Series: Applied and Numerical Harmonic Analysis
2009, XVI, 160 p. 2 illus., Hardcover
ISBN: 978-0-8176-4915-9
Examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups
Provides countless examples and unique sets of exercises at the end of each section
A perfect companion to a first course in Fourier analysis
Includes special topics such as computing Eigenvalues of the Fourier transform, applications to Banach algebras, tensor decompositions of the Fourier transform and quadratic Gaussian sums
Introduces mathematics students to subjects that are within their reach but have powerful applications that also appeal to advanced researchers and mathematicians
The only prerequisites are group theory, linear algebra, and complex analysis
Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, cryptography, algorithms, and sequence design. This self-contained book provides a thorough look at the Fourier transform, one of the most useful tools in applied mathematics.
With countless examples and unique exercise sets at the end of most sections, Fourier Analysis on Finite Abelian Groups is a perfect companion for a first course in Fourier analysis. The first two chapters provide fundamental material for a strong foundation to deal with subsequent chapters.
Series: Springer Undergraduate Mathematics Series
2010, Approx. 395 p. 179 illus., Softcover
ISBN: 978-1-84882-890-2
Due: November 2009
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates.
Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum ? nothing beyond first courses in linear algebra and multivariable calculus ? and the most direct and straightforward approach is used throughout.
New features of this revised and expanded second edition include:
a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.
Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.
Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com
Series: Operator Theory: Advances and Applications , Vol. 197
2010, Approx. 410 p., Hardcover
ISBN: 978-3-0346-0182-5
Due: November 2009
About this book
The notions of transfer function and characteristic functions proved to be fundamental in the last fifty years in operator theory and in system theory. Moshe Livsic played a central role in developing these notions, and the book contains a selection of carefully chosen refereed papers dedicated to his memory. Topics include classical operator theory, ergodic theory and stochastic processes, geometry of smooth mappings, mathematical physics, Schur analysis and system theory. The variety of topics attests well to the breadth of Moshe Livsic's mathematical vision and the deep impact of his work.
The book will appeal to researchers in mathematics, electrical engineering and physics.
Researchers in mathematics, physics and electrical engineering: particularly in linear system theory, operator theory and functional analysis
Levy process
Schur analysis
characteristic function
ergodic theory
operator theory
quantum network
smooth mapping
system theory
Series: Computational Methods in Applied Sciences , Vol. 15
2010, Approx. 260 p., Hardcover
ISBN: 978-90-481-3238-6
Due: October 2009
The present volume is comprised of contributions solicited from invitees to conferences held at the University of Houston, Jyvaskyla University, and Xi’an Jiaotong University honoring the 70th birthday of Professor Roland Glowinski. Although scientists convened on three different continents, the Editors prefer to view the meetings as single event. The three locales signify the fact Roland has friends, collaborators and admirers across the globe.
The contents span a wide range of topics in contemporary applied mathematics ranging from population dynamics, to electromagnetics, to fluid mechanics, to the mathematics of finance. However, they do not fully reflect the breath and diversity of Roland’s scientific interest. His work has always been at the intersection mathematics and scientific computing and their application to mechanics, physics, engineering sciences and more recently biology. He has made seminal contributions in the areas of methods for science computation, fluid mechanics, numerical controls for distributed parameter systems, and solid and structural mechanics as well as shape optimization, stellar motion, electron transport, and semiconductor modeling. Two central themes arise from the corpus of Roland’s work. The first is that numerical methods should take advantage of the mathematical properties of the model. They should be portable and computable with computing resources of the foreseeable future as well as with contemporary resources. The second theme is that whenever possible one should validate numerical with experimental data.
The volume is written at an advanced scientific level and no effort has been made to make it self contained. It is intended to be of interested to both the researcher and the practitioner as well advanced students in computational and applied mathematics, computational science and engineers and engineering.
