In this report we will calculate the amplitude for a scalar-to-scalars (φ3 <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Crightarrow" /> φ2φ2) decay which involves a triangle loop. We compute the real and imaginary part of the amplitude separately and will argue that this is much more straightforward and practical in this case rather than having to deal with or worry about branch cuts of logarithms. We will derive simple cutting rules closely related to the imaginary part of the amplitude. In doing this, we derive a formula that deals with expressions of the form δ[f(x,y)]δ[g(x,y)], containing two Dirac delta functions.

On étudie une sous-classe des suites b-multiplicatives rarefiées avec un pas de raréfaction p premier, et on trouve une structure asymptotique avec un exposant alphain]0,1[ et une fonction de raréfaction continue périodique. Cette structure vaut pour les suites qui contiennent des nombres complexes du disque unité (section 1.1), et aussi pour des systèmes de numération avec b chiffres successifs positifs et négatifs (section 1.2). Ce formalisme est analogue à celui décrit (pour le cas particuler de la suite de Thue-Morse) par Gelfond; Dekking; Goldstein, Kelly, Speer; Grabner; Drmota, Skalba et autres. Dans la deuxième partie, largement indépendante, on étudie la raréfaction dans les suites composées de -1,0 et +1. On se restreint davantage au cas où b engendre le groupe multiplicatif modulo p. Cette hypothèse est conjecturée (Artin) d'être vraie pour une infinité de nombres premiers. Les constantes qui apparaissent s'expriment alors comme polynômes symétriques des P(zeta^j) où P est un polynôme à coefficients entiers, zeta est une racine primitive p-ième de l'unité, $j$ parcourt les entiers de 1 à p-1 (ce lien est explicité dans la section 1.3). On définit une méthode pour étudier les valeurs de ces polynômes symétriques, basée sur la combinatoire, notamment sur le problème de comptage des solutions des congruences et des systèmes linéaires modulo p avec deux conditions supplémentaires: les résidus modulo p utilisés doivent être non nuls et différents deux à deux. L'importance est donnée à la différence entre les nombres de soluions de deux congruences qui ne diffèrent que du terme sans variable. Le cas des congruences de la forme $x_1+x_2+...+x_n=i mod p$ équivaut à un résultat connu. Le mémoire (section 2.2) lui donne une nouvelle preuve qui en fait une application originale de la formule d'inversion de Möbius dans le p.o.set des partitions d'un ensemble fini. Si au moins deux coefficients distincts sont présents, on peut classer les réponses associées à toutes les congruences possibles qui ont un ensemble fixe de coefficients (de taille d), dans un tableau qu'on va appeler un "simplexe de Pascal fini". Ce tableau est une fonction delta:N^d->Z restreinte aux points de somme des coordonnées inférieure à p (un simplexe), avec deux propriétés: l'équation récursive de Pascal y est vérifiée partout sauf les points où la somme des coefficients est multiple de p (qui seront appelés les "sources" et forment un sous-réseau de l'ensemble des points entiers), et les valeurs en-dehors du simplexe induites par l'équation sont nulles (c'est démontré, en réutilisant la méthode précédente, dans la section 2.3 et en partie 2.4). On décrit un algorithme (section 2.4) qui consiste en applications successives de l'équation dans un ordre précis, qui permet de trouver l'unique fonction delta qui vérifie les deux conditions. On applique ces résultats aux suites b-multiplicatives (dans la section 2.5). On montre aussi que le nombre de sources ne dépend que de la dimension du simplexe d et de la longueur de son côté p. On formule la conjecture (partie 2.6) qu'il serait le plus petit possible parmi les tableaux de forme d'un simplexe de la dimention fixe et taille fixe qui vérifient les mêmes conditions. On montre un premier résultat sur les systèmes de deux congruences linéaires (section 2.5.4), et on montre (section 1.4) un lien avec une méthode de Drmota et Skalba pour prouver l'absence de phénomène de Newman (dans un sens précis), décrit initialement pour la suite de Thue-Morse et tout p tel que b engendre le groupe multiplicatif modulo p, et généralisé (section 1.4) à la suite (-1)^{nombre de chiffres 2 dans l'écriture en base 3 de n} appelée "++-". Cette problématique est riche en problèmes d'algorithmique et de programmation. Différentes sections du mémoire sont illustrées dans l'Annexe. La plupart de ces figures sont inédites.

