Stanislaw M . Ulam ’ s Contributions to Theoretical Theory

THE FERMI-PASTA-ULAM LATTICE Background The Fermi-Pasta-Ulam lattice is named after the experiments

The Fermi-Pasta-Ulam lattice is named after the experiments performed by Enrico Fermi, John Pasta, and Stanislaw Ulam in 1954-5 on the Los Alamos MANIAC computer, one of the first electronic computers. As reported in Ulam’s autobiography [Uh], Fermi immediately suggested using the new machine for theoretical work, and it was decided to start by studying the vibrations of a string under the infl...

The Ulam Spiral as a Game of Life Cellular Automaton

The Ulam Spiral is a rectangular grid created by Stanislaw Ulam in 1963 to help visualize prime numbers (Ulam, 1964; 1967). It demonstrates the tendency of some polynomials to generate unusually large number of primes and the tendency for prime numbers to line up along diagonal lines. This occurrence of prime numbers along diagonals can be seen even in large spirals as well as in those spirals ...

Discrepancy theory and quasi-Monte Carlo integration

* In this article we show the deep connections between discrepancy theory on the one hand and quasi-Monte Carlo integration on the other. Discrepancy theory was established as an area of research going back to the seminal paper by Weyl (1916), whereas Monte Carlo (and later quasi-Monte Carlo) was invented in the 1940s by John von Neumann and Stanislaw Ulam to solve practical problems. The conne...

A fixed point approach to the Hyers-Ulam stability of an $AQ$ functional equation in probabilistic modular spaces

In this paper, we prove the Hyers-Ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$

Hyers-Ulam Stability of Fibonacci Functional Equation