Related papers: Inhomogeneous approximation with coprime integers …

We prove matching direct and inverse theorems for uniform polynomial approximation with $A^*$ weights (a subclass of doubling weights suitable for approximation in the $L_\infty$ norm) having finitely many zeros and not too "rapidly…

In this paper, we discuss the integer decomposition property for Cayley sums and Minkowski sums of lattice polytopes. In fact, we characterize when Cayley sums have the integer decomposition property in terms of Minkowski sums. Moreover, by…

We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an…

We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions $H\simeq R_{0,2}$, or to the real Clifford algebra $R_{0,3}$. In the quaternionic case, the approach by means of…

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…

The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a $q$-deformation of the Ehrhart series, based on the notions of harmonic spaces and Macaulay's inverse…

We introduce a quantitative version of polynomial cohomology for discrete groups and show that it coincides with usual group cohomology when combinatorial filling functions are polynomially bounded. As an application, we show that Betti…

Given a continuous function from Euclidean space to the real line, we analyze (under some natural assumption on the function), the set of values it takes on translates of lattices. Our results are of the flavor: For almost any translate,…

In this paper, the $L_q$-Minkowski problem of anisotropic $p$-torsional rigidity is considered. The existence of the solution of the $L_q$-Minkowski problem of anisotropic $p$-torsional rigidity with $0<q<1$ and $1<q\neq \frac{p}{p-1}+n$ is…

By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…

We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…

In this paper we present a surprisingly short proof of Minkowski's second theorem. The author hopes there is no mistake in it, though the argument seems to be too plain to contain one. Also, we apply the main construction of the proof to…

We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.

We introduce two new algebraic invariants, the (co)homological distances between continuous maps, which provide computable lower bounds for the homotopic distance and strictly refine the classical cup-length estimates. We then define the…

We consider a version of the nearest-codeword problem on finite fields $\mathbb{F}_q$ using the Manhattan distance, an analog of the Hamming metric for non-binary alphabets. Similarly to other lattice related problems, this problem is…

We study a class of fourth-order geometric problems modelling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, bi-harmonic surfaces in the sense of Chen, among others. We prove…

Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.

We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…

Convex integration and the holonomic approximation theorem are two well-known pillars of flexibility in differential topology and geometry. They may each seem to have their own flavor and scope. The goal of this paper is to bring some new…