Erdos proved the well-known result that every graph has a spanning, bipartite subgraph such that every vertex has degree at least half of its original degree. Bollobas and Scott conjectured that one can get a slightly weaker result if we require the subgraph to be not only spanning and bipartite, but also balanced. We prove this conjecture for graphs of maximum degree 3. The majority of the paper however, will focus on graph tiling. Graph tiling (or sometimes referred to as graph packing) is where, given a graph H, we find a spanning subgraph of some larger graph G that consists entirely of disjoint copies of H. With the Regularity Lemma and the Blow-up Lemma as our main tools, we prove an asymptotic minimum degree condition for an arbitrary bipartite graph G to be tiled by another arbitrary bipartite graph H. This proves a conjecture of Zhao and also implies an asymptotic version of a result of Kuhn and Osthus for bipartite graphs.

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The Bay of Islands Ophiolitic Complex (BOIC) is one of most well preserved and well-exposed ophiolites in the world. The BOIC consist of four massifs; these are the Table Mountain (TBL), North Arm Mountain (NAM), Blow-Me-Down Mountain (BMD) and Lewis Hills massifs. Proposed geological environments of the BOIC in Newfoundland are diverse; ranging from oceanic spreading ridge to supra-subduction setting. The BOIC has a complete ophiolite sequence as defined at the Penrose Conference (Anonymous, 1972) including ultramafic mantle rocks, ultramafic to gabbroic cumulate rocks, sheeted dikes, pillowed basaltic rocks and capping sedimentary rocks in structurally ascending order. We studied harzburgite and overlying massive dunite in the BOIC. Harzburgite is generally medium-grained, and contains olivine, orthopyroxene, Cr-spinel, clinopyroxene and rare sulfide minerals. Harzburgite is massive to strongly deformed, with local development of mylonitic shear zones. A foliation and lineation are defined by elongated and fragmented grains of orthopyroxene and Cr-spinel. Dikes, sills, veins, and irregularly-shaped bodies of dunite and pyroxenite are present throughout the harzburgite unit. Dunite is the predominant lithology of the Blow-Me-Down Mountain. It is typically fine- to medium-grained, massive, and contains minor Cr-spinel and rare sulfide minerals. Dunite contains olivine, Cr-spinel and minor pyroxenes in some samples. Olivine crystals are commonly partly replaced by serpentine along fractures and in outer rims. Bulk rock and mineral composition data suggest that harzburgites are mild to highly refractory mantle residues after partial melting. In contrast all dunite samples show a cumulate geochemical signature from a mafic melt that originated from highly refractory mantle peridotites. Our study suggest that the harzburgite in the BOIC originally formed as oceanic lithosphere at a slow spreading ridge, possibly in the vicinity of active arc systems, whereas the parental melt for dunites formed in subduction setting. The second part of this study measured trace element compositions for olivine, Cr-spinel and bulk rock of dunite. The measured bulk rock compositions are compared to those of calculated based on mineral chemistry and their abundance. This comparison suggests that the trapped melt fraction was negligible during the crystallization of the dunites. The calculated melt compositions for the dunites confirm that the melt formed in subduction setting.

This thesis contributes towards the maximal-in-time well-posedness theory of three nonlinear dispersive partial differential equations (PDEs). We are interested in questions that extend beyond the usual well-posedness theory: what is the ultimate fate of solutions? How does Hamiltonian structure influence PDE dynamics? How does randomness, within the PDE or the initial data, interact with well-posedness of the Cauchy problem? The first topic of this thesis is the analysis of blow-up solutions to the elliptic-elliptic Davey-Stewartson system, which appears in the description of surface water waves. We prove a mass concentration property for H^1-solutions, analogous to the one known for the L^2-critical nonlinear Schrodinger equation. We also prove a mass concentration result for L^2-solutions. The second topic of this thesis is the invariance of the Gibbs measure for the (gauge transformed) periodic quartic KdV equation. The Gibbs measure is a probability measure supported on H^s for s<1/2, and local solutions to the quartic KdV cannot be obtained below H^{1/2} by using the standard fixed point method. We exhibit nonlinear smoothing when the initial data are randomized, and establish almost sure local well-posedness for the (gauge transformed) quartic KdV below H^{1/2}. Then, using the invariance of the Gibbs measure for the finite-dimensional system of ODEs given by projection onto the first N>0 modes of the trigonometric basis, we extend the local solutions of the (gauge transformed) quartic KdV to global solutions, and prove the invariance of the Gibbs measure under the flow. Inverting the gauge, we establish almost sure global well-posedness of the (ungauged) periodic quartic KdV below H^{1/2}. The third topic of this thesis is well-posedness of the stochastic KdV-Burgers equation. This equation is studied as a toy model for the stochastic Burgers equation, which appears in the description of a randomly growing interface. We are interested in rigorously proving the invariance of white noise for the stochastic KdV-Burgers equation. This thesis provides a result in this direction: after smoothing the additive noise (by a fractional derivative), we establish (almost sure) local well-posedness of the stochastic KdV-Burgers equation with white noise as initial data. We also prove a global well-posedness result under an additional smoothing of the noise.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 152-167).

