A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for parabolic stochastic PDEs such that both the drift and the diffusion operators are of the second order.

In this paper, chaos based a new arithmetic crossover operator on the genetic algorithm has been proposed. The most frequent issue for the optimization algorithms is stuck on problem's defined local minimum points and it needs excessive amount of time to escape from them; therefore, these algorithms may never find global minimum points. To avoid and escape from local minimums, a chaotic arithme...

‎in the following text for arbitrary $x$ with at least two elements‎, ‎nonempty countable set $gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map‎. ‎we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney‎, ‎exact dev...

Genetic algorithms (GA) have been widely used to solve water resources system optimization. However, when applying GAs to solve large-scale and complex water reservoir system problems, premature convergence is one of the most frequently encountered difficulties and takes a large number of iterations to reach the global optimal solution and the optimization may get stuck at a local optimum. Ther...

A mathematician discussing chaos is featured in the movie "Jurassic Park". James Gleich's book "Chaos" remains on the best seller list for many months. The characters of the celebrated Broadway play "Arcadia" of Tom Stoppard discourse on the meaning of chaos. What is chaos? Chaos is a new science which establishes the omnipresence of unpredictability as a fundamental feature of common experienc...

In this article, chaotic search based constrained equilibrium optimizer algorithm (CS-CEOA) is suggested by integrating a novel heuristic approach called with chaos theory-based local for solving general non-linear programming. CS-CEOA consists of two phases, the first one (phase I) aims to detect an approximate solution, avoiding being stuck in minima. phase II, chaos-based improves performanc...