In this paper we compare the ut i l i ty of different commitment strategies in planning. Under a "least commitment strategy", plans are represented as part ia l orders and operators are ordered only when interactions are detected. We investigate claims of the inherent advantages of planning w i t h part ia l orders, as compared to planning w i t h tota l orders. By focusing our analysis on the ...

let $g$ be a finite group‎. ‎we denote by $psi(g)$ the integer $sum_{gin g}o(g)$‎, ‎where $o(g)$ denotes the order of $g in g$‎. ‎here we show that‎ ‎$psi(a_5)< psi(g)$ for every non-simple group $g$ of order $60$‎, ‎where $a_5$ is the alternating group of degree $5$‎. ‎also we prove that $psi(psl(2,7))

For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NS...

We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well a construction groups with Conradian orders whose every action on metric spaces has bounded orbits. A classical consequence the ultrafilter lemma is that group bi-orderable if and only it locally bi-orderable. show there exists model ZF in which free (ergo bi-orderable) not bi-orderable, can be giv...

The description of living beings—the “ornements” the earth in all their diversity—is a central task Jean Corbechon's fourteenth-century encyclopedia, Livre des propriétés choses, translation into French Bartholomaeus Anglicus's thirteenth-century De proprietatibus rerum, undertaken for Charles V France. This article surveys system conceptualizing nature encyclopedia. Livre's account animal, veg...