The high-level contribution of this paper is the development of a beaconless node-velocity-based stable path on-demand unicast routing protocol (NVSP) and its extension for multicasting (NVSP-M) in mobile ad hoc networks (MANETs). During the propagation of the Route-Request (RREQ) messages, every forwarding node includes its current node velocity information in the RREQs. The bottleneck velocit...

We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos. Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of Fox [10], of the including topos....

In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two posi...

We present an algorithm to compute the degree of convexity of a convex polyomino P , defined as the smallest integer k such that any two cells of P can be joined by a path in P with at most k changes of direction. The algorithm is used to generate in amortized time O(1) all k-convex polyominoes of size n.

The concept of convex extendability is introduced to answer the problem of nding the smallest distance convex simple graph containing a given tree. A problem of similar type with respect to minimal path convexity is also discussed. c © 1999 Elsevier Science B.V. All rights reserved

Article history: Received 16 April 2008 Revised 17 March 2009 Available online 2 April 2009 MSC: primary 34L15 secondary 34L40, 47J30