Related papers: Balanced Convex Partitions of Measures in $\mathbb…

We prove a bumpy metric theorem in the sense of Ma\~{n}e for non-convex Hamiltonians that are satisfying a certain geometric property.

We prove a sandwiching lemma for inner-exact locally compact Hausdorff \'etale groupoids. Our lemma says that every ideal of the reduced $C^*$-algebra of such a groupoid is sandwiched between the ideals associated to two uniquely defined…

We give a general setting for Cram\'er's large deviations theorem for the empirical means of a sequence of i.i.d. random vectors, which contains Cram\'er's theorem in a Banach space and Sanov's theorem. ----- Nous \'etablissons un cadre…

In this paper, we present a more complete version of the minimax theorem established in [7]. As a consequence, we get, for instance, the following result: Let $X$ be a compact, not singleton subset of a normed space $(E,\|\cdot\|)$ and let…

A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We…

Let $A$ be a unital associative ring and let $T^{(k)}$ be the two-sided ideal of $A$ generated by all commutators $[a_1, a_2, \dots , a_k]$ $(a_i \in A)$ where $[a_1, a_2] = a_1 a_2 - a_2 a_1$, $[a_1, \dots , a_{k-1}, a_k] = \bigl[ [a_1,…

We construct and study the space C(\R^d,n) of all partitions of \R^d into n non-empty open convex regions (n-partitions). A representation on the upper hemisphere of an n-sphere is used to obtain a metric and thus a topology on this space.…

We study generalizations of Reifenberg's Theorem for measures in $\mathbb R^n$ under assumptions on the Jones' $\beta$-numbers, which appropriately measure how close the support is to being contained in a subspace. Our main results, which…

For $k\geq i\geq 1$, let $B_{k,i}(n)$ denote the number of partitions of $n$ such that part 1 appears at most $i-1$ times, two consecutive integers l and $l+1$ appear at most $k-1$ times and if l and $l+1$ appear exactly $k-1$ times then…

We prove three main conjectures of Berkovich and Uncu (Ann. Comb. 23 (2019) 263--284) on the inequalities between the numbers of partitions of $n$ with bounded gap between largest and smallest parts for sufficiently large $n$. Actually our…

Let $\mu$ be a centered log-concave probability measure on ${\mathbb R}^n$ and let $\Lambda_{\mu}^{\ast}$ denote the Cram\'{e}r transform of $\mu$, i.e. $\Lambda_{\mu}^{\ast}(x)=\sup\{\langle…

In a normed linear space X an element x is said to be orthogonal to another element y in the sense of Birkhoff-James, written as $ x \perp_{B}y, $ iff $ \| x \| \leq \| x + \lambda y \| $ for all scalars $ \lambda.$ We prove that a normed…

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between $C(K)$ and $\ell_2$ is 2-summing. However, it is shown in \cite{J05} that the operator space analogue fails. Not every cb-map $v : \K \to OH$…

It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…

It is shown that, given a point $x\in\mathbbm{R}^d$, $d\ge 2$, and open sets $U_1,...,U_k$ containing $x$, any convex combination of the harmonic measures for $x$ with respect to $U_n$, $1\le n\le k$, is the limit of a sequence of harmonic…

We present an approach to the study of stationary measures placing Tarski's foundational work in this area within a modern category theoretic context. Guiding this work is the notion that measurable spaces equipped with symmetries carry an…

In a paper published in 2020 in Studia Mathematica, Abrahamsen et al. proved that in the real space $L_1(\mu)$, where $\mu$ is a non-zero $\sigma$-finite (countably additive non-negative) measure, norm-one elements in finite convex…

We prove a version of Gauss's Lemma. It recursively constructs polynomials {c_k} for k=0,1,...,m+n, in Z[a_i,A_i,b_j,B_j] for i=0,...,m, and j=0,1,...,n, having degree at most (m+n choose m) in each of the four variable sets, such that…

In char $k = p >0$, A. Langer proved a strong restriction theorem (in the style of H. Flenner) for semistable sheaves to a very general hypersurface of degree $d$, on certain varieties, with the condition that `char $k > d$'. He remarked…

Gr\"unbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of this inequality for hyperplanes that do not necessarily…