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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 03/2016, Volume 472, Issue 2187, p. 20150563
We derive new characterizations of the matrix Φ-entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob. 19 , 1–30. (... 
Matrix concentration inequalities | Efron-Stein inequality | Φ-entropy | 1008 | matrix concentration inequalities | Efron–Stein inequality | 157 | 1003 | 175 | 120
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2018, Volume 41, Issue 17, pp. 7599 - 7611
This paper is concerned with the fractional Schrödinger‐Poisson systems involving a Bessel operator. By using Mountain‐pass theorem and Ekeland's variational... 
multiplicity | variational principle | concentration | Bessel operator | concave‐convex | Mountain‐pass theorem | Mountain-pass theorem | concave-convex | EXISTENCE | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER | EQUATION | Weighting functions
Journal Article
ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 2018, Volume 24, Issue 1, pp. 1 - 24
We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent... 
Fractional magnetic operators | Minimization problems | Concentration compactness | EXISTENCE | MATHEMATICS, APPLIED | INEQUALITIES | concentration compactness | ELECTROMAGNETIC-FIELDS | SOBOLEV SPACES | SYMMETRY | minimization problems | COMPACTNESS | EQUATION | SEMICLASSICAL LIMIT | AUTOMATION & CONTROL SYSTEMS | SCHRODINGER-OPERATORS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2015, Volume 259, Issue 10, pp. 4989 - 5016
In this paper we prove the existence of orbitally stable standing waves for the Schrödinger operator, involving potential of the form c|x|−2, 0 Orbital stability | Hardy inequality | Hidden energy | Inverse square potential | Schrödinger equation | Standing wave | EXISTENCE | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | CRITICAL NONLINEARITIES | EQUATIONS | DECAYING RADIAL POTENTIALS | STANDING WAVES | MATHEMATICS | Schrodinger equation
Journal Article
The Journal of Physical Chemistry B, ISSN 1520-6106, 02/2013, Volume 117, Issue 6, pp. 1880 - 1885
Journal Article
Surgical Endoscopy, ISSN 0930-2794, 4/2011, Volume 25, Issue 4, pp. 1245 - 1250
Journal Article
Advances in Nonlinear Analysis, ISSN 2191-9496, 11/2018, Volume 7, Issue 4, pp. 587 - 599
Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker assumptions on the nonlinearity than known before. An... 
Brézis–Lieb splitting | uniform continuity | 58E40 | 47H30 | Superposition operator | Sobolev space | Brézis-Lieb splitting | MATHEMATICS | MATHEMATICS, APPLIED | Brezis-Lieb splitting | STATES | PERIODIC SCHRODINGER-EQUATIONS | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | MULTIBUMP SOLUTIONS
Journal Article
Journal of Occupational and Environmental Hygiene, ISSN 1545-9624, 01/2017, Volume 14, Issue 1, pp. D1 - D12
Journal Article
Inverse Problems, ISSN 0266-5611, 02/2017, Volume 33, Issue 2, p. 25005
The problem of recovering a signal of finite duration from a piece of its Fourier transform was solved at Bell Labs in the 1960's, by exploiting a 'miracle': a... 
double concentration | matrix valued orthogonal polynomials | time-band limiting | TOMOGRAPHY | MATHEMATICS, APPLIED | SPHEROIDAL WAVE-FUNCTIONS | UNCERTAINTY | ORTHOGONAL POLYNOMIALS | PHYSICS, MATHEMATICAL | FOURIER-ANALYSIS
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2016, Volume 302, pp. 312 - 326
The advection–diffusion–reaction (ADR) systems are often used to describe the chemotaxis models arising in biology. In general, the stiffness from the reaction... 
Krylov implicit integration factor | Discontinuous Galerkin | Chemotaxis model | Positivity preserving | SCHEME | MATHEMATICS, APPLIED | SYSTEMS | DIFFUSION | FINITE-ELEMENT-METHOD | EFFICIENT | Splitting | Advection | Numerical analysis | Discretization | Mathematical models | Diffusion | Galerkin methods | Concentration gradient
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2018, Volume 120, pp. 33 - 90
Let M be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a compact Lie group G, and P0 an invariant elliptic... 
Equivariant local Weyl law | [formula omitted]-bounds and concentration of eigenfunctions | Caustics | Desingularization | Stationary phase | bounds and concentration of eigenfunctions | MATHEMATICS | L-p-bounds and concentration of eigenfunctions | MATHEMATICS, APPLIED | SYMMETRY | CLUSTERS | NORMS | FORMULA
Journal Article
Bernoulli, ISSN 1350-7265, 02/2017, Volume 23, Issue 1, pp. 110 - 133
Let X, X-1,..., X-n,. be i.i.d. centered Gaussian random variables in a separable Banach space E with covariance operator Sigma: Sigma:E* -> E, Sigma u =... 
Moment bounds | Sample covariance | Effective rank | Concentration inequalities | sample covariance | effective rank | STATISTICS & PROBABILITY | EMPIRICAL PROCESSES | concentration inequalities | moment bounds
Journal Article
Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 3/2017, Volume 19, Issue 1, pp. 649 - 690
In this paper, the existence of least energy solution and infinitely many solutions is proved for the equation $$(1-\Delta )^\alpha u = f(u)$$ ( 1 - Δ ) α u =... 
Mathematical Methods in Physics | The Pohozaev identity | 35J60 | Analysis | Mountian pass theorem | Mathematics, general | Symmetric mountain pass theorem | Mathematics | Variational method | 35S05 | MATHEMATICS, APPLIED | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | NONLINEAR SCHRODINGER-EQUATION | LAPLACIAN | MATHEMATICS | R-N | SOBOLEV SPACES | GROUND-STATES
Journal Article
Milan Journal of Mathematics, ISSN 1424-9286, 12/2011, Volume 79, Issue 2, pp. 657 - 687
Journal Article
Revista Mexicana de Fisica, ISSN 0035-001X, 2016, Volume 62, Issue 5, pp. 409 - 417
In this article, an analysis of the kinetic energy operator introduced by O. von Roos is performed. Such analysis allows for determining the energy of a... 
Geometry | Parameter ambiguity | Potential energy | von Roos operator | Position-dependent effective mass | Variable concentration | QUANTUM-WELL | position-dependent effective mass | HARMONIC-OSCILLATOR | PHYSICS, MULTIDISCIPLINARY | parameter ambiguity | geometry | potential energy | GAAS | DEPENDENT EFFECTIVE-MASS | MASS SCHRODINGER-EQUATION
Journal Article