Related papers: The Lieb-Thirring inequalities: Recent results and…
In this paper, we obtain new upper bounds for the Lieb-Thirring inequality on the spheres of any dimension greater than $2$. As far as we have checked, our results improve previous results found in the literature for all dimensions greater…
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…
This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
In this paper some open problems for Painlev\'e equations are discussed. In particular the following open problems are described: (i) the Painlev\'e equivalence problem; (ii) notation for solutions of the Painlev\'e equations; (iii)…
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider,…
The purpose of this survey is to give a comprehensive introduction to some classes of classical and recent analytic inequalities in Inner Product Spaces.
The aim of this work is to improve Wilker inequalities near the origin and {\pi}/2.
We review the status of inclusive |Vub| measurements where many new results have become available recently.
In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.
In \cite{Nam} Nam proved a Lieb--Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with…
This is an informal survey of progress in Weihrauch complexity (cf arXiv:1707.03202) in the period 2018-2020. Open questions are emphasised.
Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schr\"odinger operator with a complex-valued potential.
We introduce a new class of perturbations of the Seiberg-Witten equations. Our perturbations offer flexibility in the way the Seiberg-Witten invariants are constructed and also shed a new light to LeBrun's curvature inequalities.
Recent results on finite open group transformations are reviewed.
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…
The main study of this article is the characterization of Richard's inequality, because it is closely related to Buzano's inequality. Finally, we present a newapproach for Richard's inequality, where we use the Selberg operator.
An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in arithmetic progressions.
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.