In 1974, H. Ruderman posed the following question: If $(2^m-2^n)|(3^m-3^n)$, then does it follow that $(2^m-2^n)|(x^m-x^n)$ for every integer $x$? This problem is still open. However, in 2011, M. R. Murty and V. K. Murty showed that there are only finitely many $(m,n)$ for which the hypothesis holds. In this thesis, we examine two generalizations of this problem. The first is replacing 2 and 3 with arbitrary integers $a$ and $b$. The second is to replace 2 and 3 with arbitrary algebraic integers from an imaginary quadratic field. In both of these cases we have shown that there are only finitely many $(m,n)$ for which the hypothesis holds. To get the second result we also generalized a result by Bugeaud, Corvaja and Zannier from the integers to imaginary quadratic fields. In the last half of the thesis we use the abc conjecture and some related conjectures to study some exponential Diophantine equations. We study the Pillai conjecture and the Erd\"{o}s-Woods conjecture and show that they are implied by the abc conjecture and that when we use an effective version, very clean bounds for the conjectures are implied. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-04-13 12:04:14.252

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ABC Consulting Services is a Consulting Engineering firm based in Pietermaritzburg. Primary and secondary research was conducted in an attempt to identify the key marketing issues that ABC Consulting Services faces in its internal and external environments. The primary research done on the company (micro factors) and its environment (macro factors) was in the form of qualitative descriptive research with the source of information coming from internal semi structured focus groups and questionnaires sent to selected individuals involved in the consulting engineering industry. The secondary research includes a study of the current state of the South African Consulting Engineering industry. The content analysis of the primary and secondary research resulted in the identification of six key threats in the macro environment and five main opportunities for the company to increase its current work. The key threats identified are the lack of engineering skills, the lack of skills in the client organisations, inexperienced firms in the market, tendering processes and slow payment from clients. With further unpacking of these issues, it was found that many of the issues are as a result of the lack of skills in client organisations. The opportunities identified include agricultural development for historically disadvantaged individuals, the relatively low value of the Rand making the company's services cheaper for internationally funded projects, increased infrastructure budgets as a result of the 2010 Soccer WorId Cup, agricultural development in Africa and an increase in floodline determination work. The internal resource analysis identified that that the company is very strong in terms of the quality of its human resources; however, it is under staffed for the current work load. Financially, the company is in a good position and the current environment should continue to yield very good returns in the short to medium term, however, the firm is inflexible in terms of financial commitments. The firms lack of formal marketing systems and their low client and contact bases in Government departments were identified as weaknesses. The company's facilities and processes are good and represent a strength, however there are some procedures such as quality management systems which need to be implemented. It is recommended that the company institute formal marketing procedures and market themselves to prospective clients by means of networking and doing presentations to selected prospective clients in order to inform them of the service that the company has to offer. The company should also do limited advertising in selected specialist magazines which deal with irrigation and the sugar industry. In order to establish themselves as leaders in sugarcane estate development, they should write and present papers at the annual SASTA conferences. To promote the profession, they should do presentations at high school level to encourage high school students to study engineering and at a University level; the company should offer their services to the local University for lecturing certain modules of suitable courses. This can be used as a platform for promoting the profession to the students to encourage them to stick to engineering as a career. To solve the staff shortage problem, the company should recruit two new engineers, one with approximately 3 years relevant experience and another with approximately 5 years relevant experience. / Thesis (M.B.A.)-University of KwaZulu-Natal, Pietermaritzburg, 2006.

