This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.
Contents:
Pascal Matrix, Classical Polynomials and Difference Equations (L Aceto & D Trigiante)
Logarithmic Order and Type of Indeterminate Moment Problems (C Berg & H L Pedersen)
A System of Biorthogonal Trigonometric Polynomials (E Berriochoa et al.)
On Two Problems in Lacunary Polynomial Interpolation (M G de Bruin)
A Myriad of Sierpinski Curve Julia Sets (R L Devaney)
The Comparative Index for Conjoined Bases of Symplectic Difference Systems (J V Elyseeva)
A Renaissance for a q-Umbral Calculus (T Ernst)
Fourth-Order Bessel-Type Special Functions: A Survey (W N Everitt)
On the Asymptotic Behavior of Solutions of Neuronic Difference Equations (Y Hamaya)
Computer Algebra Methods for Orthogonal Polynomials (W Koepf)
Riemann?Hilbert Problem for Generalized Nikishin System (A F Moreno)
Ideal Turbulence and Problems of Its Visualization (A N Sharkovsky)
Fine Structure of the Zeros of Orthogonal Polynomials: A Review (B Simon)
2+1 Dimensional Lattice Hierarchies Derived from Discrete Operator Zero Curvature Equations (Z-N Zhu)
and other papers
Readership: Researchers in analysis and differential equations, approximation theory and mathematical physics.
750pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-981-270-643-0
981-270-643-7
Albert Einstein, together with Theodor Kaluza and Oskar Klein, realized that extra dimensions can be used to unify the different fields of physics, as well as unifying the fields with their material sources. In fact, it was Einstein's dream to transpose the gbase woodh of the matter term in his field equations to the gmarbleh of the geometrical term. During his lifetime, this kind of unified theory achieved only partial success. But the modern approach, outlined in this bestseller, is elegant and agrees with all the classical tests. The basic idea is to unify the source and its field using the rich algebra of higher-dimensional Riemannian geometry. In other words, space, time and matter become parts of geometry.
Readership: Physicists, undergraduates and graduates.
250pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-981-270-632-4
981-270-632-1
This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations.
The other papers in this volume were specially written for the occasion of Prof Rozovskiifs 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives.
Contents:
Stochastic Evolution Equations (N V Krylov & B L Rozovskii)
Predictability of the Burgers Dynamics Under Model Uncertainty (D Blomker & J Duan)
Asymptotics for a Space-Time Wigner Transform (L Borcea et al.)
KdV Equation with Homogeneous Multiplicative Noise (A de Bouard & A Debussche)
Stochastic Fractional Burgers Equation (Z Brze?niak & L Debbi)
Optimal Compensation of Executives (A Cadenillas et al.)
The Freidlin?Wentzell LDP with Rapidly Growing Coefficients (P Chigansky & R Liptser)
Convergence Rate of Weak Approximations (D Crisan & S Ghazali)
Flow Properties of SDEs Driven by Fractional Brownian Motion (L Decreusefond & D Nualart)
Regularity for Stochastic Navier?Stokes Equation (F Flandoli & M Romito)
Rate of Convergence of Implicit Approximations (L Gyongy & A Millet)
Maximum Principle for SPDEs (N V Krylov)
Delay Estimation for Diffusion Processes (Yu A Kutoyants)
Cauchy?Dirichlet Problem for an Integro-Differential Equation (R Mikulevicius & H Pragarauskas)
Strict Solutions of Kolmogorov Equations (G Da Prato)
Readership: Graduate students and university researchers in mathematics.
420pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-981-270-662-1
981-270-662-3
Rigorous error estimates for amplitude equations are well known for deterministic PDEs, and there is a large body of literature over the past two decades. However, there seems to be a lack of literature for stochastic equations, although the theory is being successfully used in the applied community, such as for convective instabilities, without reliable error estimates at hand. This book is the first step in closing this gap.
The author provides details about the reduction of dynamics to more simpler equations via amplitude or modulation equations, which relies on the natural separation of time-scales present near a change of stability.
For students, the book provides a lucid introduction to the subject highlighting the new tools necessary for stochastic equations, while serving as an excellent guide to recent research.
