The renormalization of a quadratic-like map is studied. The threedimensional Yoccoz puzzle for an infinitely renormalizable quadratic-like map is discussed. For an unbranched quadratic-like map having the a priori complex bounds, the local connectivity of its Julia set is proved by using the three-dimensional Yoccoz puzzle. The generalized version of Sullivan’s sector theorem is discussed and i...

let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

In this article, by Partitioning of designing space, optimization speed is tried to be increased by GA. To this end, designing space search is done in two steps which are global search and local search. To achieve this goal, according to meshing in FEM, firstly, the list of sections is divided to specific subsets. Then, intermediate member of each subset, as representative of subset, is defined...