Edited by: Zhangxin Chen, Southern Methodist University, Dallas, TX, and Richard E. Ewing, Texas A & M University, College Station, TX
Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment
Expected publication date is July 11, 2002
Description
This volume contains research papers written and edited by prominent researchers working with the mathematical and numerical treatment of fluid flow and transport in porous media.
Papers are based on talks given at a 2001 Joint AMS-IMS-SIAM Summer Research Conference held at Mount Holyoke College (South Hadley, MA). Topics cover a variety of subjects such as network flow modeling, contemporary numerical methods, parallel computation, optimization, multiscale phenomena, upscaling, uncertainty reduction, well treatment, and media characterization.
The material addresses many problems originating from the applied geosciences and focuses on their common state-of-the-art mathematical and numerical treatment. This work is particularly pertinent to those working in oil exploration and other industrial applications.
The book serves as an excellent reference work for all geoscientists, mathematicians, physicists, and engineers working in this research area.
Details:
Series: Contemporary Mathematics, Volume: 295
Publication Year: 2002
ISBN: 0-8218-2807-X
Paging: 524 pp.
Binding: Softcover
F. P. Gantmacher and M. G. Krein
Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems: Revised Edition
Expected publication date is July 7, 2002
Description
Fifty years after the original Russian Edition, this classic Chelsea publication is finally available in English for the general mathematical audience. This book lays the foundation of what later became "Krein's Theory of String". The original ideas stemming from mechanical considerations are developed with exceptional clarity. A unique feature is that it can be read profitably by both research mathematicians and engineers.
The authors study in depth small oscillations of one-dimensional continua with finite or infinite number of degrees of freedom. They single out an algebraic property responsible for the qualitative behavior of eigenvalues and eigenfunctions of one-dimensional continua and introduce a subclass of totally positive matrices, which they call oscillatory matrices, as well as their infinite-dimensional generalization and oscillatory kernels. Totally positive matrices play an important role in several areas of modern mathematics, but this book is the only source that explains their simple and intuitively appealing relation to mechanics.
There are two supplements contained in the book, "A Method of Approximate Calculation of Eigenvalues and Eigenvectors of an Oscillatory Matrix", and Krein's famous paper which laid the groundwork for the broad research area of the inverse spectral problem: "On a Remarkable Problem for a String with Beads and Continued Fractions of Stieltjes".
The exposition is self-contained. The first chapter presents all necessary results (with proofs) on the theory of matrices which are not included in a standard linear algebra course. The only prerequisite in addition to standard linear algebra is the theory of linear integral equations used in Chapter 5. The book is suitable for graduate students, research mathematicians and engineers interested in ordinary differential equations, integral equations, and their applications.
Contents
・Introduction
・Review of matrices and quadratic forms
・Oscillatory matrices
・Small oscillations of mechanical systems with n degrees of freedom
・Small oscillations of mechanical systems with an infinite number of degrees of freedom
・Sign-definite matrices
・A method of approximate calculation of eigenvalues and eigenvectors of an oscillatory matrix
・On a remarkable problem for a string with beads and continued fractions of Stieltjes
・Remarks
・References
・Index
Details:
Series: AMS Chelsea Publishing
Publication Year: 2002
ISBN: 0-8218-3171-2
Paging: 310 pp.
Binding: Hardcover
John R. Harper, University of Rochester, NY
Secondary Cohomology Operations
Expected publication date is August 4, 2002
Description
Although the theory and applications of secondary cohomology operations are an important part of an advanced graduate-level algebraic topology course, there are few books on the subject. The AMS now fills that gap with the publication of the present volume.
The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among many applications considered are the Hopf invariant one theorem (for all primes p, including p = 2), Browder's theorem on higher Bockstein operations, and cohomology theory of Massey-Peterson fibrations.
Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary of more advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations.
The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for self-study or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions.
Contents
・Review of primary operations
・Segue to secondary operations
・Fundamental constructions
・Secondary cohomology operations
・Calculations with secondary operations
・The Hopf invariant
・The cohomology structure of universal examples
・Bibliography
・Index
Details:
Series: Graduate Studies in Mathematics, Volume: 49
Publication Year: 2002
Paging: 268 pp.
ISBN: 0-8218-3198-4
Binding: Hardcover
ISBN: 0-8218-3270-0
Binding: Softcover
A. Shen, Institute of Problems of Information Transmission, Moscow Independent University, Moscow, Russia, and N. K. Vereshchagin, Institute of Problems of Information Transmission, Moscow State Lomonosov University, Moscow, Russia
Basic Set Theory
Expected publication date is August 1, 2002
Description
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment.
This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma.
The text introduces all main subjects of "naive" (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Contents
・Sets and their cardinalities
・Ordered sets
・Bibliography
・Index
・Glossary
Details:
Series: Student Mathematical Library, Volume: 17
Publication Year: 2002
ISBN: 0-8218-2731-6
Paging: approximately 128 pp.
Binding: Softcover
Edited by: Michael D. Fried, University of California, Irvine, CA,
and Yasutaka Ihara, RIMS, Kyoto University, Japan
Arithmetic Fundamental Groups and Noncommutative Algebra
Expected publication date is August 11, 2002
Description
The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade.
The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group G_{mathbb Q} of the algebraic numbers and its close relatives. By analyzing how G_{mathbb Q} acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s.
Papers in Part 2 apply theta-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map.
This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.
Contents
G_{mathbb Q} action on moduli spaces of covers
・P. Debes -- Descent theory for algebraic covers
・J. S. Ellenberg -- Galois invariants of dessins d'enfants
・H. Nakamura -- Limits of Galois representations in fundamental groups along maximal degeneration of marked curves, II
・P. Bailey and M. D. Fried -- Hurwitz monodromy, spin separation and higher levels of a modular tower
・S. Wewers -- Field of moduli and field of definition of Galois covers
・Y. Ihara -- Some arithmetic aspects of Galois actions on the pro-p fundamental group of {mathbb P}^1-{0,1,infty}
・R. T. Sharifi -- Relationships between conjectures on the structure of pro-p Galois groups unramified outside p
・H. Nakamura and Z. Wojtkowiak -- On explicit formulae for l-adic polylogarithms
Curve covers in positive characteristic
・A. Tamagawa -- Fundamental groups and geometry of curves in positive characteristic
・M. Raynaud -- Sur le groupe fondamental d'une courbe complete en caracteristique p>0
・M. D. Fried and A. Mezard -- Configuration spaces for wildly ramified covers
・M. A. Garuti -- Linear systems attached to cyclic inertia
・R. Guralnick and K. F. Stevenson -- Prescribing ramification
・Special groups for covers of the punctured sphere
・S. S. Abhyankar and D. Harbater -- Desingularization and modular Galois theory
・D. Frohardt, R. Guralnick, and K. Magaard -- Genus 0 actions of groups of Lie rank 1
・H. Volklein -- Galois realizations of profinite projective linear groups
Fundamental groupoids and Tannakian categories
・S. Gelaki -- Semisimple triangular Hopf algebras and Tannakian categories
・P. H. Hai -- On a theorem of Deligne on characterization of Tannakian categories
・S. Mochizuki -- A survey of the Hodge-Arakelov theory of elliptic curves I
Details:
Series: Proceedings of Symposia in Pure Mathematics, Volume: 70
Publication Year: 2002
ISBN: 0-8218-2036-2
Paging: 569 pp.
Binding: Hardcover