Related papers: Generalized multi-scale Young measures

We prove that the Young measure associated with a Borel function f is a probability distribution of the random variable f(U), where U has a uniform distribution on the domain of f. As an auxiliary result, the fact that Young measures…

We study the mixed-integer epigraph of a special class of convex functions with non-convex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are…

In 1971 Taylor characterised all complex measures on $\mathbb{R}$ that are invertible with respect to convolution as those which can be written in the form $\delta_\gamma \ast \sigma^{\ast m} \ast \exp(\nu)$ for some $\gamma\in \mathbb{R}$,…

This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous…

In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of…

Using an inverse system of metric graphs as in: J. Cheeger and B. Kleiner, "Inverse limit spaces satisfying a Poincar\'e inequality", we provide a simple example of a metric space $X$ that admits Poincar\'e inequalities for a continuum of…

We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In…

Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…

We describe a formula for computing the product of the Young symmetrizer of a Young tableau with the Young symmetrizer of a subtableau, generalizing the classical quasi-idempotence of Young symmetrizers. We derive some consequences to the…

Let $\Gamma$ be a discrete group acting by isometries on a product $X=X_1\times X_2$ of Hadamard spaces. We further require that $X_1$, $X_2$ are locally compact and $\Gamma$ contains two elements projecting to a pair of independent rank…

In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…

In this paper we complete our construction of frame-like gauge invariant description for massive mixed symmetry tensor fields corresponding to arbitrary Young tableau with two rows started in [1]. We consider general massive theory in (A)dS…

Building on the one-to-one relationship between generalized FGM copulas and multivariate Bernoulli distributions, we prove that the class of multivariate distributions with generalized FGM copulas is a convex polytope. Therefore, we find…

In this paper we prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized…

Let $X$ be a product of locally compact rank one Hadamard spaces and $\Gamma$ a discrete group of isometries which contains two elements projecting to a pair of independent rank one isometries in each factor. In [arXiv:1308.5584] we gave a…

This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these…

Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems…

We construct $N$-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ which generalize the usual complex $(N=2)$ of differential forms. Although, for $N\geq 3$, the generalized cohomology of these…

This is the continuation of an earlier work where Godel-type metrics were defined and used for producing new solutions in various dimensions. Here a simplifying technical assumption is relaxed which, among other things, basically amounts to…

Let G be a semisimple linear algebraic group defined over rational numbers, K be a maximal compact subgroup of its real points and {\Gamma} be an arithmetic lattice. One can associate a probability measure {\mu}(H) on {\Gamma}\G for each…