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˜The œillustrated wavelet transform handbook / par Addison,, Napler. Publication : [S.l.] : Taylor & Francis, 2002 . 400 p. ; , Contents Preface Chapter 1: Getting started Chapter 2: The continuous wavelet transform 2.1 Introduction 2.2 The Wavelet 2.3 Requirements for the Wavelet 2.4 The Energy Spectrum of the Wavelet 2.5 The Wavelet Transform 2.6 Identification of Coherent Structures 2.7 Edge Detection 2.8 The Inverse Wavelet Transform 2.9 The Signal Energy: Wavelet Based Energy and Power Spectra 2.10 The Wavelet Transform in Terms of the Fourier Transform 2.11 Complex Wavelets: The Morlet Wavelet 2.12 The Wavelet Transform, Short Time Fourier Transform and Heisenberg Boxes 2.13 Adaptive Transforms: Matching Pursuits 2.14 Wavelets in Two or More Dimensions 2.15 The CWT: Computation, Boundary Effects and Viewing 2.16 Endnotes 2.16.1 Chapter Key Words and Phrases 2.16.2 Further Resources Chapter 3: The Discrete Wavelet Transform 3.1 Introduction 3.2 Frames and Orthogonal Wavelet Bases 3.2.1 Frames 3.2.2 Dyadic Grid Scaling and Orthonormal Wavelet Transforms 3.2.3 The Scaling Function and the Multiresolution Representation 3.2.4 The Scaling Equation, Scaling Coefficients and Associated Wavelet Equation 3.2.5 The Haar Wavelet 3.2.6 Coefficients from Coefficients: The Fast Wavelet Transform 3.3 Discrete Input Signals of Finite Length 3.3.1 Approximations and Details 3.3.2 The Multiresolution Algorithm - An Example 3.3.3 Wavelet Energy 3.3.4 Alternative Indexing of Dyadic Grid Coefficients 3.3.5 A Simple Worked Example: The Haar Wavelet Transform 3.4 Everything Discrete 3.4.1 Discrete Experimental Input Signals 3.4.2 Smoothing, Thresholding and Denoising 3.5 Daubechies Wavelets 3.5.1 Filtering 3.5.2 Symmlets and Coiflets 3.6 Translation Invariance 3.7 Biorthogonal Wavelets 3.8 Two-Dimensional Wavelet Transforms 3.9 Adaptive Transforms: Wavelet Packets 3.10 Endnotes 3.10.1 Chapter Key Words and Phrases 3.10.2 Further Resources CHAPTER 4: FLUIDS 4.1 Introduction 4.2 Statistical Measures 4.2.1 Moments, Energy and Power Spectra 4.2.2 Intermittency and Correlation 4.2.3 Wavelet Thresholding 4.2.4 Wavelet Selection using Entropy Measures 4.3 Engineering Flows 4.3.1 Jets, Wakes, Turbulence and Coherent Structures 4.3.2 Fluid-Structure Interaction 4.3.3 Two-Dimensional Flow Fields 4.4 Geophysical Flows 4.4.1 Atmospheric Processes 4.4.2 Ocean Processes 4.5 Other Applications in Fluids and Further Resources CHAPTER 5: ENGINEERING TESTING, MONITORING AND CHARACTERISATION 5.1 Introduction 5.2 Machining Processes: Control, Chatter, Wear and Breakage 5.3 Rotating Machinery 5.3.1 Gears 5.3.2 Shafts, Bearings and Blades 5.4 Dynamics 5.5 Chaos 5.6 Non-Destructive Testing 5.7 Surface Characterisation 5.8 Other Applications in Engineering and Further Resources 5.8.1 Impacting 5.8.2 Data Compression 5.8.3 Engines 5.8.4 Miscellaneous CHAPTER 6: MEDICINE 6.1 Introduction 6.2 The Electrocardiogram 6.2.1 ECG Timing, Distortions and Noise 6.2.2 Detection of Abnormalities 6.2.3 Heart Rate Variability 6.2.4 Cardiac Arrhythmias 6.2.5 ECG Data Compression 6.3 Neuroelectric Waveforms 6.3.1 Evoked Potentials and Event-Related Potentials 6.3.2 Epileptic Seizures and Epileptogenic Foci 6.3.3 Classification of the EEG using Artificial Neural Networks 6.4 Pathological Sounds, Ultrasounds and Vibrations 6.4.1 Blood Flow Sounds 6.4.2 Heart Sounds and Heart Rates 6.4.3 Lung Sounds 6.4.4 Acoustic Response 6.5 Blood Flow and Blood Pressure 6.6 Medical Imaging 6.6.1 Ultrasonic Images 6.6.2 Magnetic Resonance Imaging, Computed Tomography and other Radiographic Images 6.6.3 Optical Imaging 6.7 Other Applications in Medicine 6.7.1 Electromyographic Signals 6.7.2 Sleep Apnea 6.7.3 DNA 6.7.4 Miscellaneous 6.7.5 Further Resources CHAPTER 7: FRACTALS, FINANCE, GEOPHYSICS AND OTHER AREAS 7.1 Introduction 7.2 Fractals 7.2.1 Exactly Self-Similar Fractals 7.2.2 Stochastic Fractals 7.2.3 Multifractals 7.3 Finance 7.4 Geophysics 7.4.1 Properties of Subsurface Media 7.4.2 Surface Fea. 26 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

An Introduction to scientific computing : twelve computational projects solved with matlab / par Danaila, Ionut. Publication : [S.l.] : Springer, 2006 . 294 p. ; , This book provides twelve computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in the subject of numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets). The book is primarily intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Analytical methods for problems of molecular transport / par Ivchenko, I.N. Publication : [S.l.] : Springer, 2007 . 