Volume 56 , issue 1$-$2 ( 2004 )back
A unified theory of continuity1$-$12
T. Hatice Yalva\c c

Abstract

This paper further develops the theory of operations on a topological space with the aim of producing a uniform framework for the study of generalized forms of continuity. To illustrate the utility of this approach the results obtained are used to obtain many new and known characterizations of strong $\Theta$-semi-continuity, weak continuity and almost continuity.

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Keywords: Continuity, operation, unification, supratopology

MSC: 54C08

Fuzzy partitions of unity13$-$15
Francisco Gallego Lupiá\~nez

Abstract

In General Topology, there exist useful theorems on the existence of partitions of unity for paracompact regular spaces (and also for normal spaces). In this paper, we define the notion of fuzzy partition of unity and we obtain some results about this concept.

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Keywords: Fuzzy topology, partition of unity, $r$-paracompact and $S$-paracompact fuzzy topological spaces, weak inducement, normality.

MSC: 54A40; 03E72

A new variant of an iterative method for solving the complete eigenvalue of matrices17$-$21
Arif Zolić

Abstract

In a complete problem of eigenvalues of matrices of the $n$-th order the essential role is played by the development of the characteristic determinant $$ D(\lambda)=\det(A-\lambda E)$$ or some other determinant which is essentially identical to this one. There is a series of different methods by which we come to the explicit form of this polynomial. In this paper iterative formulas are derived for finding of all eigenvalues of a real matrix without developing the characteristic polynomial. The method is based on the Newton's method for solving systems of nonlinear equations.

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Keywords: Iterative method, eigenvalues of matrices.

MSC: 65F15

New approach to shocks generation for conservation laws. Example: global solution to Hopf equation23$-$46
V. G. Danilov and D. Mitrović

Abstract

We present a new method for constructing global solution to Hopf equation. Propagation and formation of nonlinear waves are described.

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Keywords: Nonlinear waves, shocks generation, Hopf equation.

MSC: 35F25

Fuzzy $\alpha$-connectedness and fuzzy $\alpha$-disconnectedness in fuzzy topological spaces47$-$56
G. Balasubramanian, V. Chandrasekar

Abstract

Various types of connectedness and disconnectedness are introduced using fuzzy $\alpha$-open sets. Several properties and characterizations of such spaces are discussed.

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Keywords: Fuzzy $\alpha$-connected, fuzzy super $\alpha$-connected, fuzzy strongly $\alpha$-connected, extremally fuzzy $\alpha$-disconnected, totally fuzzy $\alpha$-disconnected.

MSC: 54A40

Estimation a priori pout un probléme inverse de la théorie de transport57$-$61
S. Lahrech

Abstract

We establish a priori estimates result for an inverse problem of transport theory. We refer to [1], where some existence and uniqueness results are proved.

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Keywords: A priori estimates, inverse problem, transport theory.

MSC: 49N50