Edited by: Wayne Raskind, University of Southern
California, Los Angeles, CA,
and Charles Weibel, Rutgers University, New Brunswick, NJ
Description
This volume presents the proceedings of the Joint Summer Research
Conference on Algebraic K-theory held at the University
of Washington in Seattle. High-quality surveys are written by
leading experts in the field. Included is the most up-to-date
published
account of Voevodsky's proof of the Milnor conjecture relating
the Milnor K-theory of fields to Galois cohomology. This book
offers a comprehensive source for cutting-edge research on the
topic.
Contents
J.-L. Colliot-Th?l?ne -- Conjectures de type local-global sur
l'image des groupes de Chow dans la cohomologie ?tale
H. Esnault -- Algebraic theory of characteristic classes of
bundles with connection
H. Gangl and S. M?ller-Stach -- Polylogarithmic identities in
cubical higher Chow groups
T. Geisser and L. Hesselholt -- Topological cyclic homology of
schemes
H. Gillet and C. Soul? -- Filtrations on higher algebraic
K-theory
B. Kahn -- Motivic cohomology of smooth geometrically cellular
varieties
K. P. Knudson -- Integral homology of PGL_2 over elliptic curves
E. Peyre -- Application of motivic complexes to negligible
classes
J. Rognes -- Two-primary algebraic K-theory of spaces and related
spaces of symmetries of manifolds
J. Rosenberg -- A mini-course on recent progress in algebraic
K-theory and its relationship with topology and analysis
B. Totaro -- The Chow ring of a classifying space
V. Voevodsky -- Voevodsky's Seattle lectures: K-theory and
motivic cohomology
C. Weibel -- Products in higher Chow groups and motivic
cohomology
Details:
Series: Proceedings of Symposia in Pure Mathematics, Volume: 67
Publication Year: 1999
ISBN: 0-8218-0927-X
Paging: approximately 319 pp.
Binding: Hardcover
Edited by: Jan Felipe van Diejen, Universidad de
Chile, Santiago, Chile,
and Luc Vinet, Universit? de Montr?al, Qu?bec, PQ, Canada
Description
There has been revived interest in recent years in the study of
special functions. Many of the latest advances in the field
were inspired by the works of R. A. Askey and colleagues on basic
hypergeometric series and I. G. Macdonald on orthogonal
polynomials related to root systems. Significant progress was
made by the use of algebraic
techniques involving quantum groups, Hecke algebras, and
combinatorial methods.
The CRM organized a workshop for key researchers in the field to
present an overview of current trends.
This volume consists of the contributions to that workshop.
Topics include basic hypergeometric functions, algebraic and
representation-theoretic methods, combinatorics of symmetric
functions, root systems, and the connections with integrable
systems.
Contents
F. Bergeron and A. M. Garsia -- Science fiction and Macdonald's
polynomials
R. Chouikha -- On the expansion of elliptic functions and
applications
D. V. Chudnovsky and G. V. Chudnovsky -- Generalized
hypergeometric functions-Classification of identities and
explicit rational
approximations W. S. Chung, E. G. Kalnins, and W. Miller, Jr. --
Tensor products of q-superalgebras and q-series identities. I
J. F. van Diejen and J. V. Stokman -- q-Racah polynomials for BC
type root systems C. F. Dunkl -- Intertwining operators
of type B_N R. Floreanini, J. LeTourneux, and L. Vinet --
Symmetries and continuous q-orthogonal polynomials P. G. A.
Floris
-- Addition theorems for spherical polynomials on a family of
quantum spheres F. A. Gr?nbaum and L. Haine -- On a q-analogue
of the string equation and a generalization of the classical
orthogonal polynomials M. E. H. Ismail, D. R. Masson, and S. K.
Suslov
-- The q-Bessel function on a q-quadratic grid D. Kim and D.
Stanton -- Three statistics on lattice paths A. N. Kirillov
-- Quantum Grothendieck polynomials A. N. Kirillov and M. Noumi
-- q-difference raising operators for Macdonald polynomials
and the integrality of transition coefficients B. A. Kupershmidt
-- Great powers of $q$-calculus V. Spiridonov -- q-special
functions: Differential-difference equations, roots of unity, and
all that A. Strasburger -- On algebras of creation and
annihilation operators
Details:
Series: CRM Proceedings & Lecture Notes, Volume: 22
Publication Year: 1999
ISBN: 0-8218-2026-5
Paging: 276 pp.
