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Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.

Markov processes. --- Stochastic difference equations. --- Itō, Kiyosi, --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Itō, K. --- Ito, Kiesi, --- Itō, Kiyoshi, --- 伊藤淸, --- 伊藤清, --- Itō, Kiyosi, --- Itō, Kiyosi, 1915-2008. --- Stochastic difference equations --- Difference equations --- Stochastic processes --- Abelian group. --- Addition. --- Analytic function. --- Approximation. --- Bernhard Riemann. --- Bounded variation. --- Brownian motion. --- Central limit theorem. --- Change of variables. --- Coefficient. --- Complete metric space. --- Compound Poisson process. --- Continuous function (set theory). --- Continuous function. --- Convergence of measures. --- Convex function. --- Coordinate system. --- Corollary. --- David Hilbert. --- Decomposition theorem. --- Degeneracy (mathematics). --- Derivative. --- Diffeomorphism. --- Differentiable function. --- Differentiable manifold. --- Differential equation. --- Differential geometry. --- Dimension. --- Directional derivative. --- Doob–Meyer decomposition theorem. --- Duality principle. --- Elliptic operator. --- Equation. --- Euclidean space. --- Existential quantification. --- Fourier transform. --- Function space. --- Functional analysis. --- Fundamental solution. --- Fundamental theorem of calculus. --- Homeomorphism. --- Hölder's inequality. --- Initial condition. --- Integral curve. --- Integral equation. --- Integration by parts. --- Invariant measure. --- Itô calculus. --- Itô's lemma. --- Joint probability distribution. --- Lebesgue measure. --- Linear interpolation. --- Lipschitz continuity. --- Local martingale. --- Logarithm. --- Markov chain. --- Markov process. --- Markov property. --- Martingale (probability theory). --- Normal distribution. --- Ordinary differential equation. --- Ornstein–Uhlenbeck process. --- Polynomial. --- Principal part. --- Probability measure. --- Probability space. --- Probability theory. --- Pseudo-differential operator. --- Radon–Nikodym theorem. --- Representation theorem. --- Riemann integral. --- Riemann sum. --- Riemann–Stieltjes integral. --- Scientific notation. --- Semimartingale. --- Sign (mathematics). --- Special case. --- Spectral sequence. --- Spectral theory. --- State space. --- State-space representation. --- Step function. --- Stochastic calculus. --- Stochastic. --- Stratonovich integral. --- Submanifold. --- Support (mathematics). --- Tangent space. --- Tangent vector. --- Taylor's theorem. --- Theorem. --- Theory. --- Topological space. --- Topology. --- Translational symmetry. --- Uniform convergence. --- Variable (mathematics). --- Vector field. --- Weak convergence (Hilbert space). --- Weak topology.

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"Claude Cahun, Maya Deren, and Cindy Sherman were born in different countries, in different generations - Cahun in France in 1894, Deren in Russia in 1917, and Sherman in the United States in 1954. Yet they share a deeply theatrical obsession that shatters any notion of a unified self. All three try out identities from different social classes and geographic environments, extend their temporal range into the past and future, and transform themselves into heroes and villains, mythological creatures, and sex goddesses. The premise of Inverted Odysseys is that this expanded concept of the self - this playful urge to "try on" other roles - is more than a feminist or psychological issue. It is central to our global culture, to our definition of human identity in a world where the individual exists in a multicultural and multemporal environment. This book is an "odyssey" through historical, theoretical, critical, and literary perspectives on the three artists viewed in the context of these issues."--Jacket.

Photography, Artistic --- Visual Arts --- Art, Architecture & Applied Arts --- Photography --- Cahun, Claude, --- Deren, Maya --- Sherman, Cindy --- Derenkowsky, Elenora --- Derenkowsky, Eleanora --- Deren, Elenora --- Deren, Eleanora --- Bardacke, Elenora --- Bardacke, Eleanora --- Hammid, Elenora --- Hammid, Eleanora --- Hammid, Maya --- Ito, Maya --- Courlis, Claude, --- Schwob, Lucy,

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This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents:PreliminariesThe stochastic integral and Itô formulaOU processes and SDEsRandom attractorsApplicationsBibliographyIndex

Stochastic partial differential equations. --- Dynamics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- 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 --- Differential equations, Partial --- Itô's formula. --- Ornstein-Uhlenbeck processes. --- Stochastic PDEs. --- dynamical behavior. --- random attractors. --- stochastic integrals.

