Thesis (M.A.)--University of the Western Cape, 2008. / Includes bibliographical references (leaves 81- 82).

Thesis (MSc) -- Stellenbosch University, 2004. / ENGLISH ABSTRACT: In this thesis we give a survey of research done on a problem on subnormal subgroups in factorized groups G = AB, where A and B are two subgroups of G with H a subgroup of A n B which is subnormal in both A and B. It is of interest to know whether or not such a subgroup H will also be subnormal in G. During the past twenty five to thirty years some positive results were obtained in the case where G is a finite group. This was mainly due to work done by Maier and Wielandt, with results by Sidki and Casolo following shortly afterwards. Counterexamples in the case of infinite groups seemed to be extremely hard to construct. For the infinite group case, some positive results were obtained through contributions by amongst others Stonehewer, Franciosi, de Giovanni and Sysak. Most recently some alternative proofs were given by Fransman. / AFRIKAANSE OPSOMMING: In hierdie tesis poog ons om 'n oorsig te gee van navorsing uitgevoer oor 'n probleem rakende subnormale ondergroepe van 'n groep G = AB wat uitgedruk kan word as 'n produk van twee ondergroepe A en B. Daar word gepoog om te bepaal vir watter klasse van groepe dit volg dat as die ondergroep H van A se deursnede met B subnormaal is in beide A en B, sal dit impliseer dat H ook subnormaal in die groep G sal wees. Gedurende die afgelope vyf-en-twintig na dertig jaar is positiewe resultate bewys VIr eindige sodanige groepe deur veralouteurs soos Maier en Wielandt, gevolg deur Sidki en Casolo. Dit blyk dat dit nie maklik is om teenvoorbeelde te vind vir die oneindige geval nie. Daar is wel positiewe resultate gelewer vanweë bydraes deur onder andere Stonehewer, Franciosi, de Giovanni en Sysak. Meer onlangs is ook alternatiewe bewyse gegee deur Fransman.

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

The key task for a search engine advertising system is, for each query that the search engine receives, to choose what advertisement should be displayed, and in what order. This ranking order has a strong impact on the revenue the search engine receives from the ads. Meanwhile, showing the user an advertisement that they prefer to click on improves user satisfaction. Therefore, it is reasonable to set up click-through rate (CTR) as a weighted ranking criteria. In this project, we aim to develop a model capable of accurately predicting CTR of ads in the system. For ads that have been displayed repeatedly, this is empirically measurable, but for new ads, other means must be used. Combining logistic regression model with L1 regularization we are able to predict CTR for new ads based on self-defined features. The ultimate goal is to improve the convergence and performance of our advertising system, consequently increasing both revenue and user satisfaction. Second part of this report is about a study on poisson factorization recommender evaluation. As recommender systems become more and more popular, many approaches have been suggested to evaluate the performance of traditional recommenders based on Gaussian distribution. However, few evaluating approaches were designed for poisson factorization recommender. This study checked some most common evaluation methods and discussed about their appropriateness in poisson factorization recommender evaluation. / text

This is an expository thesis on integral domains which are not unique factorization domains. We focus on restoring a type of unique factorization using prime ideals within quadratic integer rings. In particular, we examine which quadratic integer rings will admit such factorization.

Anderson and Frazier defined a generalization of factorization in integral domains called tau-factorization. If D is an integral domain and tau is a symmetric relation on the nonzero nonunits of D, then a tau-factorization of a nonzero nonunit a in D is an expression a = lambda a_1 ... a_n, where lambda is a unit in D, each a_i is a nonzero nonunit in D, and a_i tau a_j for i != j. If tau = D^# x D^#, where D^# denotes the nonzero nonunits of D, then the tau-factorizations are just the usual factorizations, and with other choices of tau we get interesting variants on standard factorization. For example, if we define a tau_d b if and only if (a, b) = D, then the tau_d-factorizations are the comaximal factorizations introduced by McAdam and Swan. Anderson and Frazier defined tau-factorization analogues of many different factorization concepts and properties, and proved a number of theorems either generalizing standard factorization results or the comaximal factorization results of McAdam and Swan. Some of these concepts include tau-UFD's, tau-atomic domains, the tau-ACCP property, tau-BFD's, tau-FFD's, and tau-HFD's. They showed the implications between these concepts and showed how each of the standard variations implied their tau-factorization counterparts (sometimes assuming certain natural constraints on tau). Later, Ortiz-Albino introduced a new concept called Gamma-factorization that generalized tau-factorization. We will summarize the known theory of tau-factorization and Gamma-factorization as well as introduce several new or improved results.

Thesis (M. Phil.)--University of Hong Kong, 2008. / Also available in print.

Thesis (Ph.D.)--University of Western Australia, 2004.

Thesis (MSc)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1940. / Typescript. Includes abstract and vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.