A double sequence x = [xjk]j,k=0 is said to be convergent to a number l in the Pringsheim sense or P-convergent if for every ε > 0, there exists N ∈N, the set of natural numbers, such that |xjk − l| < ε whenever j,k > N , [5]. In this case, we write P− limx = l. In what follows, we will write [xjk] in place of [xjk]j,k=0. A double sequence x is said to be bounded if there exists a positive numb...

The purpose of this paper is to prove that every sequence of closed approximable measures defined on the Borelfield of a normal topological space with values in an abelian topological group is Cauchy convergent for all Borel sets if it is Cauchy convergent for all regular open sets. In particular every sequence of measures on the Borel-field of a perfectly normal topological space which is Cauc...

In the last nine years p-adic numbers have been successfully applied in various branches of theoretical and mathematical physics (for a review see [1-3]). One of the objects which we often encounter is a p-adic series. My interest in p-adic series is mainly motivated by the significant role they might play not only in pure but also in applied mathematics. It was initiated in 1987 [4] by an obse...

ing from the multiplication of 8\ by S2 . Special example : T* • T.* is absolutely convergent, but 1\ and T* are each divergent when r < § and * < §. In the divergent series 8/ the terms increase without limit in numerical value, as v increases without limit. The same is true of S2 . Herein lies the difference between this pair of divergent series yielding an absolutely convergent product, and ...

Following Buchberger's approach to computing a Grr obner basis of a polynomial ideal in polynomial rings, a completion procedure for nitely generated right ideals in ZH] is given, where H is an ordered monoid presented by a nite, convergent semi{Thue system ((; T). Taking a nite set F ZH] we get a (possibly innnite) basis of the right ideal generated by F , such that using this basis we have un...

In [8] and [9] J. Jarník and J.Kurzweil introduced an integration process (called PU-integral) for real valued functions on an interval of n with the use of suitably regularC-partitions of unity, instead of the usual partitions. The PU-integral is nonabsolutely convergent and in dimension one falls properly in between the Lebesgue and the Kurzweil-Henstock integrals. In [4], without assuming an...

The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

We investigated whether responses of single cells in the striate cortex of anaesthetized macaque monkeys exhibit signatures of both parvocellular (P) and magnocellular (M) inputs from the dorsal lateral geniculate nucleus (dLGN). We used a palette of 128 isoluminant hues at four different saturation levels to test responses to chromatic stimuli against a white background. Spectral selectivity w...

The notation and terminology used in this paper have been introduced in the following articles: [3], [4], [13], [5], [15], [6], [7], [16], [10], [1], [2], [8], [11], [18], [12], [17], and [9]. In this paper R, R1, R2 denote functions from N × N into R, r1, r2 denote convergent sequences of real numbers, n, m, N ,M denote natural numbers, and e, r denote real numbers. Let us consider R. We say t...