|
Luis Caffarelli
Luis Angel Caffarelli (born December 8, 1948) is an Argentine mathematician and luminary in the field of partial differential equations and their applications. Career Caffarelli was born and grew up in Buenos Aires. He obtained his Masters of Science (1968) and Ph.D. (1972) at the University of Buenos Aires. His Ph.D. advisor was Calixto Calderón. He currently holds the Sid Richardson Chair at the University of Texas at Austin. He also has been a professor at the University of Minnesota, the University of Chicago, and the Courant Institute of Mathematical Sciences at New York University. From 1986 to 1996 he was a professor at the Institute for Advanced Study in Princeton. Important results Caffarelli received great recognition with his breakthrough paper "The regularity of free boundaries in higher dimensions" published in 1977 in ''Acta Mathematica''. Since then, he has been considered one of the world's leading experts in free boundary problems and nonlinear partial differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buenos Aires
Buenos Aires ( or ; ), officially the Autonomous City of Buenos Aires ( es, link=no, Ciudad Autónoma de Buenos Aires), is the capital and primate city of Argentina. The city is located on the western shore of the Río de la Plata, on South America's southeastern coast. "Buenos Aires" can be translated as "fair winds" or "good airs", but the former was the meaning intended by the founders in the 16th century, by the use of the original name "Real de Nuestra Señora Santa María del Buen Ayre", named after the Madonna of Bonaria in Sardinia, Italy. Buenos Aires is classified as an alpha global city, according to the Globalization and World Cities Research Network (GaWC) 2020 ranking. The city of Buenos Aires is neither part of Buenos Aires Province nor the Province's capital; rather, it is an autonomous district. In 1880, after decades of political infighting, Buenos Aires was federalized and removed from Buenos Aires Province. The city limits were enlarged to include t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf Prize In Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. According to a reputation survey conducted in 2013 and 2014, the Wolf Prize in Mathematics is the third most prestigious international academic award in mathematics, after the Abel Prize and the Fields Medal. Until the establishment of the Abel Prize, it was probably the closest equivalent of a "Nobel Prize in Mathematics", since the Fields Medal is awarded every four years only to mathematicians under the age of 40. Laureates Laureates per country Below is a chart of all laureates per country (updated to 2022 laureates). Some laureates are counted more than once if have multiple citizenship. Notes See also * List of mathematics awards References External links * * * Israel-Wolf-Prizes 2015Jerusalempost Wolf Prizes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert V
{{hndis, Robert 05 ...
Robert V may refer to: * Robert V, Count of Dreux * Robert de Brus, 5th Lord of Annandale Robert V de Brus (Robert de Brus), 5th Lord of Annandale (ca. 1215 – 31 March or 3 May 1295), was a feudal lord, justice and constable of Scotland and England, a regent of Scotland, and a competitor for the Scottish throne in 1290/92 in the ... [...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 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 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 BS in both mathematics and physics in 1945. Through a summer job at the National Research Council of Canada, he came to know Ernest Courant's wife Sara Paul. She spoke to Courant's f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equations take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integro-differential Equation
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function. General first order linear equations The general first-order, linear (only with respect to the term involving derivative) integro-differential equation is of the form : \fracu(x) + \int_^x f(t,u(t))\,dt = g(x,u(x)), \qquad u(x_0) = u_0, \qquad x_0 \ge 0. As is typical with differential equations, obtaining a closed-form solution can often be difficult. In the relatively few cases where a solution can be found, it is often by some kind of integral transform, where the problem is first transformed into an algebraic setting. In such situations, the solution of the problem may be derived by applying the inverse transform to the solution of this algebraic equation. Example Consider the following second-order problem, : u'(x) + 2u(x) + 5\int_^u(t)\,dt = \theta(x) \qquad \text \qquad u(0)=0, where : \theta(x) = \left\{ \begin{array}{ll} 1, \qq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogenization (mathematics)
In mathematics and physics, homogenization is a method of studying partial differential equations with rapidly oscillating coefficients, such as : \nabla\cdot\left(A\left(\frac\right)\nabla u_\right) = f where \epsilon is a very small parameter and A\left(\vec y\right) is a 1-periodic coefficient: A\left(\vec y+\vec e_i\right)=A\left(\vec y\right), i=1,\dots, n. It turns out that the study of these equations is also of great importance in physics and engineering, since equations of this type govern the physics of inhomogeneous or heterogeneous materials. Of course, all matter is inhomogeneous at some scale, but frequently it is convenient to treat it as homogeneous. A good example is the continuum concept which is used in continuum mechanics. Under this assumption, materials such as fluids, solids, etc. can be treated as homogeneous materials and associated with these materials are material properties such as shear modulus, elastic moduli, etc. Frequently, inhomogeneous mate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Partial Differential Equation
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear system, nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem. The distinction between a linear and a nonlinear partial differential equation is usually made in terms of the properties of the Operator (mathematics), operator that defines the PDE itself. Methods for studying nonlinear partial differential equations Existence and uniqueness of solutions A fundamental question for any PDE is the existence and uniqueness of a solution for given boundary conditions. For nonlinear equations these questions are in general very hard: f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Obstacle Problem
The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find the equilibrium position of an elastic membrane whose boundary is held fixed, and which is constrained to lie above a given obstacle. It is deeply related to the study of minimal surfaces and the capacity of a set in potential theory as well. Applications include the study of fluid filtration in porous media, constrained heating, elasto-plasticity, optimal control, and financial mathematics.See . The mathematical formulation of the problem is to seek minimizers of the Dirichlet energy functional, :J = \int_D , \nabla u, ^2 \mathrmx in some domains ''D'' where the functions ''u'' represent the vertical displacement of the membrane. In addition to satisfying Dirichlet boundary conditions corresponding to the fixed boundary of the membrane, the functions ''u'' are in addition constrained to be greater than some given ''obstacle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Mathematica
''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journals".. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 4.273, ranking it 5th out of 330 journals in the category "Mathematics". Publication history The journal was established by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences. The journal was printed and distributed by Springer from 2006 to 2016. Since 2017, Acta Mathematica has been published electronically and in print by International Press. Its electronic version is open access without publishing fees. Poincaré episode The journal's "most famous episode" (according to Villani) concerns Henri Poincaré, who won a prize offered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York University
New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the non-denominational all-male institution began its first classes near City Hall based on a curriculum focused on a secular education. The university moved in 1833 and has maintained its main campus in Greenwich Village surrounding Washington Square Park. Since then, the university has added an engineering school in Brooklyn's MetroTech Center and graduate schools throughout Manhattan. NYU has become the largest private university in the United States by enrollment, with a total of 51,848 enrolled students, including 26,733 undergraduate students and 25,115 graduate students, in 2019. NYU also receives the most applications of any private institution in the United States and admission is considered highly selective. NYU is organized int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> New York University")