In this thesis, results will be presented that pertain to the global regularity of solutions to boundary value problems having the general form \begin{align} F\left[D^2u-A(\,\cdot\,,u,Du)\right] &= B(\,\cdot\,,u,Du),\quad\text{in}\ \Omega^-,\notag\\ T_u(\Omega^-) &= \Omega^+, \end{align} where $A$, $B$, $T_u$ are all prescribed; and $\Omega^-$ along with $\Omega^+$ are bounded in $\mathbb{R}^n$, smooth and satisfying notions of c-convexity and c^*-convexity relative to one another (see [MTW05] for definitions). In particular, the case where $F$ is a quotient of symmetric functions of the eigenvalues of its argument matrix will be investigated. Ultimately, analogies to the global regularity result presented in [TW06] for the Optimal Transportation Problem to this new fully-nonlinear elliptic boundary value problem will be presented and proven. It will also be shown that the A3w condition (first presented in [MTW05]) is also necessary for global regularity in the case of (1). The core part of this research lies in proving various a priori estimates so that a method of continuity argument can be applied to get the existence of globally smooth solutions. The a priori estimates vary from those presented in [TW06], due to the structure of F, introducing some complications that are not present in the Optimal Transportation case.¶ In the final chapter of this thesis, the A3 condition will be reformulated and analysed on round spheres. The example cost-functions subsequently analysed have already been studied in the Euclidean case within [MTW05] and [TW06]. In this research, a stereographic projection is utilised to reformulate the A3 condition on round spheres for a general class of cost-functions, which are general functions of the geodesic distance as defined relative to the underlying round sphere. With this general expression, the A3 condition can be readily verified for a large class of cost-functions that depend on the metrics of round spheres, which is tantamount (combined with some geometric assumptions on the source and target domains) to the classical regularity for solutions of the Optimal Transportation Problem on round spheres.

In this master thesis we have examined the possibility of pricing multiple American options, on an underlying asset with discrete dividends, with a finite difference method. We have found a good and stable way to price one American option by solving the BSM PDE backwards, while also calculating the Greeks of the option with automatic differentiation. The list of Greeks for an option is quite extensive since we have been using a local volatility surface. We have also tried to find a way to price several American options simultaneously by solving a forward PDE. Unfortunately, we haven't found any previous work that we could use with our local volatility surface, while still keeping down the computational time. The closest we got was to calculate the value of a compound option in a forward mode, but in order to use this to value an American option, we needed to go through an iterative process which calculated a forward or backward European PDE in every step.

In this thesis, we study a numerical tool named multi-mesh method within the framework of the adaptive finite element method. The aim of this method is to minimize the size of the linear system to get the optimal performance of simulations. Multi-mesh methods are typically used in multi-physics problems, where more than one component is involved in the system. During the discretization of the weak formulation of partial differential equations, a finite-dimensional space associated with an independently refined mesh is assigned to each component respectively. The usage of independently refined meshes leads less degrees of freedom from a global point of view. To our best knowledge, the first multi-mesh method was presented at the beginning of the 21st Century. Similar techniques were announced by different mathematics researchers afterwards. But, due to some common restrictions, this method is not widely used in the field of numerical simulations. On one hand, only the case of two-mesh is taken into scientists\' consideration. But more than two components are common in multi-physics problems. Each is, in principle, allowed to be defined on an independent mesh. Besides that, the multi-mesh methods presented so far omit the possibility that coefficient function spaces live on the different meshes from the trial and test function spaces. As a ubiquitous numerical tool, the multi-mesh method should comprise the above circumstances. On the other hand, users are accustomed to improving the performance by taking the advantage of parallel resources rather than running simulations with the multi-mesh approach on one single processor, so it would be a pity if such an efficient method was only available in sequential. The multi-mesh method is actually used within local assembling process, which should not be conflict with parallelization. In this thesis, we present a general multi-mesh method without the limitation of the number of meshes used in the system, and it can be applied to parallel environments as well. Chapter 1 introduces the background knowledge of the adaptive finite element method and the pioneering work, on which this thesis is based. Then, the main idea of the multi-mesh method is formally derived and the detailed implementation is discussed in Chapter 2 and 3. In Chapter 4, applications, e.g. the multi-phase flow problem and the dendritic growth, are shown to prove that our method is superior in contrast to the standard single-mesh finite element method in terms of performance, while accuracy is not reduced.

In this theses, an iterativ linear solver for the non-linear p-Poisson problem is introduced. After the theoretical convergence results some numerical examples of a fully adaptive solver are presented.

