The thesis presents six experiments designed to further understanding of effective methods of presenting Bayesian problems to a general audience. The fi rst four experiments (Part I) focus on general Bayesian reasoning. The nal two experiments (Part II) focus speci fcally on the legal domain. Experiment one compares two leading theories for Bayesian presentation: Macchi's (2000) `nested sets' approach, and Krynski and Tenenbaum's (2007) `causal' approach. It also uses a think aloud protocol, requiring thought-process recording during solution. A nested sets framing effect is found, but no causal framing effect. From the think aloud data, a fi ve-stage solution process (the `nested sets' process), modal among successful individuals, is found. In experiment two, Macchi's approach is tested on a problem with greater ecological validity. An increase in accuracy is still seen. Experiment two also fi nds that conversion of the problem to integers by participants is highly associated with accuracy. Experiment three confi rms the null causal fi nding of experiment one and fi nds that the think aloud protocol itself increases accuracy. Experiment four experimentally tests whether prompting problem conversion to integers, and prompting individuals to follow the nested sets process improve accuracy. No effect is found for conversion, but an effect is found for the nested sets process prompt. Experiment fi ve tested whether statistically untrained individuals can undertake accurate Bayesian reasoning of a legal case including necessary forensic error rates (Fenton et al., 2014). No single individual is found to provide the normative answer. Instead a range of heuristics are found. Building upon this, experiment six compares two approaches to presenting the Bayesian output of a legal case: the popular event tree diagram, and the Bayesian network diagram recommended by (Fenton et al., 2014). Without inclusion of false positives and negatives the event-tree diagram was rated more trust worthy and easy to understand than the Bayesian network diagram. However, including these error types, this pattern reversed.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: p. 213-217. / Ph.D.

by Ma Ka Chun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 50-52). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.7 / Chapter 2 --- Queueing Networks --- p.9 / Chapter 2.1 --- One-queue Networks --- p.9 / Chapter 2.2 --- Two-queue Free Networks --- p.12 / Chapter 2.3 --- Two-queue Overflow Networks --- p.13 / Chapter 2.4 --- Networks with Batch Arrivals --- p.14 / Chapter 3 --- ODE Solvers --- p.16 / Chapter 3.1 --- The Initial Value Methods --- p.16 / Chapter 3.1.1 --- The Linear System of Ordinary Differential Equations --- p.16 / Chapter 3.1.2 --- Euler's Method --- p.17 / Chapter 3.1.3 --- Runge-Kutta Methods --- p.17 / Chapter 3.1.4 --- The Stability of the IVMs --- p.19 / Chapter 3.1.5 --- Applications in Queueing Networks --- p.20 / Chapter 3.2 --- The Boundary Value Methods --- p.20 / Chapter 3.2.1 --- The Generalized Backward Differentiation For- mulae --- p.21 / Chapter 3.2.2 --- An example --- p.24 / Chapter 4 --- The Linear Equation Solver --- p.26 / Chapter 4.1 --- Iterative Methods --- p.26 / Chapter 4.1.1 --- The Jacobi method --- p.27 / Chapter 4.1.2 --- The Gauss-Seidel Method --- p.28 / Chapter 4.1.3 --- Other Iterative Methods --- p.29 / Chapter 4.1.4 --- Preconditioning --- p.29 / Chapter 4.2 --- The Multigrid Method --- p.30 / Chapter 4.2.1 --- Iterative Refinement --- p.30 / Chapter 4.2.2 --- Restriction and Prolongation --- p.30 / Chapter 4.2.3 --- The Geometric Multigrid Method --- p.33 / Chapter 4.2.4 --- The Algebraic Multigrid Method --- p.38 / Chapter 4.2.5 --- Higher Dimensional Cases --- p.38 / Chapter 4.2.6 --- Applications in Queueing Networks --- p.38 / Chapter 5 --- Numerical Experiments --- p.41 / Chapter 6 --- Concluding Remarks --- p.49 / Bibliography --- p.50

