Related papers: Approximations of Mappings
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…
This paper revives a four-decade-old problem concerning regularity theory for (continuous) constraint maps with free boundaries. Dividing the map into two parts, the distance part and the projected image to the constraint, one can prove…
Set functions with convenient properties (such as submodularity) appear in application areas of current interest, such as algorithmic game theory, and allow for improved optimization algorithms. It is natural to ask (e.g., in the context of…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
On the set of mappings of the given set, we define the product of mappings. If A is associative algebra, then we consider the set of matrices, whose elements are linear mappings of algebra A. In algebra of matrices of linear mappings we…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
The article is devoted to the study of mappings that satisfy the so-called inverse Poletsky inequality. We consider mappings of quasiextremal distance domains, domains with a locally quasiconformal boundary, and domains which are regular in…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
Many known planning tasks have inherent constraints concerning the best order in which to achieve the goals. A number of research efforts have been made to detect such constraints and to use them for guiding search, in the hope of speeding…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
We discuss a class of regions and conformal mappings which are useful in several problems of approximation theory, harmonic analysis and spectral theory.
Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse…
Establishing bounds on the accuracy achievable by localization techniques represents a fundamental technical issue. Bounds on localization accuracy have been derived for cases in which the position of an agent is estimated on the basis of a…
Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, and ultrametric complete spaces. We develop a theory of shifts of finite type for infinite alphabets. We call…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
We have studied the local and boundary behavior of mappings satisfying one estimate of the distortion of the modulus of families of paths. In particular, we have obtained conditions under which the families of the indicated mappings are…