ATP-binding cassette transporters ABCA1 and ABCG1 initiate reverse cholesterol transport generating HDL particles, whereas ABCG5/G8 promote biliary cholesterol secretion thereby facilitating the last step of reverse cholesterol transport. Mutations in the leptin axis result in obesity and dyslipidemia in ob/ob and db/db mice. These mice have defective HDL clearance, increased plasma cholesterol and decreased biliary cholesterol elimination. My studies demonstrate that ABCG5/G8 protein is low in these animals and can be restored with caloric restriction or leptin replacement. To directly test whether ABCG5/G8 alone is able to correct reverse cholesterol transport defect, liver specific ABCG5/G8 expression was achieved in db/db mice by administration of adenoviral ABCG5 and ABCG8. Restoration of biliary cholesterol is able partially to correct dyslipidemia in obese mice, but only in the presence of ezetimibe, an inhibitor of cholesterol absorption. ABCG5/G8 is the body’s primary defense against toxic effects of plant sterols. Plant sterols are used as cholesterol lowering food supplements. However, increased plasma plant sterol concentrations are associated with vascular lesions in dyslipidemic patients and animals. My in vitro studies demonstrate that individual plant sterol alter ABCA1 and ABCG1 abundance, cholesterol efflux and inflammatory cytokine secretion in macrophage foam cells at levels found in humans that consume plant sterol supplements.

Multidrug resistance-associated protein 1 (MRP1) is a member of the adenosine 5’-triphosphate (ATP)-binding cassette (ABC) transporters. MRP1 actively effluxes a variety of endogenous and exogenous substrates from cells, ultimately, working to remove these compounds from the body. MRP1 was initially discovered based on its ability to confer resistance against a variety of chemotherapeutics when overexpressed in cancer cells lines. MRP1 function is important for a number of physiological processes, including regulating cellular and extracellular levels of the anti-inflammatory leukotriene C4 (LTC4) and the antioxidant glutathione (GSH). Our studies have focused on the role of MRP1 in regulating hematopoietic stem cell (HSC) self-renewal and differentiation and the role of CK2 as a regulator of MRP1 function. Reactive Oxygen Species (ROS) cellular levels are tightly regulated and fluctuations in ROS levels affect many cellular processes, including the self-renewal and differentiation of hematopoietic stem cells and kinase signaling pathways. MRP1 regulates ROS through the transport of reduced and oxidized GSH. MRP1 is highly expressed in HSCs, therefore we hypothesized that MRP1 regulates ROS levels in HSCs via efflux of GSH. We have shown that MRP1 regulates HSC self-renewal by modulating cellular ROS via the efflux of GSH. The decrease in ROS results in downregulation of p38 activity and altered expression of a number of redox response genes. CK2 is a master regulator of the cell and controls cell growth, proliferation, death and survival. Yeast studies from our lab using Ycf1p (a homologue of MRP1) and Cka1p (a homologue of CK2) have found that Cka1p regulates Ycf1p function. This result suggests that CK2 regulates MRP1 function via phosphorylation. We have found that CK2 does regulate MRP1 function via phosphorylation of the N-terminal extension at Thr249. Using A549, H460, and HeLa cancer cell lines, we found that inhibition of CK2 with tetrabromobenzimidazole (TBBz) reduces MRP1 function and increases cellular toxicity to known MRP1 substrates.

ABCD2 (D2) has been proposed as a peroxisomal long-chain acyl-CoA transporter that is essential for very long chain fatty acid metabolism. In the livers of mice, D2 is highly induced by fenofibrate, a PPARα ligand that has been widely used as a lipid lowering agent in the treatment of hypertriglyceridemia. To determine if D2 is a modifier of fibrate responses, wild-type and D2 deficient mice were treated with fenofibrate for 14 days. The absence of D2 altered expression of gene clusters associated with lipid metabolism, including PPARα signaling. Using 3T3-L1 adipocytes, which express high levels of D2, we confirmed that knock-down of D2 modified genomic responses to fibrate treatment. We next evaluated the impact of D2 on effects of fibrates in a mouse model of dietinduced obesity. Fenofibrate treatment opposed the development of obesity, hypertriglyceridemia, and insulin resistance. However, these effects were unaffected by D2 genotype. We concluded that D2 can modulate genomic responses to fibrates, but that these effects are not sufficiently robust to alter the effects of fibrates on diet-induced obesity phenotypes. Although proposed as a peroxisomal transporter, the intracellular localization of D2, especially in adipose tissue, has not been validated with direct experimental evidence. Sequential centrifugation of mouse adipose homogenates generated a fraction enriched with D2, but lacked well-known peroxisome markers including catalase, PEX19, and ABCD3 (D3). Electron microscopic imaging of this fraction confirmed the presence of D2 protein on an organelle with evidence of a dense matrix and a diameter of ~200 nm, the typical structure and size of a microperoxisome. D2 and PEX19 antibodies recognized distinct structures in mouse adipose. Immunoisolation of the D2-containing compartment from adipose tissue confirmed the scarcity of PEX19. Proteomic profiling of the D2 compartment revealed the presence of proteins associated peroxisome, endoplasmic reticulum (ER), and mitochondria. We conclude that D2 is localized to a distinct subclass of peroxisomes that lack many peroxisome proteins and may physically associate with mitochondria and the ER.

