Bauer, I., University of Bayreuth, Germany; Catanese, F., University of Bayreuth, Germany; Kawamata, Y., University of Tokyo, Japan; Peternell, T., University of Bayreuth, Germany; Siu, Y.-T., Harvard University, Cambridge, MA, USA (Eds.)

Complex Geometry
Collection of Papers Dedicated to Hans Grauert

2002. XXII, 342 pp. Hardcover
3-540-43259-0

This book is a collection of research articles in algebraic geometry and complex analysis dedicated to Hans Grauert. The authors and editors have made their best efforts in order that these contributions should be adequate to honour the outstanding scientist. The volume contains important new results, solutions to longstanding conjectures, elegant new proofs and new perspectives for future research. The topics range from surface theory and commutative algebra, linear systems, moduli spaces, classification theory, Kahler geometry to holomorphic dynamical systems.

Keywords: Algebraic surfaces, linear systems, moduli spaces, classification theory, Kahler geometry .

Contents: From the contents: Preface.- W. Barth: Even Sets of Eight Rational Curves on a K3-surface.- T. Bauer et al.: A Reduction Map for Nef Line Bundles.- I. Bauer et al.: Canonical Rings of Surfaces Whose Canonical System has Base Points.- A. Bonifant/J.E. Fornaess: Attractors.- C. Ciliberto/K. Hulek: A Bound on Irregularity of Abelian Scrolls in Projective Space.- J.-P. Demailly: On the Frobenius Integrability of Certain Holomorphic p-Forms.- H. Flenner/M. Lubke: Analytic Moduli Spaces of Simple (Co)Framed Sheaves.- A.T. Huckleberry/J.A. Wolf: Cycle Spaces of Real Forms of SLn(C).- Y. Kawamata: On a Relative Version of Fujita Freeness Conjecture.- S. Kebekus: Characterizing the Projective Space after Cho, Miyaoka and Shepard-Barron.- S. Kebekus et al.: Manifolds With a Nef Rank 1...- K. Oguiso, D. Zhang: The Simple Group of Order 168 and K3 Surfaces.- T. Ohsawa: A Precise L2 Division Theorem.- S. Schroer/B. Siebert: Irreducible Degenerations of Primary Kodaira Surfaces.

Burger, M., ETH, Zurich, Switzerland; Iozzi, A., ETH, Zurich, Switzerland (Eds.)

Rigidity in Dynamics and Geometry
Contributions from the Programme "Ergodic Theory, Geometric Rigidity and Number Theory" Isaac Newton Institute for the Mathematical Sciences Cambridge, 5 January - 7 July 2000

2002. XIII, 492 pp. 17 figs. Hardcover
3-540-43243-4

This volume is an offspring of the special semester "Ergodic Theory, Geometric Rigidity and Number Theory" held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from January until July, 2000. Some of the major recent developments in rigidity theory, geometric group theory, flows on homogeneous spaces and Teichmuller spaces, quasi-conformal geometry, negatively curved groups and spaces, Diophantine approximation, and bounded cohomology are presented here. The authors have given special consideration to making the papers accessible to graduate students, with most of the contributions starting at an introductory level and building up to presenting topics at the forefront in this active field of research. The volume contains surveys and original unpublished results as well, and is an invaluable source also for the experienced researcher.

Keywords: Rigidity theory, dynamical systems, ergodic theory, number theory, geometricgroup theory

Contents: From the contents: M. Bourdon, H. Pajot: Quasi-Conformal Geometry and Hyperbolic Geometry.- M. Burger, N. Monod: On and Around the Bounded Cohomology of SL2.- J.-P. Conze, Y. Guivarc'h: Densite d'orbites d'actions de groupes lineaires et proprietes d'equidistribution de marches aleatoires.- M. Dodson: Exceptional Sets in Dynamical Systems and Diophantine Approximation.- R. Feres: An Introduction to Cocycle Super-Rigidity.- D. Fisher: Rigid Geometric Structures and Representations of Fundamental Groups.- A. Furman: Coarse-Geometric Perspective on Negatively Curved Manifolds and Groups.- D. Gaboriau: On Orbit Equivalence of Measure Preserving Actions.- W.M. Goldman: The Margulis Invariant of Isometric Actions on Minkowski (2+1)-Space.- S. Hersonsky, F. Paulin: Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group.- A. Iozzi: Bounded Cohomology, Boundary Maps, and Rigidity of Representations.

Hsu, J.Y., California Polytechnic State University, San Luis Obispo, CA, USA

Computer Logic
Design Principles and Applications

2002. Approx. 200 pp. 67 figs. Hardcover
0-387-95304-3

An understanding of modern computer logic - incorporating core knowledge of number systems, number conversions, Boolean algebra, memories, and logic circuits - is fundamental to further study of computer architectures, system software, and computer networks. Computer Logic: Design Principles and Applications introduces and describes the relevant concepts, principles and applications of modern computer logic design. The book is self-contained, with an introductory chapter that concisely covers the history of computing devices, as well as number systems, number conversions, signed and unsigned integers, external code, and digital and digitizing concepts. Dedicated chapters on Boolean algebra, transistor circuits, combinatorial logic circuits, and sequential logic circuits round off the work. The emphasis is on design and applications.

Contents: From the contents: Introduction: Prolog. Digital concept. Number systems. Number conversions. Unsigned integers vs. signed integers. External codes. Digitizing concepts.- Boolean algebra: Boolean constant vs. Boolean variable. Basic laws. Other logical operators. Algebraic simplifications. Karnaugh maps.- Transistor circuits: Introduction. Scale of integration. Bipolar transistors. Unipolar transistors. Electronic design issues. Digital waveforms.- Combinational logic circuits: Basic logic gates.

Jost, J., Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Compact Riemann Surfaces, 2nd ed.
An Introduction to Contemporary Mathematics

2002. XVI, 281 pp. 24 figs. Softcover
3-540-43299-X

Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmuller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this 2nd edition the author has further improved aspects of presentation of various parts of the text.

Keywords: Riemann surfaces, harmonic maps, Teichmuller theory, hyperbolic geomietry, Riemann-Roch theorem MSC ( 2000 ): 30F10 ; 30F45 ; 30F60, 58E20, 14H55

Series: Universitext.

Brenner, S.C., University of South Carolina, Columbia, SC, USA;
Scott, L.R., University of Chicago, IL, USA

The Mathematical Theory of Finite Element Methods

2nd ed. 2002. Approx. 385 pp. 41 figs. Hardcover
0-387-95451-1

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. It formalizes basic tools that are commonly used by researchers in the field but not previously published. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests. For example, courses can emphasize physical applications, or algorithmic efficiency and code development issues, or the more difficult convergence theorems of the subject. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes. Review of earlier edition: "This book represents an important contribution to the mathematical literature of finite elements. It is both a well-done text and a good reference."
(Mathematical Reviews, 1995)

Keywords: Finite Element Methods

Contents: Preface(2nd ed.).- Preface(1st ed.).- Basic Concepts.- Sobolev Spaces.- Variational Formulation of Elliptic Boundary Value Problems.- The Construction of a Finite Element of Space.- Polynomial Approximation Theory in Sobolev Spaces.- n-Dimensional Variational Problems.- Finite Element Multigrid Methods.- Additive Schwarz Preconditioners.- Max-norm Estimates.- Adaptive Meshes.- Variational Crimes.- Applications to Planar Elasticity.- Mixed Methods.- Iterative Techniques for Mixed Methods.- Applications of Operator-Interpolation Theory.- References.- Index.

Series: Texts in Applied Mathematics. VOL. 15