• Publications
  • Influence
The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
  • A. Kolmogorov
  • Mathematics
    Proceedings of the Royal Society of London…
  • 8 July 1991
§1. We shall denote by uα(P) = uα (x1, x2, x3, t), α = 1, 2, 3, the components of velocity at the moment t at the point with rectangular cartesian coordinates x1, x2, x3. In considering the
Dissipation of energy in the locally isotropic turbulence
  • A. Kolmogorov
  • Geology
    Proceedings of the Royal Society of London…
  • 1 April 1941
In my note (Kolmogorov 1941a) I defined the notion of local isotropy and introduced the quantities Bdd(r)=[ud(M′)−ud(M)]2,¯[un(M′)−un(M)¯]2, where r denotes the distance between the points M and M',
A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
The hypotheses concerning the local structure of turbulence at high Reynolds number, developed in the years 1939-41 by myself and Oboukhov (Kolmogorov 1941 a,b,c; Oboukhov 1941 a,b) were based
Foundations of the theory of probability
Theories of ProbabilityFoundations of Probabilistic Logic ProgrammingGood ThinkingStatistical Foundations of Data ScienceFoundations of Risk AnalysisFoundations of Estimation TheoryThe Foundations of
Entropy and "-capacity of sets in func-tional spaces
The article is mainly devoted to the systematic exposition of results that were published in the years 1954–1958 by K. I. Babenko [1], A. G. Vitushkin [2,3], V. D. Yerokhin [4], A. N. Kolmogorov
Logical basis for information theory and probability theory
  • A. Kolmogorov
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1 September 1968
A new logical basis for information theory as well as probability theory is proposed, based on computing complexity, according to a new approach to computing complexity.
On the Shannon theory of information transmission in the case of continuous signals
  • A. Kolmogorov
  • Computer Science
    IRE Trans. Inf. Theory
  • 1 December 1956
In addition to the scheduled program, the following two papers, by A. N. Kolmogorov and V. I. Siforov, were presented at the 1956 Symposium on Information Theory. However, the manuscripts were
On Strong Mixing Conditions for Stationary Gaussian Processes
This paper considers conditions, which guarantee strong mixing of stationary random Gaussian process $\xi (t)$. It is proved, for example, that if the spectral density $f(\lambda )$ of the process