Related papers: An information-theoretic proof of a hypercontracti…

The paper presents a counterexample to the Hodge conjecture.

We shall discuss a higher-rank Khovanskii-Teissier inequality, generalizing a theorem of Li. In the course of the proof, we develop new Hodge-Riemann bilinear relations in certain mixed settings, which in themselves slightly extend the…

An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.

We obtain simple proofs of certain inequalites for bivariate means.

We prove an isoperimetric inequalitie on the complex hyperbolic ball with Assumption \ref{assumption}}. As an application, we prove a contraction property for the holomorphic functions in Hardy and weighted Bergman spaces on the complex…

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

We present a short proof of a conjecture proposed by I. Ra\c{s}a (2017), which is an inequality involving basic Bernstein polynomials and convex functions. This proof was given in the letter to I. Ra\c{s}a (2017). The methods of our proof…

Almost uniform version of noncommutative Wiener-Wintner ergodic theorem and its extension to Besicovitch weights are proved.

We present an information theoretic proof of the nonsignalling multiprover parallel repetition theorem, a recent extension of its two-prover variant that underlies many hardness of approximation results. The original proofs used de Finetti…

The Shannon-Hagelbarger theorem states that the effective resistance across any pair of nodes in a resistive network is a concave function of the edge resistances. We give an information-theoretic proof of this result, building on the…

A refinement of the Hardy inequality has been presented by use of superquadratic function.

We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.

The strengthened data processing inequality have been proved. The general theory have been illustrated on the simple example.

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).

The aim of this paper is to prove that the parametric fundamental equation of information is hyperstable on its open as well as on its closed domain, assuming that the parameter is negative. As a corollary of the main result, it is also…

We study an inequality suggested by Littlewood, our result refines a result of Bennett.

We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors $a,b\in\mathbb{R}_+^n$ so that…

In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.

The Ingleton inequality is a classical linear information inequality that holds for representable matroids but fails to be universally valid for entropic vectors. Understanding the extent to which this inequality can be violated has been a…

The purpose of this article is to establish the dual version of the uniform cover inequality of Bollobas and Thomason.