NASA Scientific and Technical Aerospace Reports
NASA Scientific and Technical Aerospace Reports
NASA Scientific and Technical Aerospace Reports
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20060002186 Illinois Univ. at Urbana-Champaign, Urbana, IL, USA<br />
Vertex Eliminations in Graphs<br />
Rao, Vasant B.; Desai, Madhav P.; 1987 IEEE International Symposium on Circuits <strong>and</strong> Systems, Volume 2; 1987,<br />
pp. 499-502; In English; See also 20060002103<br />
Contract(s)/Grant(s): SCR-RSCH-84-06-049; Copyright; Avail.: Other Sources<br />
In this paper we introduce the notion of eliminating a vertex from a simple undirected graph which involves addition of<br />
edges to induce a clique (complete subgraph) among the neighbors of the given vertex <strong>and</strong> then deleting (removing) the vertex<br />
itself <strong>and</strong> all edges incident on it. Several problems such as Gaussian Elimination, determining the equivalent conductance<br />
between two nodes in an electrical network of resistances, <strong>and</strong> computing the transmission function between two nodes in a<br />
relay-contact switching network can be abstractly posed as successively eliminating vertices in a weighted graph. If the<br />
vertices of a graph are eliminated one-by-one in a certain order such that the degree of a vertex just prior to its elimination<br />
is bounded above by an integer k. then the total number of operations involved will clearly be linear in the number of vertices<br />
in the original graph. If such an ordering exists, we say that the graph is k-eliminable. Therefore. each of the above-mentioned<br />
problems can be solved in linear time on k-eliminable graphs. We have shown that a graph is k-eliminable if <strong>and</strong> only if it<br />
is a spanning subgraph of a k-tree. We also examine various properties of k-eliminable graphs. The complexity of finding the<br />
smallest k for which a given graph is k-eliminable is unknown; however, we suggest a heuristic polynomial-time algorithm<br />
for its solution <strong>and</strong> study its performance in a number of graphs arising in practical situations.<br />
Author<br />
Graphs (Charts); Gaussian Elimination; Electrical Resistance; Polynomials; Switching; Apexes<br />
20060002228 New Mexico Inst. of Mining <strong>and</strong> Technology, Socorro, NM, USA, New Mexico Petroleum Recovery<br />
Research Center, Socorro, NM, USA<br />
Risk Reduction with a Fuzzy Expert Exploration Tool<br />
January 2005; 286 pp.; In English<br />
Report No.(s): DE2005-841420; No Copyright; Avail.: National <strong>Technical</strong> Information Service (NTIS)<br />
Incomplete or sparse data such as geologic or formation characteristics introduce a high level of risk for oil exploration<br />
<strong>and</strong> development projects. ‘Expert’ systems developed <strong>and</strong> used in several disciplines <strong>and</strong> industries have demonstrated<br />
beneficial results when working with sparse data. State-of-the-art expert exploration tools, relying on a database, <strong>and</strong> computer<br />
maps generated by neural networks <strong>and</strong> user inputs, have been developed through the use of ‘fuzzy’ logic, a mathematical<br />
treatment of imprecise or non-explicit parameters <strong>and</strong> values. Oil prospecting risk has been reduced with the use of these<br />
properly verified <strong>and</strong> validated ‘Fuzzy Expert Exploration (FEE) Tools.’ Through the course of this project, FEE Tools <strong>and</strong><br />
supporting software were developed for two producing formations in southeast New Mexico. Tools of this type can be<br />
beneficial in many regions of the U.S. by enabling risk reduction in oil <strong>and</strong> gas prospecting as well as decreased prospecting<br />
<strong>and</strong> development costs. In today’s oil industry environment, many smaller exploration companies lack the resources of a pool<br />
of expert exploration personnel. Downsizing, volatile oil prices, <strong>and</strong> scarcity of domestic exploration funds have also affected<br />
larger companies, <strong>and</strong> will, with time, affect the end users of oil industry products in the U.S. as reserves are depleted. The<br />
FEE Tools benefit a diverse group in the U.S., allowing a more efficient use of scarce funds, <strong>and</strong> potentially reducing<br />
dependence on foreign oil <strong>and</strong> providing lower product prices for consumers.<br />
NTIS<br />
Assessments; Fuzzy Systems; Oil Exploration; Risk<br />
20060002331 California Univ., Berkeley, CA USA<br />
I. Excluded Volume Effects in Ising Cluster Distributions <strong>and</strong> Nuclear II. Multifragmentation. Multiple Chance Effects<br />
in Alpha-Particle Evaporation<br />
Breus, D. E.; Apr. 2005; 212 pp.; In English<br />
Report No.(s): DE2005-841926; No Copyright; Avail.: Department of Energy Information Bridge<br />
In Part I, geometric clusters of the Ising model are studied as possible model clusters for nuclear multifragmentation. In<br />
Part II, an explanation is offered for the recently observed oscillations in the energy spectra of particles emitted from hot<br />
compound nuclei.<br />
NTIS<br />
Alpha Particles; Evaporation; Ising Model<br />
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