Binding: Softcover
Edited by: James M. Abello, AT&T Bell
Labs-Research, Florham Park, NJ,
and Jeffrey Scott Vitter, Duke University, Durham, NC
Description
We are especially proud to announce the publication of this
DIMACS book--the 50th volume in this series published by the AMS.
The series was established out of a collaborative venture geared
to unite the cutting-edge research at DIMACS with the resources
at the AMS to produce useful, well-designed, important
mathematical and computational sciences works. This volume is a
hallmark
in this firmly grounded and well-received AMS series.
The AMS's 50th DIMACS volume is also particularly notable at this
time: The year 1999 marks the 10th anniversary of the founding
of DIMACS as a center. Participants in the DIMACS national
research project are Rutgers University, Princeton University,
AT&T Labs-Research, Bell Labs, Telcordia Technologies, and
NEC Research Institute.
The success of the joint publishing venture between the AMS and
DIMACS is excellent. We continue to work concordantly with the
Center to further their goal of playing a key national leadership
role in the development, application, and dissemination of
discrete
mathematics and theoretical computer science. This 50th DIMACS
volume isin celebration of that dynamic, ongoing partnership.
About the book:
Techniques from computer science and mathematics are used to
solve combinatorial problems in designing memory algorithms
when associated data require a hierarchy of storage devices.
These solutions employ "extended memory algorithms".
The input/output (I/O) communication between the levels of the
hierarchy is often a significant bottleneck in applications that
process massive amounts of data. Gains in performance may be
possible by incorporating locality directly into the algorithms
and managing the contents of each storage level.
The relative difference in data access speeds is most apparent
between random access memory and magnetic disks. Therefore,
much research has been devoted to algorithms that focus on the
I/O bottleneck. These algorithms are usually called
"external memory", "out-of-core", or
"I/O algorithms".
This volume presents new research results and current techniques
for the design and analysis of external memory algorithms.
The articles grew out of the workshop,"External Memory
Algorithms and Visualization" held at DIMACS. Leading
researchers were
invited to give lectures and to contribute their work. Topics
presented includeproblems in computational geometry, graph
theory, data compression, disk scheduling, linear algebra,
statistics, software libraries, text and string processing,
visualization, wavelets, and industrial applications.
The vitality of the research and the interdisciplinary nature of
the event produced fruitful ground for the compelling fusion of
ideas
and methods. This volume comprises the rich results that grew out
of that process.
Contents
J. S. Vitter -- External memory algorithms and data structures
P. B. Gibbons and Y. Matias -- Synopsis data structures for
massive data sets
I. Al-Furaih, T. Johnson, and S. Ranka -- Calculating robust
depth measures for large data sets
R. Grossi and G. F. Italiano -- Efficient cross-trees for
external memory
M. R. Henzinger, P. Raghavan, and S. Rajagopalan -- Computing on
data streams
J. Abello, P. M. Pardalos, and M. G. C. Resende -- On maximum
clique problems in very large graphs
A. Crauser, P. Ferragina, K. Mehlhorn, U. Meyer, and E. A. Ramos
-- I/O-optimal computation of segment intersections
L. Arge and P. B. Miltersen -- On showing lower bounds for
external-memory computational geometry problems
S. Toledo -- A survey of out-of-core algorithms in numerical
linear algebra
K.-P. Vo -- Concrete software libraries
K. V. Shvachko -- S(b)-tree library: An efficient way of indexing
data
M. Kallahalla and P. J. Varman -- ASP: Adaptive online parallel
disk scheduling
S. K. Das and M. C. Pinotti -- Efficient schemes for distributing
data on parallel memory systems
Y.-J. Chiang and C. T. Silva -- External memory techniques for
isosurface extraction in scientific visualization
S. T. Leutenegger and K.-L. Ma -- R-tree retrieval of
unstructured volume data for visualization
Index
Details:
Series: DIMACS: Series in Discrete Mathematics and Theoretical
Computer Science, Volume: 50
Publication Year: 1999
ISBN: 0-8218-1184-3
Paging: approximately 297 pp.
Binding: Hardcover
John B. Conway, University of Tennessee, Knoxville, TN
Description
Operator theory is a significant part of many important areas of
modern mathematics: functional analysis, differential equations,
index theory, representation theory,mathematical physics, and
more. This text covers the central themes of operator theory,
presented with the excellent clarity and style that readers have
come to associate with Conway's writing.
Early chapters introduce and review material on C*-algebras,
normal operators, compact operators and non-normal operators.
The topics include the spectral theorem, the functional calculus
and the Fredholm index. Also, some deep connections between
operator theory and analytic functions are presented.