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An alternative technique for shape morphing using a surface generating method using partial differential equations is outlined throughout this work. The boundaryvalue nature that is inherent to this surface generation technique together with its mathematical properties are hereby exploited for creating intermediate shapes between an initial shape and a final one. Four alternative shape morphing techniques are proposed here. The first one is based on the use of a linear combination of the boundary conditions associated with the initial and final surfaces, the second one consists of varying the Fourier mode for which the PDE is solved whilst the third results from a combination of the first two. The fourth of these alternatives is based on the manipulation of the spine of the surfaces, which is computed as a by-product of the solution. Results of morphing sequences between two topologically nonequivalent surfaces are presented. Thus, it is shown that the PDE based approach for morphing is capable of obtaining smooth intermediate surfaces automatically in most of the methodologies presented in this work and the spine has been revealed as a powerful tool for morphing surfaces arising from the method proposed here.

Submitted by Nadir Basilio (nadirsb@uninove.br) on 2016-05-05T21:35:50Z No. of bitstreams: 1 Veronica Cosmo Barbosa.pdf: 1397046 bytes, checksum: 42eff9bcba4d4a07a080ffb88eee8ede (MD5) / Made available in DSpace on 2016-05-05T21:35:50Z (GMT). No. of bitstreams: 1 Veronica Cosmo Barbosa.pdf: 1397046 bytes, checksum: 42eff9bcba4d4a07a080ffb88eee8ede (MD5) Previous issue date: 2015-12-03 / Based on contemporary educational management, this research targeted on the concepts of strategic management in educational institutions, democratic participatory management, and the use of management tools to support the work of the management of public schools of basic education. In this context, the Development Plan of the School (PDE-School) is presented by the Ministry of Education (MEC), as an administrative tool whose goal is to improve the administrative and academic performance of schools and the IDEB observed in the period from 2005 to 2013 pointed out problems in academic performance in schools, since the basic education schools in the municipality studied have not reached the average projected. Thus, the research turns to the PDE-School, featuring the difficulties to use the program as a strategic management tool in basic education schools in the municipality of Itaquaquecetuba, SP. To perform this, we used quantitative research, statistical and exploratory, through a questionnaire closed to the management team of sixty-three (63) basic education schools in the city using the PDE-School. The results have enhanced some difficulties in using the tool, however, indicate that it is possible to use it. The research also suggests a pedagogical approach that uses performance indicators to address the educational problems and plan actions, given this, relevant in the context of strategic management and administrative and pedagogic efficiency of the school as it is understood the importance of school staff actively participating in the educational process of the school. / Sobre la base de lagestión educativa contemporánea, esta investigación focalizada enlos conceptos de gestión estratégica enlasinstituciones educativas, lagestión democrática y participativa, y el uso de herramientas de gestión para apoyareltrabajo de lagestión de lasescuelas públicas de educación básica. En este contexto, elPlan de Desarrollo de laFacultad (PDE-School) es presentado por elMinisterio de Educación (MEC), como una herramienta administrativa cuyo objetivo es mejorareldesempeño administrativo y académico de lasescuelas y el IDEB observada enel período de 2005 a 2013 señaló problemas enelrendimiento académico enlasescuelas, ya que lasescuelas de educación básica enelmunicipioestudiado no hanllegado a la media proyectada. Así, lainvestigación se dirige a la PDE-escuela, conlasdificultades para utilizar el programa como herramienta de gestión estratégica enlasescuelas de educación básica enelmunicipio de Itaquaquecetuba, SP. Para llevar a cabo esto, se utilizólainvestigacióncuantitativa, estadística y exploratorio, a través de uncuestionario cerrado al equipo de gestión de sesenta y tres (63) escuelas de educación básica enlaciudad utilizando la PDE-School. Los resultados han caracterizado algunasdificultadesenel uso de laherramienta, sin embargo, indican que es posibleutilizarlo. La investigacióntambiénsugiereun enfoque pedagógico que utiliza indicadores de rendimiento para hacer frente a los problemas educativos y accionesdelplan, teniendoencuentaesto, relevante enel contexto de lagestión estratégica y laeficiencia administrativa y pedagógica de laescuela, ya que se entiendelaimportanciadelpersonal de laescuela participar activamenteenelproceso educativo de laescuela. / Com base na gestão educacional contemporânea, esta pesquisa mirou-se nos conceitos de gestão estratégica nas instituições de ensino, gestão democrática participativa, e na utilização de ferramentas de gestãopara auxiliar o trabalho da gestão das escolaspúblicas de educação básica. Neste contexto, o Plano de Desenvolvimento da Escola, (PDE-Escola)é apresentado pelo Ministério da Educação (MEC), como uma ferramenta administrativa cujo objetivo é melhorar o desempenho administrativo e acadêmico das escolas, uma vez que o IDEB observado no período de 2005 a 2013 apontou problemas no desempenho acadêmico nas escolas, e que as escolas de educação básica do município pesquisado não têm atingido a média projetada. Assim, a pesquisa se volta para o PDE-Escola, caracterizando as dificuldades de uso do programa como ferramenta de gestão estratégica nas escolas de educação básica no município de Itaquaquecetuba, SP. Para realização desta, utilizou-se pesquisa de natureza quantitativa, estatística e exploratória, através de questionário fechado para a equipe gestora de sessenta e três (63) escolas de educação básica do município que utilizam o PDE-Escola. Os resultados evidenciaram algumas dificuldades no uso da ferramenta, no entanto, apontam que é possível utilizá-la. A pesquisa também sugere uma postura pedagógica que utiliza os indicadores de desempenho para corrigir as dificuldades pedagógicas e planejar as ações,dado esse relevante no contexto da gestão estratégica e eficiência administrativo-pedagógica da escola, uma vez que se entende a importância da equipe escolar participando ativamente do processo pedagógico da escola.

