Related papers: Gasparyan's Inequality

Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between two multivariate distributions, we introduce a new measure…

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

In this short communication, we present a new proof for the Korn inequality in a n-dimensional context. The results are based on standard tools of real and functional analysis. For the final result the standard Poincar\'{e} inequality plays…

The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not aware of any place that a proof would be written with all…

In this note, we generalize an ancient Greek inequality about the sequence of primes to the cases of arithmetic progressions even multivariable polynomials with integral coefficients. We also refine Bouniakowsky's conjecture [16] and…

The inequality is computed through the so-called Gini index. The population is assumed to have the variable of interest distributed according to the Gamma probability distribution. The results show that the Gini index is reduced when the…

We obtain simple proofs of certain inequalites for bivariate means.

In this short note, we find an equivalent combinatorial condition only involving finite sums under which a centered Gaussian random vector with multinomial covariance matrix satisfies the Gaussian product inequality (GPI) conjecture. These…

Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…

Measuring inequalities in a multidimensional framework is a challenging problem which is common to most field of science and engineering. Nevertheless, despite the enormous amount of researches illustrating the fields of application of…

It is shown that Newton's inequalities and the related Maclaurin's inequalities provide several refinements of the fundamental Arithmetic mean - Geometric mean - Harmonic mean inequality in terms of the means and variance of positive real…

In the theory of submanifolds, the following problem is fundamental: to establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of the submanifolds.The basic relationships discovered until now…

We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is justified on physical and mathematical grounds that a subclass…

Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…

We develop a new proof of the result of L.-E.~Persson and V.D.~Stepanov \cite[Theorems 1 and 3]{Per:02}, which provides a characterization of a Hardy integral inequality involving two weights, and which can be applied to an effective…

In this paper, we will prove several new inequalities of Hardy's types with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and H\"older's inequality. To the best of the…

It was shown by E. Gluskin and V.D. Milman in [GAFA Lecture Notes in Math. 1807, 2003] that the classical arithmetic-geometric mean inequality can be reversed (up to a multiplicative constant) with high probability, when applied to…

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…

Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…

The Gini index is a function that attempts to measure the amount of inequality in the distribution of a finite resource throughout a population. It is commonly used in economics as a measure of inequality of income or wealth. We define a…