The parastrophic matrix and Weak Cayley Tables are matrices that have close ties to the character table. Work by Ken Johnson has shown that fusion of groups induces a relationship between the character tables of the groups. In this paper we will demonstrate a similar induced relationship between the parastrophic matrices and Weak Cayley Tables of the fused groups.

The focus of this thesis is an investigation of ways to detect weak dependence between two random variables X and Y. Our approach is to design tests for correlation rather than testing for dependence directly, since X and Y are not independent if they are not uncorrelated. We examined the magnified Pearson correlation after the Box-Cox transformation to determine whether X and Y are dependent. The results indicated that our approach not only has the potential to detect and evaluate the weak dependence cases that have previously been intractable, but also is conceptually simple and easy to implement.

The primary purpose of this study was to identify dimensions of weak tie relationships including characteristics (e.g., distinctive qualities, traits, or properties), functions (e.g., outcomes, purposes, or meanings derived from the interaction) and determinants of engagement to gain insight into the weak tie exchange process and develop frameworks that can be used to operationalize the concept. Data were collected through stories provided by participants during face-to-face interviews. Respondents recounted a situation when someone they did not know well and to whom they did not feel particularly close provided them with assistance. Over 70 stories were collected from 50 adults aged 65 and older who were active in their community. Stories collected were analyzed using an inductive approach that was supported by the concepts of interpersonal tie strength, loose connections, social exchange theory, and social support. Findings suggest that weak tie relationships occur in a variety of community settings and in response to a variety of daily challenges. The exchanges occur more frequently with acquaintances than strangers and the initiator of the exchange is generally the person offering support. The types of support offered are broad-based and include instrumental, emotional, and informational support. Weak tie exchanges range from one-time brief interactions to intermittent exchanges over extended periods, depending on the circumstances. Findings also suggest that weak ties have a specific task or purpose, encourage awareness about the value and purpose of social interactions, and influence participants' future social interactions. Six factors were identified as determinants of engagement in weak ties: situational factors, personal characteristics, judgments of responsibility, attitudes about helping behaviors, personal network type, and exchange history. The findings from this study provide a foundation for further conceptualization of weak ties and a framework on which to develop instruments to measure tie strength and the potential for engaging in weak tie exchanges. / Ph. D.

There has being an enormous work on finite quantum systems with variables in Zd, especially on mutually unbiased bases. The reason for this is due to its wide areas of application. We focus on partial ordering of weak mutually un-biased bases. In it, we studied a partial ordered relation which exists between a subsystem ^(q) and a larger system ^(d) and also, between a subgeometry Gq and larger geometry Gd. Furthermore, we show an isomorphism between: (i) the set {Gd} of subgeometries of a finite geometry Gd and subsets of the set {D(d)} of divisors of d. (ii) the set {hd} of subspaces of a finite Hilbert space Hd and subsets of the set {D(d)} of divisors of d. (iii) the set {Y(d)} of subsystems of a finite quantum system ^(d) and subsets of the set {D(d)} of divisors of d. We conclude this work by showing a duality between lines in finite geometry Gd and weak mutually unbiased bases in finite dimensional Hilbert space Hd.

The purpose of this study is to understand the causes of the Sierra Leonean conflict and to analyse the reconstruction programmes that followed it. Post-war reconstruction programmes must not be limited to the re-joining of families or reintegration of communities. It must also go a long way in providing an improved situation for all those affected by the war. Notably, where post-war reconstruction programmes fail to focus on the original causes of the conflict, it may result in reinforcement of the original social structures and prejudices and in continued marginalisation of certain groups. Using post-conflict Sierra Leone as a case study, the study attempts to examine the notion that ¿post-war reconstruction programmes tend to reinforce earlier social structures and prejudices rather than create opportunities for the previously marginalised¿. The work focuses on the role of the Department for International Development (DfID)-funded Community Reintegration Programme (CRP). Considering the Sierra Leone post-war scenarios, the causes and political resolution of the conflict and the situation in 2001 when the conflict officially came to an end, the thesis reviews the philosophy, planning, policies, practices and activities of donor agencies in general and CRP in particular before assessing impact on the process of rebuilding communities in Sierra Leone.

<p> The influence of a logarithmically dependent (van Hove singularity) electronic density of states is studied in the weak-coupling limit. Through analytic and numerical analysis it is found that the model can give rise to temperatures in the 100 K range, and that universal BCS ratios such as 2Δ/kBTC and ΔC/γTC do not change essentially from their constant BCS values. The consequences of this model on the calculation of the isotope effect and specific heat are discussed in detail and compared to recent experimental results.</p> / Thesis / Master of Science (MSc)

Flood cooling is primarily used to cool and lubricate the cutting tool and workpiece interface during a machining process. But the adverse health effects caused by the use of flood coolants are drawing manufacturers' attention to develop methods for controlling occupational exposure to cutting fluids. Microlubrication serves as an alternative to flood cooling by reducing the volume of cutting fluid used in the machining process. Microlubrication minimizes the exposure of metal working fluids to the machining operators leading to an economical, safer and healthy workplace environment. In this dissertation, a vegetable based lubricant is used to conduct mist, microstructure and wear analyses during end milling AISI 1018 steel using microlubrication. A two-flute solid carbide cutting tool was used with varying cutting speed and feed rate levels with a constant depth of cut. A full factorial experiment with Multivariate Analysis of Variance (MANOVA) was conducted and regression models were generated along with parameter optimization for the flank wear, aerosol mass concentration and the aerosol particle size. MANOVA indicated that the speed and feed variables main effects are significant, but the interaction of (speed*feed) was not significant at 95% confidence level. The model was able to predict 69.44%, 68.06% and 42.90% of the variation in the data for both the flank wear side 1 and 2 and aerosol mass concentration, respectively. An adequate signal-to-noise precision ratio more than 4 was obtained for the models, indicating adequate signal to use the model as a predictor for both the flank wear sides and aerosol mass concentration. The highest average mass concentration of 8.32 mg/m3 was realized using cutting speed of 80 Surface feet per minute (SFM) and a feed rate of 0.003 Inches per tooth (IPT). The lowest average mass concentration of 5.91 mg/m3 was realized using treatment 120 SFM and 0.005 IPT. The cutting performance under microlubrication is five times better in terms of tool life and two times better in terms of materials removal volume under low cutting speed and feed rate combination as compared to high cutting speed and feed rate combination. Abrasion was the dominant wear mechanism for all the cutting tools under consideration. Other than abrasion, sliding adhesive wear of the workpiece materials was also observed. The scanning electron microscope investigation of the used cutting tools revealed micro-fatigue cracks, welded micro-chips and unusual built-up edges on the cutting tools flank and rake side. Higher tool life was observed in the lowest cutting speed and feed rate combination. Transmission electron microscopy analysis at failure for the treatment 120 SFM and 0.005 IPT helped to quantify the dislocation densities. Electron backscatter diffraction (EBSD) identified 4 to 8 µm grain size growth on the machined surface due to residual stresses that are the driving force for the grain boundaries motion to reduce its overall energy resulting in the slight grain growth. EBSD also showed that (001) textured ferrite grains before machining exhibited randomly orientated grains after machining. The study shows that with a proper selection of the cutting parameters, it is possible to obtain higher tool life in end milling under microlubrication. But more scientific studies are needed to lower the mass concentration of the aerosol particles, below the recommended value of 5 mg/m3 established by Occupational Safety and Health Administration (OSHA).

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