Let Γ denote the spaces of all double entire sequences. Let Λ denote the spaces of all double analytic sequences. This paper is devoted to a study of the general properties of Nörlund double entire sequence space η ( Γ ) , Γ and also study some of the properties of η ( Γ ) and η ( Λ ) .

A Liouville function is an analytic function H : C → C with a Taylor series ∑ ∞ n=1 xn/an such the an’s form a “very fast growing” sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H .

Let {u(n)} be a higher-order linear recursive sequence. In this paper, we use the properties of error estimation and the analytic method to study the reciprocal sums of higher power of higher-order sequences. Then we establish several new and interesting identities relating to the infinite and finite sums.

By virtue of new analytic techniques, we analyze and study several strong convergence theorems for the approximation of common fixed points of asymptotically demicontractive mappings via the multistep iterative sequence with errors in Banach spaces. Our results improve and extend the corresponding ones announced by Osilike , Osilike and Aniagbosor, Igbokwe, Cho et al., Moore and Nnoli, Hu and a...

Let (R, m) be a local ring of Krull dimension d and I ⊆ R be an ideal with analytic spread d. We show that the j-multiplicity of I is determined by the Rees valuations of I centered on m. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at an O(nd) rate.

Let E be a coanalytic equivalence relation on a Polish space X and (An)n∈ù a sequence of analytic subsets of X . We prove that if lim supn∈K An meets uncountably many E-equivalence classes for every K ∈ [ù] , then there exists a K ∈ [ù] such that T n∈K An contains a perfect set of pairwise E-inequivalent elements. §

Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems control. This article provides a new method for such problems, both the scalar matrix case, based on nonstandard Riccati-type equation. The rank of solution is same as degree interpolant, thus providing natural approach to model reduction. A homotopy continuation presented applied some modeling...

The variations between homologous nucleotide sequences representative of various species are, in part, a consequence of the evolutionary history of these species. Determining the evolutionary tree from patterns in the sequences depends on inverting the stochastic processes governing the substitutions from their ancestral sequence. We present a nl.J.mber of recent (and some new) results which al...

Abstract We introduce a notion of barycenter probability measure related to the symmetric mean collection non-negative real numbers. Our definition is inspired by work Halász and Székely, who in 1976 proved law large numbers for means. study analytic properties this Halász–Székely barycenter. establish fundamental inequalities that relate list with uniformly supported on these points. As conseq...