The Doitchinov Completion of a Regular Paratopological Group

In memory of Professor D. Doitchinov ∗ This paper was written while the first author was supported by the Swiss National Science Foundation under grants 21–30585.91 and 2000-041745.94/1 and by the Spanish Ministry of Education and Sciences under DGES grant SAB94-0120. The second author was supported under DGES grant PB95-0737. During her stay at the University of Berne the third author was supported by the first author’s grant 2000-041745.94/1 from the Swiss National Science Foundation.

Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.

Tessellation with some Irregular Poligons

An idea for the use of problems of tessellation with irregular polygons in the optional activities in Information Technologies teaching are presented.

Comparing Entire Prototypes at Semigroup Homomorphisms and Specifically at Regular Languages Substitutions

The following statements are proven: A correspondence of a semigroup in another one is a homomorphism if and only if when the entire prototype of the product of images contains (always) the product of their entire prototypes. The Kleene closure of the maximal rewriting of a regular language at a regular language substitution contains in the maximal rewriting of the Kleene closure of the initial regular language at the same substitution. Let the image of the maximal rewriting of a regular language at a regular language substitution covers the entire given regular language. Then the image of any word from the maximal rewriting of the Kleene closure of the initial regular language covers by the image of a set of some words from the Kleene closure of the maximal rewriting of this given regular language everything at the same given regular language substitution. The purposefulness of the ¯rst statement is substantiated philosophically and epistemologically connected with the spirit of previous mathematical results of the author. A corollary of its is indicated about the membership problem at a regular substitution.

Converting a regular learning course Into distance course

Доклад по покана, поместен в сборника на Националната конференция "Образованието в информационното общество", Пловдив, октомври, 2006 г.

Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons

We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

Quasi-Regular Solutions for 3D Equations of Tricomi and Keldish Types

Цветан Д. Христов, Недю Ив. Попиванов, Манфред Шнайдер - Изучени са някои тримерни гранични задачи за уравнения от смесен тип. За уравнения от типа на Трикоми те са формулирани от М. Протер през 1952, като тримерни аналози на задачите на Дарбу или Коши–Гурса в равнината. Добре известно е, че новите задачи са некоректни. Ние формулираме нова гранична задача за уравнения от типа на Келдиш и даваме понятие за квазиругулярно решение на тази задача и на eдна от задачите на Протер. Намерени са достатъчни условия за единственост на такива решения.

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

About Strictly Hyperbolic Operators with Non-Regular Coefficients

2002 Mathematics Subject Classification: 35L15, 35L80, 35S05, 35S30

Criterion of Normality of the Completely Regular Topology of Separate Continuity

2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.

On strongly regular graphs with m2 = qm3 and m3 = qm2

2010 Mathematics Subject Classification: 05C50.