Arnold L. Rosenberg / Dept. of Computer Science, University of Massachusetts, Amherst, USA
Lenwood S. Heath / Dept. of Computer Science, Virginia Polytechnic Institute, Blacksburg, USA

Graph Separators, with Applications

Graph Separators with Applications is devoted to techniques for obtaining upper and lower bounds on the sizes of graph separators ・upper bounds being obtained via decomposition algorithms. The book surveys the main approaches to obtaining good graph separations, while the main focus of the book is on techniques for deriving lower bounds on the sizes of graph separators. This asymmetry in focus reflects our perception that the work on upper bounds, or algorithms, for graph separation is much better represented in the standard theory literature than is the work on lower bounds, which we perceive as being much more scattered throughout the literature on application areas. Given the multitude of notions of graph separator that have been developed and studied over the past (roughly) three decades, there is a need for a central, theory-oriented repository for the mass of results. The need is absolutely critical in the area of lower-bound techniques for graph separators, since these techniques have virtually never appeared in articles having the word `separator' or any of its near-synonyms in the title. Graph Separators with Applications fills this need.

Contents
Preface. Capsule Biographies of the Authors. 1. A Technical Introduction. 2. Applications of Graph Separators. 3. Upper Bound Techniques. 4. Lower-Bound Techniques. A. Applications of Graph Separators, Revisited. Bibliography. Index.

Kluwer Academic/Plenum Publishers
Hardbound, ISBN 0-306-46464-0
June 2001, 264 pp.

Chatterji, S.D., Ecole Polytechnique Federale, Lausanne; Remmert, R., Universitat Munster; Scharlau, W., Universitat Munster (Hrsg.)

Felix Hausdorff - Gesammelte Werke
Band IV: Analysis, Algebra und Zahlentheorie

2001. XIX, 554 S. Geb.
3-540-41760-5

Felix Hausdorff gehort zu den herausragenden Mathematikern der ersten Halfte des 20. Jahrhunderts. Eine Gesamtausgabe seiner Werke galt lange als Desideratum. Die auf 8 Bande veranschlagte Edition wird Hausdorffs gesamtes publiziertes Opus enthalten, ferner eine Reihe bemerkenswerter Stucke aus dem umfangreichen wissenschaftlichen Nachlas. Alle Texte werden von Fachleuten auf den einzelnen Gebieten sorgfaltig kommentiert; an dieser Arbeit sind mehr als 20 Mathematiker, Mathematikhistoriker, Astronomen, Philosophen und Literaturwissenschaftler aus vier Staaten beteiligt. Der vorliegende Band IV enthalt Hausdorffs Arbeiten zur Analysis, Algebra und Zahlentheorie, darunter die klassischen auch heute noch vielzitierten Texte zu Hausdorff-Mas und Hausdorff-Dimension und zum Hausdorffschen Kugelparadoxon. Aus dem Nachlas werden 19 Faszikel publiziert, ferner einige interessante Briefe.

Schlagworte: Analysis, Algebra, Zahlentheorie, Geschichte der Mathematik

Inhalt: Aus dem Inhalt: Teil I: Analysis.- A. Veroffentlichte Arbeiten: Bemerkungen uber den Inhalt von Punktmengen. Dimension und auserers Mas. Der Wertvorrat einer Bilinearform. Zur Verteilung der fortsetzbaren Potenzreihen. Uber halbstetige Funktionen. B. Arbeiten aus dem Nachlas: Beispiele divergenter trigonometrischer Reihen. Metrische und topologische Raume. Erweiterung des Systems der messbaren Mengen. Die Laguerreschen Polynome. Teil II: Algebra.- Zur Theorie der Systeme complexer Zahlen. Die symbolische Exponentialformel in der Gruppentheorie. Lipschitzsche Zahlensysteme und Studysche Nablafunktionen. Teil III: Zahlentheorie.- Zur Hilbertschen Losung des Waringschen Problems. E.Landau, Handbuch der Lehre von der Verteilung der Primzahlen. Schriftenverzeichnis Hausdorffs. Register.

Ganzha, V.G., Technische Universitat Munchen, Germany Mayr, E.W., Technische Universitat Munchen, Germany Vorozhtsov, E.V., Russian Academy of Sciences, Novosibirsk, Russia (Eds.)

Computer Algebra in Scientific Computing
CASC '01

2001. XII, 556 pp. Hardcover
3-540-42355-9

The book covers various topics of computer algebra methods, algorithms and software applied to scientific computing. An important topic presented in the book, which may be of interest to researchers and engineers, is the application of computer algebra methods to the development of new efficient analytic and numerical solvers, both for ordinary and partial differential equations. A specific feature of the book is an intense use of advanced software systems such as Mathematica, Maple etc. for the solution of problems as outlined above and for the industrial application of computer algebra for simulation. The book will be useful for researchers and engineers who apply advanced computer algebra methods for the solution of their problems.

