Hoffmann, K.-H., Caesar Foundation, Bonn, Germany, Hoppe, R.H.W., University of Augsburg, Germany, Schulz, V., Weierstrass Institute for Applied Analysis, Berlin, Germany, (Eds.)
Fast Solution of Discretized Optimization Problems
2001. 292 pages. Hardcover
ISBN 3-7643-6599-4
English
International Series of Numerical Mathematics, vol.138
Differential equations ? partial as well as ordinary ? are one of the main tools for the modeling of real world application problems. In order to appropriately treat such systems, the optimizing of discretized models plays a key role. The intention of this book is to combine approaches from both disciplines, numerical mathematics and optimization, to cope with this practically highly important problem class. It collects papers presented at the workshop "Fast solution of discretized optimization problems", which was intended to foster the development of efficient numerical solution methods for large-scale optimization problems resulting from differential equations from various applications. It will be most helpful for mathematical and engineering scientists working in an applied environment.
Losa, G.A., Istituto Cantonale di Patologia, Locarno, Switzerland, Merlini, D., Centro Ricerche in Fisica e Matematica, Locarno, Switzerland, Nonnenmacher, T.F., University of Ulm, Germany, Weibel, E.R., University of Berne, Switzerland, (Eds.)
Fractals in Biology and Medicine, Volume III
2001. Approx. 350 pages. Hardcover
ISBN 3-7643-6474-2
English
Due in October 2001
In March 2000 leading scientists gathered at the Centro Seminariale Monte Verita, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference was held over a four-day period and provided stimulating contributions from the very topical field +Fractals in Biology and Medicine+ ((kursiv)). This +Volume III+ ((kursiv)) highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes. Many biological objects, previously considered as hopelessly far from any quantitative description, are now being investigated by means of fractal methods. Researchers currently used fractals both as theoretical tools, to shed light on living systems` self-organization and evolution, and as useful techniques, capable of quantitatively analyzing physiological and pathological cell states, shapes and ultrastructures.
The book should be of interest to researchers and students from Molecular and Cell Biology, Biomedicine, Bio-Mathematics, Analytical Morphology, Immunology and Neurology, interested in the combination of mathematics and life sciences.
Thomas Hawkins, Boston University, MA
Lebesgue's Theory of Integration: Its Origins and Development
Expected publication date is November 3, 2001
Description
In this book, Hawkins elegantly places Lebesgue's early work on integration theory within in proper historical context by relating it to the developments during the nineteenth century that motivated it and gave it significance and also to the contributions made in this field by Lebesgue's contemporaries.
Hawkins was awarded the 1997 MAA Chauvenet Prize and the 2001 AMS Albert Leon Whiteman Memorial Prize for notable exposition and exceptional scholarship in the history of mathematics.
Contents
Riemann's theory of integration
The development of riemann's ideas: 1870-80
Set theory and the theory of integration
The end of the century: A period of transition
The creation of modern integration theory
Pioneering applications of the Lebesgue integral
Epilogue: The Lebesgue-Stieltjes integral
Appendix: Dini's theorem on the differentiability of continuous functions
Glossary
Special symbols
List of abbreviations
Bibliography
Index
Details:
Series: AMS Chelsea Publishing
Publication Year: 1979
ISBN: 0-8218-2963-7
Paging: 227 pp.
Binding: Hardcover
Richard L. Bishop, University of Illinois, Urbana, IL, and Richard J. Crittenden
Geometry of Manifolds
Expected publication date is October 18, 2001
From a review for the First Edition:
"This book represents an excellent treatment of a wide section of modern differential geometry ... The style is elegant and at the same time considerate for the needs of a beginner ... a great number of well chosen problems with pertinent references ... anybody who chooses to base his course on differential geometry at the graduate level on this book could do no better."
-- Mathematical Reviews
Description
From the Preface of the First Edition: "Our purpose in writing this book is to put material which we found stimulating and interesting as graduate students into form. It is intended for individual study and for use as a text for graduate level courses such as the one from which this material stems, given by Professor W. Ambrose at MIT in 1958-1959. Previously the material had been organized in roughly the same form by him and Professor I. M. Singer, and they in turn drew upon the work of Ehresmann, Chern, and E. Cartan. Our contributions have been primarily to fill out the material with details, asides and problems, and to alter notation slightly.
"We believe that this subject matter, besides being an interesting area for specialization, lends itself especially to a synthesis of several branches of mathematics, and thus should be studied by a wide spectrum of graduate students so as to break away from narrow specialization and see how their own fields are related and applied in other fields. We feel that at least part of this subject should be of interest not only to those working in geometry, but also to those in analysis, topology, algebra, and even probability and astronomy. In order that this book be meaningful, the reader's background should include real variable theory, linear algebra, and point set topology."
This volume is a reprint with few corrections of the original work published in 1964. Starting with the notion of differential manifolds, the first six chapters lay a foundation for the study of Riemannian manifolds through specializing the theory of connections on principle bundles and affine connections. The geometry of Riemannian manifolds is emphasized, as opposed to global analysis, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory. Isometric immersions are treated elegantly and from a global viewpoint. In the final chapter are the more complicated estimates on which much of the research in Riemannian geometry is based: the Morse index theorem, Synge's theorems on closed geodesics, Rauch's comparison theorem, and the original proof of the Bishop volume-comparison theorem (with Myer's Theorem as a corollary).
The first edition of this book was the origin of a modern treatment of global Riemannian geometry, using the carefully conceived notation that has withstood the test of time. The primary source material for the book were the papers and course notes of brilliant geometers, including E. Cartan, C. Ehresmann, I. M. Singer, and W. Ambrose. It is tightly organized, uniformly very precise, and amazingly comprehensive for its length.
Contents
Manifolds
Lie groups
Fibre bundles
Differential forms
Connexions
Affine connexions
Riemannian manifolds
Geodesics and complete Riemannian manifolds
Riemannian curvature
Immersions and the second fundamental form
Second variation of arc length
Theorems on differential equations
Bibliography
Subject index
Details:
Series: AMS Chelsea Publishing
Publication Year: 2001
ISBN: 0-8218-2923-8
Paging: 273 pp.
Binding: Hardcover
Lucia Rapanotti, Open University, Milton Keynes, UK
Algorithm Engineering for Integral and Dynamic Problems
Algorithm engineering aims to design the most cost-efficient computational machine that will execute an algorithm given a set of constraints, such as minimal performance or the availability of technology.
This book addresses algorithm engineering in a parallel setting, that of regular array processors. It focuses on powerful engineering techniques ・regular array synthesis ・which simultaneously embody best practice and are well-founded in mathematical theories. The core of regular array synthesis is the expression of an algorithm in terms of its computations' data dependencies and their subsequent and systematic transformation onto regular array processors.
A criticism that is often leveled against regular array synthesis is that it can only be applied to restricted classes of algorithms. In this book, after a review of the basic principles of regular array synthesis, we will show how regular array synthesis can be extended to include classes of algorithms traditionally thought to be beyond its domain of application.
Contents: Introduction ・ Regular Array Synthesis ・ Integral Recurrence Equations ・ Dynamic Recurrence Equations ・ Case Studies ・ Conclusions ・ A. Notation ・ B. Graph Theory ・ C. Convex Sets and Polyhedra ・ Aspects of Linear Algebra
Readership: Reseachers in parallel distribution systems especially systolic systems, also of interest to the wider computer science community.
Series Part: Parallel Processing, Volume 2
December, 2000 / 280 pp / Cloth / 90-5699-328-3