The book contains the text of lectures given at the third of a
series of biennial symposia in mathematical physics held in odd-numbered
years. The subject of the symposium is the frontiers of
mathematical physics. It deals with quantum phenomena and
includes topics such as string theory and quantum gravity,
particle physics and field theory, non-communative geometry,
integrable models and infinite dimensional symmetry groups,
quantum computing and information processing, and quantum chaos.
Contents:
Freydoon Mansouri Memorial Lectures
Algebras and Representations
Quantization and Quantum Gravity
D<4 Field Theories
String and Brane Worldvolumes
D>3 Field Theories and Gravity
String Theory
Loop Quantum Gravity
Lorentz Violation
Applications
Readership: Researchers, academics and postgraduates in high
energy physics, mathematical physics and atomic physics.
700pp (approx.) Pub. date: Scheduled Winter 2004
ISBN 981-256-068-8
The following topics are discussed in this volume: recent
developments in operator theory, coherent states and wavelet
analysis, geometric and topological methods in theoretical
physics and quantum field theory, and applications of these
methods of mathematical physics to problems in atomic and
molecular physics as well as the world of the elementary
particles and their fundamental interactions. Two extensive sets
of lecture notes on quantization techniques in general, and
quantum gauge theories and strings as an avenue towards quantum
geometry, are also included. The volume should be of interest to
anyone working in a field using the mathematical methods
associated with any of these topics.
Contents:
Quantization Techniques: A Quick Overview (S T Ali)
The Quantum Geometer's Universe: Particles, Interactions and
Topology (J Govaerts)
Theoretical Methods of Modern Classical and Quantum Physics:
Do Cross-Sections Determine Phase Shifts Uniquely? (D Atkinson)
Hilbert Transform or Kramers?Kronig Relations Applied to Some
Aspects of Linear and Nonlinear Physics (G Debiais)
Application of the Gibbs Sampler to the Conditional Simulation of
Rain Fields (H Onibon et al.)
The Mathematics of an Algebraic Approach to the Physics of
Hadrons (M D Slaughter)
Coherent States, Wavelets and Geometric Methods in Theoretical
Physics:
Phase Space Geometry in Classical and Quantum Mechanics (J R
Klauder)
Functional Analysis Special Functions and Orthogonal Polynomials:
On Generalized Continuous D Semi-Classical Hermite and Chebychev
Orthogonal Polynomials of Class One (E Azatassou & M N
Hounkonnou)
On a Generalization of the Method by Barbaroux et al. for the
Improvement on the Rate of Decay of an Operator Resolvent (G
Honnouvo & M N Hounkonnou)
and other papers
Readership: Researchers in mathematical physics, theoretical
physics, physical chemistry, analysis and differential equations,
atomic and quantum physics.
504pp Pub. date: Oct 2002
ISBN 981-02-4935-7
White noise analysis is an advanced stochastic calculus that
has developed extensively since three decades ago. It has two
main characteristics. One is the notion of generalized white
noise functionals, the introduction of which is oriented by the
line of advanced analysis, and they have made much contribution
to the fields in science enormously. The other characteristic is
that the white noise analysis has an aspect of infinite
dimensional harmonic analysis arising from the infinite
dimensional rotation group. With the help of this rotation group,
the white noise analysis has explored new areas of mathematics
and has extended the fields of applications.
Contents:
When is a Noise, Generalized White Noise Functionals
Idealized Elemental Random Variables and Elemental Random
Distributions
Linear Processes and Linear Fields
Harmonic Analysis Arising from the Infinite Dimensional Rotation
Group
Innovation Theory
Variational Calculus for Random Fields
White Noise Approach to the Path Integral
Reversible Fields
A Bridge to the Noncommutative Geometry
Towards the Quantum Probability
Some Thought on Stochastic Variational Equations
Readership: Researchers in probability and statistics and
mathematical physics.
250pp (approx.) Pub. date: Scheduled Winter 2004
ISBN 981-256-052-1
Quantum information is a developing multi-disciplinary field,
with many exciting links to white noise theory. This connection
is explored and presented in this work, which effectively bridges
the gap between quantum information theory and complex systems.
Arising from the Meijo Winter School and International
Conference, the lecture notes and research papers published in
this timely volume will have a significant impact on the future
development of the theories of quantum information and complexity.
This book will be of interest to mathematicians, physicists,
computer scientists as well as electrical engineers working in
this field.
Contents:
Quantum Information, Quantum Communication and Innovation (L
Accardi)
The Quantum Liouville Space (I Antoniou & Z Suchanecki)
L1-Theory for the Kolmogorov Operators of Stochstic Generalized
Burgers Equations (M Rockner & Z Sobol)
Homogenization of Infinite Dimensional Diffusion Processes with
Periodic Drift Coefficients (S Albeverio et al.)
Some Topics on White Noise Analysis (T Hida & Si Si)
On a Design of Transition Probabilities and Estimates of Cover
Times (I Kubo et al.)
Recent Progress on the White Noise Approach to the Levy Laplacian
(H-H Kuo)
An Infinite Dimensional Stochastic Process and the Levy Laplacian
Acting on WND- Valued Functions (K Nishi & K Saito)
Note on Poisson Noise (Si Si)
Note on Linear Process (Win Win Htay)
and other papers
Readership: Researchers in probability and statistics and quantum
information.
