In this thesis we study the number of periodic points of congruential monomial dynamical system. By concept of index calculus we are able to calculate the number of solutions for congruential equations. We give formula for the number of r-periodic points over prime power. Then we discuss about calculating the total number of periodic points and cycles of length r for prime power.

A comprehensive understanding of urban development is critical for moving towards the goal of sustainability. Despite a collection of urban sustainability indicator (USI) conceptual frameworks proposed and explored in practical urban sustainability assessment, establishing an integrated, well-quantified, spatially characterized USI model is still a challenging task. Therefore, based on a manuscript-style format this thesis develops a subjectively weighted integrated USI model and then applies it to the city of Saskatoon, SK, Canada, as a case study, based on quantifying a hierarchical index system. In addition, urban environmental sustainability is spatiotemporally investigated for an improved understanding of Urban Heat Island (UHI) effect. Results show that the proposed integrated USI model improved urban sustainability measurement by overcoming the shortages in existing USI models. Geospatial statistics demonstrated disparity in urban sustainability across residential neighbourhoods for Saskatoon in 2006 based on the significant clusters and outliers. It also found that population increases can possibly improve intellectual and economic well-being and promote urbanization, but may cause environmental degradation and lead to a decline in overall urban sustainability. This research also demonstrates that satellite imagery can be used to study environmental sustainability at different spatiotemporal scales. This research reveals that both urban water and green spaces had significant cooling effects on the surrounding urban LST within specific ranges. Urban surface temperature can be estimated based on a multiple linear regression model with sustainable traveling mode index and land use information as input variables. The overall significance of this research has three folds. First, it lays a preliminary theoretical foundation for a comprehensive understanding of urban sustainability based on a well-quantified integrated USI model. Second, it is relatively original with respect to improving urban sustainability measurements through the incorporation of subjective information into objective data. Third, this research has explored spatiotemporal analysis to detect urban sustainability patterns based on compiling multiple data sources using geospatial techniques. The proposed USI model is highly suitable for comparison analysis at different spatial scales as well as continuously tracking the dynamic changes. Therefore, this research can be a good practice of applying the spatiotemporal philosophy to urban geographical problems.

As part of a project to see whether potatoes with a low glycemic-index (GI) could be developed through plant breeding, the GI values of 4 new potato varieties differing in starch structure was determined in 3 studies over 2 years in human subjects. Since cooking and cooling affects starch structure the potatoes were studied both freshly cooked (boiled) and cooled. The first study showed that cooling reduced the GI of two varieties by 40-50% but had no effect in the others (treatment × variety interaction, p=0.024), an effect which was confirmed in study 2. Differences in GI were readily explained by differences in starch structure or in-vitro digestion rate. Carbohydrate malabsorption increased from 3 to 5% upon cooling, not enough to account for the reduced GI. It is concluded that the effect on GI of cooling cooked potatoes varies in different varieties. Further research is needed to understand the mechanism.

This study explores the relationship among the overall nutritional quality index (ONQI), the carbon footprint and price of 90 different foods. The ONQI and carbon footprint measure the healthiness and environmental impact of a food, respectively. Two models are estimated. The first is a hedonic model of the food price and two characteristics: ONQI and carbon footprint. A positive relationship between price and carbon footprint is found, implying higher priced foods have a larger environmental impact. The second model is a regression of ONQI on price and carbon footprint. A negative, non-linear relationship between ONQI and carbon footprint is found. This implies there is a complementary relationship between the healthiness of food and its environmental impact. Both models show that healthier food is also higher priced. This could explain why poorer consumers are less healthy than richer consumers, and why taxing food would disproportionately impact the health of the poor.

No description available.

Two dimensional photonic crystal slabs are studied theoretically and experimentally for the application of refractive index sensing with a focus on increasing both quality factor and sensitivity simultaneously. An overview of simulation and experimental techniques, along with fabrication protocols used is given. Through the use of new wafer architectures which allow for an air substrate, sensitivity is enhanced in some cases by more than a factor of 2 from our previous studies. Combining this with a novel lattice proposed which greatly reduces fabrication tolerances, experimental quality factors above 10,500 are achieved while maintaining an experimental sensitivity of above 800 nm/RIU. The effects of a finite photonic crystal slab are studied through the group velocity of guided mode resonances, with an emphasis on zero-group velocity. Future applications of the designs proposed are discussed.

No description available.

