Edited by: Donggao Deng, Zhongshan University, Guangzhou, People's Republic of China,
Daren Huang, Zhejiang University, Hangzhou, People's Republic of China,
Rong-Qing Jia, University of Alberta, Edmonton, AB, Canada,
Wei Lin, Zhongshan University, Guangzhou, People's Republic of China,
and Jianzhong Wang, Sam Houston State University, Huntsville, TX
Wavelet Analysis and Applications
Expected publication date is March 20, 2002
Description
Wavelet analysis has been one of the major research directions in science in the last decade. More and more mathematicians and scientists join this exciting research area. Certainly, wavelet analysis has had a great impact in areas such as approximation theory, harmonic analysis, and scientific computation. More importantly, wavelet analysis has shown great potential in applications to information technology such as signal processing, image processing, and computer graphics.
China has played a significant role in this development of wavelet analysis as evidenced by many fruitful theoretical results and practical applications. A conference on wavelet analysis and its applications was organized to exchange ideas and results with international research groups at Zhongshan University (Guangzhou, China). This volume contains the proceedings from that conference.
Comprised here are selected papers from the conference, covering a wide range of research topics of current interest. Many significant results are included in the study of refinement equations and refinable functions, properties and construction of wavelets, spline wavelets, multi-wavelets, wavelet packets, shift-invariant spaces, approximation schemes and subdivision algorithms, and tilings. Several papers also focus on applications of wavelets to numerical solutions of partial differential equations and integral equations, image processing and facial recognition, computer vision, and feature extraction from data.
Contents
A. Aldroubi, Q. Sun, and W.-S. Tang -- Non-uniform sampling in multiply generated shift-invariant subspaces of L^p(\mathbb{R}^d)
R. Ashino, C. Heil, M. Nagase, and R. Vaillancourt -- Multiwavelets, pseudodifferential operators and microlocal analysis
S. Basu, C. A. Micchelli, and P. Olsen -- A maximum entropy criterion for feature extraction
O. Bratteli and P. E. T. Jorgensen -- Wavelet filters and infinite-dimensional unitary groups
G. J. Chae, H. O. Kim, and R. Y. Kim -- On the Cohen-type conditions for the stabiltiy of shifts of a refinable function
W. Chen and W. Lin -- Trigonometric Hermite wavelet and natural integral equations for Stokes problem
D.-Q. Dai -- Vision, harmonic oscillator and wavelets
T. N. T. Goodman and S. L. Lee -- Some properties of refinable splines
L. Gori and F. Pitolli -- On some applications of a class of totally positive bases
B. Han and S. D. Riemenschneider -- Interpolatory biorthogonal wavelets and CBC algorithm
D. P. Hardin and T. A. Hogan -- Constructing orthogonal refinable function vectors with prescribed approximation order and smoothness
D. Huang, Z. Wang, and Z. Zhang -- On M-band wavelets having three vanishing moments
R.-Q. Jia and Q.-T. Jiang -- Approximation power of refinable vectors of functions
J. Ning -- Wavelet decomposition under translate
H. O. Kim and J. K. Lim -- Applications of shift-invariant space theory to some problems of multi-resolution analysis of L^2({\mathbb R}^d)
I. Kirat and K.-S. Lau -- On the connectedness and classification of self-affine tiles
X.-z. Liang and M.-c. Liu -- Wavelet-Galerkin methods for second kind integral equations
S. Li -- Convergence of cascade algorithms in L_p (0<p<1)
I. Ya. Novikov -- Asymptotics of zeros of Bernstein polynomials that are related to modified Daubechies wavelets
Q. Sun -- Homogeneous and nonhomogeneous refinable distributions in F^{q,\gamma}
J. Tang, S. Kawato, and J. Ohya -- A wavelet transform based face recognition system and its applications
J. Wang -- Spline wavelets in numerical resolution of partial differential equations
M. V. Wickerhauser -- Basis and convergence properties of wavelet packets
L. Yang and Y. Y. Tang -- A wavelet-based characterization of curves
P. C. Yuen, G. C. Feng, J. H. Lai, and D. Q. Dai -- Face processing and recognition technology
D.-X. Zhou -- The p-norm joint spectral radius and its applications in wavelet analysis
Details:
Series: AMS/IP Studies in Advanced Mathematics Volume: 25
Publication Year: 2002
ISBN: 0-8218-2991-2
Paging: 326 pp.
