MacMahon's Master Theorem is an important result in the theory of algebraic combinatorics. It gives a precise connection between coefficients of certain power series defined by linear relations. We give a complete proof of MacMahon's Master Theorem based on MacMahon's original 1960 proof. We also study a specific infinite dimensional matrix inverse due to C. Krattenthaler.

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<p> Low dimensional quantum magnets which display a collective singlet ground state and a gap in their magnetic excitation spectrum provide a framework for much exotic phase behavior in new materials, with high temperature superconductivity being the best appreciated example. Neutron scattering techniques can be applied to study a wide variety of problems in condensed matter physics. These techniques are particularly useful as applied to understanding the magnetic properties of quantum magnets that display exotic phases.</p> <p> SrCu2(BO3)2, is a rare example of a two-dimensional quantum magnet for which an exact theoretical solution describing its ground state is known to be a collective singlet. Previous high resolution neutron scattering measurements identified the most prominent features of the spin excitation spectrum in SrCu2(BO3)2, including the presence of one and two triplet excitations and weak dispersion characteristic of subleading terms in the spin Hamiltonian.</p> <p> The resemblance between the spin gap behavior in the Mott insulator SrCu2(BO3)2 and that associated with high temperature superconductors motivated the consideration of the significance of doping in order to understand the properties of this quantum magnetic system. For this reason, a series of neutron scattering studies on doped SrCu2(BO3)2 were initiated.</p> <p> These series of investigations began with the performance of neutron scattering measurements on a SrCu(2-x)Mgx(BO3)2 single crystal in order to introduce magnetic vacancies to the system. These results revealed the presence of new spin excitations within the singlet-triplet gap of this system. Application of a magnetic field induces Zeeman-split states associated with un-paired spins which exist as a consequence of doping with quenched non-magnetic impurities. Additional substantial broadening of both the one and two triplet excitations is observed in the doped system as compared to the pure system. Theoretical calculations are shown to qualitatively account for these features.</p> <p> These studies were extended to neutron scattering measurements on Sr(1-x)LaxCu2(BO3)2, with an aim of introducing charged carriers into this system. The broadening of the one and two triplet excitations is observed and compared to the thermally induced finite lifetime of the pure system. The temperature dependence of this broadening in Sr(1-x)LaxCu2(BO3)2 is different compared to that observed in both SrCu2(BO3)2 and SrCu(2-x)Mgx(BO3)2.</p> <p> It has also been suggested that there is a relation between the spin-lattice interaction in SrCu2(BO3)2 and the magnetic dynamics at low temperatures and high magnetic fields. For this reason there has been increased interest in the study of the crystalline structure and vibrational modes of SrCu2(BO3)2. In order to investigate the role of the lattice in the formation of the singlet ground state in SrCu2(BO3)2, a series of low and high energy neutron scattering measurements were carried out on this system to study both the crystalline structure as well as the normal modes of vibration of the lattice, the transverse acoustic and optical phonons. Transverse acoustic phonons with energies comparable to and higher than the onset of the two triplet continuum show substantially increased lifetimes on entering the singlet ground state below ~ 10 K. This may indicate the removal of the decay channel for the phonons due to the gapping of the spin excitation spectrum in SrCu2(BO3)2 at low temperatures. In high energy inelastic neutron scattering we observe broadening of optic phonons in the ~ 52 to 65 meV region on entering the low temperature singlet ground state.</p> <p> Additionally, the magnetic properties of CuMoO4, which is a triclinic quantum magnet system based on S=1/2 moments at the Cu2+ site, were studied using elastic and inelastic neutron scattering experiments. This material exhibits a first order structural phase transition at ~ 190 K as well as a magnetic phase transition at ~ 1.75 K. We were primarily interested in the low temperature magnetic properties of this material. Magnetization and heat capacity measurements as well as elastic and inelastic neutron scattering measurements were conducted on this system within the low temperature ordered phase. These studies confirm that this material has a magnetic phase transition at ~ 1.7 K. Neutron scattering results indicate that this magnetically ordered phase is characterized by a doubling of the a axis. Inelastic neutron scattering measurements revealed a gapped magnetic excitation spectrum in zero magnetic field, which could be filled in by the application of magnetic fields approaching 7 T.</p> / Thesis / Doctor of Philosophy (PhD)

