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List Of Things Named After Stanislaw Ulam
This is a (partial) list of things named after Stanislaw Ulam, a 20th-century Polish-American mathematician who also worked in physics and biological sciences: Computer science *Stan, probabilistic programming language Mathematics * Borsuk–Ulam theorem *Erdős–Ulam problem * Fermi–Pasta–Ulam–Tsingou problem *Hyers–Ulam–Rassias stability * Kuratowski–Ulam theorem *Mazur–Ulam theorem * Ulam's conjecture **Collatz conjecture ** Kelly–Ulam conjecture, or reconstruction conjecture **Ulam's packing conjecture *Ulam matrix *Ulam numbers * Ulam spiral *Ulam's game * Ulam–Warburton cellular automaton Physics * Fermi–Pasta–Ulam–Tsingou problem * Fermi–Ulam model *Teller–Ulam design See also *{{intitle, Ulam Ulam Ulam may refer to: * ULAM, the ICAO airport code for Naryan-Mar Airport, Russia * Ulam (surname) * Ulam (salad), a type of Malay salad * ''Ulam'', a Filipino term loosely translated to viand or side dish; see Tapa (Filipino cuisine) * Ulam, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanislaw Ulam
Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapons, discovered the concept of the cellular automaton, invented the Monte Carlo method of computation, and suggested nuclear pulse propulsion. In pure and applied mathematics, he proved some theorems and proposed several conjectures. Born into a wealthy Polish Jewish family, Ulam studied mathematics at the Lwów Polytechnic Institute, where he earned his PhD in 1933 under the supervision of Kazimierz Kuratowski and Włodzimierz Stożek. In 1935, John von Neumann, whom Ulam had met in Warsaw, invited him to come to the Institute for Advanced Study in Princeton, New Jersey, for a few months. From 1936 to 1939, he spent summers in Poland and academic years at Harvard University in Cambridge, Massachusetts, where he worked to establish import ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelly–Ulam Conjecture
Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to KellyKelly, P. J.A congruence theorem for trees ''Pacific J. Math.'' 7 (1957), 961–968. and Ulam.Ulam, S. M., A collection of mathematical problems, Wiley, New York, 1960. Formal statements Given a graph G = (V,E), a vertex-deleted subgraph of G is a subgraph formed by deleting exactly one vertex from G. By definition, it is an induced subgraph of G. For a graph G, the deck of G, denoted D(G), is the multiset of isomorphism classes of all vertex-deleted subgraphs of G. Each graph in D(G) is called a card. Two graphs that have the same deck are said to be hypomorphic. With these definitions, the conjecture can be stated as: * Reconstruction Conjecture: Any two hypomorphic graphs on at least three vertices are isomorphic. : (The requirement that the graphs have at least three vertices is necessary because both graphs on two vertices h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi–Ulam Model
The Fermi–Ulam model (FUM) is a dynamical system that was introduced by Poland, Polish mathematician Stanislaw Ulam in 1961. FUM is a variant of Enrico Fermi's primary work on acceleration of cosmic rays, namely Fermi acceleration. The system consists of a particle that elastic collision, collides elastically between a fixed wall and a moving one, each of infinite mass. The walls represent the magnetic mirrors with which the cosmic rays, cosmic particles collide. A. J. Lichtenberg and M. A. Lieberman provided a simplified version of FUM (SFUM) that derives from the Poincaré map, Poincaré surface of section x=const. and writes : u_=, u_n+U_\mathrm(\varphi_n), : \varphi_=\varphi_n+\frac \pmod k, where u_n is the velocity of the particle after the n-th collision with the fixed wall, \varphi_n is the corresponding phase of the moving wall, U_\mathrm is the velocity law of the moving wall and M is the stochasticity parameter of the system. If the velocity law of the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam–Warburton Automaton
The Ulam–Warburton cellular automaton (UWCA) is a 2-dimensional fractal pattern that grows on a regular grid of cells consisting of squares. Starting with one square initially ON and all others OFF, successive iterations are generated by turning ON all squares that share precisely one edge with an ON square. This is the von Neumann neighborhood. The automaton is named after the Polish-American mathematician and scientist Stanislaw Ulam and the Scottish engineer, inventor and List of amateur mathematicians, amateur mathematician Mike Warburton. Properties and relations The UWCA is a 2D 5-neighbor outer totalistic cellular automaton using rule 686. The number of cells turned ON in each iteration is denoted u(n), with an explicit formula: u(0)=0, u(1)=1, and for n \ge 2 u(n) = 4\cdot 3^ where wt(n) is the Hamming weight function which counts the number of 1's in the binary expansion of n wt(n)=n-\sum_^ \left\lfloor\frac\right\rfloor The minimum upper bound of summation for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam's Game
Ulam's game, or the Rényi–Ulam game, is a mathematical game similar to the popular game of twenty questions. In Ulam's game, a player attempts to guess an unnamed object or number by asking yes–no questions of another, but ''one'' of the answers given may be a lie. introduced the game in a 1961 paper, based on Hungary's Bar Kokhba game, but the paper was overlooked for many years. rediscovered the game, presenting the idea that there are a million objects and the answer to one question can be wrong, and considered the minimum number of questions required, and the strategy that should be adopted. gave a survey of similar games and their relation to information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a .... See also * Knights and Knaves References * * * {{ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam Spiral
