Related papers: The Lieb-Thirring inequalities: Recent results and…
We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.
Several new results in the field of Hilbert lattice equations based on states defined on the lattice as well as novel techniques used to arrive at these results are presented. An open problem of Mayet concerning Hilbert lattice equations…
A brief report on recent work on the sphere-packing problem.
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
We prove on the sphere $\mathbb{S}^2$ the Lieb--Thirring inequalities for orthonormal families of scalar and vector functions both on the whole sphere and on proper domains on $\mathbb{S}^2$. By way of applications we obtain an explicit…
A new and elementary proof of a recent result of Laptev and Weidl is given. It is a sharp Lieb-Thirring inequality for one dimensional Schroedinger operators with matrix valued potentials.
The article focuses on the problems of prime gaps and zero spacings. Possible solutions of several related problems such as the greatest lower bound, the least upper bound of the zero spacings, and the least upper bound of the prime gaps…
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
Initially motivated by their relevance in foundations of quantum mechanics and more recently by their applications in different contexts of quantum information science, violations of Bell inequalities have been extensively studied during…
We improve the Lieb-Thirring type inequalities by Demuth, Hansmann and Katriel (J. Funct. Anal. 2009) for Schr\"odinger operators with complex-valued potentials. Our result involves a positive, integrable function. We show that in the…
We prove analogues of the Lieb-Thirring and Hardy-Lieb-Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed.…
We prove an analogue of the Lieb--Thirring inequality for many-body quantum systems with the kinetic operator $\sum_i (-\Delta_i)^s$ and the interaction potential of the form $\sum_i \delta_i^{-2s}$ where $\delta_i$ is the nearest-neighbor…
In this paper, which corresponds to an updated version of the author's Habilitation lecture in Mathematics, we do an overview of several topics in elliptic problems. We review some old and new results regarding the Lane-Emden equation, both…
As part of the search for the value of the smallest upper bound of the best constant for the famous Grothendieck inequality, the so-called Grothendieck constant (a hard open problem - unsolved since 1953), we provide a further approach,…
We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…
This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…
This paper presents some new inequalities, the most important of which is the inequality given in Theorem 2.1. It can solve a class of inequalities by a unified method. An important application of the inequality given in Theorem 2.1 is to…
Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.