Contributions To General Algebra 5

This volume contains one invited lecture which was presented by the 1994 Fields Medal ist Professor E. Zelmanov and twelve other papers which were presented at the Third International Conference on Algebra and Their Related Topics at Chang Jung Christian University, Tainan, Republic of China, during the period June 26-July 1, 200l. All papers in this volume have been refereed by an international referee board and we would like to express our deepest thanks to all the referees who were so helpful and punctual in submitting their reports. Thanks are also due to the Promotion and Research Center of National Science Council of Republic of China and the Chang Jung Christian University for their generous financial support of this conference. The spirit of this conference is a continuation of the last two International Tainan Moscow Algebra Workshop on Algebras and Their Related Topics which were held in the mid-90's of the last century. The purpose of this very conference was to give a clear picture of the recent development and research in the fields of different kinds of algebras both in Taiwan and in the rest ofthe world, especially say, Russia" Europe, North America and South America. Thus, we were hoping to enhance the possibility of future cooperation in research work among the algebraists ofthe five continents. Here we would like to point out that this algebra gathering will constantly be held in the future in the southern part of Taiwan.

This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician. Contents:On the Characterization of Chebyshev Systems and on Conditions of Their Extension (Y G Abakumov)On Lagrange Polynomial Quasi-Interpolation (C K Chui et al.)The Convexity of Chebyshev Sets in Hilbert Space (F Deutsch)On the Completeness of Orthogonal Polynomials in Left-Definite Sobolev Spaces (W N Everitt et al.)A New Method for Generating Infinite Sets of Related Sequences of Orthogonal Polynomials, Starting from First-Order Initial-Value Problems (C C Grosjean)Orthogonal Polynomials on n-Spheres: Gegenbauer, Jacobi and Heun (E G Kalnins & W Miller, Jr)Extremal Problems for Polynomials and Their Coefficients (G V Milovanovi et al.)Some Recent Advances in the Theory of the Zeros and Critical Points of a Polynomial (Th M Rassias & H M Srivastava)Artificial Intelligence Today (G C Rota)A Certain Family of Generating Functions for Classical Orthogonal Polynomials (H M Srivastava)Mean Number of Real Zeros of a Random Trigonometric Polynomial. II (J E Wilkins, Jr)Orthogonal Polynomials of Many Variables and Degenerated Elliptic Equations (A Yanushauskas)and other papers Readership: Mathematicians and mathematical physicists. keywords:Polynomial Inequalities;Chebyshev Polynomials;Approximation Theory;Fourier Series;Special Functions;Lagrange Polynomials;Markov, Sobolev and Bernstein Inequalities;Orthogonal Polynomials;Generating Functions;Holographic Neural Networks;Integral Equations;Integral Transforms;Rational Approximations;Elliptic Equations;Sobolev Spaces

This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.

In this proceedings, recent development on various aspects of algebra and number theory were discussed. A wide range of topics such as group theory, ring theory, semi-group theory, topics on algebraic structures, class numbers, quadratic forms, reciprocity formulae were covered.