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This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of continuous functions, and the integral representation in compact convex sets. The third chapter presents new or little-known results, with the aim of illustrating the effectiveness of capacitary methods in the most varied fields. The last two chapters are concerned with the theory of resolvents. The fourth and last part of the English edition will be devoted to the theory of Markov processes.
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This is a systematic account of the multiplicative structure of integers, from the probabilistic point of view. The authors are especially concerned with the distribution of the divisors, which is as fundamental and important as the additive structure of the integers, and yet until now has hardly been discussed outside of the research literature. Hardy and Ramanujan initiated this area of research and it was developed by Erdös in the thirties. His work led to some deep and basic conjectures of wide application which have now essentially been settled. This book contains detailed proofs, some of which have never appeared in print before, of those conjectures that are concerned with the propinquity of divisors. Consequently it will be essential reading for all researchers in analytic number theory.
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Soil mechanics. --- Soil physics. --- Statistics. --- Probability theory
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Flood forecasting --- Flood forecasting --- Distribution (Probability theory)
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Mathematical statistics --- Cluster analysis --- Mixture distributions (Probability theory) --- Cluster analysis. --- Compound distributions (Probability theory) --- Distributions, Mixture (Probability theory) --- Mixed distributions (Probability theory) --- Mixing distributions (Probability theory) --- Mixtures of distributions (Probability theory) --- Distribution (Probability theory) --- Correlation (Statistics) --- Multivariate analysis --- Spatial analysis (Statistics) --- Mixture distributions (Probability theory).
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519.2 --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- Structural dynamics --- Congresses --- Vibration --- Stochastic systems
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