abstract: Researchers have described two fundamental conceptualizations for division, known as partitive and quotitive division. Partitive division is the conceptualization of a÷b as the amount of something per copy such that b copies of this amount yield the amount a. Quotitive division is the conceptualization of a÷b as the number of copies of the amount b that yield the amount a. Researchers have identified many cognitive obstacles that have inhibited the development of robust meanings for division involving non-whole values, while other researchers have commented on the challenges related to such development. Regarding division with fractions, much research has been devoted to quotitive conceptualizations of division, or on symbolic manipulation of variables. Research and curricular activities have largely avoided the study and development of partitive conceptualizations involving fractions, as well as their connection to the invert-and-multiply algorithm. In this dissertation study, I investigated six middle school mathematics teachers’ meanings related to partitive conceptualizations of division over the positive rational numbers. I also investigated the impact of an intervention that I designed with the intent of advancing one of these teachers’ meanings. My findings suggested that the primary cognitive obstacles were difficulties with maintaining multiple levels of units, weak quantitative meanings for fractional multipliers, and an unawareness of (and confusion due to) the two quantitative conceptualizations of division. As a product of this study, I developed a framework for characterizing robust meanings for division, indicated directions for future research, and shared implications for curriculum and instruction. / Dissertation/Thesis / Doctoral Dissertation Mathematics Education 2019

Abstract There is much rich solar energy in Taiwan situated at the subtropics;Therefore it¡¦s suitable for solar energy is utilized as the driving energy for absorption cooling system. Simultaneously the use of solar energyreduces our dependence on fossil fuel ,and reaches the goal of energy conservation and reduction of carbon footprint deeply.After establishing absorption cooling system in TRNSYS.16 platform, climate data TMY2 form for several cities of Taiwan are input to the simulation program. As a result of Taiwan climate variation, summer is getting more and more longer ; winter is getting shorter gradually .Hence we simulated program from March to October .Then system operating the parameters of solar collector area and the volume of the storage tank are varied to research those effects on the system performance. The research focuses on the simulation data for monthly solar fraction(f),seasonal solar fraction(F) as well as how much solar energy saved could transform carbon dioxide content for single effect and double effect absorption cooling system operated under the climate of the major cities in Taiwan .Those data could provide the design needs.

The purpose of this study is to investigate the implementation of problem-posing instruction on fraction in a fifth-grade elementary school of aboriginal children in Taitung. Through a pilot and integrating modified problem-posing instruction in mathematics teaching, the investigator studied the performance and learning attitude of children and analyzed the acceptability of the problem-posing teaching processes. The researcher collected data by using: own constructed fraction problems question sheet, worksheet on problem-posing, worksheet on problem-solving, the teacher¡¦s math notes on instruction, children¡¦s diaries, students¡¦ feedback surveys and post-tests of mathematical problem-solving ability. The researcher analyzed categories of children¡¦s work and contents of problems-posing that children created. Results indicated that the children made progress in problem-posing performance and ability of problem-solving and behaved positively on learning attitude. From this study, the researcher found that the majority of the students participated in this study were interested in this teaching technique, and students gained confidence in posing and solving mathematical problems. Finally, the teacher could reflect upon practice on problem-posing instruction through action research. The above results yielded instructional implications for teachers who consider integrating problem-posing teaching into mathematics instruction for elementary school children.

This work presents the design, theory, and measurement of a phase-reconfigurable reflectarray (RA) element for beamforming applications enabled by fluidic networks and colloidal dispersions. The element is a linearly polarized microstrip patch antenna loaded with a Coaxial Stub Microfluidic Impedance Transformer (COSMIX). Specifically, adjusting the concentration of highly dielectric particulate in the dispersion provides localized permittivity manipulation within the COSMIX. This results in variable impedance load on the patch and ultimately continuous, low-loss phase control of a signal reflected from the patch. Different aspects of design, modeling, and measurement are discussed for a proof-of-concept prototype and three further iterations. Initial measurements with manual injections of materials into a fabricated proof-of-concept demonstrate up to 200 degrees of phase shift and a return loss of less than 1.2 dB at the operating frequency of 3 GHz. The next design iteration addresses fabrication challenges as well the general cumbersomeness of the proof-of-concept by replacing the static material delivery system with a dynamic closed-loop fluidic network. It also makes use of a design procedure to maximize the phase sensitivity. Measurements demonstrate progressive phase shifts through dilution of the system reservoir; however, the initial measurements with this system are not in line with simulated predictions. Investigations suggest the primary culprit to be inaccurate material data. The dielectric constant of the particulate (colloidal BSTO) was overrated and the loss tangent of the fluid medium (a silicone-based oil) was underrated. After accounting for these issues the measurement a second measurement with the system demonstrates 270 degrees of phase shift with return loss of 9 dB. The next design iteration examines a trade-off between phase sensitivity and reduced losses. The design also features modifications to the fluidic system to allow for layered fabrication in the GND plane as well integration with a 2-port coaxial measurement cell. Attempted measurements discover the fluidic system cannot flow the higher concentrations of nanoparticles necessary for phase shifting. A final design iteration addresses this challenge by expanding and repositioning inlets to the fluidic system. Free space reflection measurements with this element initially demonstrate phase shifting until a buildup of nanoparticles form within the COSMIX.

