Series: Pure and Applied Mathematics Volume: 273
ISBN: 0849337399
Publication Date: 8/24/2005
Number of Pages: 336
Provides a complete treatment of Deligne theory of mixed Hodge
structures
Features an approach that employs recursive arguments on
dimension
Simplifies with easily identifiable and well-defined weight
filtrations
Includes discussion of classical Hodge theory, differential forms
on complex spaces, and mixed Hodge structures on noncompact
spaces
Differential Forms on Singular Varieties: De Rham and Hodge
Theory Simplified uses complexes of differential forms to give a
complete treatment of the Deligne theory of mixed Hodge
structures on the cohomology of singular spaces. This book
features an approach that employs recursive arguments on
dimension and does not introduce spaces of higher dimension than
the initial space. It simplifies the theory through easily
identifiable and well-defined weight filtrations. It also avoids
discussion of cohomological descent theory to maintain
accessibility. Topics include classical Hodge theory,
differential forms on complex spaces, and mixed Hodge structures
on noncompact spaces.
Table of Contents
CLASSICAL HODGE THEORY. Spectral Sequences and Mixed Hodge
Structures. Complex Manifolds, Vector Bundles, Differential Forms.
Sheaves and Cohomology. Harmonic Forms on Hermitian Manifolds.
Hodge Theory on Compact Kahlerian Manifolds. The Theory of
Residues on a Smooth Divisor. Complex Spaces. DIFFERENTIAL FORMS
ON COMPLEX SPACES. The Basic Example. Differential Forms in
Complex Spaces. Mixed Hodge Structures on Compact Spaces. MIXED
HODGE STRUCTURES ON NONCOMPACT SPACES. Residues and Hodge Mixed
Structures: Leray Theory. Residues and Mixed Hodge Structures on
Noncompact Manifolds. Mixed Hodge Structures in Noncompact Spaces:
The Basic Example. Mixed Hodge Structures on Noncompact Singular
Spaces.
Series: Lecture Notes in Pure and Applied Mathematics Volume:
244
ISBN: 082472335X
Publication Date: 8/15/2005
Number of Pages: 284
Features contributions from international experts
Presents articles from two conferences held in Spain and Portugal
in June, 2003
Highlights research results that borrow methods from neighboring
areas, such as combinatorics
Encompasses a variety of topics including blowup algebra, liaison
theory, and reduction of ideals
With International contributors, Commutative Algebra: Geometric,
Homological, Combinatorial, and Computational Aspects features
new research results that borrow methods from neighboring fields
such as combinatorics, homological algebra, polyhedral geometry,
symbolic computation, and topology. This book consists of
articles presented during two conferences held in Spain and
Portugal in June, 2003. It encompasses a variety of topics,
including blowup algebras, Castelnuovo-Mumford regularity,
integral closure and normality, Koszul homology, liaison theory,
multiplicities, polarization, and reductions of ideals. This
comprehensive volume will stimulate further research in the field.
Table of Contents
A Theorem of Eakin and Sathaye and Green's Hyperplane Restriction
Theorem. Liaison of Varieties of Small Dimension and Deficiency
Modules. Regularity Jumps for Powers of Ideals. Integral Closure
of Ideals and Annihilators of Homology. PoincarESeries of
Surface Singularities. Multi-Graded Hilbert Coefficients. Torsion
Freeness and Normality of Blowup Rings of Monomial Ideals.
Monomial Ideals via Square-Free Monomial Ideals. When Does the
Equality I2=QI Hold True in Buchsbaum Rings? Integral Closures of
Ideals in Completions of Regular Local Domains. The Components of
a Variety of Matrices with Square Zero and Submaximal Rank. The
Support of Top Graded Local Cohomology Modules. An Approach to
the Uniform Artin-Rees Theorems from the Notion of Relation Type.
Castelnuovo-Mumford Regularity and Finiteness of Hilbert
Functions. Differential Idealizers and Algebraic Free Divisors.
