相关论文: On sofic approximations of $\mathbb F_2\times\math…

In this paper we exhibit for every non amenable group that is initially sub-amenable (sometimes also referred to as LEA), two sofic approximations that are not conjugate by any automorphism of the universal sofic group. This addresses a…

We present an approximation notion for NP-hard optimization problems represented by binary functions. We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time…

Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups:…

Several questions of approximation theory are discussed: 1) can one approximate stably in $L^\infty$ norm $f^\prime$ given approximation $f_\delta, \parallel f_\delta - f \parallel_{L^\infty} < \delta$, of an unknown smooth function $f(x)$,…

The papers shows an algorithm to search for approximations of reals to rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.

We establish various results on the structure of approximate subgroups in linear groups such as SL_n(k) that were previously announced by the authors. For example, generalising a result of Helfgott (who handled the cases n = 2 and 3), we…

It was shown in a previous work of the first named author with De Chiffre, Glebsky and Thom that there exists a finitely presented group which cannot be approximated by almost-homomorphisms to the unitary groups $U(n)$ equipped with the…

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…

The main purpose of this paper is to prove some density results of polynomials in Fock spaces of slice regular functions. The spaces can be of two different kinds since they are equipped with different inner products and contain different…

Suppose that $\mathcal F$ is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that $\mathcal F$ has continuous tangent plane field and is {\sl taut}; that is, closed smooth…

This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are…

We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.

In this paper we present a method for constructing the continuous best fractal approximation in the space of bounded functions. We construct the finite-dimensional subspace of the space of bounded functions whose base consists of the…

Let $f$ be a homogeneous polynomial with rational coefficients in $d$ variables. We prove several results concerning uniform simultaneous approximation to points on the graph of $f$, as well as on the hypersurface $\{f(x_1,\dots,x_d) =…

In this paper we discuss approximation of partially smooth functions. The problem arises naturally in the study of laminated currents.

Using a recently developed $\mathcal H$-calculus we propose a unified approach to the study of rational approximations of holomorphic semigroups on Banach spaces. We provide unified and simple proofs to a number of basic results on…

In this paper, we use the canonical connection instead of Levi-Civita connection to study the smooth maps between almost Hermitian manifolds, especially, the pseudoholomorphic ones. By using the Bochner formulas, we obtian the…

We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.

A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.

This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…