Systems theory to social sciences (see David Easton's seminal development of the "political system" as an analytical construct), the original theorists explored the implications of twentieth century advances in terms of systems. People have studied subjects like complexity, self-organization, connectionism and adaptive systems in the 1940s and 1950s. In fields like cybernetics, researchers such as Norbert Wiener, William Ross Ashby, John von Neumann and Heinz von Foerster, examined complex systems mathematically. John von Neumann discovered cellular automata and self-reproducing systems, again with only pencil and paper. Aleksandr Lyapunov and Jules Henri Poincaré worked on the foundations of chaos theory without any computer
Wiener–Lévy theorem pseudo compound Poisson distribution, abbreviated DPCP. We denote it as formula_23. Wiener–Lévy theorem Wiener–Lévy theorem is a theorem in Fourier analysis, which states that a function of an absolutely convergent Fourier series has an absolutely convergent Fourier series under some conditions. The theorem was named after Norbert Wiener and Paul Lévy. Norbert Wiener first proved Wiener's 1/"f" theorem, see Wiener's theorem. It states that if has absolutely convergent Fourier series and is never zero, then its inverse also has an absolutely convergent Fourier series. Paul Levy generalized Wiener's result, showing that Let formula_1 be a absolutely convergent Fourier series with