Griebel, Michael; Schweitzer, Marc Alexander (Eds.)

Meshfree Methods for Partial Differential Equations II

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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Ischebeck, Friedrich G., Rao, Ravi A.

Ideals and Reality
Projective Modules and Number of Generators of Ideals

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.

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Naess, Atle

Galileo Galilei: When the World Stood Still

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.

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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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Fried, Michael D., Jarden

Field Arithmetic
Revised and Enlarged

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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Musiela, Marek, Rutkowski, Marek

Martingale Methods in Financial Modelling, 2nd ed.

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.

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Tevelev, Evgueni A.

Projective Duality and Homogeneous Spaces

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.

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