Related papers: Convergence theorems for several decomposition typ…

We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…

We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…

We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of…

We give the theorem of coincidence of a class of functions defined by a generalised modulus of smoothness with a class of functions defined by the order of the best approximation by algebraic polynomials. We also prove the appropriate…

This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…

We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.

Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further…

We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…

Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the…

Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…

A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating…

Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of nontrivial…

A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by…

A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…

A classical theorem of Kempner states that the sum of the reciprocals of positive integers with missing decimal digits converges. This result is extended to much larger families of "missing digits" sets of positive integers with convergent…

In general, some of the well known results of measure theory dealing with the convergence of sequences of functions such as the Dominated Convergence Theorem or the Monotone Convergence Theorem are not true when we consider arbitrary nets…

We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and strong subadditivity independent of regularity assumptions on…

By means of the derivative operator and Chu-Vandermonde convolution, four families of summation formulas involving harmonic numbers with even or odd indexes are established.