Binding: Softcover
E. B. Dynkin, Cornell University, Ithaca, NY
Diffusions, Superdiffusions and Partial Differential Equations
Expected publication date is March 23, 2002
Description
Interactions between the theory of partial differential equations of elliptic and parabolic types and the theory of stochastic processes are beneficial for both probability theory and analysis. At the beginning, mostly analytic results were used by probabilists. More recently, analysts (and physicists) took inspiration from the probabilistic approach. Of course, the development of analysis in general and of the theory of partial differential equations in particular, was motivated to a great extent by problems in physics. A difference between physics and probability is that the latter provides not only an intuition, but also rigorous mathematical tools for proving theorems.
The subject of this book is connections between linear and semilinear differential equations and the corresponding Markov processes called diffusions and superdiffusions. Most of the book is devoted to a systematic presentation (in a more general setting, with simplified proofs) of the results obtained since 1988 in a series of papers of Dynkin and Dynkin and Kuznetsov. Many results obtained originally by using superdiffusions are extended in the book to more general equations by applying a combination of diffusions with purely analytic methods. Almost all chapters involve a mixture of probability and analysis.
Similar to the other books by Dynkin, Markov Processes (Springer-Verlag), Controlled Markov Processes (Springer-Verlag), and An Introduction to Branching Measure-Valued Processes (American Mathematical Society), this book can become a classical account of the presented topics.
Contents
Introduction
Parabolic equations and branching exit Markov systems
Linear parabolic equations and diffusions
Branching exit Markov systems
Superprocesses
Semilinear parabolic equations and superdiffusions
Elliptic equations and diffusions
Linear elliptic equations and diffusions
Positive harmonic functions
Moderate solutions of Lu=\psi(u)
Stochastic boundary values of solutions
Rough trace
Fine trace
Martin capacity and classes \mathcal{N}_1 and \mathcal{N}_0
Null sets and polar sets
Survey of related results
Basic facts of Markov processes and Martingales
Facts on elliptic differential equations
Epilogue
Bibliography
Subject index
Notation index
Details:
Series: Colloquium Publications, Volume: 50
Publication Year: 2002
ISBN: 0-8218-3174-7
Paging: approximately 240 pp.
Binding: Hardcover
Edited by: Samuel J. Lomonaco, Jr.
Quantum Computation:
A Grand Mathematical Challenge for the Twenty-First Century and the Millennium
Expected publication date is March 23, 2002
Description
This book presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, D.C. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field. Interrelationships with existing mathematical research areas were emphasized as much as possible. Moreover, the course was designed so that participants with little background in quantum mechanics would, upon completion, be prepared to begin reading the research literature on quantum computation and quantum information science.
Based on audience feedback and questions, the written versions of the lectures have been greatly expanded, and supplementary material has been added. The book features an overview of relevant parts of quantum mechanics with an introduction to quantum computation, including many potential quantum mechanical computing devices; introduction to quantum algorithms and quantum complexity theory; in-depth discussion on quantum error correcting codes and quantum cryptography; and finally, exploration into diverse connections between quantum computation and various areas of mathematics and physics.
Contents
An invitation to quantum computation
S. J. Lomonaco, Jr. -- A Rosetta stone for quantum mechanics with an introduction to quantum computation
H. E. Brandt -- Qubit devices
Quantum algorithms and quantum complexity theory
S. J. Lomonaco, Jr. -- Introduction to quantum algorithms
S. J. Lomonaco, Jr. -- Shor's quantum factoring algorithm
U. V. Vazirani -- A survey of quantum complexity theory
S. J. Lomonaco, Jr. -- Grover's quantum search algorithm
Quantum error correcting codes and quantum cryptography
D. Gottesman -- An introduction to quantum error correction
S. J. Lomonaco, Jr. -- A talk on quantum cryptography or how Alice outwits Eve
More mathematical connections
A. Kitaev -- Topological quantum codes and anyons
L. H. Kauffman -- Quantum topology and quantum computing
S. J. Lomonaco, Jr. -- An entangled tale of quantum entanglement
Index
Details:
Series: Proceedings of Symposia in Applied Mathematics,Volume: 58
Publication Year: 2002
ISBN: 0-8218-2084-2
Paging: approximately 360 pp.
