Related papers: Young functions on varifolds. Part I. Functional a…

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…

Consider the lattice of all Young diagrams ordered by inclusion, and denote by Y its Hasse graph. Using the Pieri formula for Jack symmetric polynomials, we endow the edges of the graph Y with formal multiplicities depending on a real…

Previously, it has been shown that the direct correlation function for a Lennard-Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail and a simple linear correction in the core region constructed so as to…

A new yield/damage function is proposed for modelling the inelastic behaviour of a broad class of pressure-sensitive, frictional, ductile and brittle-cohesive materials. The yield function allows the possibility of describing a transition…

We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several…

This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a…

We introduce the space of grid functions, a space of generalized functions of nonstandard analysis that provides a coherent generalization both of the space of distributions and of the space of Young measures. We will show that in the space…

We introduce a new functional, named gap function, which measures the torsional instability of a partially hinged rectangular plate, aiming to model the deck of a bridge. Then we test the performances of the gap function on a plate subject…

In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze…

We characterize Young measures generated by gradients of bi-Lipschitz orientation-preserving maps in the plane. This question is motivated by variational problems in nonlinear elasticity where the orientation preservation and injectivity of…

Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…

This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…

We continue the study of convergence of multipole pluricomplex Green functions for a bounded hyperconvex domain of $\mathbb C^n$, in the case where poles collide. We consider the case where all poles do not converge to the same point in the…

Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…

In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…

Let f be a function mapping an n dimensional vector space over GF(p) to GF(p). When p is 2, Bernasconi et al. have shown that there is a correspondence between certain properties of f (e.g., if it is bent) and properties of its associated…

In this paper, we want to study the link between the presence of compact objects with some analytic structure and the global geometry of a weakly complete surface. We begin with a brief survey of some now classic results on the local…

This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…

This master thesis looks at the gradient flow of the length functional on embedded loops. The space of embedded loops is endowed with a scale structure so that the length functional becomes scale smooth. For certain underlying manifolds,…

A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.