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Correlation effects in the one-dimensional Hubbard model are studied by application of the L-resolvent method. The calculations are well beyond one-particle mean field approximation. All correlations involving two neighboring sites are included exactly and higher order correlations are approximated. The effects of varying temperature, band filling, Coulomb repulsion and external magnetic field are investigated. Two-site correlations for non-half-filled band fillings are calculated for the first time. Some exact relations between correlation functions are derived by electron-hole symmetry. Results indicate that short-range spin correlations always favor antiferromagnetic order. Large Coulomb repulsion induces a gap in the excitation spectrum and a metal-insulator transition is predicted as the Coulomb repulsion parameter is changed. / Ph. D.

ENGLISH ABSTRACT: Determining the (classical) chromatic number of a graph (i.e. finding the smallest number of colours with which the vertices of a graph may be coloured so that no two adjacent vertices receive the same colour) is a well known combinatorial optimization problem and is widely encountered in scheduling problems. Since the late 1960s the notion of the chromatic number has been generalized in several ways by relaxing the restriction of independence of the colour classes. / AFRIKAANSE OPSOMMING: Die bepaling van die (klassieke) chromatiese getal van ’n grafiek (naamlik die kleinste aantal kleure waarmee die punte van ’n grafiek gekleur kan word sodat geen twee naasliggende punte dieselfde kleur ontvang nie) is ’n bekende kombinatoriese optimeringsprobleem wat wyd in skeduleringstoepassings te¨egekom word. Sedert die laat 1960s is die definisie van die chromatiese getal op verskeie maniere veralgemeen deur die vereiste van onafhanklikheid van die kleurklasse te verslap. / Thesis (DPhil)--Stellenbosch University, 2007.

Ph.D. / The induced path number p(G) of a graph G is defined as the minimum number of subsets into which the vertex set V(G) of G can be partitioned such that each subset induces a path. In this thesis we determine the induced path number of a complete £-partite graph. We investigate the induced path number of products of complete graphs, of the complement of such products and of products of cycles. For a graph G, the linear vertex arboricity lva(G) is defined as the minimum number of subsets into which the vertex set of C can be partitioned so that each subset induces a linear forest. Since each path is a linear forest, Iva(G) p(G) for each graph C. A graph G is said to be uniquely rn-li near- forest- partition able if lva(C) = in and there is only one partition of V(G) into m subsets so that each subset induces a linear forest. Furthermore, a graph C is defined to be nz- Iva- saturated if Iva(G) < in and lva(C + e) > iii for each e E We construct graphs that are uniquely n2-linear-forest-partitionable and in-lva-saturated. We characterize those graphs that are uniquely m-linear-forest-partitionable and rn-lvasaturated. We also characterize the orders of uniquely in- path- partitionable disconnected, connected and rn-p-saturated graphs. We look at the influence of the addition or deletion of a vertex or an edge on the path partition number. If C is a graph such that p(G) = k and p(G - v) = k - 1 for every v E V(G), then we say that C is k-minus-critical. We prove that if C is a connected graph consisting of cyclic blocks Bi with p(B1 ) = b, for i = 1,2, ... ,n where ii > 2 and k bi - n+ 1, then C is k- minus- critical if and only if each of the blocks B1 is a bj- minus- critical graph.

Call number: LD2668 .T4 1985 B62 / Master of Science

The goal of this research is to validate the methodology used while investigating metrics directed verification of Unified Modeling Language (UML) based designs. This document is organized into five distinct sections. The topics discussed include an introduction to the UML, a discussion of available software metrics, a tutorial regarding the nature of design metrics, a discussion of available UML metrics, and the empirical study results. The empirical study presents detailed information regarding how UML class diagrams can be mapped to design metrics, a discussion on how the data was collected and verified, the results obtained during this study, what conclusions were drawn from the data, and recommendations for future research topics. Preliminary findings indicate that a correlation does exist between the external design complexity measure and the UML class diagrams. / Department of Computer Science

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries