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Eugene Dynkin
Eugene Borisovich Dynkin (Russian: Евге́ний Бори́сович Ды́нкин; 11 May 1924 – 14 November 2014) was a Soviet and American mathematician.[1] He has made contributions to the fields of probability and algebra, especially semisimple Lie groups, Lie algebras, and Markov processes
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Saint Petersburg
Saint
Saint
Petersburg (Russian: Санкт-Петербу́рг, tr. Sankt-Peterburg, IPA: [ˈsankt pʲɪtʲɪrˈburk] ( listen)) is Russia's second-largest city after Moscow, with five million inhabitants in 2012.[9] An important Russian port on the Baltic Sea, it has a status of a federal subject (a federal city). Situated on the Neva
Neva
River, at the head of the Gulf of Finland
Gulf of Finland
on the Baltic Sea, it was founded by Tsar
Tsar
Peter the Great
Peter the Great
on May 27 [O.S. 16] 1703
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Economic Equilibrium
In economics, economic equilibrium is a state where economic forces such as supply and demand are balanced and in the absence of external influences the (equilibrium) values of economic variables will not change. For example, in the standard textbook model of perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal.[1] Market equilibrium in this case refers to a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers. This price is often called the competitive price or market clearing price and will tend not to change unless demand or supply changes, and the quantity is called "competitive quantity" or market clearing quantity
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Soviet Union
The Soviet Union
Soviet Union
(Russian: Сове́тский Сою́з, tr. Sovétsky Soyúz, IPA: [sɐˈvʲɛt͡skʲɪj sɐˈjus] ( listen)), officially the Union of Soviet Socialist Republics (Russian: Сою́з Сове́тских Социалисти́ческих Респу́блик, tr. Soyúz Sovétskikh Sotsialistícheskikh Respúblik, IPA: [sɐˈjus sɐˈvʲɛtskʲɪx sətsɨəlʲɪsˈtʲitɕɪskʲɪx rʲɪˈspublʲɪk] ( listen)), abbreviated as the USSR (Russian: СССР, tr. SSSR), was a socialist state in Eurasia
Eurasia
that existed from 1922 to 1991. Nominally a union of multiple national Soviet republics,[a] its government and economy were highly centralized. The country was a one-party state, governed by the Communist Party with Moscow
Moscow
as its capital in its largest republic, the Russian Soviet Federative Socialist Republic
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Kazakhstan
Kazakhstan[b] (Kazakh: Қазақстан, translit. Qazaqstan, IPA: [qɑzɑqˈstɑn] ( listen); Russian: Казахстан, IPA: [kəzɐxˈstan]), officially the Republic
Republic
of Kazakhstan
Kazakhstan
(Kazakh: Қазақстан Республикасы, translit. Qazaqstan Respýblıkasy; Russian: Республика Казахстан, tr. Respublika Kazakhstan),[4][13] is the world's largest landlocked country, and the ninth largest in the world, with an area of 2,724,900 square kilometres (1,052,100 sq mi).[4][14] Kazakhstan
Kazakhstan
is the dominant nation of Central Asia
Central Asia
economically, generating 60% of the region's GDP, primarily through its oil/gas industry
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Gulag
The Gulag
Gulag
(Russian: ГУЛАГ, IPA: [ɡʊˈlak] ( listen); acronym of Glavnoye Upravleniye Lagerej, Main Camps' Administration or Chief Administration of [Corrective Labor] Camps) was the government agency in charge of the Soviet forced labor camp system that was created under Vladimir Lenin[1][2] and reached its peak during Joseph Stalin's rule from the 1930s to the 1950s. The term is also commonly used in English language to refer to any forced-labor camp in the Soviet Union, including camps that existed in post- Stalin
Stalin
times.[3][4] The camps housed a wide range of convicts, from petty criminals to political prisoners. Large numbers were convicted by simplified procedures, such as NKVD
NKVD
troikas and other instruments of extrajudicial punishment
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World War II
Allied victoryCollapse of Nazi Germany Fall of Japanese and Italian Empires Dissolution of the League of Nations Creation of the United Nations Emergence of the United States
United States
and the Soviet Union
Soviet Union
as superpowers Beginning of the Cold War
Cold War
(more...)ParticipantsAllied Powers Axis PowersCommanders and leadersMain Allied leaders Joseph Stalin Franklin D
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Master Of Science
A Master of Science
Master of Science
(Latin: Magister Scientiae; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM, or Sc.M.) is a master's degree in the field of science awarded by universities in many countries, or a person holding such a degree.[1] In contrast to the Master of Arts degree, the Master of Science
Master of Science
degree is typically granted for studies in sciences, engineering, and medicine, and is usually for programs that are more focused on scientific and mathematical subjects; however, different universities have different conventions and may also offer the degree for fields typically considered within the humanities and social sciences
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Ph.D.
A Doctor of Philosophy
Philosophy
(PhD, Ph.D., DPhil, or Dr. phil.; Latin Philosophiae doctor) is the highest academic degree awarded by universities in most countries. PhDs are awarded for programs across the whole breadth of academic fields. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy
Philosophy
degree may, in most jurisdictions, use the title Doctor (often abbreviated "Dr") or, in non-English speaking countries, variants such as "Dr. phil." with their name, and may use post-nominal letters such as "Ph.D.", "PhD" (depending on the awarding institute). The requirements to earn a PhD degree vary considerably according to the country, institution, and time period, from entry-level research degrees to higher doctorates
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USSR Academy Of Sciences
The Russian Academy of Sciences (RAS; Russian: Росси́йская акаде́мия нау́к (РАН) Rossíiskaya akadémiya naúk) consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such as libraries, publishing units, and hospitals. Headquartered in Moscow, the Academy (RAS) is considered a civil, self-governed, non-commercial organization[2] chartered by the Government of Russia. It combines the members of RAS (see below) and scientists employed by institutions
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Economic Growth
Economic growth
Economic growth
is the increase in the inflation-adjusted market value of the goods and services produced by an economy over time
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Probability Theory
Probability
Probability
theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes, which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion. Although it is not possible to perfectly predict random events, much can be said about their behavior
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Lie Group
In mathematics, a Lie group
Lie group
(pronounced /liː/ "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Norwegian mathematician Sophus Lie, who laid the foundations of the theory of continuous transformation groups. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations (differential Galois theory), in much the same way as permutation groups are used in Galois theory
Galois theory
for analysing the discrete symmetries of algebraic equations
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Eigenvalue
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that only changes by a scalar factor when that linear transformation is applied to it. More formally, if T is a linear transformation from a vector space V over a field F into itself and v is a vector in V that is not the zero vector, then v is an eigenvector of T if T(v) is a scalar multiple of v
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Stochastic Matrix
In mathematics, a stochastic matrix[1] (also termed probability matrix,[1] transition matrix,[1][2] substitution matrix, or Markov matrix[1]) is a square matrix[1] used to describe the transitions of a Markov chain.[1] Each of its entries is a nonnegative real number representing a probability.[1] It has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics.[1] The stochastic matrix was first developed by Andrey Markov
Andrey Markov
at the beginning of the 20th century.[3] There are several different definitions a
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Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (Yiddish: ישראל געלפֿאַנד‎, Russian: Изра́иль Моисе́евич Гельфа́нд; 2 September [O.S. 20 August] 1913 – 5 October 2009) was a prominent Soviet mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis
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