Related papers: The Lieb-Thirring inequalities: Recent results and…
We consider an analogue of the Lieb-Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the…
We summarise the main results from a number of our recent articles on the subject of probabilistic temperature forecasting.
We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest possible gap between consecutive primes assuming the Riemann…
This article is aimed at presenting the Schr\"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr\"odinger problem. We also give a survey of the related literature.…
In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.
We survey recent results on Calderon's inverse problem with partial data, focusing on three and higher dimensions.
We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry.…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
Progress is reviewed in the understanding of color confinement .
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
Algorithmic fairness is receiving significant attention in the academic and broader literature due to the increasing use of predictive algorithms, including those based on artificial intelligence. One benefit of this trend is that algorithm…
In the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. In this note we present a review of the main results about this topic and…
A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An…
In this paper we approximate a Schr\"odinger operator on $L^2(\R)$ by Jacobi operators on $\ell^2(\Z)$ to provide new proofs of sharp Lieb-Thirring inequalities for the powers $\gamma=1/2$ and $\gamma=3/2$. To this end we first investigate…
We survey recent results on resolutions of Hibi rings.
Obtaining explicit stability estimates in classical functional inequalities like the Sobolev inequality has been an essentially open question for 30 years, after the celebrated but non-constructive result of G. Bianchi and H. Egnell in…
Improved estimates on the constants $L_{\gamma,d}$, for $1/2<\gamma<3/2$, $d\in N$ in the inequalities for the eigenvalue moments of Schr\"{o}dinger operators are established.
We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used,…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in an earlier paper. Further, they are employed to establish new Gruss…