There are many challenges that are facing the world today. One of those challenges is HIV and AIDS. Thousands of people are infected as well as affected by the HIV and AIDS pandemic in the world. In spite of many efforts that have been done to combat the disease, HIV and AIDS is still claiming lives and leave many without their loved ones. The study of the role and place of prayer for HIV and Aids sick patients in the Vaal Triangle churches is a very important research topic, since the results will not only benefit people in the Vaal Triangle only but all people who are affected as well as infected by the disease in other areas. Churches have been given a command from the Bible to pray for the sick. However there are many misconceptions about praying for the sick especially the HIV and AIDS patients. Some of these misconceptions arise because HIV and AIDS is medically declared as an incurable disease. The effectiveness of prayer on HIV and AIDS to others is therefore questionable. Unfortunately these questions and doubts make many some people doubt the power of prayer and its effectiveness for HIV and AIDS patients. People who pray for HIV and AIDS sick persons are faced with many questions. Some of them sometimes wonder if God will answer their prayers or whether the person being prayed for will be healed or not. Others think that HIV and AIDS disease is a punishment from God and praying for the infected will be a waste of time. Some even question God’s ability to cure this disease. It is because of such questions that many avoid praying for HIV and AIDS patients. Others simply avoid praying for HIV and AIDS patients because it might reflect on them by others as lack of faith. Jesus prayed for the sick and also told the church to pray and to ask of the Father. He prayed for the sick regardless of their kind of sicknesses and as well as the causes of those sickness. He accepted those who were outcasts of society and prayed for those whose sicknesses were considered a shame in public. The church has to pray for HIV and AIDS infected people. They are not to be controlled to pray by the results of prayer or the kind and the cause of the sickness. And, issues such as whether HIV and AIDS is a punishment from God or not. Just like Jesus, the church should pray for HIV and AIDS sick people without ceasing. / MA, Biblical Studies, North-West University, Vaal Triangle Campus, 2010

Given a graph G, a K_3-decomposition of G, also called a triangle decomposition, is a set of subgraphs isomorphic to K_3 whose edges partition the edge set of G. Further, a rational K_3-decomposition of G is a non-negative rational weighting of the copies of K_3 in G such that the total weight on any edge of G equals one. In this thesis, we explore the problem of rational triangle decompositions of dense graphs. We start by considering necessary conditions for a rational triangle decomposition, which can be represented by facets of a convex cone generated by a certain incidence matrix. We identify several infinite families of these facets that represent meaningful obstructions to rational triangle decomposability of a graph. Further, we classify all facets on up to 9 vertices and check all 8-vertex graphs of degree at least four for rational triangle decomposability. As the study of graph decompositions is closely related to design theory, we also prove the existence of certain types of designs. We then explore sufficient conditions for rational triangle decomposability. A famous conjecture in the area due to Nash-Williams states that any sufficiently large graph (satisfying some divisibility conditions) with minimum degree at least 3/4v is K_3-decomposable; the same conjecture stands for rational K_3-decomposability (no divisibility conditions required). By perturbing and restricting the coverage matrix of a complete graph, we show that minimum degree of at least 22/23v is sufficient to guarantee that the given graph is rationally triangle decomposable. This density bound is a great improvement over the previously known results and is derived using estimates on the matrix norms and structures originating from association schemes. We also consider applications of rational triangle decompositions. The method we develop in the search for sufficient conditions provides an efficient way to generate certain sampling plans in statistical experimental design. Furthermore, rational graph decompositions serve as building blocks within certain design-theoretic proofs and we use them to prove that it is possible to complete partial designs given certain constraints. / Graduate / 0405

