Series: London Mathematical Society Lecture Note Series (No. 355)
Paperback (ISBN-13: 9780521715140)
3 half-tones 35 exercises 30 figures
Page extent: 164 pages
Size: 228 x 152 mm
Methods of non-equilibrium statistical mechanics play an increasingly important role in modern turbulence research, yet the range of relevant tools and methods is so wide and developing so fast that until now there has not been a single book covering the subject. As an introduction to modern methods of statistical mechanics in turbulence, this volume rectifies that situation. The book comprises three harmonised lecture courses by world class experts in statistical physics and turbulence: John Cardy introduces Field Theory and Non-Equilibrium Statistical Mechanics; Gregory Falkovich discusses Turbulence Theory as part of Statistical Physics; and Krzysztof Gawedzki examines Soluble Models of Turbulent Transport. To encourage readers to deepen their understanding of the theoretical material, each chapter contains exercises with solutions. Essential reading for students and researchers in the field of theoretical turbulence, this volume will also interest any scientist or engineer who applies knowledge of turbulence and non-equilibrium physics to their work.
* Each of the three essays gives a self-contained introduction to a topic
in modern non-equilibrium statistical physics important for theoretical
turbulence * Contains cutting edge research - this is the first time this
material has appeared in book form * Written by leaders in the field; each
essay includes exercises with solutions to help deepen theoretical understanding
1. Preface; 2. Introduction to turbulence theory Gregory Falkovich; 3. Soluble models of turbulent transport Krzysztof Gawedzki; 3. Reaction-diffusion processes John Cardy.
Series: London Mathematical Society Lecture Note Series (No. 356)
Paperback (ISBN-13: 9780521728669)
The arithmetic properties of modular forms and elliptic curves lie at the heart of modern number theory. This book develops a generalisation of the method of Euler systems to a two-variable deformation ring. The resulting theory is then used to study the arithmetic of elliptic curves, in particular the Birch and Swinnerton-Dyer (BSD) formula. Three main steps are outlined: the first is to parametrise ebigf cohomology groups using (deformations of) modular symbols. Finiteness results for big Selmer groups are then established. Finally, at weight two, the arithmetic invariants of these Selmer groups allow the control of data from the BSD conjecture. As the first book on the subject, the material is introduced from scratch; both graduate students and professional number theorists will find this an ideal introduction. Material at the very forefront of current research is included, and numerical examples encourage the reader to interpret abstract theorems in concrete cases.
* Self-contained; develops the material from basic level so accessible
to first year graduate students * Exercises, diagrams and worked examples
aid understanding and develop skills * Presents material at the very forefront
of current research, equipping the reader to understand theorems at the
cutting edge
Introduction; List of notations; 1. Background; 2. p-adic L-functions and Zeta-elements; 3. Cyclotomic deformations of modular symbols; 4. A user's guide to Hida theory; 5. Crystalline weight deformations; 6. Super Zeta-elements; 7. Vertical and half-twisted arithmetic; 8. Diamond-Euler characteristics: the local case; 9. Diamond-Euler characteristics: the global case; 10. Two-variable Iwasawa theory of elliptic curves; A. The primitivity of Zeta elements; B. Specialising the universal path vector; C. The weight-variable control theorem; Bibliography.
Series: London Mathematical Society Student Texts (No. 73)
Paperback (ISBN-13: 9780521719773)
Hardback (ISBN-13: 9780521895453)
40 line diagrams 1 table 55 graphs 175 exercises
95 figures 61 worked examples
Page extent: 232 pages
Size: 228 x 152 mm
Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.
* Only prerequisite is one semester of abstract algebra: accessible to
undergraduate and beginning graduate students * Over 150 exercises and
95 figures aid understanding and develop geometric intuition * Modern approach
with many contemporary results presented
Preface; 1. Cayley's theorems; 2. Groups generated by reflections; 3. Groups acting on trees; 4. Baumslag-Solitar groups; 5. Words and Dehn's word problem; 6. A finitely-generated, infinite, Torsion group; 7. Regular languages and normal forms; 8. The Lamplighter group; 9. The geometry of infinite groups; 10. Thompson's group; 11. The large-scale geometry of groups; Bibliography; Index.
