we analyze some properties of the distribution $q_{g,k}$ of the first component in a $k$-tuple chosen uniformly‎ ‎in the set of all the $k$-tuples generating a finite group $g$ (the limiting distribution of the product replacement algorithm)‎. ‎in particular‎, ‎we concentrate our attention on‎ ‎the study of the variation distance $beta_k(g)$ between $q_{g,k}$ and the uniform distribution‎. ‎we ...

the mordell-weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎in our previous paper, h‎. ‎daghigh‎, ‎and s‎. ‎didari‎, on the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎bull‎. ‎iranian math‎. ‎soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using selmer groups‎, ‎we have shown that for a prime $p$...

The purpose of this paper is to propose “interval scale,” a new concept defined as a set of ordered pitch-class intervals. Unlike an ordinary scale, this concept restricts usable intervals and doesn’t restrict pitch classes directly. This provides possibilities that interval scales can be used in atonal music that uses all pitch classes and can be used to express some differences in a similar w...

We prove that the pseudorandom generator introduced by Impagliazzo et al. in [INW94] with proper choice of parameters fools group products of a given finite group G. The seed length is O(log n(|G|O(1)+log 1 δ )), where n is the length of the word and δ is the allowed error. The result implies that the pseudorandom generator with seed length O(log n(2 logw) + log 1 δ )) fools read-once permutati...