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	Andrey Kolmogorov (Site not responding. Last check: 2007-10-20)
		Kolmogorov was one of the broadest of this century's mathematicians.
		Kolmogorov went on to study the motion of the planets and turbulent fluid flows, later publishing two papers in 1941 on turbulence that even today are of fundamental importance.
		Kolmogorov's notion of complexity is a measure of randomness, one that is closely related to Claude Shannon's entropy rate of an information source.
	www.exploratorium.edu /complexity/CompLexicon/kolmogorov.html (330 words)

	Kolmogorov biography
		Kolmogorov's mother had been on a journey from the Crimea back to her home in Tunoshna near Yaroslavl and it was in the home of his maternal grandfather in Tunoshna that Kolmogorov spent his youth.
		Kolmogorov was appointed a professor at Moscow University in 1931.
		If Kolmogorov made a major contribution to Hilbert's sixth problem, he completely solved Hilbert's Thirteenth Problem in 1957 when he showed that Hilbert was wrong in asking for a proof that there exist continuous functions of three variables which could not be represented by continuous functions of two variables.
	www-history.mcs.st-andrews.ac.uk /Biographies/Kolmogorov.html (2094 words)

	Andrei Nikolaevich Kolmogorov Biography \| World of Mathematics
		Andrei Nikolaevich Kolmogorov made major contributions to almost all areas of mathematics and many fields of science and is considered one of the 20th century's most eminent mathematicians.
		Kolmogorov was born in the town of Tambov in central Russia on April 25, 1903.
		Kolmogorov was also actively interested in mathematical education in the U.S.S.R., working as the chairman of the Academy of Sciences Commission of Mathematical Education.
	www.bookrags.com /biography/andrei-nikolaevich-kolmogorov-wom (1355 words)

	Andrey Kolmogorov Summary
		Kolmogorov was born in Tambov on April 25, 1903.
		Kolmogorov's father, a Russian agriculturist named Nikolai Kataev, was killed in World War I, and his mother, Mariya Kolmogorova—who was not married to Nikolai—died giving birth to their son in the town of Tambov on April 25, 1903.
		Kolmogorov, however, remained modest to the end, and, in line with his belief that a mathematician could no longer conduct valuable research after the age of 60, he retired in 1963, spending 20 years teaching high school.
	www.bookrags.com /Andrey_Kolmogorov (2461 words)

	Kolmogorov's zero-one law
		In probability theory, Kolmogorov's zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, treats of probabilities of certain "tail events" defined in terms of infinite sequences of random variables.
		In an infinite sequence of coin-tosses, the probability that a sequence of 100 consecutive heads eventually occurs, is a tail event.
		Kolmogorov's zero-one law states that the probability of any tail event is either zero or one.
	www.ebroadcast.com.au /lookup/encyclopedia/ko/Kolmogorov's_zero-one_law.html (156 words)

	Andrey Nikolaevich Kolmogorov (Site not responding. Last check: 2007-10-20)
		Andrey Nikolaevich Kolmogorov (Russian: ÐÐ½Ð´ÑÐµÌÐ¹ ÐÐ¸ÐºÐ¾Ð»Ð°ÌÐµÐ²Ð¸Ñ ÐÐ¾Ð»Ð¼Ð¾Ð³Ð¾ÌÑÐ¾Ð²) (April 25, 1903 - October 20, 1987) was a Soviet mathematician who made major advances in the fields of probability theory and topology.
		Kolmogorov quickly gained a reputation for wide-ranging erudition; as an undergraduate at Moscow State University in the; early 1920s, he published his first research paper â” not in any branch of mathematics but on landholding practices in fifteenth and sixteenth century Novgorod.
		Kolmogorov studied under Nikolai Luzin, earning his Ph.D. at Moscow State University in 1929.
	www.wikipedia-mirror.co.za /a/n/d/Andrey_Nikolaevich_Kolmogorov_9996.html (596 words)

	Biographies
		Kolmogorov was doubtless the most important Russian mathematician of the twentieth century.
		Kolmogorov began his mathematical studies at the same time as the topologist Pavel Alexandrov, the two first meeting in the summer of 1929.
		Kolmogorov was an orphan who was raised by his sister.
	tulsagrad.ou.edu /statistics/biographies/kolmogorov.htm (500 words)

	Kolmogorov
		Kolmogorov may have told this story as a joke but never-the-less jokes are only funny if there is some truth in them and undoubtedly this is the case here.
		Kolmogorov graduated from Moscow State University in 1925 and began research under Luzin 's supervision in that year.
		If Kolmogorov made a major contribution to Hilbert 's sixth problem, he completely solved Hilbert 's Thirteenth Problem in 1957 when he showed that Hilbert was wrong in asking for a proof that there exist continuous functions of three variables which could not be represented by continuous functions of two variables.
	www.weizmann.ac.il /lvov/Lecture-Online/Bib/Kolmogorov.html (2006 words)

