This thesis explores the modelling for Internal Rating Based (IRB) of Credit Risk for Small and Medium Enterprises (SMEs) as required for implementation of Basel II Accord. There has been limited previous research for this important sector of the economy. There are two major approaches: Accounting Based and Merton Type, and these are compared. To make the comparison initially a small sample is considered and simulation is used to explore the use of the two approaches. The study indicates some of the limitation of analysis for both Accounting Based and Merton Type approaches, for example the issue of colinearity for the Accounting Based approach and lack of trading of SMEs’ equity affecting the Merton Type approach. A large sample is then investigated using standard Credit Scoring approaches for the Accounting Based modelling. Different definitions of default and distress are considered to overcome the problem of low number of defaults. These approaches are found to be viable. Merton Type model is then compared to benchmark models from the Accounting Based approach. The predictions are compared over differing time horizons. It is found that Merton Type models perform well within a limited period compared to the Accounting Base approach. Overall, credit scoring models demonstrated better performance when the sample group included a considerable number of ‘Bad’ firms or cutoff point was selected so that an acceptance rate was relatively low, otherwise model’s predictive accuracy would decline. Merton model presented better predictive accuracy with higher acceptance rates. Credit scoring models was able to give early signs of default year. In addition, one may take into consideration that if the company is going to decline credit quality or raise default probability this year, Merton type models can be helpful in adjusting credit rating. When considering a loan to a company, a bank wants to know the likelihood default for duration of loan. In this sense Merton models is only useful for a relatively short loan terms.

Texture in crystalline materials, i.e. preferred orientation (PO), is of interest in terms of texture-property relationships and also in X-ray diffraction science because PO can cause serious systematic errors in quantitative phase analysis using diffraction data. The single- parameter, pole-density distribution function (PDDF), proposed by March (1932) to represent PO in diffraction analysis, is used widely it Rietveld pattern-fitting following a suggestion by Dollase (1986). While the March model is an excellent descriptor of PO for gibbsite [AI(OH)3] x-ray powder diffraction (XRPD) data (O'Connor, Li and Sitepu, 1991), the model has proved to be deficient for Rietveld modelling with molybdite [Mo03], calcite [CaCO3] and kaolinite [A12O3.2SiO2.2H2O] XRPD data (Sitepu, 1991; O'Connor, Li and Sitepu, 1992; and Sitepu, O'Connor and Li, 1996). Therefore, the March model should not be regarded as a general-purpose PDDF descriptor.This study has examined the validity of the March model using XRPD and neutron powder diffraction (NPD) instruments operated, respectively, by the Curtin Materials Research Group in Perth and by the Australian Nuclear Science and Technology Organisation at the HIFAR reactor facility at Lucas Heights near Sydney. Extensive suites of XRPD and NPD data were measured for uniaxially-pressed powders of molybdite and calcite, for which the compression was systematically varied. It is clear from the various Rietveld refinements that the March model becomes increasingly unsatisfactory as the uniaxial pressure (and, therefore, the level of PO) increases.The March model has been tested with a physical relationship developed by the author which links the March r-parameter to the uniaxial pressure via the powder bulk modulus, B. The agreement between the results obtained from directly measured values of B and from Rietveld analysis with the March model are ++ / promising in terms of deducing the powder bulk modulus from the March r-parameter.An additional test of the March model was made with NPD data for specimens mounted, first, parallel to the instrument rotation axis and, then, normal to the axis. The results have provided some further indication that the March model is deficient for the materials considered in the study.During the course of the study, it was found that there are distinct differences between the direction of the near-surface texture in calcite, as measured by XRPD, and bulk texture characterised by NPD. The NPD-derived textures appear to be correct descriptions for the bulk material in uniaxially-pressed powders, whereas the XRPD textures are heavily influenced by the pressing procedure.An additional outcome of the NPD work has been the discovery, made jointly with Dr Brett Hunter of ANSTO, that the popular LHPM Rietveld code did not allow for inclusion of PO contributions from symmetry-equivalent reflections. Revision of the code by Dr Hunter showed that there is substantial bias in Rietveld-March r-parameters if these reflections are not factored correctly into the calculations.Finally, examination of pole-figure data has underlined the extent to which the March model oversimplifies the true distributions. It is concluded that spherical harmonics modelling should be used rather than the March model as a general PO modelling tool.

