In previous studies, evidence of thermal wave behavior was found in heterogeneous materials. Thus, the overall goal of this study was to experimentally verify those results, and develop a parameter estimation scheme to estimate the thermal properties of various heterogeneous materials. Two types of experiments (Experiments 1 and 2) were conducted to verify the existence or non-existence of thermal wave behavior in heterogeneous materials. In Experiment 1 sand, ion exchanger, and sodium bicarbonate were used as test materials, while processed meat (bologna) was used in Experiment 2. The measured temperature profiles of the samples were compared with the parabolic and hyperbolic heat conduction model results. The values of thermal diffusivity and thermal conductivity were obtained using the Box-Kanemasu parameter estimation method which is based on the comparison between temperature measurements and the solutions of the theoretical model. Overall, no clear experimental evidence was found to justify the use of hyperbolic heat conduction models rather than parabolic for the materials tested. Further comprehensive experimentation using different heating rates is warranted to definitely identify the accurate type of heat conduction process associated with such materials, and to describe the physical mechanisms which produce wave-like heat conduction in heterogeneous materials. / Master of Science

Extreme value theory is used as a basis for deriving a distribution function for flood frequency analysis when runoff originates from nonhomogeneous sources. A modified least squares technique is used to estimate the parameters of the distribution function for eleven rivers. Goodness-of-fit statistics are computed and the distribution function is found to fit the data very well. The derived distribution function is recommended as a base method for flood frequency analysis for rivers exhibiting nonhomogeneous sources of runoff if further investigation also proves to be positive.

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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

Hazy images are often subject to color distortion, blurring and other visible quality degradation. Some existing CNN-based methods have shown great performance on removing the homogeneous haze, but they are not robust in the non-homogeneous case. The reason is twofold. Firstly, due to the complicated haze distribution, texture details are easy to get lost during the dehazing process. Secondly, since the training pairs are hard to be collected, training on limited data can easily lead to the over-fitting problem. To tackle these two issues, we introduce a novel dehazing network using the 2D discrete wavelet transform, namely DW-GAN. Specifically, we propose a two-branch network to deal with the aforementioned problems. By utilizing the wavelet transform in the DWT branch, our proposed method can retain more high-frequency information in feature maps. To prevent over-fitting, ImageNet pre-trained Res2Net is adopted in the knowledge adaptation branch. Owing to the robust feature representations of ImageNet pre-training, the generalization ability of our network is improved dramatically. Finally, a patch-based discriminator is used to reduce artifacts of the restored images. Extensive experimental results demonstrate that the proposed method outperforms the state-of-the-art quantitatively and qualitatively. / Thesis / Master of Applied Science (MASc)

The dissertation focuses on the initial boundary value problems (IBVPs) of a class of nonlinear Schrodinger equations posed on a half plane R x R+ and on a strip domain R x [0,L] with Dirichlet nonhomogeneous boundary data in a two-dimensional plane. Compared with pure initial value problems (IVPs), IBVPs over part of entire space with boundaries are more applicable to the reality and can provide more accurate data to physical experiments or practical problems. Although there is less research that has been made for IBVPs than that for IVPs, more attention has been paid for IBVPs recently. In particular, this thesis studies the local well-posedness of the equation for the appropriate initial and boundary data in Sobolev spaces H^s with non-negative s and investigates the global well-posedness in the H^1-space. The main strategy, especially for the local well-posedness, is to derive an equivalent integral equation (whose solution is called mild solution) from the original equation by semi-group theory and then perform the Banach fixed-point argument. However, along the process, it is essential to select proper auxiliary function spaces and prepare all the corresponding norm estimates to complete the argument. In fact, the IBVP posed on R x R+ and the one posed on R x [0,L] are two independent problems because the techniques adopted are different. The first problem is more related to the initial value problem (IVP) posed on the whole plane R^2 and the major ingredients are Strichartz's estimate and its generalized theory. On the other hand, the second problem can be studied as an IVP over a half-line and periodic domain, which is established on the analysis for series inspired by Bourgain's work. Moreover, the corresponding smoothing properties and regularity conditions of the solution are also considered. / Ph. D.

