | spectral gap | SPIN SYSTEMS | EQUATION | diffusion operator on vector fields

Log-concave probability measure | Brascamp-Lieb type inequalities | Diffusion operator on vector fields | Spectral gap | Intertwining | LOGARITHMIC SOBOLEV INEQUALITIES | DECAY | BRUNN-MINKOWSKI | CONCAVE PROBABILITY-MEASURES | COMPLETE RIEMANNIAN MANIFOLD | log- concave probability measure | ONE-DIMENSIONAL DIFFUSIONS | MATHEMATICS | POINCARE | spectral gap | SPIN SYSTEMS | EQUATION | diffusion operator on vector fields

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 2, pp. 1676 - 1689

... or Pólya inequalities, respectively. The logarithmic potential operator can be related to a nonlocal boundary value problem for the Laplacian, so we obtain...

Pólya inequality | Characteristic numbers | Rayleigh–Faber–Krahn inequality | Isoperimetric inequality | Logarithmic potential | Schatten class | Rayleigh-Faber-Krahn inequality | LAPLACIAN | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | Polya inequality | Mathematics - Functional Analysis

Pólya inequality | Characteristic numbers | Rayleigh–Faber–Krahn inequality | Isoperimetric inequality | Logarithmic potential | Schatten class | Rayleigh-Faber-Krahn inequality | LAPLACIAN | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | Polya inequality | Mathematics - Functional Analysis

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2014, Volume 16, Issue 11, pp. 2433 - 2475

This paper presents two observability inequalities for the heat equation over Omega x (0...

Spectral inequality | Heat equation | Observability inequality | Measurable set | MATHEMATICS, APPLIED | CARLEMAN INEQUALITIES | heat equation | PARABOLIC EQUATIONS | LIPSCHITZ CYLINDERS | TIME | spectral inequality | UNIQUE CONTINUATION | MATHEMATICS | measurable set | NONSMOOTH COEFFICIENTS | HEAT-EQUATION | BOUNDARY | NULL-CONTROLLABILITY | DOMAINS

Spectral inequality | Heat equation | Observability inequality | Measurable set | MATHEMATICS, APPLIED | CARLEMAN INEQUALITIES | heat equation | PARABOLIC EQUATIONS | LIPSCHITZ CYLINDERS | TIME | spectral inequality | UNIQUE CONTINUATION | MATHEMATICS | measurable set | NONSMOOTH COEFFICIENTS | HEAT-EQUATION | BOUNDARY | NULL-CONTROLLABILITY | DOMAINS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2010, Volume 249, Issue 1, pp. 118 - 135

.... Hence an optimal Poincaré inequality for triangles is derived. The proof relies on symmetry of the Neumann fundamental mode for isosceles triangles with aperture less than π / 3...

Isodiametric | Free membrane | Isoperimetric | Poincaré inequality | MATHEMATICS | BOUNDS | 1ST DIRICHLET EIGENVALUE | Poincare inequality | EIGENFUNCTIONS | Equality

Isodiametric | Free membrane | Isoperimetric | Poincaré inequality | MATHEMATICS | BOUNDS | 1ST DIRICHLET EIGENVALUE | Poincare inequality | EIGENFUNCTIONS | Equality

Journal Article