Thesis (MEd (Curriculum Studies)--Stellenbosch University, 2010. / ENGLISH ABSTRACT: The aim of this research is three-fold. Firstly I aimed to show the difficulty of the concept of proportional reasoning through empirical research. Several researchers have shown the degree of difficulty learners experience with proportional reasoning and have even indicated that many university students (and adults) do not have sound proportional reasoning skills. Piaget’s controversial developmental levels classify proportional reasoning as a higher order thinking skill in his highest level of development, formal operational thought, and claims that most people do not reach this level. The difficulty of proportional reasoning and the fact that it is a skill needed within all Learning Outcomes of Mathematical Literacy creates a predicament in terms of the difficulty of the subject in general. Is it then fair to classify Mathematical Literacy as an inferior subject in the way it has been done over the last few years if it is a subject that requires learners to operate at such a high level of thought through proportional reasoning? Secondly, I would like to confirm with the use of a baseline assessment that learners entering Grade 10 Mathematical Literacy have poor proportional reasoning skills and have emotional barriers to Mathematics and therefore Mathematical Literacy. The research will be done in three private schools located in the West Coast District of the Western Cape in South Africa. If learners in these educationally ideal environments demonstrate poor proportional reasoning skills even though they were privileged enough to have all the possible support since their formative years, then results from overcrowded government schools may be expected to be even worse. The learners in Mathematical Literacy classes often lack motivation, interest and enthusiasm when it comes to doing mathematics. Through the baseline assessment I confirm this and also suggest classroom norms and values that will help these learners to become involved in classroom activities and educational discourse. Thirdly and finally this research will focus on the design of activities that will aim to build on learners’ prior knowledge and further develop their proportional reasoning skills. I argue that activities to develop proportional reasoning should take equivalence of fractions as basis to work from. The activities will aim to help learners to set up questions in such a way that they can solve it with techniques with which they are familiar. Interconnectivity will form a vital part to this investigation. Not only do I indicate the interconnectivity between concepts in the Mathematical Literacy Learning Outcomes of the National Curriculum Statement, but I would like to make these links clear to learners when working through the proposed activities. Making links between concepts is seen as a higher order thinking skill and is part of meta-cognition which involves reflection on thoughts and processes. In short, this research can be summarised as the design of activities (with proposed activities) that aims to develop proportional reasoning by making connections between concepts and requires of learners to be active participants in their own learning. / AFRIKAANSE OPSOMMING: Die doel van hierdie navorsing is drieledig. Eerstens will ek die probleme met die konsep van proporsionele denke uitlig deur eksperimentele ontwerp navorsing. Verskeie navorsers verwys na die moeilikheidsgraad van probleme wat leerders ondervind met proporsionele denke. Sommige van hierdie navorsers het ook bevind dat verskeie universiteitstudente (en ander volwassenes) nie oor die vaardigheid van proporsionele denke beskik nie. Piaget se kontroversiële ontwikkelingsvlakke klassifiseer proporsionele denke as ‘n hoër orde denkvaardigheid in sy hoogste vlak van ontwikkeling, formele operasionele denke, en noem dat meeste mense nooit hierdie vlak bereik nie. Die hoë moeilikheidsgraad van proporsionele denke en die feit dat dit ‘n vaardigheid is wat binne al die Leeruitkomste van Wiskundige Geletterdheid benodig word veroorsaak ‘n dilemma as mens dit vergelyk met die moeilikheidsgraad van die vak oor die algemeen. Tweedens wil ek met behulp van ‘n grondfase assessering bewys dat leerders wat Graad 10 Wiskunde Geletterdheid betree swak proporsionele denkvaardighede het, gepaardgaande met emosionele weerstand teenoor Wiskunde en Wiskunde Geletterdheid. Die navorsing sal gedoen word in drie privaatskole in die Weskus distrik van die Wes-Kaap van Suid-Afrika. Indien leerders in hierdie ideale opvoedkundige omstandighede swak proporsionele denkvaardighede ten toon stel, ten spyte van die feit dat hulle bevoorreg was om sedert hulle vormingsjare alle moontlike opvoedkundige ondersteuning te geniet, dan kan verwag word dat resultate komende van oorvol staatskole selfs swakker mag wees. By leerders in Wiskunde Geletterdheid klasse kan daar gereeld ‘n gebrek aan motivering, belangstelling en entoesiasme ten opsigte van Wiskunde bespeur word. Deur gebruik van die grondfase assessering wil ek hierdie stelling bewys en ook voorstelle maak vir klaskamernorme en waardes wat sal help om die leerders meer betrokke te maak by klaskameraktiwiteite en opvoedkundige gesprekke.

