The aim of the research was to provide new sea-level index points,with the intention of identifying any cross-channel similarities and comparing the results to geophysical models of relative sea-level change. The research successfully provided new sea-level index points from the Pevensey levels, East Sussex; the Canche Estuary, Pas de Calais and the Somme Estuary, Picardie, which were validated using stratigraphic pollen,diatom,foraminiferal snd AMS radiocarbon dating analysis. The results pointed to the presence of a coastal barrier thoughout the mid-Holocene at Pevensey and the Somme which complicated the pattern of coastal sedimentation observed at these sites. A clear pattern of barrier de-stabilisation can be seen to take place either side of the Channel c.3000 years cal BP. A cross-channel comparison identified three similar transgressive events either side of the English Channel, c. 5500, 3000 and 2200 cal years BP. The observed results from each site were then compared to the predicted data( Lambeck pers.comm) .in order to determine whether the observational data could be used to validate the modelled data. The comparisons showed that for the sites in south east England the modelled data tended to over-predict sea-level rise for the mid-t o late- Holocene whereas the model tended to under-predict sea-level rise for the sites in northern France. The new observational data which the research provided could be used to further validate Lambeck's (1990,1997) geophysical model. The effects of local coastal processes, such as tidal range, crustal subsidence and barrier-dynamics were used to aid the comparisons between the pattern of sediment deposition and thus the sea-level signals. These findings suggested that reconstructions should be restricted to sites at an estuary-sized scale.

The primary objects of study in this thesis are noncommutative surfaces; that is, noncommutative noetherian domains of GK dimension 2. Frequently these rings will also be singular, in the sense that they have infinite global dimension. Very little is known about singularities of noncommutative rings, particularly those which are not finite over their centre. In this thesis, we are able to give a precise description of the singularities of a few families of examples. In many examples, we lay the foundations of noncommutative singularity theory by giving a precise description of the singularities of the fundamental examples of noncommutative surfaces. We draw comparisons with the fundamental examples of commutative surface singularities, called Kleinian singularities, which arise from the action of a finite subgroup of SL(2; k) acting on a polynomial ring. The main tool we use to study the singularities of noncommutative surfaces is the singularity category, first introduced by Buchweitz in [Buc86]. This takes a (possibly noncommutative) ring R and produces a triangulated category Dsg(R) which provides a measure of "how singular" R is. Roughly speaking, the size of this category reflects how bad the singularity is; in particular, Dsg(R) is trivial if and only if R has finite global dimension. In [CBH98], Crawley-Boevey-Holland introduced a family of noncommutative rings which can be thought of as deformations of the coordinate ring of a Kleinian singularity. We give a precise description of the singularity categories of these deformations, and show that their singularities can be thought of as unions of (commutative) Kleinian singularities. In particular, our results show that deforming a singularity in this setting makes it no worse. Another family of noncommutative surfaces were introduced by Rogalski-Sierra-Stafford in [RSS15b]. The authors showed that these rings share a number of ring-theoretic properties with deformations of type A Kleinian singularities. We apply our techniques to show that the "least singular" example has an A1 singularity, and conjecture that other examples exhibit similar behaviour. In [CKWZ16a], Chan-Kirkman-Walton-Zhang gave a definition for a quantum version of Kleinian singularities. These require the data of a two-dimensional AS regular algebra A and a finite group G acting on A with trivial homological determinant. We extend a number of results in [CBH98] to the setting of quantum Kleinian singularities. More precisely, we show that one can construct deformations of the skew group rings A#G and the invariant rings AG, and then determine some of their ring-theoretic properties. These results allow us to give a precise description of the singularity categories of quantum Kleinian singularities, which often have very different behaviour to their non-quantum analogues.

No description available.

Rearrangements are two measurable real-valued functions that have equal measure of pre-images of upper level sets. In this thesis, I will investigate several matters and problems relating to rearrangements: the relationship between assumptions on the measure space and desirable properties of the set of rearrangements, and the validity of rearrangement inequalities; generalising the Mountain Pass Lemma over rearrangements; and applying topological degree theory to boundary value problems involving rearrangements. From suppositions on the measure space, such as the measure space having finite measure and no atoms, it can proved that the set of rearrangements is contractible and locally contractible. The Mountain Pass Lemma over rearrangements can be generalised, so instead of considering continuous paths from the closed unit interval to the set of rearrangements; it will consider the continuous functions from the closed unit disc into the set of rearrangements. Topological degree theory is used to associate admissible triples of functions, sets and points with integers. These methods will be applied to a boundary value problem involving rearrangements, where the domain is almost equal to the union of balls, which has been studied using variational methods, providing new multiplicity results. The minimum number of solutions to this boundary value problem is found to be related exponentially to the number of balls contained in the domain.

