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Andrey Markov, Jr.
Andrey Andreyevich Markov (russian: Андре́й Андре́евич Ма́рков; St. Petersburg, September 22, 1903 – Moscow, October 11, 1979) was a Soviet mathematician, the son of the Russian mathematician Andrey Markov Sr, and one of the key founders of the Russian school of constructive mathematics and logic. He made outstanding contributions to various areas of mathematics, including differential equations, topology, mathematical logic and the foundations of mathematics. His name is in particular associated with Markov's principle and Markov's rule in mathematical logic, Markov's theorem in knot theory and Markov algorithm in theoretical computer science. An important result that he proved in 1947 was that the word problem for semigroups was unsolvable; Emil Post obtained the same result independently at about the same time. In 1953 he became a member of the Communist Party. In 1960, Markov obtained fundamental results showing that the classification of four ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Petersburg
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), is the second-largest city in Russia. It is situated on the Neva River, at the head of the Gulf of Finland on the Baltic Sea, with a population of roughly 5.4 million residents. Saint Petersburg is the fourth-most populous city in Europe after Istanbul, Moscow and London, the most populous city on the Baltic Sea, and the world's northernmost city of more than 1 million residents. As Russia's Imperial capital, and a historically strategic port, it is governed as a federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the site of a captured Swedish fortress, and was named after apostle Saint Peter. In Russia, Saint Petersburg is historically and culturally associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semi-Thue System
In theoretical computer science and mathematical logic a string rewriting system (SRS), historically called a semi- Thue system, is a rewriting system over strings from a (usually finite) alphabet. Given a binary relation R between fixed strings over the alphabet, called rewrite rules, denoted by s\rightarrow t, an SRS extends the rewriting relation to all strings in which the left- and right-hand side of the rules appear as substrings, that is usv\rightarrow utv, where s, t, u, and v are strings. The notion of a semi-Thue system essentially coincides with the presentation of a monoid. Thus they constitute a natural framework for solving the word problem for monoids and groups. An SRS can be defined directly as an abstract rewriting system. It can also be seen as a restricted kind of a term rewriting system. As a formalism, string rewriting systems are Turing complete. The semi-Thue name comes from the Norwegian mathematician Axel Thue, who introduced systematic treatment of strin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logicians
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1979 Deaths
Events January * January 1 ** United Nations Secretary-General Kurt Waldheim heralds the start of the ''International Year of the Child''. Many musicians donate to the ''Music for UNICEF Concert'' fund, among them ABBA, who write the song ''Chiquitita'' to commemorate the event. ** The United States and the People's Republic of China establish full Sino-American relations, diplomatic relations. ** Following a deal agreed during 1978, France, French carmaker Peugeot completes a takeover of American manufacturer Chrysler's Chrysler Europe, European operations, which are based in United Kingdom, Britain's former Rootes Group factories, as well as the former Simca factories in France. * January 7 – Cambodian–Vietnamese War: The People's Army of Vietnam and Vietnamese-backed Kampuchean United Front for National Salvation, Cambodian insurgents announce the fall of Phnom Penh, Cambodia, and the collapse of the Pol Pot regime. Pol Pot and the Khmer Rouge retreat west to an area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1903 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipknot. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolai Aleksandrovich Shanin
Nikolai Aleksandrovich Shanin (russian: Николай Александрович Шанин) (25 May 1919 Pskov – 17 September 2011) was a Russian mathematician who worked on topology and constructive mathematics. He introduced the delta-system lemma and the caliber In guns, particularly firearms, caliber (or calibre; sometimes abbreviated as "cal") is the specified nominal internal diameter of the gun barrel Gauge (firearms) , bore – regardless of how or where the bore is measured and whether the f ... of a topological space. Further reading * * External links *Nikolai Aleksandrovich Shaninat the Steklov Institute of Mathematics at St. Petersburg {{DEFAULTSORT:Shanin, Nikolai Aleksandrovich Russian mathematicians 1919 births 2011 deaths People from Pskov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gennady Semenovich Makanin
Gennady (or Gennadii or Gennadiy) Semenovich Makanin (1938–2017) was a Russian mathematician, awarded the 2010 I. M. Vinogradov Prize for a series of papers on the problem of algorithmically recognizing the solvability of arbitrary equations in free groups and semigroups. Education and career At Moscow State University he received his undergraduate degree and in 1967 his Russian Candidate of Sciences degree (PhD). His dissertation К проблеме тождества в конечно-определённых группах и полугруппах (On the identity problem in finitely-presented groups and semigroups) was supervised by Andrey Markov Jr. and Sergei Adian. Makanin spent his career (since 1966) working at the Steklov Institute of Mathematics (since 2013 as a freelance employee). From the Steklov Institute of Mathematics he received in 1977 his Russian Doctor of Sciences degree (similar to habilitation) with dissertation Проблема разрешимости ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Kushner (mathematician)
Boris Abramovich Kushner (russian: Борис Абрамович Кушнер, December 10, 1941May 7, 2019) was a mathematician, poet and essayist. His primary contribution in mathematics was in the field of Constructive Mathematical Analysis and the Theory of Constructive Numbers and Functions. He has published several books of poetry (in Russian) and a number of music, literary, and political essays (Russian and English). Dr. Kushner taught at the University of Pittsburgh at Johnstown, Pennsylvania Johnstown is a city in Cambria County, Pennsylvania, United States. The population was 18,411 as of the 2020 United States Census, 2020 census. Located east of Pittsburgh, Johnstown is the principal city of the Johnstown, Pennsylvania, Metropol .... References * B.A. Kushner, E. Mendelson (Translator). "Lectures on constructive mathematical analysis". American Mathematical Society, 1984. * Boris Kushner, Yulia Kushner (Illustrator). "Prichina Pechali - the Reason of Sadness: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halting Problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program–input pairs cannot exist. For any program that might determine whether programs halt, a "pathological" program , called with some input, can pass its own source and its input to ''f'' and then specifically do the opposite of what ''f'' predicts ''g'' will do. No ''f'' can exist that handles this case. A key part of the proof is a mathematical definition of a computer and program, which is known as a Turing machine; the halting problem is '' undecidable'' over Turing machines. It is one of the first cases of decision problems proven to be unsolvable. This proof is significant to practical computing efforts, defining a class of applications which no programming inventi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undecidable Problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run. Background A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns ''yes''. These inputs can be natural numbers, but also other values of some other kind, such as strings of a formal language. Using some encoding, such as a Gödel numbering, the strings can be encoded as natural numbers. Thus, a decision problem informally phrased in terms of a formal language is also equivalent to a set of natural numbers. To keep the formal definition simple, it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manifolds
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a Neighbourhood (mathematics), neighborhood that is homeomorphic to an open (topology), open subset of n-dimensional Euclidean space. One-dimensional manifolds include Line (geometry), lines and circles, but not Lemniscate, lemniscates. Two-dimensional manifolds are also called Surface (topology), surfaces. Examples include the Plane (geometry), plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as Graph of a function, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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