This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data. It contains an overview of mathematical prerequisites and proceeds to describe hands-on programming techniques to implement special programs for signal analysis and other applications. From the table of contents: - Mathematical Preliminaries - Programming Techniques - The Discrete Fourier Transform - Local Trigonometric Transforms - Quadrature Filters - The Discrete Wavelet Transform - Wavelet Packets - The Best Basis Algorithm - Multidimensional Library Trees - Time-Frequency Analysis - Some Applications - Solutions to Some of the Exercises - List of Symbols - Quadrature Filter Coefficients

"This beautiful book can be read as a novel presenting carefully our quest to get more and more information from our observations and measurements. Its authors are particularly good at relating it." --Pierre C. Sabatier "This is a unique text - a labor of love pulling together for the first time the remarkably large array of mathematical and statistical techniques used for analysis of resolution in many systems of importance today - optical, acoustical, radar, etc.... I believe it will find widespread use and value." --Dr. Robert G.W. Brown, Chief Executive Officer, American Institute of Physics "The mix of physics and mathematics is a unique feature of this book which can be basic not only for PhD students but also for researchers in the area of computational imaging." --Mario Bertero, Professor, University of Geneva "a tour-de-force covering aspects of history, mathematical theory and practical applications. The authors provide a penetrating insight into the often confused topic of resolution and in doing offer a unifying approach to the subject that is applicable not only to traditional optical systems but also modern day, computer-based systems such as radar and RF communications." --Prof. Ian Proudler, Loughborough University "a 'must have' for anyone interested in imaging and the spatial resolution of images. This book provides detailed and very readable account of resolution in imaging and organizes the recent history of the subject in excellent fashion.... I strongly recommend it." --Michael A. Fiddy, Professor, University of North Carolina at Charlotte This book brings together the concept of resolution, which limits what we can determine about our physical world, with the theory of linear inverse problems, emphasizing practical applications. The book focuses on methods for solving illposed problems that do not have unique stable solutions. After introducing basic concepts, the con

This book is a comprehensive tool both for self-study and for use as a text in classical geometry. It explains the concepts that form the basis for computer-aided geometric design.

Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for research scientists, Spectral Computations for Bounded Operators addresses the issue of solving eigenvalue problems for operators on infinite dimensional spaces. From a review of classical spectral theory through concrete approximation techniques to finite dimensional situations that can be implemented on a computer, this volume illustrates the marriage of pure and applied mathematics. It contains a variety of recent developments, including a new type of approximation that encompasses a variety of approximation methods but is simple to verify in practice. It also suggests a new stopping criterion for the QR Method and outlines advances in both the iterative refinement and acceleration techniques for improving the accuracy of approximations. The authors illustrate all definitions and results with elementary examples and include numerous exercises. Spectral Computations for Bounded Operators thus serves as both an outstanding text for second-year graduate students and as a source of current results for research scientists.

Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a general theory of integral representation, relaxation, and homogenization for unbounded functionals. The first part of the book builds the foundation for the general theory with concepts and tools from convex analysis, measure theory, and the theory of variational convergences. The authors then introduce some function spaces and explore some lower semicontinuity and minimization problems for energy functionals. Next, they survey some specific aspects the theory of standard functionals. The second half of the book carefully develops a theory of unbounded, translation invariant functionals that leads to results deeper than those already known, including unique extension properties, representation as integrals of the calculus of variations, relaxation theory, and homogenization processes. In this study, some new phenomena are pointed out. The authors' approach is unified and elegant, the text well written, and the results intriguing and useful, not just in various fields of mathematics, but also in a range of applied mathematics, physics, and material science disciplines.

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory. The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow's theorem, and Black's median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard-Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu's degree of similarity of two fuzzy choice functions.

Written by bestselling author Stephen Doyle, this student book will engage and motivate you throughout the course. // Endorsed by WJEC offering high quality support you can trust. // Thorough coverage of all the topics in the AS Level Applied specification. // Extra support for the problem solving and unstructured questions in the specification. // Plenty of examples with worked answers throughout to enable you to check your understanding as you progress through the course. // Answers to questions are provided in order to check your work.

Over the last decade, statisticians have developed new statistical tools in the field of spatial point processes. At the same time, observational efforts have yielded a huge amount of new cosmological data to analyze. Although the main tools in astronomy for comparing theoretical results with observation are statistical, in recent years, cosmologists have not been generally aware of the developments in statistics and vice versa. Statistics of the Galaxy Distribution describes both the available observational data on the distribution of galaxies and the applications of spatial statistics in cosmology. It gives a detailed derivation of the statistical methods used to study the galaxy distribution and the cosmological physics needed to formulate the statistical models. Because the prevalent approach in cosmological statistics has been frequentist, the authors focus on the most widely used of these methods, but they also explore Bayesian techniques that have become popular in large-scale structure studies. Describing the most popular methods, their latest applications, and the necessary mathematical and astrophysical background, this groundbreaking book presents the state of the art in the statistical description of the large-scale structure of the Universe. Cosmology's well-defined and growing data sets represent an important challenge for the statistical analysis, and therefore for the statistics community. Statistics of the Galaxy Distribution presents a unique opportunity for researchers in both fields to strengthen the connection between them and, using a common language, explore the statistical description of the universe.

Complete coverage of Differential Equations for one or two semester course Includes coverage of PDEs and linear algebra Chapter on Power Series and series solutions added to this edition Focus on modeling and applications Emphasis on numerical solutions

Radar-based imaging of aircraft targets is a topic that continues to attract a lot of attention, particularly since these imaging methods have been recognized to be the foundation of any successful all-weather non-cooperative target identification technique. Traditional books in this area look at the topic from a radar engineering point of view. Consequently, the basic issues associated with model error and image interpretation are usually not addressed in any substantive fashion. Moreover, applied mathematicians frequently find it difficult to read the radar engineering literature because it is jargon-laden and device specific, meaning that the skills most applicable to the problem's solution are rarely applied. Enabling an understanding of the subject and its current mathematical research issues, Radar Imaging of Airborne Targets: A Primer for Applied Mathematicians and Physicists presents the issues and techniques associated with radar imaging from a mathematical point of view rather than from an instrumentation perspective. The book concentrates on scattering issues, the inverse scattering problem, and the approximations that are usually made by practical algorithm developers. The author also explains the consequences of these approximations to the resultant radar image and its interpretation, and examines methods for reducing model-based error.

Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics. Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques. Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.

Bayesian Modeling in Bioinformatics discusses the development and application of Bayesian statistical methods for the analysis of high-throughput bioinformatics data arising from problems in molecular and structural biology and disease-related medical research, such as cancer. It presents a broad overview of statistical inference, clustering, and classification problems in two main high-throughput platforms: microarray gene expression and phylogenic analysis. The book explores Bayesian techniques and models for detecting differentially expressed genes, classifying differential gene expression, and identifying biomarkers. It develops novel Bayesian nonparametric approaches for bioinformatics problems, measurement error and survival models for cDNA microarrays, a Bayesian hidden Markov modeling approach for CGH array data, Bayesian approaches for phylogenic analysis, sparsity priors for protein-protein interaction predictions, and Bayesian networks for gene expression data. The text also describes applications of mode-oriented stochastic search algorithms, in vitro to in vivo factor profiling, proportional hazards regression using Bayesian kernel machines, and QTL mapping. Focusing on design, statistical inference, and data analysis from a Bayesian perspective, this volume explores statistical challenges in bioinformatics data analysis and modeling and offers solutions to these problems. It encourages readers to draw on the evolving technologies and promote statistical development in this area of bioinformatics.

Large observational studies involving research questions that require the measurement of several features on each individual arise in many fields including the social and medical sciences. This book sets out both the general concepts and the more technical statistical issues involved in analysis and interpretation. Numerous illustrative examples are described in outline and four studies are discussed in some detail. The use of graphical representations of dependencies and independencies among the features under study is stressed, both to incorporate available knowledge at the planning stage of an analysis and to summarize aspects important for interpretation after detailed statistical analysis is complete. This book is aimed at research workers using statistical methods as well as statisticians involved in empirical research.

Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions. The text introduces the two main approaches to generalized functions: (1) as a nonuniform limit of a family of ordinary functions, and (2) as a functional over a set of test functions from which properties are inherited. The second approach is developed more extensively to encompass multidimensional generalized functions whose arguments are ordinary functions of several variables. As part of a series of books for engineers and scientists exploring advanced mathematics, Generalized Calculus with Applications to Matter and Forces presents generalized functions from an applied point of view, tackling problem classes such as: Gauss and Stokes' theorems in the differential geometry, tensor calculus, and theory of potential fields Self-adjoint and non-self-adjoint problems for linear differential equations and nonlinear problems with large deformations Multipolar expansions and Green's functions for elastic strings and bars, potential and rotational flow, electro- and magnetostatics, and more This third volume in the series Mathematics and Physics for Science and Technology is designed to complete the theory of functions and its application to potential fields, relating generalized functions to broader follow-on topics like differential equations. Featuring step-by-step examples with interpretations of results and discussions of assumptions and their consequences, Generalized Calculus with Applications to Matter and Forces enables readers to construct mathematical-physical models suited to new observations or novel engineering devices.

Natural scientists perceive and classify organisms primarily on the basis of their appearance and structure- their form , defined as that characteristic remaining invariant after translation, rotation, and possibly reflection of the object. The quantitative study of form and form change comprises the field of morphometrics. For morphometrics to succeed, it needs techniques that not only satisfy mathematical and statistical rigor but also attend to the scientific issues. An Invariant Approach to the Statistical Analysis of Shapes results from a long and fruitful collaboration between a mathematical statistician and a biologist. Together they have developed a methodology that addresses the importance of scientific relevance, biological variability, and invariance of the statistical and scientific inferences with respect to the arbitrary choice of the coordinate system. They present the history and foundations of morphometrics, discuss the various kinds of data used in the analysis of form, and provide justification for choosing landmark coordinates as a preferred data type. They describe the statistical models used to represent intra-population variability of landmark data and show that arbitrary translation, rotation, and reflection of the objects introduce infinitely many nuisance parameters. The most fundamental part of morphometrics-comparison of forms-receives in-depth treatment, as does the study of growth and growth patterns, classification, clustering, and asymmetry. Morphometrics has only recently begun to consider the invariance principle and its implications for the study of biological form. With the advantage of dual perspectives, An Invariant Approach to the Statistical Analysis of Shapes stands as a unique and important work that brings a decade's worth of innovative methods, observations, and insights to an audience of both statisticians and biologists.

As introduced in Dr. Lee's 10-week class, Applied Mathematics in Hydrogeology is written for professionals and graduate students who have a keen interest in the application of mathematics in hydrogeology. Its first seven chapters cover analytical solutions for problems commonly encountered in the study of quantitative hydrogeology, while the final three chapters focus on solving linear simultaneous equations, finite element analysis, and inversion for parameter determination. Dr. Lee provides various equation-solving methods that are of interest to hydrogeologists, geophysicists, soil scientists, and civil engineers, as well as applied physicists and mathematicians. In the classroom, this same information will help students realize how familiar equations in hydrogeology are derived-an important step toward development of a student's own mathematical models. Unlike other applied mathematics books that are structured according to systematic methodology, Applied Mathematics in Hydrogeology emphasizes equation-solving methods according to topics. Hydrogeological problems and governing differential equations are introduced, including hydraulic responses to pumping in confined and unconfined aquifers, as well as transport of heat and solute in flowing groundwater.

The practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience. Ideally, this experience could be obtained by working on actual modeling problems. But time constraints often make this difficult. Applied Mathematical Modeling provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines. The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in practice. These chapters discuss the general components of the modeling process, and the evolutionary nature of successful model building. The second part provides a rich compendium of case studies, each one complete with examples, exercises, and projects.In keeping with the multidimensional nature of the models presented, the chapters in the second part are listed in alphabetical order by the contributor's last name. Unlike most mathematical books, in which you must master the concepts of early chapters to prepare for subsequent material, you may start with any chapter. Begin with cryptology, if that catches your fancy, or go directly to bursty traffic if that is your cup of tea.Applied Mathematical Modeling serves as a handbook of in-depth case studies that span the mathematical sciences, building upon a modest mathematical background. Readers in other applied disciplines will benefit from seeing how selected mathematical modeling philosophies and techniques can be brought to bear on problems in their disciplines. The models address actual situations studied in chemistry, physics, demography, economics, civil engineering, environmental engineering, industrial engineering, telecommunications, and other areas.

A CHOICE "Outstanding Academic Title," the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, third edition continues to clearly show the usefulness of this subject for both students and researchers. The research in combinatorics of permutations has advanced rapidly since this book was published in a first edition. Now the third edition offers not only updated results, it remains the leading textbook for a course on the topic. Coverage is mostly enumerative, but there are algebraic, analytic, and topological parts as well, and applications. Since the publication of the second edition, there is tremendous progress in pattern avoidance (Chapters 4 and 5). There is also significant progress in the analytic combinatorics of permutations, which will be incorporated. *A completely new technique from extremal combinatorics disproved a long-standing conjecture, and this is presented in Chapter 4. *The area of universal permutations has undergone a lot of very recent progress, and that has been noticed outside the academic community as well. This also influenced the revision of Chapter 5. *New results in stack sorting are added to Chapter 8. *Chapter 9 applications to biology has been revised. The author's other works include Introduction to Enumerative and Analytic Combinatorics, second edition (CHOICE "Outstanding Academic Title") and Handbook of Enumerative Combinatorics, published by CRC Press. The author also serves as Series Editor for CRC's Discrete Mathematics and Its Applications.

Offers an applications-oriented treatment of parameter estimation from both complete and censored samples; contains notations, simplified formats for estimates, graphical techniques, and numerous tables and charts allowing users to calculate estimates and analyze sample data quickly and easily. Furnishing numerous practical examples, this resource serves as a handy reference for statisticians, biometricians, medical researchers, operations research and quality control practitioners, reliability and design engineers, and all others involved in the analysis of sample data from skewed distributions, as well as a text for senior undergraduate and graduate students in statistics, quality control, operations research, mathematics and biometry courses.

Using theory, applications, and examples of inferences, Niche Modeling: Predictions from Statistical Distributions demonstrates how to conduct and evaluate niche modeling projects in any area of application. It features a series of theoretical and practical exercises for developing and evaluating niche models using the R statistics language. The author discusses applications of predictive modeling methods with reference to valid inferences from assumptions. He elucidates varied and simplified examples with rigor and completeness. Topics include geographic information systems, multivariate modeling, artificial intelligence methods, data handling, and information infrastructure. Above all, successful niche modeling requires a deep understanding of the process of creating and using probability. Off-the-shelf statistical packages are tailored exactly to applications but can hide problematic complexities. Recipe book implementations fail to educate users in the details, assumptions, and pitfalls of analysis, but may be able to adapt to the specific needs of each study. Examining the sources of errors such as autocorrelation, bias, long term persistence, nonlinearity, circularity, and fraud, this seminal reference provides an understanding of the limitations and potential pitfalls of prediction, emphasizing the importance of avoiding errors.

Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and Stability Theory does just that-offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism. The author uses the example of the nonlinear pendulum-giving a thorough linear and nonlinear stability analysis of its equilibrium solutions-to introduce many of the ideas associated with the mathematical argument required in infinite dimensional Hamiltonian theory needed for fluid mechanics. He examines Andrews' Theorem, derives and develops the Charney-Hasegawa-Mima (CMH) equation, presents an account of the Hamiltonian structure of the Korteweg-de Vries (KdV) equation, and discusses the stability theory associated with the KdV soliton. The book's tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book.

Chapter 1 poses 134 problems concerning real and complex numbers, chapter 2 poses 123 problems concerning sequences, and so it goes, until in chapter 9 one encounters 201 problems concerning functional analysis. The remainder of the book is given over to the presentation of hints, answers or referen

The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Both process planning and scheduling are very important functions of manufacturing, which affect together the cost to manufacture a product and the time to deliver it. This book contains various approaches proposed by researchers to integrate the process planning and scheduling functions of manufacturing under varying configurations of shops. It is useful for both beginners and advanced researchers to understand and formulate the Integration Process Planning and Scheduling (IPPS) problem effectively. Features Covers the basics of both process planning and scheduling Presents nonlinear approaches, closed-loop approaches, as well as distributed approaches Discuss the outfit of IPPS in Industry 4.0 paradigm Includes the benchmarking problems on IPPS Contains nature-algorithms and metaheuristics for performance measurements in IPPS Presents analysis of energy-efficient objective for sustainable manufacturing in IPPS

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.