	DJ Daniel's Latest Discovery - Project Kolmogorov (Site not responding. Last check: 2007-10-20)
		Kolmogorov's DDE's are in fact a set of stochastic differential equations because there is a degree of randomness involved in the population dynamics, indicated by the presence of birth and death parameters.
		For example, in Kolmogorov's equation, the randomenss arises from the likelihood for the birth of a fish species to occur, or the death of one, as indicated by the increment (decrement) in the population index
		In short, Kolmogorov's equation is to exceed previous studies in stem cells by predicting the self-renewal and differentiation path-ways with greater accuracy and sophistication than in previous stem cell research studies.
	www.newton-physics.co.uk /page6.htm (2039 words)

	Andrey Kolmogorov - Wikipedia, the free encyclopedia
		He was a founder of algorithmic complexity theory which is often referred to as simply Kolmogorov complexity theory.
		Kolmogorov works on his talk; A.M. Yaglom is at his right.
		The Legacy of Andrei Nikolaevich Kolmogorov Curriculum Vitae and Biography.
	en.wikipedia.org /wiki/Andrei_Kolmogorov (627 words)

	NationMaster - Encyclopedia: Andrey Kolmogorov
		Andrey Nikolaevich Kolmogorov (Андре́й Никола́евич Колмого́ров) (kahl-mah-GAW-raff) (April 25, 1903 in Tambov - October 20, 1987 in Moscow) was a Soviet mathematician who made major advances in the fields of probability theory and topology.
		The probability of some event (denoted) is defined with respect to a universe or sample space of all possible elementary events in such a way that must satisfy the Kolmogorov axioms.
		In probability theory, Kolmogorovs zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, called a tail event, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.
	www.nationmaster.com /encyclopedia/Andrey-Kolmogorov (1004 words)

	[No title]
		Andrei Nikolaevich Kolmogorov, born 25 April 1903 in Tambov, Russia, died 20 October 1987 in Moscow.
		Kolmogorov was born on 25 April 1903 in the town of Tambov, where his mother Mariya Yakovlevna Kolmogorova had been delayed on her way from the Crimea.
		Algorithmic information theory, or " Kolmogorov complexity theory", originated with the discovery of universal descriptions of finite objects, and a recursively invariant approach to the concepts of complexity of description, randomness and a priori probability.
	homepages.cwi.nl /~paulv/KOLMOGOROV.BIOGRAPHY.html (5574 words)

	Physicists Reconsider The Nature Of Turbulence
		Russian scientist Andrey Kolmogorov first proposed a theory of turbulence in the 1940s that was "pretty good," a theory scientists today refer to as the classical theory of turbulence.
		Essentially what Kolmogorov did was explain the flow pattern and transport properties of turbulence and distinguish turbulence from chaotic flow patterns, resulting in five recognized states.
		Kolmogorov's theory was so convincing that for many years people believed that it provided an essentially complete picture of turbulent flow, despite a gradually increasing catalogue of small discrepancies.
	www.eurekalert.org /pub_releases/1999-03/UoND-PRTN-250399.php (805 words)

	Information theory founders
		In 1925 Kolmogorov was graduated from the faculty of physics and mathematics of Moscow State University and was appointed a research associate of the faculty.
		In 1933 Kolmogorov expanded the paper into the monograph Grundbegriffe der Wahrscheinlichkeitsrechnung, which in 1950 was translated into English under the title Foundations of the Theory of Probability.
		In 1939 Kolmogorov was elected an academician of the Academy of Sciences of the U.S.S.R. and, a little later, an academician-secretary of the department of physical and mathematical sciences of the academy; the department had been established to unite and direct scientific work of the most prominent researchers in this field.
	it-science.net /kolmogorov.html (845 words)

	KOLMOGOROV BOOKS (Site not responding. Last check: 2007-10-20)
		Kolmogorov's 1941 theory is presented in a novel fashion with emphasis on symmetries (including scaling transformations) which are broken by the mechanisms producing the turbulence and restored by the chaotic character of the cascade to small scales.
		Phenomenology of turbulence in the sense of Kolmogorov 1941
		Kolmogorov was a founding member of the editorial board of the Russian journal 'Uspekhi Matematicheskikh Nauk' from 1934 till his death in 1987.
	www.kolmogorov.com /books1.html (2716 words)

	Andrey Nikolaevich Kolmogorov (Site not responding. Last check: 2007-10-20)
		Kolmogorov was one mathematicians of the of the
		Kolmogorov Andrej Koymasky - Famous Matt and GLTB - Andrei N. (April 25, 1903 - Andrei Nikolaevich Kolmogorov Kolmogorov's parents Russia Andrei N. Kolmogorov Physicist and mathematician.
		Kolmogorov was born on April 25, 1903 in Tambov, Russia, and died 20 Oct 1987 in Andrei Nikolaevich made fundamental contributions Moscow, Russia.
	andreyzump.okgobuze.info (454 words)

	Andrei Nikolaevich Kolmogorov (Site not responding. Last check: 2007-10-20)
		Kolmogorov was student (1920-1925), graduate student (1925-1929), researcher (1929-1931), and professor (1931-1987) at the University.
		Kolmogorov was Dean of the MechMath Faculty (1954-1958) and Head of the Mathematics Division (1954-1956 and 1978-till his death in 1987).
		Kolmogorov was President of the Moscow Mathematical Society from 1964 to 1966 and from 1973 to 1985.
	www.kolmogorov.com /Kolmogorov.html (4215 words)

