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Mosco Convergence
In mathematical analysis, Mosco convergence is a notion of convergence for functional (mathematics), functionals that is used in nonlinear, nonlinear analysis and set-valued analysis. It is a particular case of Γ-convergence. Mosco convergence is sometimes phrased as “weak Γ-liminf and strong Γ-limsup” convergence since it uses both the Weak topology#The strong and weak topologies, weak and strong topologies on a topological vector space ''X''. In finite dimensional spaces, Mosco convergence coincides with epi-convergence, while in infinite-dimensional ones, Mosco convergence is strictly stronger property. ''Mosco convergence'' is named after Italy, Italian mathematician Umberto Mosco, a current Harold J. Gayhttp://www.wpi.edu/Campus/Faculty/Awards/Professorship/gayprofship.html professor of mathematics at Worcester Polytechnic Institute. Definition Let ''X'' be a topological vector space and let ''X''∗ denote the continuous dual space, dual space of continuous linear fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worcester Polytechnic Institute
'' , mottoeng = "Theory and Practice" , established = , former_name = Worcester County Free Institute of Industrial Science (1865-1886) , type = Private research university , endowment = $505.5 million (2020) , accreditation = NECHE , president = Winston Wole Soboyejo (interim) , provost = Arthur Heinricher (interim) , undergrad = 4,177 , postgrad = 1,962 , city = Worcester , state = Massachusetts , country = United States , campus = Midsize City, , athletics_affiliations = , sports_nickname = Engineers , mascot = Gompei the Goat , website = , logo = WPI wordmark.png , logo_upright = .5 , faculty = 478 , coordinates = , colors = Crimson Gray , aca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