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This book contains the articles collected for the Special Issue entitled "Micro-nano Surface Functionalization of Materials and Thin Films for Optical Applications" in the journal Coatings (ISSN 2079-6412). These selected articles provide a meaningful overview of recent advances and concepts beyond the state-of-the-art regarding surface functionalization of materials and deposition of thin films to be used in optical applications. The aim was to cover all relevant aspects of the topic (simulation, design, fabrication, characterization and applications) with a special emphasis on non-conventional methods for surface modification of materials, combinations of mature fabrication routes with emerging technologies (i.e., additive manufacturing) and large-area fabrication concepts to pave the way to an industrial utilization of the developed materials. This overview comprises the recent work of reputed scientists from Germany, Austria, Spain and India on: - New developments on the scale-up deposition of transparent conductive materials by magnetron sputtering,- Design of hierarchical surface structures at different scale lengths for nanoimprinting of optical nano- and micro-structures, - Non-conventional preparation of rutile-type TiO2 films at room temperature for optical applications on heat-sensitive substrates, - Design of spectrally selective solar absorber coatings based on computational simulation and ellipsometry measurements.

reactive magnetron sputtering --- transparent conductive oxide --- electronic transport --- doping efficiency --- tin dioxide --- Nanoimprint lithography --- UV-NIL --- reversal NIL --- liquid transfer imprint lithography --- hierarchical structures --- optical micro- and nanostructures --- ITO thin films --- magnetron sputtering --- low temperature deposition --- oxygen flow --- microstructure --- optoelectronic properties --- transparent heaters --- titanium oxide films --- filtered cathodic vacuum arc --- rutile --- optical coatings --- spectrally selective absorber --- multilayer stack --- spectroscopic ellipsometry --- optical constants --- simulation

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Color is inextricably linked with architecture; as a design element and also as an inherent quality, it characterizes the shape and texture of the built fabric. The book presents extraordinary color schemes, both in terms of technology and aesthetics, for ground-breaking architecture with a wide spectrum of functions: from apartment to concert hall, from flagship store to city park.The focus is on the works of the three architects Frank O. Gehry, Jean Nouvel and Wang Shu. This is expanded by the works of other practices such as BIG, Zaha Hadid, Herzog & de Meuron, Toyo Ito and SANAA.This publication presents a compendium that documents color schemes in architecture in the context of very different aesthetic approaches. The large-format photographs by Iwan Baan, Christian Richters, Roland Halbe and Philippe Ruault fascinate with their clarity and presence. Farbe ist unlösbar mit der Architektur verbunden - als Medium der Gestaltung, aber auch als eigene Qualität prägt sie Form und Textur des Gebauten.Das Buch präsentiert Farbgestaltungen avancierter Architektur, die in technologischer wie in ästhetischer Hinsicht außerordentlich sind, für ein breites Spektrum von Bauaufgaben: vom Apartment zur Konzerthalle, vom Flagship Store zum Stadtpark.Im Vordergrund stehen Werke der drei Architekten Frank O. Gehry, Jean Nouvel und Wang Shu. Erweitert wird das Spektrum durch Arbeiten anderer Büros wie beispielsweise BIG, Zaha Hadid, Herzog & de Meuron, Toyo Ito und SANAA.Mit dieser Darstellung liegt ein Kompendium vor, das Farbgestaltung in der Architektur in sehr unterschiedlichen ästhetischen Auffassungen dokumentiert. Die großformatigen Fotografien von Iwan Baan, Christian Richters, Roland Halbe und Philippe Ruault faszinieren durch ihre Klarheit und Präsenz.

Couleurs --- Gehry, Frank Owen --- Nouvel, Jean, --- Wang, Shu, --- 72.017 --- 72.039 --- Architectuur en kleur ; vorm en kleur ; 21ste eeuw --- Architectuur ; licht en schaduw ; kleuren en texturen --- Gehry, Frank O. --- Nouvel, Jean --- Wang Shu --- BIG ; Bjarke Ingels Group --- Boeri, Stefano --- Hadid, Zaha --- Herzog & de Meuron --- Steven Holl Architects --- Ito, Toyo --- Lui Jiakun --- Michael Manzan Architecture --- Mazzanti, Giancarlo --- Ruiz-Geli, Enric ; Cloud 9 --- SANAA --- Architectuur ; kleur, licht, compositie --- Architectuurgeschiedenis ; 2000 - 2050 --- Wang, Shu --- Couleurs. --- Gehry, Frank O --- Architecture. --- Architects. --- Color in architecture. --- Architectural polychromy --- Buildings --- Color in building --- Architecture --- Interior decoration --- Polychromy --- Professional employees --- Architecture, Western (Western countries) --- Building design --- Construction --- Western architecture (Western countries) --- Art --- Building --- Color --- Design and construction --- Gehry, Frank O., --- Boeri, Stefano. --- Itō, Toyoo, --- Mazzanti, Giancarlo. --- Ruiz Geli, Enric. --- Jiakun, Lui. --- Geli, Enric Ruiz --- Mazzanti Sierra, Giancarlo --- Sierra, Giancarlo Mazzanti --- Ito, Toyo, --- Yidong, Fengxiong, --- 伊東豊雄, --- Shu, Wang, --- 王澍, --- Wang Shu, --- Gehry, Frank, --- Goldberg, Frank, --- Gehry, Frank Owen, --- Goldberg, Ephraim Owen, --- Zaha Hadid Architects. --- Herzog & de Meuron. --- Steven Holl Architects. --- Michael MalZan Architecture. --- Cloud 9 (Firm) --- Honduras. --- S.A.N.A.A. --- Cloud9 (Firm) --- Holl Architects --- Herzog et de Meuron --- Herzog und de Meuron --- Herzog and de Meuron --- ZHA --- Dones arquitectes. --- Arquitectes --- Architecture, Primitive