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Peter Lax
Peter David Lax (born Lax Péter Dávid; 1 May 1926) is a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics. Lax has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields. In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003. Life and education Lax was born in Budapest, Hungary to a Jewish family. Lax began displaying an interest in mathematics at age twelve, and soon his parents hired Rózsa Péter as a tutor for him. His parents Klara Kornfield and Henry Lax were both physici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population of 1,752,286 over a land area of about . Budapest, which is both a city and county, forms the centre of the Budapest metropolitan area, which has an area of and a population of 3,303,786; it is a primate city, constituting 33% of the population of Hungary. The history of Budapest began when an early Celtic settlement transformed into the Roman town of Aquincum, the capital of Lower Pannonia. The Hungarians arrived in the territory in the late 9th century, but the area was pillaged by the Mongols in 1241–42. Re-established Buda became one of the centres of Renaissance humanist culture by the 15th century. The Battle of Mohács, in 1526, was followed by nearly 150 years of Ottoman rule. After the reconquest of Buda in 1686, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lax Functor
In category theory, a discipline within mathematics, the notion of lax functor between bicategories generalizes that of functors between categories Category, plural categories, may refer to: Philosophy and general uses *Categorization, categories in cognitive science, information science and generally *Category of being * ''Categories'' (Aristotle) *Category (Kant) * Categories (Peirce) * .... Let ''C,D'' be bicategories. We denote composition idiagrammatic order A ''lax functor P from C to D'', denoted P: C\to D, consists of the following data: * for each object ''x'' in ''C'', an object P_x\in D; * for each pair of objects ''x,y ∈ C'' a functor on morphism-categories, P_: C(x,y)\to D(P_x,P_y); * for each object ''x∈C'', a 2-morphism P_:\text_\to P_(\text_x) in ''D''; * for each triple of objects, ''x,y,z ∈C'', a 2-morphism P_(f,g): P_(f);P_(g)\to P_(f;g) in ''D'' that is natural in ''f: x→y'' and ''g: y→z''. These must satisfy three commutative diagrams, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norbert Wiener Prize
The Norbert Wiener Prize in Applied Mathematics is a $5000 prize awarded, every three years, for an outstanding contribution to "applied mathematics in the highest and broadest sense." It was endowed in 1967 in honor of Norbert Wiener by MIT's mathematics department and is provided jointly by the American Mathematical Society and Society for Industrial and Applied Mathematics. The recipient of the prize has to be a member of one of the awarding societies. Winners * 1970: Richard E. Bellman * 1975: Peter D. Lax * 1980: Tosio Kato and Gerald B. Whitham * 1985: Clifford S. Gardner * 1990: Michael Aizenman and Jerrold E. Marsden * 1995: Hermann Flaschka and Ciprian Foias * 2000: Alexandre J. Chorin and Arthur Winfree * 2004: James A. Sethian * 2007: Craig Tracy and Harold Widom * 2010: David Donoho * 2013: Andrew Majda * 2016: Constantine M. Dafermos * 2019: Marsha Berger and Arkadi Nemirovski * 2022: Eitan Tadmor See also * List of mathematics awards * Prizes named after pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chauvenet Prize
The Chauvenet Prize is the highest award for mathematical expository writing. It consists of a prize of $1,000 and a certificate, and is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. The prize is named in honor of William Chauvenet and was established through a gift from J. L. Coolidge in 1925. The Chauvenet Prize was the first award established by the Mathematical Association of America. A gift from MAA president Walter B. Ford in 1928 allowed the award to be given every 3 years instead of the originally planned 5 years. Winners *1925 G. A. Bliss *1929 T. H. Hildebrandt *1932 G. H. Hardy *1935 Dunham Jackson *1938 G. T. Whyburn *1941 Saunders Mac Lane *1944 R. H. Cameron *1947 Paul Halmos *1950 Mark Kac *1953 E. J. McShane *1956 Richard H. Bruck *1960 Cornelius Lanczos *1963 Philip J. Davis *1964 Leon Henkin *1965 Jack K. Hale & Joseph P. LaSalle *1967 Guido Weiss *1968 Mark ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann Prize
The John von Neumann Prize (until 2019 named John von Neumann Lecture Prize) was established in 1959 with funds from IBM and other industry corporations, and is awarded for "outstanding and distinguished contributions to the field of applied mathematical sciences and for the effective communication of these ideas to the community". It is considered the highest honor bestowed by the Society for Industrial and Applied Mathematics (SIAM). The recipient receives a monetary award and presents a survey lecture at the SIAM Annual Meeting. Selection process Anybody is able to nominate a mathematician for the prize. Nominations are reviewed by a selection committee, consisting of members of SIAM who serve two-year appointments. The committee selects one recipient for the prize nine months before the SIAM Annual Meeting and forwards their nomination to SIAM's Executive Committee and Vice President for Programs. Past lecturers *1960: Lars Valerian Ahlfors *1961: Mark Kac *1962: Jean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul R
Paul may refer to: *Paul (given name), a given name (includes a list of people with that name) *Paul (surname), a list of people People Christianity *Paul the Apostle (AD c.5–c.64/65), also known as Saul of Tarsus or Saint Paul, early Christian missionary and writer *Pope Paul (other), multiple Popes of the Roman Catholic Church *Saint Paul (other), multiple other people and locations named "Saint Paul" Roman and Byzantine empire *Lucius Aemilius Paullus Macedonicus (c. 229 BC – 160 BC), Roman general *Julius Paulus Prudentissimus (), Roman jurist *Paulus Catena (died 362), Roman notary *Paulus Alexandrinus (4th century), Hellenistic astrologer *Paul of Aegina or Paulus Aegineta (625–690), Greek surgeon Royals *Paul I of Russia (1754–1801), Tsar of Russia *Paul of Greece (1901–1964), King of Greece Other people *Paul the Deacon or Paulus Diaconus (c. 720 – c. 799), Italian Benedictine monk *Paul (father of Maurice), the father of Maurice, Byzan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Integral Operator
