This report describes the governing equation and boundary conditions for a marine propeller operating in a uniform flow field of inviscid and irrotational fluid. A method is presented by which the velocity and pressure on the blade surface of the propeller can be numerically simulated, using hyperboloidal, constant strength source and doublet panels. Accuracy of the numerical method is verified through comparison with analytically known results and the ability of the numerical simulation to predict the thrust and torque on a propeller in open water is assessed through comparison with published experimental results. The thrust and torque results for the propeller are near the experimental measurements but do not converge to a common value as the panel size decreases.

In this dissertation we developed theoretical models to analyse Gaussian and multinomial distributions. The analysis is focused on classification in high dimensional feature spaces and provides a basis for dealing with issues such as data sparsity and feature selection (for Gaussian and multinomial distributions, two frequently used models for high dimensional applications). A Naïve Bayesian philosophy is followed to deal with issues associated with the curse of dimensionality. The core treatment on Gaussian and multinomial models consists of finding analytical expressions for classification error performances. Exact analytical expressions were found for calculating error rates of binary class systems with Gaussian features of arbitrary dimensionality and using any type of quadratic decision boundary (except for degenerate paraboloidal boundaries). Similarly, computationally inexpensive (and approximate) analytical error rate expressions were derived for classifiers with multinomial models. Additional issues with regards to the curse of dimensionality that are specific to multinomial models (feature sparsity) were dealt with and tested on a text-based language identification problem for all eleven official languages of South Africa. / Thesis (M.Ing. (Computer Engineering))--North-West University, Potchefstroom Campus, 2009.

In this dissertation we developed theoretical models to analyse Gaussian and multinomial distributions. The analysis is focused on classification in high dimensional feature spaces and provides a basis for dealing with issues such as data sparsity and feature selection (for Gaussian and multinomial distributions, two frequently used models for high dimensional applications). A Naïve Bayesian philosophy is followed to deal with issues associated with the curse of dimensionality. The core treatment on Gaussian and multinomial models consists of finding analytical expressions for classification error performances. Exact analytical expressions were found for calculating error rates of binary class systems with Gaussian features of arbitrary dimensionality and using any type of quadratic decision boundary (except for degenerate paraboloidal boundaries). Similarly, computationally inexpensive (and approximate) analytical error rate expressions were derived for classifiers with multinomial models. Additional issues with regards to the curse of dimensionality that are specific to multinomial models (feature sparsity) were dealt with and tested on a text-based language identification problem for all eleven official languages of South Africa. / Thesis (M.Ing. (Computer Engineering))--North-West University, Potchefstroom Campus, 2009.