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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),

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A Course of modern analysis / par Whittaker, E.T. Publication : [S.l.] : Cambridge University Press, 1996 . 616 p. ; , This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever. 23 cm. Date : 1996 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Convex analysis / par Rockafellar,, R.T. Publication : [S.l.] : Princeton University Press, 1996 . 469 p. ; , Broché. 23 cm. Date : 1996 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Dynamical systems X : general theory of vortices / par Kozlov, V.V. Publication : [S.l.] : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2002 . 190 p. ; , ReliØ. 24 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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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),

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Nonlinear systems : analysis, stability, and control / par Sastry,, S.M.L. Publication : [S.l.] : Springer-Verlag New York Inc., 1999 . 704 p. ; , Relié. 24 cm. Date : 1999 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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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),

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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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