DERVISH ORDERS OF CONSTANTINOPLE

DERVISH - An Office-Navigating Robot

ion The real world is so finely grained that any attempt to plan using a highly detailed model of reality is doomed because of enormous computational complexity. DERVISH avoids this pitfall by reasoning about an abstraction of the real world that is based on a quantization of the world into a set of states; each state corresponds to a node on the topological map or a hallway segment between two...

On orders induced by implications

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...

Converse Lagrange Theorem Orders and Supersolvable Orders

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...

Extending Partial Orders to Dense Linear Orders

Circle Orders , N - gon Orders and the Crossing Number of Partial Orders

Let F={P1,...,Pm} be a family of sets. A partial order P(F, <) on F is naturally defined by the condition Pi< Pj iff Pi is contained in Pj. When the elements of F are disks (i.e. circles together with their interiors), P(F, <) is called a circle order; if the elements of F are n-polygons, P(F, <) is called an n-gon order. In this paper we study circle orders and n-gon orders. The crossing numbe...