<p> The semiconductor distributed feedback (DFB) laser is mainly characterised by the single-longitudinal-mode operation with a narrow spectral linewidth, which leads to its wide application in fiber-optic communication systems. Several numerical models ranging from physics-based to phenomenological ones have been developed with different level of complexities and for different applications. However, with the continuous improvement in designs of DFB lasers, more efficient simulation methods with sufficient accuracy are highly desirable. In this thesis, I mainly focus on developing new one-dimensional (ID) simulation methods of DFB lasers with improved computational efficiency and physical insight without compromise on accuracy. Further, a new design idea for DFB lasers are explored and investigated by using the simulation techniques developed.</p> <p> Starting with the well-known ID time-dependent coupled-wave equations, we have examined two different solution schemes, i.e. the traveling wave model (TWM) and the standing wave model (SWM). The TWM has the merits of straightforward implementation, and being able to simulate a large variety of the structure even if the laser cavity has a small quality factor (Q-factor). Firstly, the existing time-domain solution schemes are reviewed and compared under a unified framework. A high-order split-step traveling wave method is then developed. Its validity and efficiency are examined through the comparison made with the conventional split-step scheme.</p> <p> For laser structures with large variations of the carrier/photon density, however, the TWM is not computationally economical. The SWM on the other hand has its advantages in dealing with the laser cavity with a relatively large Q-factor. Two different standing wave models are proposed to simulate the index-coupled and gain-coupled DFB lasers, respectively. The complexities of these two numerical models are further reduced through an approximation made on the time-dependent carrier distribution. Finally, the proposed SWMs are reduced to a similar form to the rate equation formulations for establishing the linkage between the 1D model and the rate equation model. More physical insights into the conventional and powerful rate equations will be gained through this linkage.</p> <p> The final part of the thesis focus on the analysis of a novel design of single-mode operation DFB laser employing the dispersive grating. The design idea is verified by the proposed SWM.</p> / Thesis / Doctor of Philosophy (PhD)

<p> The problems of dimensional synthesis and of balancing of linkages are formulated as multifactor optimization problems. Using the new techniques developed in the thesis to solve these problems, a general computer program has been written to be a design aid for such problems. A guide to usage and a complete documentation for this computer program are included in the thesis. </p> / Thesis / Master of Engineering (MEngr)

Narcissism is currently being redefined as a multidimensional construct. While some researchers hold that narcissism remains a unidimensional phenomenon, others have suggested that bi- and tridimensional conceptualizations may better represent the construct as well as align more succinctly with the experiences of individuals with varying levels of narcissistic traits. Also, since the latter conceptualizations offer a broader assessment of narcissistic tendencies, they may provide greater accuracy in identifying differing narcissistic phenotypes (e.g., malignant vs vulnerable). Given the variety in conceptualizations of narcissism, it remains an open area as to how their respective domains are associated with various risk factors and behavioral outcomes, particularly within antagonistic forms of narcissism. This thesis explored the multidimensional approaches to defining narcissism and examined the associations between narcissistic traits and attachment style, self-concept, self-esteem, emotion regulation, and aggression. Also, the current study explored how differences in college degree (business vs. psychology) and gender may influence the expression of narcissism and associations with attachment style. Overall, the study provides results relevant for a tridimensional view of narcissism and adds to the literature on narcissism's link with factors involved in personality pathology, gender, and choice of college degree.

