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John Nash (mathematician)
John Forbes Nash Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Nobel Prize in Economics. In 2015, Louis Nirenberg and he were awarded the Abel Prize for their contributions to the field of partial differential equations. As a graduate student in the Princeton University Department of Mathematics, Nash introduced a number of concepts (including Nash equilibrium and the Nash bargaining solution), which are now considered central to game theory and its applications in various sciences. In the 1950s, Nash discovered and proved the Nash embedding theorems by solving a system of nonlinear partial differential equations arising in Riemannian geometry. This work, also introducing a preliminary form of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bluefield, West Virginia
Bluefield is a city in Mercer County, West Virginia, United States. The population was 9,658 at the 2020 United States census, 2020 census. It is the principal city of the Bluefield micropolitan area extending into Virginia, which had a population of 106,363 in 2020. The city is home to Bluefield State University, a public historically black university serving nearly 1,300 students. History The European-American history of Bluefield began in the 18th century, when the Davidson and Bailey families settled in a rugged and remote part of what is now southern West Virginia. Others joined them, and they built a small village with a mill, a church, a one-room schoolhouse, and a fort for defending the settlement against invasions by the Shawnee tribe, which had a village on the banks of the Bluestone River. In 1882, the descendants of the Davidson and Bailey families sold a portion of their land, when Captain John Fields of the Norfolk and Western Railway pioneered the area and began b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash–Moser Theorem
In the mathematical field of analysis, the Nash–Moser theorem, discovered by mathematician John Forbes Nash and named for him and Jürgen Moser, is a generalization of the inverse function theorem on Banach spaces to settings when the required solution mapping for the linearized problem is not bounded. In contrast to the Banach space case, in which the invertibility of the derivative at a point is sufficient for a map to be locally invertible, the Nash–Moser theorem requires the derivative to be invertible in a neighborhood. The theorem is widely used to prove local existence for non-linear partial differential equations in spaces of smooth functions. It is particularly useful when the inverse to the derivative "loses" derivatives, and therefore the Banach space implicit function theorem cannot be used. History The Nash–Moser theorem traces back to Nash (1956), who proved the theorem in the special case of the isometric embedding problem. It is clear from his paper that hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Nirenberg
Louis Nirenberg (February 28, 1925 – January 26, 2020) was a Canadian-American mathematician, considered one of the most outstanding Mathematical analysis, mathematicians of the 20th century. Nearly all of his work was in the field of partial differential equations. Many of his contributions are now regarded as fundamental to the field, such as his maximum principle, strong maximum principle for second-order parabolic partial differential equations and the Newlander–Nirenberg theorem in complex geometry. He is regarded as a foundational figure in the field of geometric analysis, with many of his works being closely related to the study of complex analysis and differential geometry. Biography Nirenberg was born in Hamilton, Ontario to Ukrainian Jewish immigrants. He attended Baron Byng High School and McGill University, completing his Bachelor of Science, BS in both mathematics and physics in 1945. Through a summer job at the National Research Council (Canada), National R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reinhard Selten
Reinhard Justus Reginald Selten (; 5 October 1930 – 23 August 2016) was a German economics, economist, who won the 1994 Nobel Memorial Prize in Economic Sciences (shared with John Harsanyi and John Forbes Nash, John Nash). He is also well known for his work in bounded rationality and can be considered one of the founding fathers of experimental economics. Biography Selten was born in Wrocław, Breslau (Wrocław) in Province of Lower Silesia, Lower Silesia, now in Poland, to a Jewish father, Adolf Selten (a blind bookseller; d. 1942Roberts, Sam"Reinhard Selten, Whose Strides in Game Theory Led to a Nobel, Dies at 85" New York ''Times'', September 2, 2016. Retrieved 2016-09-03.), and Protestant mother, Käthe Luther.O'Connor, J J, and E F Robertson"Reinhard Selten" ''www-history.mcs.st-and.ac.uk'', November 2010. Retrieved 2016-09-03. Reinhard Selten was raised as Protestant. After a brief family exile in Saxony and Austria, Selten returned to Hesse, Germany, after the wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Harsanyi
John Charles Harsanyi (; May 29, 1920 and August 9, 2000) was a Hungarian-American economist who spent most of his career at the University of California, Berkeley. He was the recipient of the Nobel Memorial Prize in Economic Sciences in 1994. Harsanyi is best known for his contributions to the study of game theory and its application to economics, specifically for his developing the highly innovative analysis of games of incomplete information, so-called Bayesian games. He also made important contributions to the use of game theory and economic reasoning in political and moral philosophy (specifically utilitarian ethics) as well as contributing to the study of equilibrium selection. For his work, he was a co-recipient along with John Nash and Reinhard Selten of the 1994 Nobel Memorial Prize in Economic Sciences. He moved to the United States in 1956, and spent most of his life there. According to György Marx, he was one of The Martians. Early life Harsanyi was born on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The New York Times
''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of the longest-running newspapers in the United States, the ''Times'' serves as one of the country's Newspaper of record, newspapers of record. , ''The New York Times'' had 9.13 million total and 8.83 million online subscribers, both by significant margins the List of newspapers in the United States, highest numbers for any newspaper in the United States; the total also included 296,330 print subscribers, making the ''Times'' the second-largest newspaper by print circulation in the United States, following ''The Wall Street Journal'', also based in New York City. ''The New York Times'' is published by the New York Times Company; since 1896, the company has been chaired by the Ochs-Sulzberger family, whose current chairman and the paper's publ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae 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 existence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Algebraic Geometry
In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial mappings). Semialgebraic geometry is the study of semialgebraic sets, i.e. real-number solutions to algebraic inequalities with-real number coefficients, and mappings between them. The most natural mappings between semialgebraic sets are semialgebraic mappings, i.e., mappings whose graphs are semialgebraic sets. Terminology Nowadays the words 'semialgebraic geometry' and 'real algebraic geometry' are used as synonyms, because real algebraic sets cannot be studied seriously without the use of semialgebraic sets. For example, a projection of a real algebraic set along a coordinate axis need not be a real algebraic set, but it is always a semialgebraic set: this is the Tarski–Seidenberg theorem. Related fields are o-minimal theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alicia Nash
Alicia Esther Nash (née Lardé Lopez-Harrison; January 1, 1933 – May 23, 2015) was a Salvadoran-American physicist. The wife of mathematician John Forbes Nash Jr., she was a mental-health care advocate, who gave up her professional aspirations to support her husband and son, who were both diagnosed with schizophrenia. Her life with Nash was chronicled in the 1998 book, ''A Beautiful Mind'' by Sylvia Nasar, as well as in the 2001 film of the same title directed by Ron Howard, in which she was portrayed by Jennifer Connelly."Alicia Nash’s beautiful, complex, rebellious life" ''Toronto Star'', May 29, 2015. Retrieved May 30, 2015. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