Later chapters cover more advanced topics, such as
representations of C*-algebras, compact perturbations and von
Neumann
algebras. Major results, such as the Sz.-Nagy Dilation Theorem,
the Weyl-von Neumann-Berg Theorem and the classification of
von Neumann algebras, are covered, as is a treatment of Fredholm
theory.These advanced topics are at the heart of current
research.
The last chapter gives an introduction to reflexive subspaces,
i.e., subspaces of operators that are determined by their
invariant
subspaces. These, along with hyperreflexive spaces, are one of
the more successful episodes in the modern study of asymmetric
algebras.
Professor Conway's authoritative treatment makes this a
compelling and rigorous course text, suitable for graduate
students who
have had a standard course in functional analysis.
Contents
Introduction to C*-algebras
Normal operators
Compact operators
Some non-normal operators
More on C*-algebras
Compact perturbations
Introduction to von Neumann algebras
Reflexivity
Bibliography
Index
List of symbols
Details:
Series: Graduate Studies in Mathematics, Volume: 21
Publication Year: 2000
ISBN: 0-8218-2065-6
Paging: 372 pp.
Binding: Hardcover
Gerald Teschl, Institut fur Mathematik, Universitat Wien, Vienna, Austria
View a PDF or PostScript sample for this item.
Description
This volume can serve as an introduction and a reference source
on spectral and inverse spectral theory of Jacobi operators
(i.e., second order symmetric difference operators) and
applications of those theories to the Toda and Kac-van Moerbeke
hierarchy.
Beginning with second order difference equations, the author
develops discrete Weyl-Titchmarsh-Kodaira theory, covering all
classical aspects, such as Weyl $m$-functions, spectral
functions, the moment problem, inverse spectral theory, and
uniqueness
results.
Teschl then investigates more advanced topics, such as locating
the essential, absolutely continuous, and discrete spectrum,
subordinacy, oscillation theory, trace formulas, random
operators, almost periodic operators, (quasi-)periodic operators,
scattering theory, and spectral deformations. Utilizing the Lax
approach, he introduces the Toda hierarchy and its modified
counterpart, the Kac-van Moerbeke hierarchy. Uniqueness and
existence theorems for solutions, expressions for solutions
in terms of Riemann theta functions, the inverse scattering
transform, B?cklund transformations, and soliton solutions are
derived.
This text covers all basic topics of Jacobi operators and
includes recent advances. It is suitable for use as a text at the
advanced
graduate level. (R) Mathematica is a registered trademark of
Wolfram Research Inc.
Contents
Jacobi operators
Jacobi operators
Foundations of spectral theory for Jacobi operators
Qualitative theory of spectra
Oscillation theory
Random Jacobi operators
Trace formulas
Jacobi operators with periodic coefficients
Reflectionless Jacobi operators
Quasi-periodic Jacobi operators and Riemann theta functions
Scattering theory
Spectral deformations-Commutation methods
Completely integrable nonlinear lattices
The Toda system
The initial value problem for the Toda system
The Kac-van Moerbeke system
Notes on literature
Compact Riemann surfaces-A review
Herglotz functions
Jacobi difference equations with Mathematica(R)
Bibliography
Glossary of notations
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 72
Publication Year: 1999
ISBN: 0-8218-1940-2
Paging: 344 pp.
Binding: Hardcover
Alberto Candel, California Institute of
Technology, Pasadena, CA,
and Lawrence Conlon, Washington University, St.
Louis, MO
Description
This is the first of two volumes on the qualitative theory of
foliations. This volume is divided into three parts.
The book is extensively illustrated throughout and provides a
large number of examples.
Part 1 is intended as a "primer" in foliation theory. A
working knowledge of manifold theory and topology is a
prerequisite.
Fundamental definitions and theorems are explained to prepare the
reader for further exploration of the topic. This section
places considerable emphasis on the construction of examples,
which are accompanied by many illustrations.
Part 2 considers foliations of codimension one. Using very
hands-on geometric methods, the path leads to a complete
structure theory (the theory of levels), which wasestablished by
Conlon along with Cantwell, Hector, Duminy, Nishimori,
Tsuchiya, et al. Presented here is the first and only full
treatment of the theory of levels in a textbook.
Part 3 is devoted to foliations of higher codimension, including
abstract laminations (foliated spaces). The treatment
emphasizes the methods of ergodic theory: holonomy-invariant
measures and entropy. Featured are Sullivan's theory
of foliation cycles, Plante's theory of growth of leaves, and the
Ghys, Langevin, Walczak theory of geometric entropy.
