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Conductivity and viscosity of dilute solutions of lithium nitrate and cadmium iodide in binary and ternary mixtures of acetone with methyl alcohol, ethyl alcohol and water ...Mahin, Edward G., January 1908 (has links)
Thesis (Ph. D.)--John Hopkins University. / Biography.
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Conductivity and viscosity of dilute solutions of lithium nitrate and cadmium iodide in binary and ternary mixtures of acetone with methyl alcohol, ethyl alcohol and water ...Mahin, Edward G., January 1908 (has links)
Thesis (Ph. D.)--John Hopkins University. / Biography.
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The Reflected Quasipotential: Characterization and ExplorationFarlow, Kasie Geralyn 06 May 2013 (has links)
The Reflected Quasipotential V(x) is the solution to a variational problem that arises in the study of reflective Brownian motion. Specifically, the stationary distributions of reflected Brownian motion satisfy a large deviation principle (with respect to a spatial scaling parameter) with V(x) as the rate function. The Skorokhod Problem is an essential device in the construction and analysis of reflected Brownian motion and our value function V(x). Here we characterize V(x) as a solution to a partial differential equation H(DV(x))=0 in the positive n-dimensional orthant with appropriate boundary conditions. H(p) is the Hamiltonian and DV(x) is the gradient of V(x). V(x) is continuous but not differentiable in general. The characterization will need to be in terms of viscosity solutions. Solutions are not unique, thus additional qualifications will be needed for uniqueness. In order to prove our uniqueness result we consider a discounted version of V(x) in a truncated region and pass to the limit. In addition to this characterization of V(x) we explore the possibility of cyclic optimal paths in 3 dimensions. / Ph. D.
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Numerical Methods for Optimal Trade ExecutionTse, Shu Tong January 2012 (has links)
Optimal trade execution aims at balancing price impact and timing risk. With respect to the mathematical formulation of the optimization problem, we primarily focus on Mean Variance (MV) optimization, in which the two conflicting objectives are maximizing expected revenue (the flip side of trading impact) and minimizing variance of revenue (a measure of timing risk). We also consider the use of expected quadratic variation of the portfolio value process as an alternative measure of timing risk, which leads to Mean Quadratic Variation (MQV) optimization.
We demonstrate that MV-optimal strategies are quite different from MQV-optimal strategies in many aspects. These differences are in stark contrast to the common belief that MQV-optimal strategies are similar to, or even the same as, MV-optimal strategies. These differences should be of interest to practitioners since we prove that the classic Almgren-Chriss strategies (industry standard) are MQV-optimal, in contrary to the common belief that they are MV-optimal.
From a computational point of view, we extend theoretical results in the literature to prove that the mean variance efficient frontier computed using our method is indeed the complete Pareto-efficient frontier. First, we generalize the result in Li (2000) on the embedding technique and develop a post-processing algorithm that guarantees Pareto-optimality of numerically computed efficient frontier. Second, we extend the convergence result in Barles (1990) to viscosity solution of a system of nonlinear Hamilton Jacobi Bellman partial differential equations (HJB PDEs).
On the numerical aspect, we combine the techniques of similarity reduction, non-standard interpolation, and careful grid construction to significantly improve the efficiency of our numerical methods for solving nonlinear HJB PDEs.
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Numerical Methods for Optimal Trade ExecutionTse, Shu Tong January 2012 (has links)
Optimal trade execution aims at balancing price impact and timing risk. With respect to the mathematical formulation of the optimization problem, we primarily focus on Mean Variance (MV) optimization, in which the two conflicting objectives are maximizing expected revenue (the flip side of trading impact) and minimizing variance of revenue (a measure of timing risk). We also consider the use of expected quadratic variation of the portfolio value process as an alternative measure of timing risk, which leads to Mean Quadratic Variation (MQV) optimization.
We demonstrate that MV-optimal strategies are quite different from MQV-optimal strategies in many aspects. These differences are in stark contrast to the common belief that MQV-optimal strategies are similar to, or even the same as, MV-optimal strategies. These differences should be of interest to practitioners since we prove that the classic Almgren-Chriss strategies (industry standard) are MQV-optimal, in contrary to the common belief that they are MV-optimal.
From a computational point of view, we extend theoretical results in the literature to prove that the mean variance efficient frontier computed using our method is indeed the complete Pareto-efficient frontier. First, we generalize the result in Li (2000) on the embedding technique and develop a post-processing algorithm that guarantees Pareto-optimality of numerically computed efficient frontier. Second, we extend the convergence result in Barles (1990) to viscosity solution of a system of nonlinear Hamilton Jacobi Bellman partial differential equations (HJB PDEs).
On the numerical aspect, we combine the techniques of similarity reduction, non-standard interpolation, and careful grid construction to significantly improve the efficiency of our numerical methods for solving nonlinear HJB PDEs.
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C¹,α regularity for boundaries with prescribed mean curvatureWelch, Stephen William 01 December 2012 (has links)
In this study we provide a new proof of C¹,α boundary regularity for finite perimeter sets with flat boundary which are local minimizers of a variational mean curvature formula. Our proof is provided for curvature term H∈LΩ. The proof is a generalization of Cafarelli and C#243;rdoba's method, and combines techniques from geometric measure theory and the theory of viscosity solutions which have been developed in the last 50 years. We rely on the delicate interplay between the global nature of sets which are variational minimizers of a given functional, and the pointwise local nature of comparison surfaces which satisfy certain PDE. As a heuristic, in our proof we can consider the curvature as an error term which is estimated and controlled at each point of the calculation.