Hung Kin Ting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 126-129). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Inverse Problems --- p.1 / Chapter 1.2 --- Applications of Inverse Problems --- p.2 / Chapter 1.3 --- Least-squares Solutions --- p.4 / Chapter 1.4 --- Discrete Systems --- p.4 / Chapter 1.5 --- "Discretization, Regularization and Regularization Pa- rameters" --- p.5 / Chapter 1.6 --- Outline of the Thesis --- p.6 / Chapter 2 --- Some Basic Concepts and Mathematical Tools --- p.8 / Chapter 2.1 --- Singular Value Decomposition (SVD) --- p.8 / Chapter 2.2 --- Generalized Singular Value Decomposition (GSVD) --- p.13 / Chapter 2.3 --- White Noises --- p.16 / Chapter 3 --- Regularized Solutions --- p.18 / Chapter 3.1 --- Derivation of Regularized Solutions --- p.18 / Chapter 3.2 --- Discrete Picard Condition --- p.20 / Chapter 3.3 --- Relationship between Discrete Picard Condition and Regularized Solution --- p.21 / Chapter 3.4 --- Checking for the Discrete Picard Condition --- p.22 / Chapter 4 --- Different Discretization Approaches --- p.23 / Chapter 4.1 --- Problem 1 - Volterra Integral Equation of the First Kind --- p.25 / Chapter 4.2 --- Examples of Problem 1 --- p.30 / Chapter 4.3 --- Problem 2 - Fredholm Integral Equation of the First Kind --- p.49 / Chapter 4.4 --- Examples of Problem 2 --- p.53 / Chapter 4.5 --- Conclusion --- p.57 / Chapter 5 --- Effect of Different Kinds of Observation Data and Differential Operators on Accuracy --- p.59 / Chapter 5.1 --- Pointwise Observation Data --- p.60 / Chapter 5.2 --- Pointwise Observation Data of Heat Fluxes at the Boundary --- p.69 / Chapter 5.3 --- Observation Data with Heat Fluxes --- p.80 / Chapter 5.4 --- Conclusion --- p.89 / Chapter 6 --- L-curve --- p.90 / Chapter 6.1 --- Properties of L-curve --- p.93 / Chapter 6.2 --- L-curve in Log-Log Scale --- p.100 / Chapter 6.3 --- Disadvantages of the L-curve Method --- p.100 / Chapter 7 --- Algorithms of Finding the Corner of L-curve --- p.105 / Chapter 7.1 --- Cubic Spline Curve Fitting --- p.105 / Chapter 7.2 --- Conic Section Fitting --- p.106 / Chapter 7.3 --- Triangle Method --- p.109 / Chapter 8 --- Implementation of the L-curve Method --- p.111 / Chapter 8.1 --- Our Algorithm --- p.111 / Chapter 8.2 --- Numerical Experiments --- p.112 / Chapter 8.3 --- Conclusion --- p.124 / Bibliography --- p.126

Lai Kim Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 55-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Likelihood Ratio Test Statistic --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Formulation --- p.6 / Chapter 2.3 --- Likelihood Ratio Type Statistic --- p.7 / Chapter 2.4 --- Dirichlet Distribution --- p.8 / Chapter 2.5 --- Edgeworth Expansion --- p.12 / Chapter 3 --- Divided Difference --- p.15 / Chapter 3.1 --- Introduction --- p.15 / Chapter 3.2 --- Definition of Divided Difference --- p.15 / Chapter 3.3 --- Theorem --- p.17 / Chapter 3.4 --- Proof of the Theorem --- p.18 / Chapter 3.5 --- Application of Theorem --- p.19 / Chapter 4 --- Computational Results --- p.22 / Chapter 4.1 --- Introduction --- p.22 / Chapter 4.2 --- Critical Values for Moderate and Large Sample Sizes --- p.22 / Chapter 4.3 --- Critical Values for Small Sample Sizes --- p.23 / Chapter 4.3.1 --- Exact Critical Values --- p.23 / Chapter 4.3.2 --- Edgeworth Expansion Results --- p.23 / Chapter 4.3.3 --- Simulation Results --- p.23 / Chapter 4.4 --- Power --- p.24 / Chapter 5 --- Illustrative Examples --- p.29 / Chapter 5.1 --- Stanford Heart Transplant Data --- p.29 / Chapter 5.1.1 --- The Data --- p.29 / Chapter 5.1.2 --- Result --- p.31 / Chapter 5.2 --- Air Conditioning Data --- p.31 / Chapter 5.2.1 --- The Data --- p.31 / Chapter 5.2.2 --- Result --- p.32 / Chapter 5.3 --- Insulating Fluid Failure Data --- p.33 / Chapter 5.3.1 --- The Data --- p.33 / Chapter 5.3.2 --- Result --- p.33 / Chapter 6 --- Conclusion and Further Research Topic --- p.35 / Chapter 6.1 --- Conclusion --- p.35 / Chapter 6.2 --- Further Research Topic --- p.38 / Appendix A --- p.39 / Appendix B --- p.46 / Bibliography --- p.55

