Series: Cambridge Studies in Advanced Mathematics (No. 104)
Hardback (ISBN-13: 9780521863209 | ISBN-10: 0521863201)
Many problems in science and engineering are described by
nonlinear differential equations, which can be notoriously
difficult to solve. Through the interplay of topological and
variational ideas, methods of nonlinear analysis are able to
tackle such fundamental problems. This graduate text explains
some of the key techniques in a way that will be appreciated by
mathematicians, physicists and engineers. Starting from
elementary tools of bifurcation theory and analysis, the authors
cover a number of more modern topics from critical point theory
to elliptic partial differential equations. A series of
Appendices give convenient accounts of a variety of advanced
topics that will introduce the reader to areas of current
research. The book is amply illustrated and many chapters are
rounded off with a set of exercises.
* Contains both classical and more modern advanced techniques and
is an ideal introduction to Nonlinear Analysis
* Ideal for graduate students and academic researchers in
Mathematics and Physics
* Series of Appendices introduces reader to advanced areas of
current research
* Discusses both topological and variational tools
Contents
Preface; 1. Preliminaries; Part I. Topological Methods: 2. A
primer on bifurcation theory; 3. Topological degree, I; 4.
Topological degree, II: global properties; Part II. Variational
Methods, I: 5. Critical points: extrema; 6. Constrained critical
points; 7. Deformations and the Palais-Smale condition; 8. Saddle
points and min-max methods; Part III. Variational Methods, II: 9.
Lusternik-Schnirelman theory; 10. Critical points of even
functionals on symmetric manifolds; 11. Further results on
Elliptic Dirichlet problems; 12. Morse theory; Part IV.
Appendices: Appendix 1. Qualitative results; Appendix 2. The
concentration compactness principle; Appendix 3. Bifurcation for
problems on Rn; Appendix 4. Vortex rings in an ideal fluid;
Appendix 5. Perturbation methods; Appendix 6. Some problems
arising in differential geometry; Bibliography; Index.
Series: London Mathematical Society Lecture Note Series (No.
339)
Paperback (ISBN-13: 9780521694698 | ISBN-10: 0521694698)
'Groups St Andrews 2005' was held in the University of St Andrews
in August 2005 and this first volume of a two-volume book
contains selected papers from the international conference. Four
main lecture courses were given at the conference, and articles
based on their lectures form a substantial part of the
Proceedings. This volume contains the contributions by Peter
Cameron (Queen Mary, London) and Rostislav Grogorchuk (Texas
A&M, USA). Apart from the main speakers, refereed survey and
research articles were contributed by other conference
participants. Arranged in alphabetical order, these articles
cover a wide spectrum of modern group theory. The regular
Proceedings of Groups St Andrews conferences have provided
snapshots of the state of research in group theory throughout the
past 25 years. Earlier volumes have had a major impact on the
development of group theory and it is anticipated that this
volume will be equally important.
* Contains expository articles by leading mathematicians in group
theory
* Forms part of an extensive four-yearly series of such volumes
which have shaped the direction of research in group theory
* Provides a snapshot of the state of research in group theory
Contents
Introduction; 1. Aspects of infinite permutation groups Peter J.
Cameron; 2. Self-similarity and branching in group theory
Rostislav Grigorchuk and Zoran Sunic; 3. On surface groups:
motivating examples in combinatorial group theory Peter
Ackermann, Benjamin Fine and Gerhard Rosenberger; 4. Nilpotent p-algebras
and factorized p-groups Bernhard Amberg and Lev Kazarin; 5.
Classification of finite groups by the number of element
centralizers Ali Reza Ashrafi and Bijan Taeri; 6. Algorithmic use
of the Mal'cev correspondence Bjoern Assmann; 7. Minimal but
inefficient presentations for semi-direct products of finite
cyclic monoids Firat Ates and A. Sinan C evik; 8. The modular
isomorphism problem for finite p-groups with a cyclic subgroup of
index p2 Czeslaw Baginski and Alexander Konovalov; 9. On one-generated
formations A. Ballester-Bolinches, Clara Calvo and R. Esteban-Romero;
10. New results on products of finite groups A. Ballester-Bolinches,
John Cossey and M. C. Pedraza-Aguilera; 11. Radical locally
finite T-groups A. Ballester-Bolinches, H. Heineken and Tatiana
Pedraza; 12. Explicit tilting complexes for the Broue conjecture
on 3-blocks Ayala Bar-Ilan, Tzviya Berrebi, Genadi Chereshnya,
Ruth Leabovich, Mikhal Cohen and Mary Schaps; 13. Conjugacy
classes of p-regular elements in p-solvable groups Antonio
Beltran and Maria Jose Felipe; 14. An algorithm for the unit
group of the Burnside ring of a finite group Robert Boltje and
Gotz Pfeiffer; 15. Integral group ring of the first Mathieu
simple group Victor Bovdi and Alexander Konovalov; 16. Embedding
properties in direct products B. Brewster, A. Martinez-Pastor and
M. D. Perez-Ramos; 17. Malcev presentations for subsemigroups of
groups - a survey Alan J. Cain; 18. Finite groups with extremal
conditions on sizes of conjugacy classes and on degrees of
irreducible characters David Chillag and Marcel Herzog; 19.