Nesta tese apresentamos uma contribuição para o estudo da transição do retrato de fase de uma equação diferencial descontínua específica ao longo de uma linha de descontinuidade. A equação diferencial que tratamos neste trabalho é a das linhas de curvatura principal de uma superfície S contendo uma curva distinguida B e imersa em R^3. A linha de descontinuidade é a curva B, a qual é o bordo comum de duas superfícies suaves justapostas que formam S. Na primeira parte do trabalho consideramos a superfície seccionalmente suave, S = S+ U B U S-, obtida pela justaposição de S+ e S- ao longo do bordo comum B. O estudo da configuração principal de S nos casos em que as linhas de curvatura principal das superfícies S+ e S- tem contato quadrático ou cruzam transversalmente B foi feito por comparação com a configuração principal de uma superfície suave, obtida de S pelo processo da \"regularização\" ao longo da curva de descontinuidade B. Na segunda parte do trabalho estudamos as linhas de curvatura principal de uma superfície S em R^3 com bordo B e da superfície suave obtida de S através dos processos de engrossamento e regularização definidos por Garcia e Sotomayor em [5], onde os autores consideraram o caso genérico, sem pontos umbílicos e contato quadrático de uma linha de curvatura principal com B. Damos aqui continuidade ao estudo feito em [5] analisando o caso de contato cúbico com o bordo B. Obtivemos que dos pontos da curva bordo comum B de contato quadrático e de cruzamento transversal emergem, sobre a superfície regularizada, pontos umbílicos Darbouxianos dos tipos D1 e D3, enquanto que, para o ponto sobre B de contato cúbico obtivemos pontos umbílicos Darbouxianos dos tipos D1, D2 e D3 e também pontos umbílicos não Darbouxianos dos tipos D12 e D23. [5] Garcia, R., and Sotomayor, J. Umbilic and tangential singularities on configurations of principal curvature lines. Anais da Academia Brasileira de Ciências 74, 1 (2002), 117. / In this work we present a contribution to the study of the transition of the phase portrait of a specific discontinuous differential equation along a line of discontinuity. The differential equations under consideration will be that of the principal curvature lines of a surface S with a distinguished curve B immersed in R^3, where the line of discontinuity is the curve B which is the common border of two smooth surfaces attached to make up S. In the first part of the work we consider a piecewise smooth surface S = S+ U B U S-, obtained by the juxtaposition of two smooth surfaces S+ and S- along their common border B. The analysis of the principal configuration of S in the cases where the principal curvature lines of the surfaces S+ and S- have quadratic contact or cross transversally B was carried out by comparison with a smooth surface, obtained from S by the \"regularization\" along the discontinuity curve B. In the second part of the work we study the principal curvature lines of a surface S in R^3 with boundary B and of the smooth surface obtained from S by thickening and smoothing introduced by Garcia and Sotomayor in [5], where they considered the generic case of no umbilic points and at most quadratic contact of principal lines with B. Here we pursue the study in [5] and analyze the case of cubic contact with the border B. We established that while from quadratic contact points with B emerge on the smoothed surface Darbouxian umbilics of D1 and D3 types, from the cubic contact points appear Darbouxian umbilics of types D1, D2 and D3 as well as non Darbouxian points of types D12 and D23. [5] Garcia, R., and Sotomayor, J. Umbilic and tangential singularities on configurations of principal curvature lines. Anais da Academia Brasileira de Ciências 74, 1 (2002), 117.

Losing interdental gingival tissue can lead to a phenomemon known as black triangles. The absence of the interdental papilla (the so called 'black triangle disease') can cause patients problems with appearance, phonetics and with the impaction of food. The gingival soft tissues form the framework and the architecture of the dentition and, in the maxillary anterior region of the mouth, play an important role in dental aesthetics. If there is any change to the shape and/or symmetry of the gingivae through developmental, pathologic or iatrogenic factors, there can be a significant and detrimental change in the appearance and balance of the natural dentition and any prosthetic tooth replacement. In this clinical research study, we find that the radiographic measurement of the distance of the contact point to the crest of the bone is a valid and reliable tool to use. This method also adds strength to predicting black triangles as the results are similar to earlier studies and the numbers used in this study was nearly twice as much.

Acupuncture has been used for thousands of years to treat a wide range of diseases, but the mechanisms involved in the process have remained a mystery. The present study measures EEG responses to stimulation of a specific acupuncture point, GB37 (Guang Ming), with two different types of manual needle stimulation. Previous studies stimulated for a maximum of 2 minutes. The present study reflects the normal acupuncture treatment time of 20 minutes, with EEG recordings during and for 10 minutes prior to and after stimulation. Our results show no changes in the global spatial and temporal properties of EEG during and shortly after acupuncture treatment of acupoint GB37. The second part of this study examines the global protein expression of glutamic acid decarboxylase (GAD) knockout mice. GAD is the rate-limiting enzyme in the synthesis of GABA, the major inhibitory neurotransmitter in the brain. The protein content of wild type, hetero-, and homozygous GAD knockout mice brains were determined using a LC-MS-based gel-free shotgun profiling of complex protein mixtures. The data was analyzed using the Raculovic algorithm to determine the proteins differences. A short list of 32 proteins was determined with four that have been shown to be significant proteins that influence cell survival and excitotoxicity in the brain and have potential relationships with GABA. These proteins include VATPase, Glutamine synthetase, Beta-synuclein, and Micortuble associated protein (MAP). The proteomics results provide a preliminary best guess list of proteins influencing GAD and GABA production. / by Michael L. Marshall. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

No description available.

