This work should serve as a source of information on the issue of production scheduling. The work is particularly focused on the relatively new terms in optimization of processing of production batches area, such as flowshop and its modifications in the form of so-called hybrid flowshop. The work is divided into five chapters. The first chapter consists of an introduction. In the second chapter I mention the theory of scheduling, the third part deals with the history of flowshop and in the fourth part I check the functionality of new models on real data. In conclusion I summarize the contents of work, comment resulting calculations and deliver the practical usage of flowshop.

京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第22317号 / 医博第4558号 / 新制||医||1040(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 松田 道行, 教授 斎藤 通紀, 教授 篠原 隆司 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

付記する学位プログラム名: 霊長類学・ワイルドライフサイエンス・リーディング大学院 / 京都大学 / 新制・課程博士 / 博士(理学) / 甲第23052号 / 理博第4729号 / 新制||理||1678(附属図書館) / 京都大学大学院理学研究科生物科学専攻 / (主査)教授 平田 聡, 教授 幸島 司郎, 教授 伊谷 原一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Magister Educationis - MEd / This study analysed the modelling competencies of grade 11 learners and also explored the degree to which the learners’ competency in setting up a mathematical model inhibits the development of an acceptable solution for word problems. The research data comprised 30 learners drawn from a secondary school in the Western Cape Province, South Africa. Data was collected via a task-based activity response sheet containing five word problems linked to either one of the following concepts: rectangle, two-digit number, average speed and petrol price. Learners’ responses were graded into four categories viz: correct, partially correct, incorrect and no response. Thereafter, the modelling competency framework was used to diagnose the modelling competencies of the sampled learners.

The main goal of the master’s thesis SIMULATION OF INTERCONNECTION OF SOLAR CELLS IN MATLAB is introduction of conversion principle of solar radiation into electrical energy in photovoltaic cells. The thesis deals with mathematical models and equations that describe the solar cell and their interconnection. The main task was to develop a user interface program using MATLAB. The produced program is intended to simulate a single cells or series connection, parallel or in series – parallel cells, and so simulate a photovoltaic panel.

The aim of this thesis is to describe the most frequent models describing population dynamics and then to perform some numerical experiments in the MATLAB environment. These simulations should validate our theoretical results. The models are sorted from the basic models to the most complicated and are divided into the models which describe dynamics of one population and models of coexistence of two biological species. The master's thesis icludes also a program for drawing graphs and trajectories of solutions of models described in this thesis including a description of this MATLAB program.

A two-dimensional, finite-element, porous-media flow model is developed to simulate stratified bi-directional flow of brine through the earth embankment carrying the Southern Pacific Railroad across Great Salt Lake. The model is part of a two-year research program whose objective is to develop a computer model of circulation in Great Salt Lake. This overall model is to be used as a predictive device for salinity distributions and circulation patterns in the lake. The porous media flow model is designed to establish flow rates through the Southern Pacific Railroad causeway embankment which traverses the north central part of he lake and divides it into two bodies of water. The study first develops the mathematical equations which describe two-dimensional stratified bi-directional flow of a fluid through porous media. Next , the problem is numerically posed as a boundary value problem in terms of pressure. This formulation is then solved by an iterative finite element scheme which employs quadratic, isoparametric, quadrilateral elements. The study also investigates two possible means of performing an analysis of stratified bi-directional flow with a pressure formulation by either posing the problem as a single boundary value problem with two densities of fluid within, or as two single-density boundary value problems coupled at the density interface. The single boundary formulation did not converge with the techniques attempted due to numerical instability at the density interface. The numerical model developed enables one to calculate fluid flow rates as well as the locations of the free surface and density-interface. The model simulation investigates many lake variables which affect brine flows through the embankment. Realistic model parameters are used which cover the range of actual values observed on the lake for the years 1968 through 1972. The numerical results presented in the study are given in terms of generalized dimensionless variables. The numerical results appeared to be in agreement with previously performed stratified bi-directional Hele-Shaw model studies. The major lake parameters affecting flow rates through the causeway were the free surface head difference, the southside lake surface elevation and the difference in fluid densities between the upper and lower layers of the embankment . The southward density flow was found to be completely cut off for certain combinations of lake parameters. Lack of adequate field data collected on the embankment has left both the geometry and the coefficient of permeability of the fill in question, preventing a rigorous verification of the model' s ability to predict actual flows. More field data are also necessary to establish whether there is stratification on the north side of the embankment which can greatly affect flow calculations. A high Reynold's number was found for flow through the embankment, raising a question as to the validity of the Darcian flow assumption used in the analysis. However, the establishment of the true Reynold's number can only be verified through the collection of more empirical data.

