In print, 2005
ISBN 90 6764 427 7
Hardback (xviii, 922 pp.)
This monograph can be regarded as a result of the activity of
many mathematicians of the 20th century in the field of classical
Fourier series and the theory of approximation of periodic
functions, beginning with H. Lebesgue, D. Jackson, and S. N.
Bernstein.
The key point of the monograph is the classification of periodic
functions introduced by the author and developed methods that
enable one to solve, within the framework of a common approach,
traditional problems of approximation theory for large
collections of periodic functions, including, as particular
cases, the well-known Weyl--Nagy and Sobolev classes as well as
classes of functions defined by convolutions with arbitrary
summable kernels. The developed methods enable one to solve
problems of approximation theory not only in the periodic case
but also in the case where objects of approximation are functions
locally integrable on the entire axis and functions defined by
Cauchy-type integrals in domains of the complex plane bounded by
rectifiable Jordan curves.
The main results are fairly complete and are presented in the
form of either exact or asymptotically exact equalities.
Most results of the monograph represent the latest achievements,
which have not yet been published in existing monographs. First
of all, this refers to problems of regularity and saturation of
linear processes of summation and the convergence rate of Fourier
series in different metrics, approximation by interpolation
polynomials, approximation of locally integrable functions by
entire functions of exponential type, and approximation of Cauchy
integrals in Jordan domains by Faber polynomials.
The monograph also contains entirely new results aimed at the
construction of approximation theory in general linear spaces.
The present monograph is, in many respects, a store of knowledge
accumulated in approximation theory by the beginning of the third
millennium and serving for its further development.
Readership: The monograph is intended for specialists in the
field of mathematical and harmonic analysis, approximation
theory, the theory of Fourier series, and their applications,
lecturers, post-graduate students, and students of mathematical
departments of universities.
This volume contains a valuable collection of research
articles by active and well-known mathematicians in differential
geometry and mathematical physics, contributed to mark Professor
Kouei Sekigawa’s 60th birthday. The papers feature many new and
significant results while also reviewing developments in the
field. The illustrious career of Professor Sekigawa and his
encounters with friends in mathematics is a special highlight of
the volume.
Contents:
On g-Natural Metrics with Constant Scalar Curvature on Unit
Tangent Sphere Bundles (M T K Abbassi & O Kowalski)
Magnetic Mean Operators on a Kahler Manifold (T Adachi)
Yang?Mills Fields Analogue of Biharmonic Maps (C Bejan & H
Urakawa)
Invariant and Anti-Invariant Unit Vector Fields (T Q Binh, E
Boeckx & L Vanhecke)
A New Structure on Unit Tangent Sphere Bundles (J T Cho & S H
Chun)
Complete k-Curvature Homogeneous Pseudo-Riemannian Manifolds 0-Modeled
on an Indecomposible Symmetric Space (P Gilkey & Nikcevic)
Miyaoka?Yau Inequality and Complex Hyperbolicity (M Itoh)
On the Discontinuity of Affine Motions and Auslander’s
Conjecture (T Kawabe)
Infinitesimal Fourier Transformation for the Space of Functionals
(T Nitta & T Okada)
Recent Progress on Real Hypersurfaces in Complex Two-Plane
Grassmannians (Y J Suh)
Isotropic Kahler Immersions into a Complex Quadric (K Tsukada)
and other papers
Readership: Post-graduates and researchers in differential
geometry, global analysis and mathematical physics.
276pp Pub. date: Jul 2005
ISBN 981-256-417-9
The selected papers in this volume cover all the most
important areas of ring theory and module theory such as
classical ring theory, representation theory, the theory of
quantum groups, the theory of Hopf algebras, the theory of Lie
algebras and Abelian group theory. The review articles, written
by specialists, provide an excellent overview of the various
areas of ring and module theory ? ideal for researchers looking
for a new or related field of study. Also included are original
articles showing the trend of current research.
Contents:
Constructing Morphic Rings (J-L Chen et al.)
Rings Whose Simple Modules Have Some Properties (Y Hirano)
On a Left H-Ring with Nakayama Automorphism (J Kado)
On Lifting Properties of Modules (Y Kuratomi)
A Survey of Morphic Modules and Rings (W K Nicholson)
Flat Cover and Cotorsion Envelope Commute (P Rothmaler)
From Galois Field Extensions to Galois Comodules (R Wisbauer)
Galois Coverings of Selfinjective Algebras by Twisted Repetitive
Algebras (K Yamagata)
and other papers
Readership: Algebraists in particular non-commutative ring
theorists.
336pp Pub. date: Aug 2005
ISBN 981-256-425-X
The Nobel Symposium in 2003 on String Theory and Cosmology was
a gathering of many of the most active and distinguished
scientists in the world, including Stephen Hawking, 2004 Nobel
Prize winner David Gross, and Andrei Linde. The experts,
comprising both theoreticians and experimentalists, were given
the opportunity to discuss the present status of their respective
subjects. Throughout the symposium, special attention was given
to the connections between the fields: the questions posed ranged
from “Can cosmology be used to test string theory?” to “Can
string theory answer deep questions about cosmology?” The
symposium marked a new era in the understanding of the science of
the very small and the very large. This book is a unique document
that reflects upon the state of fundamental physics at a
historically important moment in time.
