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The thesis considers and examines methods of surface propagation, where the normal velocity of the surface depends on the local curvature and the gradient of the surface. Such fronts occur in many different physical situations from the growth of crystals to the spreading of flames. A number of different methods are considered to find solutions to these physical problems. First the motion is modelled by partial differential equations and numerical methods are developed for solving these equations. The numerical methods involve characteristic, finite differences and transformation of the equations. Stability of the solutions is also briefly considered. Secondly the fronts are modelled by using a cellular approach which subdivides space into regions of small cells. The fronts are assumed to propagate through the region according to stochastic rules. Monte-Carlo simulations are carried out using this approach. Results of the simulations are carried out in two-dimensions and three-dimensions for a number of interesting physical examples.

In metrology, measurement uncertainty is understood as a range in which the true value of the measurement is likely to fall in. The recent years have seen a rapid development in evaluation of measurement uncertainty. ISO Guide to the Expression of Uncertainty in Measurement (GUM 1995) is the primary guiding document for measurement uncertainty. More recently, the Supplement 1 to the "Guide to the expression of uncertainty in measurement" – Propagation of distributions using a Monte Carlo method (GUM SP1) was published in November 2008. A number of software tools for measurement uncertainty have been developed and made available based on these two documents. The current software tools are mainly desktop applications utilising numeric computation with limited mathematical model handling capacity. A novel and generic web-based application, web-based Knowledge-Based Decision Support System (KB-DSS), has been proposed and developed in this research for measurement uncertainty evaluation. A Model-View-Controller architecture pattern is used for the proposed system. Under this general architecture, a web-based KB-DSS is developed based on an integration of the Expert System and Decision Support System approach. In the proposed uncertainty evaluation system, three knowledge bases as sub-systems are developed to implement the evaluation for measurement uncertainty. The first sub-system, the Measurement Modelling Knowledge Base (MMKB), assists the user in establishing the appropriate mathematical model for the measurand, a critical process for uncertainty evaluation. The second sub-system, GUM Framework Knowledge Base, carries out the uncertainty evaluation process based on the GUM Uncertainty Framework using symbolic computation, whilst the third sub-system, GUM SP1 MCM Framework Knowledge Base, conducts the uncertainty calculation according to the GUM SP1 Framework numerically based on Monte Carlo Method. The design and implementation of the proposed system and sub-systems are discussed in the thesis, supported by elaboration of the implementation steps and examples. Discussions and justifications on the technologies and approaches used for the sub-systems and their components are also presented. These include Drools, Oracle database, Java, JSP, Java Transfer Object, AJAX and Matlab. The proposed web-based KB-DSS has been evaluated through case studies and the performance of the system has been validated by the example results. As an established methodology and practical tool, the research will make valuable contributions to the field of measurement uncertainty evaluation.

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This research examines how the Targeted Separation Incentive Program, currently underway by the Navy, is being administered to bring about the voluntary separations of junior officers to meet the requirements of the Navyâ s most recent force reduction. This study evaluates the effects of past separation incentive programs as well as the current compensation package that the service-member may receive which is outlined in the Fiscal Year 2006 National Defense Authorization Act. In addition, an analysis was conducted of the costs associated with retaining the service-member versus the personal costs of that individual of leaving. The objective of this thesis is to evaluate the Department of the Navyâ s (DoN) Targeted Separation Incentive Program in order to see if this program can adequately meet the goals of the current force reduction and whether or not savings can be realized through alternative separation programs.

El fenómeno de ordenación químico en las aleaciones binarias influye directa y fuertemente sobre sus propiedades físicas tales como resistividad eléctrica, capacidad calorífica, constantes elásticas, coeficiente de Hall, etc. Las aleaciones binarias con tendencia a ordenamiento químico a bajas temperaturas, como el sistema Cu-Au y Fe-Al, son interesantes debido a sus importantes propiedades eléctricas y de resistencia a altas temperaturas. El objetivo principal del trabajo es investigar el fenómeno de transición de fases orden¬-desorden en las aleaciones binarias mediante la simulación con el método Monte Carlo y el algoritmo de Metrópolis. Usamos el modelo ABV de la aleación binaria para simular los sistemas AB3 y AB (Cu3AuyFeAl) considerando internaciones atómicas de pares hasta los terceros vecinos más próximos. La dinámica fue introducida por medio de una vacan¬te que intercambia de posición con los átomos vecinos más próximos con cierta probabilidad; además aplicamos condiciones periódicas de frontera para evitar efectos de borde. Una vez logrado el equilibrio térmico a la temperatura requerida se almacenan los datos para calc¬ular la energía del sistema, el calor específico y los parámetros de orden de largo (LRO) y Corto alcance (SRO) de Warren ¬Cowley. En base a los datos obtenidos se han determinado la temperatura crítica de transición orden -desorden para los sistemas estudiados. También hallamos las probabilidades de formación de clústeres (agregados) en la aleación en un amplio rango de temperaturas así como en un rango de concentración de una de las componentes.

The counterparty credit risk is particularly hard to simulate and this thesis is only the second work so far, which considers effective simulation of couterparty risk. There are two new approaches to stochastic modelling, which are useful with respect to ef- ficient simulation of counterparty risk. These are Path-Dependent Simulation (PDS) and Direct-Jump to Simulation date (DJS). It had been show that DJS is far more ef- fective, when it comes counterparty risk simulation of path-independent derivatives. We focus on a portfolio of interest rate swaps, which are effectively path-dependent. DJS approach yields estimates with much lower variance than PDS approach. But as expected, the DJS is also much more computationally intensive. The increase in computing time in majority of cases wipes out any gains in lower variance and PDS approach is shown to be more effective, when computing time is taken into account. We also show that in practice the convergence rate of Monte Carlo method signif- icantly underestimates the true reduction in variance, which can be achieved with increasing number of scenarios. JEL Classification C02, C15, C63, G01, G12, G32 Keywords Monte Carlo, CVA, Exposure, Variance Author's e-mail robberth.cz@gmail.com Supervisor's e-mail boril.sopov@gmail.com

Presenta los modelos estocásticos de los problemas resultantes del tratamiento estadístico dado a los coeficientes, así como algunos métodos de resolución utilizados para calcular los momentos estadísticos de las soluciones. Presenta la discretización de las ecuaciones de las realizaciones en el contexto de Monte Carlo. Realiza simulaciones numéricas.

This course project is made up of two parts. Part one is an investigation and implementation of pricing of financial derivatives using numerical methods for the solution of partial differential equations. Part two is an introduction of Monte Carlo methods in financial engineering. The name of course is MA573:Computational Methods in Financial Mathematics, spring 2009, given by Professor Marcel Blais.