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Variational Inequality
In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the first variation of the involved potential energy. Therefore, it has a variational origin, recalled by the name of the general abstract problem. The applicability of the theory has since been expanded to include problems from economics, finance, optimization and game theory. History The first problem involving a variational inequality was the Signorini problem, posed by Antonio Signorini in 1959 and solved by Gaetano Fichera in 1963, according to the references and : the first papers of the theory were and , . Later on, Guido Stampacchia proved his generalization to the Lax–Milgram ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaetano Fichera
Gaetano Fichera (8 February 1922 – 1 June 1996) was an Italian mathematician, working in mathematical analysis, linear elasticity, partial differential equations and several complex variables. He was born in Acireale, and died in Rome. Biography He was born in Acireale, a town near Catania in Sicily, the elder of the four sons of Giuseppe Fichera and Marianna Abate. His father Giuseppe was a professor of mathematics and influenced the young Gaetano starting his lifelong passion. In his young years he was a talented football player. On 1 February 1943 he was in the Italian Army and during the events of September 1943 he was taken prisoner by the Nazist troops, kept imprisoned in Teramo and then sent to Verona: he succeeded in escaping from there and reached the Italian region of Emilia-Romagna, spending with partisans the last year of war. After the war he was first in Rome and then in Trieste, where he met Matelda Colautti, who became his wife in 1952. Education and aca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Space
In mathematics, any vector space ''V'' has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on ''V'', together with the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the . When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called the ''continuous dual space''. Dual vector spaces find application in many branches of mathematics that use vector spaces, such as in tensor analysis with finite-dimensional vector spaces. When applied to vector spaces of functions (which are typically infinite-dimensional), dual spaces are used to describe measures, distributions, and Hilbert spaces. Consequently, the dual space is an important concept in functional analysis. Early terms for ''dual'' include ''polarer Raum'' ah ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subset
In mathematics, set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ''B''. The relationship of one set being a subset of another is called inclusion (or sometimes containment). ''A'' is a subset of ''B'' may also be expressed as ''B'' includes (or contains) ''A'' or ''A'' is included (or contained) in ''B''. A ''k''-subset is a subset with ''k'' elements. The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the join and meet are given by intersection and union, and the subset relation itself is the Boolean inclusion relation. Definition If ''A'' and ''B'' are sets and every element of ''A'' is also an element of ''B'', then: :*''A'' is a subset of ''B'', denoted by A \subseteq B, or equivalently, :* ''B'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banach Space
In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly. Maurice René Fréchet was the first to use the term "Banach space" and Banach in turn then coined the term " Fréchet space." Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century. Banach spaces play a central role in functional analysis. In other areas of analysis, the spaces under study are often Banach spaces. Definition A Banach space is a complete n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques-Louis Lions
Jacques-Louis Lions (; 3 May 1928 – 17 May 2001) was a French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John von Neumann Lecture prize in 1986 and numerous other distinctions.Jacques-Louis Lions Casinapioiv.va. Retrieved on 9 May 2016. isces.org Lions is listed as an ISI highly cited researcher. Biography After being part of the French Résistance in 1943 and 1944, J.-L. Lions entered t ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean. Due to its several coastal territories, France has the largest exclusive economic zone in the world. France borders Belgium, Luxembourg, Germany, Switzerland, Monaco, Italy, Andorra, and Spain in continental Europe, as well as the Netherlands, Suriname, and Brazil in the Americas via its overseas territories in French Guiana and Saint Martin. Its eighteen integral regions (five of which are overseas) span a combined area of and contain clos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brixen
Brixen (, ; it, Bressanone ; lld, Porsenù or ) is a town in South Tyrol, northern Italy, located about north of Bolzano. Geography First mentioned in 901, Brixen is the third largest city and oldest town in the province, and the artistic and cultural capital of the valley. It is located at the confluence of the Eisack and Rienz rivers, north of Bolzano and south of the Brenner Pass, on the Italy-Austrian border. It is flanked on the eastern side by the Plose and Telegraph (Monte Telegrafo) mountains (2,504 m) and on the western side by the Königsanger (Monte Pascolo) (2,436 m) mountain. Brixen is especially known as a major skiing resort (the Plose). Other activities include hydroelectric power, orchards, and vineyards. ''Frazioni'' ''Frazioni'' / incorporated villages: Afers (Eores), Albeins (Albes), Elvas, Gereuth, Karnol, Klerant (Cleran), Kranebitt (Costa d'Elvas), Mahr (La Mara), Mairdorf, Mellaun (Meluno), Milland, Pairdorf (Perara), Pinzagen (Pinzago), Plab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graduate Student
Postgraduate or graduate education refers to academic or professional degrees, certificates, diplomas, or other qualifications pursued by post-secondary students who have earned an undergraduate (bachelor's) degree. The organization and structure of postgraduate education varies in different countries, as well as in different institutions within countries. While the term "graduate school" or "grad school" is typically used in North America, "postgraduate" is often used in countries such as (Australia, Bangladesh, India, Ireland, New Zealand, Pakistan, South Africa, and the UK). Graduate degrees can include master's degrees, doctoral degrees, and other qualifications such as graduate certificates and professional degrees. A distinction is typically made between graduate schools (where courses of study vary in the degree to which they provide training for a particular profession) and professional schools, which can include medical school, law school, business school, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georges Duvaut
Georges may refer to: Places * Georges River, New South Wales, Australia * Georges Quay (Dublin) *Georges Township, Fayette County, Pennsylvania Other uses *Georges (name) * ''Georges'' (novel), a novel by Alexandre Dumas * "Georges" (song), a 1977 song originally recorded by Pat Simon and covered by Sylvie Vartan * Georges (store), a department store in Melbourne, Australia from 1880 to 1995 * Georges (''Green Card'' character) People with the surname * Eugenia Georges, American anthropologist * Karl Ernst Georges (1806–1895), German classical philologist and lexicographer, known for his edition of Latin-German dictionaries. See also * École secondaire Georges-P.-Vanier, a high school in Hamilton, Ontario, Canada * École secondaire Georges-Vanier in Laval, Quebec, Canada * French cruiser ''Georges Leygues'', commissioned in 1937 * French frigate ''Georges Leygues'' (D640), commissioned in 1979 * George (other) * Georges Creek (other) * Georges Creek Coal an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coin
A coin is a small, flat (usually depending on the country or value), round piece of metal or plastic used primarily as a medium of exchange or legal tender. They are standardized in weight, and produced in large quantities at a mint in order to facilitate trade. They are most often issued by a government. Coins often have images, numerals, or text on them. ''Obverse'' and its opposite, ''reverse'', refer to the two flat faces of coins and medals. In this usage, ''obverse'' means the front face of the object and ''reverse'' means the back face. The obverse of a coin is commonly called ''heads'', because it often depicts the head of a prominent person, and the reverse ''tails''. Coins are usually made of metal or an alloy, or sometimes of man-made materials. They are usually disc shaped. Coins, made of valuable metal, are stored in large quantities as bullion coins. Other coins are used as money in everyday transactions, circulating alongside banknotes. Usually the highest va ... [...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] |
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