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Joseph Fels Ritt
Joseph Fels Ritt (August 23, 1893 – January 5, 1951) was an American mathematician at Columbia University in the early 20th century. He was born and died in New York. After beginning his undergraduate studies at City College of New York, Ritt received his B.A. from George Washington University in 1913. He then earned a doctorate in mathematics from Columbia University in 1917 under the supervision of Edward Kasner. After doing calculations for the war effort in World War I, he joined the Columbia faculty in 1921. He served as department chair from 1942 to 1945, and in 1945 became the Davies Professor of Mathematics.. In 1932, George Washington University honored him with a Doctorate in Science,. and in 1933 he was elected to join the United States National Academy of Sciences. He has 463 academic descendants listed in the Mathematics Genealogy Project, mostly through his student Ellis Kolchin. Ritt was an Invited Speaker with talk ''Elementary functions and their inverses'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the United States, and is more than twice as populous as second-place Los Angeles. New York City lies at the southern tip of New York State, and constitutes the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the world by urban landmass. With over 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York is one of the world's most populous megacities, and over 58 million people live within of the city. New York City is a global cultural, financial, entertainment, and media center with a significant influence on commerce, health care and life sciences, research, technology, education, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Algebra
In mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations, which are unary functions that are linear and satisfy the Leibniz product rule. A natural example of a differential field is the field of rational functions in one variable over the complex numbers, \mathbb(t), where the derivation is differentiation with respect to t. Differential algebra refers also to the area of mathematics consisting in the study of these algebraic objects and their use in the algebraic study of differential equations. Differential algebra was introduced by Joseph Ritt in 1950. Open problems The biggest open problems in the field include the Kolchin Catenary Conjecture, the Ritt Problem, and The Jacobi Bound Problem. All of these deal with the structure of differential ideals in differential rings. Differential ring A ''differential ring'' is a ring R equipped with one or more '' derivations' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Members Of The United States National Academy Of Sciences
Member may refer to: * Military jury, referred to as "Members" in military jargon * Element (mathematics), an object that belongs to a mathematical set * In object-oriented programming, a member of a class ** Field (computer science), entries in a database ** Member variable, a variable that is associated with a specific object * Limb (anatomy), an appendage of the human or animal body ** Euphemism for penis * Structural component of a truss, connected by nodes * User (computing), a person making use of a computing service, especially on the Internet * Member (geology), a component of a geological formation * Member of parliament * The Members, a British punk rock band * Meronymy, a semantic relationship in linguistics * Church membership, belonging to a local Christian congregation, a Christian denomination and the universal Church * Member, a participant in a club or learned society A learned society (; also learned academy, scholarly society, or academic association) is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1951 Deaths
Events January * January 4 – Korean War: Third Battle of Seoul – Chinese and North Korean forces capture Seoul for the second time (having lost the Second Battle of Seoul in September 1950). * January 9 – The Government of the United Kingdom announces abandonment of the Tanganyika groundnut scheme for the cultivation of peanuts in the Tanganyika Territory, with the writing off of £36.5M debt. * January 15 – In a court in West Germany, Ilse Koch, The "Witch of Buchenwald", wife of the commandant of the Buchenwald concentration camp, is sentenced to life imprisonment. * January 20 – Winter of Terror: Avalanches in the Alps kill 240 and bury 45,000 for a time, in Switzerland, Austria and Italy. * January 21 – Mount Lamington in Papua New Guinea 1951 eruption of Mount Lamington, erupts catastrophically, killing nearly 3,000 people and causing great devastation in Oro Province. * January 25 – Dutch author Anne de Vries releases the first volume of his children's nove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1893 Births
