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Axel Thue
Axel Thue (; 19 February 1863 – 7 March 1922) was a Norwegian mathematician, known for his original work in diophantine approximation and combinatorics. Work Thue published his first important paper in 1909. He stated in 1914 the so-called word problem for semigroups or Thue problem, closely related to the halting problem In computability theory (computer science), 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 for .... Ronald V. Book and Friedrich Otto, ''String-rewriting Systems'', Springer, 1993, , p. 36. His only known PhD student was Thoralf Skolem. The esoteric programming language Thue is named after him. Publications * * See also * * * * * * * * References External links Axel Thue private archiveexists at NTNU University LibrarDorabiblioteket 1863 births 1922 deaths 20th-century Norwegian mathematicians ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tønsberg
Tønsberg (), historically Tunsberg, is a List of towns and cities in Norway, city in Tønsberg Municipality in Vestfold county, Norway. It is located about south-southwest of the capital city of Oslo on the western coast of the Oslofjord near its mouth onto the Skagerrak. The city is the most populous metropolis in Vestfold county. Tønsberg also serves as the administrative centre for Vestfold county and the seat of the County governor (Norway), County Governor of Vestfold og Telemark. Tønsberg is generally regarded as the oldest city in Norway, founded in the 9th century. Snorri Sturluson mentions the town in Harald Hårfagre's saga (written around 1220) before the battle at Hafrsfjord, which historians have traditionally dated to the year 872, therefore the town was in existence by 871 at the latest. This dating is again based on Are Frode's book, Íslendingabók. Using this information, Tønsberg celebrated its one-thousandth anniversary in 1871 and its 1100th anniversary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prouhet–Thue–Morse Constant
In mathematics, the Prouhet–Thue–Morse constant, named for , Axel Thue, and Marston Morse, is the number—denoted by —whose binary expansion 0.01101001100101101001011001101001... is given by the Prouhet–Thue–Morse sequence. That is, : \tau = \sum_^ \frac = 0.412454033640 \ldots where is the element of the Prouhet–Thue–Morse sequence. Other representations The Prouhet–Thue–Morse constant can also be expressed, without using , as an infinite product, : \tau = \frac\left -\prod_^\left(1-\frac\right)\right This formula is obtained by substituting ''x'' = 1/2 into generating series for : F(x) = \sum_^ (-1)^ x^n = \prod_^ ( 1 - x^ ) The continued fraction expansion of the constant is ; 2, 2, 2, 1, 4, 3, 5, 2, 1, 4, 2, 1, 5, 44, 1, 4, 1, 2, 4, 1, … Yann Bugeaud and Martine Queffélec showed that infinitely many partial quotients of this continued fraction are 4 or 5, and infinitely many partial quotients are greater than or equal to 50. Transcendence Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1922 Deaths
Events January * January 7 – Dáil Éireann (Irish Republic), Dáil Éireann, the parliament of the Irish Republic, ratifies the Anglo-Irish Treaty by 64–57 votes. * January 10 – Arthur Griffith is elected President of Dáil Éireann, the day after Éamon de Valera resigns. * January 11 – The first successful insulin treatment of diabetes is made, by Frederick Banting in Toronto. * January 15 – Michael Collins (Irish leader), Michael Collins becomes Chairman of the Provisional Government of the Irish Free State. * January 26 – Italian forces occupy Misrata, Italian Libya, Libya; the Pacification of Libya, reconquest of Libya begins. February * February 6 ** Pope Pius XI (Achille Ratti) succeeds Pope Benedict XV, to become the 259th pope. ** The Washington Naval Treaty, Five Power Naval Disarmament Treaty is signed between the United States, United Kingdom, Empire of Japan, Japan, French Third Republic, France and Kingdom of Italy, Italy. Japan returns some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1863 Births
Events January * January 1 – Abraham Lincoln signs the Emancipation Proclamation during the third year of the American Civil War, making the abolition of slavery in the Confederate States of America an official war goal. The signing proclaimed the freedom of 3.1 million of the nation's four million slaves and immediately frees 50,000 of them, with the rest freed as the Union Army advances. This event marks the start of America's Reconstruction era, Reconstruction Era. * January 2 – Master Lucius Tar Paint Company (''Teerfarbenfabrik Meister Lucius''), predecessor of Hoechst AG, Hoechst, as a worldwide Chemical, chemical manufacturing brand, founded in a suburb of Frankfurt am Main, Germany. * January 4 – Founding date of the New Apostolic Church, a Christian and chiliastic church, in a schism with the Catholic Apostolic Church in Hamburg, Germany. * January 7 – In the Cantons of Switzerland, Swiss canton of Ticino, the village of Bedretto is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Für Die Reine Und Angewandte Mathematik
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of the first major mathematical journals that was not a proceedings of an academy. It has published many notable papers, including works of Niels Henrik Abel, Georg Cantor, Gotthold Eisenstein, Carl Friedrich Gauss and Otto Hesse. It was edited by Carl Wilhelm Borchardt from 1856 to 1880, during which time it was known as ''Borchardt's Journal''. The current editor-in-chief is Daniel Huybrechts (Rheinische Friedrich-Wilhelms-Universität Bonn). Past editors * 1826–1856: August Leopold Crelle * 1856–1880: Carl Wilhelm Borchardt * 1881–1888: Leopold Kronecker, Karl Weierstrass Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 � ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ronald V
Ronald is a masculine given name derived from the Old Norse ''Rögnvaldr'', Hanks; Hardcastle; Hodges (2006) p. 234; Hanks; Hodges (2003) § Ronald. or possibly from Old English '' Regenweald''. In some cases ''Ronald'' is an Anglicised form of the Gaelic '' Raghnall'', a name likewise derived from ''Rögnvaldr''. The latter name is composed of the Old Norse elements ''regin'' ("advice", "decision") and ''valdr'' ("ruler"). ''Ronald'' was originally used in England and Scotland, where Scandinavian influences were once substantial, although now the name is common throughout the English-speaking world. A short form of ''Ronald'' is ''Ron''. Pet forms of ''Ronald'' include ''Roni'' and '' Ronnie''. ''Ronalda'' and ''Rhonda'' are feminine forms of ''Ronald''. ''Rhona'', a modern name apparently only dating back to the late nineteenth century, may have originated as a feminine form of ''Ronald''. Hanks; Hardcastle; Hodges (2006) pp. 230, 408; Hanks; Hodges (2003) § Rhona. The names ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halting Problem
In computability theory (computer science), 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. The halting problem is ''Undecidable problem, undecidable'', meaning that no general algorithm exists that solves the halting problem for all possible program–input pairs. The problem comes up often in discussions of computability since it demonstrates that some functions are mathematically Definable set, definable but not Computable function, computable. A key part of the formal statement of the problem is a mathematical definition of a computer and program, usually via a Turing machine. The proof then shows, for any program that might determine whether programs halt, that a "pathological" program exists for which makes an incorrect determination. Specifically, is the program that, when called with some input, passes its own s ... [...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, in which all function symbols have an arity of at most 1. As a formalism, string rewriting systems are Turing complete. The semi-Thue name comes from the Norwegian mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number ''p''/''q'' is a "good" approximation of a real number ''α'' if the absolute value of the difference between ''p''/''q'' and ''α'' may not decrease if ''p''/''q'' is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of simple continued fractions. Knowing the "best" approximations of a given number, the main problem of the field is to find sharp upper and lower bounds of the above difference, expressed as a function of the denominator. It appears that these bounds depend on the nature of the real numbers to be approximated: the lower bound for the approximation of a rational number by another rational number i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