Preface (W. Fitzgibbon, Y. Kuznetsov, P. Neittaanmaki, J.Periaux, O.Pironneau); List of Contributors; Roland Glowinski: The Unconventional and Unexpected Path of a Mathematician (W Fitzgibbon and J.Periaux); The Scientific Career of Roland Glowinski (Olivier Pironneau); Janos Turi and Alain Bensoussan: On a Class of Partial Differential Equations with Nonlocal Dirichlet Boundary Conditions; Martin Berggren: A Unified Discrete-Continuous Sensitivity Analysis Method for Shape Optimization; J. Tambaca , S. Canic and D. Paniagua, M.D., A Novel Approach to Modeling Coronary Stents Using a Slender Curved Rod Model: A Comparison Between Fractured Xience-like and Palmaz-like Stents; Vincenzo Capasso and Daniela Morale: On the Stochastic Modelling of Interacting Populations. A Multiscale Approach Leading to Hybrid Models; Enrique Fernandez-Cara: Remarks on the Controllability of Some Parabolic Equations and Systems; M. Hintermuller and R.H.W. Hoppe: Goal Oriented Mesh Adaptivity for Mixed Control-State Constrained Elliptic Optimal Control Problems; Dan Joseph: Fluid Dynamics of Mixtures of Incompressible Miscible Liquids; Gerard Meurant: Analytic Bounds for Diagonal Elements of Functions of Matrices; Kazufumi Ito and Qin Zhang: Feedback Solution and Receding Horizon Control Synthesis for a Class of Quantum Control Problems; Yinggao Zheng, Hiroshi Suito, and Hideo Kawarada: Demand Forecasting Method Based on Stochastic Processes and Its Validation Using Real-World Data; Olli Mali and Sergey Repin: Two-Sided Estimates of the Solution Set for the Reaction-Diffusion Problem with Uncertain Data; Pekka Neittaanmaki and Sergey Repin: Guaranteed Error Bounds for Conforming Approximations of the Stationary Maxwell's Problem; M. Flueck, T. Hofer, A. Janka, and J. Rappaz: Numerical Methods for Ferromagnetic Plates; Jari Toivanen: A Componentwise Splitting Method for Pricing American Options under the Bates Model; Xu Zhang, Chuang Zheng, and Enrique Zuazua: Exact Controllability of the Time Discrete Wave Equation: a Multiplier Approach.
Series: Developments in Mathematics , Vol. 20
2009, X, 181 p. 10 illus., Hardcover
ISBN: 978-1-4419-0159-0
Due: October 2009
This monograph is the first devoted exclusively to the development of the theory of numerical semigroups. In this concise, self-contained text, graduate students and researchers will benefit from this broad exposition of the topic.
Key features of "Numerical Semigroups" include:
- Content ranging from the basics to open research problems and the latest advances in the field;
- Exercises at the end of each chapter that expand upon and support the material;
- Emphasis on the computational aspects of the theory; algorithms are presented to provide effective calculations;
- Many examples that illustrate the concepts and algorithms;
- Presentation of various connections between numerical semigroups and number theory, coding theory, algebraic geometry, linear programming, and commutative algebra would be of significant interest to researchers.
"Numerical Semigroups" is accessible to first year graduate students, with only a basic knowledge of algebra required, giving the full background needed for readers not familiar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in other fields such as algebraic geometry, number theory, and linear programming.
Series: Stochastic Modelling and Applied Probability , Vol. 38
1998. Corr. 2nd printing, 2010, XVI, 420 p., Softcover
ISBN: 978-3-642-03310-0
Due: October 15, 2009
The theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events which decay exponentially in the parameter. Originally developed in the context of statistical mechanics and of (random) dynamical systems, it proved to be a powerful tool in the analysis of systems where the combined effects of random perturbations lead to a behavior significantly different from the noiseless case. The volume complements the central elements of this theory with selected applications in communication and control systems, bio-molecular sequence analysis, hypothesis testing problems in statistics, and the Gibbs conditioning principle in statistical mechanics.
Starting with the definition of the large deviation principle (LDP), the authors provide an overview of large deviation theorems in ${{\rm I\!R}}^d$ followed by their application. In a more abstract setup where the underlying variables take values in a topological space, the authors provide a collection of methods aimed at establishing the LDP, such as transformations of the LDP, relations between the LDP and Laplace's method for the evaluation for exponential integrals, properties of the LDP in topological vector spaces, and the behavior of the LDP under projective limits. They then turn to the study of the LDP for the sample paths of certain stochastic processes and the application of such LDP's to the problem of the exit of randomly perturbed solutions of differential equations from the domain of attraction of stable equilibria. They conclude with the LDP for the empirical measure of (discrete time) random processes: Sanov's theorem for the empirical measure of an i.i.d. sample, its extensions to Markov processes and mixing sequences and their application.
Preface to the second edition.- Preface to the first edition.- Introduction.- LDP for Finite Dimensional Space.- Applications - The Finite Dimensional Case.- General Principles.- Sample Path Large Deviations.- The LDP for Abstract Empirical Measures.- Applications of Empirical Measures LDP.- Appendices.- Bibliography.- General Conventions.- Index of Notation.- Index.