Abstract Introduction: H.J.-Haase developed a systematic set of tests for evaluating binocular vision called the Pola Test. The Pola Test measures associated phoria and stereoacuity at distance and near using a variety of different targets for each. This testing method and interpretation is referred to as MKH-Haase (Measuring and Correcting Methodology after H.J.Haase ???the MKH) method. The MKH method is more commonly used in Germany and other European countries than English speaking countries. The MKH-Haase method has been considered a reliable method for prescribing prisms to symptomatic binocular vision patients. Purpose: To investigate the test-retest reliability of binocular vision measurements using the MKH-Haase series of tests that comprise the Pola Test. In addition, I will compare the Pola results with other associated phoria and stereoacuity tests used in North America. Methods: Thirty-four symptomatic and 40 asymptomatic subjects (based on a symptoms questionnaire) participated in this study. Associated phoria and stereoacuity with different tests, including the Pola Test at distance and near, were measured for those subjects on two different sessions. Not all of subjects were tested with all tests. Only 30 subjects in each group completed all of tests. The Pola Test protocol requires the associated phoria and stereoacuity to be measured twice within a session; once with the Polariods oriented with their axes at 45o and 135o and again with the axes switched. Results: Within and between-sessions repeatability of MKH-Haase associated phoria and stereoacuity tests results revealed that most of MKH-Haase associated phoria and stereoacuity tests showed good repeatability within and between-sessions at both distance and near. However, there were a few exceptions to this general finding. Distance horizontal associated phoria values for the Cross Test and Pointer Test at the first session, and the distance Double Pointer Test values at the second session showed some differences between the two views. Between-sessions repeatability of the associated phoria tests did not show any significant differences. For the stereoacuity tests, the differences between the two disparities were statistically significant at the first session for the symptomatic group Line Test and asymptomatic group Step Test. For the second session at distance, the differences were significant with Step Test for both groups. The differences between sessions for both disparities were not significant for most of tests. The symptomatic group???s Step Test for crossed disparity and asymptomatic group's Step Test for uncrossed disparity were exceptions. A repeated measures ANOVA test was conducted to compare different associated phoria tests. Horizontal associated phoria tests without central fusion lock were significantly different from those with central fusion lock at distance and near. Comparison of different stereoacuity tests was conducted by comparing the number of subjects who could identify specific stereothreshold values. Results showed that at both distance and near, there were no significant differences between contour and global stereoacuity tests based on number of subjects who could attain 60 sec of arc or better. Discussion and Conclusion: Most of MKH-Haase associated phoria and stereoacuity charts have reasonable within and between-sessions repeatability. However, some associated phoria tests showed some differences especially with subjects who had higher values. Although there was a significant difference between various horizontal associated phoria tests at distance and near, most of the values differed by around 0.50 ???. The exception was the difference between the Wesson Card and Disparometer. The Wesson card was more exo by 1.50 ??? than the Disparometer. Vertical associated phoria tests did not show any significant differences. Although MKH-Haase chart can measure local stereothreshold down to 10 sec of arc at distance, the AO Slide is easier to perceive. Random dot stereoacuity can be measured with MKH-Haase charts at distance down to 30 sec of arc. All of the contour stereoacuity tests are comparable at near. However, the MKH-Haase chart was easier to perceive. The Random Dot Randot test would be more useful for fast screening purposes. Random dot MKH-Haase test would be easier than TNO Test to measure random dot stereothreshold at near.

