Hardback (ISBN-13: 9780521519861)
Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model equations; this generally requires numerical methods. This book presents numerical methods and associated computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the associated PDE model.
* Includes line-by-line analysis and solutions for computer code associated
with model equations * Offers a detail presentation of ODE/PDE mathematical
models * Methodology covers a broad spectrum of problems in science, engineering
and applied mathematics
1. An introduction to the Method of Lines (MOL); 2. A one-dimensional, linear partial differential equation; 3. Green’s function analysis; 4. Two nonlinear, variable coeffcient, inhomogeneous PDEs; 5. Euler, Navier-Stokes and Burgers equations; 6. The Cubic Schrodinger Equation (CSE); 7. The Korteweg-deVries (KdV) equation; 8. The linear wave equation; 9. Maxwell’s equations; 10. Elliptic PDEs: Laplace's equation; 11. Three-dimensional PDE; 12. PDE with a mixed partial derivative; 13. Simultaneous, nonlinear, 2D PDEs in cylindrical coordinates; 14. Diffusion equation in spherical coordinates; Appendix 1: partial differential equations from conservation principles: the anisotropic diffusion equation; Appendix 2: order conditions for finite difference approximations; Appendix 3: analytical solution of nonlinear, traveling wave partial differential equations; Appendix 4: implementation of time varying boundary conditions; Appendix 5: the DSS library; Appendix 6: animating simulation results.
Series: Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (No. 28)
Hardback (ISBN-13: 9780521847940)
Why didn't the matter in our Universe annihilate with antimatter immediately
after its creation* The study of CP violation may help to answer this fundamental
question. This book presents theoretical tools necessary to understand
this phenomenon. Reflecting the explosion of new results over the last
decade, this second edition has been substantially expanded. It introduces
charge conjugation, parity and time reversal, before describing the Kobayashi-Maskawa
(KM) theory for CP violation and our understanding of CP violation in kaon
decays. It reveals how the discovery of B mesons has provided a new laboratory
to study CP violation with KM theory predicting large asymmetries, and
discusses how these predictions have been confirmed since the first edition
of this book. Later chapters describe the search for a new theory of nature's
fundamental dynamics. This book is suitable for researchers in high energy,
atomic and nuclear physics and the history and philosophy of science.
* Substantially expanded to cover the explosion of new results over the
last decade * Presents the theoretical tools necessary to understand CP
violation, from basic principles to the front-line of research * Suitable
for researchers in high energy, atomic and nuclear physics and the history
and philosophy of science
Foreword; Part I. Basics of CP Violation: 1. Prologue; 2. Prelude: C, P
and T in classical dynamics; 3. C, P and T in non-relativistic quantum
mechanics; 4. C, P and T in relativistic quantum theories; 5. The arrival
of strange particles; 6. Quantum mechanics of neutral particles; Part II.
Theory and Experiments: 7. The quest for CP violation in K decays - a marathon;
8. The KM implementation of CP violation; 9. The theory of KL → ππ decays;
10. Paradigmatic discoveries in B physics; 11. Let the drama unfold - B
CP phenomenology; 12. Rare K and B decays - almost perfect laboratories;
13. CPT violation - could it be in K and B decays*; 14. CP violation in
charm decays - the dark horse; 15. The strong CP problem; Part III. Looking
Beyond the Standard Model: 16. Quest for CP violation in the neutrino sector;
17. Possible corrections to the KM ansatz: right-handed currents and non-minimal
Higgs dynamics; 18. CP violation without nonperturbative dynamics - top
quarks and charged leptons; 19. SUSY - providing shelter for Higgs dynamics;
20. Minimal flavour violation and extra dimensions; 21. Baryogenesis in
the universe; Part IV. Summary: 11. Summary and Perspectives; References;
Index.
Series: Cambridge Tracts in Mathematics (No. 178)
Hardback (ISBN-13: 9780521509770)
Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this book treats positive characteristic phenomena from an analytic viewpoint. Building on the basic objects introduced by L. Carlitz - such as the Carlitz factorials, exponential and logarithm, and the orthonormal system of Carlitz polynomials - the author develops a kind of differential and integral calculi. He also expands on the basics of an analytic theory of (Carlitz's) differential equations, providing a useful foundation for the study of various special functions. The differential calculus is extended to a type of Rota's umbral calculus, and an investigation is made of the corresponding rings of differential operators. A theory of quasi-holonomic modules over these rings, having some common features with holonomic modules in the sense of Bernstein, is also connected to some special functions in the spirit of Zeilberger's theory.
* The first treatment of positive characteristic phenomena from the analytic
viewpoint * Provides a foundation for the study of various special functions
* For researchers and graduate students in mathematical analysis and number
theory
Preface; 1. Orthonormal systems and their applications; 2. Calculus; 3. Differential equations; 4. Special functions; 5. The Carlitz rings; Bibliography; Index.
