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Artificial intelligence. Robotics. Simulation. Graphics --- Electronics and optics of solids --- Crystals --- Potential theory (Mathematics) --- Crystallography --- Digital computer simulation --- Cristaux --- Potentiel, Théorie du --- Cristallographie --- Defects --- Congresses --- Data processing --- Défauts --- Congrès --- Informatique --- Potentiel, Théorie du --- Défauts --- Congrès --- Congresses.

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Stochastic processes --- Mathematical potential theory --- Brownian movements --- Potential theory (Mathematics) --- Markov processes --- Mouvement brownien --- Potentiel, Théorie du --- Markov, Processus de --- Potential, Theory of --- 519.218 --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Mathematical analysis --- Mechanics --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Capillarity --- Liquids --- Matter --- Special stochastic processes --- Properties --- 519.218 Special stochastic processes --- Potentiel, Théorie du --- Processus stochastiques

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Offers an overview of the knowledge of gastrointestinal immunology and the commensal microbiology of the gut. This book includes chapters dedicated to methodologies used to investigate the microbiota and host: molecular analysis of microbial diversity and gnotobiotic research.

Biomedicine. --- Biomedicine general. --- Immunology. --- Medicine. --- Médecine --- Immunologie --- Bacterial Physiology. --- Gastrointestinal system. --- Gastrointestinal Tract. --- Gastrointestinal system --- Gastrointestinal Tract --- Physiology --- Microbiology --- Bacterial Physiological Phenomena --- Biology --- Biological Science Disciplines --- Digestive System --- Microbiological Phenomena --- Phenomena and Processes --- Natural Science Disciplines --- Anatomy --- Disciplines and Occupations --- Microbiology & Immunology --- Health & Biological Sciences --- Immunology --- Anatomies --- Natural Sciences --- Physical Sciences --- Discipline, Natural Science --- Disciplines, Natural Science --- Natural Science --- Natural Science Discipline --- Physical Science --- Science, Natural --- Science, Physical --- Sciences, Natural --- Sciences, Physical --- Microbial Concepts --- Microbial Phenomena --- Microbiologic Concepts --- Microbiological Phenomenon --- Microbiological Process --- Phenomena, Microbiologic --- Microbiologic Phenomena --- Microbiological Processes --- Concept, Microbial --- Concept, Microbiologic --- Concepts, Microbial --- Concepts, Microbiologic --- Microbial Concept --- Microbiologic Concept --- Phenomena, Microbial --- Phenomena, Microbiological --- Phenomenon, Microbiological --- Process, Microbiological --- Processes, Microbiological --- Ailmentary System --- Alimentary System --- Biologic Sciences --- Biological Science --- Science, Biological --- Sciences, Biological --- Biological Sciences --- Life Sciences --- Biologic Science --- Biological Science Discipline --- Discipline, Biological Science --- Disciplines, Biological Science --- Life Science --- Science Discipline, Biological --- Science Disciplines, Biological --- Science, Biologic --- Science, Life --- Sciences, Biologic --- Sciences, Life --- Bacterial Physiological Concepts --- Bacterial Physiological Phenomenon --- Bacterial Process --- Physiology, Bacterial --- Bacterial Physiology --- Bacterial Processes --- Bacterial Physiological Concept --- Concept, Bacterial Physiological --- Concepts, Bacterial Physiological --- Phenomena, Bacterial Physiological --- Phenomenon, Bacterial Physiological --- Process, Bacterial --- Processes, Bacterial --- Bacteria --- GI Tract --- Digestive Tract --- Digestive Tracts --- GI Tracts --- Gastrointestinal Tracts --- Gastro-intestinal system --- Gastrointestinal tract --- GI tract --- Tract, Gastrointestinal --- Tract, GI --- physiology --- Conformal mapping --- -Functions of complex variables --- -Potential theory (Mathematics) --- -Complex variables --- Conformal representation of surfaces --- Mapping, Conformal --- Transformation, Conformal --- Surfaces, Representation of --- -Analysis--?<061.3> --- Immunobiology --- Life sciences --- Serology --- Clinical sciences --- Medical profession --- Human biology --- Medical sciences --- Pathology --- Physicians --- Functional analysis --- Functions of complex variables --- Potential theory (Mathematics) --- 517 <061.3> --- Geometric function theory --- Mappings (Mathematics) --- Transformations (Mathematics) --- 517 <061.3> Analysis--?<061.3> --- Analysis--?<061.3> --- Congresses --- Complex analysis --- Congresses. --- Health Workforce --- Fonctions d'une variable complexe --- Fonctions de plusieurs variables complexes --- Functions of complex variables - Congresses --- Conformal mapping - Congresses --- Potential theory (Mathematics) - Congresses --- Functional analysis - Congresses --- Theorie du potentiel

