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Let G = (a,b,c,...) be a groupoid and T a topology for G with U_a denoting an open set in T that contains the element a. The topology T is admissible for G if for every a·b=c and U_c there exist U_a and U_b such that U_a·U_b c U_c. G is said to be topologically trivial if the only admissible topologies for G are the discrete and indiscrete. It is shown that finite groups are topologically trivial if and only if they are simple. It is shown that finite topologically trivial semigroups are necessarily groups. Various classes of topologically trivial groupoids are examine, and it is shown that there exist topologically trivial groupoids of every order. G is said to be right (analogously left) topologically trivial if one can find elements a·b = c in G and U_c in T such that a·U_b ⊈ U_c for all U_b in T whenever T is not trivial. G is said to be totally topologically trivial if one can find a·b = c in G and U_c in T such that a·U_b ⊈ U_c and U_a·b ⊈ U_c for all U_a and U_b in T whenever T is not trivial. Right, left, and total topologically triviality are studies for various algebraic systems. A continuity condition that always holds is exhibited as are new proofs for several old theorems. Consequences of imposing the tower topology on various algebraic systems are examined. If the proper subset I contained in the groupoid G is such that the null set, the set G, and each singleton set of the elements in G-I form the basis for an admissible topology for G, then I is called a generalized ideal in G. Properties of generalized ideals are studied at length. A function t from a groupoid G to another groupoid is called a local homomorphism if for each a and b in G there exist r and s in G such that a·b = r·s and such that t(r·s) = t(r)·t(s). Several properties of local homomorphisms are examined. / Ph. D.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25108号 / 理博第5015号 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 田中 貴浩, 准教授 久徳 浩太郎, 教授 橋本 幸士 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

For many decades zirconium alloys have been commonly used in the nuclear power industry as fuel cladding material. Besides their good corrosion resistance and acceptable mechanical properties the main reason for using these alloys is the low neutron absorption. Zirconium alloys are exposed to a very severe environment during the nuclear fission process and there is a demand for better design of this material. To meet this requirement a thermodynamic database is useful to support material designers. In this thesis some aspects of the development of a thermodynamic database for zirconium alloys are presented. A thermodynamic database represents an important facility in applying thermodynamic equilibrium calculations for a given material providing: 1) relevant information about the thermodynamic properties of the alloys e.g. amount and composition of phases, oxygen activity, heat capacity etc, and 2) significant information for the manufacturing process e.g. heat treatment temperature. The basic information in the database is first the unary data, i.e. pure elements; those are taken from the compilation of the Scientific Group Thermodata Europe (SGTE) and then the binary and ternary systems. All phases present in those binary and ternary systems are described by means of the Gibbs energy as a function of composition and temperature. Many of those binary systems have been taken from published or unpublished works and others have been assessed in the present work. The elements included in the databse are: C, Fe, Cr, Nb, Ni, Mo, O, Si, Sn, and Zr + H, and the assessment performed under this thesis are: Cr-Sn, Mo-Zr, Sn-Zr, Fe-Nb-Zr and Nb-O-Zr. All the calculations have been made using Thermo-Calc software and the representation of the Gibbs energy obtained by applying Calphad technique with some use of ab initio calculations. / QC 20100902