abstract: In this dissertation, the results of our comprehensive computational studies of disordered jammed (i.e., mechanically stable) packings of hard particles are presented, including the family of superdisks in 2D and ellipsoids in 3D Euclidean space. Following a very brief introduction to the hard-particle systems, the event driven molecular dynamics (EDMD) employed to generate the packing ensembles will be discussed. A large number of 2D packing configurations of superdisks are subsequently analyzed, through which a relatively accurate theoretical scheme for packing-fraction prediction based on local particle contact configurations is proposed and validated via additional numerical simulations. Moreover, the studies on binary ellipsoid packing in 3D are briefly discussed and the effects of different geometrical parameters on the final packing fraction are analyzed. / Dissertation/Thesis / Masters Thesis Materials Science and Engineering 2014

This research was designed to examine the role of the physical properties of the mathematical tools, in children’s learning in the context of adding two fractions. My two research questions were: (1) How does the feedback from the mathematical tools play a mediating role between the physical actions of the child with respect to the mathematical affordances of the tools and the child’s thinking about and learning and knowing of solving addition of fractions problems? And (2) What role is played by mathematical tools in the emergence of a Zone of Proximal Development during the child’s solving of addition of fractions problems? To address these questions, I interviewed 13 grade 7 students in Ottawa, Ontario, in groups of two and in three rounds of 30-minute interviews per group. The results showed that the physical properties of the tools play a role in how children perceived the mathematical affordances of the tool, attached mathematical meaning to the tools, created mathematical artefacts and solved the addition of fractions problems. Moreover, the findings show that in children’s interactions with mathematical tools, at times, the Zone of Proximal Development (ZPD) emerged, with the guidance provided by the tools. I conclude that children’s interaction with the tools provided them the possibility of learning newer forms of reflections, expressions and actions in relation to adding two fractions. This learning was a result of a complex and intertwined relationship between the immediate physical properties and affordances of the tool, the traces of the thoughts of the designer of the tools, as well as the children’s previous knowing of fractions. With this study, I extend the Vygotskian notion of the more knowledgeable other within the ZPD to include not only agents (children and adults) but also tools.

La structure chimique d’une flamme laminaire de prémélange suitée de n-butane (nC4H10/O2/N2) pour deux conditions de richesse (Φ=2,16 et 2,32) a été déterminée expérimentalement et par modélisation à pression atmosphérique. L’acquisition des profils de fraction molaire des espèces stables a été réalisée par chromatographie en phase gazeuse et par spectroscopie infrarouge. Les profils de température ont été obtenus par Fluorescence Induite par Laser du monoxyde d’azote. Le mécanisme développé dans cette étude contient 279 espèces impliquées dans 1422 réactions réversibles. La comparaison des profils de concentration modélisés et expérimentaux dans le cas des espèces analysées a permis de valider le modèle. Un accord satisfaisant est observé entre les résultats expérimentaux et modélisés et l’effet de la richesse est bien pris en compte par le mécanisme chimique. Le modèle cinétique a aussi été testé sur une large gamme de conditions opératoires issues de la littérature (données globales et détaillées) et a été comparé à d’autres mécanismes de la littérature. Les schémas réactionnels de formation et de consommation ont été établis et permettent de mettre en évidence les voies réactionnelles de formation du premier cycle aromatique. Les fractions volumiques de suie ont été mesurées par Incandescence Induite par Laser pour les deux richesses de flamme. / Chemical structure of a laminar premixed sooting n-butane flame (nC4H10/O2/N2) operating at two equivalence ratio (Φ=2,16 and 2,32) has been investigated at atmospheric pressure. Acquisition of mole fraction profiles of stable species is accomplished by gas chromatography and infrared spectroscopy. The temperature profiles are obtained by Laser induced Fluorescence of nitric oxide. In this work, the developed mechanism contains 279 species involved in 1422 reversible reactions. The comparison between modelled and experimental profiles was used to validate the model and a good agreement was observed. The effect of equivalence ratio is well captured by the mechanism. The kinetic model was also tested on a wide range of operating conditions found in the literature (global and detailed data) and has been compared to other mechanism from the literature. Formations and consumptions kinetic schemes were established to highlight the reaction path of the first aromatic ring. Soot volume fractions are measured by Laser Induced Incandescence for the both equivalence ratio.