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis presents a method to accurately determine the location and amount of pedestrians detected by different vehicles equipped with a Pedestrian Autonomous Emergency Braking (PAEB) system, taking into consideration the inherent inaccuracy of the pedestrian sensing from these vehicles. In the thesis, a mathematical model of the pedestrian information generated by the PAEB system in the V2V network is developed. The Greedy-Medoids clustering algorithm and constrained hierarchical clustering are applied to recognize and reconstruct actual pedestrians, which enables a subject vehicle to approximate the number of the pedestrians and their estimated locations from a larger number of pedestrian alert messages received from many nearby vehicles through the V2V network and the subject vehicle itself. The proposed methods determines the possible number of actual pedestrians by grouping the nearby pedestrians information broadcasted by different vehicles and considers them as one pedestrian. Computer simulations illustrate the effectiveness and applicability of the proposed methods. The results are more integrated and accurate information for vehicle Autonomous Emergency Braking (AEB) systems to make better decisions earlier to avoid crashing into pedestrians.

The uterine endometrium undergoes cyclical phases of cell proliferation, cell differentiation, and menstruation under the influence of the ovarian hormones, estrogen and progesterone. Since the data necessary to create a classical kinetic model of these signaling pathways is lacking, we used a Boolean network approach that includes the influences of various growth factors and the differential expression of their receptors under the influence of estrogen and progesterone. Results show a gain in endometrial tissue and loss of tissue during menstruation that mirrors what can be expected over the course of a normal menstrual cycle in women, where the endometrium typically reaches a thickness of approximately 10 mm. We utilized an existing model of the normal menstrual cycle that was used to predict hormonal changes following administration of GnRH analogues. We adapted this model to provide the hormonal and ovarian compartments that would interact with our model of the endometrial cycle.

<p>Ion exchange equilibrium data can be used to predict the viability of a proposed process. Ion exchange equilibria have been studied considerably since the 1950's but the complexity of the basic research has tended to reduce its direct usefulness to the practising engineer. This research has been undertaken to determine if a moderately simple method of experimentation and analysis could be applied to predict ion exchange equilibria to within limits of accuracy acceptable to engineers.</p> <p> The first step in the research was to develop a simple mathematical model for a binary system to calculate the selectivity coefficient and resin capacity from batch experiments. The model was successfully applied for the exchange of Na+ with five heavy metal ions: Ni²⁺; Cu²⁺; Cd²⁺; Pb²⁺ and Zn²⁺ on a typical commercial resin (Dowex HCR-W2). The binary parameters were then used to predict the equilibrium values for several ternary systems. From these ternary experiments, it was determined that binary data can be used to predict ternary systems if the selectivity coefficients of the two ions involved are either almost equal or differed by at least a factor of five. A kinetic effect was proposed to explain the discrepancies observed between the predicted and experimental values for the intermediate ratios of selectivity coefficients of the involved ions, although further work is required to confirm this hypothesis.</p> <p> Several packed bed experiments were performed to check some of the results from the binary and ternary system experiments and as exploratory work for future research. These experiments confirmed the capacity data calculated from the binary system experiments and were consistent with the trends observed in the ternary system experiments.</p> / Thesis / Master of Engineering (ME)