Thesis (M.A.)--Boston University / The problem of finding the solution to a general eliptic type partial differential equation, when the boundary values are given, is generally referred to as the Dirichlet Problem. In this paper I consider the special eliptic equation of ∇2 J=0 which is Laplace's equation, and I limit myself to the case of two dimensions. Subject to these limitations I discuss five proofs for the existence of a solution to Laplace's equation for arbitrary regions where the boundary values are given. [TRUNCATED]

Neste trabalho apresentamos com detalhes as provas de três teoremas e algumas de suas consequências sobre a questão da existência e unicidade de soluções para o Problema de Dirichlet para a Equação das Superfícies de Curvatura Média Constante H sobre domínios Ω limitados do plano não necessariamente convexos. As hipóteses relacionam a condição do círculo exterior de Ω, a norma C2 do dado do bordo e H. / In this work we present with detail the proof of three theorems and some of its consequences on existence and uniqueness of solutions to the Dirichlet Problem for the Constant Mean Curvature H Surface Equation on a bounded not necessarily convex domain of the plane. The hypothesis relates the exterior circle condition of Ω, the C2 norm of boundary date and H.

Neste trabalho apresentamos com detalhes as provas de três teoremas e algumas de suas consequências sobre a questão da existência e unicidade de soluções para o Problema de Dirichlet para a Equação das Superfícies de Curvatura Média Constante H sobre domínios Ω limitados do plano não necessariamente convexos. As hipóteses relacionam a condição do círculo exterior de Ω, a norma C2 do dado do bordo e H. / In this work we present with detail the proof of three theorems and some of its consequences on existence and uniqueness of solutions to the Dirichlet Problem for the Constant Mean Curvature H Surface Equation on a bounded not necessarily convex domain of the plane. The hypothesis relates the exterior circle condition of Ω, the C2 norm of boundary date and H.

Neste trabalho apresentamos com detalhes as provas de três teoremas e algumas de suas consequências sobre a questão da existência e unicidade de soluções para o Problema de Dirichlet para a Equação das Superfícies de Curvatura Média Constante H sobre domínios Ω limitados do plano não necessariamente convexos. As hipóteses relacionam a condição do círculo exterior de Ω, a norma C2 do dado do bordo e H. / In this work we present with detail the proof of three theorems and some of its consequences on existence and uniqueness of solutions to the Dirichlet Problem for the Constant Mean Curvature H Surface Equation on a bounded not necessarily convex domain of the plane. The hypothesis relates the exterior circle condition of Ω, the C2 norm of boundary date and H.

Orientador: Djairo Guedes de Figueiredo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T02:46:15Z (GMT). No. of bitstreams: 1 Ponce_AugustoCesar_M.pdf: 3854563 bytes, checksum: be51c3115a25502f8b3aa55466a6484c (MD5) Previous issue date: 2000 / Resumo: Este trabalho tem por objetivo principal o estudo de alguns desenvolvimentos históricos do problema de Dirichlet, desde suas origens no século 18. Nós adotamos um tratamento puramente matemático, apresentando na primeira parte uma discussão detalhada dos métodos clássicos utilizados no estudo do prblema de Dirichlet para a equação de Laplace. Na segunda e na terceira parte, consideramos o caso mais geral do problema de Dirichlet semilinear, inicialmente num contexto de minimização do funcional associado, e, em seguida, tratamos do problema na presença de simetria, em cujo caso é possível concluir a existência de uma seqüência ilimitada de soluções / Abstract: The main goal of this dissertation is to study some historical developments of the Dirichlet problem since its early beginnings during the eighteenth century. We used a strictly mathematical approach, giving in the first part a detailed discussion of the classical methods developed to handle Dirichlet problem for Laplace's equation. In the second and third parts we consider the more general case of a semilinear Dirichlet problem. First the discussion is in the context of minimization of the associated functional, and then we handle this problem when symmetry is involved. In such a case it is possible to conclude the existence of an unbounded sequence of solutions / Mestrado / Mestre em Matemática

Orientador: Rodney Carlos Bassanezi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-16T23:56:46Z (GMT). No. of bitstreams: 1 Weber_OlivioAugusto_M.pdf: 759549 bytes, checksum: f0b81e3f28b2afb0624e858de5685536 (MD5) Previous issue date: 1977 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática

Orientador: Rodney Carlos Bassanezi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-07-20T00:20:32Z (GMT). No. of bitstreams: 1 Andrade_AntonioFernandoPradode_M.pdf: 1093212 bytes, checksum: 45967fce9ccd797d7bbc0e1726ce8a42 (MD5) Previous issue date: 1977 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática

Investigating the immunoglobulin repertoire is a means of understanding the adaptive immune response to infectious disease or vaccine challenge. The data examined are typically generated using high-throughput sequencing on samples of immunoglobulin variable-region genes present in blood or tissue collected from human or animal subjects. The analysis of these large, diverse collections provides a means of gaining insight into the specific molecular mechanisms involved in generating and maintaining a protective immune response. It involves the characterization of distinct clonal populations, specifically through the inference of founding alleles for germline gene segment recombination, as well as the lineage of accumulated mutations acquired during the development of each clone. Germline gene segment inference is currently performed by aligning immunoglobulin sequencing reads against an external reference database and assigning each read to the entry that provides the best score according to the metric used. The problem with this approach is that allelic diversity is greater than can be usefully accommodated in a static database. The absence of the alleles used from the database often leads to the misclassification of single-nucleotide polymorphisms as somatic mutations acquired during affinity maturation. This trend is especially evident with the rhesus macaque, but also affects the comparatively well-catalogued human databases, whose collections are biased towards samples from individuals of European descent. Our project presents novel statistical methods for immunoglobulin repertoire analysis which allow for the de novo inference of germline gene segment libraries directly from next-generation sequencing data, without the need for external reference databases. These methods follow a Bayesian paradigm, which uses an information-theoretic modelling approach to iteratively improve upon internal candidate gene segment libraries. Both candidate libraries and trial analyses given those libraries are incorporated as components of the machine learning evaluation procedure, allowing for the simultaneous optimization of model accuracy and simplicity. Finally, the proposed methods are evaluated using synthetic data designed to mimic known mechanisms for repertoire generation, with pre-designated parameters. We also apply these methods to known biological sources with unknown repertoire generation parameters, and conclude with a discussion on how this method can be used to identify potential novel alleles.

<p> In this thesis, we shall solve the classical Dirichlet problem for a ball in n-dimensional Euclidean space, and then point out that the classical Dirichlet problem is not always solvable. Following Wiener and Brelot, we then introduce a generalized Dirichlet problem for any bounded region in n-dimensional Euclidean space and establish necessary and sufficient conditions for its solution. We show that the solution of the generalized Dirichlet problem coincides with the solution of the classical Dirichlet problem whenever the latter exists. Finally, we characterize those regions for which the classical Dirichlet problem is solvable by considering the boundary behaviour of those functions for which the generalized problem is solvable.</p> / Thesis / Master of Science (MSc)

Supply chains are complex systems. Researchers in the Social and Decision Analytics Laboratory (SDAL) at Virginia Tech worked with a major global supply chain company to simulate an end-to-end supply chain. The supply chain data includes raw materials, production lines, inventory, customer orders, and shipments. Including contributions of this author, Pires, Sabin, Higdon et al. (2017) developed simulations for the production, customer orders, and shipments. Customer orders are at the center of understanding behavior in a supply chain. This dissertation continues the supply chain simulation work by improving the order simulation. Orders come from a diverse set of customers with different habits. These habits can differ when it comes to which products they order, how often they order, how spaced out those orders times are, and how much of each of those products are ordered. This dissertation is unique in that it relies extensively on Dirichlet and multiscale methods to tackle supply-chain order simulation. Multiscale model methodology is furthered to include Dirichlet models which are used to simulate order times for each customer and the collective system on different scales. / Doctor of Philosophy / This dissertation continues the supply chain simulation work of researchers (Pires et al. (2017)) in the Social and Decision Analytics Laboratory (SDAL) at Virginia Tech by improving the order simulation. Orders come from a diverse set of customers with different habits. These habits can di er when it comes to which products they order, how often they order, how spaced out those orders times are, and how much of each of those products are ordered. This dissertation is unique from the previous work at SDAL which considered few of these factors in order simulation and introduces statistical methodologies to deal with the complex nature of simulating an entire supply chain's orders.