409 p. ; , The Kinetic Theory of Gases has applications in many areas of science and technology as well as in our understandings of many natural processes and phenomena from the nano-scale up to the cosmic-scale. Some of the fields and topics affected include manufacturing, health care, weather, defence, pollution, aerospace science and engineering, and others. In particular, the interactions of rarefied gases with surfaces are of great interest because such interactions can have pronounced effects on the behaviour exhibited by those systems in all of the above fields. Such fundamental things as the transfer of mass, momentum, and energy between the components of a system can be significantly altered by such interactions. Collectively this transfer is typically described in terms of Rarefied Gas Dynamics and Transport Theory which generally go hand-in-hand with the Kinetic Theory of Gases. When this transport involves small particles suspended in a gas such as air, it is typically termed Aerosol Mechanics. Thus, this book should prove to be a very useful tool in virtually all application areas involving the Kinetic Theory of Gases, Rarefied Gas Dynamics, Transport Theory, and Aerosol Mechanics. This book is designed to serve a dual function. It is intended that it be capable of serving as a teaching instrument, either in a classroom environment or independently, for the study of basic analytical methods and mathematical techniques that may be used in the Kinetic Theory of Gases and is primarily suitable for use in graduate level physics and engineering courses on the subject. This book should also prove to be useful as a reference for scientists and engineers working in the fields of Rarefied Gas Dynamics and Aerosol Mechanics. In addition, the material in this book may prove to be of interest to individuals working in such areas as Physical Chemistry, Chemical Engineering, or any other applied discipline in which gas-surface interactions can be expected to play a significant role. 24 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Applied shape optimization for fluids / par Mohammadi,, B. Publication : [S.l.] : Oxford University Press, USA, 2001 . 272 p. ; , Deals with shape optimization for fluids, with the equations needed for understanding them, and numerical simulations. Introduces tools of optimal shape design, such as automatic differentiation, approximate gradients, and automatic mesh refinement. 24 cm. Date : 2001 Disponibilité : Exemplaires disponibles: La bibliothèque des sciences de l'ingénieur (1),

Applied stochastic processes / par Lefebvre, Mario. Publication : [S.l.] : Springer, 2006 . 382 p. ; , Applied Stochastic Processes uses a distinctly applied framework to present the most important topics in the field of stochastic processes. Key features: -Presents carefully chosen topics such as Gaussian and Markovian processes, Markov chains, Poisson processes, Brownian motion, and queueing theory -Examines in detail special diffusion processes, with implications for finance, various generalizations of Poisson processes, and renewal processes -Serves graduate students in a variety of disciplines such as applied mathematics, operations research, engineering, finance, and business administration -Contains numerous examples and approximately 350 advanced problems, reinforcing both concepts and applications -Includes entertaining mini-biographies of mathematicians, giving an enriching historical context -Covers basic results in probability Two appendices with statistical tables and solutions to the even-numbered problems are included at the end. This textbook is for graduate students in applied mathematics, operations research, and engineering. Pure mathematics students interested in the applications of probability and stochastic processes and students in business administration will also find this book useful. 23 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Dynamics of viscous compressible fluids / par Feireisl,, Eduard. Publication : [S.l.] : Oxford University Press, USA, 2004 . 224 p. ; , The book develops the most recent ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. Two main goals are pursued: (I) global existence theory within the framework of variational (weak) solutions for the full system of the Navier-Stokes equations supplemented with large data; and (II) optimal existence results for the barotropic flows with respect to the available a priori estimates. The book is intended to be a compact and self-contained presentation of the most recent results of the mathematical theory of viscous compressible fluids. In order to place the text in better perspective, each chapter is concluded with a section devoted to historical notes including references to all-important and new results. The material is by no means intended to be the last word on the subject but rather to include possible directions of future research. It is aimed at research mathematicians, theoretical physicists, engineers and graduate students. 24 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Foundations and applications of mis : a model theory approach / par Takahara, Yasuhiko. Publication : [S.l.] : Springer, 2006 . 