Benedicks, Michael; Jones, Peter W.; Smirnov, Stanislav (Eds.)
Perspectives in Analysis
Essays in Honor of Lennart Carleson's 75th Birthday
Series: Mathematical Physics Studies, Vol. 27
2005, XIV, 378 p. 9 illus. with DVD-Rom., Hardcover
ISBN: 3-540-30432-0
About this book
The purpose of the essays collected in this volume is to consider
the future of analysis and related areas of physics. It is
published in honor of Lennart Carleson, who has devoted much of
his career to broadening the scope of harmonic analysis. Written
by leading mathematicians and mathematical physicists, the
articles should inspire new avenues of research. The collection
shows the impressive relationship between physical intuition and
mathematical analysis. These essays give confidence that the
meeting ground between these areas of mathematics and physics
will only grow more fertile in the future.
Table of contents
The Rosetta Stone of L-Functions.- New Encounters in
Combinatorial Number Theory: From the Kakeya Problem to
Cryptography.- Perspectives and Challenges to Harmonic Analysis
and Geometry in High Dimensions: Geometric Diffusions as a Tool
for Harmonic Analysis and Structure Definition of Data.- Open
Questions on the Mumford-Shah Functional.- Multi-Scale Modeling.-
Mass in Quantum Yang-Mills Theory (Comment on a Clay Millennium
Problem).- On Scaling Properties of Harmonic Measure.- The
Heritage of Fourier.- The Quantum-Mechanical Many-Body Problem:
The Bose Gas.- Meromorphic Inner Functions, Toeplitz Kernels and
the Uncertainty Principle.- Heat Measures and Unitarizing
Measures for Berezinian Representations on the Space of Univalent
Functions in the Unit Disk.- On Local and Global Existence and
Uniqueness of Solutions of the 3D Navier-Stokes System on R3.-
Analysis on Lie Groups: An Overview of Some Recent Developments
and Future Prospects.- Encounters with Science.
Sidharth, B.G. (Ed.)
Great Ideas of Physics
Series: Fundamental Theories of Physics, Vol. 149
2006, Approx. 245 p., Hardcover
ISBN: 1-4020-4359-7
About this book
The B.M. Birla Science Centre, part of the Birla Group (a
multinational conglomerate which is over 100 years old), has
blossomed into India’s foremost institution for the
dissemination of science. Shortly after its inauguration in 1985
the Centre started a series of lectures by Nobel Laureates and
other scientists of international renown, usually in Physics and
Astronomy, sometimes in Life Sciences and Chemistry.
The present collection mostly consists of lectures on frontier
topics in Physics and Astronomy. The transcript of each lecture
is preceded by a short introduction to, and biography of, the
Nobel Laureate/Scientist in question.
The lectures are aimed at, and accessible to, a wide non-specialist
but higher educated audience.
Table of contents
Introduction; B.G. Sidharth. Fifty Years of Cosmology; Fred Hoyle.
AstroParticle Physics; Abdus Salam. Science as an Adventure;
Hermann Bondi. The Early Universe; William Fowler. The Long-Term
Future of Particle Accelerators; Simon van der Meer. Energy and
Evolution; George Porter. The Wonders of Pulsars; Antony Hewish.
Is the Future Given? Changes in our Description of Nature; Ilya
Prigogine. Bubbles, Foams and other Fragile Objects; J.-P. De
Gennes. Beyond the Standard Model: Will it be the Theory of
Everything? Yuval Ne’eman. Living Joyfully with Complexity in
Chemistry and Culture; Roald Hoffmann. A Confrontation with
Infnity; Gerard ’tHooft. The Creative and Unpredictable
Interaction of Science and Technology; Charles Townes. The Link
Between Neutrino Masses and Proton Decay in Supersymmetric
Unification; Jogesh Pati. The Nature of Discovery in Physics;
Douglas D. Osheroff. Symmetry in the Micro World ? A Conversation
with Nobel Laureate Eugene Wigner; B.G. Sidharth
Komjath, Peter, Totik, Vilmos
Problems and Theorems in Classical Set Theory
Series: Problem Books in Mathematics
2006, Approx. 525 p., Hardcover
ISBN: 0-387-30293-X
Due: January 2006
About this textbook
This volume contains a variety of problems from classical set
theory. Many of these problems are also related to other fields
of mathematics, including algebra, combinatorics, topology and
real analysis. The problems vary in difficulty, and are organized
in such a way that earlier problems help in the solution of later
ones. For many of the problems, the authors also trace the
history of the problems and then provide proper reference at the
end of the solution.