Hardback (ISBN-13: 9780521518253)
Gilles Kahn was one of the most influential figures in the development of computer science and information technology, not only in Europe but throughout the world. This volume of articles by several leading computer scientists serves as a fitting memorial to Kahn’s achievements and reflects the broad range of subjects to which he contributed through his scientific research and his work at INRIA, the French National Institute for Research in Computer Science and Control. The authors also reflect upon the future of computing: how it will develop as a subject in itself and how it will affect other disciplines, from biology and medical informatics, to web and networks in general. Its breadth of coverage, topicality, originality and depth of contribution, make this book a stimulating read for all those interested in the future development of information technology.
* Consists of 26 essays, each written by leading researchers in their field
* Topics addressed range from semantics, to medical imaging, to bio-informatics,
and beyond * Combines more traditional topics with advanced and contemporary
research in computer science
Preface; List of contributors; 1. Determinacy in a synchronous π-calculus
Roberto Amadio and Mehdi Dogguy; 2. Classical coordination mechanisms in
the chemical model Jean-Pierre Banatre, Pascal Fradet and Yann Radenac;
3. Sequential algorithms as bistable maps Pierre-Louis Curien; 4. The semantics
of dataflow with firing Edward A. Lee and Eleftherios Matsikoudis; 5. Kahn
networks at the dawn of functional programming David B. MacQueen; 6. A
simple type-theoretic language: mini-TT Thierry Coquand, Yoshiki Kinoshita,
Bengt Nordstrom, and Makoto Takeyama; 7. Program semantics and infinite
regular terms Bruno Courcelle; 8. Algorithms for equivalence and reduction
to minimal form for a class of simple recursive equations Bruno Courcelle,
Gilles Kahn, and Jean Vuillemin; 9. Generalized finite developments Jean-Jacques
Levy; 10. Semantics of program representation graphs G. Ramalingam and
Thomas Reps; 11. Tribute to a great meta-technologist - from centaur to
the meta-environment Paul Klint; 12. Towards a theory of document structure
Bengt Nordstrom; 13. Grammars as software libraries Aarne Ranta; 14. The
Leordo computation system Erik Sandewall; 15. Theorem proving support in
programming language semantics Yves Bertot; 16. Nominal verification of
algorithm W Christian Urban and Tobias Nipkow; 17. A constructive denotational
semantics for Kahn networks in Coq Christine Paulin-Mohring; 18. Asclepios:
a research project-team at INRIA for the analysis and simulation of biomedical
images Nicholas Ayache, Olivier Clatz, Herve Delingette, Gregoire Malandain,
Xavier Pennec and Maxime Sermesant; 19. Proxy caching in split TCP: dynamics,
stability and tail asymptotics Francois Baccelli, Giovanna Carofiglio,
and Serguei Foss; 20. Two-by-two static, evolutionary, and dynamic games
Pierre Bernhard and Frederic Hamelin; 21. Reversal strategies for adjoint
algorithms Laurent Hascoet; 22. Reflections on INRIA and the role of Gilles
Kahn Alain Bensoussan; 23. Can a systems biologist fix a tamagotchi* Luca
Cardelli; 24. Computational science: a new frontier for computing Andrew
Herbert; 25. The descendants of centaur: a personal view on Gilles Kahn’s
work Emmanuel Ledinot; 26. The tower of informatic models Robin Milner.
Series: Encyclopedia of Mathematics and its Applications (No. 121)
Hardback (ISBN-13: 9780521873086)
It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches.
* Inclusion of relevant background material makes this suitable as an introduction
for postgraduate students and researchers from other areas * Compiles a
wide range of methods and results, some of which are previously unpublished,
into one single, accessible source * Contains an extensive index, a detailed
table of contents and thorough internal referencing
Preface; Introduction; Part I. Modules: 1. Pp conditions; 2. Purity; 3. Pp pairs and definable subcategories; 4. Pp-types and pure-injectivity; 5. The Ziegler spectrum; 6. Rings of definable scalars; 7. m-dimension and width; 8. Examples; 9. Ideals in mod-R; A. Model theory; Part II. Functors: 10. Finitely presented functors; 11. Serre subcategories and localisation; 12. The Ziegler spectrum and injective functors; 13. Dimensions; 14. The Zariski spectrum and the sheaf of definable scalars; 15. Artin algebras; 16. Finitely accessible and presentable additive categories; 17. Spectra of triangulated categories; B. Languages for definable categories; C. A model theory/functor category dictionary; Part III. Definable categories: 18. Definable categories and interpretation functors; D. Model theory of modules: an update; E. Glossary; Main examples; Bibliography; Index.