Events January–March * January 2 – Webb C. Ball introduces railroad chronometers, which become the general railroad timepiece standards in North America. * Mark Twain started writing Puddn'head Wilson. * January 6 – The Washington National Cathedral is chartered by Congress; the charter is signed by President Benjamin Harrison. * January 13 ** The Independent Labour Party of the United Kingdom has its first meeting. ** U.S. Marines from the ''USS Boston'' land in Honolulu, Hawaii, to prevent the queen from abrogating the Bayonet Constitution. * January 15 – The ''Telefon Hírmondó'' service starts with around 60 subscribers, in Budapest. * January 17 – Overthrow of the Kingdom of Hawaii: Lorrin A. Thurston and the Citizen's Committee of Public Safety in Hawaii, with the intervention of the United States Marine Corps, overthrow the government of Queen Liliuokalani. * January 21 ** The Cherry Sisters first perform in Marion, Iowa. ** The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ritt's Polynomial Decomposition Theorem
In mathematics, a polynomial decomposition expresses a polynomial ''f'' as the functional composition g \circ h of polynomials ''g'' and ''h'', where ''g'' and ''h'' have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time. Polynomials which are decomposable in this way are composite polynomials; those which are not are indecomposable polynomials or sometimes prime polynomials J.F. Ritt, "Prime and Composite Polynomials", ''Transactions of the American Mathematical Society'' 23:1:51–66 (January, 1922) (not to be confused with irreducible polynomials, which cannot be factored into products of polynomials). The degree of a composite polynomial is always a composite number, the product of the degrees of the composed polynomials. The rest of this article discusses only univariate polynomials; algorithms also exist for multivariate polynomials of arbitrary degree. Examples In the simp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ritt Theorem
In mathematics, exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential function. Definition In fields An exponential polynomial generally has both a variable ''x'' and some kind of exponential function ''E''(''x''). In the complex numbers there is already a canonical exponential function, the function that maps ''x'' to '' e''''x''. In this setting the term exponential polynomial is often used to mean polynomials of the form ''P''(''x'', ''e''''x'') where ''P'' ∈ C 'x'', ''y''is a polynomial in two variables. There is nothing particularly special about C here; exponential polynomials may also refer to such a polynomial on any exponential field or exponential ring with its exponential function taking the place of ''e''''x'' above. Similarly, there is no reason to have one variable, and an exponential polynomial in ''n'' variables would be of the form ''P''(''x''1, ..., ''x''''n'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bôcher Prize
Bocher is a surname. Notable people with the surname include: *Christiane Bøcher (1798–1874), Norwegian stage actress who was engaged at the Christiania Offentlige Theater * Édouard Bocher (1811–1900), French politician who was one of the founders of the Conférence Molé-Tocqueville * Herbert Böcher (1903–1983), German middle-distance runner who competed in the 1928 Summer Olympics *Joan Bocher (died 1550), English Anabaptist burned at the stake for heresy * Main Bocher (1890–1976), American fashion designer who founded the fashion label Mainbocher *Maxime Bôcher (1867–1918), American mathematician who published about 100 papers on differential equations, series, and algebra *Tyge W. Böcher (1909–1983), Danish botanist, evolutionary biologist, plant ecologist and phytogeographer See also *Bôcher Memorial Prize, founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher *Bôcher's theorem can refer to one of two theorems proved by the American ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wu's Method Of Characteristic Set
Wenjun Wu's method is an algorithm for solving multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wen-Tsun Wu. This method is based on the mathematical concept of characteristic set introduced in the late 1940s by J.F. Ritt. It is fully independent of the Gröbner basis method, introduced by Bruno Buchberger (1965), even if Gröbner bases may be used to compute characteristic sets. Wu's method is powerful for mechanical theorem proving in elementary geometry, and provides a complete decision process for certain classes of problem. It has been used in research in his laboratory (KLMM, Key Laboratory of Mathematics Mechanization in Chinese Academy of Science) and around the world. The main trends of research on Wu's method concern systems of polynomial equations of positive dimension and differential algebra where Ritt's results have been made effective. Wu's method has been applied in various scientific fields, like biology, computer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Algebraic Group
In mathematics, a differential algebraic group is a differential algebraic variety with a compatible group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ... structure. Differential algebraic groups were introduced by . References * * Algebraic groups {{group-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
