In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

1-way quantum finite state automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. We introduce 2-tape 1-way quantum finite state automaton (2T1QFA(2))which is a modified version of 1-way 2-head quantum finite state automaton(1QFA(2)). In this paper, we repla...

A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N -qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and partitionings of the corresponding Pauli graph are embodied in the geometry of the generalized q...

Classically, formal orthogonal polynomials are studied with respect to a linear functional, which gives rise to a moment matrix with a Hankel structure. Moreover, in most situations, the moment matrix is supposed to be strongly regular. This implies a number of algebraic properties which are well known, like for example the existence of a three-term recurrence relation (characterised by a tridi...

Recursion relation between intensity of hierarchical objects at neighbouring levels of a hierarchical tree, strength of coupling between them and level distribution of nodes of the hierarchical tree is proposed. Regular (including Fibonacci), degenerate and irregular trees are considered. It is shown that the strength of hierarchical coupling is a exponentially, logarithmically or power law dec...

We review a general, space and time eecient technique for delivering a sequence of values computable by a recurrence relation, in the order opposing the data-dependencies of the recurrence. The technique provides a series of time/space tradeoos we characterize by parameter K > 0. Namely, N values can be delivered against the grain in O(KN) time and O(KN 1=K) space. This basic idea is not new, b...

Ontology mapping is one of the core tasks for ontology interoperability. It is aimed to find semantic relationships between entities (i.e. concept, attribute, and relation) of two ontologies. It benefits many applications, such as integration of ontology based web data sources, interoperability of agents or web services. To reduce the amount of users’ effort as much as possible, (semi-) automat...

This paper rst presents some new results on excluded functional dependencies, i.e., FDs which do not hold on a given relation schema. In particular, we show how excluded dependencies relate to Armstrong relations, and we state criteria for deciding whether a set of excluded dependencies characterizes a set of FDs. In the rest of the paper, complexity issues related to the following three proble...

A new relation between morphisms in a category is introduced – roughly speaking (accurately in the categories Set and Top), f ‖ g iff morphisms w : dom(f) → dom(g) never map subobjects of fibres of f non-constantly to fibres of g. (In the algebraic setting replace fibre with kernel.) This relation and a slight weakening of it are used to define “connectedness” versus “disconnectedness” for morp...