Waseda University, Tokyo, Japan 29 - 31 October 2003Tokyo University of Science, Tokyo, Japan 1 - 3 November 2003
International Institute of Advanced Study, Kyoto, Japan 5 - 7 November 2003
Meijo University, Nagoya, Japan 8 - 9 November 2003
This volume contains a valuable collection of articles
presented at a conference on Automorphic Forms and Zeta Functions
in memory of Tsuneo Arakawa, an eminent researcher in modular
forms in several variables and zeta functions. The book begins
with a review of his works, followed by 16 articles by experts in
the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida,
Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T
Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T
Sugano, and D Zagier. A variety of topics in the theory of
modular forms and zeta functions are covered: Theta series and
the basis problems, Jacobi forms, automorphic forms on Sp(1, q),
double zeta functions, special values of zeta and L-functions,
many of which are closely related to Arakawa’s works.
This collection of papers illustrates Arakawa's contributions and
the current trends in modular forms in several variables and
related zeta functions.
Contents:
Tsuneo Arakawa and His Works
Estimate of the Dimensions of Hilbert Modular Forms by Means of
Differential Operators (H Aoki)
Marsden?Weinstein Reduction, Orbits and Representations of the
Jacobi Group (R Berndt)
On Eisenstein Series of Degree Two for Squarefree Levels and the
Genus Version of the Basis Problem I (S Bocherer)
Double Zeta Values and Modular Forms (H Gangl et al.)
Type Numbers and Linear Relations of Theta Series for Some
General Orders of Quaternion Algebras (K-I Hashimoto)
Skew-Holomorphic Jacobi Forms of Higher Degree (S Hayashida)
A Hermitian Analog of the Schottky Form (M Hentschel & A
Krieg)
The Siegel Series and Spherical Functions on O(2n)/(O(n) x O(n))
(Y Hironaka & F Sato)
Koecher?Maas Series for Real Analytic Siegel Eisenstein Series (T
Ibukiyama & H Katsurada)
A Short History on Investigation of the Special Values of Zeta
and L-Functions of Totally Real Number Fields (T Ishii & T
Oda)
Genus Theta Series, Hecke Operators and the Basis Problem for
Eisenstein Series (H Katsurada & R Schulze-Pillot)
The Quadratic Mean of Automorphic L-Functions (W Kohnen et al.)
Inner Product Formula for Kudla Lift (A Murase & T Sugano)
On Certain Automorphic Forms of Sp(1,q) (Arakawa's Results and
Recent Progress) (H-A Narita)
On Modular Forms for the Paramodular Groups (B Roberts & R
Schmidt)
SL(2,Z)-Invariant Spaces Spanned by Modular Units (N-P Skoruppa
& W Eholzer)
Readership: Researchers and graduate students in number theory or
representation theory as well as in mathematical physics or
combinatorics.
400pp Pub. date: Jan 2006
ISBN 981-256-632-5
The maximum principle induces an order structure for partial
differential equations, and has become an important tool in
nonlinear analysis. This book is the first of two volumes to
systematically introduce the applications of order structure in
certain nonlinear partial differential equation problems.
The maximum principle is revisited through the use of the
Krein?Rutman theorem and the principal eigenvalues. Its various
versions, such as the moving plane and sliding plane methods, are
applied to a variety of important problems of current interest.
The upper and lower solution method, especially its weak version,
is presented in its most up-to-date form with enough generality
to cater for wide applications. Recent progress on the boundary
blow-up problems and their applications are discussed, as well as
some new symmetry and Liouville type results over half and entire
spaces. Some of the results included here are published for the
first time.
Contents:
Krein-Rutman Theorem and the Principal Eigenvalue
Maximum Principles Revisited
The Moving Plane Method
The Method of Upper and Lower Solutions
The Logistic Equation
Boundary Blow-Up Problems
Symmetry and Liouville Type Results Over Half and Entire Spaces
Readership: Researchers and postgraduate students in partial
differential equations.
200pp Pub. date: Jan 2006
ISBN 981-256-624-4
Waseda University, Tokyo, Japan 29 - 31 October 2003the main purpose of this volume is to emphasize the
multidisciplinary aspects of this very active new line of
research in which concrete technological and industrial
realizations require the combined efforts of experimental and
theoretical physicists, mathematicians and engineers.
