1st Edition, 2008, XXIV, 256 p. 6 illus., Hardcover
ISBN: 978-1-4020-8490-4
Due: May 2008
Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species).
This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painleve test. If the equation under study passes the Painleve test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions.
The examples chosen to illustrate these methods are mostly taken from physics. These include on the integrable side the nonlinear Schrodinger equation (continuous and discrete), the Korteweg-de Vries equation, the Henon-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in optical fibers, turbulence, etc), the Kuramoto-Sivashinsky equation (phase turbulence), the Kolmogorov-Petrovski-Piskunov equation (KPP, a reaction-diffusion model), the Lorenz model of atmospheric circulation and the Bianchi IX cosmological model.
Written at a graduate level, the book contains tutorial text as well as detailed examples and the state of the art on some current research.
Researchers in mathematical physics and pure and applied mathematics; graduate students in mathematics and physics; other scientists including physicists, chemists, and engineers, who need some aspect of Painleve equations or the Painleve property in their work and would use the book as a reference for results
Series: Lecture Notes in Mathematics , Vol. 1948
2008, Approx. 270 p., Softcover
ISBN: 978-3-540-68480-0
Due: July 2008
Recent years have seen dramatic progress in shape recognition algorithms applied to ever-growing image databases. They have been applied to image stitching, stereo vision, image mosaics, solid object recognition and video or web image retrieval. More fundamentally, the ability of humans and animals to detect and recognize shapes is one of the enigmas of perception.
The book describes a complete method that starts from a query image and an image database and yields a list of the images in the database containing shapes present in the query image. A false alarm number is associated to each detection. Many experiments will show that familiar simple shapes or images can reliably be identified with false alarm numbers ranging from 10-5 to less than 10-300.
Technically speaking, there are two main issues. The first is extracting invariant shape descriptors from digital images. The second is deciding whether two shape descriptors are identifiable as the same shape or not. A perceptual principle, the Helmholtz principle, is the cornerstone of this decision.
These decisions rely on elementary stochastic geometry and compute a false alarm number. The lower this number, the more secure the identification. The description of the processes, the many experiments on digital images and the simple proofs of mathematical correctness are interlaced so as to make a reading accessible to various audiences, such as students, engineers, and researchers.
1.Introduction.- Part I Extracting Image boundaries: 2.Extracting Meaningful Curves from Images.- Part II Level Line Invariant Descriptors: 3.Robust Shape Directions.- 4.Invariant Level Line Encoding.- Part III Recognizing Level Lines: 5.A Contrario Decision: the LLD Method.- 6.Meaningful Matches: Experiments on LLD and MSER.- Part V The SIFT Method: 10.The SIFT Method.- 11.Securing SIFT with A Contrario Techniques.- A.Keynotes.- A.1.Cluster Analysis Reader’s Digest.- A.2.Three classical methods for object detection based on spatial coherence.- A.3.On the Negative Association of Multinomial Distributions.- B.Algorithms.- B.1.LLD Method Summary.- B.2.Improved MSER Method Summary.- B.3.Improved SIFT Method Summary.- References.- Index.
Series: Lecture Notes in Mathematics , Vol. 1949
Subseries: Fondazione C.I.M.E., Firenze
2008, Approx. 230 p., Softcover
ISBN: 978-3-540-68266-0
Due: July 15, 2008
Pseudo-differential operators were initiated by Kohn, Nirenberg and Hormander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century.
The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.
Luigi Rodino, ManWah Wong: Preface.- Hans Feichtinger, Franz Luef, and Elena Cordero: Banach Gelfand Triples for Gabor Analysis.- Bernard Helffer: Four Lectures in Semiclassical Snalysis for non Self-adjoint Problems with Applications to Hydrodynamic Instability. Michael P. Lamoureux, Gary F. Margrave: An Introduction to Numerical Methods of Pseudodifferential Operators.- Nicolas Lerner: Some facts about the Wick calculus.- Joachim Toft: Schatten Properties for Pseudo-Differential Operators on Modulation Spaces.
Series: Universitext
2008, Approx. 210 p., Softcover
ISBN: 978-0-387-78752-7
Due: August 22, 2008
* Will become a standard reference on the subject
* Intended for graduate students and keeps prerequisites to a minimum
* Gives provocative examples in the simplest and most accessible terms
* The author is an expert who has originated many important ideas in the subject
Introduction to Siegel Modular Forms and Dirichlet Series gives a concise and self-contained introduction to the multiplicative theory of Siegel modular forms, Hecke operators, and zeta functions, including the classical case of modular forms in one variable. It serves to attract young researchers to this beautiful field and makes the initial steps more pleasant. It treats a number of questions that are rarely mentioned in other books. It is the first and only book so far on Siegel modular forms that introduces such important topics as analytic continuation and the functional equation of spinor zeta functions of Siegel modular forms of genus two.
* New, simplified approaches and a fresh outlook on classical problems
* The abstract theory of Heckea?“Shimura rings for symplectic and related groups
* The action of Hecke operators on Siegel modular forms
* Applications of Hecke operators to a study of the multiplicative properties of Fourier coefficients of modular forms
* The proof of analytic continuation and the functional equation (under certain assumptions) for Euler products associated with modular forms of genus two
*Numerous exercises
Preface.- Introduction: The Two Features of Arithmetical Zeta Functions.- Modular Forms.- Dirichlet Series of Modular Forms.- Hecke-Shimura Rings of Double Cosets.- Hecke Operators.- Euler Factorization of Radial Series.- Conclusion: Other Groups, Other Horizons.- Notes.- Short Bibliography