Gorenstein Rings Call the Tune. On Free Integral Extensions
Generated by One Element. Degeneration of G-Dimension of Modules.
0-19-851620-7
Publication date: 25 August 2005
Clarendon Press 520 pages, 40 halftones, 234mm x 156mm
Description
The second volume of an excellent exposition of the role of
mysticism in mathematics and philosophy
Provides a coherent exposition of Brouwerian topology
Analyses the roots and practice of intuitionism
Fascinating insights into the European mathematical community
Provides an analysis of the role of Dutch academia in
mathematical research
Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the
development of mathematics and in wider Dutch history. A
mathematical genius with strong mystical and philosophical
leanings, he advocated the intuitionist view of mathematics and
science as a constructive mental activity. This drew him into a
discussion with David Hilbert, the leading advocate of the
formalist school, about the nature of mathematics, a debate which
made Brouwer a legend during his lifetime. He also contributed
significantly to research in topology, and was a member of the
socio- linguistic Signific Circle.
As well as his diverse mathematical interests he had a great
impact in wider Dutch society. His keen sense of justice made him
a party in many conflicts, both scientific and political. He
would often be involved in controversial issues, such as the
campaign to undo the boycott of German scientists, and this made
him a figure both of admiration and embarrassment in his native
Holland. Although his abilities won him offers from prestigious
universities such as Berlin and Gottingen, he preferred to stay
in Amsterdam, so that he could pursue a life of quiet
unconventionality in the artist community at Laren.
This book, the second in a two volume set, provides a
sophisticated analysis of this crucial era of mathematical
research, but also gives an important insight into the wider life
of one of the most fascinating characters involved.
Readership: Graduate students and researchers in logic, computer
science, topology, and the history of mathematics. Anyone
interested in nineteenth and twentieth century history of science.
Contents
Preface
12 The Fathers of Dimension
13 Progress, recognition, and frictions
14 From Berlin to Vienna
15 The three Battles
16 The Thirties
17 War and Occupation
18 Postwar Events
19 The travelling Emeritus
20 Appendix
References
Index
Series: Graduate Student Series in Physics
ISBN: 0750304928
Publication Date: 9/1/2004
Number of Pages: 313
This book is devoted to the cosmological implications of the
gauge theories of particle physics and of string theory. It
presumes some prior knowledge of these subjects, such as that
provided in the authors' previous books Introduction to Gauge
Field Theory and Supersymmetric Gauge Field Theory and String
Theory, but it is self-contained. Like the earlier books it is
intended as an introductory textbook for a first course on the
subject at graduate student level.
As it cooled after the hot big bang, it is likely that the
universe passed through a series of phase transitions in which
the successive gauge symmetries of the higher-temperature phase
were spontaneously broken. The survival to the present of relics
of these phase transitions is discussed, as is that of more
generic relics (baryons, neutrinos, axions) and supersymmetric
particles (neutralinos and gravitinos).
Recent observations confirm that the universe is very flat and
extremely homogeneous. The most plausible explanation of this is
that the universe passed through an inflationary era. The
constraints on the presumed underlying field theory are studied
and the possibility of satisfying these in a supersymmetric
theory or in supergravity theory is discussed.
Finally, black hole solutions of the supergravity theory that
approximates string theory at low energies are considered, and
the insight that string theory affords into the microscopic
origin of the Bekenstein-Hawking entropy is discussed.
Cosmology in Gauge Field Theory and String Theory will provide a
modern introduction to these important problems from a particle
physicist's perspective.
Table of Contents
1 The standard model of cosmology
2 Phase transitions in the early universe
3 Topological defects
4 Baryogenesis
5 Relic neutrinos and axions
6 Supersymmetric dark matter
7 Inflationary cosmology
8 Inflation in supergravity
9 Superstring cosmology
10 Black holes in string theory
Index
Series: Statistics and Computing
2nd ed., 2005, XVIII, 694 p. 410 illus., 319 in colour.,
Hardcover
ISBN: 0-387-24544-8
About this book
This book was written for statisticians, computer scientists,
geographers, researchers, and others interested in visualizing
data. It presents a unique foundation for producing almost every
quantitative graphic found in scientific journals, newspapers,
statistical packages, and data visualization systems. While the
tangible results of this work have been several visualization
software libraries, this book focuses on the deep structures
involved in producing quantitative graphics from data. What are
the rules that underlie the production of pie charts, bar charts,
scatterplots, function plots, maps, mosaics, and radar charts?
