This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found.
Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.
Contents:
Prologue
Sequences
Power Series Functions
Functional Equations without Differentiation
Functional Equations with Differentiation
Functional Equations with Iteration
Readership: Engineers, mathematicians, physicists, advanced undergraduates and graduates in mathematics.
280pp (approx.) Pub. date: Scheduled Spring 2008
ISBN 978-981-279-334-8
This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
Contents:
Complex White Noise and Infinite Dimensional Unitary Group (T Hida)
A New Explicit Formula for the Solution of the Black?Merton?Scholes Equation (J A Goldstein et al.)
An Infinite Dimensional Fourier?Mehler Transform and the Levy Laplacian (K Saito)
Quantum Stochastic Dilation of Symmetric Covariant Completely Positive Semigroups with Unbounded Generator (D Goswami & K B Sinha)
Donsker’s Functional Calculus and Related Questions (P-L Chow & J Potthoff)
Stochastic Analysis of Tidal Dynamics Equation (U Manna et al.)
Spaces of Test and Generalized Functions of Arcsine White Noise (A Riahi & H Ouerdiane)
Probability Measures with Sub-additive Principal Szego?Jacobi Parameters (A I Stan)
Adapted Solutions to the 3D Backward Stochastic Navier?Stokes Equations (P Sundar & H Yin)
White Noise Analysis in the Theory of 3-manifold Quantum Invariants (A Hahn)
Complex Ito Formulas (M Redfern)
Volatility Models of the Yield Curve (V Goodman)
Readership: Graduate-level researchers in stochastic analysis, mathematical physics and financial mathematics.
300pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-981-277-954-0
This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as E Bannai, P Hilton, M Jambu, I Kotsireas, B Schein and A Smoktunowicz.
Contents:
A Finitely Presented Group with Almost Solvable Conjugacy Problem (K Kalorkoti)
Recent Progress on the Existence of Weighing Matrices Constructed from Two Circulants (I S Kotsireas & C Koukouvinos)
Automorphisms of Free Algebras of Schreier Varieties of Algebras (A Survey) (A A Mikhalev)
Simply Transitive Semigroups of Binary Relations (B M Schein)
On rpp Semigroups, Their Subclasses and Their Generalizations (K P Shum)
Conformal Field Theory and Modular Functor (K Ueno)
Context-Free Languages Consisting of Nonprimitive Words: A New Proof of Ito?Katsura Theorem (P Domosi & M Ito)
Algebras Derived by Surjective Hypersubstitutions (K Denecke & R Srithus)
Stability of the Theory of Existentially Closed S-Sets (V Gould & J Fountain)
Grobner?Shirshov Bases for Dialgebras, Lie Algebras and Groups (L A Bokut & Y Chen)
and other papers
Readership: Researchers in algebras, combinatorics and theoretical computer science.
400pp (approx.) Pub. date: Scheduled Spring 2008
ISBN 978-981-279-000-2
This important book presents all the major works of Professor Wen-Tsun Wu, a widely respected Chinese mathematician who has made great contributions in the fields of topology and computer mathematics throughout his research career.
The book covers Wu’s papers from 1948 to 2005 and provides a comprehensive overview of his major achievements in algebraic topology, computer mathematics, and history of ancient Chinese mathematics. In algebraic topology, he discovered Wu classes and Wu formulas for Stiefel?Whitney classes of sphere bundles or differential manifolds, established an imbedding theory with an application to the layout problem of integrated circuits, and introduced the I*-functors which turns the “rational homotopy theory” created by D Sullivan into algorithmic form. In computer mathematics, he discovered Wu’s method of mechanical theorem proving by means of computers, which has been applied to prove and even discover on the computers hundreds of non-trivial theorems in various kinds of elementary and differential geometries. He also discovered a new effective method of polynomial equations solving, which has been used to solve problems raised from the fields of robotics and mechanisms, CAGD, computer vision, theoretic physics, celestial mechanics, and chemical equilibrium computation.
Contents:
On the Product of Sphere Bundles and the Duality Theorem Modulo Two
On Universal Invariant Forms
The Out-In Complementary Principle
On Chern Numbers of Algebraic Varieties with Arbitrary Singularities
On the Foundation of Algebraic Differential Geometry
On a Finiteness Theorem About Optimization Problems
On Surface-Fitting Problem in CAGD
On the Development of Real Number System in Ancient China
and other papers
Readership: Mathematicians; computer experts and non-experts interested in mathematics, and computer science.
500pp (approx.) Pub. date: Scheduled Spring 2008
ISBN 978-981-279-107-8
In the recent half-century, many mathematicians have investigated various problems on several equations of mixed type and obtained interesting results, with important applications to gas dynamics. However, the Tricomi problem of general mixed type equations of second order with parabolic degeneracy has not been completely solved, particularly the Tricomi and Frankl problems for general Chaplygin equation in multiply connected domains posed by L Bers, and the existence, regularity of solutions of the above problems for mixed equations with non-smooth degenerate curve in several domains posed by J M Rassias.
The method revealed in this book is unlike any other, in which the hyperbolic number and hyperbolic complex function in hyperbolic domains, and the complex number and complex function in elliptic domains are used. The corresponding problems for first order complex equations with singular coefficients are first discussed, and then the problems for second order complex equations are considered, where we pose the new partial derivative notations and complex analytic methods such that the forms of the above first order complex equations in hyperbolic and elliptic domains are wholly identical. In the meantime, the estimates of solutions for the above problems are obtained, hence many open problems including the above Tricomi?Bers and Tricomi?Frankl?Rassias problems can be solved.
Contents:
Elliptic Complex Equations of First Order
Elliptic Complex Equations of Second Order
Hyperbolic Complex Equations of First and Second Orders
First Order Complex Equations of Mixed Type
Second Order Linear Equations of Mixed Type
Second Order Quasilinear Equations of Mixed Type
Readership: Graduate students and academics in analysis, differential equations and applied mathematics.
456pp Pub. date: Dec 2007
ISBN 978-981-277-942-7
This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.
The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, parabolic geometries, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture “Leonhardt Euler ? 300 years on” by R Wilson. Notable contributors include A Asada, Manuel de Leon, Jurgen Eichhorn, J-H Eschenburg and Ivan Kolar.
Contents:
Riemannian Geometry
Submanifolds
Geometric Structures
Variational Calculus on Manifolds
Differential Equations
Geometric Methods in Physics
Readership: Researchers in differential geometry and mathematical physics.
500pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-981-279-060-6
981-279-060-8
Some books discuss chaos control methods and some others review nonlinear phenomena of circuits and systems, but few books have discussed the applications of chaos control methods in circuits and systems. In fact, circuits and systems require different considerations and the various chaos control methods should be applied accordingly. The scope and the emphasis of this book are to bridge the gap between chaos control methods and circuits and systems.
Contents:
Time Delay Feedback Control
Fuzzy Control
Sliding Mode Control
DC/DC Converters
PWM H-Bridge Inverters
Chua Circuits
Turbo Decoders
Phase Lock Loops
Sigma Delta Modulators
Epileptiform Bursting
Biomedical Systems
Readership: Graduates, researchers, academics, applied mathematicians and physicists in engineering and science.
250pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-981-279-056-9
981-279-056-X US