Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...

we find recursive formulae for the number of perfect matchings in a graph g by splitting g into subgraphs h and q. we use these formulas to count perfect matching of p hypercube qn. we also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in g, is the graph constructed from by deleting edges with an en...

A specialization scenario provides a programmer friendly mechanism communicating the information about specialization opportunities to partial evaluators. Unfortunately, the process of generating suitable scenarios remains an art only mastered by programmers with in-depth knowledge about partial evaluation. Existing works on generating scenarios either rely on a brute-force approach to generate...

‎let $g$ be a group and $a=aut(g)$ be the group of automorphisms of‎ ‎$g$‎. ‎then the element $[g,alpha]=g^{-1}alpha(g)$ is an‎ ‎autocommutator of $gin g$ and $alphain a$‎. ‎also‎, ‎the‎ autocommutator subgroup of g is defined to be‎ ‎$k(g)=langle[g,alpha]|gin g‎, ‎alphain arangle$‎, ‎which is a‎ ‎characteristic subgroup of $g$ containing the derived subgroup‎ ‎$g'$ of $g$‎. ‎a group is defined...

We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...

Imagine the situation: “One day, you notice an old country woman crossing a downtown street, just about to put one foot down on the rails of the streetcar line. [...] Suppose, now, that at the very moment she puts her foot on the rail a streetcar comes rushing down the tracks toward her. If the old woman does not notice the car and continues across the tracks nothing will happen. But if someone...

The development of terrestrial laser scanning (TLS) has opened new avenues in the study trees. Although TLS provides valuable information on structural elements, fine-scale analysis, e.g., at annual shoots (AS) scale, is currently not possible. We present a model to segment and classify AS from tree skeletons into finite set “physiological ages” (i.e., state specialization physiological age (PA...

The Effect of Children on Specialization and Coordination of Partners’ Activities This paper first documents the extent of the specialization in time use in couple families, and the impact of children on this specialization. It then examines the links between the time allocations of partners in couple families, the impact of children on these links, and the effects these factors have on special...