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Viscosity Solution
In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael G. Crandall as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE). It has been found that the viscosity solution is the natural solution concept to use in many applications of PDE's, including for example first order equations arising in dynamic programming (the Hamilton–Jacobi–Bellman equation), differential games (the Hamilton–Jacobi–Isaacs equation) or front evolution problems, as well as second-order equations such as the ones arising in stochastic optimal control or stochastic differential games. The classical concept was that a PDE : F(x,u,Du,D^2 u) = 0 over a domain x\in\Omega has a solution if we can find a function ''u''(''x'') continuous and differentiable over the entire domain such that x, u, Du, D^2 u satisfy the above equation at every point. If a scalar equation is degenerat ... [...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 mathematical analysis, 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 mathematical object, abstract objects and the use of pure reason to proof (mathematics), prove them. These objects consist of either abstraction (mathematics), abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of inference rule, deductive rules to already established results. These results include previously proved theorems, axioms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vanishing Viscosity Solutions
Vanishing may refer to: Entertainment *Vanishing, a type of magical effect. Mathematics * The mathematical concept, see root of a function Music * A song from the A Perfect Circle album ''Thirteenth Step'' * A song from ''Mariah Carey'' (album) * A song by Bryan Adams from ''Waking Up the Neighbours'' * A song by Barenaked Ladies from ''Barenaked Ladies Are Me ''Barenaked Ladies Are Me'' is the seventh full-length original-material studio album by Barenaked Ladies. It was their first original-material album since ''Everything to Everyone'' in 2003. It was released in September 2006 internationally. The ...'' Art and literature * ''A Void'', 1969 French novel, also translated under the titles ''A Vanishing'' and ''Vanish'd'' * ''Vanishing'' (2022 film), a French-South Korean film * ''The Vanishing'' (other), various films and novels See also * Vanish (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Jensen (mathematician)
Robert William Jensen (born July 14, 1958) is a former professor of journalism from the University of Texas at Austin. From 1992 to 2018 he taught graduate and undergraduate courses in media law, ethics, and politics. He has focused much of his work on the critique of pornography and of masculinity, developed in his 2017 book, ''The End of Patriarchy: Radical Feminism for Men''. He also has written about white privilege and institutional racism. He also sits on the editorial board of the academic journal ''Sexualization, Media, and Society''. Early life Jensen grew up in Fargo, North Dakota. Education In 1981, he received a Bachelor of Science degree from Moorhead State University (now Minnesota State University, Moorhead), and in 1985, he received a Master of Arts degree in journalism and public affairs from American University. In 1992 he completed his Ph.D. in media law and ethics in the School of Journalism and Mass Communication at the University of Minnesota. Career ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel Journal Of Mathematics
'' Israel Journal of Mathematics'' is a peer-reviewed mathematics journal published by the Hebrew University of Jerusalem (Magnes Press). Founded in 1963, as a continuation of the ''Bulletin of the Research Council of Israel'' (Section F), the journal publishes articles on all areas of mathematics. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.70, and its 2009 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... was 0.754. External links * Mathematics journals Publications established in 1963 English-language journals Bimonthly journals Hebrew University of Jerusalem {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lawrence C
Lawrence may refer to: Education Colleges and universities * Lawrence Technological University, a university in Southfield, Michigan, United States * Lawrence University, a liberal arts university in Appleton, Wisconsin, United States Preparatory & high schools * Lawrence Academy at Groton, a preparatory school in Groton, Massachusetts, United States * Lawrence College, Ghora Gali, a high school in Pakistan * Lawrence School, Lovedale, a high school in India * The Lawrence School, Sanawar, a high school in India Research laboratories * Lawrence Berkeley National Laboratory, United States * Lawrence Livermore National Laboratory, United States People * Lawrence (given name), including a list of people with the name * Lawrence (surname), including a list of people with the name * Lawrence (band), an American soul-pop group * Lawrence (judge royal) (died after 1180), Hungarian nobleman, Judge royal 1164–1172 * Lawrence (musician), Lawrence Hayward (born 1961), British ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Convergence
