Related papers: Effective count of integer points on ternary affin…
We give uniform upper bounds for the number of integral points of bounded height on affine hypersurfaces, which generalise earlier results of Browning,Heath-Brown and the author.
Testing hypotheses of goodness-of-fit about mixture distributions on the basis of independent but not necessarily identically distributed random vectors is considered. The hypotheses are given by a specific distribution or by a family of…
In this paper, we consider a problem of counting rational points near self-similar sets. Let $n\geq 1$ be an integer. We shall show that for some self-similar measures on $\mathbb{R}^n$, the set of rational points $\mathbb{Q}^n$ is…
We consider two families of algebraic varieties $Y_n$ indexed by natural numbers $n$: the configuration space of unordered $n$-tuples of distinct points on $\mathbb{C}$, and the space of unordered $n$-tuples of linearly independent lines in…
An effective quantum number determining with high accuracy the levels ordering in arbitrary centrally symmetric potentials for any space dimensionality is introduced and calculated by means of certain universal methods based on the known…
The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions…
This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal discrete integral…
We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.
This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn's problem, the…
The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary…
We present here an extension of the Wang-Landau Monte Carlo method which allows us to get very accurate estimates of the full probability distributions of several observables after a quantum quench for large systems, whenever the relevant…
Intermittent maps of the interval are simple and widely-studied models for chaos with slow mixing rates, but have been notoriously resistant to numerical study. In this paper we present an effective framework to compute many ergodic…
We investigate the subject of speed of mixing for operators on infinite dimensional Hilbert spaces which are strongly mixing with respect to a nondegenerate Gaussian measure. We prove that there is no way to find a uniform speed of mixing…
Let $\mathbf{k}$ be a closed field of characteristic zero. We prove that all monomial ideals sit in the curvilinear component of the Hilbert scheme of points of the affine space $\mathbb{A}_{\mathbf{k}}^n$, answering a long-standing…
We offer a new proof that a certain q-analogue of multinomial coeffi- cients furnishes a q-counting of the set of permutations of an associated multiset of positive integers, according to the number of inversions in such arrangements. Our…
In the study of the cyclicity of a function $f$ in reproducing kernel Hilbert spaces an important role is played by sequences of polynomials $\{p_n\}_{n\in \mathbb{N}}$ called \emph{optimal polynomial approximants} (o.p.a.). For many such…
We present the concept of the \emph{information efficiency of functions} as a technique to understand the interaction between information and computation. Based on these results we identify a new class of objects that we call…
The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be shown via an alternative class of…
We develop a numerical method for computing with orthogonal polynomials that are orthogonal on multiple, disjoint intervals for which analytical formulae are currently unknown. Our approach exploits the Fokas--Its--Kitaev Riemann--Hilbert…
We consider elliptic partial differential equations with diffusion coefficients that depend affinely on countably many parameters. We study the summability properties of polynomial expansions of the function mapping parameter values to…