Table of contents
Foreword.- Problems: Operations on sets.- Countability.-
Equivalence.- Continuum.- Sets of reals and real functions.-
Ordered sets.- Order types.- Ordinals.- Ordinal arithmetic.-
Cardinals.- Partially ordered sets.- Transfinite enumeration.-
Euclidean spaces.- Zorn's lemma.- Hamel bases.- The continuum
hypothesis.- Ultrafilters on w.- Families of sets.- The Banach-Tarski
paradox.- Stationary sets in w1.- Stationary sets in larger
cardinals.- Canonical functions.- Infinite graphs.- Partition
relations.- \triangle systems.- Set mappings.- Trees.- The
measure problem.- Stationary sets.- The axiom of choice.- Well
founded sets and the axiom of foundation.- Solutions: Operations
on sets.- Countability.- Equivalence.- Continuum.- Sets of reals
and real functions.- Ordered sets.- Order types.- Ordinals.-
Ordinal arithmetic.- Cardinals.- Partially ordered sets.-
Transfinite enumeration.- Euclidean spaces.- Zorn's lemma.- Hamel
bases.- The continuum hypothesis.- Ultrafilters on w Families of
sets The Banach-Tarski paradox Stationary sets in w1.- Stationary
sets in larger cardinals.- Canonical functions.- Infinite graphs.-
Partition relations.- \triangle-systems.- Set mappings.- Trees.-
The measure problem.- Stationary sets.- The axiom of choice Well
founded sets and the axiom of foundation.- Appendix.- Glossary of
Concepts.- Glossary of Symbols.- Index.
Erdmann, Karin, Wildon, Mark
Introduction to Lie Algebras
Series: Springer Undergraduate Mathematics Series
2006, Approx. 260 p. 10 illus., Softcover
ISBN: 1-84628-040-0
Due: February 2006
About this textbook
Lie groups and Lie algebras have become essential to many parts
of mathematics and theoretical physics, with Lie algebras a
central object of interest in their own right.
Based on a lecture course given to fourth-year undergraduates,
this book provides an elementary introduction to Lie algebras. It
starts with basic concepts. A section on low-dimensional Lie
algebras provides readers with experience of some useful examples.
This is followed by a discussion of solvable Lie algebras and a
strategy towards a classification of finite-dimensional complex
Lie algebras. The next chapters cover Engel's theorem, Lie's
theorem and Cartan's criteria and introduce some representation
theory. The root-space decomposition of a semisimple Lie algebra
is discussed, and the classical Lie algebras studied in detail.
The authors also classify root systems, and give an outline of
Serre's construction of complex semisimple Lie algebras. An
overview of further directions then concludes the book and shows
the high degree to which Lie algebras influence present-day
mathematics.
The only prerequisite is some linear algebra and an appendix
summarizes the main facts that are needed. The treatment is kept
as simple as possible with no attempt at full generality.
Numerous worked examples and exercises are provided to test
understanding, along with more demanding problems, several of
which have solutions.
Introduction to Lie Algebras covers the core material required
for almost all other work in Lie theory and provides a self-study
guide suitable for undergraduate students in their final year and
graduate students and researchers in mathematics and theoretical
physics.
Table of contents
Introduction.- Ideals and Homomorphisms.- Low Dimensional Lie
Algebras.- Solvable Lie Algebras and a Rough Classification.-
Subalgebras of gl(V).- Engel’s Theorem and Lie’s Theorem.-
Some Representation Theory.- Representations of sl (2,C).- Cartan’s
Criteria.- The Root Space Decomposition.- Root Systems.- The
Classical Lie Algebras.- The Classification of Root Systems.-
Simple Lie Algebras.- Further Directions.- Appendices: Linear
Algebra; Weyl's Theorem; Cartan Subalgebras; Weyl Groups.-
Solutions to Selected Exercises.- Bibliography.- Index.
Calderer, Maria-Carme T.; Terentjev, Eugene M. (Eds.)
Modeling of Soft Matter
Series: The IMA Volumes in Mathematics and its Applications,
Vol. 141
2005, X, 250 p., Hardcover
ISBN: 0-387-29167-9
Due: January 2006
About this book
The physics of soft matter - materials such as elastomers, gels,
foams and liquid crystals - is an area of intense interest and
contemporary study. Moreover, soft matter plays a role in a wide
variety of important processes and application. For example, gel
swelling and dynamics are an essential part of many biological
and individual processes, such as motility mechanisms in bacteria
and the transport and absorption of drugs. Ferroelectrics, liquid
crystals, and elastomers are being used to design ever faster
switching devices. Experimental studies, such as scattering,
optical and electron microscopy, have provided a great deal of
detailed information on structures. But the integration of
mathematical modeling and analysis with experimental approaches
promises to greatly increase our understanding of structure-property
relationships and constitutive equations. The workshop on
Modeling of Soft Matter has taken such an integrated approach. It
brought together researchers in applied and computational
mathematical fields such as differential equations, dynamical
systems, analysis, and fluid and solid mechanics, and scientists
and engineers from a variety of disciplines relevant to soft
matter physics. An important outcome of the workshop has been to
identify beautiful and novel scientific problems arising in soft
matter that are in need of mathematical modeling and appear
amenable to it and so to set the stage for further research. This
volume presents a collection of papers representing the key
aspects of the topics discussed at depth in the course of the
workshop.
Table of contents
Foreword.- Preface.- An energetic variational formulation with
phase field methods for interfacial dynamics of complex fluids:
advantages and challenges.- Non-equilibrium statistical mechanics
of nematic liquids.- Anisotropy and heterogeneity of nematic
polymer nano-composite lm properties.- Non-Newtonian constitutive
equations using the orientational order parameter.- Surface order
forces in nematic liquid crystals.- Modelling line tension in
wetting.- Variational problems and modeling of ferroelectricity
in chiral smectic C liquid crystals.- Stripe-domains in nematic
elastomers: old and new.- Numerical simulation for the mesoscale
deformation of disordered reinforced elastomers.- Stress
transmission and isostatic states of non-rigid particulate
systems.- List of workshop participants