The calculus of variations is one of the oldest subjects in
mathematics, yet is very much alive and is still evolving.
Besides its mathematical importance and its links to other
branches of mathematics, such as geometry or differential
equations, it is widely used in physics, engineering, economics
and biology.
This book serves both as a guide to the expansive existing
literature and as an aid to the non-specialist Emathematicians,
physicists, engineers, students or researchers Ein discovering
the subjects most important problems, results and techniques.
Despite the aim of addressing non-specialists, mathematical rigor
has not been sacrificed; most of the theorems are either fully
proved or proved under more stringent conditions.
The book, containing more than seventy exercises with detailed
solutions, is well designed for a course both at the
undergraduate and graduate levels.
Contents:
Preliminaries
Classical Methods
Direct Methods
Regularity
Minimal Surfaces
Isoperimetric Inequality
Solutions to the Exercises
Readership: Graduate students in analysis and differential
equations.
240pp Pub. date: Nov 2004
ISBN 1-86094-499-X
ISBN 1-86094-508-2(pbk)
This volume is a collection of dedicated reviews covering all
aspects of theoretical high energy physics and some aspects of
solid state physics. Some of the papers are broad reviews of
topics that span the entire field while others are surveys of
authorsf personal achievements. This is the most comprehensive
review collection reflecting state of the art at the end of 2004.
An important and unique aspect is a special effort the authors
have invested in making the presentation pedagogical.
Contents:
SL(2,Z) Action on Three-Dimensional Conformal Field Theories with
Abelian Symmetry (E Witten)
The Search for a Holographic Dual to AdS3xS3xS3xS1
Chern?Simons Gauge Theory and the AdS3/CFT2 Correspondence (S
Gukov et al.)
Spinning Strings and AdS/FT Duality (A A Tseytlin)
TASI 2003 Lectures on AdS/CFT (J Maldacena)
The Three-String Vertex for a Plane-Wave Background (J H Schwarz)
A New Hat or the c=1 Matrix Model (M R Douglas et al.)
Small Instantons, Little Strings and Free Fermions (A Losev et al.)
AdS and dS Entropy from String Junctions or the Function of
Junction Conjunctions (E Silverstein)
Low-Dimensional Sisters of Seiberg?Witten Effective Theory (A V
Smilga)
From Super-Yang?Mills Theory to QCD: Planar Equivalence and Its
Implications (A Armoni et al.)
This is How It Was c (I Kogan)
Readership: Upper-level undergraduates, graduates, researchers,
academics, theorists in high energy physics, string theory,
quantum chromodynamics, solid state theory.
2000pp (approx.) Pub. date: Scheduled Spring 2005
ISBN 981-238-955-5(set)
This book focuses on a prototype of creative causal processes
termed BIOS and how the concept can be applied to the physical
world, in medicine and in social science. This book presents
methods for identifying creative features in empirical data;
studies showing biotic patterns in physical, biological, and
economic processes; mathematical models of bipolar (positive and
negative) feedback that generate biotic patterns. These studies
support the hypothesis that natural processes are creative (not
determined) and causal (not random) and that bipolar feedback
plays a major role in their evolution. Simple processes precede,
coexist, constitute and surround the complex systems they
generate (priority of the simple). In turn, complex processes
feedback and transform simpler ones (supremacy of the complex).
Contents:
Empirical:
Research Program: A Science of Creation
Mathematical Ideas: Bios and Biotic Feedback (with L Kauffman)
Methods and Empirical Studies: Bios Data Analysis:
Diversification, Asymmetry, Phase Plane of Opposites, Repetition,
Rise and Fall Measures of Information (with M Patel)
Trigonometric Analysis of Opposites (with L Carlson-Sabelli)
Novelty, Causation, and Recurrence (Isometry Method), Complexes:
Recurrence and Wavelet Plots, Simplicity and Nonrandom Complexity
(with A Sugerman)
The Biotic Pattern of Heart Rate Variation
The Biotic Expansion of the Universe
Novelty in DNA
A Theory of Natural Creation:
Mathematics as Natural Science
Bios Hypothesis
Creation Theory (action, opposition, modules and systems)
Mathematical Genesis (lattice, group and topology)
Co-creation:
Biotic Thermodynamics
The Infinite Attractor of Evolution
Biotic Evolution
Biotic Earth, Biotic Climate
Biotic Processes in Economics
Biological Priority and Psychological Supremacy in Medicine,
Psychology and Sociology
An Overview of Applications: Co-Creation Practice:
Education, Nursing and Psychodrama (with L Carlson-Sabelli)
A Manner of Thinking: Mathematical Priority and Psychological
Supremacy
Bios Data Analyzer (computer programs for time series analysis)
Readership: Researchers in the natural and human sciences
interested in the application of mathematical methods and ideas;
physicians, economists, sociologists, psychologists, biologists,
physicists, applied mathematicians and philosophers of science.
600pp (approx.) Pub. date: Scheduled Spring 2005
ISBN 981-256-103-X
ISBN 981-256-167-6(pbk)