This thesis shows how to test the fit of a data set to a number of different models, using Watson’s U2 statistic for both grouped and continuous data. While Watson’s U2 statistic was introduced for continuous data, in recent work, the statistic has been adapted for grouped data. However, when using Watson’s U2 for continuous data, the asymptotic distribution is difficult to obtain, particularly, for some skewed circular distributions that contain four or five parameters. Until now, U2 asymptotic points are worked out only for uniform distribution and the von Mises distribution among all circular distributions. We give U2 asymptotic points for the wrapped exponential distributions, and we show that U2 asymptotic points when data are grouped is usually easier to obtain for other more advanced circular distributions. In practice, all continuous data is grouped into cells whose width is decided by the accuracy of the measurement. It will be found useful to treat such data as grouped with sufficient number of cells in the examples to be analyzed. When the data are treated as grouped, asymptotic points for U2 match well with the points when the data are treated as continuous. Asymptotic theory for U2 adopted for grouped data is given in the thesis. Monte Carlo studies show that, for reasonable sample sizes, the asymptotic points will give good approximations to the p-values of the test.

This work examines various asymptotic edge-decomposition problems on graphs. A G-group divisible design (G-GDD) of type [g_1, ..., g_u] and index lambda is a decomposition of the edges of the complete lambda-fold multipartite graph H, with groups (maximal independent sets) G_1, ..., G_n, |G_i| = g_i, into graphs (blocks) isomorphic to G. We shall also examine special types of G-GDDs (such as G-frames) and prove that, given all parameters except u, these structures exist for all asymptotically large u satisfying the necessary conditions. Our primary technique is to invoke a useful theorem of Lamken and Wilson on edge-colored graph decompositions. The basic construction for k-RGDDs shall be outlined at the end of the thesis.

The equatorial atmosphere harbours a large spectrum of waves that are trapped near and travel along the equator. These equatorially trapped waves interact nonlinearly with each other, with the extra-tropics and with the planetary-barotropic waves. Here, we consider advected shallow water equations that represent interactions of these equatorial waves, associated with the first baroclinic mode, with prescribed meridional-barotropic shears. We present three well-known numerical schemes for handling this system and discuss the risk of applying them crudely to equatorial waves. We study the properties of these waves, such as their phase speed and their trapping around the equator, using two approaches: linear analysis and the time evolutions of the system derived by meridional projection of the barotropic-first baroclinic system. We show that in the sheared environment the symmetric (anti-symmetric) equatorial waves excite other symmetric (anti-symmetric) equatorial waves of the same wavenumber and of different strengths.

Given a factor code [pi] from a shift of finite type X onto an irreducible sofic shift Y, and a fully supported ergodic measure v on Y we give an explicit upper bound on the number of ergodic measures on X which project to v and have maximal entropy among all measures in the fiber [pi]-1{v}. This bound is invariant under conjugacy. We relate this to an important construction for finite-to-one symbolic factor maps.

We present a model of coupled transcriptional-translational ultradian oscillators (TTOs) as a possible mechanism for the circadian rhythm observed at the cellular level. It includes nonstationary Poisson interactions between the transcriptional proteins and their affined gene sites. The associated reaction-rate equations are nonlinear ordinary differential equations of stochastic switching type. We compute the deterministic limit of this system, or the limit as the number of gene-proteins interactions per unit of time becomes large. In this limit, the random variables of the model are simply replaced by their limiting expected value. We derive the Kolmogorov equations — a set of partial differential equations —, and we obtain the associated moment equations for a simple instance of the model. In the stationary case, the Kolmogorov equations are linear and the moment equations are a closed set of equations. In the nonstationary case, the Kolmogorov equations are nonlinear and the moment equations are an open-ended set of equations. In both cases, the deterministic limit of the moment equations is in agreement with the deterministic state equations.