Orientador: José Geraldo Pereira / Banca: Antônio José Accioly / Banca: Yuri Obukhov / Banca: José Wadih Maluf / Banca: Ilya Lvovich Shapiro / Resumo: Com o objetivo de entender como a torção descreve a interação gravitacional no contexto do Equivalente Teleparalelo da Relatividade Geral, obtemos os campos de tetrada, a conexão de Weitzenböck e o tensor de torção relativo a um espaço-tempo com simetria esférica de Schwarzschild. As mesmas grandezas são também obtidas para o caso do espaço-tempo estacionário com simetria axial de Kerr, assim como para o acoplamento spin-órbita. Mostra-se que, no limite de campo fraco, as partes tensorial e vetorial da torção de Schwarzschild combinam-se para dar o potencial newtoniano, enquanto que a torção axial, nas aproximações de campo fraco e rotação lenta, aparece como o componente gravito-magnética do campo gravitacional. A torção axial, portanto, é a responsável pelo efeito Lense-Thirring. Para o acoplamento spin-órbita, mostra-se que o acoplamento gravitacional da torção axial com o spin corresponde à interação spin-rotação, com a parte axial da torção representando a velocidade angular de rotação. Por outro lado, considerando a variedade de Weitzenböck como uma seqüência apropriada de redes discretas, composta de um número crescente de simplexos cada vez mais menores, obtém-se o análogo discreto da ação teleparalela, assim como suas correspondentes equações de campo. Para isso, assume-se que o interior de cada simplexo (polígino de Delaunay) é plano, e o comprimento l entre qualquer par de vértices serve como a variável independente, de maneira que a torção resulta localizada na hipersuperfície bidemensional (triângulo de deslocamento, ou hinge) da rede. / Abstract: As an attempt to understand the mechanism through which torsion describes the gravitational interaction in the context of the teleparallel equivalent of general relativity, we obtain the tetradm the Weitzenböck connection, and the torsion fields of the spherical symmetric Schwarzschild solution. The same magnitudes are obtained for the case of the stationary axi-symmetric Kerr solution, as well as for the rotation-spin coupling. It is shown that, inthe weak field limit, the vector and the tensor parts of the Schwarzschild torsion combine themselves to yield the newtonian force, whereas in the slow-rotation and weak-field approximation, the axial torsion of the Kerr solution is shown to paly the role of the gravitomagnetic component of the gravitational field. The axial torsion, therefore, is the responsible for the Lense-Thirring effect. Concerning the spin-rotation coupling, it is shown that the gravitational coupling of the axial torsion with spin corresponds to the rotation-spin interaction, with the axial torsion playing the role of the rotational angular velocity. On the order hand, by considering the Weitzenböck manifold as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller and smaller simplices, it is obtained the discrete analogues of the teleparallel action, as well as the corrresponding simplicial vacuum field equation. This is done by considering the interior of each simplex (Delaunay lattice) as flat, and the link lengths l betwenn any pair of vertices as independent variables, so that torsions turns out to be localized in the two dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. / Doutor

Triangle enumeration is an important element in graph analysis, and because of this it is a topic that has been studied extensively. Although the formulation is simple, for large networks the computation becomes challenging as we have to deal with memory limitation and efficiency. Many algorithms have been proposed to overcome these problems. Some use distributed computing, where the computation is distributed among many machines in a cluster. However, this approach has a high cost in terms of hardware resources and energy. In this thesis we studied triangle counting/listing algorithms for both directed and undirected graphs, and searched for methods to do the computation on a single machine. Through detailed analysis, we found some ways to improve the efficiency of the computation. Programs that implement the algorithms were built and tested on large networks with up to almost a billion nodes. The results were then analysed and discussed. / Graduate

