This book provides an introduction to representations of both
finite and compact groups. The proofs of the basic results are
given for the finite case, but are so phrased as to hold without
change for compact topological groups with an invariant integral
replacing the sum over the group elements as an averaging tool.
Among the topics covered are the relation between representations
and characters, the construction of irreducible representations,
induced representations and Frobenius reciprocity. Special
emphasis is given to exterior powers, with the symmetric group Sn
as an illustrative example. The book concludes with a chapter
comparing the representations of the finite group SL2(p) and the
non-compact Lie group SL2(?).
Contents:
Basic Representation Theory-I
Basic Representation Theory-II
Induced Representations and Their Characters
Multilinear Algebra
Representations of Compact Groups
Lie Groups
SL2(?)
Readership: Advanced undergraduates and graduate students in
algebra.
156pp Pub. date: Oct 2004
ISBN 1-86094-482-5
ISBN 1-86094-484-1(pbk)
Series : Algebras and Applications , Vol. 4
2004, XXII, 484 p., Hardcover
ISBN: 1-4020-2028-7
About this book
This book covers the beautiful theory of resolutions of surface
singularities in characteristic zero. The primary goal is to
present in detail, and for the first time in one volume, two
proofs for the existence of such resolutions. One construction
was introduced by H.W.E. Jung, and another is due to O. Zariski.
Jung's approach uses quasi-ordinary singularities and an explicit
study of specific surfaces in affine three-space. In particular,
a new proof of the Jung-Abhyankar theorem is given via
ramification theory. Zariski's method, as presented, involves
repeated normalisation and blowing up points. It also uses the
uniformization of zero-dimensional valuations of function fields
in two variables, for which a complete proof is given. Despite
the intention to serve graduate students and researchers of
Commutative Algebra and Algebraic Geometry, a basic knowledge on
these topics is necessary only. This is obtained by a thorough
introduction of the needed algebraic tools in the two appendices.
Table of contents
Preface. Note to the Reader. Terminology. I: Valuation Theory. 1.
Marot Rings. 2. Manis Valuation Rings. 3. Valuation Rings and
Valuations. 4. The Approximate Theorem for Independent Valuations.
5. Extensions of Valuations. 6. Extending Valuations to Algebraic
Overfields. 7. Extensions of Discrete Valuations. 8. Ramification
Theory of Valuations. 9. Extending Valuations to Non-Algebraic
Overfields. 10. Valuations of Algebraic Function Fields. 11.
Valuations Dominating a Local Domain. II: One-Dimensional
Semilocal Cohen-Macaulay Rings. 1. Transversal Elements. 2.
Integral Closure of One-Dimensional Semilocal Cohen-Macaulay
Rings. 3. One-Dimensional Analytically Unramified and
Analytically Irreducible CM-Rings. 4. Blowing up Ideals. 5.
Infinitely Near Rings. III: Differential Modules and Ramification.
1. Introduction. 2. Norms and Traces. 3. Formally Unramified and
Ramified Extensions. 4. Unramified Extensions and Discriminants.
5. Ramification for Quasilocal Rings. 6. Integral Closure and
Completion. IV: Formal and Convergent Power Series Rings. 1.
Formal Power Series Rings. 2. Convergent Power Series Rings. 3.
Weierstras Preparation Theorem. 4. The Category of Formal and
Analytic Algebras. 5. Extensions of Formal and Analytic Algebras.
V: Quasiordinary Singularities. 1. Fractionary Power Series. 2.
The Jung-Abhyankar Theorem: Formal Case. 3. The Jung-Abhyankar
Theorem: Analytic Case. 4. Quasiordinary Power Series. 5. A
Generalized Newton Algorithm. 6. Strictly Generated Semigroups.
VI: The Singularity Zq = XYp. 1. Hirzebruch-Jung Singularities. 2.
Semigroups and Semigroup Rings. 3. Continued Factions. 4. Two-Dimensional
Cones. 5. Resolution of Singularities. VII: Two-Dimensional
Regular Local Rings. 1. Ideal Transform. 2. Quadratic Transforms
and Ideal Transforms. 3. Complete Ideals. 4. Factorization of
Complete Ideals. 5. The Predecessors of a Simple Ideal. 6.