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-30T13:20:26Z No. of bitstreams: 1 arquivo total.pdf: 931700 bytes, checksum: fa2250c9a71513dd14a73f23193f0cfa (MD5) / Made available in DSpace on 2016-03-30T13:20:26Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 931700 bytes, checksum: fa2250c9a71513dd14a73f23193f0cfa (MD5) Previous issue date: 2014-02-26 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this paper we prove the compactness of the full set of solutions of the Yamabe problem when n 24. We begin with the study of basic properties of blow-up points and then prove sharp pointwise estimates that will be crucial for the proof of Weyl Vanishing Theorem in these dimensions. The compactness problem then reduces to show the positivity of a certain quadratic form. We also show that this quadratic form has negative eingenvalues, if n 25. It is noteworthy that during this process the Positive Mass Theorem is a key tool in obtaining the main result. / Neste trabalho provaremos a compacidade do conjunto de solu cões do problema de Yamabe quando n 24. Iniciaremos com o estudo das propriedades báasicas de pontos de blow-up e em seguida provaremos estimativas pontuais, ótimas em certo sentido, que ser~ao de fundamental importância para a demonstra cão do Teorema do Anulamento de Weyl nestas dimensoes. O problema de compacidade ent~ao se reduz a mostrar a positividade de uma certa forma quadr atica. Provaremos ainda que, se n 25, tal forma quadr atica tem autovalores negativos. Vale ressaltar que durante tal processo o Teorema de Massa Positiva ser a uma ferramenta chave na obten cão do resultado principal.

This thesis focuses on the flourishing music-publishing industry in England in the second half of the seventeenth century, and examines its relationship to and influence on the activities of professional musicians. Music publishing as a commercial entity developed in England during this period, particularly, but not exclusively, through the endeavours of the Playford family. By placing the printed music books within the social and cultural contexts in which they were produced, this thesis explores the consequences of printing on the musical text, understanding the purposes for which the printed book was created and how different functions of print affected the musical texts that they contained. A detailed examination of the printed music sources sheds light on how publication (including posthumous publication) related to the image and status of the composer, and draws attention to the interaction between public music-making, compositional activity and music publishing during this period. Through an investigation of the contemporary printed outputs of five case-study composers - William Lawes, Henry Lawes, Matthew Locke, Henry Purcell and John Blow - this thesis explores the individual nature of the composers' relationships with the printed music book trade and how their contemporary printed outputs relate to their overall compositional output. This is followed by a detailed analytical study of specific compositions by the five case-study composers, examining both contemporary manuscript and printed sources, in order to determine to what extent the commercial print market influenced professional musical creativity. Different versions of compositions of certain genres, particularly secular vocal works, were disseminated via print as opposed to manuscript, and these alternative versions appear to have been instigated by both composers and stationers. This approach to examination of contemporary sources calls for the contextual consideration of sources and the musical texts within them.

