An Introduction to the Kolmogorov–Bernoulli Equivalence, Gabriel Ponce; R?gis Var?o

Автор: Angelo Vulpiani; Roberto Livi
Название: The Kolmogorov Legacy in Physics
ISBN: 3642057861 ISBN-13(EAN): 9783642057861
Издательство: Springer
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Автор: Ming Li; Paul M.B. Vit?nyi
Название: An Introduction to Kolmogorov Complexity and Its Applications
ISBN: 1489984453 ISBN-13(EAN): 9781489984456
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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: Li Ming
Название: Introduction to Kolmogorov Complexity and Its Applications
ISBN: 3030112977 ISBN-13(EAN): 9783030112974
Издательство: Springer
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Описание: This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features.This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the G?cs-Ku?era theorem, the Day-G?cs theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lov?sz local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution.Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface.As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.

Автор: Kichoon Yang
Название: Exterior Differential Systems and Equivalence Problems
ISBN: 0792315936 ISBN-13(EAN): 9780792315933
Издательство: Springer
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Описание: This monograph presents a concise account of exterior differential system theory so that it can be quickly applied to problems. The first part deals with the general theory, while the second part focuses on applications to problems in differential geometry.

Автор: Ellis
Название: Automorphisms and Equivalence Relations in Topological Dynamics
ISBN: 1107633222 ISBN-13(EAN): 9781107633223
Издательство: Cambridge Academ
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Описание: An original and self-contained treatment of some key ideas in the abstract theory of topological dynamics, focussing on the role of automorphisms and equivalence relations. This approach leads to simpler proofs of classical results and provides motivation for further study, making this lucid book ideal for graduate students and researchers.

Автор: Andrei N. Kolmogorov; Adolf-Andrei P. Yushkevich
Название: Mathematics of the 19th Century
ISBN: 3034899335 ISBN-13(EAN): 9783034899338
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Описание: The general principles by which the editors and authors of the present edition have been guided were explained in the preface to the first volume of Mathemat- ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, number theory, and probability theory (Nauka, Moscow 1978;

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: 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: 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: 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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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: 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.