Thesis (MComm) -- Stellenbosch University, 2002. / ENGLISH ABSTRACT: Consider a data set with a categorical response variable and a set of explanatory variables. The response variable can have two or more categories and the explanatory variables can be numerical or categorical. This is a typical setup for a classification analysis, where we want to model the response based on the explanatory variables. Traditional statistical methods have been developed under certain assumptions such as: the explanatory variables are numeric only and! or the data follow a multivariate normal distribution. hl practice such assumptions are not always met. Different research fields generate data that have a mixed structure (categorical and numeric) and researchers are often interested using all these data in the analysis. hl recent years robust methods such as classification trees have become the substitute for traditional statistical methods when the above assumptions are violated. Classification trees are not only an effective classification method, but offer many other advantages. The aim of this thesis is to highlight the advantages of classification trees. hl the chapters that follow, the theory of and further developments on classification trees are discussed. This forms the foundation for the CART software which is discussed in Chapter 5, as well as other software in which classification tree modeling is possible. We will compare classification trees to parametric-, kernel- and k-nearest-neighbour discriminant analyses. A neural network is also compared to classification trees and finally we draw some conclusions on classification trees and its comparisons with other methods. / AFRIKAANSE OPSOMMING: Beskou 'n datastel met 'n kategoriese respons veranderlike en 'n stel verklarende veranderlikes. Die respons veranderlike kan twee of meer kategorieë hê en die verklarende veranderlikes kan numeries of kategories wees. Hierdie is 'n tipiese opset vir 'n klassifikasie analise, waar ons die respons wil modelleer deur gebruik te maak van die verklarende veranderlikes. Tradisionele statistiese metodes is ontwikkelonder sekere aannames soos: die verklarende veranderlikes is slegs numeries en! of dat die data 'n meerveranderlike normaal verdeling het. In die praktyk word daar nie altyd voldoen aan hierdie aannames nie. Verskillende navorsingsvelde genereer data wat 'n gemengde struktuur het (kategories en numeries) en navorsers wil soms al hierdie data gebruik in die analise. In die afgelope jare het robuuste metodes soos klassifikasie bome die alternatief geword vir tradisionele statistiese metodes as daar nie aan bogenoemde aannames voldoen word nie. Klassifikasie bome is nie net 'n effektiewe klassifikasie metode nie, maar bied baie meer voordele. Die doel van hierdie werkstuk is om die voordele van klassifikasie bome uit te wys. In die hoofstukke wat volg word die teorie en verdere ontwikkelinge van klassifikasie bome bespreek. Hierdie vorm die fondament vir die CART sagteware wat bespreek word in Hoofstuk 5, asook ander sagteware waarin klassifikasie boom modelering moontlik is. Ons sal klassifikasie bome vergelyk met parametriese-, "kernel"- en "k-nearest-neighbour" diskriminant analise. 'n Neurale netwerk word ook vergelyk met klassifikasie bome en ten slote word daar gevolgtrekkings gemaak oor klassifikasie bome en hoe dit vergelyk met ander metodes.

Two different aluminium alloys, AA6111 (Al-Mg-Si) and AA7055 (Al-Mg-Zn), were chosen as the aluminium alloys to be welded with DC04, and two welding methods (USW and FSSW) were selected to prepare the welds. Selected pre-welded joints were then annealed at T=400 - 570oC for different times. Kinetics growth data was collected from the microstructure results, and the growth behaviour of the IMC layer was found to fit the parabolic growth law. A grain growth model was built to predict the grain size as a function of annealing time. A double-IMC phase diffusion model was applied, together with grain growth model, to predict the thickness of each phase as a function of annealing time in the diffusion process during heat treatment. In both material combinations and with both welding processes a similar sequence of IMC phase formation was observed during the solid state welding. η-Fe2Al5 was found to be the first IMC phase to nucleate. The IMC islands then spread to form a continuous layer in both material combinations. With longer welding times a second IMC phase, θ-FeAl3, was seen to develop on the aluminium side of the joints. Higher fracture energy was received in the DC04-AA6111 joints than in the DC04-AA7055 joints. Two reasons were claimed according to the microstructure in the two joints. The thicker IMC layers were observed in the DC04-AA7055 joints either before or after heat treatment, due to the faster growth rate of the θ phase. In addition, pores were left in the aluminium side near the interface as a result of the low melting point of AA7055.The modelling results for both the diffusion model and grain growth model fitted very well with the data from the static heat treatment. Grain growth occurred in both phases in the heat treatment significantly, and was found to affect the calculated activation energy by the grain boundary diffusion. At lower temperatures in the phases with a smaller grain size, the grain boundary diffusion had a more significant influence on the growth rate of the IMC phases. The activation energies for the grain boundary diffusion and lattice diffusion were calculated as 240 kJ/mol and 120 kJ/mol for the η phase, and 220 kJ/mol and 110 kJ/mol for the θ phase, respectively. The model was invalid for the growth of the discontinuous IMC layers in USW process. The diffusion model only worked for 1-Dimensional growth of a continuous layer, which was the growth behaviour of the IMC layer during heat treatment. However, due to the highly transient conditions in USW process, the IMC phases were not continuous and uniform even after a welding time of 2 seconds. Therefore, the growth of the island shaped IMC particles in USW was difficult to be predicted, unless the nucleation stage was taken into consideration.

Thesis (Ph. D.)--University of California, San Diego, 2004. / Vita. Includes bibliographical references (leaves 189-190).

