Related papers: A Note on Carleman's Inequality

An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n^{-1/2}, the same as in the classical case.…

The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal…

We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.

This note relies mainly on a refined version of the main results of the paper by F. Catrina and D. Costa (J. Differential Equations 2009). We provide very short and self-contained proofs. Our results are sharp and minimizers are obtained in…

In this paper, we establish a weight identity for stochastic beam equation by means of the multiplier method. Based on this identity, we first establish the global Carleman estimate for the special system with zero initial value and end…

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…

We modify the approach to the arithmetical form of the large sieve by relying on the Parseval identity rather than on an approximate Bessel inequality and as a consequence, improve on the weighted large sieve inequality beyond what was…

In this article, we obtain a weighted version of Polya inequality in Cn whose unweighted form was established by V. Zakharyuta in USSR Sbornik, 25 (1975), 350-364.

In this paper we prove the validity of a formula for computing the Alexander invariant which was originally conjectured by Bar-Natan and Dancso in [BND].

In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…

We state Bennequin inequalities in the relative case, and show that the relative invariants are additive under relative connected sums. We show they exhibit similar limitations as their classical analogues. We study relatively Legendrian…

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 formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

New cases of the multiplicity conjecture are considered.

We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our arguments build on certain weighted inequalities based on…

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive…

Chen and Cheung [C.-P. Chen, W.-S. Cheung, Sharpness of Wilker and Huygens type inequalities, J. Inequal. Appl. 2012 (2012) 72, \url{http://dx.doi.org/10.1186/1029-242X-2012-72}] established sharp Wilker and Huygens-type inequalities. These…

As an extension of a central limit theorem established by Svante Janson, we prove a Berry-Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically…