الصفحة 1
الصفحة 1
Nonlinear Smoothing and Multiresolution Analysis
This monograph presents a new theory for analysis, comparison and design of nonlinear smoothers, linking to established practices. Although a part of mathematical morphology, the special properties yield many simple, powerful and illuminating results leading to a novel nonlinear multiresolution analysis with pulses that may be as natural to vision as wavelet analysis is to acoustics. Similar to median transforms, they have the advantages of a supporting theory, computational simplicity, remarkable consistency, full trend preservation, and a Parceval-type identity.
Moment Analysis for Subsurface Hydrologic Applications
This book deals with the concept of moments, and how they find application in subsurface hydrologic problems-particularly those dealing with solute transport. This book will be very valuable to researchers who are beginning to learn about moment analysis, and will also be of interest to advanced researchers as well. Both temporal and spatial moments are dealt with in some detail for a wide variety of problems. Several examples using experimental data, both from laboratory columns and field experiments, are provided to give the readers a clear idea about the scope of this method. Apart from conventional uses of moments for solute transport problems, this book contains chapters dealing with use of moments in interval computing, vapour phase transport applications, transfer functions to subsurface tile drains, and construction of breakthrough curves from knowledge of moments.
Modelli Dinamici Discreti = Discrete Dynamic Models
Discrete mathematical modeling is one of the driving factors in modern mathematics research, and has played a role of synthesis between different disciplines, becoming a tool for qualitative and quantitative analysis in applied sciences. This volume provides an introduction to the analysis of discrete dynamic systems, following a modeling approach. An examination of a wide range of examples, models, and motivations drawn from Biology, Demography, Engineering and Economics, is followed by the presentation of the tools for the study of linear and non-linear scalar dynamical systems, with particular attention to stability analysis. The linear difference equations are studied in detail and an elementary introduction to the Z and DFT transforms is provided. One chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector dynamical systems and the applications of Markov chains are the subject of three chapters.
Metodi Matematici della Fisica = Mathematical Methods of Physics
This text draws its origin from my old notes, prepared for the course of Mathematical Methods of Physics and gradually arranged, refined and updated over the course of many years of teaching. The aim has always been to provide as simple and direct a presentation as possible of the mathematical methods relevant to Physics: Fourier series, Hilbert spaces, linear operators, functions of complex variables, Fourier and Laplace transforms, distributions. In addition to these basic topics, a brief introduction to the first notions of group theory, Lie algebras and symmetries in view of their applications to Physics is presented in the Appendix.
Measure Theory and Probability Theory
The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics.Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms.
Geometric Algebra for Computer Graphics
The first five chapters review the algebras of real numbers, complex numbers, vectors, and quaternions and their associated axioms, together with the geometric conventions employed in analytical geometry. As well as putting geometric algebra into its historical context, John Vince provides chapters on Grassmann’s outer product and Clifford’s geometric product, followed by the application of geometric algebra to reflections, rotations, lines, planes and their intersection. The conformal model is also covered, where a 5D Minkowski space provides an unusual platform for unifying the transforms associated with 3D Euclidean space.
Fundamentals of image data mining : Analysis, features, classification and retrieval
Presents a comprehensive review of the essentials of image data mining, and the latest cutting-edge techniques used in the field. The coverage spans all aspects of image analysis and understanding, offering deep insights into areas of feature extraction, machine learning, and image retrieval. The theoretical coverage is supported by practical mathematical models and algorithms, utilizing data from real-world examples and experiments. Topics and features: Describes essential tools for image mining, covering Fourier transforms, Gabor filters, and contemporary wavelet transforms / Develops many new exercises (most with MATLAB code and instructions) / Includes review summaries at the end of each chapter / Analyses state-of-the-art models, algorithms, and procedures for image mining / Integrates new sections on pre-processing, discrete cosine transform, and statistical inference and testing / Demonstrates how features like color, texture, and shape can be mined or extracted for image representation / Applies powerful classification approaches: Bayesian classification, support vector machines, neural / networks, and decision trees / Implements imaging techniques for indexing, ranking, and presentation, as well as database visualization
Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
In this book the author studies Fourier transforms using Deligne-Lusztig induction and the Lie algebra version of Lusztig’s character sheaves theory. He conjectures a commutation formula between Deligne-Lusztig induction and Fourier transforms that he proves in many cases. As an application the computation of the values of the trigonometric sums (on reductive Lie algebras) is shown to reduce to the computation of the generalized Green functions and to the computation of some fourth roots of unity.
Foundation Mathematics for Computer Science : A Visual Approach
In this second edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the original book and written new chapters on combinatorics, probability, modular arithmetic and complex numbers. These subjects complement the existing chapters on number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers.
Equity Valuation Using Multiples : An Empirical Investigation
Andreas Schreiner examines the role of multiples in equity valuation. He transforms the standard multiples valuation method into a comprehensive framework for using multiples in valuation practice, which corresponds to economic theory and is consistent with the results of a broad empirical study of European and U.S. equity markets.
Engineering Optics
Engineering Optics is a book for students who want to apply their knowledge of optics to engineering problems, as well as for engineering students who want to acquire the basic principles of optics. It covers such important topics as optical signal processing, holography, tomography, holographic radars, fiber optical communication, electro- and acousto-optic devices, and integrated optics (including optical bistability). As a basis for understanding these topics, the first few chapters give easy-to-follow explanations of diffraction theory, Fourier transforms, and geometrical optics. Practical examples, such as the video disk, the Fresnel zone plate, and many more, appear throughout the text, together with numerous solved exercises. There is an entirely new section in this updated edition on 3-D imaging.
Digital Phase Lock Loops : Architectures and Applications
This exciting new book covers various types of digital phase lock loops. It presents a comprehensive coverage of a new class of digital phase lock loops called the time delay tanlock loop (TDTL). It also details a number of architectures that improve the performance of the TDTL through adaptive techniques that overcome the conflicting requirements of the locking rage and speed of acquisition. These requirements are of paramount importance in many applications including wireless communications, consumer electronics and others. Digital Phase Lock Loops then illustrates the process of converting the TDTL class of digital phase lock loops for implementation on an FPGA-based reconfigurable system. These devices are being utilized in software-defined radio, DSP-based designs and many other communication and electronic systems to implement complex high-speed algorithms.
Determining Spectra in Quantum Theory
The main objective of this book is to give a collection of criteria available in the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition. at the total spectral measure associated with it;often studying such ameasure meant looking at some transform of the measure. The transforms were of the form f,?(A)f which is expressible, by the spectral theorem, as ?(x)dµ (x) for some finite measure µ . The two most widely used functions were the sx ?1 exponential function?(x)=e and the inverse function?(x)=(x?z) . These functions are “usable” in the sense that they can be manipulated with respect to addition of operators, which is what one considers most often in the spectral theory of Schrodinger type operators. Starting with this basic structure we look at the transforms of measures from which we can recover the measures and their components in Chapter 1. In Chapter 2 we repeat the standard spectral theory of selfadjoint op- ators. The spectral theorem is given also in the Hahn–Hellinger form. Both Chapter 1 and Chapter 2 also serve to introduce a series of definitions and notations, as they prepare the background which is necessary for the criteria in Chapter 3.
Continuous-Time Systems
The book systematically covers major foundations of the systems theory. First, the quantitative and qualitative methods of systems description are presented along with the stability analysis. The representation of linear time-invariant systems in the time domain is provided using the convolution, ordinarily differential equations (ODEs), and state space. In the frequency domain, these systems are analyzed using the Fourier and Laplace transforms. The linear time-varying systems are represented using the general convolution, ODEs, and state space. The nonlinear time-invariant systems are described employing the Taylor and Volterra series expansions, ODEs, state space, and approximate methods such as averaging, equivalent linearization, and describing function. Finally, the representation of nonlinear time-varying systems is given using the Taylor and Volterra series, ODEs, modulation functions method, and state space modelling.
Continuous-Time Signals
The book systematically covers major principle foundations of the signals theory. The representation of signals in the frequency domain (by Fourier transform) is considered with strong emphasis on how the spectral density of a single waveform becomes that of its burst and then the spectrum of its train. Different kinds of amplitude and angular modulations are analyzed noticing a consistency between the spectra of modulating and modulated signals. The energy and power presentation of signals is given along with their correlation properties. Finally, presenting the bandlimited and analytic signals, the book elucidates the methods of their description, transformation (by Hilbert transform), and sampling.
Mathematical methods for engineers and scientists 3 : Fourier analysis, partial differential equations and variational methods
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow.
Mathematical methods for engineers and scientists 2 : Vector analysis, ordinary differential equations and laplace transforms
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow.
Mathematical methods for engineers and scientists 1 : Complex analysis, determinants and matrices
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow.
Communication Systems
Presents main concepts of mobile communication systems, both analog and digitalIntroduces concepts of probability, random variables and stochastic processes and their applications to the analysis of linear systemsIncludes five appendices covering Fourier series and transforms, GSM cellular systems and more
Astronomical image and data analysis
With information and scale as central themes, this comprehensive survey explains how to handle real problems in astronomical data analysis using a modern arsenal of powerful techniques. It treats those innovative methods of image, signal, and data processing that are proving to be both effective and widely relevant. The coverage includes chapters or appendices on: detection and filtering; image compression; multichannel, multiscale, and catalog data analytical methods; wavelets transforms, Picard iteration, and software tools. This second edition of Starck and Murtagh's highly appreciated reference again deals with topics that are at or beyond the state of the art. It presents material which is more algorithmically oriented than most alternatives and broaches new areas like ridgelet and curvelet transforms. Throughout the book various additions and updates have been made.
