Alexander V. Mikhalev - Böcker

This monograph is devoted to the investigation of differential and difference dimension theory. The differential dimension polynomial describes in exact terms the degree of freedom of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. Difference algebra arises from the study of algebraic difference equations and therefore bears a considerable resemblance to its differential counterpart. Difference algebra was developed in the same period as differential algebra and it has the same founder, J. Ritt. It grew to a mathematical area with its own ideas and methods mainly due to the work of R. Cohn, who raised difference algebra to the same level as differential algebra. The relatively new science of computer algebra has given strong impulses to the theory of dimension polynomials, now that packages such as MAPLE enable the solution of many problems which cannot be solved otherwise. Applications of differential and difference dimension theory can be found in many fields of mathematics, as well as in theoretical physics, system theory and other areas of science.This book should be of interest to researchers and graduate students whose work involves differential and difference equations, algebra and number theory, partial differential equations, combinatorics and mathematical physics.

This is the first monograph on the theory of endomorphism rings of Abelian groups. The theory is a rapidly developing area of algebra and has its origin in the theory of operators of vector spaves. The text contains additional information on groups themselves, introducing new concepts, methods, and classes of groups. All the main fields of the theory of endomorphism rings of Abelian groups from early results to the most recent are covered. Neighbouring results on endomorphism rings of modules are also mentioned. The text has many pedagogical features: all the necessary definitions and formulations of assertions on Abelian groups, rings, and modules are gathered in the first two sections; summaries of results; exercises of varying difficulty in each section; lesser known facts on rings and modules are presented with proofs; and comments at the end of each chapter together with a brief historical review as well as a look at the future direction of modern research.

No detailed description available for "Infinite Dimensional Lie Superalgebras".

No detailed description available for "Monoids, Acts and Categories".

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals

SFCA/FPSAC (Series Formelles et Combinatoire Algebrique/Formal Power Se- ries and Algebraic Combinatorics) is a series of international conferences that are held annually since 1988, alternating between Europe and North America. They usually take place at the end of the academic year, between June and July depending on the local organizing constraints. SFCA/FPSAC has now become one of the most important annual inter- national meetings for the algebraic and bijective combinatorics community. The conference is indeed one of the key international exchange place of ideas between all researchers involved in this emerging exciting area. SFCA/FPSAC'OO is the 12th in the series. It will take place in Moscow (Russia) from June 26 to June 30, 2000. Previous SFCA/FPSAC conferences were organized in Lille (88), Paris (90), Bordeaux (91), Montreal (92), Florence (93), Rutgers (94), Marne-la-Vallee (95), Minneapolis (96), Vienna (97), Toronto (98) and Barcelona (99).SFCA/FPSAC'OO is co-organized by the Center of New Information Tech- nologies (CNIT) of Moscow State University, the Laboratoire d'Informatique AI- gorithmique : Fondements et Applications (LIAFA) of University Paris 7 and the Maison de l'Informatique et des Mathematiques Discretes (MIMD). The SFCA/FPSAC'OO conference covers all main areas of algebraic combi- natorics and bijective combinatorics (including asymptotic analysis, all sorts of enumeration, representation theory of classical groups and classical Lie algebras, symmetric functions, etc). A special stress was also put this year on combinato- rial and computer algebra.

SFCA/FPSAC (Series Formelles et Combinatoire Algebrique/Formal Power Se- ries and Algebraic Combinatorics) is a series of international conferences that are held annually since 1988, alternating between Europe and North America. They usually take place at the end of the academic year, between June and July depending on the local organizing constraints. SFCA/FPSAC has now become one of the most important annual inter- national meetings for the algebraic and bijective combinatorics community. The conference is indeed one of the key international exchange place of ideas between all researchers involved in this emerging exciting area. SFCA/FPSAC'OO is the 12th in the series. It will take place in Moscow (Russia) from June 26 to June 30, 2000. Previous SFCA/FPSAC conferences were organized in Lille (88), Paris (90), Bordeaux (91), Montreal (92), Florence (93), Rutgers (94), Marne-la-Vallee (95), Minneapolis (96), Vienna (97), Toronto (98) and Barcelona (99).SFCA/FPSAC'OO is co-organized by the Center of New Information Tech- nologies (CNIT) of Moscow State University, the Laboratoire d'Informatique AI- gorithmique : Fondements et Applications (LIAFA) of University Paris 7 and the Maison de l'Informatique et des Mathematiques Discretes (MIMD). The SFCA/FPSAC'OO conference covers all main areas of algebraic combi- natorics and bijective combinatorics (including asymptotic analysis, all sorts of enumeration, representation theory of classical groups and classical Lie algebras, symmetric functions, etc). A special stress was also put this year on combinato- rial and computer algebra.

This book is the first monograph wholly devoted to the investigation of differential and difference dimension theory. The differential dimension polynomial describes in exact terms the degree of freedom of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. Difference algebra arises from the study of algebraic difference equations and therefore bears a considerable resemblance to its differential counterpart. Difference algebra was developed in the same period as differential algebra and it has the same founder, J. Ritt. It grew to a mathematical area with its own ideas and methods mainly due to the work of R. Cohn, who raised difference algebra to the same level as differential algebra. The relatively new science of computer algebra has given strong impulses to the theory of dimension polynomials, now that packages such as MAPLE enable the solution of many problems which cannot be solved otherwise. Applications of differential and difference dimension theory can be found in many fields of mathematics, as well as in theoretical physics, system theory and other areas of science.Audience: This book will be of interest to researchers and graduate students whose work involves differential and difference equations, algebra and number theory, partial differential equations, combinatorics and mathematical physics.

This book is the first monograph on the theory of endomorphism rings of Abelian groups. The theory is a rapidly developing area of algebra and has its origin in the theory of operators of vector spaves. The text contains additional information on groups themselves, introducing new concepts, methods, and classes of groups. All the main fields of the theory of endomorphism rings of Abelian groups from early results to the most recent are covered. Neighbouring results on endomorphism rings of modules are also mentioned.