‎let $pa$ be a commutative banach algebra and $ex$ be a left banach $pa$-module‎. ‎we study the set‎ ‎$dec_{pa}(ex)$ of all elements in $pa$ which induce a decomposable multiplication operator on $ex$‎. ‎in the case $ex=pa$‎, ‎$dec_{pa}(pa)$ is the well-known apostol algebra of $pa$‎. ‎we show that $dec_{pa}(ex)$ is intimately related with the largest spectrally separable subalgebra of $pa$ and...

We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong complete separability. For each these four conditions, we investigate which monoids have property that all their (finitely generated) acts satisfy condition. In particular, prove that: over a finite are completely separable (and hence other three condi...

This paper describes an approach to system design called the dialectical. In this approach, the design and its environment, including the people involved, are assumed to form an inseparable whole. The whole and its parts are subject to interaction and change throughout the entire design process. Using this approach, a number of aspects of system design are covered, and a model for design proces...

Recent research has to a limited extent explored the nature of collaborative knowledge construction in 3D environments. In this paper we describe this issue by identifying two collaboration patterns that are manifested in the students’ dialogues and actions in a particular 3D learning environment. The theoretical framework is found within socio-cultural perspectives that view learning as social...

While demands for large scale improvements in education systems increase worldwide, education system structures continuously fail to meet, or even make notable advancements, toward these demands. Inseparable from this problem is the very similar way in which education systems are managed. Educational managerial structures have become so universal, perpetual, and therefore, deeply ingrained in s...

For a finite cyclic Galois extension of fields K/k of degree n and a separable polynomial of degree dn or dn−1, we construct an explicit smooth compactification X → Pk of the affine normic bundle X0 given by NK/k(~z) = P (x) 6= 0, extending the map X0 → Ak, where (~z, x) 7→ x. The construction makes no assumption of the characteristic of k, making it a suitable departure point for studying the ...

But this picture of a ”block universe”, composed of a timeless web of ”world-lines”in a four-dimensional space, however strongly suggested by the theory of relativity, is a piece of gratuitous metaphysics. Since the concept of change, of something happening, is an inseparable component of the common-sense concept of time and a necessary component of the scientist’s view of reality, it is quite ...

A disjoint NP-pair is a pair (A,B) of nonempty, disjoint sets A and B such that both A and B belong to the complexity class NP.1 We let DisjNP denote the collection of all disjoint NP-pairs. A separator of a disjoint NP-pair (A,B) is a set S such that A ⊆ S and B ⊆ S (Figure 1). A fundamental question is whether (A,B) has a separator belonging to P. In this case the pair is P-separable; otherwi...

Two games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a pri...