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W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi’s measure and thin obstacles.
Minimal surfaces --- Geometric measure theory --- Surfaces, Minimal --- Mathematics. --- Measure theory. --- Measure and Integration. --- Measure theory --- Maxima and minima --- Math --- Science --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)
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Functional analysis --- Algebraic topology --- Banach algebras. --- Measure algebras. --- Semigroups. --- Functional analysis. --- Banach, Algèbres de --- Algèbres de mesures --- Semi-groupes --- Analyse fonctionnelle --- 51 <082.1> --- Mathematics--Series --- Banach, Algèbres de --- Algèbres de mesures --- Banach algebras --- Measure algebras --- Semigroups --- Group theory --- Algebras, Measure --- Harmonic analysis --- Measure theory --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Analyse harmonique (mathématiques)
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This volume contains a selection of articles on the theme ""vector measures, integration and applications"" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in the area and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, and functional analysis. The material is of interest to experts, young res
Numerical integration -- Congresses. --- Operator theory -- Congresses. --- Vector-valued measures -- Congresses. --- Mathematics --- Engineering & Applied Sciences --- Calculus --- Applied Mathematics --- Physical Sciences & Mathematics --- Vector-valued measures --- Functional analysis --- Measures, Vector-valued --- Mathematics. --- Measure theory. --- Operator theory. --- Measure and Integration. --- Operator Theory. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Math --- Science --- Measure theory --- Radon measures
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The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malliavin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial structures arising from the study of chaotic random variables related to infinitely divisible random measures. The combinatorial structures involved are those of partitions of finite sets, over which Möbius functions and related inversion formulae are defined. This combinatorial standpoint (which is originally due to Rota and Wallstrom) provides an ideal framework for diagrams, which are graphical devices used to compute moments and cumulants of random variables. Several applications are described, in particular, recent limit theorems for chaotic random variables. An Appendix presents a computer implementation in MATHEMATICA for many of the formulae.
Stochastic partial differential equations. --- Stochastic integrals. --- Gaussian processes. --- Integrals, Stochastic --- Banach spaces, Stochastic differential equations in --- Hilbert spaces, Stochastic differential equations in --- SPDE (Differential equations) --- Stochastic differential equations in Banach spaces --- Stochastic differential equations in Hilbert spaces --- Mathematics. --- Measure theory. --- Economics, Mathematical. --- Probabilities. --- Combinatorics. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Measure and Integration. --- Distribution (Probability theory) --- Stochastic processes --- Stochastic analysis --- Differential equations, Partial --- Distribution (Probability theory. --- Finance. --- Math --- Science --- Combinatorics --- Algebra --- Mathematical analysis --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical . --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Mathematical economics --- Econometrics --- Mathematics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology
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This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.
Differentiable dynamical systems. --- Electronic books. -- local. --- Point mappings (Mathematics). --- Differentiable dynamical systems --- Point mappings (Mathematics) --- Spectral theory (Mathematics) --- Mathematics --- Geometry --- Calculus --- Physical Sciences & Mathematics --- Equations, Recurrent --- Mappings, Point (Mathematics) --- Recurrence relations in functional differential equations --- Recurrent equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Dynamics. --- Ergodic theory. --- Fourier analysis. --- Measure theory. --- Operator theory. --- Number theory. --- Analysis. --- Dynamical Systems and Ergodic Theory. --- Fourier Analysis. --- Number Theory. --- Measure and Integration. --- Operator Theory. --- Number study --- Numbers, Theory of --- Algebra --- Functional analysis --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Analysis, Fourier --- Mathematical analysis --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- 517.1 Mathematical analysis --- Math --- Science --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Functional differential equations --- Mappings (Mathematics) --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Dynamique différentiable --- Applications ponctuelles (mathématiques) --- Théorie spectrale (mathématiques) --- Hilbert space --- Dynamique différentiable --- Applications ponctuelles (mathématiques) --- Théorie spectrale (mathématiques)
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