Pseudo-Riemannian geometry is an active research field not
only in differential geometry but also in mathematical physics
where the higher signature geometries play a role in brane theory.
An essential reference tool for research mathematicians and
physicists, this book also serves as a useful introduction to
students entering this active and rapidly growing field. The
author presents a comprehensive treatment of several aspects of
pseudo-Riemannian geometry, including the spectral geometry of
the curvature tensor, curvature homogeneity, and
Stanilov?Tsankov?Videv theory.
Contents:
The Geometry of the Riemann Curvature Tensor
Curvature Homogeneous Generalized Plane Wave Manifolds
Other Pseudo-Riemannian Manifolds
The Curvature Tensor
Complex Osserman Algebraic Curvature Tensors
Stanilov?Tsankov Theory
Readership: Researchers in differential geometry and mathematical
physics.
400pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-1-86094-785-8
1-86094-785-9
This graduate-level monographic textbook treats applied
differential geometry from a modern scientific perspective. Co-authored
by the originator of the world’s leading human motion simulator
? “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical
system, modeled by differential-geometric tools ? this is the
first book that combines modern differential geometry with a wide
spectrum of applications, from modern mechanics and physics, via
nonlinear control, to biology and human sciences. The book is
designed for a two-semester course, which gives mathematicians a
variety of applications for their theory and physicists, as well
as other scientists and engineers, a strong theory underlying
their models.
Contents:
Technical Preliminaries: Tensors, Actions and Functors
Applied Manifold Geometry
Applied Bundle Geometry
Applied Jet Geometry
Geometrical Path Integrals and Their Applications
Readership: Researchers and graduates in pure and applied
mathematics, and mathematical physics.
1300pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-981-270-614-0
981-270-614-3
This book introduces some important progress in the theory of
Calderon-Zygmund singular integrals, oscillatory singular
integrals, and Littlewood-Paley theory over the last decade. It
includes some important research results by the authors and their
cooperators, such as singular integrals with rough kernels on
Block spaces and Hardy spaces, the criterion on boundedness of
oscillatory singular integrals, and boundedness of the rough
Marcinkiewicz integrals. These results have frequently been cited
in many published papers.
Contents:
Hardy-Littlewood Maxial Operator
Singular Integral Operators
Fractional Integral Operators
Oscillatory Singular Integrals
Littlewood?Paley Operator
Readership: Graduate students and researchers in analysis and
other related mathematical fields.
300pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-981-270-623-2
981-270-623-2
This volume gathers the contributions from top-notch
mathematicians such as Samuel Krushkal, Reiner Kuhnau, Chung Chun
Yang, Vladimir Miklyukov and others.
It will help researchers solve problems on complex analysis and
potential theory and discusses various applications in
engineering. The contributions also update the reader on recent
developments in the field.
Contents:
Speed of Approximation to Degenerate Quasiconformal Mappings and
Stability Problems (V M Miklyukov)
Decompositions of Meromorphic Functions Over Small Function
Fields (P Li & C-C Yang)
Strengthened Moser's Conjecture and Finsler Geometry of Grunsky
Coefficients (S Krushkal)
Geometric Approach in the Theory of Generalized Quasiconformal
Mappings (A Golberg)
Grunsky Inequalities, Fredholm Eigenvalues, Reflection
Coefficients (R Kuhnau)
Geometry of the General Beltrami Equations (B Bojarski)
Asymptotic Expansions of the Solutions to the Heat Equations with
Generalized Initial Value Functions (K Yoshino & Y Oka)
Sums of Reciprocal Eigenvalues (B Dittmar)
Separately Quasi-Nearly Subharmonic Functions (J Riihentaus)
Open Problems on Hausdorff Operators (E Liflyand)
Harmonic Commutative Banach Algebras and Spatial Potential Fields
(S A Plaksa)
On the Existence of Harmonic Differential Forms with Prescribed
Singularities (E Malinnikova)
and other papers
Readership: Researchers in applied mathematics, analysis and
differential equations, and approximation theory.
600pp (approx.) Pub. date: Scheduled Fall 2007
ISBN 978-981-270-598-3
981-270-598-8
Series on Knots and Everything - Vol. 40
This volume gathers the contributions from the international
conference "Intelligence of Low Dimensional Topology 2006,"
which took place in Hiroshima in 2006. The aim of this volume is
to promote research in low dimensional topology with the focus on
knot theory and related topics. The papers include comprehensive
reviews and some latest results.
Contents:
Cohomology for Self-Distributivity in Coalgebras (J Scott Carter
& M Saito)
Prime Knots with Arc Index up to 10 (G T Jin et al.)
Quandles with Good Involutions, Their Homology Groups, and Knot
Invariants (S Kamada)
The L-Move and Virtual Braids (L Kauffman)
On the Surface-Link Groups (A Kawauchi)
The Volume of a Hyperbolic Simplex and Iterated Integrals (T
Kohno)
p-Adic Framed Braids and p-Adic Markov Traces (J Juyumaya & S
Lambropoulou)
Arithmetic Topology After Hida Theory (M Morishita & Y
Terashima)
Principal Analytic Link-Theory in Surface Singularity Links (W D
Neumann & A Pichon)
Equivariant Quantum Invariants of the Infinite Cyclic Covers of
Knot Complements (T Ohtsuki)
What Is a Welded Link? (C Rourke)
Yamada Polynomial and Khovanov Cohomology (V Vershinin & A
Vesnin)
and other papers
Readership: Researchers interested in knot theory.
420pp (approx.) Pub. date: Scheduled Fall 2007
ISBN 978-981-270-593-8
981-270-593-7