360 p. ; , Foundations and Applications of MIS presents a unique systems theory approach to management information system (MIS) development. It covers an outline of the approach, providing a theoretical foundation for MIS from the systems theoretic viewpoint before presenting practical feasibility of the approach using applications ranging from a transaction processing system to a solver system. The author also describes his newly developed extended Prolog programming language, which takes full advantage of the mathematical framework employed. High-level mathematics is combined with sophisticated software engineering in this approach to address the practical problem area of designing MISs; it is the synergy of these two areas with underlying systems thinking that gives this book its unique identity. The book assumes a working knowledge of elementary set theory, logic and familiarity with some systems concepts such as automation models. Senior and graduate students, researchers in management information systems, systems engineers and systems scientists will find this book useful. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Juridiques, Economiques et de Gestion (1),

From vectors to tensors / par Ruiz-Tolosa,, Juan R. Publication : [S.l.] : Springer, 2005 . 550 p. ; , This textbook, deals with tensors that are treated as vectors, and has a practical orientation. In addition to dealing with the classical topics of tensor books, new tensor concepts are introduced, such as the rotation of tensors, the transposer tensor, the eigentensors, the permutation tensor structure, etc. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. In fact, the computational algebra is formulated in matrix form to facilitate its implementation on computers. For the first time tensor contraction is formulated in terms of matrix operations. A computer package, written in Mathematica, is available through Internet that complements the book.   In summary, the book is not a standard book on tensors because of its orientation, the many novel contributions included in it, the careful notation and the stretching-condensing techniques used for most of the transformations used in the book. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Heavy-tail phenomena : probabilistic and statistical modeling / par Resnick, Sidney I. Publication : [S.l.] : Springer, 2006 . 406 p. ; , This comprehensive text  gives an interesting  and useful blend  of the mathematical, probabilistic and statistical tools used in heavy-tail analysis.  Heavy tails are characteristic of many  phenomena where the probability of a single huge value impacts heavily.  Record-breaking insurance losses,  financial-log returns, files sizes stored on a server, transmission rates of files are all examples of  heavy-tailed phenomena. Key features: * Unique  text devoted to heavy-tails * Emphasizes both probability modeling and statistical methods for fitting models.   Most  treatments focus on one or the other but not both * Presents broad applicability  of heavy-tails to the fields of data networks, finance (e.g., value-at- risk), insurance, and hydrology * Clear, efficient and coherent exposition, balancing  theory and actual data to show the applicability and limitations of certain methods * Examines in detail the mathematical properties of the methodologies as well as their implementation in  Splus or R statistical languages * Exposition driven by numerous examples and exercises Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Hydrodynamics / par F.R.S.,, Sir Horace Lamb M.A. LL.D. Sc.D. Publication : [S.l.] : Cambridge University Press, 1993 . 768 p. ; , This reissue of the classic 1932 edition of Lamb's Hydrodynamics is an indication of the lasting value of the work. Constantly in use since its first publication in 1892, this book is the definitive reference work for all fluid dynamicists. The new foreword by Professor R. Caflisch highlights the prominence of this treatise in the field and outlines the development of fluid mechanics that led to its publication. He also resolves possible conflicts with modern notation. Despite the rapid pace of research in modern fluid mechanics study and the advent of high-speed computers, Lamb's work remains a relevant, timeless classic. 24 cm. Date : 1993 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Mathematical analysis and numerical methods for science and technology : physical origins and classical methods / Volume 1 : par Dautray, Robert. Publication : [S.l.] : Springer, 2000 . 722 p. ; , These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems:! a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences. The main physical examples examined in the 6 volumes are presented in Chapter I: Classical Fluids and the Navier-Stokes System; Linear Elasticity, Linear Viscoelasticity, Electromagnetism and Maxwell's Equation, Neutronics, and Quantum Physics. Then a first examin! ation of the mathematical model. 24 cm. Date : 2000 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Mathematical methods in risk theory / par Bþhlmann,, Hans. Publication : [S.l.] : Springer, 1996 . 210 pages ; , From the reviews: "The huge literature in risk theory has been carefully selected and supplemented by personal contributions of the author, many of which appear here for the first time. The result is a systematic and very readable book, which takes into account the most recent developments of the field. It will be of great interest to the actuary as well as to the statistician who wants to become familiar with the subject." Math. Reviews Vol. 43 "It is a book of fundamental importance for all interested in the application or teaching of the subject and a significant addition to the literature." Journal of the Royal Statistical Society (England) 1971 " This latest addition to the literature of risk theory is a masterful work.." Transactions, Soc of Actuaries meetings 65. 24 cm. Date : 1996 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Juridiques, Economiques et de Gestion (1),

