In this thesis we will consider divisibility properties of some recurrent sequences, Newman polynomials and computer calculations in those and related questions of number theory. / Čia nagrinėsime rekurenčiųjų sekų dalumo savybes, Niumano polinomus ir kompiuterių panaudojimąatliekant įvairius skaičiavimus, susijusius su minėtais skaičių teorijos klausimais.

Šioje disertacijoje bus nagrinėjamos rekurenčiųjų sekų dalumo savybės, Niumano polinomai ir kompiuterių panaudojimas atliekant įvairius matematinius skaiciavimus, susijusius su minėtais skaičių teorijos klausimais. / In this thesis we will consider divisibility properties of some recurrent sequences, Newman polynomials and computer calculations in those and related questions of number theory.

Paleochannels are a major cause of roof failure in underground coal mines in southeastern Kentucky. Models that predict the location and geometry of paleochannels are essential to assist in mine planning and development. Data from approximately 506 coal exploration drill holes were subjected to second-order trend-surface analysis to identify stacking or offsetting relationships between sandstone bodies in adjacent stratigraphic intervals. The stacking of sandstone bodies within adjacent intervals suggests the presence of synsedimentary faulting. This model suggests that continued movement along the faults created topographic lows attracted paleodrainages and accommodated thick accumulations of sandstone in approximately the same areas through time. Trend-surface residuals analysis successfully located areas of potential synsedimentary faulting within the study area. An additional 7,189 elevation data points for the top of the Newman Limestone, interpreted from oil and gas records, were utilized to locate sub-Pennsylvanian System faults within the study area. The correlation between faults associated with the coal measures identified using second-order trend-surface analysis and faults affecting the Newman Limestone suggests Pennsylvanian synsedimentary faults were preceded by older Paleozoic fault movement. The greater availability of oil and gas subsurface data makes this relationship an important tool for predicting locations of fault-controlled coal measure paleochannels.

This Dissertation covers three aspects of General Relativity: inequivalent Einstein metrics on Lie Group Manifolds, proving the Hoop Conjecture for Black Rings, and investigating ergoregions in magnetised black hole spacetimes. A number of analytical and numerical techniques are employed to that end. It is known that every compact simple Lie Group admits a bi-invariant homogeneous Einstein metric. We use two ansatze to probe the existence of additional inequivalent Einstein metrics on the Lie Group SU (n). We provide an explicit construction of 2k + 1 and 2k inequivalent Einstein metrics on SU (2k) and SU (2k + 1) respectively. We prove the Hoop Conjecture for neutral and charged, singly and doubly rotating black rings. This allows one to determine whether a rotating mass distribution has an event horizon, that it is in fact a black ring. We investigate ergoregions in magnetised black hole spacetimes. We show that, in general, rotating charged black holes (Kerr-Newman) immersed in an external magnetic field have ergoregions that extend to infinity near the central axis unless we restrict the charge to q = amB and keep B below a maximal value. Additionally, we show that as B is increased from zero the ergoregion adjacent to the event horizon shrinks, vanishing altogether at a critical value, before reappearing and growing until it is no longer bounded as B becomes greater than the maximal value.

This study engaged with the architecture of the ‘Initial Structure’ at Newman College, 1915-1918, so as to establish this building’s place in the oeuvre of Walter Burley Griffin (1876-1937). Griffin’s architecture at Newman College was unparalleled in Melbourne yet it has never been the subject of a comprehensive study. Further, a measure for Griffin’s creative method and architectural style has not been developed to date although much scholarship has been devoted to the identification of events and works in Griffin’s career. Furthermore a substantive analysis of the architecture of Walter Burley Griffin was lacking that defined and distinguished his work from that of the so-called ‘Prairie School’, and of Frank Lloyd Wright. / Walter Burley Griffin was the conceptual designer of Newman College, while Marion Mahony Griffin (1871-1961), his wife and architectural practice partner was its facilitator. An evaluation of Griffin’s university education, 1895-1899, drew out the compositional concepts of parti, types and architectonics, as his own preferred means of working. Griffin’s mature style in the college design was also indebted to his architectural practice and experiences in Chicago, 1899-1914. An initial assumption in this study was that Griffin was eclectic, as were the American predecessors he admired, Thomas Jefferson and Henry Hobson Richardson, as were Griffin’s contemporaries, Louis Henri Sullivan and Frank Lloyd Wright. Thus the sources of Griffin’s architectural ideas, elements, and methods of composition, have been traced in this study. / American campus designs were surveyed and comparisons made with the other three late 19th Century college buildings at the University of Melbourne to distinguish Griffins’ innovations in college planning, construction and form at Newman College. The description of the commissioning, committee-work and program for the Newman College building revealed the social and political idealism that linked Griffin with his supporters among Melbourne’s Roman Catholic community. Griffin worked with ‘structure’ in mind, both compositional and constructional. Particular partis, typologies and architectonic patterns have been 3 identified in the compositional structures of the college building design. Similarly Griffin’s adaptations of new and exploratory building techniques were investigated. / Griffin’s sources were not only American. He derived inspiration equally from seminal European and Asian precedents, which provided instances of an underlying compositional structure. In the architecture of Newman College the composite plans, mixed construction techniques and materials, and richly layered forms allowed Griffin scope to express ideal college purposes, spiritual universality, and organic wholeness.

Master of Visual Arts / The title Normal What refers to a group of paintings that emerged from my Masters of Visual Arts 2004/05 studio project. Individual paintings are chronological self portrait reflecting upon my own experiences and those in the wider community who at some point in their lives have had to endure the struggles, and negative stigma that is so often attached to those who have become marginalised and detached from mainstream society. People found in this category include the disabled, homeless, unemployed, and those with addiction problems. Each painting bears a close connection with techniques associated with abstract expressionist painting. This radiates through the vast expanse of drips, stains and explosions which appear to suffocate the paintings delicate monochrome surface. Strong references to Kristeva’s theory on Abjection arrive through the aggressive and violent outbursts of paint that evoke an atmosphere of symbolic horror, personal dysfunction and social oppression. This emerges out of the shadows and private spaces of the painting’s domestic interior. Deep emotional, psychological, sociological sensitivities are raised throughout my studio practice. Combined with a series of unresolved tensions, and questions surrounding normality run deep a consequence of society’s push for normality are being felt most acutely by those effected by this form of sociology. The ideas raised through my studio project had a profound influence on the research being conducted for the dissertation. Kristeva’s theory on Abjection, along side the practices of Eva Hesse, Barnett Newman, Agnes Martin emerged from a group of highly emotional abstract paintings. This strengthened the connection between the studio project and the dissertation. Aimed at deepening a personal understanding an commitment to researching the subject of normality and how it could be successfully articulated through a visual narrative.

Thesis (M. Div.)--St. Vladimir's Orthodox Theological Seminary, Crestwood, N.Y., 1993. / Includes bibliographical references (leaf [45]).

Thesis (S.T.L.)--Catholic University of America, 1992. / This is an electronic reproduction of TREN, #029-0266. Includes bibliographical references (leaves 164-170).

Thesis (S.T.L.)--Catholic University of America, 1995. / This is an electronic reproduction of TREN, #029-0351. Includes bibliographical references (leaves 367-371).

Thesis (S.T.L.)--Catholic University of America, 1995. / Includes bibliographical references (leaves 367-371).