The digitization of classical control systems presents a number of challenges and opportunities with respect to the miniaturization, distribution, reliability verification and obsolescence of both the controller and the underlying system under control. A method for the design of proportional-integral-derivative (PID) compensators realized in the form of all-digital components is presented. All-digital refers to a system implementation that is realizable with a wide range of digital logic components including discrete digital logic elements and programmable logic devices (PLDs) such as field-programmable gate arrays. The proportional, integral and derivative components of the classical PID control law were re-envisioned in terms of frequency of occurrences or counts for adaptation to combinatorial and sequential digital logic. Modification of the control scheme around this newly formed representation of system error enables the development of a PID-like FPGA-based or PLD-based controller. Details of the design of an all-digital PID-like controller including abstract, causal block diagrams and a MATLAB® and Simulink® based implementation are presented. The compensator was simulated in a velocity tracking DC motor control application and was found to perform comparably to that of a classical PID based control. Methods for assessing the resultant stability of an all-digital PID compensated system under control are discussed.

過去國內之抵押貸款提前清償與逾期還款之相關研究，在實證研究上最主要利用邏輯斯迴歸或是比例轉機模型( Proportional hazard model )分析影響一般住宅抵押貸款人提前清償與逾期還款之因素，並估計一般住宅抵押貸款人提前清償之機率。本文選擇採用研究抵押貸款時，國內未曾使用之卜瓦松迴歸( Poisson regression model )來估計比例轉機模型假設下影響提前清償與違約變數之參數，以研究影響抵押貸款借款人之提前償還與違約因素。 本研究結合比例轉機模型與卜瓦松迴歸模型，目的在結合兩模型之優點，在處理時間相依之共變數效率提高，並且在處理多重時間尺度的方程式較偏最大概似估計法直接，以得到較佳的研究成果。另外，過去國內提前清償與違約之文獻中並未加入利率走勢之變數，本研究加入再融資利率對31∼90天期商業本票利率之比率與再融資利率波動性兩變數，以考慮利率走勢對貸款者提前清償及違約行為之影響。 模型中的解釋變數包括地區、季節、抵押貸款年齡、貸款成數、貸款人年齡、性別、婚姻狀況、教育程度、職業、屋齡、房屋坪數、所得、貸款金額、月付額對薪資比、再融資利率/31∼90天期商業本票利率、再融資利率波動性等十六項。實證結果在提前清償部份，顯著正向之變數有貸款年齡、屋齡、房屋坪數、所得、月付額與薪資比，顯著負向之變數包括季節、再融資利率對31∼90天期商業本票利率之比率、貸款金額。在違約部份，顯著正向之變數包括貸款年齡、貸款成數、年齡、所得、月付額與薪資比、再融資利率對31∼90天期商業本票利率之比率；顯著負向之變數包括季節、教育程度及貸款金額。

