A directed graph G = ( V , E ) is given by a finite vertex set V and an edge set E C V× V. We choose two distinct vertices s e Vand t~ Vthat we consider as source and sink respectively. A path (from s to t) is a sequence of distinct edges (s, xl ), (xl, Xz) . . . . . (Xrj, Xr), (Xr, t) for some r. Denote by P the set of all such paths. For an edge e e E let PeCP be the set of paths passing thro...

Consider a simple polyhedron P, possibly non-convex, composed of n triangular regions (faces), in which each region has an associated positive weight. The cost of travel through each region is the distance traveled times its weight. We present and experimentally study several algorithms to compute an approximate weighted geodesic shortest path, 0 (s; t), between two points s and t on the surfac...

Let P and Q be disjoint polygons in the plane. We consider problems of finding an optimal bridge (p, q), p ∈ ∂P and q ∈ ∂Q, such that the length of the longest path from a point in P , passing through the bridge (p, q), to a point Q is minimized. We propose efficient algorithms for three problems according to whether P and Q are convex or not. The algorithms developed can be easily extended to ...

Integrated metamorphic and geochronological data place new constraints on the metamorphic evolution of a Neoproterozoic orogen in east Antarctica. Granulite-facies rocks from a 150 km stretch of the Kemp Land coast reflect peak conditions involving T 870^9908C at P 7 4^10 kbar, with pressure increasing westward towards an Archaean craton. Electron microprobe-derived (ThþU)^Pb monazite ages from...

Crawford, T., and Levene, C. I. (1952). 7. Path. Bact., 64, 523. Duguid, J. B. (1946). Ibid., 58, 207. Gunning, A. J., Pickering, G. W., Robb-Smith, A. H. T., and Russell, R. W. R. (1964a). Quart. 7. Med., 33, 133. (1964b). Ibid., 33, 155. McLetchie, N. G. B. (1952). Amner. 7. Path., 28, 413. Ross, J. P. (1936). Proc. roy. Soc. Med., 29, 872. Russell, R. W. R. (1963). Lancet, 2, 1354. Skovborg,...

Supporting intelligent and trustworthy maritime path planning decisions, Int. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Plea...

1 Semantics for timed Petri nets used in case study 5 model An (untimed) Petri net 6] is deened by the triple (P; T; F) with P a nite set of places, T a nite set of transitions, P \T = ;, and F (P T)(T P) a set of relations. The state of the untimed Petri net is the marking m : P ! Z + , assigning to each place p the number of tokens m(p) present in the place p: The set t := fp 2 P j (p; t) 2 F...

Proof. Denote by 1 the unit element of B. Let a ∈ B×. We show that 1 and a can be connected by a path in B×. Let A be the subalgebra of B generated by 1 and a. That is A = {P (a) : P (t) ∈ C[t]}. Because A× ⊂ B×, it suffices to find a path in A× that connects 1 with a. First, we determine all multiplicative functionals of A. Since A is a linear subspace of B, it is finite dimensional. Then ther...

A side skirt is a planar rooted tree T, T≠P2, where the root of T vertex degree at least two, and all other vertices except leaves are three. reduced Halin graph or skirted plane G=T∪P, skirt, P path connecting in order determined by embedding T. The structure graphs contains both symmetry asymmetry. For n≥2 Pn=v1v2v3⋯vn as length n−1, we call Cartesian product G Pn, n-generalized prism over G....