The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's ''Mathematical Games'' column in ''Scientific American'' a short time later. It is constructed by writing the positive integers in a square spiral and specially marking the prime numbers. Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes. Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial ''x''2 − ''x'' + 41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems. In particular, no quadratic polynomial has eve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam Numbers
In mathematics, the Ulam numbers comprise an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence (the (1, 2)-Ulam sequence) starts with ''U''1 = 1 and ''U''2 = 2. Then for ''n'' > 2, ''U''''n'' is defined to be the smallest integer that is the sum of two distinct earlier terms in exactly one way and larger than all earlier terms. Examples As a consequence of the definition, 3 is an Ulam number (1 + 2); and 4 is an Ulam number (1 + 3). (Here 2 + 2 is not a second representation of 4, because the previous terms must be distinct.) The integer 5 is not an Ulam number, because 5 = 1 + 4 = 2 + 3. The first few terms are :1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, 48, 53, 57, 62, 69, 72, 77, 82, 87, 97, 99, 102, 106, 114, 126, 131, 138, 145, 148, 155, 175, 177, 180, 182, 189, 197, 206, 209, 219, 221, 236, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam Matrix
In mathematical set theory, an Ulam matrix is an array of subsets of a cardinal number with certain properties. Ulam matrices were introduced by Stanislaw Ulam Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapon ... in his 1930 work on measurable cardinals: they may be used, for example, to show that a real-valued measurable cardinal is weakly inaccessible. Definition Suppose that κ and λ are cardinal numbers, and let ''F'' be a λ-complete filter on λ. An Ulam matrix is a collection of subsets ''A''αβ of λ indexed by α in κ, β in λ such that *If β is not γ then ''A''αβ and ''A''αγ are disjoint. *For each β the union of the sets ''A''αβ is in the filter ''F''. References * Set theory {{settheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam's Packing Conjecture
Ulam's packing conjecture, named for Stanislaw Ulam, is a conjecture about the highest possible packing density of identical convex solids in three-dimensional Euclidean space. The conjecture says that the optimal density for packing congruent spheres is smaller than that for any other convex body. That is, according to the conjecture, the ball is the convex solid which forces the largest fraction of space to remain empty in its optimal packing structure. This conjecture is therefore related to the Kepler conjecture about sphere packing. Since the solution to the Kepler conjecture establishes that identical balls must leave ≈25.95% of the space empty, Ulam's conjecture is equivalent to the statement that no other convex solid forces that much space to be left empty. Origin This conjecture was attributed posthumously to Ulam by Martin Gardner, who remarks in a postscript added to one of his ''Mathematical Games'' columns that Ulam communicated this conjecture to him in 1972. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collatz Conjecture
The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence. It is named after mathematician Lothar Collatz, who introduced the idea in 1937, two years after receiving his doctorate. It is also known as the problem, the conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem. The sequence of n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stan (software)
Stan is a probabilistic programming language for statistical inference written in C++.Stan Development Team. 2015Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0/ref> The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function. Stan is licensed under the New BSD License. Stan is named in honour of Stanislaw Ulam, pioneer of the Monte Carlo method. Stan was created by a development team consisting of 34 members that includes Andrew Gelman, Bob Carpenter, Matt Hoffman, and Daniel Lee. Interfaces The Stan language itself can be accessed through several interfaces: * CmdStan – a command-line executable for the shell, * CmdStanR and rstan – R software libraries, * CmdStanPy and PyStan – libraries for the Python programming language, * MatlabStan – integration with the MATLAB numerical computing environment, * Stan.jl – integration with the Julia programming langua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam's Conjecture (other)
{{Mathematical disambiguation ...
Ulam's conjecture may refer to: * The Collatz conjecture * The reconstruction conjecture * Ulam's packing conjecture Ulam's packing conjecture, named for Stanislaw Ulam, is a conjecture about the highest possible packing density of identical convex solids in three-dimensional Euclidean space. The conjecture says that the optimal density for packing congruent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
