Let G be a finite group, and let F be a formation of finite group. We say that a subgroup H of G is p F -normal in G if there exists a normal subgroup T of G such that HT is a permutable Hall subgroup of G and G G H H T H / ) ( is contained in the F-hypercenter ) / ( G F H G Z of G H G / . In this note, we get some results about the p F -normal subgroups and then use them to study the structure...

In this paper, we survey loop parallelization algorithms, analyzing the dependence representations they use, the loop transformations they generate, the code generation schemes they require, and their ability to incorporate various optimizing criteria such as maximal parallelism detection, permutable loop detection, minimization of synchronizations, easiness of code generation, etc. We complete...

In the framework of fully permutable loops, tiling is a compiler technique (also known as ‘loop blocking’) that has been extensively studied as a source-to-source program transformation. Little work has been devoted to the mapping and scheduling of the tiles on to physical parallel processors. We present several new results in the context of limited computational resources and assuming communic...

We characterize the set of all n-ary quasigroups of order 4: every n-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an n-ary quasigroup can be represented as a composition of k-ary and (n− k +1)-ary quasigroups for some k from 2 to n−1, where the order of arguments in the representation can differ from the original order. The set of semilinea...

In the framework of fully permutable loops, tiling has been extensively studied as a sourceto-source program transformation. However, little work has been devoted to the mapping and scheduling of the tiles on physical processors. Moreover, targeting heterogeneous computing platforms has, to the best of our knowledge, never been considered. In this paper we extend tiling techniques to the contex...

This paper is devoted to the study of systems of nonlinear functional differential equations with time-dependent coefficients and multiple variable increasing delays represented by functions gi(t) < t. The solution is found in terms of a piecewise-defined matrix function. Using our representation of the solution and Gronwall’s, Bihari’s and Pinto’s integral inequalities, asymptotic stability re...