Water resources in South Africa are scarce, and should therefore be protected against pollutants, also from persistent organic pollutants (POPs). This is emphasised by the Stockholm Convention on POPs, which aims at reducing and ultimately eliminating POPs. South Africa signed and ratified the treaty, and it became international law on 17 May 2004. POPS are highly stable, toxic, hydrophobic and lipophilic compounds, with the ability to accumulate in biological tissues. Previous research had shown that dioxin-like POPS are present in the aquatic environments of South Africa, with the highest concentrations of these substances measured in industrialised areas of South Africa. The present study aimed at investigating the extent of polychlorinated dibenzo-para-dioxin (PCDD), polychlorinated dibenzo-furan (PCDF) and polychlorinated biphenyl (PCB) pollution in the Vaal Triangle, by targeting aquatic sediments and biota. Sediment samples were collected from the Blesbok Spruit, Taaibos Spruit, Leeu Spruit and Suikerbosrand River, and fish tissue samples were collected from Blesbok Spruit and Suikerbosrand River, to determine bio-accumulation. The samples were extracted with organic solvents, cleaned-up and fractionated. Raw extracts and fractions were analysed with the H4IIE-luc reporter gene bio-assay. This bio-assay is a rapid, sensitive and relatively cost-effective method, which measures the effects of dioxin-like compounds on rat hepatoma cells, transfected with firefly luciferase gene. Selected samples were analysed with gas chromatographylmass spectrometry (GCIMS) to confirm results. Only one site had quantifiable amounts of dioxin-like substances in the sediment, measured to be 52.35 ng/kg [Effective Concentration 50 (EC 50)]. This value exceeds many of the European and USA quality guidelines, proposed for sediments. No dioxin-like substances were found in fish tissues. The absence of PCDD/Fs and PCBs in aquatic sediments and fish tissues from the Vaal Triangle area might be due to the climatic conditions of the area, dilution effects in streams, and degradation of these compounds by UV-radiation and microbial organisms. / Thesis (M. Environmental Science (Water Science))--North-West University, Potchefstroom Campus, 2007.

The primary objective of this study was to identify and investigate the main restrictions automation suppliers encounter when attempting to promote and sell their products into the local Vaal Triangle manufacturing industry. Through the literature study that was conducted, a general investigation into the supply chains of some of the most prominent manufacturing industries within the geographical demarcation were analysed. Two manufacturing industries were chosen namely Sasol and Rand Water. The different criteria upon which they qualify their suppliers were identified and the reasoning behind it discussed. The identified criteria included product compliance restrictions; commercial restrictions as well as limitations placed on suppliers by the consumer themselves where suppliers are restricted to only a few per product or service. The commercial restrictions were identified as the only restrictions the supplier has total control over and for this reason, was investigated in detail. These commercial restrictions included the supplier's NOSA, ISO and CIDB rating, as well as their BBBEE status. After the literature review, an empirical study was conducted by making use of a questionnaire which was developed alongside the conduction of the literature study. This questionnaire was sent out to the top management of the identified local automation suppliers to be filled out. The completed questionnaires were analysed by the Statistical Consultation Services of the North-West University (Potchefstroom campus). After the reliability and validity of the questionnaire had been determined, the basic demographical information of the respondents was analysed. An assessment of the 12 constructs measured in the study was done and the relationships between the demographic variables and the constructs were identified. Following the detailed analysis, conclusions on the demographic information of the respondents as well as between all the demographic variables and the constructs measured which had practical significance were discussed. Practical recommendations regarding compliance to the commercial restriction studied were made. The success of the study was determined mainly based on the achievement of the primary and secondary objectives. The study concluded by making suggestions for further research on the topic at hand. / Thesis (M.B.A.)--North-West University, Potchefstroom Campus, 2011.

Various data structures have been proposed for representing the connectivity of manifold triangle meshes. For example, the Extended Corner Table (ECT) stores V+6T references, where V and T respectively denote the vertex and triangle counts. ECT supports Random Access and Traversal (RAT) operators at Constant Amortized Time (CAT) cost. We propose two novel variations of ECT that also support RAT operations at CAT cost, but can be used to represent and process Simplicial 2-Complexes (S2Cs), which may represent star-connecting, non-orientable, and non-manifold triangulations along with dangling edges, which we call sticks. Vlist stores V+3T+3S+3(C+S-N) references, where S denotes the stick count, C denotes the number of edge-connected components and N denotes the number of star-connecting vertices. Ering stores 6T+3S+3(C+S-N) references, but has two advantages over Vlist: the Ering implementation of the operators is faster and is purely topological (i.e., it does not perform geometric queries). Vlist and Ering representations have two principal advantages over previously proposed representations for simplicial complexes: (1) Lower storage cost, at least for meshes with significantly more triangles than sticks, and (2) explicit support of side-respecting traversal operators which each walks from a corner on the face of a triangle t across an edge or a vertex of t, to a corner on a faces of a triangle or to an end of a stick that share a vertex with t, and this without ever piercing through the surface of a triangle.