Uniformization. 7. Resolution of Surface Singularities II:
Blowing up and Normalizing. Appendices. A: Results from Classical
Algebraic Geometry. 1. Generalities. 2. Affine and Finite
Morphisms. 3. Products. 4. Proper Morphisms. 5. Algebraic Cones
and Projective Varieties. 6. Regular and Singular points. 7.
Normalization of a Variety. 8. Desingularization of a Variety. 9.
Dimension of Fibres. 10. Quasifinite Morphisms and Ramification.
11. Divisors. 12. Some Results on Projections. 13. Blowing up. 14.
Blowing up: the Local Rings. B: Miscellaneous Results. 1. Ordered
Abelian Groups. 2. Localization. 3. Integral Extensions. 4. Some
Results on Graded Rings and Modules. 5. Properties of the Rees
Ring. 6. Integral Closure of Ideals. 7. Decomposition Group and
Inertia Group. 8. Decomposable Rings. 9. The Dimension Formula.
10. Miscellaneous Results. Bibliography. Index of Symbols. Index.
Series : NATO Science Series II: Mathematics, Physics and
Chemistry , Vol. 182
2005, VII, 432 p., Hardcover
ISBN: 1-4020-2945-4
ISBN: 1-4020-2946-2 Paper ed.
About this book
This book offers a modern updated review on the most important
activities in today dynamical systems and statisitical mechanics
by some of the best experts in the domain. It gives a
contemporary and pedagogical view on theories of classical and
quantum chaos and complexity in hamiltonian and ergodic systems
and their applications to anomalous transport in fluids, plasmas,
oceans and atom-optic devices and to control of chaotic transport.
The book is issued from lecture notes of the International Summer
School on "Chaotic Dynamics and Transport in Classical and
Quantum Systems" held in Cargese (Corsica) 18th to the 30th
August 2003. It reflects the spirit of the School to provide
lectures at the post-doctoral level on basic concepts and tools.
The first part concerns ergodicity and mixing, complexity and
entropy functions, SRB measures, fractal dimensions and
bifurcations in hamiltonian systems. Then, models of dynamical
evolutions of transport processes in classical and quantum
systems have been largly explained. The second part concerns
transport in fluids, plasmas and reacting media. On the other
hand, new experiments of cold optically trapped atoms and
electrodynamics cavity have been thoroughly presented. Finally,
several papers bears on synchronism and control of chaos. The
target audience of the proceedings are physicists ,
mathematicians and all scientists involved in Chaos and Dynamical
Systems Theory and their fondamental applications in Physics and
in the Science of Complex and Nonlinear phenomena.
Table of contents
Content: Part I : Theory P. Collet ; A SHORT ERGODIC THEORY
REFRESHER M. Courbage; Notes on Spectral Theory, Mixing and
Transport V. Affraimovich, L. Glebsky:; Complexity, Fractal
Dimensions and Topological Entropy in Dynamical Systems G.M.
Zaslavsky, V. Afraimovich: WORKING WITH COMPLEXITY FUNCTIONS G.