Firstly, we consider the following critical elliptic Neumann problem --Deltau + muu = uN+2N-2 , u > 0 in O; 6u6n = 0 on ∂O, where O is a smooth bounded domain in RN , N ≥ 7, mu is a large positive number and nu denotes exterior unit normal vector. We show that at a positive nondegenerate local minimum point Q0 of the mean curvature function, for any fixed integer K ≥ 2, there exists a mu K > 0 such that for mu > muK, the above problem has K -- bubble solution umu concentrating at the same point Q 0. Precisely, we show that umu has K local maximum points Qm1,...,Qm K ∈ ∂O with the property that umQmj ∼mN-22 ,Qmj→Q0 , j = 1, ..., K, and mN-3N Q'1 m,...,Q'K m approaches an optimal configuration that minimizes the following functional RQ'1,...,Q 'K=c1 j=1K4Q' j+c2 i≠j1&vbm0;Q' i-Q'j&vbm0;N-2 where Qmi=Qm i,1,...,Qmi,N-1 ,Qmi,N:= Q'i m,Qmi,N , c1, c2 > 0 are two generic constants and ϕ(Q) = Q T GQ with G = (∇ijH(Q0)). / In my thesis, I will address different concentration phenomena for some second order elliptic problems. / Lastly, we consider the problem &egr;2Delta u -- u + uq = 0 in a smooth bounded domain O ⊂ R2 with Neumann boundary condition where &egr; > 0 is a small parameter and q > 1. We prove for some explicit &egr;'s the existence of positive solution u&egr; concentrating at any connected component of ∂O, exponentially small in &egr; at any positive distance from it. / Secondly, we study positive solutions of the equation &egr;2Delta u -- u + uN+2N-2 = 0, where N = 3, 4, 5, and &egr; > 0 is small, with Neumann boundary condition in a smooth bounded domain O ⊂ RN . We prove that, along some sequence {&egr;j} with &egr;j → 0, there exists a solution with an interior bubble at an innermost part of the domain and a boundary layer on the boundary ∂O. / Wang, Liping. / "June 2008." / Adviser: Jun Cheng Wei. / Source: Dissertation Abstracts International, Volume: 70-03, Section: B, page: 1707. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 107-117). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

In [DS1,2,3], Denker and Sato initiated a new point of view to study the problem. They identified the Sierpinski gasket as a Martin boundary of some canonical Markov chain and used the associated theory to consider the problem. In this thesis, we will extend their result so as to be applicable to all single-point connected monocyclic post critically finite (m.p.c.f.) self-similar sets. / In the first chapter, we review some basic facts of the self-similar sets and the Martin boundaries, and we prove that every m.p.c.f. self-similar set K is homeomorphic to the quotient space of the symbolic space associated with K, moreover, the homeomorphism is a Lipschitz equivalence for some special m.p.c.f. self-similar sets. / In the second chapter, we first prove that the quotient space of the symbolic space associated with K is homeomorphic to the Martin boundary with respect to the state space associated with K if K is a single-point connected m.p.c.f. self-similar set. Combining this result and the result in the first chapter, we conclude that every single-point connected m.p.c.f. self-similar set can be identified with the Martin boundary of some canonical Markov chain. Then for the 3-level Sierpinski gasket, we prove that there exists a one to one relation between the strongly P-harmonic functions on the 3 state space and K-harmonic functions constructed by Kigami. / In the third chapter, we define a new Markov chain on the pentagasket K which is a single-point connected m.p.c.f. self-similar also. Under the new Markov chain, we prove that K can be identified with the Martin boundary of the new Markov chain and that there exists a one to one relation between the strongly P-harmonic functions and the K-harmonic functions. / One of the fundamental problems in fractal analysis is to construct a Laplacian on fractals. Since fractals, like the Sierpinski gasket and the pentagasket, do not have any smooth structures, it is not possible to construct it from the classical point of view. Hence, until now there is no systematic way to define such a notion on the general class of fractals. / There are two approaches for the problem which have achieved some success in certain special situations. The first one is a probabilistic approach via constructing Brownian motions on self-similar sets. The second approach is an analytical one proposed by Kigami. He approximated the underlying self-similar set K by an increasing sequence of finite sets equipped with the discrete Laplacians Hm in a consistent way. He showed that if K is strongly symmetric, then Hm converge to a Laplacian on K. / by Ju, Hongbing. / "March 2008." / Adviser: Lau Ka Sing. / Source: Dissertation Abstracts International, Volume: 70-03, Section: B, page: 1702. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 91-94). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

