Preface 1
Foreword 3
Samegai's Waters 5
K. Ardakov and K. A. Brown
Ring-Theoretic Properties of Iwasawa Algebras: A Survey 7--33
G. Banaszak, W. Gajda, P. Krason
On the Image of l-Adic Galois Representations for Abelian
Varieties of Type I and II 35--75
Siegfried Bocherer, A. A. Panchishkin
Admissible p-adic Measures Attached to Triple Products of
Elliptic Cusp Forms 77--132
David Burns and Matthias Flach
On the Equivariant Tamagawa Number Conjecturefor Tate Motives,
Part II. 133--163
David Burns and Otmar Venjakob
On the Leading Terms of Zeta Isomorphisms and
p-Adic L-functions in Non-Commutative Iwasawa Theory 165--209
Kevin Buzzard and Frank Calegari
The 2-adic Eigencurve is Proper. 211--232
L. Clozel, E. Ullmo
Equidistribution Adelique des Tores et Equidistribution des
Points CM 233--260
Robert Coleman and Ken McMurdy
Fake CM and the Stable Model of X_0(Np^3) 261--300
Daniel Delbourgo
Lambda-Adic Euler Characteristics of Elliptic Curves 301--323
Ehud de Shalit
Coleman Integration Versus
Schneider Integration on Semistable Curves 325--334
Ralph Greenberg
On The Structure of Certain Galois Cohomology Groups 335--391
Michael Harris, Jian-Shu Li, Christopher M. Skinner
p-Adic L-Functions for Unitary Shimura Varieties
I: Construction of the Eisenstein Measure 393--464
Haruzo Hida
Anticyclotomic Main Conjectures 465--532
Frazer Jarvis
Optimal Levels for Modular Mod 2 Representations over Totally
Real Fields 533--550
Kazuya Kato
Universal Norms of p-Units in Some Non-Commutative Galois
Extensions 551--565
Shinichi Kobayashi
An Elementary Proof of the Mazur-Tate-Teitelbaum Conjecture for
Elliptic Curves 567--575
Barry Mazur, William Stein, John Tate
Computation of p-Adic Heights and Log Convergence 577--614
Robert Pollack and Tom Weston
Kida's Formula and Congruences 615--630
P. Schneider, J. Teitelbaum
Banach-Hecke Algebras and p-Adic Galois Representations 631--684
Anthony J. Scholl
Higher Fields of Norms and (phi,Gamma)-Modules 685--709
Joseph H. Silverman
Divisibility Sequences and Powers of Algebraic Integers 711--727
Richard Taylor
On the Meromorphic Continuation of Degree Two L-Functions 729--779
J. Tilouine
Siegel Varieties and p-Adic Siegel Modular Forms 781--817
J.-P. Wintenberger
On p-Adic Geometric Representations of G_Q 819--827
Hardback (ISBN-13: 9780521858410)
The past decade has witnessed dramatic developments in the field
of theoretical physics. This book is a comprehensive introduction
to these recent developments. It contains a review of the
Standard Model, covering non-perturbative topics, and a
discussion of grand unified theories and magnetic monopoles. It
introduces the basics of supersymmetry and its phenomenology, and
includes dynamics, dynamical supersymmetry breaking, and electric-magnetic
duality. The book then covers general relativity and the big bang
theory, and the basic issues in inflationary cosmologies before
discussing the spectra of known string theories and the features
of their interactions. The book also includes brief introductions
to technicolor, large extra dimensions, and the Randall-Sundrum
theory of warped spaces. This will be of great interest to
graduates and researchers in the fields of particle theory,
string theory, astrophysics and cosmology. The book contains
several problems, and password protected solutions will be
available to lecturers at www.cambridge.org/9780521858410.
* Provides reader with tools to confront limitations of the
Standard Model
* Includes several exercises and problems
* Solutions are available to lecturers at www.cambridge.org/9780521858410
Contents
Part I. Effective Field Theory: The Standard Model,
Supersymmetry, Unification: 1. Before the Standard Model; 2. The
Standard Model; 3. Phenomenology of the Standard Model; 4. The
Standard Model as an effective field theory; 5. Anomalies.
instantons and the Strong CP Problem; 6. Grand unification; 7.