This work aims at improving the previously developed design procedure accounting for anisotropic dimensional changes on sintering. The goal of the project is both enlarging the reference database and investigating in depth the parameters responsible for anisotropic dimensional changes. The effects of green density, geometry, and compaction parameters (compaction speed hold down force and hold down time) on the anisotropy of dimensional changes on sintering were investigated. Ring shaped parts made of eight different iron-based materials were investigated in order to cover a large range of dimensional changes and different sintering mechanisms. The work is divided into two main parts. The first part focuses on investigating the effects of green density and geometry on the anisotropic dimensional changes, also enlarging the database. The application of the design methodology previously developed showed the significant role of anisotropy in the compaction plane for accurate prediction of dimensional changes, which was not highlighted previously. To solve this critical point a new anisotropy parameter is proposed and implemented in the design procedure. With the new anisotropy parameter, prediction of dimensional changes was improved while another critical point was highlighted, which is the scatter in the database. In order to have a reliable design procedure, database must be as accurate as possible, as demonstrated by a careful analysis on data processing. In the second part, the effect of compaction parameters on the anisotropy of dimensional changes on sintering was investigated, with a focus on the anisotropy in the compaction plane highlighted in the first part. No direct correlations were found between anisotropy of dimensional changes and compaction parameters, but compaction settings leading to lower anisotropy in the compaction plane were highlighted. Application of design methodology confirmed that the accuracy of predictions is higher when the sampling is less scattered. Also, a numerical study based on the experimental results was done to evaluate the possibility of neglecting anisotropy in the compaction plane for predicting dimensional changes. It was demonstrated that neglecting anisotropy in the compaction plane is acceptable, for some materials produced using the compaction settings minimizing such anisotropy. Additionally, a correlation between springback during ejection of the parts after compaction and anisotropy in the compaction plane was found.

The automobile industry has set the demand regarding Powder Metallurgy (PM) parts for decades, since this near-net shape technology is a cost-effective manufacturing process allying good mechanical properties with dimensional and geometrical precision. Aiming at the future of the electric automobiles high production and demand, many changes are on the way to guarantee the competitiveness of PM against other manufacturing process. The high costs of alloying elements such as Ni and Cu, the changes in health and safety regulations as well as light weighting of components are the topics of major importance in the field of PM and focus of main R&amp;D around the globe. The use of high temperature sintering and different alloying elements are possible solutions to overcome properties obtained by using Ni as an alloying element sintered at conventional temperatures. Materials with Cr, Mo and Si were investigated using high temperature sintering (1180°C and 1250°) in comparison to traditionally high Ni materials sintered at conventional temperature (1120°C). The dimensional stability, geometrical precision, density, and microstructure of ring-shaped specimens were studied by using a coordinate measuring machine (CMM) and the effect of HTS on the mechanical properties were estimated through the fraction of the load bearing section. The effect of HTS on the dimensional precision and geometrical stability was later investigated in real parts manufactured by industrial partners through an EPMA Club Project. The 4%Ni material sintered at 1120°C was also compared to Ni-less/Ni-free materials sintered at 1250°C using tensile testing, impact testing, and hardness. The use of HTS to improve the mechanical properties without impairing the dimensional and geometrical stability was confirmed in parts with both low and high complexity designs. This project sets the blueprint for future material developments using HTS as manufacturing process.

Listeria monocytogenes is a deadly, Gram-positive foodborne pathogen that is ubiquitous in the environment. The bacterium expresses a number of virulence and stress adaptation proteins that support its pathogenic capabilities. Two-dimensional gel electrophoresis (2-DE) was used to map L. monocytogenes surface proteins, which play a central role in virulence, and to examine protein expression by L. monocytogenes grown on ready-to-eat meat, an important source of Listeria infections. A novel method for solubilization of surface proteins from L. monocytogenes for 2-DE was developed. Additionally, the unique proteome expressed by L. monocytogenes grown on a meat matrix was uncovered. The developed solubilization method will facilitate efforts to identify and routinely compare surface proteins of Listeria by 2-DE. Furthermore, the 2-DE database of proteins expressed by L. monocytogenes grown on a meat matrix will allow further understanding of the interactions of Listeria with its food environment that influence its ability to cause disease.

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