Contents:
Coherent Quantum Control of Λ-Atoms Through the Stochastic Limit
(L Accardi)
Information, Innovation and Elemental Random Field (T Hida)
Joint Extension of States of Fermion Subsystems (H Araki)
Emergence of White Noise Equations from Classical Quantum
Mechanics (A Boukas)
Saturation of an Entropy Bound and Quantum Markov States (D Petz)
Quantum Entanglement, Purification, and Linear-Optics Quantum
Gates with Photonic Qubits (P Walther & A Zeilinger)
Group Theory of Dynamical Maps (E C G Sudarshan)
Quantum Logical Gates Realized by Beam Splittings (W Freudenberg
et al.)
Generalized Sectors and Adjunctions (I Ojima)
Note on Quantum Mutual Type Measures and Capacity (N Watanabe)
Structure of Linear Processes (S Si)
An Infinite Dimensional Laplacian Acting on Some Class of Levy
White Noise Functionals (K Sait・
Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H
Fichtner et al.)
Noncanonical Representations of a Multi-Dimensional Brownian
Motion (Y Hibino)
and other papers
Readership: Researchers in quantum physics and theoretical
physics.
350pp (approx.) Pub. date: Scheduled Summer 2006
ISBN 981-256-614-7
This book is the first monograph devoted exclusively to
strange nonchaotic attractors (SNA), recently discovered objects
with a special kind of dynamical behavior between order and chaos
in dissipative nonlinear systems under quasiperiodic driving. A
historical review of the discovery and study of SNA, mathematical
and physically-motivated examples, and a review of known
experimental studies of SNA are presented. The main focus is on
the theoretical analysis of strange nonchaotic behavior by means
of different tools of nonlinear dynamics and statistical physics
(bifurcation analysis, Lyapunov exponents, correlations and
spectra, renormalization group). The relations of the subject to
other fields of physics such as quantum chaos and solid state
physics are also discussed.
Readership: Graduate students and researchers in nonlinear
science.
228pp (approx.) Pub. date: Scheduled Summer 2006
ISBN 981-256-633-3
This book provides an introduction to the propagator theory.
Propagators are two-parameter families of linear operators, also
known as evolution operators, evolution families, non-autonomous
semigroups, etc., which are often used as mathematical models of
a system evolving in a changing environment. Although this book
concerns such diverse subjects as analysis, semigroup theory,
probability theory, mathematical physics, and partial
differential equations, it is unified by the Feynman?Kac
propagator which describes the evolution of a physical system in
the presence of time-dependent absorption and excitation. The
theory of Feynman?Kac propagators with potentials from non-autonomous
Kato classes is presented in the book for the first time. This
book is suitable as an advanced textbook for graduate courses.
Contents:
Transition Functions and Markov Processes
Markov Property
Forward and Backward Transition Functions
Markov Processes Generated by Transition Functions
Space-Time Processes
Path Properties of Stochastic Processes: Separability and
Progressive Measurability
Path Properties of Stochastic Processes: One-Sided Continuity and
Continuity
Reciprocal Transition Functions and Processes
Path Properties of Reciprocal Processes
Examples of Markov Processes
Propagators: General Theory
Forward and Backward Propagators on Banach Spaces
Free Forward and Backward Propagators
Kolmogorov’s Forward and Backward Equations
Feller?Dynkin Propagators and the Continuity Properties of Markov
Processes
Stopping Times and Strong Markov Property
Strong Markov Property with Respect to Families of Measures
Feller?Dynkin Propagators and Completions of Sigma-Algebras
Feller?Dynkin Propagators and Standard Processes
Non-Autonomous Kato Classes of Measures and Functionals of Markov
Processes
Additive and Multiplicative Functionals
Transition Probability Functions, Potentials of Time-Dependent
Measures, and Non-Autonomous Kato Classes
Backward Transition Probability Functions, and Non-Autonomous
Kato Classes
Weighted Non-Autonomous Kato Classes
Examples of Functions and Measures in Non-Autonomous Kato Classes
Fundamental Solutions to Non-Divergence Form Parabolic Equations
and Transition Densities
Fundamental Solutions to Divergence Form Parabolic Equations and
Transition Densities
Construction of the Additive Functional Associated with a Time-Dependent
Measure
Exponential Estimates for Non-Autonomous Functionals
Probabilistic Description of Non-Autonomous Kato Classes
Feynman-Kac Propagators
Schrodinger Semigroups with Kato Class Potentials
Smoothing by Feynman-Kac Propagators
Feller, Feller-Dynkin, and BUC-Property of Feynman-Kac
Propagators
Duhamel's Formula for Feynman-Kac Propagators
Feynman-Kac Propagators and Viscosity Solutions
Readership: Graduate students and researchers in mathematical
analysis, partial differential equations, and probability theory.