Natural convection as a heat transfer mechanism plays a major role in the functioning of many heat transfer devices, such as heat exchangers, energy storage, thermal management and solar collectors. All of these have a large impact on the generation of solar power. Considering how common these devices are not only in power generation cycles, but in a majority of other thermal uses it is clear that increased performance for natural convection heat transfer will have consequences of a high impact. As such, the purpose of this study is to experimentally study the natural convection heat transfer behaviour of a relatively new class of fluids where nano-sized particles are mixed into a base fluid, also known as a nanofluids. Nanofluids have attracted widespread interest as a new heat transfer fluid due to the fact that the addition of nanoparticles considerably increases the thermophysical properties of the nanofluids when compared to those of the base fluid. Furthermore, if these nanoparticles show magnetic behaviour, huge increases in the thermal conductivity and viscosity of the nanofluid can be obtained if the fluid is exposed to a proper magnetic field. With this in mind, the study aimed to experimentally show the behaviour of these so-called magnetic nanofluids in natural convection heat transfer applications. In this study, the natural convection heat transfer of a magnetic nanofluid in a differentially heated cavity is investigated with and without an applied external magnetic field. The effects of volume concentration and magnetic field configuration are investigated. Spherical nanoparticles with a diameter of 20 nm are used with a volume concentration ranging between 0.05% and 0.3%, tested for the case with no magnetic field, while only a volume concentration of 0.1% was used in the magnetic cases. The experiments were conducted for a range of Rayleigh numbers in . The viscosity of the nanofluid was determined experimentally, while an empirical model from the literature was used to predict the thermal conductivity of the nanofluids. An empirical correlation for the viscosity was determined, and the stability of various nanofluids was investigated. Using heat transfer data obtained from the cavity, the average heat transfer coefficient, as well as the average Nusselt number for the nanofluids, is determined. It was found that a volume concentration of 0.05% showed an increase of 3.75% in heat transfer performance. For the magnetic field study, it was found that the best-performing magnetic field enhanced the heat transfer performance by 1.58% compared to the 0.1% volume concentration of the nanofluid with no magnetic field. / Dissertation (MEng)--University of Pretoria, 2017. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

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Ovarian cancer is considered to be one of the deadliest gynecological diseases. Over 21,000 women are expected to be diagnosed with this fatal disease in 2020 alone. Obesity, but more specifically a high waist-to-hip ratio, is indicative of abdominal obesity and has been correlated with increased risk of ovarian cancer. How abdominal obesity contributes to this increased risk has not been clearly delineated but much of the current research has been focused on the role of adipocytes. However, in addition to the adipocytes, abdominal white adipose tissue contains the stromal vascular fraction (SVF) which includes stem and progenitor cell populations, immune cells, and fibroblasts. Since the SVF can also be recruited by the cancer cells, we investigated how obesity affects the survival and metastatic potential of cancer cells by investigating changes in the expression of genes that contribute to survival, proliferation, migration, adherence, and invasion. We used culture conditions that mimic the non-permissive peritoneal environment. Cancer related genes, such as Dkc1, Ccnd2, Lig4, and Snai2, were upregulated when adipose derived stem cells (ADSC) were added into MOSE-LTICv spheroids. It was found that peritoneal serous fluid (PSF) from obese mice significantly increased migration of MOSE-LTICv (Serum vs PSF, 517.8 vs 1158.6). These studies brought new knowledge into the field of obesity and ovarian cancer risk and provided direction for future studies involving potential cellular and molecular targets for ovarian cancer diagnosis and treatment. / Master of Science / Ovarian cancer affects many women in the United States. Obesity or more specifically, carrying more weight around the waist, can affect a woman's risk of developing ovarian cancer. Abdominal fat needs to be researched to see if abdominal obesity can affect ovarian cancer on the cellular level. Researchers have looked into how fat cells, known as adipocytes, can affect the progression of ovarian cancer, but more research needs to be done on the contributions of other cells found within adipose tissue. Other cells in abdominal fat include cells such as immune cells, stem and progenitor cells and fibroblasts. We have explored how adipose stem cells from obese mice affect the DNA or "the blueprints" of the cells, survival, and progression of mouse ovarian cancer cells. We found that when adipose stem cells are combined with ovarian cancer cells the expression of certain genes or particular "blueprints" increased. The genes whose expression increased included Dkc1, Ccnd2, Lig4, and Snai2 and when deregulated can cause ovarian cancer cells to become more aggressive. The abdominal fluid from obese mice was found to increase migration of ovarian cancer cells which simulates an increase in metastatic potential. This information has given new insight into the obesity and ovarian cancer relationship.