Magnetic monopoles and solitons; 8. Technicolor: a first attempt
to explain hierarchies; Part II. Supersymmetry: 9. Supersymmetry;
10. A first look at supersymmetry breaking; 11. The minimal
supersymmetry Standard Model; 12. Supersymmetric grand
unification; 13. Supersymmetric dynamics; 14. Dynamical
supersymmetry breaking; 15. Theories with more than four
conserved supercharges; 16. More supersymmetric dynamics; 17. An
introduction to general relativity; 18. Cosmology; 19.
Astroparticle physics and inflation; Part III. String Theory: 20.
Introduction; 21. The Bosonic string; 22. The superstring; 23.
The heterotic string; 24. Effective actions on ten dimensions; 25.
Compactification of string theory; 26. Compactification of
strings; 27. Dynamics of strong theory at weak coupling; 28.
Beyond weak coupling: non-perturbative string theory; 29. Large
and warped extra dimensions; 30. Coda: where are we headed?; Part
IV. The Appendices: Appendix A. Two component spinors; Appendix B.
Goldstone?s theorem and the pi mesons; Appendix C. Some practice
with the path integral in field theory; Appendix D. The beta-function
in supersymmetric Yang-Mills theory; Index.
Series: Chapman & Hall/CRC Applied Mathematics &
Nonlinear Science Volume: 10
ISBN: 1584886633
Publication Date: 11/2/2006
Number of Pages: 528
Provides a large collection of exact solutions of a wide class of
nonlinear evolution PDEs
Includes many applications from the areas of fluid mechanics,
reaction-diffusion, thin film theory, wave propagation, and gas
dynamics
Supplies numerous open-ended mathematical problems of principal
interest, including blow-up aspects, applications to moving-mesh
methods, and discrete operators
Contains standard nonlinear models as well as new examples, such
as modifications of thin film, nonlinear dispersion, and Harry
Dym equations with nonlinearities
Features exact solutions on invariant subspaces for some
unharmonic lattices
Exact Solutions and Invariant Subspaces of Nonlinear Partial
Differential Equations in Mechanics and Physics is the first book
to provide a systematic construction of exact solutions via
linear invariant subspaces for nonlinear differential operators.
Acting as a guide to nonlinear evolution equations and models
from physics and mechanics, the book focuses on the existence of
new exact solutions on linear invariant subspaces for nonlinear
operators and their crucial new properties.
This practical reference deals with various partial differential
equations (PDEs) and models that exhibit some common nonlinear
invariant features. It begins with classical as well as more
recent examples of solutions on invariant subspaces. In the
remainder of the book, the authors develop several techniques for
constructing exact solutions of various nonlinear PDEs, including
reaction-diffusion and gas dynamics models, thin-film and
Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton)
equations, KdV-type and Harry Dym models, quasilinear magma
equations, and Green-Naghdi equations. Using exact solutions,
they describe the evolution properties of blow-up or extinction
phenomena, finite interface propagation, and the oscillatory,
changing sign behavior of weak solutions near interfaces for
nonlinear PDEs of various types and orders.
The techniques surveyed in Exact Solutions and Invariant
Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics serve as a preliminary introduction to the
general theory of nonlinear evolution PDEs of different orders
and types.
Contents
Series: Cambridge Monographs on Applied and Computational Mathematics (No. 24)
Hardback (ISBN-13: 9780521865593)
The goal of learning theory is to approximate a function from sample values. To attain this goal learning theory draws on a variety of diverse subjects, specifically statistics, approximation theory, and algorithmics. Ideas from all these areas blended to form a subject whose many successful applications have triggered a rapid growth during the last two decades. This is the first book to give a general overview of the theoretical foundations of the subject emphasizing the approximation theory, while still giving a balanced overview. It is based on courses taught by the authors, and is reasonably self-contained so will appeal to a broad spectrum of researchers in learning theory and adjacent fields. It will also serve as an introduction for graduate students and others entering the field, who wish to see how the problems raised in learning theory relate to other disciplines.
* Balanced view, with rigorous approach to issues of practical importance
* First book to adopt the approximation theory viewpoint
* Will appeal to mathematicians as well as statisticians and computer scientists
Contents
Preface; Foreword; 1. The framework of learning; 2. Basic hypothesis spaces; 3. Estimating the sample error; 4. Polynomial decay approximation error; 5. Estimating covering numbers; 6. Logarithmic decay approximation error; 7. On the bias-variance problem; 8. Regularization; 9. Support vector machines for classification; 10. General regularized classifiers; Bibliography; Index.