Keywords: Computer algebra, scientific computing, symbolic computation

Rordam, M., University of Copenhagen, Denmark Stormer, E., University of Oslo, Norway

Classification of Nuclear C*-Algebras. Entropy in Operator Algebras

2001. Approx. 415 pp. Hardcover
3-540-42305-2

This EMS volume consists of two parts, written by leading scientists in the field of operator algebras and non-commutative geometry. The first part, written by M.Rordam, is on Elliott's classification program for nuclear C*-algebras. The emphasis is on the work of Kirchberg and the spectacular results by Kirchberg and Phillips giving a nearly complete classification, in terms of K-theoretic invariants, in the purely infinite case. This part of the program is described with almost full proofs beginning with Kirchberg's tensor product theorems and Kirchberg's embedding theorem for exact C*-algebras. The classification of finite simple C*-algebras starting with AF-algebras, and continuing with AT- and AH-algebras is covered, but mostly without proofs. The second part, written by E.Stormer, is a survey of the theory of of noncommutative entropy of automorphisms of C*-algebras and von Neumann algebras from its initiation by Connes and Stormer in 1975 till 2001.

Keywords: C * -algebras, classifications, K-theory, entropy

Contents: Part I. Classification of Nuclear, Simple C*-Algebras, M.Rordam: 1. AF-algebras and their Classification.- 2. Preliminaries.- 3. Classification results for finite C*-algebras.- 4. Purely infinite simple C*-algebras.- 5. On O 2.- 6. Nuclear and exact C*-algebras and exact C*-algebras.- 7. Tensor products by O 2 and O Oinfty.- 8. Classification of Kirchberg algebras.- Part II. A Survey of Noncommutative Dynamical Entropy, E. Stormer: Introduction.- 1. Entropy in finite von Neumann algebras.- 2. Entropy in C*-algebras.- 3. Bogoliubov automorphisms.- 4. The entropy of Sauvageot and Thouvenot.- 5. Voiculescu's approximation entropies.- 6. Crossed products.- 7. Free products.- 8. Binary shifts.- 9. Generators.- 10. The variational principle.

Series: Encyclopaedia of Mathematical Sciences. VOL. 126

Albert, J., Bowling Green State University, Bowling Green, OH, USA
Bennett, J.M., Bellcore, Fair Haven, NJ, USA

Curve Ball
Baseball, Statistics, and the Role of Chance in the Game

2001. XVIII, 350 pp. Softcover
0-387-98816-5

A look at baseball data from a statistical modeling perspective! There is a fascination among baseball fans and the media to collect data on every imaginable event during a baseball game and this book addresses a number of questions that are of interest to many baseball fans. These include how to rate players, predict the outcome of a game or the attainment of an achievement, making sense of situational data, and deciding the most valuable players in the World Series. Aimed at a general audience, the text does not assume any prior background in probability or statistics, although a knowledge of high school abgebra will be helpful.

Contents: Introduction.- Simple Models.- Situational Effects.- How Do We Evaluate Players.- Clutch Hitting.- Streakiness.- Does The Best Team Win?- Predicting Results.- Wrap-Up.

Calude, C.S., / Dinneen, M.J., University of Auckland, New Zealand
Sburlan, S., Ovidius University, Constanta, Romania (Eds.)

Combinatorics, Computability and Logic
Proceedings of the Third International Conference on
Combinatorics, Computability and Logic (DMTCS'01)

2001. X, 251 pp. Softcover
1-85233-526-2

This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001.
The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover topics such as: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability, complexity and constructive mathematics; discrete mathematics, combinatorial computing and category theory; logic, nonmonotonic logic and hybrid systems; molecular computing.

Contents: Invited papers: Early Computer Science Adventures of a Mathematician. Sequentially Continuity in Constructive Mathematics. Recursive Functions: An Archeological Look. The Number of Graphs and Digraphs with a Fixed Diameter and Connectivity.- Contributed papers: Some Results for Some Conjectures in Addition Chains. A Highly Random Number. Dini's Theorem: a Constructive Case Study. Even Linear Simple Matrix Languages: Formal Language Aspects. Pseudo-BCK Algebras: An Extension of BCK Algebras. P -Immune Sets with Holes Lack Self-Reducibility Properties. Lex Ideals of Generalized MV-Algebras. Armstrong Systems on Ordered Sets. Unicycle Bipartite Graphs with Only Uniquely Restricted Maximum Matchings. On Relax-ability of Word-Order by D-grammars. On the Structure of Linear Cellular Automata. Monotonically Computable Real Numbers. Apartness as a Relation Between Subsets. How Large is the Set of Disjunctive Sequences? A Loopless Generation of Bitstrings without p Consecutive Ones. Greedy Algorithms for the Lower and Upper Chromatic Numbers.

Series: Discrete Mathematics and Theoretical Computer Science.