Conjugacy class structure in simple algebraic groups Martin Cook;
20. On automorphisms of products of groups Jill Dietz; 21. Linear
groups with infinite central dimension Martyn R. Dixon and Leonid
A. Kurdachenko; 22. G-automata, counter languages and the Chomsky
hierarchy Murray Elder; 23. An embedding theorem for groups
universally equivalent to free nilpotent groups Benjamin Fine,
Anthony M. Gaglione and Dennis Spellman; 24. Irreducible word
problems in groups Ana R. Fonseca, Duncan W. Parkes and Richard M.
Thomas; 25. Recent growth results Eric M. Freden and Teresa
Knudson.
Series: London Mathematical Society Lecture Note Series (No.
340)
Paperback (ISBN-13: 9780521694704 | ISBN-10: 0521694701)
'Groups St Andrews 2005' was held in the University of St Andrews
in August 2005 and this second volume of a two-volume book
contains selected papers from the international conference. Four
main lecture courses were given at the conference, and articles
based on their lectures form a substantial part of the
Proceedings. This volume contains the contributions by John
Meakin (Lincoln, Nebraska) and Akos Seress (Ohio State). Apart
from the main speakers, refereed survey and research articles
were contributed by other conference participants. Arranged in
alphabetical order, these articles cover a wide spectrum of
modern group theory. The regular Proceedings of Groups St Andrews
conferences have provided snapshots of the state of research in
group theory throughout the past 25 years. Earlier volumes have
had a major impact on the development of group theory and it is
anticipated that this volume will be equally important.
* Contains expository articles by leading mathematicians in group
theory
* Forms part of an extensive four-yearly series of such volumes
which have shaped the direction of research in group theory
* Provides a snapshot of the state of research in group theory
Contents
Introduction; 1. Groups and semigroups: connections and contrasts
John Meakin; 2. Toward the classification of s-arc transitive
graphs Akos Seress; 3. Non-cancellation group computation for
some finitely generated nilpotent groups Habtay Ghebrewold; 4.
Permutation and quasi-permutation representations of the
Chevalley groups Maryam Ghorbany; 5. The shape of solvable groups
with odd order S. P. Glasby; 6. Embedding in finitely presented
lattice-ordered groups: explicit presentations for constructions
A. M. W. Glass, Vincenzo Marra and Daniele Mundici; 7. A note on
abelian subgroups of p-groups George Glauberman; 8. On kernel
flatness Akbar Golchin; 9. On proofs in finitely presented groups
George Havas and Colin Ramsay; 10. Computing with 4-Engel groups
George Havas and M. R. Vaughan-Lee; 11. On the size of the
commutator subgroup in finite groups Marcel Herzog, Gil Kaplan
and Arieh Lev; 12. Groups of infinite matrices Waldemar
Holubowski; 13. Triply factorised groups and nearrings Peter
Hubert; 14. On the space of cyclic trigonal Riemann surfaces of
genus 4 Milagros Izquierdo and Daniel Ying; 15. On simple Kn-groups
for n = 5, 6 A. Jafarzadeh and A. Iranmanesh; 16. Products of
Sylow subgroups and the solvable radical Gil Kaplan and Dan Levy;
17. On commutators in groups Luise-Charlotte Kappe and Robert
Fitzgerald Morse; 18. Inequalities for the Baer invariant of
finite groups Saeed Kayvanfar; 19. Automorphisms with
centralizers of small rank Evgeny Khukhro and Victor Mazurov; 20.
2-signalizers and normalizers of Sylow 2-subgroups in finite
simple groups Anatoly S. Kondratiev and Victor D. Mazurov; 21. On
properties of abnormal and pronormal subgroups in some infinite
groups Leonid A. Kurdachenko, Javier Otal and Igor Ya. Subbotin;
22. P-localizing group extensions Karl Lorensen; 23. On the n-covers
of exceptional groups of Lie type Maria Silvia Lucido; 24.
