Volume 56 , issue 1$-$2 ( 2004 ) | back |

A unified theory of continuity | 1$-$12 |

**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.

**Keywords:** Continuity, operation, unification, supratopology

**MSC:** 54C08

Fuzzy partitions of unity | 13$-$15 |

**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.

**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 matrices | 17$-$21 |

**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.

**Keywords:** Iterative method, eigenvalues of matrices.

**MSC:** 65F15

New approach to shocks generation for conservation laws. Example: global solution to Hopf equation | 23$-$46 |

**Abstract**

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

**Keywords:** Nonlinear waves, shocks generation, Hopf equation.

**MSC:** 35F25

Fuzzy $\alpha$-connectedness and fuzzy $\alpha$-disconnectedness in fuzzy topological spaces | 47$-$56 |

**Abstract**

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

**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 transport | 57$-$61 |

**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.

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

**MSC:** 49N50