This thesis details an experimental and computational investigation of the relationship between exhaust system geography, the exhaust port pressure history and the gas exchange process in reciprocating four-stroke engines. The study was conducted in four phases. In the first phase, an extensive experimental programme was undertaken, during which key engine performance indicators together with exhaust and intake system manifold pressure and temperature data were recorded on a Rover 1.4 litre 16-valve K series engine. Measured data from each test were used to validate computational predictions. In the second phase the effect of the phasing of pressure waves at the exhaust port was systematically studied using a modified version of the validated model. The relationships between key engine performance indicators and the pressure at the exhaust port during specific periods of the exhaust event were identified. In the third phase, exhaust system gas dynamics were studied and the effect of exhaust system junctions and components on the transmitted and reflected characteristics of pressure waves were investigated. A method was identified by which the dynamic pressure history at the exhaust port could be broken down into its principal incident and reflected pressure wave components.

<p>This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. For the desingularized elliptic self fiber product, we use an isotypic decomposition of the motive to deduce the Murre conjectures. We also prove a result about the intersection product. For the Fano surface of lines, we prove the finite-dimensionality of the Chow motive. Finally, we prove that an ample hypersurface on an Abelian variety possesses a Chow-Kunneth decomposition for which a motivic version of the Lefschetz hyperplane theorem holds.</p> / Dissertation

This thesis addresses possible improvements in the efficiency (thrust) of surface piercing propellers; in particular with respect to the angle of the propeller shaft came to mind. Preliminary calculations based on the basic pitch/diameter geometry suggest that about 3-5% efficiency is lost if the shaft is parallel to the flow, compared to skewed a few degrees in the "paddlewheel" direction at certain speeds. More accurate calculations based on the lift characteristics of each blade, on the angle of attack and the flow of water over each blade and given a set of basic assumption on the over all performance of each blade, as the blade enters and leaves the water; are used to determine the increase in efficiency. Full scale experimental results are also presented in support of the calculations.

Many onboard ship operations demand full radio coverage over the entire ship, not only indoor, but also from the interior spaces to the other decks. Onboard a ship, specifically in the upper decks, radio wave propagation is subjected to fading that would impede the quality and reliability of data links and communication. One example is the performance of unmanned aerial vehicle (UAV) data and communications links. The purpose of this thesis is to analyze, model, and simulate some communication scenarios that occur on naval ships using Urbana. Starting from known inputs (frequency, ship compartment geometry, material properties, propagation computation model, and antenna type), analytical results reflecting the propagation mechanisms and coverage area are presented. Variable inputs can then be optimized to achieve a desired signal distribution for a specific shipboard environment. The ship models were created by Rhino, a well-known Windows-based computer drawing software. The values of the signals received on the different points in the main deck are computed for different frequencies and powers. The results are used to draw conclusions of the deployment of antennas on the ship as well as operational aspects such as UAV flight paths.

The phenomenon of spiral wave propagation in Belousov-Zhabotinsky media is a remarkable example of self-organisation. This distinctive waveform arises in a variety of excitable systems. The primary objective of the work described in this thesis is the construction and analysis of deterministic reaction-diffusion models in terms of partial differential equations, to explain the local and global geometry of the spiral pattern. The secondary objective is to design experiments that enable observation and recording of evolving chemical waves in three dimensional Belousov-Zhabotinsky media. A mathematical formulation of the one dimensional A-w system based on a hierarchy of trial phase functions is introduced. A Schr8dinger type boundary value problem in an eigen sub-domain is established; an algebraic formula for the wave number spectrum and an analytical representation for the concentration amplitude are derived. This formulation suggests a piece-wise linear approach to X-w systems in higher dimensions. The concentrations are expressible in terms of real combinations of solutions to the Helmholtz equation with complex wave number and the solutions are matched by using continuity, differentiability and threshold conditions. A detailed analysis of the existence of solutions to piece-wise linear A-w systems in two dimensions is presented; existence is demonstrated by solving the matching equations. A stability analysis completes the discussion. Plots of the concentration contours characterised by the matching parameters are included. These contours simulate the cross-section of the scroll wave observed in experiments carried out in three dimensional media. The experimental design allows direct observation of undistorted three dimensional chemical waves in situ. The kinematics, dynamics and transformations of a variety of three dimensional scroll-based structures are recorded. The dominant waveforms are simple scroll waves. In addition, transient but significant events such as fission of a complex structure are recorded.

This thesis presents a series of theorems and proofs describing a twenty-five point geometry in which exists exactly thirty lines.

It is said that a topologist is a mathematician who can not tell the difference between a doughnut and a coffee cup. The surfaces of the two objects, viewed as topological spaces, are homeomorphic to each other, which is to say that they are topologically equivalent. In this thesis, we acknowledge some of the most well-known examples of surfaces: the sphere, the torus, and the projective plane. We then observe that all surfaces are, in fact, homeomorphic to either the sphere, the torus, a connected sum of tori, a projective plane, or a connected sum of projective planes. Finally, we delve into algebraic topology to determine that the aforementioned surfaces are not homeomorphic to one another, and thus we can place each surface into exactly one of these equivalence classes.

A qualitative three phase research study was undertaken to explore the geometric thinking of Grade 6 teachers in the context of low performance of the Gauteng learners in the International Competitions and Assessments for Schools (ICAS) tests in 2006. The van Hiele theory of geometric thinking was used as a theoretical framework. Data was collected by means of document analysis, teachers responding in writing to ICAS items and task based interviews. This research shows that the ICAS items map very well with the National Curriculum Statement (NCS) Assessment Standards and the van Hiele levels. The mapping of the 82 geometry ICAS items to the (NCS) Assessments Standards and the van Hiele levels revealed that 59% of the ICAS items were at van Hiele level 2 across all grades and therefore accessible to the majority of the learners. The written responses conducted with 40 ACE teachers and the task based interviews conducted with six teachers indicate that the majority of teachers are not at the required level of geometric thinking as expected by the NCS Assessment Standards and the van Hiele levels. This finding has serious implications for classroom practice in the learning and teaching of geometry in primary schools. The challenge for teacher education is to take into consideration the relationship between language and the van Hiele levels; the use of van Hiele levels in the development of teachers’ geometric thinking and the possible use of the van Hiele levels in identifying, explaining and rectifying geometric misconceptions.

"The purpose of the study is to determine if there is a difference between students who study certain topics from plane geometry using a geoboard and those who study the same topics in the conventional classroom. A three part criterion test will be used as the evaluative instrument"--Introduction. / Typescript. / "December, 1971." / "Submitted to the Department of Mathematics Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: E. D. Nichols, Professor Directing Dissertation. / Includes bibliographical references.

Projective geometry is a branch of mathematics which is foundationally based on an axiomatic system. In this thesis, six axioms for two-dimensional projective geometry are chosen to build the structure for proving some further results like Pappus' and Pascal's theorems. This work is mainly in synthetic geometry.