In this dissertation, we apply Bayesian and Empirical Bayes methods for reliability growth models based on the power law process. We also apply Bayes methods for the study of microarrays, in particular, in the selection of differentially expressed genes. The power law process has been used extensively in reliability growth models. Chapter 1 reviews some basic concepts in reliability growth models. Chapter 2 shows classical inferences on the power law process. We also assess the goodness of fit of a power law process for a reliability growth model. In chapter 3 we develop Bayesian procedures for the power law process with failure truncated data, using non-informative priors for the scale and location parameters. In addition to obtaining the posterior density of parameters of the power law process, prediction inferences for the expected number of failures in some time interval and the probability of future failure times are also discussed. The prediction results for the software reliability model are illustrated. We compare our result with the result of Bar-Lev,S.K. et al. Also, posterior densities of several parametric functions are given. Chapter 4 provides Empirical Bayes for the power law process with natural conjugate priors and nonparametric priors. For the natural conjugate priors, two-hyperparameter prior and a more generalized three-hyperparameter prior are used. In chapter 5, we review some basic statistical procedures that are involved in microarray analysis. We will also present and compare several transformation and normalization methods for probe level data. The objective of chapter 6 is to select differentially expressed genes from tens of thousands of genes. Both classical methods (fold change, T-test, Wilcoxon Rank-sum Test, SAM and local Z-score and Empirical Bayes methods (EBarrays and LIMMA) are applied to obtain the results. Outputs of a typical classical method and a typical Empirical Bayes Method are discussed in detail.

To assemble the fulcrum of bascule bridges, a trunnion is immersed into liquid nitrogen so that it can be shrunk fit into the hub. This is followed by immersing the resulting trunnion-hub assembly into liquid nitrogen so that it can be then shrunk fit into the girder. On one occasion in Florida, when the trunnion-hub assembly was put into liquid nitrogen, development of cracks on the hub was observed. Experimental and numerical studies conducted since 1998 at University of South Florida show that the cracking took place due to combination of high interference stresses in the trunnion-hub assembly, low fracture toughness of steel at cryogenic temperatures, and steep temperature gradients due to sudden cooling. In this study, we are studying the benefit of staged cooling to avoid cracking in the trunnion-hub assembly when it is cooled down for shrink fitting. We looked at three cooling processes - 1) Direct immersion into liquid nitrogen 2) Immersion into a refrigerated chamber, then liquid nitrogen 3) Immersion into a refrigerated chamber, then a dry-ice/alcohol bath, and finally liquid nitrogen. The geometry of the trunnion-hub assembly was approximated by a composite made of two infinitely long hollows cylinders. The transient problem of temperature distribution and the resulting stresses was solved using finite difference method. Using critical crack lengths and Von-Mises stress as failure criteria, the three cooling processes were compared. The study showed that the minimum critical crack length and stress ratio is increased by as much as 200% when cooling first in refrigerated air followed by liquid nitrogen. However, there is little benefit from adding dry-ice/alcohol as an intermediate step in the cooling process.

在求無限期非均質馬可夫決策過程（nonhomogeneous Markov decisinon processes）第一期的的最佳解時，我們通常要將它表示成有限期的動態規劃問題。動態規劃可以用合成函數型式表示，也可以用最常見的線性規劃型式表示。 　　合成函數型式在傳統上是一直被認為「中看而不中用」，動態規劃的教科書中，只有在開場白中，介紹一下這種簡潔、漂亮的數學型式，然後就被完全打入冷宮，認為線性規劃型式才是真正實用、真正能讓電腦去執行求解的型式。在一般期刊的文獻中甚至根本不提這種表示法，而是花大篇篇幅在它所衍生的線性規劃技術上作文章，最典型的例子是Bean, Hopp and Duenyas(1992) 在OR期刊所發表的論文。 　　本文將完全針對這個問題的合成函數型式，討論它的一些性質，我們可以利用這些性質，設計出一個非常簡單、有效率的演算法。 / Hopp, Bean and Duenyas(1992) formulate a mixed integer program (MIP) to determine whether a finite time horizon is a forecast horizon in a nonhomogeneous Markov decision process(NMDP). Their formula are solved by complex Bender's decomposition In this thesis, we make an examination in details of the contraction property and affine mapping property of NMDP. By these properties we are relieved of the complex MIP formula and Bender's decomposition algorithm. The main contribution of the thesis is to show that it is not necessary to determine the optimal policies by running through the whole feasible solution space of their MIP problem. We only need to check a finite number of vertices at a polyhedral set shaped by the solution of the NMDP. The analysis shows insights into the NMDP and facilitate the prosess in determining the forecast horizon. Furthermore, this NMDP formulation is presented in the form of a simple dynamic function which is different from the linear program presented by Hopp, Bean and Duenyas.

For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.