Related papers: Pointwise linear separation property and infinite …
We derive several new bounds for the problem of difference sets with local properties, such as establishing the super-linear threshold of the problem. For our proofs, we develop several new tools, including a variant of higher moment…
We extend a discrepancy bound of Lagarias and Pleasants for local weight distributions on linearly repetitive Delone sets and show that a similar bound holds also for the more general case of Delone sets without finite local complexity if…
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calder\'on's and Zygmund's theory of first order…
In Euclidean spaces, every closed, bounded, convex set can be characterized by two equivalent notions of separation properties. This is not true in general for arbitrary Banach spaces. In this work, we present a ball separation…
We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the geometry of a particular linear projection, giving necessary…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.
We investigate necessary and sufficient conditions for the extendibility and boundedness of Gaussian curvature, Mean curvature and principal curvatures near all types of singularities on fronts. We also study the convergence to infinite…
We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV…
We formulate and discuss a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure…
Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…
We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a…
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…
We study a relation between three different formulations of theorems on separable determination - one using the concept of rich families, second via the concept of suitable models and third, a new one, suggested in this paper, using the…
We improve a recent result by giving the optimal conclusion possible both to the frequent universality criterion and the frequent hypercyclicity criterion using the notion of A-densities, where A refers to some weighted densities sharper…
In this paper we define a class of coverage processes with infinitely divisible finite dimensional distributions and a particular type of correlation structure that can be thought of as generalizations of the classical Ornstein--Uhlenbeck…
This article analyzes the geometric properties of an idempotent, non-associative algebraic structure that extends the Max-Times semiring. This algebraic structure is useful for studying systems of Max-Times and Max-Plus equations, employing…
In various places in the literature it is stated that every separable linear order embeds into the real line. This is, however, not the case, at least not with respect to the usual definition of separability. We correct this misconception.
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…