Samsonov,A.

Strain Solitons in Solids and How to Construct Them.

(Chapman & Hall/CRC Monographs & Surveys in Pure and Applied Mathematics, Series)

Dec. 2000 220 pp.
0-8493-0684-1

Although the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice. Inspired by this apparent contradiction, Strain Solitons in Solids and How to Construct Them refines the existing theory, explores how to construct a powerful deformation pulse in a waveguide without plastic flow or fracture, and proposes a direct method of strain soliton generation, detection, and observation. The author focuses on the theory, simulation, generation, and propagation of strain solitary waves in a nonlinearly elastic, straight cylindrical rod under finite deformations. He introduces the general theory of wave propagation in nonlinearly elastic solids and shows, from first principles, how its main ideas can lead to successful experiments. In doing so, he develops a new approach to solving the corresponding doubly dispersive equation (DDE) with dissipative terms, leading to new explicit and exact solutions. He also shows that the method is applicable to a variety of nonlinear problems. First discovered in virtual reality, nonlinear waves and solitons in solids are finally moving into the genuine reality of physics, mechanics, and engineering. Strain Solitons in Solids and How to Construct Them shows how to balance the mathematics of the problem with the application of the results to experiments and ultimately to generating and observing solitons in solids.

Vinogradov,S./Smith,P./Vinogradova,E.

Canonical Problems in Scattering and Potential Theory Set.

(Chapman & Hall/CRC Monographs & Surveys in Pure and Applied Mathematics, Series)

Dec. 2000
1-58488-164-X

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified. Part 1: Canonical Structures in Potential Theory develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. Part 2: Acoustic and Electromagnetic Diffraction by Canonical Structures examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures.

Zhigliavsky,A./Golyandina,N./Nekrutin,V.

Analysis of Time Series Structure: SSA and Related Techniques.

(Monographs on Statistics and Applied Probability, vol. 90)

Dec. 2000 320 pp.
1-58488-194-1

Over the last 15 years, singular spectrum analysis (SSA) has proven very successful. It has already become a standard tool in climatic and meteorological time series analysis and well known in nonlinear physics and signal processing. However, despite the promise it holds for time series applications in other disciplines, SSA is not widely known among statisticians and econometrists, and although the basic SSA algorithm looks simple, understanding what it does and where its pitfalls lay is by no means simple. Analysis of Time Series Structure: SSA and Related Techniques provides a careful, lucid description of its general theory and methodology.

Part I introduces the basic concepts, and sets forth the main findings and results, then presents a detailed treatment of the methodology. After introducing the basic SSA algorithm, the authors explore forecasting and apply SSA ideas to change-point detection algorithms.

Part II is devoted to the theory of SSA. Here the authors formulate and prove the statements of Part I. They address the singular value decomposition (SVD) of real matrices, time series of finite rank, and SVD of trajectory matrices.

Based on the authors' original work and filled with applications illustrated with real data sets, this book offers an outstanding opportunity to obtain a working knowledge of why, when, and how SSA works. It builds a strong foundation for successfully using the technique in applications ranging
from mathematics and nonlinear physics to economics, biology, oceanology, social science, engineering, financial econometrics, and market research.

Chou,K.-S./Zhu,X.-P.

The Curve Shortening Problem.

Dec. 2000 256 pp.
1-58488-213-1

Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature. For the first time, The Curve Shortening Problem collects and illuminates those results in a comprehensive, rigorous, and self-contained account of the fundamental results. The authors present a complete treatment of the Gage-Hamilton theorem, a clear, detailed exposition of Grayson's convexity theorem, a systematic discussion of invariant solutions, applications to the existence of simple closed geodesics on a surface, and a new, almost convexity theorem for the generalized curve shortening problem. Many questions regarding curve shortening remain outstanding. With its careful exposition and complete guide to the literature, The Curve Shortening Problem provides not only an outstanding starting point for graduate students and new investigations, but a superb reference that presents intriguing new results for those already active in the field.

Salaff,S./Yau,S.-T.

Ordinary Differential Equations. (Tentative)

2001 72 pp.
1-57146-065-9

This short introducticn to ordinary differential equations emerged from the course given by the authors at Chung Chi College, Chinese University of Hong Kong. It introduces students to differential equations in 8 brief lessons. Due to its simplicity, it has been helpful in similar courses around the vcrld. Now for the first time, it is being distributed to a large audience. Contents:Existence, Uniqueness, and continuous dependence Ccntinuation of solutions The linear equation Power series solutions Linear systems with constant coefficients Limit cycles I

Chen,W./Wang,C./Li,A-M./Simon,U./Wiehe,M./Verstraelen,L.(eds.)

Geometry and Topology of Submanifolds, X:
a Volume Dedicated to Professor S S Chern
on the Occasion of His 89th Birthday Peking Univ., 1999.

Dec. 2000 360 pp.
981-02-4476-2

Contents: Progress in Affine Differential Geometry - Problem List and Continued Bibliography (T Binder & U Simon); On the Classification of Timelike Bonnet Surfaces (W H Chen & H Z Li); Affine Hyperspheres with Constant Affine Sectional Curvature (F Dillen et al.); Geometric Properties of the Curvature Operator (P Gilkey); On a Question of S S Chern Concerning Minimal Hypersurfaces of Spheres (I Hiric( & L Verstraelen); Parallel Pure Spinors on Pseudo-Riemannian Manifolds (I Kath); Twistorial Construction of Spacelike Surfaces in Lorentzian 4-Manifolds (F Leitner); Nirenberg's Problem in 90's (L Ma); A New Proof of the Homogeneity of Isoparametric Hypersurfaces with (g,m) = (6,1) (R Miyaoka); Harmonic Maps and Negatively Curved Homogeneous Spaces (S Nishikawa): Biharmonic Morphisms Between Riemannian Manifolds (Y L Ou); Intrinsic Properties of Real Hypersurfaces in Complex Space Forms (P J Ryan); On the Nonexistence of Stable Minimal Submanifolds in Positively Pinched Riemannian Manifolds (Y B Shen & H Q Xu); Geodesic Mappings of the Ellipsoid (K Voss); r-Invariants and the Poincare-Hopf Index Formula (W Zhang); and other papers.

Delgado,J./Lacomba,E./Perez-Chavela,E./Libre,J.(eds.)

Hamiltonian Systems and Celestial Mechanics: Hamsys-98;
Proceedings of the III Int'l Symposium, Patzcuaro.

Dec. 2000
981-02-4463-0

This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and CelestialMechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems,billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through therefereeing process typical of a mathematical research journal.

Dupont,J.

Scissors Congruences, Group Homology and Characteristic Classes.

Dec. 2000 180 pp.
981-02-4507-6(hardcover)
981-02-4508-4(softcover)

These lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chin-Han Sah on various aspects of Hilbert's Third Problem: Are two Euclidean polyhedra with the same volume "scissors-congruent", i.e. can they be subdivided into finitely many pairwise congruent pieces? The book starts from the classical solution of this problem by M Dehn. But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of groups, algebraic K-theory, characteristic classes for flat bundles, and invariants for hyperbolic manifolds. Some of the material, particularly in the chapters on projective configurations, is published here for the first time.