本研究之主要貢獻為發展適合台灣營造綜合險保單（本體損失險）之風險曲線。 先前由Salzmann (1963)及Ludwig (1998)之相關研究，係採用美國市場之損失經驗，考量不同保單之承保範圍、不同保險標的、及不同之承保風險，直接引用美國市場風險曲線於台灣市場之通用性值得釐清。 本研究回顧台灣營造綜合險保單之承保範圍及除外條款，依據西元一九九六年至兩千年之損失經驗，發現台灣營造綜合險之損率深受天然災害如地震、颱風、豪雨所影響。 再保險安排可分成兩大類，一是比例再保險; 另一是非比例再保險。風險曲線是非比例再保險常用之計價方式之一。 比較先前之研究，本研究之風險曲線分佈集中在低層其主要之原因如下:- 一、 分析標的之可能最大損失(PML)偏低: PML代表某一特定危險所可能造成之可能最大損失。以道路工程為例，其可能最大損失小於30%之保額。由於道路工程大多綿延數十公里甚或更長，其工程本身呈線狀之分佈。換言之，非常不可能會有單一損失其損失金額超過保額之30%。 因此，道路工程之損失分佈不平均且分佈集中在低層。 二、 營造綜合險保期偏長: 營造工程其中一個特性為多年期的保險期間。 因為工程之進行往往需要花超過一年的時間來完成，因此，營造綜合險全損(損失金額等於保額)之機率，遠小於財產險因火災造成全損之機率。 三、 分析之承保風險不同: Salzmann (1963)僅針對火災此一危險因子來從事她的研究。就我們所知，美國大多數住宅皆是木造，屬可燃性建材，火災造成之影響相當大。 相反地，本研究標的大多利用不可燃性建材來興建，如鋼鐵或混凝土，故火災之影響性相對較小。 關鍵字: 非比例再保險、風險基礎計價、營造綜合保險 / The major contribution of this research is to develop the exposure curves suitable for the Taiwan Contractor’s All Risks (CAR) Insurance (Material Damage Cover). The exposure curves generated in Salzmann (1963) and Ludwig (1998) were originated from the loss experience in the United States. Considering the different types of policies, different types of risks, and different types of perils, the applicability of those curves in Taiwan market is discussable. This study reviews the scope of coverage, insuring clause and exclusions of the Taiwan Contractor’s All Risks Insurance. According to the loss records between 1996 and 2000, it’s understood that the result of the Contractor’s All Risks Insurance is highly influenced by the natural catastrophic perils, such as earthquake, typhoon and heavy rains. The reinsurance placement can be categorized into proportional and non-proportional reinsurance or called excess of loss reinsurance. Exposure rating is one of the common pricing methods for the excess of loss reinsurance. Compared with those two previous researches done by Salzmann (1963) and Ludwig (1998), the outcome of this analysis shows an unbalanced loss distribution which leans to the lower layers that is mainly because of the following reasons: - (1) Low PML percentage of analyzed risks: The PML represents the Probable Maximum Loss subject to a certain type of peril. Taking a road construction project as an example, the PML of a road construction project is less than 30% of the total sum insured. Usually, the length of a road construction project is tens of kilometers or even much longer. In consideration of its linear shape, it’s very unlikely to have a loss exceeding 30% of its total sum insured. Therefore there was very few or nil loss data above the 30% of the total sum insured that’s the reason why the loss distribution is unbalanced and leans to the lower layers. (2) Long Construction Period of a CAR Project: A character of a CAR project is having a multiple-year policy period because the construction work usually takes more than one year to be completed. Therefore the possibility to have a total loss case, loss amount equal to the total sum insured, is much less than a property risk with a fire scenario. (3) Types of Perils Analyzed: Salzmann (1963) carried out her research by analyzing the peril of fire covered under the homeowners’ policies. As we know, most of the houses in the United States are the wooden structures, which are combustible. Oppositely, the risks in this research are mostly constructed by using the non-combustible materials, such as steel or reinforced concrete. Keywords: excess of loss, non-proportional reinsurance, exposure rating, and contractor’s all risks insurance.

This thesis deals with chemical plants constituted by parallel batch-continuous production lines with shared resources. For such plants, it is highly desirable to have optimal operation schedules which determine the starting times of the various batch processes and the flow rates of the continuous processes in order to maximize the average plant productivity and to have a continuous production without interruptions. This optimization problem is constrained by the limitation of the resources that are shared by the reactors and by the capacities of the various devices that constitute the plant. Such plants are "hybrid" by nature because they combine both continuous-time dynamics and discrete-event dynamics. The formalism of "Hybrid Automata" is there fore well suited for the design of plant models. The first contribution of this thesis is the development of a hybrid automaton model of the chemical plant in the Matlab-Simulink-Stateflow environment and its use for the design of an optimal periodic schedule that maximises the plant productivity. Using a sensitivity analysis and the concept of Poincaré; map, it is shown that the optimal schedule is a stable limit cycle of the hybrid system that attracts the system trajectories starting in a wide set of initial conditions. The optimal periodic schedule is valid under the assumption that the hybrid model is an exact description of the plant. Under perturbations on the plant parameters, it is shown that two types of problems may arise. The first problem is a drift of the hybrid system trajectory which can either lead to a convergence to a new stable sub-optimal schedule or to a resource conflict. The second problem is a risk of overflow or underflow of the output buffer tank. The second contribution of the thesis is the analysis of feedback control strategies to avoid these problems. For the first problem, a control policy based on a model predictive control (MPC) approach is proposed to avoid resource conflicts. The feedback control is run on - line with the hybrid Simulink-Stateflow simulator used as an internal model. For the solution of the second problem, a classical PI control is used. The goal is not only to avoid over- or under-filling of the tank but also to reduce the amplitude of outflow rate variations as much as possible. A methodological analysis for the PI controller tuning is presented in order to achieve an acceptable trade-off between these conflicting objectives.

