Series on Knots and Everything - Vol. 38
This volume is a collection of papers on various areas of current
interest in mathematical biology, such as epidemic disease
modeling, including the effects of vaccination and strain
replacement; immunology, such as T-Cell dynamics and the
mechanism of phagocytosis; knot theory; DNA computation; and
Boolean networks.
Contents:
・Methylation of DNA may be Useful as a Computation Tool:
Experimental Evidence (S Gal)
・Dynamics of Random Boolean Networks (J Lynch)
・Unknots and DNA (L Kauffman)
・Developing a Mathematical Model of Phagocytosis: A Learning
Approach (N Macura)
・An Age-Structured Model of T-Cell Populations (B Kohler)
・Modeling and Simulation of Age- and Space-Structured
Biological Systems (B Ayati)
・Nutrient-Plankton Interaction with a Toxin in a Variable Input
Nutrient Environment (S Jang)
・On the Mechanism of Strain Replacement in Epidemic Models with
Vaccination (M Martcheva)
Readership: Researchers, graduate students in mathematics,
mathematical biology and computer science.
200pp (approx.) Pub. date: Scheduled Winter 2006
ISBN 981-270-015-3
Series in Pure Mathematics - Vol. 26
Translation generalized quadrangles play a key role in the theory
of generalized quadrangles, comparable to the role of translation
planes in the theory of projective and affine planes. The notion
of translation generalized quadrangle is a local analogue of the
more global "Moufang Condition", a topic of great
interest, also due to the classification of all Moufang polygons.
Attention is thus paid to recent results in that direction, but
also many of the most important results in the general theory of
generalized quadrangles that appeared since 1984 are treated.
Translation Generalized Quadrangles is essentially self-contained,
as the reader is only expected to be familiar with some basic
facts on finite generalized quadrangles. Proofs that are either
too long or too technical are left out, or just sketched. The
three standard works on generalized quadrangles are (co-)authored
by the writers of this book: "Finite Generalized Quadrangles"
(1984) by S E Payne and J A Thas, "Generalized Polygons"
(1998) by H Van Maldeghem, and "Symmetry in Finite
Generalized Quadrangles" (2004) by K Thas.
Contents:
・Generalized Quadrangles
・Regularity, Antiregularity and 3-Regularity
・Elation and Translation Generalized Quadrangles
・Generalized Quadrangles and Flocks
・Good Eggs
・Generalized Quadrangles, Nets and the Axiom of Veblen
・Ovoids and Subquadrangles
・Translation Generalized Ovals
・Moufang Sets and Translation Moufang Sets
・Configurations of Translation Points
・Moufang Quadrangles with a Translation Point
・Translation Ovoids in Translation Quadrangles
・Translation Generalized Quadrangles in Projective Space
・Open Problems
Readership: Researchers in incidence geometry, combinatorics and
finite geometries. Also suitable as a textbook for a graduate
course.
350pp (approx.) Pub. date: Scheduled Winter 2006
ISBN 981-256-951-0
Ever since 1911, the Solvay Conferences have shaped modern
physics. The 23rd edition, chaired by 2004 Nobel Laureate David
Gross, did not break with that tradition. It gathered most of the
leading figures working on the central problem of reconciling
Einstein痴 theory of gravity with quantum mechanics.
These proceedings give a broad overview with unique insight into
the most fundamental issues raised by this challenge for 21st
century physics, by distinguished renowned scientists. The
contributions cover: the status of quantum mechanics, spacetime
singularities and breakdown of classical space and time,
mathematical structures underlying the most promising attempts
under current development, spacetime as an emergent concept, as
well as cosmology and the cosmological constant puzzle. A
historical overview of the Solvay conferences by historian of
sciences Peter Galison opens the volume.
In the Solvay tradition, the volume also includes the discussions
among the participants ・many of which were quite lively and
illustrate dramatically divergent points of view ・carefully
edited and reproduced in full.
Contents:
・Historical Introduction on Solvay Conferences (P Galison)
・Generalized Quantum Mechanics for Quantum Spacetime (J Hartle)
・Singularities (G Gibbons)
・Mathematical Structures (R Dijkgraaf)
・Emergent Spacetime (N Seiberg)
・The Cosmological Constant and the String Landscape (J
Polchinski)
Readership: Graduate students and researchers in physics and
mathematics.
350pp (approx.) Pub. date: Scheduled Fall 2006
ISBN 981-256-952-9
ISBN 981-256-953-7(pbk)
Singularity theory appears in numerous branches of
mathematics, as well as in many emerging areas such as robotics,
control theory, imaging, and various evolving areas in physics.