La zéaralénone (ZEN) est une mycotoxine produite par des Fusarium qui contaminent les cultures céréalières. Oestrogéno-mimétique et perturbateur endocrinien, ses effets toxiques concernent l'appareil reproducteur. En amont de l'évaluation du risque lié à une exposition à de faibles doses de ZEN, nous nous sommes intéressés à l'effet de la ZEN sur le niveau d'expression de transporteurs ABC majeurs. Ces pompes d'efflux sont présentes dans les barrières de l'organisme (notamment les barrières testiculaires et placentaires) où elles jouent un rôle dans la protection des tissus contre la toxicité de leurs substrats xénobiotiques. Dans ce travail nous avons d'abord caractérisé le métabolisme et la distribution tissulaire de la ZEN chez le rat, puis avons évalué son effet respectivement à court et long terme sur l'expression des transporteurs ABC après une exposition gestationnelle et néonatale. Nos résultats mettent en évidence des différences de comportement toxicocinétique de la ZEN en fonction du genre et du statut hormonal, et une réelle exposition fœtale et néonatale via la mère. La ZEN module l'expression des transporteurs ABC majeurs in vivo (dans les organes maternels, le foie foetal, le testicule du jeune adulte exposé J1-J5). Les résultats obtenus sur modèles in vitro (lignées sertolienne et placentaire) suggèrent que ces modulations sont liées en partie à l'interaction de la ZEN avec les récepteurs aux oestrogènes. Les conséquences d'une modulation de l'expression des transporteurs ABC induite par la ZEN pourraient être dramatiques pour le développement et la santé des individus à l'âge adulte et doivent être évaluées

Magistro darbą "Produktų rinkinio formavimas, remiantis pelningumo analize" sudaro 3 dalys, 65 puslapiai, 8 lentelės ir 13 paveikslėlių. Pirmoje dalyje pateikiama gamybinio produkto sąvoka, aiškinamasi produktų gyvavimo ciklo analizės svarba produktų rinkinio formavimui. Kiekvienos įmonės tikslas yra kuo geriau patenkinti savo vartotojų poreikius bei gauti kuo didesnį pelną. Siekdama šio tikslo įmonė turi parinkti pelningus ir paklausius produktus. Vienų produktų realizacijos apimtys gali sudaryti didžiąją dalį apimčių, tačiau nešti mažai pelno. Dėl šios priežasties svarbu išsiaiškinti pelningus produktus ar produktų linijas ir priimti sprendimus dėl jų formavimo. Produktų rinkinio planavimas yra dinamiškas procesas, todėl reikia staigiai reaguoti į rinkos pasikeitimus, vartotojų poreikių kitimą, atsargų valdymą. Taigi, produktų rinkinio analizę būtina atlikti kuo dažniau ir reaguoti į bent kokius rodiklių pakitimus. Šiame darbe bus atliekama UAB „Carlo Gavazzi Industry Kaunas“ kelių pjūvių produktų rinkinio analizė, kurios tikslas pateikti kuo tikslesnius nurodymus dėl nagrinėjamo produktų rinkinio formavimo. Įmonės gaminių struktūros ir produktų rinkinio kitimas daro nemažą įtaką daugeliui kitų ekonominių rodiklių, tokių kaip gamybos apimtys pinigine išraiška (atskirų gaminių kainos skirtingos), medžiagų imlumas, savikaina, pelnas ir pelningumas. Dėl šios priežasties reikia analizuoti produktų rinkinio ir struktūros kitimą bei jų įtaką įmonės veiklos rodikliams... [toliau žr. visą tekstą] / The subject of the work is a product portfolio of production outfit. The work consists of 65 pages. There are 8 tables and 13 pictures. Each company has an intension to meet the requirements of its customers and to make as much profit as it is possible. While achieving this goal a company has to assort profitable and marketable products. It is necessary to improve particular goods or to eliminate certain products from the product portfolio in the process of product portfolio planning. This work includes analysis of few product portfolio sections. The goal of the analysis is to produce precise guidelines on formation of product portfolio under consideration. The aim of the company is to find out which products or product line is profitable and to make a decision because of their planning. Product portfolio planning is a dynamic process either. Variation of production outfits product structure and product portfolio influences many other economic factors such as output in money terms (individual products have different prices), material intensity, cost price, benefit, profitability. Taking chosen production outfit into account, it is necessary to resolve product reduction problem. An enterprise wants to reject some products because of production optimization and profit magnifying. Some product groups were segregated while using methods of product portfolio analysis in this work. Inquiring production outfit has a product portfolio with 1856 product units. The company produces a... [to full text]