In chapter 1, we focus on the full potential equation in an infinite nozzle with some decay cross-sections and prove the existence and stability of the transonic shock wave; which is a solution to a free boundary value problem for a quasi-linear mix-typed partial differential equation with the position of shock as a free boundary. To achieve this conclusion, we reduce it to a free boundary value problem for a quasi-linear elliptic equation in an unbounded domain. The crucial step in our analysis is to derive some uniform a priori estimates in such a domain. Then we apply the fixed point theorem to establish the existence of solutions to the full potential equation. / In chapter 2, we study the short time existence of discontinuous shock front solutions of the pressure gradient system which is the Euler system without inertial terms, where the initial data can have shock discontinuities of arbitrary strength which lie on a given smooth initial surface with arbitrary geometry. These shock solutions are constructed via a classical iteration scheme. The key step is to obtain the uniform stability for the related linearized equation by calculating the Lopatinski's determinant, which enables us to modify the technique of Majda and establish the local existence of solutions to the pressure gradient system without the structural constraints as for the full Euler system. / In this thesis we study two kinds of multi-dimensional shock phenomena for the compressible fluid dynamics. / Xie Feng. / "December 2005." / Adviser: Zhou Ping Xin. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6446. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 71-80). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Orientador: Paula da Cruz Landim / Banca: Maria Antonia Benutti / Banca: Ana Gabriela Godinho Lima / Resumo: O sistema atual de produção e consumo, banal e desenfreado, tem gerado graves problemas ambientais, colocando em risco a sobrevivência da própria humanidade. A questão ambiental vem sendo cada vez mais discutida por toda a sociedade, empresas e governo, nas mais variadas áreas de estudo. O design, como área de conhecimento, também cria propostas de forma a combater a degradação do meio ambiente e criar um futuro mais sutentável. Neste contexto, este estudo busca investigar como as empresas no pólo joalheiro de Limeira lidam com as questões ambientais, integrando design e sustentabilidade na concepção e produção de suas peças. Para tanto, foi elaborado um referencial teórico onde se buscou apresentar os principais conceitos de sustentabilidade, ecodesign, bem como o mercado joalheiro e o pólo em questão. Foi realizado um estudo de caso com as empresas do setor a fim de obter dados para traçar um perfil de como são tratadas as questões ambientais e sua integração com o design / Abstract: The current system of consumption and production, banal and unrestrained, is resposible for serious environmental problems, threatening the own survival of humanity. The environmental issu has been increasingly discussed by the whole society, business and government in several areas of study. Design, as a knowledge area also creates purposes in order to content environmental degradation and establish a more sustainable future. Thus, this study gains investigate how companies in Limeira (SP)'s Complex deal with environmental matters, integrating design and sustainability in creation e production of their parts. To this end, was developed a theoretical framework, where is shown the main concepts of sustainability, design for environmental, as well as the jewerly market and the complex in question. It has a case study of the sector companies to obtain data for a profile of how to they treat environmental issues as well their integration with design / Mestre

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