The " chaos game " is a well-known algorithm by which one may construct a pictorial representation of an iterative process. The resulting sets are known as fractals and can be mathematically characterized by measures of dimension as well as by their associated recurrence relations. Using the chaos game algorithm, is it possible to derive meaningful structure out of our own genetic encoding, and...

A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension d is proposed. The relation between d and d − 2 dimensional integrals is given in terms of a differential operator for which an explicit formula can be obtained for each Feynman diagram. We show how the method works for one-, two-and three-loop integrals. The...

Using a simple factorization scheme we obtain the recurrence-shift relations of the polynomial functions of Aldaya, Bisquert and Navarro-Salas (ABNS), F N n (ω c √ N x), i.e., one-step first-order differential relations referring to N , as follows. Firstly, we apply the scheme to the polynomial degree confirming the recurrence relations of Aldaya, Bisquert and Navarro-Salas, but also obtaining ...

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...