Thesis (MTech(Electrical Engineering))--Cape Peninsula University of Technology, 2010 / Optimal control of fermentation processes is necessary for better behaviour of the process in order to achieve maximum production of product and biomass. The problem for optimal control is a very complex nonlinear, dynamic problem requiring long time for calculation Application of decomposition-coordinating methods for the solution of this type of problems simplifies the solution if it is implemented in a parallel way in a cluster of computers. Parallel computing can reduce tremendously the time of calculation through process of distribution and parallelization of the computation algorithm. These processes can be achieved in different ways using the characteristics of the problem for optimal control. Problem for optimal control of a fed-batch, batch and continuous fermentation processes for production of biomass and product are formulated. The problems are based on a criterion for maximum production of biomass at the end of the fermentation process for the fed-batch process, maximum production of metabolite at the end of the fermentation for the batch fermentation process and minimum time for achieving steady state fermentor behavior for the continuous process and on unstructured mass balance biological models incorporating in the kinetic coefficients, the physiochemical variables considered as control inputs. An augmented functional of Lagrange is applied and its decomposition in time domain is used with a new coordinating vector. Parallel computing in a Matlab cluster is used to solve the above optimal control problems. The calculations and tasks allocation to the cluster workers are based on a shared memory architecture. Real-time control implementation of calculation algorithms using a cluster of computers allows quick and simpler solutions to the optimal control problems.

abstract: Efforts to privilege STEM (Science, Technology, Engineering, and Mathematics) disciplines, initiatives, and industries in American discourse are arguably the foremost expressions of scientific authority in contemporary educational policy. Citing a diverse body of STEM literature, I discuss the histories and rationales that sustain the promotion of STEM. In doing so, I appropriate two concepts -Michel Foucault's Regime of Truth and Hayden White's Emplotment- for the purpose of analyzing the complex interests embodied by STEM discourse. I argue that the Sputnik Narrative is the prevailing story in STEM advocacy discourse. I claim that STEM advocates typically emplot this history as a Romance. Furthermore, I classify two major bases of appeal (rationales) that appear within this literature to justify STEM projects and proposals, "competition" and "equity." Throughout my writing, I cite discursive strategies for challenging and reimagining STEM history. My goal in indicating these sites of narrative possibilities is broaden the discursive field to new, perhaps liberating possibilities. / Dissertation/Thesis / M.A. Social and Philosophical Foundations of Education 2014

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In this investigation an attempt was made to determine the misconceptions that engineering students have of the idea of a limit. A comprehensive literature study showed that there are a number of common misconceptions that students normally form. The empirical investigation was done in two phases. A questionnaire on the idea of a limit was given to the students during the first phase. During the second phase six interviews were conducted. The findings were grouped according to the nature of a limit and students' views on the relationship between the continuity of a function at a point and the limit at that point. An analysis of these findings led to the identification of the misconceptions that these students have of the idea of a limit. / In hierdie ondersoek is gepoog om die wanbegrippe wat ingenieursstudente van die limietbegrip vorm, bloot te stel. 'n Omvattende literatuurstudie het 'n aantal algemene wanbegrippe aan die lig gebring. Die empiriese ondersoek het in twee fases plaasgevind. Tydens die eerste fase is 'n vraelys aan die studente gegee in 'n poging om meer te wete te kom van hulle begrip van 'n limiet. Die vraelys is opgevolg deur ses onderhoude. Die responsies is gegroepeer in terme van die aard van 'n limiet en studente se sienings van die kontinuiteit van 'n funksie by 'n punt en die limiet by daardie punt. Die analisering van hierdie responsies het die identifisering van 'n aantal wanbegrippe by hierdie groep studente moontlik gemaak. / Educational Studies / M.Ed. (with specialisation in Mathematics Education)

The study involved BTec National (level 3) engineering students studying at a large Further Education College in the South West region. The disciplines of Electrical/Electronic, Mechanical, Operations and Maintenance, Manufacturing, Telecommunications and Fabrication where all included in the study. Several students were sent by their employers on day release programmes and apprenticeships, and these formed the majority of the part time students. There were also other employed students who attended full time for terms 1 and 3 as part of a block release programme. The remaining students were full time, and mainly 16-18 years old. The study focused upon the core mathematics module everyone studied, and mathematical resources which were available through a virtual learning environment. The resources used layering, enabling earlier work to be built on and applied. Two separate cohorts were studied after substantial changes had been made to the qualification standards. The main findings were that the mathematics resources were very useful support, had a significant positive impact on student success, and enhanced the student experience. They helped part time students, especially, to improve their confidence and their achievements. The unlimited availability of these resources were a major consideration in their usefulness. The use of layering within the mathematics unit enabled better recall and comprehension.