The Southern parts of Africa have the highest prevalence of HIV-infected people and South Africa is the country with the highest number of infections in the world. There is still no cure for AIDS, but anti-HIV medicine can prolong and enhance the quality of life of an HIV infected person. Patient adherence with antiretroviral therapy is extremely low due to difficult dosing intervals, problematic dosage forms, instability of the antiretrovirals (ARVs) and the severe side-effects caused by these drugs; this leads to resistance of HIV to these drugs. Pheroid™ technology is a patented delivery system. Pheroid™ vesicles were used during this study. The entrapment of an active within the Pheroid™ would generally provide a safer, more effective formulation than the active alone. This could mean that the amount of drug needed for treatment of HIV can be decreased while producing fewer adverse effects and reducing the price of treatment. The main objectives of this study were to optimise and validate the cell viability and viral replication assays that can be used in an in vitro viral infection model. The MTT assay was used to asses the viability of the cells and to determine the toxicity of the antiretroviral drugs and Pheroid™ on the cells. HIV-1 assays were evaluated and used to determine the viral replication in the cells. Two different continuous cell lines were chosen for this study, an anchorage dependent GHOST cell line and suspended M7-Luc cells. Both these cell lines were best infected with the SWl virus. SWl is a subtype C, CXCR4 utilising virus. Subtype C is responsible for 60 % of the HIV infections worldwide and is the prevalent subtype in SUb-Saharan Africa .. Infection enhancers were not added to the cells to improve viral infection since it was observed that the Pheroid™ in combination with DEAE-dextran or Polybrene caused cytotoxicity probably by disrupting the cell's membrane. Antioxidants were added to the Pheroid ™ formulation since it was observed that the viability of the cells incubated with the Pheroid™ decreased as the Pheroid ™ matured. The added antioxidants had no significant effect on the cells. Abacavir (ABC) was chosen as the test substance for this study since it showed low cytotoxicity in cell cultures and is water soluble and would not present solubility issues in the media. It was entrapped within the Pheroid™ and its in vitro efficacy and toxicity was tested on HIV-infected and uninfected cell cultures. One directlHIV-specific (p24 antigen ELISA assay) and one indirect (Luciferase) assays were used to asses the inhibition of HIV replication caused by ABC. The p24 antigen ELISA (Enzyme-Linked ImmunoSorbent Assay) assay required a lot of washing steps and were rather expensive to use. The Luciferase assay was only used on the M7-Luc cells; this assay was sensitive, inexpensive and easy to use. The MTT (3-(4,5-demethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide) viability assay was used to measure the toxicity caused by the Pheroid ™ and/or ABC on the cells. MTT is a widely used quantitative colorimetric assay to measure the viability of cells. The vitamin E and antioxidants contained in the Pheroid ™ reduced the MTT and produced results that were misinterpreted as enhanced viability when the Pheroid™ was present during MTT analysis. To prevent this problem an additional washing step should be introduced prior to analysis to reduce the interference of the Pheroid ™ with analytical methods. In conclusion, the efficacy of ABC entrapped within the Pheroid™ is still inconclusive and further studies will have to be done. MTT should be used with care for viability analysis of cells incubated in the presence of Pheroid TM. / Thesis (M.Sc. (Pharmaceutics))--North-West University, Potchefstroom Campus, 2009.