Contents:
Supernovae and Dark Energy (J L Tonry)
Studying Dark Energy with Supernovae: Now, Soon, and the Not-Too-Distant
Future (S Perlmutter)
What Have We Learned from Cosmic Microwave Background
Fluctuations? (D N Spergel)
Quintessential Ideas (P J Steinhardt)
Prospects of Inflation (A Linde)
A Non Singular Universe (S Hawking)
Unconventional Scenarios and Perturbations Therein (G Veneziano)
Holographic Cosmology 3.0 (T Banks & W Fischler)
Bouncing Universes in String Theory? (J Polchinski)
Remarks on Tachyon Driven Cosmology (A Sen)
Beyond Inflation: A Cyclic Universe Scenario (N Turok & P J
Steinhardt)
Creating Naked Singularities and Negative Energy (G T Horowitz)
Filtering Gravity: Modification at Large Distances? (G Dvali)
Cosmological Singularities in String Theory (D Kutasov)
Where Do We Stand in Fundamental (String) Theory (D J Gross)
Readership: Scientists in the fields of particle physics, string
theory, cosmology and astronomy.
108pp Pub. date: Aug 2005
ISBN 981-256-433-0
This short but rigorous book approaches the main ideas of
linear algebra through carefully selected examples and relevant
applications. It is intended for students with various interests
in mathematics, as well as established scientists seeking to
refresh their basic mathematical culture.
The book is also a good introduction to functional analysis and
quantum theory since it discusses the general principles of
linear algebra without finiteness assumptions.
Contents:
Linear Systems: Elimination Method
Vector Spaces
Matrix Multiplication
Linear Maps
The Rank Theorem
Eigenvectors and Eigenvalues
Inner-Product Spaces
Symmetric Operators
Duality
Determinants
Applications
Normal Operators
Readership: Undergraduate students in mathematics, physics,
chemistry, computer science and engineering.
388pp Pub. date: Aug 2005
ISBN 981-256-432-2
ISBN 981-256-499-3(pbk)
The development of new computational techniques and better
computing power has made it possible to attack some classical
problems of algebraic geometry. The main goal of this book is to
highlight such computational techniques related to algebraic
curves. The area of research in algebraic curves is receiving
more interest not only from the mathematics community, but also
from engineers and computer scientists, because of the importance
of algebraic curves in applications including cryptography,
coding theory, error-correcting codes, digital imaging, computer
vision, and many more.
This book covers a wide variety of topics in the area, including
elliptic curve cryptography, hyperelliptic curves,
representations on some Riemann?Roch spaces of modular curves,
computation of Hurwitz spectra, generating systems of finite
groups, Galois groups of polynomials, among other topics.
Contents:
A New Proof for the Non-Degeneracy of the Frey?Ruck Pairing and a
Connection to Isogenies Over the Base Field (E F Schaefer)
Elliptic Curve Torsion Points and Division Polynomials (I A
Burhanuddin & M A Huang)
Detecting Complex Multiplication (J D Achter)
Simple Numerical Uniformatization of Elliptic Curves (M Seppala)
On the Moduli Space of Klein Four Covers of the Projective Line (D
Glass & R Pries)
Field of Moduli and Field of Definition for Curves of Genus 2 (G
Cardona & J Quer)
Explicit Computation of Hurwitz Spectra (R Vogeler)
Non-Normal Bely p-Gonal Surfaces (A Wootton)
Hyperelliptic Curves of Genus 3 with Prescribed Automorphism
Group (J Gutierrez et al.)
Curves Over Finite Fields with Many Points: An Introduction (J
Voight)
Hyperelliptic Curves of Genus 3 and 4 in Characteristic 2 (Y
Demirbas)
Modular Representations on Some Riemann?Roch Spaces of Modular
Curves X(N) (D Joyner & A Ksir)
Genus Two Curves Covering Elliptic Curves: A Computational
Approach (T Shaska)
A Question About Pic(X) as a G-Module (D Goldstein et al.)
Galois Groups of Prime Degree Polynomials with Nonreal Roots (A
Bialostocki & T Shaska)
Counting Generating Systems of a Finite Group from Given
Conjugacy Classes (R Staszewski et al.)
Group Action on Genus 3 Curves and Their Weierstrass Points (H
Babu & P Venkataraman)
Readership: Researchers in mathematics and computer science.
288pp Pub. date: Aug 2005
ISBN 981-256-459-4
The relatively new concepts of the Henstock?Kurzweil and
McShane integrals based on Riemann type sums are an interesting
challenge in the study of integration of Banach space-valued
functions. This timely book presents an overview of the concepts
developed and results achieved during the past 15 years. The
Henstock?Kurzweil and McShane integrals play the central role in
the book. Various forms of the integration are introduced and
compared from the viewpoint of their generality. Functional
analysis is the main tool for presenting the theory of summation
gauge integrals.
Contents:
Bochner Integral
Dunford and Pettis Integrals
McShane and Henstock?Kurzweil Integrals
More on the McShane Integral
Comparison of the Bochner and McShane Integrals
Comparison of the Pettis and McShane Integrals
Primitive of the McShane and Henstock?Kurzweil Integrals
Generalizations of Some Integrals
Readership: Graduate students and lecturers in mathematics.
312pp Pub. date: Aug 2005
ISBN 981-256-428-4