Introduction: The discovery of new solutions to Einstein's field equations has long been a problem in General Relativity. However due to new techniques of Newman and Penrose [1], Carter [2] and others there has been a considerable proliferation of new solutions in recent times. Consequently a new problem has arisen. How are we to interpret the new solutions physically? The tools available, despite a spate of papers in the past fifteen years, remain inadequate although often sophisticated. Any attempts at physical interpretations of metrics are beset with difficulties. There is always the possibility that two entirely different physical pictures will emerge. For example a direct approach would be to attempt an "infilling" of the metric, that is, an extension of the metric into the region occupied by the gravitating matter. However even for the Kerr [1] metric the infilling is by no means unique, in fact a most natural "infilling" turns out to be unphysical (Israel [1]). Yet few people would doubt the physical significance of the Kerr metric. Viewed in this light our attempt to discuss, among other things, the physical interpretation of type D metrics is slightly ambitious. However the problems with regard to this type of metric are not as formidable as for most of the other metrics, since we have been able to integrate the geodesic equations. Nevertheless it is still not possible to produce complete answers to all the questions posed. After a chapter on Mathematical preliminaries the study divides naturally into four sections. We start with an outline of the Hamilton-Jacobi theory of Rund [1] and then go on to show how this theory can be applied to the Carter [2] metrics. In the process we lay a foundation in the calculus of variations for Carter's work. This leads us to the construction of Killing tensors for all but one of the Kinnersley [1] type D vacuum metrics and the Cartei [2] metrics which are not necessarily vacuum metrics. The geodesic equations, for these metrics, are integrated using the Hamilton-Jacobi procedure. The remaining chapters are devoted to the Kinnersley [1] type D vacuum metrics. We omit his class I metrics since these are the Schwarzschild metrics, and have been studied in detail before. Chapter three is devoted to a general study of his class II a metric, a generalisation of the Kerr [1] and NUT (Newman, Tamburino and Unti [1]) metrics. We integrate the geodesic equations and discuss certain general properties: the question of geodesic completeness, the asymptotic properties, and the existence of Killing horizons. Chapter four is concerned with the interpretation of the new parameter 'l', that arises in the class II a and NUT metrics. This parameter was interpreted by Demianski and Newman [1] as a magnetic monopole of mass. Our work centers on the possibility of obtaining observable effects from the presence of 'l'. We have been able to show that its presence is observable, at least in principle, from a study of the motion of particles in the field. In the first place, if l is comparable to the mass of the gravitating system, a comparatively large perihelion shift is to be expected. The possibility of anomalous behaviour in the orbits of test particles, quite unlike anything that occurs in a Newtonian or Schwarzschild field, also arises. In the fifth chapter the Kinnersley class IV metrics are considered. These metrics, which in their simplest form have been known for some time, present serious problems and no interpretations have been suggested. Our discussion is essentially exploratory and the information that does emerge takes the form of suggestions rather than conclusions. Intrinsically the metrics give the impression that interesting results should be obtainable since they are asymptotically flat in certain directions. However the case that we have dealt with does not appear to represent a radiation metric.

In 1975, Sheehan conjectured that every simple 4-regular hamiltonian graph has a second Hamilton cycle. If Sheehan's Conjecture holds, then the result can be extended to all simple d-regular hamiltonian graphs with d at least 3. First, we survey some previous results which verify the existence of a second Hamilton cycle if d is large enough. We will then demonstrate some techniques for finding a second Hamilton cycle that will be used throughout this paper. Finally, we use these techniques and show that for certain 4-regular Hamiltonian graphs whose automorphism group is large enough, a second Hamilton cycle exists.

In this thesis, we consider second-order fully nonlinear partial differential equations of elliptic type. Our aim is to develop computational methods using convergent difference schemes for stationary Hamilton-Jacobi equations with Dirichlet and Neumann type boundary conditions in arbitrary two-dimensional domains. First, we introduce the notion of viscosity solutions in both continuous and discontinuous frameworks. Next, we review Barles-Souganidis approach using monotone, consistent, and stable schemes. In particular, we show that these schemes converge locally uniformly to the unique viscosity solution of the first-order Hamilton-Jacobi equations under mild assumptions. To solve the scheme numerically, we use Euler map with some initial guess. This iterative method gives the viscosity solution as a limit. Moreover, we illustrate our numerical approach in several two-dimensional examples.

