31409070
Hermite interpolation with a pair of spirals
Abstract The Hermite interpolation problem in the plane considered here is to join two points and to match given unit tangent vectors and signed curvatures at the two points with various G 2 curves consisting of a pair of spirals. The rotation of the tangent vector of the interpolating curve from one point to the other is restricted to being less than π. The necessary and sufficient conditions for the existence of each of the various curves are given.
1283266
A guided clothoid spline
Abstract A method is described whereby a G 2 planar curve consisting of clothoid (Cornu spiral) segments, circular arcs and straight line segments is constructed. The curve passes through given points, is expressed parametrically, and has the attractive feature that the arc length and curvature are piecewise linear functions of the parameter. The given points through which the curve passes must be restricted somewhat so that a unique clothoid exists between each pair of points.
115238984
Commuting Continuous Flows on Manifolds
206570506
Quickly Excluding a Planar Graph
Abstract In an earlier paper, the first two authors proved that for any planar graph H , every graph with no minor isomorphic to H has bounded tree width; but the bound given there was enormous. Here we prove a much better bound. We also improve the best known bound on the tree-width of planar graphs with no minor isomorphic to a g × g grid.
12699179
Developing the Software Engineering Team
Teamwork is often considered one of the most important "generic skills" that we can provide to graduates entering the information technology profession. Often though, through the rush of covering important content, we short change our students by giving them limited opportunities to learn how to work effectively in teams. Students also often complain that although they are expected to work in teams on projects, they are never given any advice or guidance on how to work in a team (Hart and Stone, 2002). Or, if they are given guidance, it is often from a business perspective that students find difficult to integrate into their software development practice.In this paper we discuss a course-spanning initiative to help students learn teamwork skills. This initiative starts in first year by emphasising a core set of skills directly related to working in teams. These skills are applied in small software development teams, with close tutor supervision focusing students on teamwork rather than upon individual software development. The theme then continues into second and third year where the growing sophistication of the students' teamwork skills is complemented by increasing their independence and requiring students to apply a professional software engineering process as a development team. By the end of their course students are then in a position to work together effectively solving complex problems for a real industry client.
10283778
An Internet-based platform for testing generation scheduling auctions
The paper describes the uses and architecture of a network-centered computing-rich software platform called PowerWeb. PowerWeb was designed and built as a simulation environment for experimentally testing various power exchange auction markets through tournaments. It is designed to host simulations of a competitive "day-ahead" electric energy market in the content of a restructured electric power industry. The PowerWeb environment is meant to be flexible so as to accommodate different "rules of the game". The authors describe its interactive, distributed and Web-based character.
206570580
Sachs' Linkless Embedding Conjecture
Abstract We prove Sachs′ conjecture that a graph can be embedded in 3-space so that it contains no non-trivial link (in the sense of knot theory) if and only if it contains as a minor none of the seven graphs obtainable from K 6 by Y − Δ and Δ − Y exchanges. We also show the following: (i) A graph admits such a "linkless" embedding if and only if it admits a "panelled" embedding, one such that every circuit of the graph bounds a disc disjoint from the remainder of the graph. This was a conjecture of Bohme. (ii) An embedding is panelled if and only if for every subgraph, its complement in 3-space has free fundamental group. This extends a theorem of Scharlemann and Thompson, who proved it for planar graphs. (iii) If two panelled embeddings of the same graph are "different," that is, are not related by an orientation-preserving homeomorphism of the 3-space, then there is a subgraph which is a subdivision of K 5 or K 3, 3 such that the two induced embeddings of this subgraph are still different.
29982810
A proposal for object oriented Modula-2