300pp (approx.) Pub. date: Scheduled Summer 2006
ISBN 981-256-557-4
This book presents basic elements of the theory of Hilbert
spaces and operators on Hilbert spaces, culminating in a proof of
the spectral theorem for compact, self-adjoint operators on
separable Hilbert spaces. It exhibits a construction of the space
of pth power Lebesgue integrable functions by a completion
procedure with respect to a suitable norm in a space of
continuous functions, including proofs of the basic inequalities
of Holder and Minkowski. The Lp-spaces thereby emerges in direct
analogy with a construction of the real numbers from the rational
numbers. This allows grasping the main ideas more rapidly. Other
important Banach spaces arising from function spaces and sequence
spaces are also treated.
Contents:
Basic Elements of Metric Topology
New Types of Function Spaces
Theory of Hilbert Spaces
Operators on Hilbert Spaces
Spectral Theory
Fredholm Theory (by Mirza Karamehmedovic)
Readership: Undergraduates in mathematical and physical sciences,
and electrical and electronic engineering.
200pp (approx.) Pub. date: Scheduled Summer 2006
ISBN 981-256-563-9
ISBN 981-256-686-4(pbk)
Series on Knots and Everything - Vol. 37
Geometry, Language and Strategy is a way of looking at game
theory or strategic decision-making from a scientific
perspective, using standard equations from the fields of
engineering and physics. To better approximate reality, it
extends game theory beyond the two-player set piece.
The book begins where former game theory literature ends ? with
multi-person games on a world stage. It encompasses many of the
variables encountered in strategic planning, using mathematics
borrowed from physics and engineering, rather than the economic
models which have not proven to be good in predicting reality.
Contents:
Rules of the Game
Acceleration of Strategic Mass
Game Symmetries
Analysis
Graphical Presentation
Problems
Appendices:
Thermodynamics
Symmetry in Differential Geometry
Central Strategies
Single Strategy Model
Single Strategy Numerical Solutions
Streamlines
Player Fluid
Readership: Mathematicians and scientists who wish to broaden
their understanding of economic possibilities using game theory.
250pp (approx.) Pub. date: Scheduled Summer 2006
ISBN 981-256-617-1
Phase transition phenomena arise in a variety of relevant real
world situations, such as melting and freezing in a solid?liquid
system, evaporation, solid?solid phase transitions in shape
memory alloys, combustion, crystal growth, damage in elastic
materials, glass formation, phase transitions in polymers, and
plasticity.
The practical interest of such phenomenology is evident and has
deeply influenced the technological development of our society,
stimulating intense mathematical research in this area.
This book analyzes and approximates some models and related
partial differential equation problems that involve phase
transitions in different contexts and include dissipation effects.
Contents:
Mathematical Models Including a Hysteresis Operator (T Aiki)
Modelling Phase Transitions via an Entropy Equation: Long-Time
Behavior of the Solutions (E Bonetti)
Global Solution to a One Dimensional Phase Transition Model with
Strong Dissipation (G Bonfanti & F Luterotti)
A Global in Time Result for an Integro-Differential Parabolic
Inverse Problem in the Space of Bounded Functions (F Colombo et
al.)
Weak Solutions for Stefan Problems with Convections (T Fukao)
Memory Relaxation of the One-Dimensional Cahn?Hilliard Equation (S
Gatti et al.)
Mathematical Models for Phase Transition in Materials with
Thermal Memory (G Gentili & C Giorgi)
Hysteresis in a First Order Hyperbolic Equation (J Kopfova)
Approximation of Inverse Problems Related to Parabolic Integro-Differential
Systems of Caginalp Type (A Lorenzi & E Rocca)
Gradient Flow Reaction/Diffusion Models in Phase Transitions (J
Norbury & C Girardet)
New Existence Result for a 3-D Shape Memory Model (I Pawlow &
W M Zajaczkowski)
Analysis of a 1-D Thermoviscoelastic Model with Temperature-Dependent
Viscosity (R Peyroux & U Stefanelli)
Global Attractor for the Weak Solution of a Class of Viscous
Cahn?Hilliard Equations (R Rossi)
Stability for Phase Field Systems Involving Indefinite Surface
Tension Coefficients (K Shirakawa)
Geometric Features of p-Laplace Phase Transitions (E Valdinoci)
Readership: Applied mathematicians and researchers in analysis
and differential equations.
350pp (approx.) Pub. date: Scheduled Summer 2006
ISBN 981-256-650-3