Nesta tese apresentamos uma contribuição para o estudo da transição do retrato de fase de uma equação diferencial descontínua específica ao longo de uma linha de descontinuidade. A equação diferencial que tratamos neste trabalho é a das linhas de curvatura principal de uma superfície S contendo uma curva distinguida B e imersa em R^3. A linha de descontinuidade é a curva B, a qual é o bordo comum de duas superfícies suaves justapostas que formam S. Na primeira parte do trabalho consideramos a superfície seccionalmente suave, S = S+ U B U S-, obtida pela justaposição de S+ e S- ao longo do bordo comum B. O estudo da configuração principal de S nos casos em que as linhas de curvatura principal das superfícies S+ e S- tem contato quadrático ou cruzam transversalmente B foi feito por comparação com a configuração principal de uma superfície suave, obtida de S pelo processo da \"regularização\" ao longo da curva de descontinuidade B. Na segunda parte do trabalho estudamos as linhas de curvatura principal de uma superfície S em R^3 com bordo B e da superfície suave obtida de S através dos processos de engrossamento e regularização definidos por Garcia e Sotomayor em [5], onde os autores consideraram o caso genérico, sem pontos umbílicos e contato quadrático de uma linha de curvatura principal com B. Damos aqui continuidade ao estudo feito em [5] analisando o caso de contato cúbico com o bordo B. Obtivemos que dos pontos da curva bordo comum B de contato quadrático e de cruzamento transversal emergem, sobre a superfície regularizada, pontos umbílicos Darbouxianos dos tipos D1 e D3, enquanto que, para o ponto sobre B de contato cúbico obtivemos pontos umbílicos Darbouxianos dos tipos D1, D2 e D3 e também pontos umbílicos não Darbouxianos dos tipos D12 e D23. [5] Garcia, R., and Sotomayor, J. Umbilic and tangential singularities on configurations of principal curvature lines. Anais da Academia Brasileira de Ciências 74, 1 (2002), 117. / In this work we present a contribution to the study of the transition of the phase portrait of a specific discontinuous differential equation along a line of discontinuity. The differential equations under consideration will be that of the principal curvature lines of a surface S with a distinguished curve B immersed in R^3, where the line of discontinuity is the curve B which is the common border of two smooth surfaces attached to make up S. In the first part of the work we consider a piecewise smooth surface S = S+ U B U S-, obtained by the juxtaposition of two smooth surfaces S+ and S- along their common border B. The analysis of the principal configuration of S in the cases where the principal curvature lines of the surfaces S+ and S- have quadratic contact or cross transversally B was carried out by comparison with a smooth surface, obtained from S by the \"regularization\" along the discontinuity curve B. In the second part of the work we study the principal curvature lines of a surface S in R^3 with boundary B and of the smooth surface obtained from S by thickening and smoothing introduced by Garcia and Sotomayor in [5], where they considered the generic case of no umbilic points and at most quadratic contact of principal lines with B. Here we pursue the study in [5] and analyze the case of cubic contact with the border B. We established that while from quadratic contact points with B emerge on the smoothed surface Darbouxian umbilics of D1 and D3 types, from the cubic contact points appear Darbouxian umbilics of types D1, D2 and D3 as well as non Darbouxian points of types D12 and D23. [5] Garcia, R., and Sotomayor, J. Umbilic and tangential singularities on configurations of principal curvature lines. Anais da Academia Brasileira de Ciências 74, 1 (2002), 117.

O conhecido Teorema de Poincaré afirma: O número de rotação de homeomorfismo do círculo S^1 que preserva orientação é racional se, e somente se, o homeomorfismo possui um ponto periódico cujo período é igual ao denominador de tal racional. Na presente dissertação estudamos resultados análogos, ao resultado acima mencionado, para homeomorfismos do anel A=S^1 x I homotópicos à identidade. Mais precisamente, estudaremos o famoso Teorema de Poincaré - Birkhoff e algumas versões devidas a J. Franks. Isto será feito impondo algumas condições no conjunto de rotação, o qual é uma generalização do número de rotação para homeomorfismos do círculo. / The well known Poincaré's Theorem state: The rotation number of an orientation preserving circle homeomorphism is rational if, only if, the homeomorphism has a periodic point of period equal to denominator of the rational. In this monograph we study results analogous, to the result above mentioned, for homeomorphisms of A=S^1 x I homotophics to the identity. More precisely, we study the famous Poincaré - Birkhoff Theorem and some versions obtained by J. Franks. This it will be done imposing some conditions in the rotation set, which is generalization of the rotation number for circle homeomorphisms.