by E Cartan; translated by V V Goldberg (New Jersey Institute of Technology, USA)

RIEMANNIAN GEOMETRY IN AN ORTHOGONAL FRAME

Elie Cartan's book Geometry of Riemannian Manifolds (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925・6. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926・7 were different ・he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book Riemannian Geometry in an Orthogonal Frame (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fiber bundle of a submanifold, etc. The book of ﾉlie Cartan was available neither in English nor in French. It has now been translated into English by Vladislav V Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition.


Readership: Senior undergraduates, graduate students and researchers in geometry and topology.

300pp (approx.) Pub. date: Scheduled Winter 2001
ISBN 981-02-4746-X
ISBN 981-02-4747-8(pbk)

edited by M M Hafez & J J Chattot (University of California, Davis, USA)

INNOVATIVE METHODS FOR NUMERICAL
SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

This book consists of 20 review articles dedicated to Prof. Philip Roe on the occasion of his 60th birthday and in appreciation of his original contributions to computational fluid dynamics. The articles, written by leading researchers in the field, cover many topics, including theory and applications, algorithm developments and modern computational techniques for industry.

Contents:

"A One-Sided View": The Real Story (B van Leer)
Collocated Upwind Schemes for Ideal MHD (K G Powell)
The Penultimate Scheme for Systems of Conservation Laws: Finite Difference ENO with Marquina's Flux Splitting (R P Fedkiw et al.)
A Finite-Element-Based Level-Set for Multiphase Flows (B Engquist & A-K Tornberg)
The GHOST Fluid Method for Viscous Flows (R P Fedkiw & Xu Dong Liu)
Factorizable Schemes for the Equations of Fluid Flow (D Sidilkover)
Evolution Galerkin Methods as Finite Difference Schemes (K W Morton)
Fluctuation Distribution Schemes on Adjustable Meshes for Scalar Hyperbolic Equations (M J Baines)
Superconvergent Lift Estimates Through Adjoint Error Analysis (M B Giles & N A Pierce)
Somewhere Between the Lax妨endroff and Roe Schemes for Calculating Multidimensional Compressible Flows (A Lerat et al.)
Flux Schemes for Solving Nonlinear Systems of Conservation Laws (J M Ghidaglia)
A Lax妨endroff Type Theorem for Residual Schemes (R Abgrall et al.)
Kinetic Schemes for Solving Saint坊enant Equations on Unstructured Grids (M O Bristeau & B Perthame)
Nonlinear Projection Methods for Multi-Entropies Navier亡tokes Systems (C Berthon & F Coquel)
A Hybrid Fluctuation Splitting Scheme for Two-Dimensional Compressible Steady Flows (P De Palma et al.)
Some Recent Developments in Kinetic Schemes Based on Least Squares and Entropy Variables (S M Deshpande)
Difference Approximation for Scalar Conservation Law ・Consistency with Entropy Condition from the Viewpoint of Oleinik's E-Condition (Hideaki Aiso)
Lessons Learned from the Blast Wave Computation Using Overset Moving Grids ・Grid Motion Improves the Resolution (Kozo Fujii)

Readership: Researchers and graduate students in numerical and computational mathematics in engineering.

500pp Pub. date: Scheduled Winter 2001
ISBN 981-02-4810-5

edited by M Ito (Kyoto Sangyo University, Japan), Gh Paun (Institute of Mathematics, Romanian Academy, Romania) & S Yu (University of Western Ontario, Canada)

WORDS, SEMIGROUPS, AND TRANSDUCTIONS
Festschrift in Honor of Gabriel Thierrin

This is an excellent collection of papers dealing with combinatorics on words, codes, semigroups, automata, languages, molecular computing, transducers, logics, etc., related to the impressive work of Gabriel Thierrin. This volume is in honor of Professor Thierrin on the occasion of his 80th birthday.

Contents:

Some Operators on Families of Fuzzy Languages and Their Monoids (P R J Asveld)
Liars, Demons, and Chaos (C S Calude et al.)
Conditional Grammars with Restrictions by Syntactic Parameters (J Dassow)
Circularity and Other Invariants of Gene Assembly in Ciliates (A Ehrenfeucht et al.)
Catenation Closed Pairs and Forest Languages (C-M Fan & H-J Shyr)
Valence Grammars with Target Sets (H Fernau & R Stiebe)
Minimal Recognizers and Syntactic Monoids of DR Tree Languages (F G馗seg & M Steinby)
Visualizing Languages Using Primitive Powers (T Head)
Disjunctivity (H J・gensen)
String Operations Suggested by DNA Biochemistry: The Balanced Cut Operation (L Kari & A Paun)
How to Generate Binary Codes Using Context-Free Grammars (L K疽zonyi)
Generation and Parsing of Morphism Languages by Uniquely Parallel Parsable Grammars (J Lee & K Morita)
On the Generative Power of Iterated Transductions (V Manca)
Words, Dyck Paths, Trees, and Bijections (H Prodinger)
Iterated Morphisms with Complementarity on the DNA Alphabet (A Salomaa)
Topologies for the Set of Disjunctive w-Words (L Staiger)
and other papers.

Readership: Researchers in mathematics and computer science.

452pp Pub. date: Scheduled Winter 2001
ISBN 981-02-4739-7

by N Jacob (University of Wales Swansea, UK)

PSEUDO-DIFFERENTIAL OPERATORS AND MARKOV PROCESSES
Volume 1: Fourier Analysis and Semigroups

After recalling essentials of analysis ? including functional analysis, convexity, distribution theory and interpolation theory ? this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students.

Contents:

Essentials of Analysis: Calculus Results
Convexity
Some Interpolation Theory
Fourier Analysis and Convolution Semigroups: Fourier Transform in S and S'
Bounded Borel Measures and Positive Definite Functions
Convolution Semigroups and Negative Definite Functions
Bernstein Functions and Subordination
Levy-Khinchin Formula
Fourier Multiplier Theorems
One-Parameter Semigroups: Strongly Continuous and Analytic Contraction Semigroups
Subordinate Semigroups
Generators of Feller Semigroups
Dirichlet Forms and their Generators

Readership: Graduate students, researchers and lecturers in analysis & differential equations, stochastics, probability & statistics, and mathematical physics.

500pp (approx.) Pub. date: Scheduled Winter 2001
ISBN 1-86094-293-8

by A V Kelarev (University of Tasmania, Australia)

RING CONSTRUCTIONS AND APPLICATIONS

This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature.
Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs.

Contents:

Preliminaries
Graded Rings
Examples of Ring Constructions
The Jacobson Radical
Groups of Units
Finiteness Conditions
Varieties and Graded Rings
Gradings of Matrix Rings
Examples of Applications
Open Problems

Readership: Graduate students and researchers using ring constructions in their work.

200pp (approx.) Pub. date: Scheduled Summer 2002
ISBN 981-02-4745-1