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Function spaces and potential theory
Authors: ---
ISSN: 00727830 ISBN: 3540570608 9783540570608 364208172X 3662032821 Year: 1996 Volume: 314 Publisher: Berlin Heidelberg New York : Springer,

Fine regularity of solutions of elliptic partial differential equations
Authors: ---
ISSN: 00765376 ISBN: 9780821803356 0821803352 Year: 1997 Volume: 51 Publisher: Providence : American Mathematical Society,

Probabilités et potentiels.
Authors: ---
ISBN: 2705613722 Year: 1975 Volume: 1372, <1385, 1410 Publisher: Paris : Hermann,

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Extremum Problems for Eigenvalues of Elliptic Operators
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ISBN: 9783764377052 3764377054 3764377062 9786610627769 128062776X Year: 2006 Publisher: Basel : Birkhäuser Basel : Imprint: Birkhäuser,

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Abstract

Problems linking the shape of a domain or the coefficients of an elliptic operator to the sequence of its eigenvalues are among the most fascinating of mathematical analysis. In this book, we focus on extremal problems. For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case of functions of eigenvalues. We investigate similar questions for other elliptic operators, such as the Schrödinger operator, non homogeneous membranes, or the bi-Laplacian, and we look at optimal composites and optimal insulation problems in terms of eigenvalues. Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory.

Applied multivariate analysis.
Author:
ISBN: 0387953477 9780387953472 9780387227719 9786610009466 1280009462 0387227717 Year: 2002 Publisher: Pittsburgh Springer

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Univariate statistical analysis is concerned with techniques for the analysis of a single random variable. This book is about applied multivariate analysis. It was written to p- vide students and researchers with an introduction to statistical techniques for the ana- sis of continuous quantitative measurements on several random variables simultaneously. While quantitative measurements may be obtained from any population, the material in this text is primarily concerned with techniques useful for the analysis of continuous obser- tions from multivariate normal populations with linear structure. While several multivariate methods are extensions of univariate procedures, a unique feature of multivariate data an- ysis techniques is their ability to control experimental error at an exact nominal level and to provide information on the covariance structure of the data. These features tend to enhance statistical inference, making multivariate data analysis superior to univariate analysis. While in a previous edition of my textbook on multivariate analysis, I tried to precede a multivariate method with a corresponding univariate procedure when applicable, I have not taken this approach here. Instead, it is assumed that the reader has taken basic courses in multiple linear regression, analysis of variance, and experimental design. While students may be familiar with vector spaces and matrices, important results essential to multivariate analysis are reviewed in Chapter 2. I have avoided the use of calculus in this text.

Keywords

Mathematical statistics --- Multivariate analysis. --- Analyse multivariée --- Multivariate analysis --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- #SBIB:303H520 --- Methoden sociale wetenschappen: techniek van de analyse, algemeen --- -519.535 --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Matrices --- Electronic information resources --- E-books --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Potential theory (Mathematics). --- Probabilities. --- Statistics. --- Analysis. --- Potential Theory. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Statistics for Social Science, Behavioral Science, Education, Public Policy, and Law. --- Global analysis (Mathematics). --- Distribution (Probability theory. --- Mathematical statistics. --- Statistics for Social Sciences, Humanities, Law. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistics . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- 517.1 Mathematical analysis


Book
GI Microbiota and Regulation of the Immune System
Authors: --- ---
ISBN: 9780387095509 0387799893 9780387799896 9786612037948 1282037943 0387095500 1489988165 3540095500 3540348611 Year: 2008 Volume: 743 Publisher: New York, NY : Springer New York,

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Abstract

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.

Keywords

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

Introduction to Fourier analysis on Euclidean spaces
Authors: --- ---
ISBN: 140088389X 069108078X 9781400883899 9780691080789 Year: 1971 Volume: 32 Publisher: Princeton : Princeton University Press,

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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.

Keywords

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

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