Binding: Hardcover
Yasumasa Nishiura, Hokkaido University, Sapporo, Japan
Far-from-Equilibrium Dynamics
Expected publication date is April 14, 2002
Description
This book is devoted to the study of evolution of nonequilibrium systems. Such a system usually consists of regions with different dominant scales, which coexist in the space-time where the system lives. In the case of high nonuniformity in special direction, one can see patterns separated by clearly distinguishable boundaries or interfaces.
The author considers several examples of nonequilibrium systems. One of the examples describes the invasion of the solid phase into the liquid phase during the crystallization process. Another example is the transition from oxidized to reduced states in certain chemical reactions. An easily understandable example of the transition in the temporal direction is a sound beat, and the author describes typical patterns associated with this phenomenon.
The main goal of the book is to present a mathematical approach to the study of highly nonuniform systems and to illustrate it with examples from physics and chemistry. The two main theories discussed are the theory of singular perturbations and the theory of dissipative systems. A set of carefully selected examples of physical and chemical systems nicely illustrates the general methods described in the book.
Contents
Separation and unification of scales
Amplitude equations
Marginal stability criterion and pattern selection
Pattern formation
Method of singular limit analysis
Transient dynamics
Future perspectives
Bibliography
Index
Details:
Series: Translations of Mathematical Monographs,Volume: 209
Publication Year: 2002
ISBN: 0-8218-2625-5
Paging: approximately 336 pp.
Binding: Softcover
Edited by: A. Chenciner, Institute de Mecanique Celeste, Paris, France,
R. Cushman, University of Utrecht, Netherlands,
and C. Robinson and Z. Xia, Northwestern University, Evanston, IL
Celestial Mechanics:
Dedicated to Donald Saari for his 60th Birthday
Expected publication date is March 20, 2002
Description
This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, IL) in celebration of Donald Saari's sixtieth birthday. Many leading experts and researchers presented their recent results.
Don Saari's significant contribution to the field came in the late 1960s through a series of important works. His work revived the singularity theory in the n-body problem which was started by Poincare and Painleve. Saari's solution of the Littlewood conjecture, his work on singularities, collision and noncollision, on central configurations, his decompositions of configurational velocities, etc., are still much studied today and were reflected throughout the conference.
This volume covers various topics of current research, from central configurations to stability of periodic orbits, from variational methods to diffusion mechanisms, from the dynamics of secular systems to global dynamics of the solar systems via frequency analysis, from Hill's problem to the low energy transfer orbits and mission design in space travel, and more. This classic field of study is very much alive today and this volume offers a comprehensive representation of the latest research results.
Contents
A. Albouy and J. Llibre -- Spatial central configurations for the 1 + 4 body problem
E. Belbruno -- Analytic estimation of weak stability boundaries and low energy transfers
F. Beukers and R. Cushman -- The complex geometry of the spherical pendulum
A. Chenciner -- Action minimizing periodic orbits in the Newtonian n-body problem
M. Corbera and J. Llibre -- On symmetric periodic orbits of the elliptic Sitnikov problem via the analytic continuation method
W. S. Koon, J. E. Marsden, S. D. Ross, and M. W. Lo -- Constructing a low energy transfer between Jovian moons
E. A. Lacomba, J. Llibre, and E. Perez-Chavela -- The generalized Sitnikov problem
C. Marchal -- Reflexions on the future of celestial mechanics
R. Moeckel -- Generic drift on Cantor sets of annuli
R. Montgomery -- Action spectrum and collisions in the planar three-body problem
P. H. Rabinowitz and E. W. Stredulinsky -- A variational shadowing method
C. Robinson -- Symbolic dynamics for transition tori
C. Simo -- Dynamical properties of the figure eight solution of the three-body problem
Y.-S. Sun, J.-L. Zhou, J.-Q. Zheng, and M. Valtonen -- Diffusion in comet motion
Q. Wang -- The Hill's region of the four-body problem
Z. Xia -- Some of the problems that Saari didn't solve
Details:
Series: Contemporary Mathematics,Volume: 292
Publication Year: 2002
ISBN: 0-8218-2902-5
Paging: approximately 280 pp.
Binding: Softcover