Background. Level of detail is an optimization technique used by several modern games. The level of detail systems uses simplified triangular meshes to determine the optimal combinations of 3D-models to use in order to meet a user-defined criterion for achieving fast performance. Prior work has also pre-computed level of detail settings to only apply the most optimal settings for any given view in a 3D scene. Objectives. The aim of this thesis is to determine the difference in image quality between a custom level of detail pre-preprocessing approach proposed in this paper, and the level of detail system built in the game engine Unity. This is investigated by implementing a framework in Unity for the proposed level of detail pre-preprocessing approach in this paper and designing representative test scenes to collect all data samples. Once the data is collected, the image quality produced by the proposed level of detail pre-preprocessing approach is compared to Unity's existing level of detail approach using perceptual-based metrics. Methods. The method used is an experiment. Unity's method was chosen because of the popularity of the engine, and it was decided to implement the proposed level of detail pre-preprocessing approach also in Unity to have the most fair comparison with Unity's implementation. The two approaches will only differ in how the level of detail is selected, the rest of the rendering pipeline will be exactly the same. Results. The pre-preprocessing time ranged between 13 to 30 hours. The results showed only a small difference in image quality between the two approaches, Unity's built-in system provides a better overall image quality in two out of three test scenes. Conclusions. Due to the pre-processing time and no overall improvement, it was concluded that the proposed level of detail pre-preprocessing approach is not feasible.

M.Ed. (Educational Psychology) / The purpose of this study was to evaluate the effectiveness of academic support program in the National Diploma Business Administration to determine. It is primarily a literature review but questionnaires were analyzed. Academic support programs at other tertiary institutions studied. There are also different types of academic support programs look. At the Vaal Triangle Technikon is the academic support program in Business Administration phased due to the need to students who exist for the course. Since type as a prerequisite to the course serves, many of them students from attending the course. It also happens that even students to are admitted on the basis of a typing or computer course to a training center or college is not able to cope...

This thesis describes the synthesis of ruthenium based molecular clusters and their characterisation. Chapter 2 introduces the concept that the very large zero-field splitting (D = 2.9 cm–1) in the S = 5/2 ground state of [Ru2Mn(μ3-O)(tBuCO2)6(py)3] can be modelled by antisymmetric exchange effects. This is supported by measurement of the single ion D values from the Fe2Mn analogue. The same model is applied to the Ru2Ni analogue to describe the zero-field splitting in the S = 1 ground state, (DGS = +8.0 cm–1 from DNi = -4.0 cm–1) in Chapter 3.Chapters 3 and 4 give the full characterisation of each of the two families, [MIII2MII(μ3-O)(tBuCO2)6(py)3] (MIII = Ru or Fe, MII = Mn, Co, Ni or Zn), through IR, electronic absorption and NMR spectroscopy and are structurally characterised by X-ray diffraction. The total spin ground states and zero-field splitting of those ground states have been ascertained by SQUID magnetometry and EPR spectroscopy. Due to the redox activity of the Ru2M complexes chemical oxidations led to the isolation of [RuIII2CoIIIO(tBuCO2)6(py)3]+ (5) and [RuIIIRuIVNiIIO(tBuCO2)6(py)3]+ (6); the locus of their oxidation was determined with the aid of X-ray absorption spectroscopy (XAS).Chapter 5 shows that due to the ease of the substitution of the terminal ligand in Ru2M they can be linked to other molecular clusters with N-donor ligands, in this case [Cr7NiF8(tBuCO2)15(O2CC5H4N)][NH2Pr2] in order to synthesise [Ru2NiO(tBuCO2)6(py)(Cr7NiF8(tBuCO2)15(O2CC5H4N))2][NH2Pr2]2. In situ oxidation experiments have also been carried out to assess the switchabilty of the redox active linker. Chapter 6 demonstrates a new structural archetype for tetranuclear ruthenium mixed-metal complexes, with the formula, [Ru2M2(µ3-OH)2(tBuCO2)7(py)4], where M is either Co (1) or Ni (2). SQUID magnetometry and EPR spectroscopy have determined the spin ground states as, Seff = 1/2 in 1 and S = 3/2 in 2. The magnetic anisotropy in 2 has been determined as +2.02 cm–1 for the S = 3/2 ground state.