This comprehensive volume has something to offer a broad spectrum
of readers: from beginners to advanced students
to professional researchers. Packed with a wealth of
illustrations and copious examples at varying degrees of
difficulty,
this highly-accessible text offers the first full treatment in
the literature of the theory of levels for foliated manifolds of
codimension one. It would make an elegant supplementary text for
a topics course at the advanced graduate level.
Contents
The foundations
Foliated manifolds
Holonomy
Basic constructions
Asymptotic properties
Codimension one
Basic structures
Compact leaves
General position
Generalized Poincar?-Bendixson theory
Foliations without holonomy
Arbitrary codimension
Foliation cycles
Foliated spaces
Growth, invariant measures and geometry of leaves
Entropy of foliations
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics,
Publication Year: 2000
ISBN: 0-8218-0809-5
Paging: 394 pp.
Binding: Hardcover
ISBN: 0-89871-442-7
Several features make this book unique. The first is the
systematic use of bordered matrix methods in the numerical
computation and continuation of various bifurcations. The second
is a detailed treatment of bialternate matrix
products and their Jordan structure. Govaerts discusses their use
in the numerical methods for Hopf and related
bifurcations. A third feature is a unified treatment of
singularity theory, with and without a distinguished bifurcation
parameter, from a numerical point of view. There is also a
discussion of the numerical methods for
symmetry-breaking bifurcations, up to the fundamental cases
covered by the equivariant branching lemma.
Jean Dickinson Gibbons, Ingram Olkin, and Milton Sobel
Classics in Applied Mathematics 26
1999 / xxvi + 569 pages / Softcover / ISBN 0-89871-439-7
There is a dichotomy in modern statistics that distinguishes
between analyses done before an experiment is completed and those
done
afterward. Ranking and selection methods are useful in both of
these categories. The authors provide an alternative to the
overused "testing the
null hypothesis" when what the practitioner really needs is
a method of ranking k given populations, selecting the t best
populations, or some
similar goal. That need and purpose is as important today as when
the subject was first developed nearly 50 years ago.
Contents
Chapter 1: The Philosophy of Selecting and Ordering Populations;
Chapter 2: Selecting the One Best Population for Normal
Distributions with
Common Known Variance; Chapter 3: Selecting the One Best
Population for Other Normal Distribution Models; Chapter 4:
Selecting the
One Best Population Bionomial (or Bernoulli) Distributions;
Chapter 5: Selecting the One Normal Population with the Smallest
Variance;
Chapter 6: Selecting the One Best Category for the Multinomial
Distribution; Chapter 7: Nonparametric Selection Procedures;
Chapter 8:
Selection Procedures for a Design with Paired Comparisons;
Chapter 9: Selecting the Normal Population with the Best
Regression Value;
Chapter 10: Selecting Normal Populations Better than a Control;
Chapter 11: Selecting the t Best Out of k Populations; Chapter
12: Complete
Ordering of k Populations; Chapter 13: Subset Selection (or
Elimination) Procedures; Chapter 14: Selecting the Best Gamma
Population;
Chapter 15: Selection Procedures for Multivariate Normal
Distributions; Appendix A: Tables for Normal Means Selection
Problems;
Appendix B: Figures for Normal Means Selection Problems; Appendix
C: Table of the Cumulative Standard Normal Distribution F(z);
Appendix D: Table of Critical Values for the Chi-Square
Distribution; Appendix E: Tables for Binomial Selection Problems;
Appendix F:
Figures for Binomial Selection Problems; Appendix G: Tables for
Normal Variances Selection Problems; Appendix H: Tables for
Multinomial
Selection Problems; Appendix I: Curtailment Tables for the
Multinomial Selection Problem; Appendix J: Tables of the
Incomplete Beta
Function; Appendix K: Tables for Nonparametric Selection
Problems; Appendix L: Tables for Paired-Comparison Selection
Problems;
Appendix M: Tables for Selecting from k Normal Populations Those
Better Than a Control ; Appendix N: Tables for Selecting the t
Best
Normal Populations; Appendix O: Table of Critical Values of
Fisher's F Distribution; Appendix P: Tables for Complete Ordering
Problems;
Appendix Q: Tables for Subset Selection Problems; Appendix R:
Tables for Gamma Distribution Problems; Appendix S: Tables for
Multivariate Selection Problems; Appendix T: Excerpt of Table of
Random Numbers; Appendix U: Table of Squares and Square Roots;
Bibliography; References for Applications; Index for Data and
Examples; Name Index; Subject Index.