In mathematical analysis, Fourier integral operators have become an important tool in the theory of partial differential equations. The class of Fourier integral operators contains differential operators as well as classical integral operators as special cases. A Fourier integral operator T is given by: :(Tf)(x)=\int_ e^a(x,\xi)\hat(\xi) \, d\xi where \hat f denotes the Fourier transform of f, a(x,\xi) is a standard symbol which is compactly supported in x and \Phi is real valued and homogeneous of degree 1 in \xi. It is also necessary to require that \det \left(\frac\right)\neq 0 on the support of ''a.'' Under these conditions, if ''a'' is of order zero, it is possible to show that T defines a bounded operator from L^ to L^. Examples One motivation for the study of Fourier integral operators is the solution operator for the initial value problem for the wave operator. Indeed, consider the following problem: : \frac\frac(t,x) = \Delta u(t,x) \quad \mathrm \quad (t,x) \in \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Solver
A Riemann solver is a numerical method used to solve a Riemann problem. They are heavily used in computational fluid dynamics and computational magnetohydrodynamics. Definition Generally speaking, Riemann solvers are specific methods for computing the numerical flux across a discontinuity in the Riemann problem. They form an important part of high-resolution schemes; typically the right and left states for the Riemann problem are calculated using some form of nonlinear reconstruction, such as a flux limiter or a WENO method, and then used as the input for the Riemann solver. Exact solvers Sergei K. Godunov is credited with introducing the first exact Riemann solver for the Euler equations, by extending the previous CIR (Courant-Isaacson-Rees) method to non-linear systems of hyperbolic conservation laws. Modern solvers are able to simulate relativistic effects and magnetic fields. More recent research shows that an exact series solution to the Riemann problem exists, which may c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beurling–Lax Theorem
In mathematics, the Beurling–Lax theorem is a theorem due to and which characterizes the shift-invariant subspaces of the Hardy space H^2(\mathbb,\mathbb). It states that each such space is of the form : \theta H^2(\mathbb,\mathbb), for some inner function In complex analysis, the Hardy spaces (or Hardy classes) ''Hp'' are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In ... \theta. See also * H2 References * * * * Jonathan R. Partington, ''Linear Operators and Linear Systems, An Analytical Approach to Control Theory'', (2004) London Mathematical Society Student Texts 60, Cambridge University Press. * Marvin Rosenblum and James Rovnyak, ''Hardy Classes and Operator Theory'', (1985) Oxford University Press. Hardy spaces Theorems in analysis Invariant subspaces {{mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lax–Wendroff Theorem
In computational mathematics, the Lax–Wendroff theorem, named after Peter Lax and Burton Wendroff, states that if a conservative numerical scheme for a hyperbolic system of conservation laws converges, then it converges towards a weak solution. See also * Lax–Wendroff method * Godunov's scheme In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by S. K. Godunov in 1959, for solving partial differential equations. One can think of this method as a conservative finite-vol ... References * Randall J. LeVeque, Numerical methods for conservation laws, Birkhäuser, 1992 Numerical differential equations Computational fluid dynamics Theorems in analysis {{Mathapplied-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lax–Wendroff Method
The Lax–Wendroff method, named after Peter Lax and Burton Wendroff, is a numerical method for the solution of hyperbolic partial differential equations, based on finite difference A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for t ...s. It is second-order accurate in both space and time. This method is an example of explicit time integration where the function that defines the governing equation is evaluated at the current time. Definition Suppose one has an equation of the following form: \frac + \frac = 0 where and are independent variables, and the initial state, is given. Linear case In the linear case, where , and is a constant, u_i^ = u_i^n - \frac A\left u_^ - u_^ \right+ \frac A^2\left u_^ -2 u_^ + u_^ \right Here n refers to the t dimension and i refers to the x di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lax–Friedrichs Method
The Lax–Friedrichs method, named after Peter Lax and Kurt O. Friedrichs, is a numerical method for the solution of hyperbolic partial differential equations based on finite differences. The method can be described as the FTCS (forward in time, centered in space) scheme with a numerical dissipation term of 1/2. One can view the Lax–Friedrichs method as an alternative to Godunov's scheme, where one avoids solving a Riemann problem at each cell interface, at the expense of adding artificial viscosity. Illustration for a Linear Problem Consider a one-dimensional, linear hyperbolic partial differential equation for u(x,t) of the form: : u_t + au_x = 0\, on the domain : b \leq x \leq c,\; 0 \leq t \leq d with initial condition : u(x,0) = u_0(x)\, and the boundary conditions : u(b,t) = u_b(t)\, : u(c,t) = u_c(t).\, If one discretizes the domain (b, c) \times (0, d) to a grid with equally spaced points with a spacing of \Delta x in the x-direction and \Delta t in the t-dir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