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Solid state physics --- Many-body problem --- Green's functions --- Physique de l'état solide --- Problème des N corps --- Green, Fonctions de --- 538.9 --- 538.9 Physics of condensed matter (in liquid state and solid state) --- Physics of condensed matter (in liquid state and solid state) --- Physics --- Solids --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Statistical physics --- Green's functions. --- Many-body problem. --- Solid state physics.

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The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Harmonic analysis. --- Harmonic functions. --- Functions, Harmonic --- Laplace's equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Harmonic analysis. Fourier analysis --- Harmonic analysis --- Fourier analysis --- Harmonic functions --- Analyse harmonique --- Analyse de Fourier --- Fonctions harmoniques --- Fourier Analysis --- Fourier, Transformations de --- Euclide, Espaces d' --- Bessel functions --- Differential equations, Partial --- Fourier series --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Banach algebras --- Time-series analysis --- Analysis, Fourier --- Fourier analysis. --- Basic Sciences. Mathematics --- Analysis, Functions --- Analysis, Functions. --- Calculus --- Mathematical analysis --- Mathematics --- Fourier, Transformations de. --- Euclide, Espaces d'. --- Potentiel, Théorie du --- Fonctions harmoniques. --- Potential theory (Mathematics) --- Analytic continuation. --- Analytic function. --- Banach algebra. --- Banach space. --- Bessel function. --- Borel measure. --- Boundary value problem. --- Bounded operator. --- Bounded set (topological vector space). --- Cartesian coordinate system. --- Cauchy–Riemann equations. --- Change of variables. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Complex plane. --- Conformal map. --- Conjugate transpose. --- Continuous function (set theory). --- Continuous function. --- Convolution. --- Differentiation of integrals. --- Dimensional analysis. --- Dirichlet problem. --- Disk (mathematics). --- Distribution (mathematics). --- Equation. --- Euclidean space. --- Existential quantification. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fubini's theorem. --- Function (mathematics). --- Function space. --- Green's theorem. --- Hardy's inequality. --- Hardy–Littlewood maximal function. --- Harmonic function. --- Hermitian matrix. --- Hilbert transform. --- Holomorphic function. --- Homogeneous function. --- Inequality (mathematics). --- Infimum and supremum. --- Interpolation theorem. --- Interval (mathematics). --- Lebesgue integration. --- Lebesgue measure. --- Linear interpolation. --- Linear map. --- Linear space (geometry). --- Line–line intersection. --- Liouville's theorem (Hamiltonian). --- Lipschitz continuity. --- Locally integrable function. --- Lp space. --- Majorization. --- Marcinkiewicz interpolation theorem. --- Mean value theorem. --- Measure (mathematics). --- Mellin transform. --- Monotonic function. --- Multiplication operator. --- Norm (mathematics). --- Operator norm. --- Orthogonal group. --- Paley–Wiener theorem. --- Partial derivative. --- Partial differential equation. --- Plancherel theorem. --- Pointwise convergence. --- Poisson kernel. --- Poisson summation formula. --- Polynomial. --- Principal value. --- Quadratic form. --- Radial function. --- Radon–Nikodym theorem. --- Representation theorem. --- Riesz transform. --- Scientific notation. --- Series expansion. --- Singular integral. --- Special case. --- Subharmonic function. --- Support (mathematics). --- Theorem. --- Topology. --- Total variation. --- Trigonometric polynomial. --- Trigonometric series. --- Two-dimensional space. --- Union (set theory). --- Unit disk. --- Unit sphere. --- Upper half-plane. --- Variable (mathematics). --- Vector space. --- Fourier, Analyse de --- Potentiel, Théorie du. --- Potentiel, Théorie du --- Espaces de hardy