Through perturbation analysis, a study of the role of Brinkman viscosity in the propagation of finite amplitude harmonic waves is carried out. Interplay between various parameters, namely, frequency, Reynolds number and beta are investigated. For systems with physically realizable Reynolds numbers, departure from the Darcy Jordan model (DJM) is noted for high frequency signals. Low and high frequency limiting cases are discussed, and the physical parameters defining the acoustic propagation are obtained. Through numerical analyses, the roles of Brinkman viscosity, the Darcy coefficient, and the coefficient of nonlinearity on the evolution of finite amplitude harmonic waves is stud- ied. An investigation of acoustic blow-ups is conducted, showing that an increase in the magnitude of the nonlinear term gives rise to blow-ups, while an increase in the strength of the Darcy and/or Brinkman terms mitigate them. Finally, an analytical study via a regular perturbation expansion is given to support the numerical results. In order to gain insight into the formation and evolution of nonlinear standing waves un- der the Brinkman model, a numerical analysis is conducted on the weakly nonlinear model based on Brinkman’s equation. We develop a finite difference scheme and conduct a param- eter study. An examination of the Brinkman, Darcy, and nonlinear terms is carried out in the context of their roles on shock formation. Finally, we compare our findings to those of previous results found in similar nonlinear equations in other fields. So as to better understand the behavior of finite-amplitude harmonic waves under a Brinkman-based poroacoustic model, approximations and transformations are used to recast the Brinkman equation into the damped Burger’s equation. An examination is carried out for the two special solutions of the damped Burger’s equation: the approximate solution to the damped Burger’s equation and the boundary value problem given an initial sinusoidal pulse. The effects of the Darcy coefficient, Reynolds number, and nonlinear coefficient on these solutions are investigated.

Thesis advisor: Thomas C. Chiles / Elevating intracellular cAMP levels can result in a wide range of anti-inflammatory effects and growth arrest and apoptosis in cancer cells, marking phosphodiesterases (PDEs) as potential targets for inflammatory diseases and cancer treatment. PDE7A is proposed to be a new therapeutic target for its ubiquitous expression in proinflammatory and immune cells. A Barbituric acid based compound, BC12 was identified as an in vitro PDE7 inhibitor in fission-yeast-based high-throughput screen. Analysis of this compound on the activation of Jurkat T lymphocytes, mouse and human primary T cells reveals inhibition of IL-2 production, though cell viability is not significantly impacted. Real-time RT-PCR and mRNA stability assays indicate that the inhibition of IL-2 production by BC12 is attributable to transcriptional repression without accelerating IL-2 mRNA decay. By contrast, compounds of similar structure with that of BC12 exhibit varying effects on IL-2 production that does not correlate with their in vitro PDE7 inhibitory activity, suggesting that the in vivo target of BC12 responsible for these effects may not be PDE7. Our study further reveals that BC12 inhibits IL-2 transcription through targeting NFAT and NFkB-mediated pathways. Preliminary investigation on other T helper cell cytokine secretion indicates that BC12 has a potential to selectively inhibit Th2 cytokines. Our data suggest that BC12 may present a novel anti-inflammatory drug for its immunosuppressive and potential immunomodulatory effects. Analysis of BC12 on a human B-cell line and a monocytic cell line demonstrate its pro-apoptotic effects in a dose-dependent manner. Titration of BC12 on human diffuse large B-cell lymphoma (DLBCL), LY18 cells, and human primary B cells reveals that BC12 induces cell death more effectively in DLBCL LY18 cells than normal B cells, suggesting the anti-cancer potential of this compound. / Thesis (PhD) — Boston College, 2013. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Biology.

Neste trabalho estudaremos uma classe de problemas não locais do tipo Neumann. Consideramos o caso linear não homogêneo, bem como o semi-linear com não linearidades globalmente Lipschitz. Procuramos escrever um trabalho auto-contido. Apresentamos alguns resultados clássicos de Análise e suas aplicações no contexto de equação de evolução não local. Na introdução, apresentamos uma motivação para tais equações tendo em vista os fenômenos de reação e difusão baseados no trabalho de P. Fife. / In this work we will study a class of nonlocal problems of the Neumann type. We consider the non-homogeneous linear case as well as the semi-linear one with globally Lipschitz non-linearities. We seek to write a self-contained work with some classic results of Analysis and its applications in the context of non-local evolution equations. In the introduction, we present a motivation for such equations in view of the phenomena of reaction and diffusion based on the work of P. Fife