Series : Lecture Notes in Computational Science and
Engineering , Vol. 43
2005, Approx. 300 p., Softcover
ISBN: 3-540-23026-2
Due: January 2005
About this book
The numerical treatment of partial differential equations with
particle methods and meshfree discretization techniques is a very
active research field both in the mathematics and engineering
community. Due to their independence of a mesh, particle schemes
and meshfree methods can deal with large geometric changes of the
domain more easily than classical discretization techniques.
Furthermore, meshfree methods offer a promising approach for the
coupling of particle models to continuous models. This volume of
LNCSE is a collection of the papers from the proceedings of the
Second International Workshop on Meshfree Methods held in
September 2003 in Bonn. The articles address the different
meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their
application in applied mathematics, physics and engineering. The
volume is intended to foster this new and exciting area of
interdisciplinary research and to present recent advances and
results in this field.
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Series : Springer Monographs in Mathematics
2005, XIII. 313 p., Hardcover
ISBN: 3-540-23032-7
Due: December 7, 2004
About this book
This monograph tells the story of a philosophy of J-P. Serre and
his vision of relating that philosophy to problems in affine
algebraic geometry. It gives a lucid presentation of the Quillen-Suslin
theorem settling Serre's conjecture. The central topic of the
book is the question of whether a curve in $n$-space is a set-theoretic
complete intersection, depicted by the central theorems of
Ferrand, Szpiro, Cowsik-Nori, Mohan Kumar, Boratynski. The book
gives a comprehensive introduction to basic commutative algebra,
together with the related methods from homological algebra, which
will enable students who know only the fundamentals of algebra to
enjoy the power of using these tools. At the same time, it also
serves as a valuable reference for the research specialist and as
potential course material, because the authors present, for the
first time in book form, an approach here that is an intermix of
classical algebraic K-theory and complete intersection
techniques, making connections with the famous results of Forster-Swan
and Eisenbud-Evans. A study of projective modules and their
connections with topological vector bundles in a form due to
Vaserstein is included. Important subsidiary results appear in
the copious exercises. Even this advanced material, presented
comprehensively, keeps in mind the young student as potential
reader besides the specialists of the subject.
Table of contents
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2005, Approx. 260 p. 21 illus., 18 in colour., Hardcover
ISBN: 3-540-21961-7
Due: November 2004
About this biography
"I, Galileo, son of the late Vincenzio Galilei, Florentine,
aged seventy years ...kneeling before you Most Eminent and
Reverend Lord Cardinals ...I abjure, curse, detest the aforesaid
errors and heresies."Galileo Galilei in Rome, 22 June 1633,
before the men of the Inquisition.In the small village of
Arcetri, on a wooded hillside just south of Florence, an old man
sat writing his will. He had to make a journey to Rome and wanted
to be prepared for every eventuality. If the plague did not get
him on the road, the strain of travelling might finish him off;
in addition he had been ill most of the autumn, with dizziness,
stomach pains and a serious hernia. And even if he survived these
difficulties, and the cold winter wind from the Apennines did not
give him pneumonia, he had no idea what awaited him in Rome, only
that his arrival was unlikely to be celebrated with a special
mass. The mathematician and physicist Galileo Galilei is one of
the most famous scientists of all times. The story of his life
and times, of his epoch-making experiments and discoveries, of
his stubbornness and pride, of his patrons in the house of
Medici, of his enemies and friends in their struggle for truth -
all is brought vividly to life in this book. Atle NA|ss has
written a gripping account of one of the great figures in
European history.He was awarded the Brage Prize, the most
prestigious literary prize in Norway.
Table of contents
Prologue: A journey to Rome 5 The musician's son 7 A gifted young
Tuscan 11 To Rome and the Jesuits 14 A Surveyor of Inferno 17 The
spheres from the tower 19 From Pisa to Padua 22 Signs in the sky
24 De Revolutionibus Orbium Coelestium 28 Lecturer and designer
31 A professor's commitments 33 Modern physics is born 35 A new
star in an unchanging sky? 38 Drawing close to a court 40 The
balls fall into place 43 The Roman style 45 The tube with the
long perspective 47 A new world 49 Jupiter's sons 53 Johann
Kepler, Imperial Mathematician 56 Several signs in the sky 60
Friendship and power 64 A dispute about objects that float in
water 68 Sun, stand thou still upon Gibeon! 71 The letter to
Castelli 74 "How to go to heaven, not how the heavens go"
77 Foolish and absurd in philosophy, formally heretical 80 The
hammer of the heretics 83 Deaths and omens 86 Comets portend
disaster 91 Weighing the words of others on gold-scales 95 A
marvellous combination of circumstances 99 War and heresy 102
European power struggle and Roman nephews 105 The old and the new
107 "An advantageous decree" 111 Two wise men - and a
third 113 The Inquisition's chambers 117 Diplomacy in the time of
the plague 122 An order from the top 126 "Nor further to
hold, teach, or defend it in any way whatsoever" 131
Convinced with reasons 135 "I, Galileo Galilei" 139
Eternity 143 A death and two new sciences 148 The meeting with
infinity 152 "That universe ... is not any greater than the
space I occupy" 156 Epilogue 159 Postscript 164 Appendix 166
Sources 167 Name Index 172 References 175
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Series : Ergebnisse der Mathematik und ihrer Grenzgebiete. 3.