Device-to-device (D2D) communication is a promising new feature in LTE-Advanced networks. It is brought up to enable efficient discovery and communication between proximate devices. With D2D capability, devices in physical proximity could be able to discover each other using LTE radio technology and to communicate with each other via a direct data path. This thesis is concerned with the design, coordination and testing of a hybrid D2D and cellular network. Design requirements and choices in physical and MAC layer functions to support D2D discovery and communication underlaying LTE networks are analyzed. In addition, a centralized scheduling strategy in base station is proposed to coordinate D2D data communication operating in LTE spectrum. The scheduling strategy combines multiple techniques, including mode selection, resource and power allocation, to jointly achieve an overall user performance improvement in a cell. Finally the performances of D2D data communication underlaying LTE system are calibrated in a multi-link scenario via system-level simulation.

The goal of this dissertation is to evaluate the effectiveness of model predictive control (MPC) for a magnetically suspended flywheel energy storage uninterruptible power supply (FlyUPS). The reason this research topic was selected was to determine if an advanced control technique such as MPC could perform better than a classical control approach such as decentralised Proportional-plus-Differential (PD) control. Based on a literature study of the FlyUPS system and the MPC strategies available, two MPC strategies were used to design two possible MPC controllers were designed for the FlyUPS, namely a classical MPC algorithm that incorporates optimisation techniques and the MPC algorithm used in the MATLAB® MPC toolbox™. In order to take the restrictions of the system into consideration, the model used to derive the controllers was reduced to an order of ten according to the Hankel singular value decomposition of the model. Simulation results indicated that the first controller based on a classical MPC algorithm and optimisation techniques was not verified as a viable control strategy to be implemented on the physical FlyUPS system due to difficulties obtaining the desired response. The second controller derived using the MATLAB® MPC toolbox™ was verified to be a viable control strategy for the FlyUPS by delivering good performance in simulation. The verified MPC controller was then implemented on the FlyUPS. This implementation was then analysed in order to validate that the controller operates as expected through a comparison of the simulation and implementation results. Further analysis was then done by comparing the performance of MPC with decentralised PD control in order to determine the advantages and limitations of using MPC on the FlyUPS. The advantages indicated by the evaluation include the simplicity of the design of the controller that follows directly from the specifications of the system and the dynamics of the system, and the good performance of the controller within the parameters of the controller design. The limitations identified during this evaluation include the high computational load that requires a relatively long execution time, and the inability of the MPC controller to adapt to unmodelled system dynamics. Based on this evaluation MPC can be seen as a viable control strategy for the FlyUPS, however more research is needed to optimise the MPC approach to yield significant advantages over other control techniques such as decentralised PD control. / Thesis (MIng (Computer and Electronic Engineering))--North-West University, Potchefstroom Campus, 2013

The mechanisms that control growth processes in biology tissues have attracted continuous research interest despite their complexity. With the emergence of big data experimental approaches there is an urgent need to develop statistical and computational models to fit the experimental data and that can be used to make predictions to guide future research. In this work we apply statistical methods on growth process of different biological tissues, focusing on development of neuron dendrites and tumor cells. We first examine the neuron cell growth process, which has implications in neural tissue regenerations, by using a computational model with uniform branching probability and a maximum overall length constraint. One crucial outcome is that we can relate the parameter fits from our model to real data from our experimental collaborators, in order to examine the usefulness of our model under different biological conditions. Our methods can now directly compare branching probabilities of different experimental conditions and provide confidence intervals for these population-level measures. In addition, we have obtained analytical results that show that the underlying probability distribution for this process follows a geometrical progression increase at nearby distances and an approximately geometrical series decrease for far away regions, which can be used to estimate the spatial location of the maximum of the probability distribution. This result is important, since we would expect maximum number of dendrites in this region; this estimate is related to the probability of success for finding a neural target at that distance during a blind search. We then examined tumor growth processes which have similar evolutional evolution in the sense that they have an initial rapid growth that eventually becomes limited by the resource constraint. For the tumor cells evolution, we found an exponential growth model best describes the experimental data, based on the accuracy and robustness of models. Furthermore, we incorporated this growth rate model into logistic regression models that predict the growth rate of each patient with biomarkers; this formulation can be very useful for clinical trials. Overall, this study aimed to assess the molecular and clinic pathological determinants of breast cancer (BC) growth rate in vivo.