Contents:
Formal Derivation of Amplitude Equations
Rigorous Results on Bounded Domains, SDEs as Amplitude Equations
Applications:
Approximation of Invariant Measures
Pattern Formation Below Criticality
Approximate Center Manifold
Large Domains, SPDEs as Amplitude Equations
Readership: Researchers and postgraduates in mathematics or applied sciences.
140pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-981-270-637-9
981-270-637-2
Series on Knots and Everything - Vol. 39
This is the first of three volumes collecting the original and now classic works in topology written in the 50s?60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated gSingular homologies of fibre spaces.h
This is the translation of the Russian edition published in 2005 with one entry (Milnorfs lectures on the h-cobordism) omitted.
Contents:
Smooth Manifolds and Their Applications in Homotopy Theory (L S Pontrjagin)
Some Global Properties of Differentiable Manifolds (R Thom)
Homotopy Properties of Thom Complexes (S P Novikov)
Generalized Poincarefs Conjecture in Dimension Greater Than Four (S Smale)
On the Structure of Manifolds (S Smale)
On the Formal Group Laws in Unoriented and Complex Cobordism Theory (D Quillen)
Formal Groups and Their Role in the Algebraic Topology Approach (V M Buchstaber, A S Mishchenko & S P Novikov)
Formal Groups, Power Systems and Adams Operators (V M Buchstaber & S P Novikov)
Readership: Researchers in homotopy topology and history of mathematics.
370pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-981-270-559-4
981-270-559-7
This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kahler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences ? topological, geometrical and algebraic ? are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.
Contents:
Calculus on Smooth Manifolds
The Hodge Theory of a Smooth, Compact, Oriented, Riemannian Manifold
Complex Manifolds
Hermitean Linear Algebra
Hermitean Manifolds
Kahler Manifolds
The Hard Lefschetz Theorem and the Hodge?Riemann Bilinear Relations
Mixed Hodge Structures, Semi-Simplicity and Approximation
Readership: Undergraduate and graduate students in mathematics.
120pp (approx.) Pub. date: Scheduled Fall 2007
ISBN 978-1-86094-800-8
1-86094-800-6
This unique book provides a unified and systematic account of internal, external and unsteady slow viscous flows, including the latest advances of the last decade, some of which are due to the author. The book shows how the method of eigenfunctions, in conjunction with least squares, can be used to solve problems of low Reynolds number flows, including three-dimensional internal and unsteady flows, which until recently were considered intractable. Although the methods used are quantitative, much stress is laid on understanding the qualitative nature of these intriguing flows. A secondary purpose of the book is to explain how the complex eigenfunction method can be used to solve problems in science and engineering.
Although primarily aimed at graduate students, academics and research engineers in the areas of fluid mechanics and applied mathematics, care has been taken, through the use of numerous diagrams and much discussion, to explain to the non-specialist the qualitative features of these complex flows.
Contents:
Physical Background
Least Squares and Eigenfunction Expansions
The Lid Driven Container (LDC)
Similarity Solutions, Streamlines and Eddies in Planar Flows
The New Embedding Method for Complex Geometries
The Singular LDC Problem and Its Resolution
Stokes Flows in Special Geometries
Planar Thermal, Mixed and Thermocapillary (Marangoni) Convection
General Features of Three-Dimensional (3D) Flows
3D Flow in a Cylinder and in a Liquid Bridge
3D Corner Eddies
3D Flow in Rectangular Container
3D Thermal Convection in a Cylinder
Eddy Structure in an Oscillating LDC
Applications to Mixing in LDCs and Viscous Attenuation
The Oseen Equations for External Flows
Flows Past Bluff Bodies and Arbitrary Streamlined Bodies
Readership: Graduate students, academics and research scientists working in the areas of fluid mechanics and applied mathematics; engineers and applied scientists working in technologies involving mixing, convection, materials processing and in geophysics etc.
350pp (approx.) Pub. date: Scheduled Fall 2007
ISBN 978-1-86094-780-3
1-86094-780-8
ISBN 978-1-86094-781-0(pbk)
1-86094-781-6(pbk)