In a time when our nation is particularly divided and confused about its identity, Hamilton, the Broadway musical created by Lin-Manuel Miranda has become an example of art's ability to unify disparate ideological, socio-economic and racial groups. The play's reception deserves study to understand how both liberals and conservatives can agree upon an interpretation of a musical that celebrates diversity in race and representation. Celebration and interpretation of the play has been so widespread that a public has emerged, furthering the influence of the play's ideas. This public is unique in a time when most people cocoon themselves in communities with shared identities and philosophies. But the public of Hamilton reflects the historical origins of a public: a group willing to shelve their personal interests to discuss a shared cultural artifact and experience. The argument then of this paper is two-fold: first, that theater is a cultural artifact worthy of rhetorical discussion since Hamilton evidences that art can have tremendous influence on changing the values and ideas of society; and second, that the best way to understand the impact and influence of a play is not by examining the artifact directly but the public and its discourse in response to the experience of encountering the play. This body of criticism provides better insight into the reception and interpretation of theater as a rhetorical and aesthetic work. Ultimately, it is difficult to determine the long-lasting influence of the play but the public discussion has shown that art can have a unifying rhetorical effect.

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This research paper describes a working-class suburban neighborhood for the pre-WWII period 1900-1940. The data are accumulated from tax assessment records, as these are extremely accurate and contain a large variety of information suitable for this study. The main objective is to describe the characteristics of Union Park in Hamilton, Ontario, using the years 1911, 1921 and 1931 as representative of the time period. Three areas of concern were focused on: the occupational characteristics of the inhabitants, describing the inhabitants homes based on building values, and determining characteristics of construction in the area as either owner-built or speculatively built. In general the results show that the area was predominantly working-class, the homes were very cheap in relative value and that the area was primarily owner-built for the period of study. Interesting variations were observed and possible reasons for such variations are suggested. / Thesis / Bachelor of Science (BSc)

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

No description available.

<p> Previous workers in the Hamilton area have pointed out the occurance of lead and zinc mineralization within the Mid-Silurian carbonate beds. They also mentioned the existance of bitumens in these rock units.</p> <p> Analysis of 30 dolomite samples and separated bitumens by atomic absorption for Cu, Pb, Zn showed that the localization of the metals in the carbonates was controlled by the concentration of the bitumens in the rocks.</p> <p> Analysis of 5 bitumens samples by atomic absorption for Cu, Pb, Zn suggested that the bitumens act merely as a reducing agent and are not preferred sites for base metal accumulation.</p> / Thesis / Bachelor of Science (BSc)

<p> This study investigates variables associated with residential mobility and migration at the ecological level. The aim of the study is to test the application of factor analysis to a more specific subject than the description of the whole urban structure. </p> <p> Theoretical formulations about urban growth, urban ecology and mobility are examined, together with empirical research in these fields, to determine variables considered to be associated with changes in residence. The indicators of variables chosen for analysis are from census data and city reports, and each census tract of the chosen urban area is assigned a value for each indicator. The area selected for the study is the Hamilton Metropolitan Area, Ontario. </p> <p> The results of the analysis reveal that most of the variation in the variables is accounted for by two factors: dwelling type and household composition, and economic status. These are the same factors which have been identified in factorial ecologies of geaeral urban structure. </p> The remaining factors are more associated with mobility, and reveal that different origins of movers and migrants are associated with different characteristics and geographical distributions. The hypotheses concerning the relationships with age, population growth and distance from the city centre are supported by the analysis, and the size and direction of movement is generally as expected. However, the hypothesis of increasing economic status with increasing distance migrated is not confirmed: migrants from abroad and different provinces tend to migrate to areas or lower economic status than migrants from Ontario or from the Hamilton metropolitan fringe. </p> <p> This study recognises the limitations of a factorial ecology of residential mobility. Particular care should be exercised in the selection of variables and measures of these variables. Factorial ecology is a descriptive tool, and further analysis of apparent association between variables should be undertaken to determine their statistical significance. </p> <p> The study emphasises the contribution of factorial ecology to the description of areal associations of more specific subjects such as residential mobility, and possibly for other social phenomena. As such, it provides a means for parsimonious description of aspects of urban social geography. </p> / Thesis / Master of Arts (MA)