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions (f_n) converges uniformly to a limiting function f on a set E if, given any arbitrarily small positive number \epsilon, a number N can be found such that each of the functions f_N, f_,f_,\ldots differs from f by no more than \epsilon ''at every point'' x ''in'' E. Described in an informal way, if f_n converges to f uniformly, then the rate at which f_n(x) approaches f(x) is "uniform" throughout its domain in the following sense: in order to guarantee that f_n(x) falls within a certain distance \epsilon of f(x), we do not need to know the value of x\in E in question — there can be found a single value of N=N(\epsilon) ''independent of x'', such that choosing n\geq N will ensure that f_n(x) is within \epsilon of f(x) ''for all x\in E''. In contrast, pointwise convergence of f_n to f merely guarantees that for any x\in E giv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communications On Pure And Applied Mathematics
''Communications on Pure and Applied Mathematics'' is a monthly peer-reviewed scientific journal which is published by John Wiley & Sons on behalf of the Courant Institute of Mathematical Sciences. It covers research originating from or solicited by the institute, typically in the fields of applied mathematics, mathematical analysis, or mathematical physics. The journal was established in 1948 as the ''Communications on Applied Mathematics'', obtaining its current title the next year. According to the '' Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 3.219. References External links * Mathematics journals Monthly journals Wiley (publisher) academic journals Publications established in 1948 English-la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duke Mathematical Journal
''Duke Mathematical Journal'' is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue included a paper by Solomon Lefschetz. Leonard Carlitz served on the editorial board for 35 years, from 1938 to 1973. The current managing editor is Richard Hain (Duke University). Impact According to the journal homepage, the journal has a 2018 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 2.194, ranking it in the top ten mathematics journals in the world. References External links * Mathematics journals Mathematical Journal Publications established in 1935 Multilingual journals English-language journals French- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transactions Of The American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages. See also * ''Bulletin of the American Mathematical Society'' * ''Journal of the American Mathematical Society'' * '' Memoirs of the American Mathematical Society'' * ''Notices of the American Mathematical Society'' * '' Proceedings of the American Mathematical Society'' External links * ''Transactions of the American Mathematical Society''on JSTOR JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ... American Mathematical Society academic journals Mathematics journals Publications established in 1900 {{math-journal-s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vanishing Viscosity
Vanishing may refer to: Entertainment *Vanishing, a type of magical effect. Mathematics * The mathematical concept, see root of a function Music * A song from the A Perfect Circle album ''Thirteenth Step'' * A song from ''Mariah Carey'' (album) * A song by Bryan Adams from ''Waking Up the Neighbours'' * A song by Barenaked Ladies from ''Barenaked Ladies Are Me ''Barenaked Ladies Are Me'' is the seventh full-length original-material studio album by Barenaked Ladies. It was their first original-material album since ''Everything to Everyone'' in 2003. It was released in September 2006 internationally. The ...'' Art and literature * ''A Void'', 1969 French novel, also translated under the titles ''A Vanishing'' and ''Vanish'd'' * ''Vanishing'' (2022 film), a French-South Korean film * ''The Vanishing'' (other), various films and novels See also * Vanish (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirichlet Boundary Condition
In the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, ''essential'' or Dirichlet boundary condition is defined by weighted-integral form of a differential equation. The dependent unknown ''u in the same form as the weight function w'' appearing in the boundary expression is termed a ''primary variable'', and its specification constitutes the ''essential'' or Dirichlet boundary condition. The question of finding solutions to such equations is known as the Dirichlet problem. In applied sciences, a Dirichlet boundary condition may also be referred to as a fixed boundary condition. Examples ODE For an ordinary differential equation, for instance, y'' + y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barrier Function
In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value on a point increases to infinity as the point approaches the boundary of the feasible region of an optimization problem. Such functions are used to replace inequality constraints by a penalizing term in the objective function that is easier to handle. The two most common types of barrier functions are inverse barrier functions and logarithmic barrier functions. Resumption of interest in logarithmic barrier functions was motivated by their connection with primal-dual interior point methods. Motivation Consider the following constrained optimization problem: :minimize :subject to where is some constant. If one wishes to remove the inequality constraint, the problem can be re-formulated as :minimize , :where if , and zero otherwise. This problem is equivalent to the first. It gets rid of the inequality, but introduces the issue that the penalty function , and there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