Gallavotti; SRB distribution for Anosov maps P. Gaspard;
DYNAMICAL SYSTEMS THEORY OF IRREVERSIBILITY W.T. Strunz; ASPECTS
OF OPEN QUANTUM SYSTEM DYNAMICS E. Shlizerman, V. R. Kedar;
ENERGY SURFACES AND HIERARCHIES OF BIFURCATIONS. M. Combescure;
Phase-Space Semiclassical Analysis.Around Semiclassical Trace
Formulae Part II : Applications A. Kaplan et al; ATOM-OPTICS
BILLIARDS F. Family et al; CONTROL OF CHAOS AND SEPARATION OF
PARTICLES IN INERTIA RATCHETS F. Bardou; FRACTAL TIME RANDOM WALK
AND SUBRECOIL LASER COOLING CONSIDERED AS RENEWAL PROCESSES WITH
INFINITE MEAN WAITING TIMES X. Leoncini et al; ANOMALOUS
TRANSPORT IN TWO-DIMENSIONAL PLASMA TURBULENCE E. Ott et al; THE
ONSET OF SYNCHRONISM IN GLOBALLY COUPLED ENSEMBLES OF CHAOTIC AND
PERIODIC DYNAMICAL UNITS A.Iomin, G.M. Zaslavsky; QUANTUM
BREAKING TIME FOR CHAOTIC SYSTEMS WITH PHASE SPACE STRUCTURES S.V.Prants;
HAMILTONIAN CHAOS AND FRACTALS IN CAVITY QUANTUM ELECTRODYNAMICS
M. Cencini et al; INERT AND REACTING TRANSPORT M. A. Zaks;
ANOMALOUS TRANSPORT IN STEADY PLANE FLOWS OF VISCOUS FLUIDS J. Le
Sommer, V. Zeitlin; TRACER TRANSPORT DURING THE GEOSTROPHIC
ADJUSTMENT IN THE EQUATORIAL OCEAN A. Ponno; THE FERMI-PASTA-ULAM
PROBLEM IN THE THERMODYNAMIC LIMIT
235 pages 15 line diagrams 150 exercises 15 figures 80 worked
examples
Hardback | October 2004
ISBN:0-88385-737-5
This book is a collection of materials gathered by the author
while teaching real analysis over a period of years. It is
intended for use as a supplement to a traditional analysis
textbook, or to provide material for seminars or independent
study in analysis and its historical development. The book
includes historical and biographical information, a wide range of
problem types, selected readings on a variety of topics, and many
references for additional study. Since all these materials are
collected into a single book, teachers and students can easily
choose items most suitable for their purpose. Teachers may use
the book as a supplement to their courses, while students may
read much of the book on their own. No other book has been
written specifically as a supplement for a real analysis course.
Contents
1. Review of calculus; 2. Analysis problems; 3. Essays; 4.
Selected readings; Annotated bibliography; Additional references;
Index.
Reviews
eThe book offers even more than its title suggests: a true
trove of resources for students (and their teachers) who face the
exciting - but often rough - passage from the routine
calculations of elementary calculus to the deeper arguments and
insights of real analysis. There are gems here for average
students who need review; for the quickest students who need
mathematical challenges; for teachers who need ideas; and for
everyone with a taste for mathematical highlights and culture.f
Paul Zorn, St Olaf College
eBrabenec has provided a rich smorgasbord of mathematical
analysis - including a host of problems, historical essays, and
selected readings-from which no one should go away hungry.f
William Dunham, Muhlenberg College
Print ISBN: 0-8247-4059-9
Series Volume: 264
This item is part of the Pure and Applied Mathematics series.
Description
This Second Edition contains an up-to-date discussion of interval
methods for solving systems of nonlinear equations and global
optimization problems. The latter can be unconstrained or have
inequality and/or equality constraints. Provided algorithms are
guaranteed to find and bound all solutions to these problems
despite bounded errors in data, in approximations, and from use
of rounded arithmetic.
This edition expands and improves various aspects of its
forerunner and features significant new discussions, such as
those on the use of consistency methods to enhance algorithm
performance. It is shown that proof of existence and uniqueness
of solutions can be obtained as a simple byproduct of computing a
solution.
Employing a closed set-theoretic foundation for interval
computations, Global Optimization Using Interval Analysis, Second
Edition simplifies algorithm construction and increases
generality of interval arithmetic.
Providing methods for solving perturbed systems of nonlinear
equations and optimization problems?and including problems
containing integers and nondifferentiable functions?this
reference/text authoritatively informs nonlinear mathematical
analysts, applied mathematicians, operations theorists, hardware
and software engineers, programmers, and graduate-level students
in these disciplines.
Table of Contents
Foreword
Preface to the Second Edition
Preface to the First Edition
Introduction
Interval Numbers and Arithmetic
Functions of Intervals
Closed Interval Systems
Linear Equations
Inequalities
Taylor Series and Slope Expansions
Quadratic Equations and Inequalities
Nonlinear Equations of One Variable
Consistencies
Systems of Nonlinear Equations
Unconstrained Optimization
Constrained Optimization
Inequality Constrained Optimization
Equality Constrained Optimization
The Full Monty
Perturbed Problems and Sensitivity Analysis
Miscellany
References
Index