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Mathematical potential theory  517.57  Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions  Harmonic functions.  Potential theory (Mathematics)  Potential theory (Mathematics).  517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions  Harmonic functions  Fonctions harmoniques  Potentiel, Théorie du
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Harmonic analysis. Fourier analysis  Ordered algebraic structures  517.986.6  Harmonic analysis of functions of groups and homogeneous spaces  517.986.6 Harmonic analysis of functions of groups and homogeneous spaces  Potential theory (Mathematics)  Locally compact Abelian groups.  Potentiel, Théorie du  Groupes abéliens localement compacts  Potential theory (Mathematics).  Potentiel, Théorie du.  Groupes abéliens localement compacts  Fourier, Transformations de  Locally compact Abelian groups  Fourier transformations
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Potential theory (Mathematics)  Harmonic functions  Martingales (Mathematics)  Potentiel, Théorie du  Fonctions harmoniques  Martingales (Mathématiques)  517.57  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mathematical analysis  Mechanics  Stochastic processes  Functions, Harmonic  Laplace's equations  Bessel functions  Differential equations, Partial  Fourier series  Harmonic analysis  Lamé's functions  Spherical harmonics  Toroidal harmonics  Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions  Harmonic functions.  Martingales (Mathematics).  Potential theory (Mathematics).  517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions  Potentiel, Théorie du  Martingales (Mathématiques)  Mathematical potential theory  Probability theory  Processus stochastiques  Probabilités.  Probabilities
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Probability theory  Mathematical potential theory  Measure theory. Mathematical integration  Probabilities  Measure theory  Potential theory (Mathematics)  Martingales (Mathematics)  Probabilités  Mesure, Théorie de la  Potentiel, Théorie du  Martingales (Mathématiques)  Potential, Theory of  519.2  681.3*G3  Stochastic processes  Green's operators  Green's theorem  Potential functions (Mathematics)  Mathematical analysis  Mechanics  Lebesgue measure  Measurable sets  Measure of a set  Algebraic topology  Integrals, Generalized  Measure algebras  Rings (Algebra)  Probability. Mathematical statistics  Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing)  Measure theory.  Probabilities.  Martingales (Mathematics).  Potential theory (Mathematics).  681.3*G3 Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing)  519.2 Probability. Mathematical statistics  Probabilités  Mesure, Théorie de la  Potentiel, Théorie du  Martingales (Mathématiques)  Processus stochastiques  Probabilités.
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Partial differential equations  Boundary value problems  Green's functions  Mathematical physics  Problèmes aux limites  Green, Fonctions de  Physique mathématique  517.95  Physical mathematics  Physics  Functions, Green's  Functions, Induction  Functions, Source  Green functions  Induction functions  Source functions  Differential equations  Potential theory (Mathematics)  Boundary conditions (Differential equations)  Functions of complex variables  Initial value problems  Mathematics  Boundary value problems.  Green's functions.  Mathematical physics.  517.95 Partial differential equations  Problèmes aux limites  Physique mathématique  Differential equations, Linear  Équations aux dérivées partielles linéaires  Équations différentielles linéaires
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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  Timeseries 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)
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Solid state physics  Manybody 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  nbody problem  Problem of many bodies  Problem of nbodies  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.  Manybody problem.  Solid state physics.
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The idea that the microbial communities within the GI tract have a profound influence on general human health actually originated with Russian scientist Elie Metchnikov at the turn ofthe last century. Also known as the "fatherofimmunol ogy", Metchnikovbelievedthat putrefactivebacteriain the gut were responsible for enhancing the aging process. He theorized that ingestion ofhealthy bacteria found in fermented foods could counteract toxic bacteria and was the key to good health. His theories concerning good bacteria and health can be found in his treatise "The ProlongationofLife: Optimistic Studies".Thesewritings promptedJapanesescientist Minoru Shirotatobegin investigationofhow fermentative bacteriaimprove health. He succeededin isolating astrainofLactobacillusthat could survive passage through the intestine, while promoting a healthy balance ofmicrobes. The "Shirota strain" is still used today in the fermented beverage Yakult.It is clear from a commercial standpoint that these ideas have inspired the development of a probiotic industry, which has expanded greatly in the U.S. over the past 510 years.
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  Gastrointestinal 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
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