Related papers: An alternating proof of sharp inequalities related…

We consider the one-dimensional John-Nirenberg inequality: $$ |\{x\in I_0:|f(x)-f_{I_0}|>\a\}|\le C_1|I_0|\exp\Big(-\frac{C_2}{\|f\|_{*}}\a\Big). $$ A. Korenovskii found that the sharp $C_2$ here is $C_2=2/e$. It is shown in this paper that…

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.

The purpose of this work is to give a direct proof of the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups based on Hadwiger-Ohmann's one of the classical Brunn-Minkowski inequality in Euclidean space.

We prove a sharp H\"older estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has {\em unit determinant}. Our result…

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

In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell.…

We develop tools to prove D\'iaz and Park's sharpness conjecture (see [8]) for fusion systems admitting tame families of fusion subsystems (see Theorem A). We use such tools to prove the conjecture for all Benson-Solomon fusion systems (see…

We settle in the affirmative the Graham-Sloane conjecture.

By use of a modified Nunokawa's lemma, we obtain some new conditions for univalence. Also, some sharp inequalities concerning univalent functions are presented.

New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator P\'olya-Szeg\"o inequality to arbitrary…

We combine an extended version of Bailey's transform with an identity of Bressoud and with some identities of Berkovich and Warnaar to prove a variety of positivity results for alternating sums involving partition functions.

In this note, we derive non trivial sharp bounds related to the weighted harmonic-geometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of…

We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work. In particular, we obtain improvements on the sharp constants in some of the inequalities previously considered by these authors, and also prove…

Using nonstandard analysis (NSA), the proof of the Laplace's formula is given. The usage of NSA reduces the intricacy of taking limit, and the crude line of the proof would be clearly seen, compared to the done with the rigorous classical…

In this paper we establish the best constant of an anisotropic Gagliardo-Nirenberg-type inequality related to the Benjamin-Ono-Zakharov-Kuznetsov equation. As an application of our results, we prove the uniform bound of solutions for such a…

We prove some isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We then relate them to inequalities involving the higher order mean-curvature integrals. We also apply our…

We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.

We derive analytic formulas for the alternating projection method applied to the cone $\mathbb{S}^n_+$ of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a…

In this paper we consider a weighted version of one dimensional discrete Hardy's Inequality on half-line with power weights of the form $n^\alpha$. Namely we consider: \begin{equation} \sum_{n=1}^\infty |u(n)-u(n-1)|^2 n^\alpha \geq…