Those less interested in the theoretical and mathematical
foundations can still get a sense of the richness and structure
of the system by examining the numerous and often unique color
graphics it can produce. The second edition is almost twice the
size of the original, with six new chapters and substantial
revision. Much of the added material makes this book suitable for
survey courses in visualization and statistical graphics.
Table of contents
Introduction.- How to Make a Pie.- Data.- Variables.- Algebra.-
Scales.- Statistics.- Geometry.- Coordinates.- Aesthetics.-
Facets.- Guides.- Space.- Time.- Uncertainty.- Analysis.- Control.-
Automation.- Reader.- Coda.
Series: Algorithms and Combinatorics, Vol. 21
, 2006, XVI, 597 p., Hardcover
ISBN: 3-540-25684-9
About this textbook
This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way. The book contains complete but concise proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added.
"The second edition (with corrections and many updates) of this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization."
Table of contents
Preface.- Introduction.- Graphs.- Linear Programming.- Linear Programming Algorithms.- Integer Programming.- Spanning Trees and Arborescences.- Shortest Paths.- Network Flows.- Minimum Cost Flows.- Maximum Matchings.- Weighted Matching.- b-Matchings and T-Joins.- Matroids.- Generalizations of Matroids.- NP-Completeness.- Approximation Algorithms.- The Knapsack Problem.- Bin Packing.- Multicommodity Flows and Edge-Disjoint Paths.- Network Design Problems.- The Traveling Salesman Problem.- Facility Location.- Notation Index.- Author Index.- Subject Index.
Series: Mathematiques et Applications, Vol. 49
2006, XIII, 175 p. 21 illus., Softcover
ISBN: 3-540-27238-0
About this textbook
Cet ouvrage presente les modeles d'interaction onde-matiere faisant intervenir une description quantique de la matiere (optique quantique), ainsi que des modeles classiques qui en sont derives. L'objectif est de decrypter pour des lecteurs mathematiciens ces modeles habituellement decrits dans des livres de physique et de donner les resultats mathematiques et les methodes numeriques existants. Ces resultats, reflets de sujets de recherche actuels faisant intervenir des outils mathematiques varies, sont detailles pour etre accessibles a des etudiants ayant un niveau DEA. Les parties numeriques de ce livre peuvent egalement interesser des physiciens desirant effectuer des simulations.
Table of contents
I Le modele de Maxwell-Bloch: Contexte physique.- Modele physique.- Analyse mathematique.- Simulations numeriques.- Bibliographie.- II Une hierarchie de modeles: Equations de taux.- Expressions classiques de la polarisation.- Equations d'enveloppe.- Bibliographie.- III Considerations numeriques: Discretisation des equations de Bloch.- Discretisation des equations de Maxwell.- Couplage Maxwell-Bloch.- Modeles classiques.- Bibliographie.- Tendances pour l'avenir.- Bibliographie de la conclusion.- Appendices : A Constantes physiques.- B Mesures physiques.- C Notations.- Bibliographie des appendices.- Table des figures.- Index.
Summary
In most physical, chemical, biological and economic phenomena it is quite natural to assume that the system not only depends on the present state but also on past occurrences. These circumstances are mathematically described by partial differential equations with delay. This book presents, in a systematic fashion, how delay equations can be studied in Lp-history spaces.
Appendices offering supplementary information and a comprehensive index make this book an ideal introduction and research tool for mathematicians, chemists, biologists and economists.
Details
ISBN: 1-56881-243-4
Year: 2005
Format: Hardcover
Pages: 272