Thesis (M.Sc. (Mathematics)) - Rhodes University, 2008. / A thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in Mathematics.

Thesis (Ph. D.)--University of Iowa, 2005. / Includes bibliographical references (leaves 141-147).

Thesis (Ph. D.)--Open University. BLDSC no. DX212302.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 104-107).

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 81-85).

Thesis (Ph. D.)--University of Texas at Austin, 2009. / Title from PDF title page (University of Texas Digital Repository, viewed on Sept. 9, 2009). Vita. Includes bibliographical references and index.

Thesis (M.S.)--Brigham Young University. Dept. of Mechanical Engineering, 2005. / Includes bibliographical references (p. 59-61).

Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Within lattice theory, an interesting question asked is whether a given abstract lattice may be represented concretely as subsets of a closure system on a topological space. This is true for boolean algebras, bounded distributive lattices and arbitrary bounded lattices. In particular, there are a multitude of ways to represent bounded lattices. We present some of these ideas, as well as an analysis of the differences between them. We further investigate the attempts that were made to extend the above representations to lattices endowed with operators, in particular the work done on bounded distributive lattices with operators. We then make a new contribution by extending this work to arbitrary bounded lattices with operators. We also show that the so-called sufficiency operator has a relational representation in the bounded lattice case. / AFRIKAANSE OPSOMMING: Binne die raamwerk van tralie teorie word die vraag soms gevra of ’n gegewe tralie konkreet veteenwoordig kan word as subversamelings van ’n afsluitingssisteem op ’n topologiese ruimte. Die voorgenoemde is waar vir, onder andere, boolse algebras, begrensde distributiewe tralies en algemene begrensde tralies. Daar is veral vir begrensde tralies menigte maniere om hul te verteenwoordig. Ons bied sommige van hierdie idees voor, asook ’n analiese van die verskille daarin teenwoordig. Verder ondersoek ons ook sommige van die maniere waarop tralies tesame met operatore verteenwoordig kan word. Ons sal spesiale aandag gee aan distributiewe tralies met operatore, soos gedoen in, met die idee om die voorgenoemde uit te brei na algemene begrensde tralies met operatore. Ons toon dan verder aan dat die sogenoemde voldoende operator ook ’n relasionele verteenwoordiging het in die begrensde tralie geval.

FundaÃÃo de Amparo à Pesquisa do Estado do Cearà / Seja p um nÃmero primo Ãmpar. Uma famÃlia de reticulados (p-1)-dimensional produzindo novos empacotamentos pra vÃrios valores de p no intervalo [149... 3001] à apresentado. O resultado à obtido atravÃs da modificaÃÃo da construÃÃo de Craig e considerando conveniente escolhidos Z-submÃdulos de Q (ζ), onde ζ à raiz p-Ãsima primitiva da unidade. Para p ≥ 59, à mostrado que a densidade de centro do reticulado (p-1)-dimensional na nova famÃlia à pelo menos 2 vezes a densidade de centro do (p-1)-dimensional reticulado de Craig. / Let p an odd prime. A family of (p-1)-dimensional over-lattices yielding new record packings for several values of p in interval [149... 3001] is presented. The result is obtained by modifying Craig's construction and considering conveniently chosen Z-submodules of Q (ζ), where ζ is a primitive pth root of unity. For p ≥ 59, it is shown that the center density of the (p-1)-dimensional lattice in the new family is at least twice the center density of the (p-1)-dimensional Craig lattice.

Ph.D. (Mathematics) / Our objective in this thesis is to investigate two fundamental questions concerning Riesz operators de ned on a Banach space. Recall that Riesz operators are generalizations of compact operators in the sense that Riesz operators have the same spectral properties as compact operators. However, they do not possess the same algebraic properties as compact operators. Our rst question that we investigate is: When is a Riesz operator a nite rank operator? This question is motivated from the fact that if a compact operator de ned on a Banach space has closed range, then it is a nite rank operator. Also, Ghahramani proved that a compact homomorphism de ned on a C -algebra is a nite rank operator, see . Martin Mathieu, in his paper, generalized the result of Ghahramani by proving that a weakly compact homomorphism de ned on a C -algebra is a nite rank operator...