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[pt] UNICIDADE DE SOLUÇÕES LP-FORTES / [en] UNIQUENESS OF LP-STRONG SOLUTIONSGABRIEL GOMES FIGUEIREDO 26 September 2023 (has links)
[pt] Esta dissertação de mestrado aborda um estudo aprofundado do artigo [2].
No Capítulo 2, são introduzidas as definições e conceitos fundamentais
necessários para a análise teórica subsequente. Uma proposição é
demonstrada, estabelecendo a existência de uma expansão de Taylor para
funções em um determinado espaço, enfatizando o papel do expoente de
Escauriaza.
O capítulo continua apresentando dois lemas que relacionam subsoluções
e supersoluções em termos de viscosidade e propriedades de normas. A
primeira versão do lema considera a relação entre a dimensão do espaço e
a norma, enquanto a segunda versão utiliza o expoente de Escauriaza para
obter resultados mais refinados. Também são apresentados dois resultados
que explicam a relação entre diferentes noções de soluções viscosas e sua
conexão com os espaços de Sobolev.
As propriedades dos operadores de Pucci são discutidas como conclusão
deste capítulo. No Capítulo 3, a dissertação estabelece a definição da
geometria da fronteira do domínio em questão. Em seguida, um importante
lema é demonstrado, estabelecendo a existência de soluções fortes em um
determinado espaço, explorando a regularidade das funções envolvidas com
base nesse lema.
Os conceitos de super-diferenciabilidade e sub-diferenciabilidade são
introduzidos, desempenhando um papel crucial na compreensão
do comportamento das soluções viscosas e suas relações com
derivadas de ordem superior. Um resultado geral que amplia essas
definições é apresentado. Duas versões em que a função u é duas
vezes super-diferenciável são discutidas, considerando o espaço Ld e posteriormente o espaço Lp
, de modo que p menor que d.
A dissertação prossegue demonstrando a relação entre sub-solução
Lp-viscosidade e sub-solução Lp-forte quando u pertence a um espaço
específico. Em seguida, é mostrado que os limites uniformes de soluções
também são soluções. Por fim, é apresentado o resultado principal da
dissertação, demonstrando a unicidade das soluções fortes. / [en] This master s thesis delves into an in-depth study of the article [2]. Chapter2 begins by introducing fundamental definitions and concepts essential forthe subsequent theoretical analysis. A proposition is then demonstrated,establishing the existence of a Taylor expansion for functions in a givenspace, emphasizing the role of the Escauriaza exponent.The chapter proceeds to present two lemmas that relate subsolutions andsupersolutions in terms of viscosity and properties of norms. The firstversion of the lemma considers the relationship between the dimension ofspace and the norm, while the second version uses the Escauriaza exponentto obtain more refined results. Two results are shown to explain that explainthe relationship between different notions of viscous solutions and theirconnection with Sobolev spaces.The properties of the Pucci operators are discussed at the conclusion of thischapter. Chapter 3 begins by establishing the definition of the boundarygeometry of the domain in question. An important lemma is demonstrated,which establishes the existence of strong solutions in a given space andexplores the regularity of the functions involved based on this lemma.The concepts of superdifferentiability and subdifferentiability areintroduced, playing a crucial role in understanding the behavior of viscoussolutions and their relationships with higher order derivatives. A generalresult that extends these definitions is presented. The dissertation discussestwo versions wherein the function u is twice super-differentiable, consideringthe space Ld and later the space Lp, so that p less than d.The dissertation goes on to demonstrate the relationship between Lp-viscosity sub-solution and Lp-strong sub-solution when u belongs to aspecific space. Next, it is shown that the uniform limits of solutions arealso solutions. Finally, the main result of the dissertation is presented,demonstrating the uniqueness of strong solutions.
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Generalized Solutions to Several Problems in Open Channel Hydraulics / 開水路水理学におけるいくつかの問題に対する一般化解MEAN, Sovanna 24 September 2021 (has links)
京都大学 / 新制・課程博士 / 博士(農学) / 甲第23527号 / 農博第2474号 / 新制||農||1087(附属図書館) / 学位論文||R3||N5358(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 藤原 正幸, 教授 中村 公人, 准教授 宇波 耕一 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DGAM
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Multi-player pursuit-evasion differential gamesLi, Dongxu 30 November 2006 (has links)
No description available.
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Verallgemeinerte Charakteristiken am Beispiel hyperbolischer ErhaltungsgleichungenSchenk, Matthias 16 November 2017 (has links)
In dieser Arbeit werden wir Systeme von Erhaltungsgleichungen betrachten. Dabei handelt es sich um hyperbolische Systeme erster Ordnung. Durch hyperbolische Differentialgleichungen werden Wellen und deren Ausbreitung beschrieben, skalare Differentialgleichungen erster Ordnung sind immer hyperbolisch. Wichtige Beispiele für hyperbolische Erhaltungsgleichungen sind die nichtviskose Burgersgleichung, die Buckley-Leverett-Gleichung zur Beschreibung von Zweiphasenströmungen, die Eulergleichungen der nichtviskosen Strömungsmechanik und bestimmte Gleichungen der Magnetohydrodynamik. Ausserdem finden sie auch Anwendung in Verkehrsflussmodellen, beispielsweise beim Modell von Lighthill, Whitham und Richards.
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