Related papers: The Lieb-Thirring inequalities: Recent results and…
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
In this paper we obtain the estimates on some dynamic integral inequalities in three variables which can be used to study certain dynamic equations. We give some applications to convey the importance of our result.
We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$ with $\gamma\ge 3/2$ and arbitrary $d\ge…
The purpose of this text is twofold. We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute to the topic with some observations on constructive…
We present a review of results that have been obtained in the past twenty-five years concerning the $L^p$-Hardy inequality with distance to the boundary. We concentrate on results where the best Hardy constant is either computed exactly or…
The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality versions in the integral form. The obtained sharp Hardy-Rellich…
A criterion is established for the validity of multilinear inequalities of a class considered by Brascamp and Lieb, generalizing well-known inequalities of Holder, Young, and Loomis-Whitney. This is a companion to a recent paper by the same…
The main aim of this book is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator…
In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.
Socio-economic inequalities are manifested in different aspects of our social life. We discuss various aspects, beginning with the evolutionary and historical origins, and discussing the major issues from the social and economic point of…
This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to…
We provide a detailed overview of the various approaches that were proposed to date to solve the task of Open Information Extraction. We present the major challenges that such systems face, show the evolution of the suggested approaches…
We show that, under very general definitions of a kinetic energy operator $T$, the Lieb-Thirring inequalities for sums of eigenvalues of $T-V$ can be derived from the Sobolev inequality appropriate to that choice of $T$.
We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.
We give a survey on recent developments on nonlinear Schr\"odinger equations with dissipative structure based on the authors' recent works.
We give an historical account, including recent progress, on some problems of Erd\H os in number theory.
To determine the sharp constants for the one dimensional Lieb--Thirring inequalities with exponent gamma in (1/2,3/2) is still an open problem. According to a conjecture by Lieb and Thirring the sharp constant for these exponents should be…
We present in an informal way some recent results concerning a possible overlapping between classical unpredictability and quantum indeterminism.