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Ce livre est une introduction à l'analyse des signaux par la technique des ondelettes, méthode qui permet souvent de faire mieux ressortir les caractéristiques des signaux que la traditionnelle décomposition en série de Fourier. Les premiers chapitres consistent en une introduction aux décompositions de types "; temps-fréquence "; des fonctions et des signaux, assortie de quelques exemples simples. Des aspects plus spécifiques sont ensuites traités : l'utilisation des ondelettes pour la caractérisation des singularités dans les fonctions et les signaux – avec une brève incursion dans le monde des fractales –, ainsi que l'analyse temps-fréquence proprement dite, etc. Un troisième volet est consacré au problème de discrétisation des représentations temps- fréquence continues. La dernière partie couvre des aspects plus géométriques. L'ouvrage s'adresse aux étudiants en troisième cycle de physique ou de mathématiques – certains points sont abordables dès le deuxième cycle – et aux élèves des écoles d'ingénieurs. Il intéressera aussi les chercheurs et les ingénieurs ayant à résoudre des problèmes d'analyse et de traitement du signal. L'originalité de son approche est de rassembler en une seule étude les aspects géométriques et algorithmiques du sujet. Il fournit certains algorithmes directement applicables.

Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis

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The book contains six chapters. The use of the progressive regressive strategy for biometrical authentication through the use of human gait and face images was investigated. A new lossy image compression technique that uses singular value decomposition and wavelet difference reduction technique was proposed. The best wavelet packet based selection algorithm and its application in image denoising was discussed. The scaling factor threshold estimator in different color models using a discrete wavelet transform for steganographic algorithms was presented. The extraction of features appearing in current signal using wavelet analysis when there is rotor fault of eccentricity and broken rotor bar was debated. The application of the empirical wavelet transform for seismic anomalies detection in ultralow-frequency geomagnetic signals was illustrated.

Image compression. --- Transformations (Mathematics) --- Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis --- Algorithms --- Differential invariants --- Geometry, Differential --- Image data compression --- Data compression (Telecommunication) --- Mathematical modelling

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This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Topological Groups. --- Potential theory (Mathematics). --- Differential equations, partial. --- Harmonic analysis. --- Functional analysis. --- Global differential geometry. --- Topological Groups, Lie Groups. --- Potential Theory. --- Partial Differential Equations. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Differential Geometry. --- Geometry, Differential --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Groups, Topological --- Continuous groups --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Partial differential equations --- Topological groups. --- Lie groups. --- Partial differential equations. --- Differential geometry. --- Differential geometry --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Lie groups --- Potential theory (Mathematics) --- Harmonic analysis --- Functional analysis

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The EQ-5D instrument, as a standardized, cross-culturally validated measure of self-assessed health has a hugely important role in understanding population health within and across countries. Over the past two decades a wealth of international population health survey data have been accumulated by the EuroQol Group from research conducted in many countries across four continents. One of the success factors of the EQ-5D instruments has been the easy availability of national or international sets of EQ-5D data, as well as clear explanations and guidance for users. There is an unmet need to produce a comprehensive book that captures up-to-date and expanded information of EQ-5D self-reported health and index values. EQ-5D population norms and cross-country analyses are provided from representative national surveys of 20 countries and additional regional surveys. This book will be a must for those who believe that how people report and value health is very important.

Algebra --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Topological groups. --- Lie groups. --- Harmonic analysis. --- Functional analysis. --- Mathematical physics. --- Topological Groups, Lie Groups. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Mathematical Physics. --- Physical mathematics --- Physics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Math --- Science --- Topological Groups. --- Medicine. --- Public health. --- Medical research. --- Biomedicine, general. --- Public Health. --- Quality of Life Research. --- Biomedicine general --- Public Health --- Quality of Life Research --- Population Health --- EQ-5D --- Quality-of-Life --- Utilities

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For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

signal processing --- thermodynamics --- heat pulse experiments --- quantum mechanics --- variational formulation --- Wigner function --- nonholonomic constraints --- thermal expansion --- homogeneous spaces --- irreversible processes --- time-slicing --- affine group --- Fourier analysis --- non-equilibrium processes --- harmonic analysis on abstract space --- pseudo-temperature --- stochastic differential equations --- fourier transform --- Lie Groups --- higher order thermodynamics --- short-time propagators --- discrete thermodynamic systems --- metrics --- heat equation on manifolds and Lie Groups --- special functions --- poly-symplectic manifold --- non-Fourier heat conduction --- homogeneous manifold --- non-equivariant cohomology --- Souriau-Fisher metric --- Weyl quantization --- dynamical systems --- symplectization --- Weyl-Heisenberg group --- Guyer-Krumhansl equation --- rigged Hilbert spaces --- Lévy processes --- Born–Jordan quantization --- discrete multivariate sine transforms --- continuum thermodynamic systems --- interconnection --- rigid body motions --- covariant integral quantization --- cubature formulas --- Lie group machine learning --- nonequilibrium thermodynamics --- Van Vleck determinant --- Lie groups thermodynamics --- partial differential equations --- orthogonal polynomials