The Vaal Triangle is renowned for its highly industrialised activities. With the addition of domestic fuel burning, vehicle exhaust, mining and agricultural activities, the Vaal Airshed has become highly polluted. The concerns of the elevated concentrations in the area were raised by the Department of Environmental Affairs and Tourism (DEAT) when the Vaal Region was declared the first priority area on 21 April 2006. The basis for this declaration includes: areas that exceed or may exceed air quality standards, areas associated with significant air quality impacts and areas requiring specific air quality management actions to rectify the situation. The purpose of this study is to determine the Status Quo of the Vaal Airshed. The emissions inventory for the study area includes industrial operations, mining activities, domestic fuel burning and vehicle tailpipe emissions along major national and regional routes. Priority pollutants (i.e. sulphur dioxide, nitrogen dioxide and inhalable particulate matter) are assessed with the aid of the US Environmental Protection Agency approved CALPUFF modelling suite, a non-steady-state Lagrangian Gaussian puff dispersion model. From the dispersion simulations an air quality impact assessment is undertaken. The major findings of the air quality assessment indicate that particulate concentrations are elevated over most areas of the Vaal Airshed, particularly in residential areas where domestic coal burning occurs and areas neighbouring major industrial operations. Similarly, elevated sulphur dioxide concentrations occur over industrial and domestic coal burning areas. Elevated nitrogen dioxide concentrations have a regional impact over the Vaal Airshed. Priority areas are identified based on the predicted ambient air concentrations from the priority pollutants and exposure potential. Source contributions are investigated based on the extent of their emissions and basis of impacts. Copyright / Dissertation (MSc)--University of Pretoria, 2009. / Geography, Geoinformatics and Meteorology / Unrestricted

Triangle counting is a major graph problem with several applications in social network analysis, anomaly detection, etc. A considerable amount of work has contributed to approximately computing the global triangle counts using several computational models. One of the most popular streaming models considered is Edge Streaming in which the edges arrive in the form of a graph stream. We categorize the existing literature into two categories: Fixed Memory (FM) approach, and Fixed Probability (FP) approach. As the size of the graphs grows, several challenges arise such as memory space limitations, and prohibitively long running time. Therefore, both FM and FP categories exhibit some limitations. FP algorithms fail to scale for massive graphs. We identified a limitation of FM category $i.e.$ FM algorithms have higher computational time than their FP variants. In this work, we present a new category called the Hybrid approach that overcomes the limitations of both FM and FP approaches. We present two new algorithms that belong to the hybrid category: Neighbourhood Hybrid Multisampling (NHMS) and Triest/ThinkD Hybrid Sampling (THS) for estimating the number of global triangles in graphs. These algorithms are highly scalable and have better running time than FM and FP variants. We experimentally show that both NHMS and THS outperform state-of-the-art algorithms in space-efficient environments. / Graduate

Business owners' lack of strategies to prevent and detect occupational fraud in small retail businesses in the United States could result in substantial financial losses or insolvency. Grounded in Cressey's fraud triangle, the purpose of this multiple case study was to explore internal control strategies 6 owners of small retail businesses in southeastern Pennsylvania used to prevent and detect occupational fraud. Face-to-face interviews, observations, and documentation are the data collection techniques I used in this study. Data were transcribed, coded, analyzed, and member checked to identify emergent themes. Six themes emerged from the thematic analysis: financial impact, transaction responsibility and monitoring, networking and business models, communication, separation of duties, and training. The results of this study indicated areas for action that owners of small retail businesses could take to prevent and detect occupational fraud. Strategies business owners could implement to protect their businesses from occupational fraud include monitoring, employee identity documents to track employee activity, separation of duties, and communication with employees. The implications of this study for positive social change include the potential for social entrepreneurship because small business owners create employment opportunities for members of the community, including high school students with the desire to run small retail businesses. Small business owners serve their communities by focusing on wealth distribution, including donations to local charities that foster economic stability with positive effects on society.