Related papers: The Ptolemaean Inequality in H--type groups

We discuss Heisenberg uncertainty inequality for groups of the form $K \ltimes \mathbb{R}^n$, $K$ is a separable unimodular locally compact group of type I. This inequality is also proved for Gabor transform for several classes of groups of…

In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.

In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

This note concerns Loomis-Whitney inequalities in Heisenberg groups $\mathbb{H}^n$: $$|K| \lesssim \prod_{j=1}^{2n}|\pi_j(K)|^{\frac{n+1}{n(2n+1)}}, \qquad K \subset \mathbb{H}^n.$$ Here $\pi_{j}$, $j=1,\ldots,2n$, are the vertical…

Let $N$ be normal subgroup of a finite group $G$, $p$ be a prime, $P$ be a Sylow $p$-subgroup of $G$ and $\theta$ be a $P$-invariant irreducible character of $N$. Suppose that $G/N$ is a $p$-solvable group. In this note we show that,…

This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we…

It is proved that, if $K$ is a complete discrete valuation field of mixed characteristic $(0,p)$ with residue field satisfying a mild condition, then any abelian variety over $K$ with potentially good reduction has finite…

Let $L$ be the sublaplacian and $T$ the partial Laplacian with respect to central variables on H-type groups. We investigate a class of invariant differential operators by the joint functional calculus of $L$ and $T$. We establish…

In this note we prove an inequality involving primes and the product of consecutive primes.

In this article we describe how the celebrated result by Lions, Papanicolau and Varadhan on the Homogenization of Hamilton-Jacobi equation can be extended beyond the Euclidean setting. More specifically, we show how to obtain a…

We obtain some new inequalities of Chebyshev Type.

In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and solve some special cases for a spherical correlation…

We develop a Hodge theoretic invariant for families of projective manifolds that measures the potential failure of an Arakelov-type inequality in higher dimensions, one that naturally generalizes the classical Arakelov inequality over…

Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p-adic L-functions for the symmetric powers of f, thus verifying general conjectures of Dabrowski and…

Let $G$ be a finite $p$-group and let Aut$(G)$ denote the full automorphism group of $G$. In the recent past, there has been interest in finding necessary and sufficient conditions on $G$ such that certain subgroups of Aut$(G)$ are equal.…

We prove a $p$-nilpotency criterion for finite groups in terms of the element orders of its $p'$-reduced sections that extends a nilpotency criterion by T{\u{a}}rn{\u{a}}uceanu.

We establish an inequality which involves a non-negative function defined on the vertices of a finite $m$-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree…

Computations in the cohomology of finite groups.

Let $p$ be a fixed odd prime number, $\mu$ be a Hida family over the Iwasawa algebra of one variable, $\rho_{\mu}$ its Galois representation, $\mathbb{Q}_\infty/\mathbb{Q}$ the $p$-cyclotomic tower and $S$ the variable of the cyclotomic…