Positively discriminating groups O. Macedonska; 25. Automorphism
groups of some chemical graphs G. A. Moghani, A. R. Ashrafi and M.
R. Admadi; 26. On c-normal subgroups of some classes of finite
groups Z. Mostaghim; 27. Fong characters and their fields of
values Lucia Sanus; 28. Arithmetical properties of finite groups
W. J. Shi; 29. On prefrattini subgroups of finite groups: a
survey X. Soler-Escriva; 30. Frattini extensions and class field
theory Th. Weigel; 31. The nilpotency class of groups with fixed
point free automorphisms of prime order Lawrence Wilson.
Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-13: 9780521866965 | ISBN-10: 0521866960)
Functional integration successfully entered physics as path
integrals in the 1942 Ph.D. dissertation of Richard P. Feynman,
but it made no sense at all as a mathematical definition. Cartier
and DeWitt-Morette have created, in this book, a new approach to
functional integration. The book is self-contained: mathematical
ideas are introduced, developed generalised and applied. In the
authors' hands, functional integration is shown to be a robust,
user-friendly and multi-purpose tool that can be applied to a
great variety of situations, for example: systems of
indistinguishable particles; Aharanov-Bohm systems;
supersymmetry; non-gaussian integrals. Problems in quantum field
theory are also considered. In the final part the authors outline
topics that can be profitably pursued using material already
presented.
* A mathematician and a physicist, with a mutual interest in each
other's disciplines, use their complementary interests and
expertise to illuminate the powerful technique of functional
integration
* Functional integration is applied to a great variety of systems
and shown to be a robust, user-friendly and multipurpose tool
* Suitable for graduate theoretical physicists wanting to deepen
their understanding of the functional integration technique
Contents
Part I. The Physical and Mathematical Environment: 1. The
physical and mathematical environment; Part II. Quantum Mechanics:
2. First lesson: Gaussian integrals; 3. Selected examples; 4.
Semiclassical expansion - WKB; 5. Semiclassical expansion -
beyond WKB; 6. Quantum dynamics: path integrals and operator
formalism; Part III. Methods from Differential Geometry: 7.
Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10.
Grassmann analysis: applications; 11. Volume elements,
divergences, gradients; Part IV. Non-Gaussian Applications: 12.
Poisson processes in physics; 13. A mathematical theory of
Poisson processes; 14. First exit time - energy problems; Part V.
Problems in Quantum Field Theory: 15. Renormalization 1: an
introduction; 16. Renormalization 2: scaling; 17. Renormalization
3: combinatorics Marcus Bery; 18. Volume elements in quantum
field theory Bryce DeWitt; Part VI. Projects: 19. Projects;
Appendix A. Forward and backward integrals: spaces of pointed
paths; Appendix B. Product integrals; Appendix C. A compendium of
Gaussian integrals; Appendix D. Wick calculus Alexander Wurm;
Appendix E. Jacobi operator; Appendix F. Change of variables of
integration; Bibliography; Index.
Hardback (ISBN-13: 9780521854528 | ISBN-10: 0521854520)
Critical phenomena is one of the most exciting areas of modern
physics. This book provides a thorough but economic introduction
into the principles and techniques of the theory of critical
phenomena and the renormalization group, from the perspective of
modern condensed matter physics. Assuming basic knowledge of
quantum and statistical mechanics, the book discusses phase
transitions in magnets, superfluids, superconductors, and gauge
field theories. Particular attention is given to modern topics
such as gauge field fluctuations in superconductors, the
Kosterlitz-Thouless transition, duality transformations, and
quantum phase transitions - all of which are at the forefront of
today's physics research. This book contains numerous problems of
varying degrees of difficulty, with solutions. These problems
provide readers with a wealth of material to test their
understanding of the subject. It is ideal for graduate students
and more experienced researchers in the fields of condensed
matter physics, statistical physics, and many-body physics.
* Has a straightforward and economic style of presentation
allowing readers to quickly get to the essence of the material
* Includes a modern selection of topics including several not
found in other books
* Contains fully solved and original problems
Contents
1. Introduction; 2. Ginzburg-Landau-Wilson theory; 3.
Renormalization group; 4. Superconducting transition; 5. Near
lower critical dimension; 6. Kosterlitz-Thouless transition; 7.
Duality in higher dimensions; 8. Quantum phase transitions;
Appendix A. Hubbard-Stratonovich transformation; Appendix B.
Linked-cluster theorem; Appendix C. Gauge fixing for long-range
order; Appendix D. Bibliography; Index.