Barley has been receiving increased attention as a human food due to the health benefits associated with β-glucan fiber and its potential as a low glycemic index (GI) functional food. Research has shown a relationship between the physico-chemical properties of β-glucan and the physiological effects, which may be altered by processing. However, it is not known if the physiological effects of consuming barley are affected by variations in chemical composition among cultivars or by common processing methods such as pearling or milling. The primary objective of this thesis was to characterize the effects of differences in cultivar starch and fibre content, level of pearling and milling on the GI, satiety and the physico-chemical properties of β-glucan. Nine barley cultivars varying in starch-type and β-glucan content were studied in three experiments in separate groups of ten healthy participants. Blood glucose and satiety ratings were measured and the GI was calculated. Total starch, total fibre, β-glucan, molecular weight (MW), solubility and β-glucan viscosity were determined in vitro. Results showed that GI varied by cultivar (CDC-Fibar, 26 ± 3 vs. AC-Parkhill, 35 ± 4, P < 0.05) and pearling (WG, 26 ± 4 vs. WP 35 ± 3, P < 0.05). When two cultivars were milled and processed to wet pasta the GI increased by 184% (P < 0.05). The pearled wet pasta had a significantly lower GI compared to the whole grain (P < 0.05). Boiled barley kernels tended to elicit greater satiety than white bread, but the difference was not significant. In both the boiled barley kernels and the wet pasta, pearling did not affect the MW, viscosity and solubility. MW did not significantly differ between cultivars but solubility and viscosity did (P < 0.05). The wet pasta had significantly lower MW, solubility, viscosity but not β-glucan content than the boiled barley kernels (P < 0.05). In conclusion, pearling did not have an effect but milling and extruding resulted in significant reduction in MW, solubility and viscosity. The GI of barley is influenced significantly by cultivar, pearling and milling. Further studies are required to determine the effect on satiety.

Barley has been receiving increased attention as a human food due to the health benefits associated with β-glucan fiber and its potential as a low glycemic index (GI) functional food. Research has shown a relationship between the physico-chemical properties of β-glucan and the physiological effects, which may be altered by processing. However, it is not known if the physiological effects of consuming barley are affected by variations in chemical composition among cultivars or by common processing methods such as pearling or milling. The primary objective of this thesis was to characterize the effects of differences in cultivar starch and fibre content, level of pearling and milling on the GI, satiety and the physico-chemical properties of β-glucan. Nine barley cultivars varying in starch-type and β-glucan content were studied in three experiments in separate groups of ten healthy participants. Blood glucose and satiety ratings were measured and the GI was calculated. Total starch, total fibre, β-glucan, molecular weight (MW), solubility and β-glucan viscosity were determined in vitro. Results showed that GI varied by cultivar (CDC-Fibar, 26 ± 3 vs. AC-Parkhill, 35 ± 4, P < 0.05) and pearling (WG, 26 ± 4 vs. WP 35 ± 3, P < 0.05). When two cultivars were milled and processed to wet pasta the GI increased by 184% (P < 0.05). The pearled wet pasta had a significantly lower GI compared to the whole grain (P < 0.05). Boiled barley kernels tended to elicit greater satiety than white bread, but the difference was not significant. In both the boiled barley kernels and the wet pasta, pearling did not affect the MW, viscosity and solubility. MW did not significantly differ between cultivars but solubility and viscosity did (P < 0.05). The wet pasta had significantly lower MW, solubility, viscosity but not β-glucan content than the boiled barley kernels (P < 0.05). In conclusion, pearling did not have an effect but milling and extruding resulted in significant reduction in MW, solubility and viscosity. The GI of barley is influenced significantly by cultivar, pearling and milling. Further studies are required to determine the effect on satiety.

The Capital Asset Pricing model (CAPM) is the most widely used equity valuation model in both the United States of America (U.S.) and South Africa, thus its importance in corporate finance cannot be underestimated. The largest criticism of the CAPM lies in the difficulties with estimating its parameters and in particular the return on the market parameter. Roll (1977) believed that it is impossible to estimate the market portfolio let alone find a good proxy for it. The common trend amongst practitioners is to use a broad based stock index such as the S&P 500 or in South Africa‟s case the All Share Index (ALSI) as a proxy for the market portfolio. However these methods are questionable, as the market portfolio theoretically contains all risky assets held in proportion to their market value, and stock indices ignore large asset classes such as bonds. Furthermore, using a broad based stock index in the South African context ignores South African specific problems such as the supposed segregation of the market to the Resource and Financial and Industrial sectors. Therefore the purpose of this study was to determine whether simply using the broad based stock index, the ALSI, as a proxy for the market portfolio would suffice or whether the inclusion of debt instruments and the acknowledgement of the segregation on the JSE would enhance the proxy‟s performances. First a set of theoretical requirements that a proxy must satisfy to be considered a suitable proxy for the market portfolio were derived. Then a review of literature on the matter was undertaken, which showed that studies in both the U.S. and South Africa had had mixed results. Next, the various proxies were formed, and tested using the two-pass regression method. The two-pass regressions that were run with the model comprising solely of the ALSI as a proxy, produced a negative sloping SML. This result suggested an inverse relationship between risk and return, which is contradictory to the theory set out in chapters two and three. Thus robustness tests were performed on the model, but none solved the problem. Next the proposed multifactor models were tested to see if they would enhance the results of the first model. Although the results improved slightly, they too did not solve the problem. Thus, in conclusion it was found that incorporating a bond index into the proxy for the market portfolio did not significantly enhance the use of the CAPM in South Africa. / Thesis (M.Com.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.