The purpose of this proceedings volume is to cover recent
developments in singularity theory and to introduce young
researchers from developing countries to singularities in
geometry and topology.
The contributions discuss singularities in both complex and real
geometry. As such, they provide a natural continuation of the
previous school on singularities held at ICTP (1991), which is
recognized as having a major influence in the field.
Contents:
・Introduction to Basic Toric Geometry (G Barthel et al.)
・Metric Theory of Singularities ? Lipschitz Geometry of
Singular Spaces (L Birbrair)
・Poincare?Hopf Theorem for Singular Varieties (J-P Brasselet)
・Lectures on Monodromy (W Ebeling & S Gusein-Zade)
・Computational Aspects of Singularities (A Frubis-Kruger)
・Lagrangian and Legendrian Varieties and Stability of Their
Projections (V Goryunov & V Zakalyukin)
・A Lefschetz Theorem on the Picard Group of Complex Projective
Varieties (H Hamm & Le Dung Trang)
・Problems in Topology of the Complement to Plane Singular
Curves (A Libgober)
・Monodromy and p1 of Discriminant (M Lonne)
・Topology of Degeneration of Riemann Surfaces (Y Matsumoto)
・Graded Roots and Singularities (A Nemethi)
・Chern Classes and Thom Polynomials (T Ohmoto)
・Tangential Alexander Polynomials and Non-Reduced Degeneration
(M Oka)
・McKay Correspondence for Quotient Surface Singularities (O
Riemenschneider)
・On Milnor Fibration Theorem for Real and Complex Singularities
(J Seade)
・Logarithmic Vector Fields and Multiplication Table (S Tanabe)
・and other papers
Readership: Researchers in geometry and topology.
600pp (approx.) Pub. date: Scheduled Winter 2006
ISBN 981-270-022-6
This book provides an introduction to elliptic and parabolic
equations. While there are numerous monographs focusing
separately on each kind of equations, there are very few books
treating these two kinds of equations in combination. This book
presents the related basic theories and methods to enable readers
to appreciate the commonalities between these two kinds of
equations as well as contrast the similarities and differences
between them.
Contents:
・Preliminary Knowledge
・L2 Theory of Linear Elliptic Equations
・L2 Theory of Linear Parabolic Equations
・De Giorgi Iteration and Moser Iteration
・Harnack’s Inequalities
・Schauder’s Estimates for Linear Elliptic Equations
・Schauder’s Estimates for Linear Parabolic Equations
・Existence of Classical Solutions for Linear Equations
・Lp Estimates on Solutions for Linear Equations and the
Existence of Strong Solutions
・Fixed Point Method
・Topological Degree Method
・Monotone Method
・Degenerate Equations
Readership: Scholars and graduate students in mathematics,
especially, in partial differential equations.
400pp (approx.) Pub. date: Scheduled Winter 2006
ISBN 981-270-025-0
ISBN 981-270-026-9(pbk)
The geometry of Hessian structures is a fascinating emerging
field of research connected with many important pure mathematical
branches such as affine differential geometry, homogeneous spaces
and cohomology. This systematic introduction to the subject first
develops the fundamentals of Hessian structures and then
describes these related fields as applications of the theory.
Contents:
・Affine Spaces and Connections
・Hessian Structures
・Curvatures for Hessian Structures
・Regular Convex Cones
・Hessian Structures and Affine Differential Geometry
・Hessian Structures and Information Geometry
・Cohomology on Flat Manifolds
・Compact Hessian Manifolds
・Symmetric Spaces with Invariant Hessian Structures
・Homogeneous Spaces with Invariant Hessian Structures
・Homogeneous Spaces with Invariant Projectively Flat
Connections
Readership: Mathematicians and mathematics graduate students.
250pp (approx.) Pub. date: Scheduled Spring 2007
ISBN 981-270-031-5
This is the first book devoted to the numerical solution of
general problems with periodic and oscillating solutions. It
encompasses all the recent research in this area and compares
various techniques on the solution of the Schrodinger equation
and related problems from several disciplines such as astronomy
and mathematics.
Contents:
・Theory for the Construction of Numerical Methods for the
Schrodinger Equation
・Numerical Methods with Constant Coefficients
・Numerical Methods with Coefficients Dependent on the Frequency
of the Problem
・Other Numerical Methods
・Numerical Method for 2D Schrodinger Equation
・Numerical Applications
Readership: Applied mathematicians, physicists, chemists,
material scientists and computational scientists.
500pp (approx.) Pub. date: Scheduled Spring 2007
ISBN 1-86094-697-6