Just over half (50:6%) of the population of South Sudan lives on less than one US Dollar a day. Three quarters of the population live below the poverty line (NBS, Poverty Report, 2010). Generally, effective government policy to reduce unemployment and eradicate poverty focuses on stimulating new businesses. Micro and small enterprises (MSEs) are the major source of employment and income for many in under-developed countries. The objective of this study is to identify factors that determine business success and failure in South Sudan. To achieve this objective, generalized linear models, survey logistic models, the generalized linear mixed models and multiple correspondence analysis are used. The data used in this study is generated from the business survey conducted in 2010. The response variable, which is defined as business success or failure was measured by profit and loss in businesses. Fourteen explanatory variables were identified as factors contributing to business success and failure. A main effect model consisting of the fourteen explanatory variables and three interaction effects were fitted to the data. In order to account for the complexity of the survey design, survey logistic and generalized linear mixed models are refitted to the same variables in the main effect model. To confirm the results from the model we used multiple correspondence analysis. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

Longitudinal data tend to be correlated and hence posing a challenge in the analysis since the correlation has to be accounted for to obtain valid inference. We study various statistical methods for such correlated longitudinal binary responses. These models can be grouped into five model families, namely, marginal, subject-specific, transition, joint and semi-parametric models. Each one of the models has its own strengths and weaknesses. Application of these models is carried out by analyzing data on patient’s adherence status to highly active antiretroviral therapy (HAART). One other complicating issue with the HAART adherence data is missingness. Although some of the models are flexible in handling missing data, they make certain assumptions about missing data mechanisms, the most restrictive being missing completely at random (MCAR). The test for MCAR revealed that dropout did not depend on the previous outcome. A logistic regression model was used to identify predictors for the patients’ first month’s adherence status. A marginal model was then fitted using generalized estimating equations (GEE) to identify predictors of long-term HAART adherence. This provided marginal population-based estimates, which are important for public health perspective. We further explored the subject’s specific effects that are unique to a particular individual by fitting a generalized linear mixed model (GLMM). The GLMM was also used to assess the association structure of the data. To assess whether the current optimal adherence status of a patient depended on the previous adherence measurements (history) in addition to the explanatory variables, a transition model was fitted. Moreover, a joint modeling approach was used to investigate the joint effect of the predictor variables on both HAART adherence status of patients and duration between successive visits. Assessing the association between the two outcomes was also of interest. Furthermore, longitudinal trajectories of observed data may be very complex especially when dealing with practical applications and as such, parametric statistical models may not be flexible enough to capture the main features of the longitudinal profiles, and so a semiparametric approach was adopted. Specifically, generalized additive mixed models were used to model the effect of time as well as interactions associated with time non-parametrically. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

Shannon showed that the codes with random-like codeword weight distribution are capable of approaching the channel capacity. However, the random-like property can be achieved only in codes with long-length codewords. On the other hand, the decoding complexity for a random-like codeword increases exponentially with its length. Therefore, code designers are combining shorter and simpler codes in a pseudorandom manner to form longer and more powerful codewords. In this research, a method for designing non-binary compound codes with moderate to high coding rate is proposed. Based on this method, non-binary single parity-check (SPC) codes are considered as component codes and different iterative decoding algorithms for decoding the constructed compound codes are proposed. The soft-input soft-output component decoders, which are employed for the iterative decoding algorithms, are constructed from optimal and sub-optimal a posteriori probability (APP) decoders. However, for non-binary codes, implementing an optimal APP decoder requires a large amount of memory. In order to reduce the memory requirement of the APP decoding algorithm, in the first part of this research, a modified form of the APP decoding algorithm is presented. The amount of memory requirement of this proposed algorithm is significantly less than that of the standard APP decoder. Therefore, the proposed algorithm becomes more practical for decoding non-binary block codes. The compound codes that are proposed in this research are constructed from combination of non-binary SPC codes. Therefore, as part of this research, the construction and decoding of the non-binary SPC codes, when SPC codes are defined over a finite ring of order q, are presented. The concept of finite rings is more general and it thus includes non-binary SPC codes defined over finite fields. Thereafter, based on production of non-binary SPC codes, a class of non-binary compound codes is proposed that is efficient for controlling both random-error and burst-error patterns and can be used for applications where high coding rate schemes are required. Simulation results show that the performance of the proposed codes is good. Furthermore, the performance of the compound code improves over larger rings. The analytical performance bounds and the minimum distance properties of these product codes are studied. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2013.