	Probability theory - ExampleProblems.com
		"Pure" mathematicians usually take probability theory to be the study of probability spaces and random variables — an approach introduced by Kolmogorov in the 1930s.
		For an algebraic alternative to Kolmogorov's approach, see algebra of random variables.
		Some statisticians will assign probabilities only to events that are random, i.e., random variables, that are outcomes of actual or theoretical experiments; those are frequentists.
	www.exampleproblems.com /wiki/index.php/Probability_theory (782 words)

	nullismo 2
		In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object.
		Strings whose Kolmogorov complexity is small relative to the string's size are not considered to be complex.
		The notion of Kolmogorov complexity is surprisingly deep and can be used to state and prove impossibility results akin to Gödel's incompleteness theorem and Turing's halting problem.
	nullismo.splinder.com (2036 words)

	Convergence of Fourier series (Site not responding. Last check: 2007-10-20)
		Contrariwise, Andrey Kolmogorov, in his very first paper published when he was 21, constructed an example of a function in L
		Andrey Kolmogorov, Une série de Fourier-Lebesgue divergente presque partout, Fundamenta math.
		Andrey Kolmogorov, Une série de Fourier-Lebesgue divergente partout, C. Acad.
	www.tocatch.info /en/Convergence_of_Fourier_series.htm (1768 words)

	Physics of Fluids - Lecture 3
		All that they 'see'is the rate at which energy is tranferred to them by the bigger scales and that this energy at their smaller scales gets dissipated by the action of viscosity.
		Kolmogorov also argued, that the scale at which this happens must be such that the Reynolds number at that particular scale is of order one.
		The relation known as Kolmogorov's relation, is not exact but it provides the scaling of turbulence and gives us the order of magnitude of ε.
	kramerslab.tn.tudelft.nl /~rob/Courses/PhysicsOfFluids/html-lectures/Lecture3.3.3.html (703 words)

	Andrey Kolmogorov
		Kolmogorov was one of the developers of probability theory.
		In 1939 he was elected to the Soviet Academy of Sciences, receiving the Lenin Prize in 1965 and the Order of Lenin on six separate occasions.
		Kolmogorov later extended his work to study the motion of the planets and the turbulent flow of air from a jet engine, later publishing two papers on turbulence which are even today of fundamental importance.
	www.exploratorium.edu /complexity/lexicon/kolmogorov.html (156 words)

	Good Math has moved to ScienceBlogs: Some good math: An Introduction ...
		Kolmogorov and Chaitin didn't know each other at the time they independently invented the same mathematical formalization (in fact, Chaitin was a teenager at the time!), a fact which led to some friction.
		Chaitin and Kolmogorov saw this as a big deal: using an algorithmic approach to how to process information, you could prove something very simply, which would require a much more complicated proof using other methods.
		According to Kolmogorov and Chaitin, the fundamental amount of information contained in a string (called the string's information entropy after Shannon), is the shortest string of program + data for a computing device that can generate that string.
	goodmath.blogspot.com /2006/03/some-good-math-introduction-to.html (1658 words)

	Randomness at AllExperts
		In the early 1960s Gregory Chaitin, Andrey Kolmogorov and Ray Solomonoff introduced the notion of algorithmic randomness, in which the randomness of a sequence depends on whether it is possible to compress it.
		In the 19th century scientists used the idea of random motions of molecules in the development of statistical mechanics in order to explain phenomena in thermodynamics and the properties of gases.
		In communication theory, randomness in a signal is called noise and is opposed to that component of its variation that is causally attributable to the source, the signal.
	en.allexperts.com /e/r/ra/randomness.htm (1950 words)

	Probability axioms (Site not responding. Last check: 2007-10-20)
		The probability P of some event E, denoted P(E), is defined with respect to a "universe", or sample space Ω, of all possible elementary events in such a way that P must satisfy the Kolmogorov axioms.
		Alternatively, a probability can be interpreted as a measure on a σ-algebra of subsets of the sample space, those subsets being the events, such that the measure of the whole set equals 1.
		The following three axioms are known as the Kolmogorov axioms, after Andrey Kolmogorov who developed them.
	www.tocatch.info /en/Axioms_of_probability.htm (548 words)

	Wikinfo \| Algorithmic information theory (Site not responding. Last check: 2007-10-20)
		The chief idea is to define the complexity (or Kolmogorov complexity) of a string as the length of the shortest program which, when run without any input, outputs that string.
		The field was developed by Andrey Kolmogorov, Ray Solomonoff and Gregory Chaitin starting in the late 1960s.
		It has the desirable properties of statistical invariance (the inference transforms with a re-parameterisation, such as from polar co-ordinates to Cartesian co-ordinates), statistical consistency (even for very hard problems, MML will converge to any underlying model) and efficiency (the MML model will converge to any true underlying model about as quickly as is possible).
	www.wikinfo.org /wiki.php?title=Algorithmic_information_theory (989 words)

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