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Jürgen Moser
Jürgen Kurt Moser (July 4, 1928 – December 17, 1999) was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations. Life Moser's mother Ilse Strehlke was a niece of the violinist and composer Louis Spohr. His father was the neurologist Kurt E. Moser (July 21, 1895 – June 25, 1982), who was born to the merchant Max Maync (1870–1911) and Clara Moser (1860–1934). The latter descended from 17th century French Huguenot immigrants to Prussia. Jürgen Moser's parents lived in Königsberg, German empire and resettled in Stralsund, East Germany as a result of the second world war. Moser attended the Wilhelmsgymnasium (Königsberg) in his hometown, a high school specializing in mathematics and natural sciences education, from which David Hilbert had graduated in 1880. His older brother Friedrich Robert Ernst (Friedel) Moser (August 31, 1925 – January 14, 1945) served in the German A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Königsberg
Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named in honour of King Ottokar II of Bohemia. A Baltic port city, it successively became the capital of the Królewiec Voivodeship, the State of the Teutonic Order, the Duchy of Prussia and the provinces of East Prussia and Prussia. Königsberg remained the coronation city of the Prussian monarchy, though the capital was moved to Berlin in 1701. Between the thirteenth and the twentieth centuries, the inhabitants spoke predominantly German, but the multicultural city also had a profound influence upon the Lithuanian and Polish cultures. The city was a publishing center of Lutheran literature, including the first Polish translation of the New Testament, printed in the city in 1551, the first book in Lithuanian and the first Lutheran ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Håkan Eliasson
Lars Håkan Eliasson (born 13 July 1952) is a Swedish mathematician. Biography Eliasson received in 1984 his PhD from the University of Stockholm under Jürgen Moser with thesis ''Hamiltonian systems with Poisson commuting integrals''. He was a professor at the Royal Institute of Technology in Stockholm and then became a professor at the University of Paris VII (Denis Diderot) and the Institut de mathématiques de Jussieu of the Universities Paris VI and VII and the CNRS. His research deals with dynamical systems, quasiperiodic motion, the problem of small denominators in perturbation theory, the KAM Theory and multiscale analysis in perturbation theory, Hamiltonian partial differential equations, and localization and diffusion in quasiperiodic Schrödinger operators. In 1998 he was an Invited Speaker at the International Congress of Mathematicians in Berlin. In 2005 and in 2012 he was at the Institute for Advanced Study. In 1990 he received the Wallenberg Prize from th 1995 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian System
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can be studied in both Hamiltonian mechanics and dynamical systems theory. Overview Informally, a Hamiltonian system is a mathematical formalism developed by Hamilton to describe the evolution equations of a physical system. The advantage of this description is that it gives important insights into the dynamics, even if the initial value problem cannot be solved analytically. One example is the planetary movement of three bodies: while there is no closed-form solution to the general problem, Poincaré showed for the first time that it exhibits deterministic chaos. Formally, a Hamiltonian system is a dynamical system characterised by the scalar function H(\boldsymbol,\boldsymbol,t), also known as the Hamiltonian. The state of the system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cantor Medal
The Cantor medal of the Deutsche Mathematiker-Vereinigung is named in honor of Georg Cantor, the first president of the society. It is awarded at most every second year during the yearly meetings of the society. The prize winners are mathematicians who are associated with the German language. Prize winners * 1990 Karl Stein. * 1992 Jürgen MoserThe Georg Cantor Medal of the ''Deutsche Mathematiker-Vereinigung'' , , retrieved 5 June 2014. * 1994 Erhard Heinz [...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 This list of mathematics awards is an index to articles about notable awards for mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Craig Watson Medal
400px, James Craig Watson Medal The James Craig Watson Medal was established by the bequest of James Craig Watson, an astronomer the University of Michigan between 1863 and 1879, and is awarded every 1-4 years by the U.S. National Academy of Sciences for contributions to astronomy. Recipients SourcNational Academy of Sciences See also * List of astronomy awards * List of awards named after people References {{DEFAULTSORT:Watson Medal Watson Watson may refer to: Companies * Actavis, a pharmaceutical company formerly known as Watson Pharmaceuticals * A.S. Watson Group, retail division of Hutchison Whampoa * Thomas J. Watson Research Center, IBM research center * Watson Systems, make ... Awards established in 1887 Awards of the United States National Academy of Sciences 1887 establishments in the United States ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George David Birkhoff Prize
