Introduction to Kolmogorov Complexity and Its Applications, Li Ming

Автор: Ming Li; Paul M.B. Vit?nyi
Название: An Introduction to Kolmogorov Complexity and Its Applications
ISBN: 1489984453 ISBN-13(EAN): 9781489984456
Издательство: Springer
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Описание: Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications.

Автор: Gabriel Ponce; R?gis Var?o
Название: An Introduction to the Kolmogorov–Bernoulli Equivalence
ISBN: 303027389X ISBN-13(EAN): 9783030273897
Издательство: Springer
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Описание: This book offers an introduction to a classical problem in ergodic theory and smooth dynamics, namely, the Kolmogorov–Bernoulli (non)equivalence problem, and presents recent results in this field. Starting with a crash course on ergodic theory, it uses the class of ergodic automorphisms of the two tori as a toy model to explain the main ideas and technicalities arising in the aforementioned problem. The level of generality then increases step by step, extending the results to the class of uniformly hyperbolic diffeomorphisms, and concludes with a survey of more recent results in the area concerning, for example, the class of partially hyperbolic diffeomorphisms. It is hoped that with this type of presentation, nonspecialists and young researchers in dynamical systems may be encouraged to pursue problems in this area.

Автор: A. Shen, V.A. Uspensky, N. Vereshchagin
Название: Kolmogorov Complexity and Algorithmic Randomness
ISBN: 1470431823 ISBN-13(EAN): 9781470431822
Издательство: Mare Nostrum (Eurospan)
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Описание: Offers a textbook-style exposition of the basic notions of complexity and randomness; and covers some recent work done by participants of the "Kolmogorov seminar" in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.

Автор: Osamu Watanabe
Название: Kolmogorov Complexity and Computational Complexity
ISBN: 3642777376 ISBN-13(EAN): 9783642777370
Издательство: Springer
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Описание: The mathematical theory of computation has given rise to two important ap- proaches to the informal notion of "complexity": Kolmogorov complexity, usu- ally a complexity measure for a single object such as a string, a sequence etc., measures the amount of information necessary to describe the object.

Автор: Bjorn Birnir
Название: The Kolmogorov-Obukhov Theory of Turbulence
ISBN: 1461462614 ISBN-13(EAN): 9781461462613
Издательство: Springer
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Описание: The Kolmogorov-Obukhov Theory of Turbulence develops a statistical theory of turbulence from the stochastic Navier-Stokes equation and the physical theory, that was proposed by Kolmogorov and Obukhov in 1941.

Автор: Vladimir M. Tikhomirov
Название: Selected Works of A. N. Kolmogorov
ISBN: 9401053472 ISBN-13(EAN): 9789401053471
Издательство: Springer
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Описание: The Praesidium of the USSR Academy of Sciences has decided to publish three volumes of Selected Works of A.N. Kolmogorov, one of the most prominent mathematicians of the 20th century. The creative work of A.N. Kolmogorov is exceptionally versatile. In his studies on trigonometric and orthogonal series, theory of measure and inte- gral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in- formation theory, many conceptual and fundamental problems were solved and new questions were posed which gave rise to a great number of investigations. A.N. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of basic results, with many applications to mechanics, geophysics, linguistics, biology and other branches of knowledge. This edition includes the most important papers by A.N. Kolmogorov on mathematics and natural science. It does not include philosophical and ped- agogical studies of A.N. Kolmogorov, his articles written for the "Bol'shaya Sov'etskaya Entsiklopediya," papers on prosody and various applications of mathematics and publications on general questions. The material of this edition was selected and grouped by A.N. Kolmogorov.

Автор: Sergey Bagdasarov
Название: Chebyshev Splines and Kolmogorov Inequalities
ISBN: 3034897812 ISBN-13(EAN): 9783034897815
Издательство: Springer
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Автор: Angelo Vulpiani; Roberto Livi
Название: The Kolmogorov Legacy in Physics
ISBN: 3642057861 ISBN-13(EAN): 9783642057861
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Автор: Gabriella Pinzari
Название: Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem
ISBN: 1470441020 ISBN-13(EAN): 9781470441029
Издательство: Mare Nostrum (Eurospan)
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Описание: Proves the existence of an almost full measure set of $(3n-2)$-dimensional quasi-periodic motions in the planetary problem with $(1+n)$ masses, with eccentricities arbitrarily close to the Levi-Civita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed.

Автор: Kolmogorov Andrei N., Shiryaev Albert N.
Название: Selected Works III: Information Theory and the Theory of Algorithms
ISBN: 9402417109 ISBN-13(EAN): 9789402417104
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Описание: Papers by A. V. Kolmogorov.- 1. On the notion of algorithm.- 2. On the general definition of the quantity of information.- 3. The theory of transmission of information.- 4. Amount of information and entropy for continuous distributions.- 5. New metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces.- 6. To the definition of algorithms.- 7. ?-entropy and ?-capacity of sets in functional spaces.- 8. Various approaches to estimating the complexity of approximate representation and calculation of functions.- 9. On tables of random numbers.- 10. Three approaches to the definition of the notion of amount of information.- 11. On the realization of networks in three - dimensional space.- 12. To the logical foundations of the theory of information and probability theory.- 13. The combinatorial foundations of information theory and the probability calculus.- Comments and addenda.- On works in information theory and some of its applications.- Information theory.- Algorithmic information theory.- ?-entropy and ?-capacity.- Tables of random numbers.- Realization of networks in 3-dimensional space.- Ergodic theory.- Kolmogorov's algorithms or machines.- From A. N. Kolmogorov's recollections.- Appendix 1. Report to the mathematical circle about square pavings.- Appendix 2. On operations on sets. II.- Afterword.

Автор: N.V. Krylov; G. Da Prato; M. R?ckner; J. Zabczyk
Название: Stochastic PDE`s and Kolmogorov Equations in Infinite Dimensions
ISBN: 3540665455 ISBN-13(EAN): 9783540665458
Издательство: Springer
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Цена: 35360.00 T
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Описание: Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables, connected with stochastic differential equations in finite or infinite dimensional spaces. These equations can be studied both by probabilistic and by analytic methods.

Автор: Vladimir I. Bogachev, Nicolai V. Krylov, Michael Rockner, Stanislav V. Shaposhnikov
Название: Fokker-Planck-Kolmogorov Equations
ISBN: 1470425580 ISBN-13(EAN): 9781470425586
Издательство: Mare Nostrum (Eurospan)
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Описание: This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.