La presente investigación fue elaborada con el fin de determinar el impacto financiero de la NIIF 11 Acuerdos Conjuntos en la toma de decisiones de las empresas constructoras del distrito de San Isidro en el año 2017. Para cumplir con lo anterior, la investigación se basará en la aplicación de la Norma Internacional de Información Financiera 11 “Acuerdos Conjuntos”, emitida el 12 de mayo del 2011, cuya aplicación inició a partir del 1 de enero del 2013. La norma mencionada tiene cambios sustanciales en la clasificación de los acuerdos conjuntos y será necesario para su correcta aplicación que esté soportada en un proceso adecuado de procesamiento y análisis de información. El presente trabajo se basará en empresas del sector construcción del distrito de San Isidro que cotizan en bolsa de valores que presentan información financiera al 31 de diciembre del 2017. El sector construcción conforme con el Instituto Nacional de Estadística e Informática (INEI) creció en 2.20% en el año 2017. Tras una caída considerable del PBI sector construcción en los años 2015 y 2016 experimenta un importante crecimiento al cierre del año 2017. Por otro lado, las empresas constructoras suelen recurrir al uso de alianzas estratégicas que implican una colaboración empresarial para proyectos específicos, lo cual requerirá un análisis según lo dispuesto por la IFRS 11 Acuerdos Conjuntos. Por todo ello en esta investigación se busca averiguar si el impacto financiero de la NIIF 11 Acuerdos Conjuntos influye negativamente en la toma de decisiones de las empresas constructoras de San Isidro. Para validar nuestras hipótesis, se realizó encuestas a empresas del sector construcción de San Isidro y, además, se recurrió a expertos en NIIF 11 y en el sector construcción para la realización de entrevistas a profundidad. Finalmente, se realizó un caso práctico para evaluar el impacto financiero de la presente investigación. Además, se realizó validaciones estadísticas para nuestras hipótesis tanto principal como secundarias mediante la herramienta denominada ji-cuadrado (o chi cuadrado) y para validar la confiabilidad de nuestra encuesta el estadístico de Alfa de Cronbach. En base a lo anteriormente mencionado se concluyó que el impacto financiero de la NIIF 11 Acuerdos Conjuntos influye negativamente en la toma de decisiones de las empresas constructoras de San Isidro en el año 2017. / The present investigation was elaborated in order to determine the financial impact of the IFRS 11 Joint Agreements in the decision making of the construction companies of San Isidro in the year 2017. To comply with the above, the investigation is based on the application of The International Financial Reporting Standard 11 "Joint Agreements", issued on May 12, 2011, whose application began on January 1, 2013. The aforementioned regulation has substantial changes in the classification of joint agreements and will be necessary for its Correct application is supported in an adequate process of information processing and analysis. This work will be based on companies in the construction sector of San Isidro that are listed on the stock exchange and are medium or large companies. The construction sector settled with the National Institute (INEI) grew by 2.20% in the year 2017. After a considerable decline in the GDP construction sector in 2015 and 2016 experienced an important growth at the end of 2017. On the other hand, the construction companies usually resort to the use of strategic alliances that imply a business collaboration for specific projects, which requires an analysis in accordance with the provisions of IFRS 11 Joint Agreements. For all this, this research seeks to find out the financial impact of IFRS 11 Joint Agreements negatively influence the decision making of the construction companies of San Isidro. To validate our hypothesis, it will be published to companies in the construction sector and, in addition, experts will be used to carry out in-depth interviews and, finally, a practical case will be made to evaluate the financial impact of the present investigation. In addition, statistical validations have been carried out for our hypotheses, both main and secondary, using the chi-square tool (or chi-square) and to validate the reliability of our survey the Cronbach's Alpha statistic. Based on the, it was concluded that the financial impact of IFRS 11 Joint Agreements negatively influences the decision making of the construction companies of San Isidro in 2017. / Tesis

Survival analysis is an effective tool for conservation studies, since it measure the risk of an event that is important for the survival of populations and preservation of biodiversity. In this thesis three different models for survival analysis are used to estimate the age at breeding between two genetically different populations of brown trout. These populations are an evolutionary enigma, since they apparently coexist in direct competition with each other, which according to ecological theory should not happen. Thus it is of interest if differences between them can be identified. The data consists of brown trouts and has been collected over 20 years. The models are the Cox Proportional Hazards model, the Complementary Log-Log Link model and the Log Logistic Accelerated Failure-Time model. The Cox model were estimated in three different ways due to the nonproportional hazards in the estimates of time to breeding, which gave different interpretations of the same model. All of the models agree that the population B breed at younger ages than the population A, which suggests that the two populations have different reproductive strategies.