MODAL ARRAY SIGNAL PROCESSING : PRINCIPLES AND APPLICATIONS OF ACOUSTIC WAVEFIELD DECOMPOSITION / par Teutsch, Heinz. Publication : [S.l.] : Springer, 2007 . 253 p. ; , Many applications of acoustic signal processing, such as teleconferencing and surveillance systems, require an estimate of several parameters present in the observed acoustic wavefield. The most important parameters are the number as well as the location of active acoustic sources. This book deals with the problem of detecting and localizing multiple simultaneously active wideband acoustic sources by applying the notion of wavefield decomposition using circular and spherical microphone arrays. The decomposed wavefield representation is used to serve as a basis for so-called modal array signal processing algorithms, which have the significant advantage over classical array signal processing algorithms that they inherently support multiple wideband acoustic sources. A rigorous derivation of modal array signal processing algorithms for unambiguous source detection and localization as well as performance evaluations by means of measurements using an actual real-time capable implementation are discussed. 24 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des sciences de l'ingénieur (1),

Numerical approximation methods for elliptic boundary value problems : finite and boundary elements / par Steinbach, Olaf. Publication : [S.l.] : Springer, 2007 . 388 p. ; , The book contains chapter summaries and excercises at the end of each chapter. 24 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Pfaffian systems, K-symplectic systems / par Awane, A. Publication : [S.l.] : Springer, 2000 . 260 p. ; , The geometrical view of mechanics is based on the study of certain exterior systems, the most classical of which are Pfaffian systems. In this book, we present the classification theorems (Frobenius, Darboux) and the local classification of Pfaffian systems of five variables, following Cartan. We also present a new class of exterior systems, called k-symplectic systems, generalizing the notion of symplectic form. These systems permit us to write in the language of exterior forms the equations proposed by Nambu for a model of statistical mechanics. Audience: This book is aimed at graduate students and at research workers in the field of mathematics, differential geometry, statistical mechanics, mathematics of physics and Lie algebras. 25 cm. Date : 2000 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Stochastic differential equations : an introduction with applications / par k̲sendal,, Bernt. Publication : [S.l.] : Springer, 2003 . 374 p. ; , This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. 24 cm. Date : 2003 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

The Geometry of biological time / par Winfree, Arthur T. Publication : [S.l.] : Springer, 2001 . 808 p. ; , From cell division to heartbeat, clocklike rhythms pervade the activities of every living organism. The cycles of life are ultimately biochemical in mechanism but many of the principles that dominate their orchestration are essentially mathematical. The Geometry of Biological Time describes periodic processes in living systems and their non-living analogues in the abstract terms of nonlinear dynamics. Enphasis is given in phase singularities, waves, and mutual synchronization in tissues composed of many clocklike units. Also provided are descriptions of the best-studied experimental systems such as chemical oscillators, pacemaker neurons, circadian clocks, and excitable media organized into biochemical and bioelectrical wave patterns in two and three dimensions. No theoretical background is assumed; the required notions are introduced through an extensive collection of pictures and easily understood examples. This extensively updated new edition incorporates the fruits of two decades' further exploration guided by the same principles. Limit cycle theories of circadian clocks are now applied to human jet lag and are understood in terms of the molecular genetics of their recently discovered mechanisms. Supercomputers reveal the unforeseen architecture and dynamics of three-dimensional scroll waves in excitable media. Their role in life-threatening electrical aberrations of the heartbeat is exposed by laboratory experiments and corroborated in the clinic. These developments trace back to three basic mathematical ideas. 24 cm. Date : 2001 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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