Water resources in South Africa are scarce, and should therefore be protected against pollutants, also from persistent organic pollutants (POPs). This is emphasised by the Stockholm Convention on POPs, which aims at reducing and ultimately eliminating POPs. South Africa signed and ratified the treaty, and it became international law on 17 May 2004. POPS are highly stable, toxic, hydrophobic and lipophilic compounds, with the ability to accumulate in biological tissues. Previous research had shown that dioxin-like POPS are present in the aquatic environments of South Africa, with the highest concentrations of these substances measured in industrialised areas of South Africa. The present study aimed at investigating the extent of polychlorinated dibenzo-para-dioxin (PCDD), polychlorinated dibenzo-furan (PCDF) and polychlorinated biphenyl (PCB) pollution in the Vaal Triangle, by targeting aquatic sediments and biota. Sediment samples were collected from the Blesbok Spruit, Taaibos Spruit, Leeu Spruit and Suikerbosrand River, and fish tissue samples were collected from Blesbok Spruit and Suikerbosrand River, to determine bio-accumulation. The samples were extracted with organic solvents, cleaned-up and fractionated. Raw extracts and fractions were analysed with the H4IIE-luc reporter gene bio-assay. This bio-assay is a rapid, sensitive and relatively cost-effective method, which measures the effects of dioxin-like compounds on rat hepatoma cells, transfected with firefly luciferase gene. Selected samples were analysed with gas chromatographylmass spectrometry (GCIMS) to confirm results. Only one site had quantifiable amounts of dioxin-like substances in the sediment, measured to be 52.35 ng/kg [Effective Concentration 50 (EC 50)]. This value exceeds many of the European and USA quality guidelines, proposed for sediments. No dioxin-like substances were found in fish tissues. The absence of PCDD/Fs and PCBs in aquatic sediments and fish tissues from the Vaal Triangle area might be due to the climatic conditions of the area, dilution effects in streams, and degradation of these compounds by UV-radiation and microbial organisms. / Thesis (M. Environmental Science (Water Science))--North-West University, Potchefstroom Campus, 2007.

The primary objective of this study was to identify and investigate the main restrictions automation suppliers encounter when attempting to promote and sell their products into the local Vaal Triangle manufacturing industry. Through the literature study that was conducted, a general investigation into the supply chains of some of the most prominent manufacturing industries within the geographical demarcation were analysed. Two manufacturing industries were chosen namely Sasol and Rand Water. The different criteria upon which they qualify their suppliers were identified and the reasoning behind it discussed. The identified criteria included product compliance restrictions; commercial restrictions as well as limitations placed on suppliers by the consumer themselves where suppliers are restricted to only a few per product or service. The commercial restrictions were identified as the only restrictions the supplier has total control over and for this reason, was investigated in detail. These commercial restrictions included the supplier's NOSA, ISO and CIDB rating, as well as their BBBEE status. After the literature review, an empirical study was conducted by making use of a questionnaire which was developed alongside the conduction of the literature study. This questionnaire was sent out to the top management of the identified local automation suppliers to be filled out. The completed questionnaires were analysed by the Statistical Consultation Services of the North-West University (Potchefstroom campus). After the reliability and validity of the questionnaire had been determined, the basic demographical information of the respondents was analysed. An assessment of the 12 constructs measured in the study was done and the relationships between the demographic variables and the constructs were identified. Following the detailed analysis, conclusions on the demographic information of the respondents as well as between all the demographic variables and the constructs measured which had practical significance were discussed. Practical recommendations regarding compliance to the commercial restriction studied were made. The success of the study was determined mainly based on the achievement of the primary and secondary objectives. The study concluded by making suggestions for further research on the topic at hand. / Thesis (M.B.A.)--North-West University, Potchefstroom Campus, 2011.

