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Flowgraph models are directed graph models for describing the dynamic changes in a stochastic process. They are one class of multistate models that are applied to analyse time-to-event data. The main motivation of the flowgraph models is to determine the distribution of the total waiting times until an event of interest occurs in a stochastic process that progresses through various states. This thesis applies the methodology of flowgraph models to the study of Markov and SemiMarkov processes. The underlying approach of the thesis is that the access to the moment generating function (MGF) and cumulant generating function (CGF), provided by Mason’s rule enables us to use the Method of Moments (MM) which depends on moments and cumulant. We give a new derivation of the Mason’s rule to compute the total waiting MGF based on the internode transition matrix of a flowgraph. Next, we demonstrate methods to determine and approximate the distribution of total waiting time based on the inversion of the MGF, including an alternative approach using the Pad´e approximation of the MGF, which always yields a closed form density. For parameter estimation, we extend the Expectation-Maximization (EM) algorithm to estimate parameters in the mixture of negative weight exponential density. Our second contribution is to develop a bias correction method in the Method of Moments (BCMM). By investigating methods for tail area approximation, we propose a new way to estimate the total waiting time density function and survival

The experimental data and results demonstrated here illustrate the preparation and application of mesoporous metal oxides in energy storage, adsorption, and catalysis. First, a new method of controlling the pore size and wall thickness of mesoporous silica was developed by controlling the calcination temperature. A series of such silica were used as hard templates to prepare the mesoporous metal oxide Co₃O₄. Using other methods, such as varying the silica template hydrothermal treatment temperature, using colloid silica, varying the materials ratio etc., a series of mesoporous β-MnO₂ with different pore size and wall thickness were prepared. By using these materials it has been possible to explore the influence of pore size and wall thickness on the rate of lithium intercalation into mesoporous electrode. There is intense interest in lithium intercalation into titanates due to their potential advantages (safety, rate) replacing graphite for new generation Li-ion battery. After the preparation of an ordered 3D mesoporous anatase the lithium intercalation as anode material has been investigated. To the best of our knowledge, there are no reports of ordered crystalline mesoporous metal oxides with microporous walls. Here, for the first time, the preparation and characterization of three dimensional ordered crystalline mesoporous α-MnO₂ with microporous wall was described, in which K+ and KIT-6 mesoporous silica act to template the micropores and mesopores, respectively. It was used as a cathode material for Li-ion battery. Its adsorption behavior and magnetic property was also surveyed. Following this we described the preparation and characterization of mesoporous CuO and reduced Cu[subscript(x)]O, and demonstrated their application in NO adsorption and delivery. Finally a series of crystalline mesoporous metal oxides were prepared and evaluated as catalysts for the CO oxidation.