Let X be a (real or complex) Banach space, its dual Banach space will be denoted by X *. We use standard notation and terminology of Banach space theory, see J.Lindenstrauss and L.Tzafriri [LT]. By a subspace we mean a linear, but not necessarily closed, subspace. We also assume some knowledge of general topology and ordinal numbers, see P.S.Aleksandrov[A]. Definition 1.1. Let A be a subset of ...

In this note we show, following W. Holsztynski, that there is a continuous metric d on R such that any finite metric space is isometrically embeddable into (R, d). Let M be a family of metric spaces. A metric space U is said to be a universal space for M if any space from M is (isometrically) embeddable in U . Fréchet [2] proved that l (the space of all bounded sequences of real numbers endowed...

The dynamics of real-world systems often involve multiple processes that influence system state. The timescales that these processes operate on may be separated by orders of magnitude or may coincide closely. Where timescales are not separable, the way that they relate to each other will be important for understanding system dynamics. In this paper, we present a short overview of how modellers ...

Using various facts about principal bundles over a space, we give a unified treatment of several theorems about the structure of stable separable continuous-trace algebras, their automorphisms, and their AT-theory. We also present a classification of real continuous-trace algebras from the same point of view. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 46 L 05, 4...

This article is concerned with Galois theory for iterative differential fields (ID-fields) in positive characteristic. More precisely, we consider purely inseparable Picard-Vessiot extensions, because these are the ones having an infinitesimal group scheme as iterative differential Galois group. In this article we prove a necessary and sufficient condition to decide whether an infinitesimal gro...

This paper is continuation of the study of the 1-box pattern in permutations introduced previously by the authors. We derive a two-variable generating function for the distribution of this pattern on 132-avoiding permutations, and then study some of its coefficients providing a link to the Fibonacci numbers. We also find the number of separable permutations with two and three occurrences of the...

My main focus, as requested by the editors, is the changing governance of welfare. But changes in this regard are inseparable from broader changes in the welfare regimes that emerged in advanced western capitalist states in the postwar Atlantic Fordist boom. Thus I will also discuss the social and economic functions that current welfare regimes are expected to perform and the scales on which th...

In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General biCohen-Macaulay graphs are classified up to separation. The inseparable bi-CohenMacaulay graphs are determined. We establish a bijection between the set of all trees and the set of inseparable bi-Cohen-Macaulay graphs.

Technology has become an inseparable part of everyday life, as we use it at home, at work, in school etc. For education, technology is frequently used as a tool to support classroom-based learning. However, an emerging challenge is the application of technology, beyond the traditional classroom, to a diverse mix of pedagogical techniques. Traditional education is based on the process of transmi...