Οι μετασχηματιστές ισχύος αποτελούν τα κρισιμότερα στοιχεία ενός Συστήματος Ηλεκτρικής Ενέργειας από την άποψη κόστους, χρησιμότητας και επικινδυνότητας. Επομένως είναι ιδιαίτερα σημαντικός ο έλεγχος της υγείας των μετασχηματιστών και της λειτουργικής τους ικανότητας. Η παρούσα διπλωματική εργασία ασχολείται με το διαγνωστικό έλεγχο των μεγάλων μετασχηματιστών ελαίου. Για το σκοπό αυτό θεωρείται αναγκαίο να γίνει πρώτα μία αναλυτική αναφορά στους μετασχηματιστές και στις ιδιότητές τους. Στο κεφάλαιο 1 γίνεται μία σύντομη εισαγωγή σχετική με τα Σ.Η.Ε. ώστε να καταστεί σαφής ο ρόλος των μετασχηματιστών σε αυτά. Στο κεφάλαιο 2 περιγράφονται λεπτομερώς οι αρχές λειτουργίας και τα κατασκευαστικά στοιχεία των μετασχηματιστών καθώς και τα προβλήματα που προκύπτουν σε αυτούς εξαιτίας της λειτουργίας τους ή από την πάροδο των ετών. Το κεφάλαιο 3 ασχολείται με τη λειτουργική κατάσταση και τη διάρκεια ζωής των μετασχηματιστών και την εξάρτησή τους από την κατάσταση της μόνωσης. Στο κεφάλαιο 4 παρατίθενται όλες οι κλασικές μέθοδοι που χρησιμοποιούνται για την παρακολούθηση και τη διάγνωση σφαλμάτων στους μετασχηματιστές. Επίσης περιγράφονται η κατάταξη των μετασχηματιστών ανάλογα με την ικανότητά τους να παραμείνουν σε λειτουργία και η ένταξη της παρακολούθησής τους στον έλεγχο του συστήματος. Το κεφάλαιο 5 επικεντρώνεται στη μέθοδο Duval, μία μέθοδο διάγνωσης που συγκαταλέγεται στην κατηγορία των Χημικών Μεθόδων και ειδικότερα της Ανάλυσης των Διαλυμένων Αερίων στο λάδι. Στο κεφάλαιο αυτό γίνεται η περιγραφή της μεθόδου και η παράθεση του προγράμματος που εφαρμόζει τη μέθοδο. Τα παραρτήματα αποσαφηνίζουν κάποιες λεπτομέρειες σχετικές με τη μέθοδο Duval, χρήσιμες για την κατάστρωση του κώδικα. / Power transformers are the most critical components of an Electric Power System (E.P.S.) as far as their cost, usefulness and level of risk are concerned. Therefore their maintenance as well as their health and ability to stay in service check are of great importance. This thesis deals with the diagnostics of large oil immersed transformers. Consequently it is considered necessary to begin with a detailed description of power transformers and their attributes. In Chapter 1 a short introduction of E.P.S. is taking place in order to clarify the role of power transformers in them. In Chapter 2 the principles of operation, the manufacturing elements as well as the malfunctions that occur in a transformer because of their use or in the course of time are described in detail . Chapter 3 deals with the operation condition, life-span and the dependency of a transformer on the insulation system condition. In Chapter 4 all the common used techniques for condition monitoring and fault diagnosis of a transformer are displayed. Furthermore the order of the transformers depending on their ability to maintain in operative condition is described as well as the incorporation of their monitoring in the system inspection. Chapter 5 is focused on the Duval method which is a chemical method for fault diagnosis and more specifically a dissolved gas analysis. In this chapter the Duval method is described in detail along with the description of the program that uses this method. The adjuncts clarify some details regarding the Duval method which are necessary for the comprehension of the program.

The Northern Triangle area made up by El Salvador, Guatemala, and Honduras faces a growing gang phenomenon responsible for the growth of violence and instability in the region. Many factors have contributed to the rise of gangs in the region, however, I argue that the deportation of Central American immigrants who became active gang members in the United States play a significant role in the growth of gangs. I analyze the impact of the lack of collaboration between the United States and the nations of the Northern Triangle, especially in the lack of reintegration programs and the other factors that could have influenced or spurred the escalation of gang activity such as a failed recovery process following the civil wars of the 1970s and 1980s and the state repression policies. Furthermore, I assess how the lack of collaboration between the United States and Northern Triangle region in the deportation of criminal immigrants has impacted the transnationalization of the two largest Central American gangs, Mara Salvatrucha and Barrio 18. Due to the lack of quantitative data on gang size and membership, I conduct my analysis utilizing various studies that have been conducted in the three nations and data regarding homicide and deportation rates. Ultimately, I find that while the U.S. deportees played an important role in altering the characteristics and nature of Central American gangs, a variety of other factors were significant in their growth. Additionally, I find their assignation as Transnational Criminal Organizations premature and inconclusive due to their weak organizational and communication structure. Finally, I question whether gangs are truly the cause of high levels of violence in each of the nations of the Northern Triangle, determining that the Central American gang phenomenon cannot be assessed or treated as a singular issue. Instead, it is imperative to acknowledge the conditions at play in each country.