500pp (approx.) Pub. date: Scheduled Winter 2004
ISBN 981-256-047-5
This lecture notes volume encompasses four indispensable mini
courses delivered at Wuhan University with each course containing
the material from five one-hour lectures. Readers are brought up
to date with exciting recent developments in the areas of
asymptotic analysis, singular perturbations, orthogonal
polynomials, and the application of Gevrey asymptotic expansion
to holomorphic dynamical systems. The book also features
important invited papers presented at the conference. Leading
experts in the field cover a diverse range of topics from partial
differential equations arising in cancer biology to transonic
shock waves.
Contents:
Special Functions and Orthogonal Polynomials (M E H Ismail)
Singular Perturbations and Reaction Diffusion Equations (M J Ward)
Five Lectures on Asymptotics (R Wong)
A Perturbation Model for the Growth of ZnS Crystals (C S Bohun et
al.)
Limitations and Modifications on Black-Scholes Model (L Jiang
& X Ren)
Exact Boundary Controllability of Unsteady Flows in a Network of
Open Canals (T Li)
On Partial Differential Equations Arising in Cancer Biology (B D
Sleeman)
On the Singularities of Solutions of Nonlinear Partial
Differential Equations in the Complex Domain (H Tahara)
Transonic Shock Waves (Z Xin)
and other papers
Readership: Graduate students, researchers, academics and
lecturers in mathematical physics.
400pp (approx.) Pub. date: Scheduled Winter 2004
ISBN 981-256-055-6
The book collects a series of papers centered on two main
streams: Feynman path integral approach to Quantum Mechanics and
statistical mechanics of quantum open systems. Key authors
discuss the state-of-the-art within their fields of expertise. In
addition, the volume includes a number of contributed papers with
new results, which have been thoroughly refereed.
The contributions in this volume highlight emergent research in
the area of stochastic analysis and mathematical physics,
focusing, in particular on Feynman functional integral approach
and, on the other hand, in quantum probability. The book is
addressed to an audience of mathematical physicists, as well as
specialists in probability theory, stochastic analysis and
operator algebras.
Contents:
Rigorous Feynman Path Integrals, with Applications to Quantum
Theory, Gauge Fields, and Topological Invariants (S Albeverio et
al.)
Vassiliev Invariants and Functional Integration without
Integration (L H Kauffman)
Wiener Analysis and Cyclic Homology (R Leandre)
On the Affine Metaplectic Group (O Rask)
Open Quantum Systems and Classical Trajectories (R Rebolledo)
Fourier-Feynman Transforms on Wiener Spaces (I Yoo et al.)
On Quantum Stochastic Dynamics. Some Recent Developments (A W
Majewski)
Non Adapted Transformations of the Wiener Measure (A B Cruzeiro)
and other papers
Readership: Academic, specialists in mathematical physics and
probability.
312pp Pub. date: Sept 2004
ISBN 981-256-064-5
ISBN 4-946552-14-6
Contents
Invited lectures
Fernando Cobos
Spaces of trilinear forms on Hilbert space
Henryk Hudzik
Geometry of some classes of Banach function spaces
Compact embeddings of function spaces
Lech Maligranda
Type, cotype and convexity properties of quasi-Banach spaces
Kichi-Suke Saito
Absolute norms on and the geometrical structure
Wataru Takahashi
Convergence theorems and projections in Banach spaces
Contributed talks
Sachiko Atsushiba
Strong convergence theorems for commutative nonexpansive
semigroups in general in Banach spaces
Luz M. Fernandez-Cabrera
On inclusion indices of function spaces
Junichi Fujii, Masatoshi Fujii, Yuki Seo and Masaru Tominaga
On generalized Kantorovich inequalities
Aoi Honda, Yoshiaki Okazaki and Hiroshi Sato
Absolute continutity of discrete one-sided random translation
Mikio Kato and Takayuki Tamura
Some geometric conditions related to fixed point property for -direct
sums of Banach spaces X Y$
Jun Kawabe
Weak convergence of vector measures
Misako Kikkawa and Wataru Takahashi
Iterative method for approximation of common fixed points of
infinite nonexpansive mappings in a Hilbert spaces
Yasunori Kimura
On Mosco convergence for a sequence of closed convex subsets of
Banach spaces
Fumiaki Kohsaka and Wataru Takahashi
Minimization theorems in Banach spaces with applications
Ken-ichi Mitani and Kichi-Suke Saito
The James constant and von Neumann-Jordan constant of absolute
norms on
Eiichi Nakai
Generalized fractional integrals on Orlicz-Morrey spaces
Amiran Gogatishvili, Shinya Moritoh, Miyuki Niwa and Takuya
Sobukawa
Interpolation theorems for block-Lorentz spaces
Takuya Sobukawa
Results and problems in extrapolation theorem on Lp spaces
Tomonari Suzuki
Properties of fixed-point sets of nonexpansive mappings in Banach
spaces with Opial's property
Yasuji Takahashi, Yasutaka Yamada and Mikio Kato
On Hanner-type inequalities for Banach spaces
Kenjiro Yanagi
Some inequalities appearing in classical and quantum information
theory