Folge / A Series of Modern Surveys in Mathematics , Vol. 11
2nd rev. and enlarged ed., 2005, Approx. 770 pp., Hardcover
ISBN: 3-540-22811-X
Due: October 18, 2004
About this book
Field Arithmetic explores Diophantine fields through their
absolute Galois groups. This largely self-contained treatment
starts with techniques from algebraic geometry, number theory,
and profinite groups. Graduate students can effectively learn
generalizations of finite field ideas. We use Haar measure on the
absolute Galois group to replace counting arguments. New
Chebotarev density variants interpret diophantine properties.
Here we have the only complete treatment of Galois
stratifications, used by Denef and Loeser, et al, to study Chow
motives of Diophantine statements. Progress from the first
edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed)
fields. We once believed PAC fields were rare. Now we know they
include valuable Galois extensions of the rationals that present
its absolute Galois group through known groups. PAC fields have
projective absolute Galois group. Those that are Hilbertian are
characterized by this group being pro-free. These last decade
results are tools for studying fields by their relation to those
with projective absolute group. There are still mysterious
problems to guide a new generation: Is the solvable closure of
the rationals PAC; and do projective Hilbertian fields have pro-free
absolute Galois group (includes Shafarevich's conjecture)?
Table of contents
Infinite Galois Theory and Profinite Groups. - Valuations and
Linear Disjointness. - Algebraic Function Fields of One Variable.
- The Riemann Hypothesis for Function Fields. - Plane Curves. -
The Chebotarev Density Theorem. - Ultraproducts. - Decision
Procedures. - Algebraically Closed Fields. - Elements of
Algebraic Geometry. - Pseudo Algebraically Closed Fields. -
Hilbertian Fields. - The Classical Hilbertian Fields. -
Nonstandard Structures. - Nonstandard Approach to Hilbert's
Irreducibility Theorem. - Galois Groups over Hilbertian Fields. -
Free Profinite Groups. - The Haar Measure. - Effective Field
Theory and Algebraic Geometry. - The Elementary Theory of e-Free
PAC Fields. - Problems of Arithmetical Geometry. - Projective
Groups and Frattini Covers. - PAC Fields and Projective Absolute
Galois Groups. - Frobenius Fields. - Free Profinite Groups of
Infinite Rank. - Random Elements in Free Profinite Groups. -
Omega-Free PAC Fields.
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Series : Stochastic Modeling and Applied Probability , Vol. 36
(Series title changed from "Applications of Mathematics")
2005, Approx. 530 p. , Hardcover
ISBN: 3-540-20966-2
Due: November 2004
About this book
In the 2nd edition some sections of Part I are omitted for better
readability, and a brand new chapter is devoted to volatility
risk. As a consequence, hedging of plain-vanilla options and
valuation of exotic options are no longer limited to the Black-Scholes
framework with constant volatility. The theme of stochastic
volatility also reappears systematically in the second part of
the book, which has been revised fundamentally, presenting much
more detailed analyses of the various interest-rate models
available: the author's perspective throughout is that the choice
of a model should be based on the reality of how a particular
sector of the financial market functions, never neglecting to
examine liquid primary and derivative assets and identifying the
sources of trading risk associated. This long-awaited new edition
of an outstandingly successful, well-established book,
concentrating on the most pertinent and widely accepted modelling
approaches, provides the reader with a text focused on practical
rather than theoretical aspects of financial modelling.
Table of contents
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Series : Encyclopaedia of Mathematical Sciences , Vol. 133
Volume package: Enc.Mathematical Sciences Invariant Theory
2005, Approx. 260 p., Hardcover
ISBN: 3-540-22898-5
Due: November 3, 2004
About this book
Projective duality is a very classical notion naturally arising
in various areas of mathematics, such as algebraic and
differential geometry, combinatorics, topology, analytical
mechanics, and invariant theory, and the results in this field
were until now scattered across the literature. Thus the
appearance of a book specifically devoted to projective duality
is a long-awaited and welcome event. Projective Duality and
Homogeneous Spaces covers a vast and diverse range of topics in
the field of dual varieties, ranging from differential geometry
to Mori theory and from topology to the theory of algebras. It
gives a very readable and thorough account and the presentation
of the material is clear and convincing. For the most part of the
book the only prerequisites are basic algebra and algebraic
geometry. This book will be of great interest to graduate and
postgraduate students as well as professional mathematicians
working in algebra, geometry and analysis.
Table of contents