The Bay of Islands Ophiolitic Complex (BOIC) is one of most well preserved and well-exposed ophiolites in the world. The BOIC consist of four massifs; these are the Table Mountain (TBL), North Arm Mountain (NAM), Blow-Me-Down Mountain (BMD) and Lewis Hills massifs. Proposed geological environments of the BOIC in Newfoundland are diverse; ranging from oceanic spreading ridge to supra-subduction setting. The BOIC has a complete ophiolite sequence as defined at the Penrose Conference (Anonymous, 1972) including ultramafic mantle rocks, ultramafic to gabbroic cumulate rocks, sheeted dikes, pillowed basaltic rocks and capping sedimentary rocks in structurally ascending order. We studied harzburgite and overlying massive dunite in the BOIC. Harzburgite is generally medium-grained, and contains olivine, orthopyroxene, Cr-spinel, clinopyroxene and rare sulfide minerals. Harzburgite is massive to strongly deformed, with local development of mylonitic shear zones. A foliation and lineation are defined by elongated and fragmented grains of orthopyroxene and Cr-spinel. Dikes, sills, veins, and irregularly-shaped bodies of dunite and pyroxenite are present throughout the harzburgite unit. Dunite is the predominant lithology of the Blow-Me-Down Mountain. It is typically fine- to medium-grained, massive, and contains minor Cr-spinel and rare sulfide minerals. Dunite contains olivine, Cr-spinel and minor pyroxenes in some samples. Olivine crystals are commonly partly replaced by serpentine along fractures and in outer rims. Bulk rock and mineral composition data suggest that harzburgites are mild to highly refractory mantle residues after partial melting. In contrast all dunite samples show a cumulate geochemical signature from a mafic melt that originated from highly refractory mantle peridotites. Our study suggest that the harzburgite in the BOIC originally formed as oceanic lithosphere at a slow spreading ridge, possibly in the vicinity of active arc systems, whereas the parental melt for dunites formed in subduction setting. The second part of this study measured trace element compositions for olivine, Cr-spinel and bulk rock of dunite. The measured bulk rock compositions are compared to those of calculated based on mineral chemistry and their abundance. This comparison suggests that the trapped melt fraction was negligible during the crystallization of the dunites. The calculated melt compositions for the dunites confirm that the melt formed in subduction setting.

We study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of particles, and develop a numerical method capable of detecting collisions of many point particles without the use of pairwise computations, or very refined adaptive timestepping. We show that when the system is in an appropriate parameter regime, the hydrodynamic limit of the empirical mass density of the system is a solution to a nonlinear Fokker-Planck equation, such as the Patlak-Keller-Segel (PKS) model, or its multispecies variant. We then show that the presented numerical method is well-suited for the simulation of the formation of finite-time singularities in the PKS, as well as PKS pre- and post-blow-up dynamics. Additionally, we present numerical evidence that blow-up with an increasing total second moment in the two species Keller-Segel system occurs with a linearly increasing second moment in one component, and a linearly decreasing second moment in the other component.

Emotionally triggered involuntary violent behaviour not attributed to a mental disorder: conceptual criteria and their reliability. This study conceptualised emotionally triggered involuntary violent behaviour (ETIVB), developed criteria for the identification of ETIVB, and examined their validity and reliability. South Africa criminal courts allow for a defence called “non-pathological criminal incapacity”. It refers inter alia to extreme emotional arousal triggering involuntary violent behaviour. This is usually called an “emotional storm” or a so-called “psychological blow automatism”. Psychiatrists are often called to give expert testimony in this regard, but there is no conceptual clarity or criteria upon which to base it. This difficulty is compounded by the requirement set by the criminal courts that the behaviour may not be attributed to a mental disorder (in this thesis the terms mental disorder and mental illness are used interchangeably). The first advance in obtaining clarity was afforded by focusing on the behaviour as distinct from 1) legal and jurisprudential considerations as well as 2) whether the behaviour is (not) attributed to mental disorder. The subsequent research questions driving the study were, “what counts as ETIVB?” In particular, what counts respectively as „emotional triggered‟, „involuntary‟, „violent‟, and „behaviour‟. Through conceptual methods suggested in the work of J.L. Austin, draft ETIVB-criteria were developed and then repetitively applied to a set of 28 cases. Twenty seven of these cases involved a charge of murder. The other one had behaved violently, but was not charged. The criteria were refined and their content validity derived by a repetitive to-and-fro process between comparative exploration of the concepts and their empirical application to the set of cases. The criteria were formulated into an instrument by which a psychiatrist can identify ETIVB. In addition provision was made to record whether ETIVB is, or is not, attributed to specific causes including mental disorder, but only as an attribution that follows after ETIVB has been identified. The ETIVB-instrument was subjected to reliability testing among 14 psychiatrists and 10 psychiatrists in training. They applied the ETIVB-criteria to a set of 5 externally validated case summaries. The participants had first been trained in the use of the instrument by considering other example cases. Statistical analyses of inter-rater reliability were performed. The modified kappa agreement ranged from 0.388 (fair) to 0.636 (substantial) across study cases for all criteria A.1 – H.1. The criteria for violence had exceptionally high inter-rater agreement, all being 0.947 and higher. The complexity of the ETIVB-construct transpired when inter-rater reliability analyses were compared between cases in that different cases posed different challenges for inter-rater agreement. The reliability testing across cases however, showed which less agreed-upon items would benefit from refinement. / Thesis (PhD)--University of Pretoria, 2015. / gm2015 / Psychiatry / PhD / Unrestricted