Description
Distributed by Elsevier Science on behalf of Science Press. Available internationally for the first time, this book introduces the basic concepts and theory of the stability of numerical methods for solving differential equations, with emphasis on delay differential equations and basic techniques for proving stability of numerical methods. It is a desirable reference for engineers and academic researchers and can also be used by graduate students in mathematics, physics, and engineering.
Audience
Mathematicians, graduate students in mathematics, physics and engineering, and research scholars and engineers in control theory, population dynamics, electrical networks, environmental science, biology, bioecology, and life science.
Contents
Linear Multistep Methods; Runge-Kutta Methods; BDF Methods and Block Methods; Stability of Methods for Linear DDEs; Linear Systems of DDEs; Nonlinear Delay Differential Equations; Neutral Delay Differential Equations; Delay Volterra Integral Equations; Equations with Variable Delays
Bibliographic & ordering Information
Paperback, 295 pages, publication date: AUG-2007
ISBN-13: 978-7-03-016317-2
ISBN-10: 7-03-016317-6
Description
Distributed by Elsevier Science on behalf of Science Press. This book is mainly designed for graduate students who are interested in the theory of BCK and BCI-algebras. It introduces the general theoretical basis of BCI-algebras, omitting difficult proofs and abstract topics which are less necessary for beginners to learn. With abundant examples and exercises arranged after each section, it provides readers with easy-to-follow steps into this field.
Audience
Mathematicians and graduate students who are interested in BCK and BCI-algebra.
Contents
Introduction; General Theory; Commutative BCK-Algebras; Positive Implicative and Implicative BCK-Algebras; BCI-Algebras with Condition(S); Normal BCI-Algebras; Radicals and Ideals
Bibliographic & ordering Information
Paperback, 356 pages, publication date: AUG-2007
ISBN-13: 978-7-03-015411-8
ISBN-10: 7-03-015411-8
Description
Distributed by Elsevier Science on behalf of Science Press. This book discusses the accuracy of various finite element approximations and how to improve them, with the help of extrapolations and super convergence's post-processing technique. The discussion is based on asymptotic expansions for finite elements and finally reduces to the technique of integration by parts, embedding theorems and norm equivalence lemmas. The book is also devoted to explaining the origin of theorems.
Audience
Mathematicians and graduate students in mathematics, physics, and engineering.
Contents
Euler's Algorithm and Finite Element Method; Function Spaces and Norm Equivalence Lemmas; From ? to Eigenvalue Computation of PDEs; Expansion of Integrals on Rectangular Elements; Expansion of Integrals on Triangle Elements; Quasi-super convergence and Quasi-expansion; Postprocessing
Bibliographic & ordering Information
Hardbound, 320 pages, publication date: AUG-2007
ISBN-13: 978-7-03-016656-2
ISBN-10: 7-03-016656-6
This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas.
Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.
Contents:
Modulei Space of Killing Helices of Low Orders on a Complex Space Form (T Adachi)
KCC and Linear Stability for the Parkinson Tremor Model (V Balan)
The Camassa-Holm Equation as a Geodesic Flow For H1 Right-Invariant Metric (A Constantin & R I Ivanov)
Fermi-Walker Parallel Transport, Time Evolution of a Space Curve and the Schringer Equation as a Moving Curve (R Dandoloff)
Complex Submanifolds and Lagrangian Submanifolds Associate with Minimal Surfaces in Tori (N Ejiri)
Soliton Equations with Deep Reductions. Generalized Fourier Transforms (V Gerdjikov et al.)
Existence and Uniqueness Results for the Schringer ・Poisson System Below the Energy Norm (A M Ivanov & G P Venkov)
Exact Solutions of the Manakov System (N A Kostov)
Cluster Sets and Periodicity in Some Structure Fractals (J Lawrynowicz et al.)
Dispersion and Asymptotic Profiles for Kichhoff Equations (T Matsuyama & M Ruzhansky)
On the Hypoellipticity of Some Classes of Overdetermined Systems of Differential and Pseudodifferential Operators (P R Popivanov)
Baklund Transformations and Riemann-Hilbert Problem for N Wave Equations with Additional Symmetries (T Valchev)
and other papers
Readership: Researchers in analysis, differential geometry and mathematical physics.
352pp Pub. date: Jun 2007
ISBN 978-981-270-790-1
This unique text presents the new domain of consistent non-linear counterparts for all basic objects and tools of linear algebra, and develops an adequate calculus for solving non-linear algebraic and differential equations. It reveals the non-linear algebraic activity as an essentially wider and diverse field with its own original methods, of which the linear one is a special restricted case.
This volume contains a detailed and comprehensive description of basic objects and fundamental techniques arising from the theory of non-linear equations, which constitute the scope of what should be called non-linear algebra. The objects of non-linear algebra are presented in parallel with the corresponding linear ones, followed by an exposition of specific non-linear properties treated with the use of classical (such as the Koszul complex) and original new tools. This volume extensively uses a new diagram technique and is enriched with a variety of illustrations throughout the text. Thus, most of the material is new and is clearly exposed, starting from the elementary level. With the scope of its perspective applications spreading from general algebra to mathematical physics, it will interest a broad audience of physicists; mathematicians, as well as advanced undergraduate and graduate students.
Contents:
Solving Equations. Resultants
Evaluation of Resultants and Their Properties
Discriminants of Polylinear Forms
Examples of Resultants and Discriminants
Eigenspaces, Eigenvalues and Resultants
Iterated Maps
Potential Applications
Readership: Undergraduate and graduate students, and academics.
250pp (approx.) Pub. date: Scheduled Fall 2007
ISBN 978-981-270-800-7
The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.
The book’s guiding philosophy is, in the words of Newton, that “in learning the sciences examples are of more use than precepts”. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.
While we present most of the local aspects of classical differential geometry, the book has a “global and analytical bias”. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincare duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss?Bonnet theorem.
We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lp and Holder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.
The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.
Contents:
Manifolds
Natural Constructions on Manifolds
Calculus on Manifolds
Riemannian Geometry
Elements of the Calculus of Variations
The Fundamental Group and Covering Spaces
Cohomology
Characteristic Classes
Classical Integral Geometry Elliptic Equations on Manifolds
Dirac Operators
600pp Pub. date: Scheduled Winter 2007
ISBN 978-981-270-853-3