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In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

Differential equations. --- Mathematical analysis. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- 517.1 Mathematical analysis --- Mathematical analysis --- 517.91 Differential equations --- Differential equations --- Mathematics. --- Analysis (Mathematics). --- Partial differential equations. --- Probabilities. --- Partial Differential Equations. --- Probability Theory and Stochastic Processes. --- Analysis. --- Differential equations, partial. --- Distribution (Probability theory. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Partial differential equations --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Stochastic partial differential equations. --- Inequalities (Mathematics)

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In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

Mathematics --- Differential geometry. Global analysis --- Partial differential equations --- Differential equations --- Mathematical analysis --- Operational research. Game theory --- Probability theory --- differentiaalvergelijkingen --- analyse (wiskunde) --- waarschijnlijkheidstheorie --- stochastische analyse --- statistiek --- wiskunde --- kansrekening

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Pauvreté généralisée causée par la surpopulation, familles nombreuses et nécessiteuses, croissance démographique irrépressible, absence, avant les politiques de Mao, de tout contrôle des naissances ... les préjugés au sujet de la Chine ont la vie dure. Ce livre, d'entrée de jeu, attaque les idées reçues sur la population chinoise, idées pour la plupart héritées des vieilles thèses malthusiennes datant du début du xixe siècle. Surpeuplement, misère, fécondité, mariage ... tout est ici remis en question. Les auteurs abordent le phénomène de la population chinoise sur plusieurs fronts, réussissant ainsi à en donner une vision globale. Ils mettent dans une nouvelle lumière l'explosion démographique des années 1960-1975, où la population passa de 600 millions à près de 850 millions, puis les débuts du contrôle des naissances jusqu'à la politique de l'enfant unique en vigueur depuis 1985. Ils renouvellent ainsi notre compréhension non seulement de la démographie de la Chine, mais aussi de son histoire, de sa société et de son économie. Et comprendre la Chine aujourd'hui, c'est mieux comprendre le monde que nous habitons.

Birth control --- Family planning

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The book lies at the interface of mathematics, social media analysis, and data science. Its authors aim to introduce a new dynamic modeling approach to the use of partial differential equations for describing information diffusion over online social networks. The eigenvalues and eigenvectors of the Laplacian matrix for the underlying social network are used to find communities (clusters) of online users. Once these clusters are embedded in a Euclidean space, the mathematical models, which are reaction-diffusion equations, are developed based on intuitive social distances between clusters within the Euclidean space. The models are validated with data from major social media such as Twitter. In addition, mathematical analysis of these models is applied, revealing insights into information flow on social media. Two applications with geocoded Twitter data are included in the book: one describing the social movement in Twitter during the Egyptian revolution in 2011 and another predicting influenza prevalence. The new approach advocates a paradigm shift for modeling information diffusion in online social networks and lays the theoretical groundwork for many spatio-temporal modeling problems in the big-data era.

Partial differential equations. --- Application software. --- Communication. --- Partial Differential Equations. --- Computer Appl. in Social and Behavioral Sciences. --- Communication Studies. --- Differential equations, Partial. --- Communication, Primitive --- Mass communication --- Sociology --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Partial differential equations