Series: Encyclopedia of Mathematics and its Applications (No. 122)
Hardback (ISBN-13: 9780521854191)
12 line diagrams 180 exercises 12 figures
Page extent: 500 pages
Size: 228 x 152 mm
Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Eulerfs famous paper eContinued Fractions, Observationf is included as an Addendum.
* Considers the modern state of continued fractions and orthogonal polynomials
from Euler's point of view, giving a full account of his work on the subject
* Outlines Brouncker's formula; Euler's discoveries of the Gamma and Beta
functions; Markoff's Theorem on the Lagrange spectrum and its relation
with Jean Bernoulli sequences; Brouncker's method as a solution to Fermatfs
question on Pell's equation * Contains the first English translation of
Euler's eContinued Fractions, Observationf, 1739, with comments relating
it to Brounckerfs proof
Preface; 1. Continued fractions: real numbers; 2. Continued fractions: Algebra; 3. Continued fractions: Analysis; 4. Continued fractions: Euler; 5. Continued fractions: Euler's Influence; 6. P-fractions; 7. Orthogonal polynomials; 8. Orthogonal polynomials on the unite circle; A1. Continued fractions, Observations; Bibliography; Index.
Series: London Mathematical Society Lecture Note Series (No. 353)
Paperback (ISBN-13: 9780521718219)
9 half-tones 2 tables 25 figures 30 worked examples
Page extent: 384 pages
Size: 228 x 152 mm
Presenting important trends in the field of stochastic analysis, this collection of thirteen articles provides an overview of recent developments and new results. Written by leading experts in the field, the articles cover a wide range of topics, ranging from an alternative set-up of rigorous probability to the sampling of conditioned diffusions. Applications in physics and biology are treated, with discussion of Feynman formulas, intermittency of Anderson models and genetic inference. A large number of the articles are topical surveys of probabilistic tools such as chaining techniques, and of research fields within stochastic analysis, including stochastic dynamics and multifractal analysis. Showcasing the diversity of research activities in the field, this book is essential reading for any student or researcher looking for a guide to modern trends in stochastic analysis and neighbouring fields.
* Written by leading experts; showcases diversity of research in stochastic
analysis * Many state-of-the-art survey articles offer valuable source
of inspiration for future research * Ideal for students or researchers
working in probability and stochastic analysis; also treats applications
in physics and biology
Preface; Part I. Foundations and techniques in stochastic analysis: 1.
Random variables - without basic space Gotz Kersting; 2. Chaining techniques
and their application to stochastic flows Michael Scheutzow; 3. Ergodic
properties of a class of non-Markovian processes Martin Hairer; 4. Why
study multifractal spectra* Peter Morters; Part II. Construction, simulation,
discretisation of stochastic processes: 5, Construction of surface measures
for Brownian motion Nadia Sidorova and Olaf Wittich; 6. Sampling conditioned
diffusions Martin Hairer, Andrew Stuart and Jochen VoÀ; 7. Coding and
convex optimization problems Steffen Dereich; Part III. Stochastic analysis
in mathematical physics: 8. Intermittency on catalysts Jurgen Gartner,
Frank den Hollander and Gregory Maillard; 9. Stochastic dynamical systems
in infinite dimensions Salah-Eldin A. Mohammed; 10. Feynman formulae for
evolutionary equations Oleg G.Smolyanov; 11. Deformation quantization in
infinite dimensional analysis Remi Leandre; Part IV. Stochastic analysis
in mathematical biology: 12. Measure-valued diffusions, coalescents and
genetic inference Matthias Birkner and Jochen Blath; 13. How often does
the ratchet click* Facts, heuristics, asymptotics Alison M. Etheridge,
Peter Pfaffelhuber and Anton Wakolbinger.