The pollution of South Africa’s water resources puts a strain on an already stressed natural resource. One of the main pollution sources is industrial effluents such as acid mine drainage (AMD) and other mining effluents. These effluents usually contain high levels of acidity, heavy metals and sulphate. A popular method to treat these effluents before they are released into the environment is lime neutralisation. Although this method is very effective to raise the pH of the effluent as well as to precipitate the heavy metals, it can only partially remove the sulphate. Further treatment is required to reduce the sulphate level further to render the water suitable for discharge into the environment. A number of sulphate removal methods are available and used in industry. These methods can be divided into physical (membrane filtration, adsorption/ion exchange), chemical (chemical precipitation) and biological sulphate reduction processes. A literature study was conducted in order to compare these different methods. The ABC (Alkali – Barium – Calcium) Desalination process uses barium carbonate to lower the final sulphate concentration to an acceptable level. Not only can the sulphate removal be controlled due to the low solubility of barium sulphate, but it can also produce potable water and allows valuable by–products such as sulphur to be recovered from the sludge. The toxic barium is recycled within the process and should therefore not cause additional problems. In this study the sulphate removal process, using barium carbonate as reactant, was investigated. Several parameters have been investigated and studied by other authors. These parameters include different barium salts, different barium carbonate types, reaction kinetics, co–precipitation of calcium carbonate, barium–to–sulphate molar ratios, the effect of temperature and pH. The sulphate removal process was tested and verified on three different industrial effluents. The results and conclusions from these publications were used to guide the experimental work. A number of parameters were examined under laboratory conditions in order to find the optimum conditions for the precipitation reaction to take place. This included mixing rotational speed, barium–to–sulphate molar ratio, initial sulphate concentration, the effect of temperature and the influence of different barium carbonate particle structures. It was found that the reaction temperature and the particle structure of barium carbonate influenced the process significantly. The mixing rotational speed, barium–to–sulphate dosing ratios and the initial sulphate concentration influenced the removal process, but not to such a great extent as the two previously mentioned parameters. The results of these experiments were then tested and verified on AMD from a coal mine. The results from the literature analysis were compared to the experiments conducted in the laboratory. It was found that the results reported in the literature and the laboratory results correlated well with each other. Though, in order to optimise this sulphate removal process, one has to understand the sulphate precipitation reaction. Therefore it is recommended that a detailed reaction kinetic study should be conducted to establish the driving force of the kinetics of the precipitation reactions. In order to upgrade this process to pilot–scale and then to a full–scale plant, continuous reactor configurations should also be investigated. The sulphate removal stage in the ABC Desalination Process is the final treatment step. The effluent was measured against the SANS Class II potable water standard and was found that the final water met all the criteria and could be safely discharged into the environment. / Thesis (M.Ing. (Chemical Engineering))--North-West University, Potchefstroom Campus, 2012.