The George David Birkhoff Prize in applied mathematics is awarded – jointly by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM) – in honour of George David Birkhoff (1884–1944). It is currently awarded every three years for an outstanding contribution to: "applied mathematics in the highest and broadest sense". The recipient of the prize has to be a member of one of the awarding societies, as well as a resident of the United States of America, Canada or Mexico. The prize was established in 1967 and currently (2020) amounts to US$5,000. Recipients See also * List of mathematics awards * Prizes named after people A prize is an award to be given to a person or a group of people (such as sporting teams and organizations) to recognize and reward their actions and achievements. Notes {{DEFAULTSORT ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volterra Lattice
In mathematics, the Volterra lattice, also known as the discrete KdV equation, the Kac–van Moerbeke lattice, and the Langmuir lattice, is a system of ordinary differential equations with variables indexed by some of the points of a 1-dimensional lattice. It was introduced by and and is named after Vito Volterra. The Volterra lattice is a special case of the generalized Lotka–Volterra equation describing predator–prey interactions, for a sequence of species with each species preying on the next in the sequence. The Volterra lattice also behaves like a discrete version of the KdV equation. The Volterra lattice is an integrable system, and is related to the Toda lattice The Toda lattice, introduced by , is a simple model for a one-dimensional crystal in solid state physics Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and .... It is also used as a model for Langmuir waves in plas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outer Billiard
Outer billiards is a dynamical system based on a convex shape in the plane. Classically, this system is defined for the Euclidean plane but one can also consider the system in the hyperbolic plane or in other spaces that suitably generalize the plane. Outer billiards differs from a usual dynamical billiard in that it deals with a discrete sequence of moves ''outside'' the shape rather than inside of it. Definitions The outer billiards map Let P be a convex shape in the plane. Given a point x0 outside P, there is typically a unique point x1 (also outside P) so that the line segment connecting x0 to x1 is tangent to P at its midpoint and a person walking from x0 to x1 would see P on the right. (See Figure.) The map F: x0 -> x1 is called the ''outer billiards map''. The inverse (or backwards) outer billiards map is also defined, as the map x1 -> x0. One gets the inverse map simply by replacing the word ''right'' by the word ''left'' in the definition given above. The figu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trudinger's Theorem
In mathematical analysis, Trudinger's theorem or the Trudinger inequality (also sometimes called the Moser–Trudinger inequality) is a result of functional analysis on Sobolev spaces. It is named after Neil Trudinger (and Jürgen Moser). It provides an inequality between a certain Sobolev space norm and an Orlicz space norm of a function. The inequality is a limiting case of Sobolev imbedding and can be stated as the following theorem: Let \Omega be a bounded domain in \mathbb^n satisfying the cone condition. Let mp=n and p>1. Set : A(t)=\exp\left( t^ \right)-1. Then there exists the embedding : W^(\Omega)\hookrightarrow L_A(\Omega) where : L_A(\Omega)=\left\. The space :L_A(\Omega) is an example of an Orlicz space In mathematical analysis, and especially in real, harmonic analysis and functional analysis, an Orlicz space is a type of function space which generalizes the ''L'p'' spaces. Like the ''L'p'' spaces, they are Banach spaces. The spaces are n .... Referen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harnack Inequality
In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by . Harnack's inequality is used to prove Harnack's theorem about the convergence of sequences of harmonic functions. , and generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Such results can be used to show the interior regularity of weak solutions. Perelman's solution of the Poincaré conjecture uses a version of the Harnack inequality, found by , for the Ricci flow. The statement Harnack's inequality applies to a non-negative function ''f'' defined on a closed ball in R''n'' with radius ''R'' and centre ''x''0. It states that, if ''f'' is continuous on the closed ball and harmonic on its interior, then for every point ''x'' with , ''x'' − ''x''0, = ''r'' 0 (depending only on ''K'', \tau, t-\tau, and the coefficients of \mathcal) such that, for each t\in(\tau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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