This work is concerned with the formulation and analysis of a simplified GinzburgLandau type model of superconductivity which is valid for large K and large magnetic field strengths. This model, referred to as the High kappa model, is derived via formal asymptotic expansion of the full, time-dependent Ginzburg-Landau equations. The model accounts for the effects of both applied magnetic fields and currents of constant magnitude. A notable feature of our model is that the systems for the leading order terms for the magnetic potential and the order parameter are decoupled. Finite element approximations of the High kappa model are introduced using standard Galerkin discretization in space and Backward-Euler and Crank-Nicolson discretization schemes in time. We establish existence and uniqueness results for the fully-discrete equations as well as optimal L2 and HI error estimates for the Backward-Euler-Galerkin and the Crank-Nicolson-Galerkin problems. Computational experiments are performed with several combinations of spatial and time discretizations of the High kappa model equations. Among other things our numerical approximations show good agreement for rates of convergence in space and time with the corresponding theoretical values. Finally, some well known steady-state and dynamic phenomena valid for type II superconductors are illustrated numerically. / Ph. D.

In this thesis we provide an existence result for a regularized model of viscoelastic non- newtonian fluid. We consider incompressible fluid with shear rate dependent viscosity and with Cauchy stress tensor capable to describe stress relaxation. An elastic part of the Cauchy stress tensor is governed by Oldroyd-type differential equation. In particular, we are interested in fluids with strong shear thinning effect. We prove that if the viscosity function µ (D) is such that tensor µ (D) D is p-coercive, monotone and has (p − 1)-growth for p > 6 5 and some other additional assumptions are satisfied, then there exists a solution to the system of PDEs describing the flow in a bounded domain. The proof is not simple because the convective term is not integrable with a high power. The problem is solved using Lipschitz truncation method for evolution PDEs. 1

The idea of type has always been a crucial factor in the field of architecture. Not only it works as a dominator in the design process of architecture but also it supplies the certain ways through which architecture communicates with the observer. In order to understand the interaction between architecture and the observer the idea of type appears as a critical point. This study will be an attempt to understand the dialogue of type and model in architecture. Throughout the research Anthony Vidler&rsquo / s article &ldquo / Third Typology&rdquo / will be used as the main outline to see the development of type within the theory of architecture and various typologies. The interaction between type and model will be dealed as a field of communication where meaning in architecture is situated. In this attempt the theory of language will be the main reference to understand the relation between type and model.

This dissertation explores the estimation of endogenous treatment effects in the presence of heterogeneous responses. A Bayesian Nonparametric approach is taken to model the heterogeneity in treatment effects. Specifically, I adopt the Dirichlet Process Mixture (DPM) model to capture the heterogeneity and show that DPM often outperforms Finite Mixture Model (FMM) in providing more flexible function forms and thus better model fit. Rather than fixing the number of components in a mixture model, DPM allows the data and prior knowledge to determine the number of components in the data, thus providing an automatic mechanism for model selection. Two DPM models are presented in this dissertation. The first DPM model is based on a two-equation selection model. A Dirichlet Process (DP) prior is specified on some or all the parameters of the structural equation, and marginal likelihoods are calculated to select the best DPM model. This model is used to study the incentive and selection effects of having prescription drug coverage on total drug expenditures among Medicare beneficiaries. The second DPM model utilizes a three-equation Roy-type framework to model the observed heterogeneity that arises due to the treatment status, while the unobserved heterogeneity is handled by separate DPM models for the treated and untreated outcomes. This Roy-type DPM model is applied to a data set consisting of 33,081 independent individuals from the Medical Expenditure Panel Survey (MEPS), and the treatment effects of having private medical insurance on the outpatient expenditures are estimated. Key Words: Treatment Effects, Endogeneity, Heterogeneity, Finite Mixture Model, Dirichlet Process Prior, Dirichlet Process Mixture, Roy-type Modeling, Importance Sampling, Bridge Sampling

