Pisot Number
Charles Pisot (2 March 1910 – 7 March 1984) was a French mathematician. He is chiefly recognized as one of the primary investigators of the numerical set associated with his name, the Pisot–Vijayaraghavan numbers. He followed the classical path of great French mathematicians by studying at the École Normale Supérieure on Ulm street, where he was received first at the agrégation in 1932. He then began his academic career at the Bordeaux University before being offered a chair at the Science Faculty of Paris and at the École Polytechnique. He was a member of Bourbaki. Also of interest is the recently solved Pisot conjecture on rational functions. (For a technical account and bibliography see Umberto Zannier's paper in the ''Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Jo ...
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Pisot–Vijayaraghavan Number
In mathematics, a Pisot–Vijayaraghavan number, also called simply a Pisot number or a PV number, is a real algebraic integer greater than 1, all of whose Galois conjugates are less than 1 in absolute value. These numbers were discovered by Axel Thue in 1912 and rediscovered by G. H. Hardy in 1919 within the context of diophantine approximation. They became widely known after the publication of Charles Pisot's dissertation in 1938. They also occur in the uniqueness problem for Fourier series. Tirukkannapuram Vijayaraghavan and Raphael Salem continued their study in the 1940s. Salem numbers are a closely related set of numbers. A characteristic property of PV numbers is that their powers approach integers at an exponential rate. Pisot proved a remarkable converse: if ''α'' > 1 is a real number such that the sequence : \, \alpha^n\, measuring the distance from its consecutive powers to the nearest integer is square-summable, or ''ℓ'' 2, then ''α'' is a Pisot n ...
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Obernai
Obernai ( Alsatian: ''Owernah''; german: Oberehnheim) commune in the Bas-Rhin department in Alsace in north-eastern France. It lies on the eastern slopes of the Vosges mountains. Obernai is a rapidly growing city, its number of inhabitants having gone up from 6,304 in 1968 to 11,279 in 2017. History A neolithic necropole has been uncovered dating between 5,000 and 4,600 BC; 27 individuals were buried there in wooden coffins. This appears to be a continuation of groups from the Linear Pottery culture who were located also on the eastern side of the Rhine. The Obernai region, which was the property of the dukes of Alsace in the 7th century, is the birthplace of St. Odile, daughter of the Duke, who would become the Patron Saint of Alsace. The Obernai name first appears in 1240, when the village acquires the status of town under the tutelage of the Hohenstaufen family. The town then prospered. It became a member of the Décapole in 1354, an alliance of ten towns of the Holy R ...
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Nicolas Bourbaki
Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure - PSL (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in analysis. Over time the project became much more ambitious, growing into a large series of textbooks published under the Bourbaki name, meant to treat modern pure mathematics. The series is known collectively as the '' Éléments de mathématique'' (''Elements of Mathematics''), the group's central work. Topics treated in the series include set theory, abstract algebra, topology, analysis, Lie groups and Lie algebras. Bourbaki was founded in response to the effects of the First World War which caused the death of a generation of French mathematicians; as a result, young university instructors were forced to use dated texts. While teaching at the University of Strasbourg, Henri Cartan complained to his colleague André Weil of the inade ...
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École Normale Supérieure Alumni
École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoie, a French commune * École-Valentin, a French commune in the Doubs département * Grandes écoles, higher education establishments in France * The École, a French-American bilingual school in New York City Ecole may refer to: * Ecole Software This is a list of notable video game companies that have made games for either computers (like PC or Mac), video game consoles, handheld or mobile devices, and includes companies that currently exist as well as now-defunct companies. See the lis ...

École Polytechnique Faculty
École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoie, a French commune * École-Valentin, a French commune in the Doubs département * Grandes écoles, higher education establishments in France * The École, a French-American bilingual school in New York City Ecole may refer to: * Ecole Software This is a list of notable video game companies that have made games for either computers (like PC or Mac), video game consoles, handheld or mobile devices, and includes companies that currently exist as well as now-defunct companies. See the lis ...

People From Obernai
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of p ...
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1984 Deaths
Events January * January 1 – The Bornean Sultanate of Brunei gains full independence from the United Kingdom, having become a British protectorate in 1888. * January 7 – Brunei becomes the sixth member of the Association of Southeast Asian Nations (ASEAN). * January 10 ** The United States and the Vatican City, Vatican (Holy See) restore full diplomatic relations. ** The Victoria, Seychelles, Victoria Agreement is signed, institutionalising the Indian Ocean Commission. *January 24 – Steve Jobs launches the Macintosh 128K, Macintosh personal computer in the United States. February * February 3 ** Dr. John Buster and the research team at Harbor–UCLA Medical Center announce history's first embryo transfer from one woman to another, resulting in a live birth. ** STS-41-B: Space Shuttle Challenger, Space Shuttle ''Challenger'' is launched on the 10th Space Shuttle mission. * February 7 – Astronauts Bruce McCandless II and Robert L. Stewart make the first untethered spac ...
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1910 Births
Year 191 ( CXCI) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Apronianus and Bradua (or, less frequently, year 944 ''Ab urbe condita''). The denomination 191 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Parthia * King Vologases IV of Parthia dies after a 44-year reign, and is succeeded by his son Vologases V. China * A coalition of Chinese warlords from the east of Hangu Pass launches a punitive campaign against the warlord Dong Zhuo, who seized control of the central government in 189, and held the figurehead Emperor Xian hostage. After suffering some defeats against the coalition forces, Dong Zhuo forcefully relocates the imperial capital from Luoyang to Chang'an. Before leaving, Dong Zhuo orders his troops to loot the tombs of t ...
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Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The ...
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Umberto Zannier
Umberto Zannier (born 25 May 1957, in Spilimbergo, Italy) is an Italian mathematician, specializing in number theory and Diophantine geometry. Education Zannier earned a Laurea degree from University of Pisa and studied at the Scuola Normale Superiore di Pisa with Ph.D. supervised by Enrico Bombieri. Career Zannier was from 1983 to 1987 a researcher at the University of Padua, from 1987 to 1991 an associate professor at the University of Salerno, and from 1991 to 2003 a full professor at the Università IUAV di Venezia. From 2003 to the present he has been a Professor in Geometry at the Scuola Normale Superiore di Pisa. In 2010 he gave the Hermann Weyl Lectures at the Institute for Advanced Study. He was a visiting professor at several institutions, including the Institut Henri Poincaré in Paris, the ETH Zurich, and the Erwin Schrödinger Institute in Vienna. With Jonathan Pila he developed a method (now known as the Pila-Zannier method) of applying O-minimality to number-t ...
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Rational Function
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field ''K''. In this case, one speaks of a rational function and a rational fraction ''over K''. The values of the variables may be taken in any field ''L'' containing ''K''. Then the domain of the function is the set of the values of the variables for which the denominator is not zero, and the codomain is ''L''. The set of rational functions over a field ''K'' is a field, the field of fractions of the ring of the polynomial functions over ''K''. Definitions A function f(x) is called a rational function if and only if it can be written in the form : f(x) = \frac where P\, and Q\, are polynomial functions of x\, and Q\, is not the zero function. The domain of f\, is the set of all valu ...
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