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Battery technology is a great candidate for energy storage applications. The need for high-performance and cost-effective batteries has motivated researchers to put much effort into improving battery performance. In this work, we attempt to understand the elements that affect the microstructure and performance of two battery systems. The first part of this work focuses on the investigation of transport and structural properties of porous electrodes in an alkaline electrolyte. A DC polarization method was deployed for tortuosity measurements. An apparatus was designed to flow specified current through and measure the voltage drop over the porous electrodes. Using a modified Ohm's law, effective diffusion coefficient and associated tortuosity were determined. Multiple compositions (different types and amounts of conductive additives) were tested to understand the effects of composition on the transport properties. As a validation and to further understand the tests, a model was developed and used for data analysis. The second part of this dissertation describes simulations of the manufacturing process of a Li-ion electrode. LAMMPS, a particle simulator, was used for this meso-scale particle-based simulation. The interactions between particles were understood by model-experiment comparisons of the macroscopic properties such as viscosity of the slurry and elasticity of the dried film. The microstructure created by this simulation was consistent with the one we observed in SEM/ FIB images. Although the emphasis was the drying process in this part, some preliminary coating and calendering simulations are presented. Finally, the effects of electrode heterogeneity were investigated by a Newman-type model and tomographic images. An electronic conductivity map was initially generated over a Li-ion cathode. Then SEM/FIB images of specified high, middle, and low conductivity regions were taken to confirm heterogeneity. For modeling purposes, three regions of high, middle, and low ionic resistance were considered connected in parallel, representing the real electrode heterogeneity. Multiple cases of heterogeneities such as non-uniform ionic resistance and active material loading at low, middle, and high charge-discharge rates were studied. The results show that higher rates increase non-uniformities of dependent properties such as temperature, current density, positive and negative electrodes states of charge, and charge and discharge capacities especially in charging cases.

In this study, the evolution of the numerical water wave models with the theoretical background and the governing equations are briefly discussed and a numerical model MIKE21 BW which can be applied to wave problems in nearshore zone is presented. The numerical model is based on the numerical solution of the Boussinesq type equations formulated on time domain. Nonlinearity and frequency dispersion is included in the model. In order to make comparison between the results of nonlinear shallow water equations with Boussinesq terms, MIKE21 BW and NAMIDANCE are applied to the problem of wave propagation in the long distances and runup on simple and composite slopes. The numerical experiments are applied to Dat&ccedil / a Marina and the results are compared to the results of the physical experiments on wave disturbance in Dat&ccedil / a Marina. In these comparisons the reflection characteristics of different coastal boundaries in the harbor area are tested and the internal parameters in the model are calibrated accordingly. The numerical model MIKE21 BW is applied to skenderun harbor as a case study. The input wave parameters are selected from the wave climate study for Iskenderun Harbor. The model is set up and the agitation inside the harbor is computed according to four different incoming wave scenarios. The disturbance maps inside the harbor for different incoming wave scenarios are obtained. The critical regions v of the harbor according to disturbance under different wave conditions are presented and discussed.

In a developing oil-based economy like Libya the availability of finance is largely affected by the availability of oil revenues which are subjected to disturbances and shocks. Therefore, the decision to save and invest a certain ratio of the country's aggregate output is, to large extent, determined (and affected) by the shocks in the oil markets rather than the requirements of economic development. In this study an attempt is made to determine the optimal rate of saving and investment, both defined as a ratio of the aggregate output, according to the requirements of economic development. For this purpose, a neo-classical Ramsey-type model for Libya is constructed and applied to obtain theoretically and empirically the optimal saving and investment rate during the period (1965-1991). The results reveal that Libya was investing over the optimal level during the oil boom of 1970s and less than the optimal level during the oil crisis of 1980s. In addition, an econometric investigation of the determinants of actual investment by sector (agriculture, non-oil industry, and services) is carried out in order to shed lights on how possible it is for Libya to adjust actual investment towards its optimal level. It is found that, as expected, the most important factor which can be used in this respect is the oil revenues or, generally, the availability of finance. In addition, the study reveals that investment in agriculture is associated, during the period of study, with a very low marginal productivity of capital whereas marginal productivity was higher in both non-oil industry and services. Finally, the study investigates also the future potential saving and investment rates and concludes that the economy, which has already reached its steady state, can be pushed out towards further growth if the economy can be able to increase the level of per worker human capital, proxied by the secondary school enrolment as a percentage of population. / Secretariat of Higher Education in Libya and Libyan Interests Section in London