Master of Science / Department of Mathematics / Natalia Rojkovskaia / The topic of limits and sequences run through the math syllabi from high school to graduate school. However rigorous proofs of this concept is not seen up until a students second year in college or even later. This text is aimed at presenting proofs of limits of sequences at a level accessible to high school and undergraduate students who are interested in learning such proofs. The ''Epsilon-N" definition of the limit with proofs using this definition is presented in the text. We also look at properties of limits of sequences and their proofs as well as sequences without limits (that is sequences that diverge). We include some graphical representations of some sequences which can help one to determine whether a sequence will converge or diverge. Finally, the text contains a good number of exercises for the reader, some solved and others with hints to direct the reader in solving them.

Let P(ε) = P0 + A(ε) be a stochasticity preserving analytic perturbation of a stochastic matrix P0. We characterize the hybrid Cesaro limit lim 1 N(ε) Pk(ε), ε↓0 N(ε) ∑ where N(ε) ↑ ∞ as ε ↓ 0, when P0 has eigenvalues on the unit circle in the complex plane other than 1.

This dissertation studies volatility measurement and modeling issues when asset prices are subject to price limits based on Bayesian approaches. Two types of estimators are developed to consistently estimate integrated volatility in the presence of price limits. One is a realized volatility type estimator, but using both realized asset prices and simulated asset prices. The other is a discrete sample analogue of integrated volatility using posterior samples of the latent volatility states. These two types of estimators are first constructed based on the simple log-stochastic volatility model in Chapter 2. The simple log-stochastic volatility framework is extended in Chapter 3 to incorporate correlated innovations and further extended in Chapter 4 to accommodate jumps and fat-tailed innovations. For each framework, a MCMC algorithm is designed to simulate the unobserved asset prices, model parameters and latent states. Performances of both type estimators are also examined using simulations under each framework. Applications to Chinese stock markets are also provided. / Thesis (Ph.D, Economics) -- Queen's University, 2014-01-22 10:29:12.507

To date, the 50 km/h General Urban Speed Limit (GUSL) has been implemented to some local residential streets in the City of Port Adelaide Enfield (hereafter referred to as Port Adelaide), South Australia as a Local Area Traffic Management (LATM) scheme since March 2003 aiming to reduce travel speeds and traffic volumes so as to enhance road safety and amenity of residential areas. Port Adelaide is located approximately nine kilometres away from the North-west of Adelaide Central Business District (CBD). There are major express highways and freight roads enclosing Port Adelaide, and within the boundaries is composed of many arterial and collector roads. All of these arterial roads and some major collector roads line in north-south direction. As a result of these geographical characteristics, Port Adelaide is a city covering the major direct routes for residents and major freight route for goods transport in the north-west suburbs. / However, one of the problems occurring in Port Adelaide seems to be characteristics of grid road networks lacking clear road hierarchy, which can be seen from many local streets connecting directly with nearby arterial and/or collector roads. Furthermore, as described previously Port Adelaide consists of many freight routes, arterial routes, and these characteristics cause another problem. Traffic is induced to divert to local streets, which are relatively straight, and uses them as an alternative route causing many problems to residents in the local area due to travel demands during rush hour. To this point, it can be seen that the 50 km/h GUSL scheme might not be as efficient as it should be in deterring through traffic since the implementation of traffic management has not covered a macro scale, which in this case is arterial roads forming a connective grid. / This study seeks to present the analysis of traffic data in terms of traffic volumes, mean speed and 85th percentile on three different local residential streets during weekday and soma crash data analysis is also done on two study streets. The expected results of this study may be taken as samples for further research in future. / Thesis (MTransportSysEngineering)--University of South Australia, 2006.

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This dissertation seeks to explain the puzzle in the state politics literature which expects females to benefit from the enactment of term limits, but initial research finds the number of female in office decreases after the implementation of term limits. Examining this puzzle involves three separate stand-alone chapters which explore female candidate emergence (1), success rates (2), and women-friendly state legislative districts (3). The goal of the dissertation is to reconcile the puzzle while adding insight into how female candidates behave at the state-level. Overall, I find that term limits increases female descriptive representation by increasing the likelihood a female candidate will run and win an election.

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This study is an investigation into methods of developing ergonomic guidelines for automotive assembly tasks involving insertion of small parts. The study was conducted in four major parts: 1) a method of determining and evaluating subjective exertion limits was modified and tested, 2) a large dataset was collected from an industrial population in 10 simulated assembly line tasks, 3) a smaller dataset was collected from a student population to assess hand dominance effects, and 4) strength data obtained was compared with a strength prediction model to determine if the model could predict manual insertion forces. The traditional method of psychophysical data collection requires participants to extrapolate sensations from a relativity short session to judge if the task could be done for a much longer period. Maximum acceptable limits (MALs) are typically derived from having participants adjust a weight, resistance, or frequency to an acceptable level. The present study evaluated a relatively new method of collecting MAL data for simple, single-digit exertions where participants were asked to determine an MAL by self-adjusting and then regulating to maintain the exertion level. Results showed that MAL values obtained from a series of self-regulated exertions were independent of both analysis method and duration (5 minutes vs. 25 minutes) used for evaluation, and that the method was repeatable both within and between sessions. Ergonomic guidelines are often obtained from the strength capacity for a certain task, as it is important to ensure that workers possess sufficient strength to accomplish a task. As task demands increase, however, a larger percentage of a worker's strength capability in required, and other factors, such as performance and worker comfort, tend to be compromised. In this work, both strength capacity and subjective limits were obtained for a variety of simulated tasks to facilitate development of guidelines for the specific tasks. The relationship between these two measures (maximum force, acceptable force) was determined, and acceptable limits were found to be approximately 55% of population strength capacity, with correlations (R2) ranging from 0.40 to 0.60 depending on the task, suggesting the subjective limits and strength capacity are related in these tasks. Hand dominance was found to have a small (5%), but significant (p = 0.006) effect on strength capability, and no significant effect on subjective limit. Biomechanical strength prediction models can be used to assess loads placed on the human performing various tasks. One of the more popular models, Three-Dimensional Static Strength Prediction Program, is often used for heavy material handling tasks, such as lifting or pushing. The tasks studied presently, however, are manual insertions, requiring localized force application rather than whole body exertion. The prediction capabilities of this strength prediction model were compared with strength values obtained from the simulated assembly tasks. Results indicated that the model was not successful when predicting localized force, accounting for only 40% of the observed variance in strength (R2 = 0.4) / Master of Science

Flammability limit is a significant safety issue for industrial processes. A certain amount of flammability limit data for pure hydrocarbons are available in the literature, but for industrial applications, there are conditions including different combinations of fuels at standard and non-standard conditions, in which the flammability limit data are scarce and sometimes unavailable. This research is two-fold: (i) Performing experimental measurements to estimate the lower flammability limits and upper flammability limits of binary hydrocarbon mixtures, conducting experimental data numerical analysis to quantitatively characterize the flammability limits of these mixtures with parameters, such as component compositions, flammability properties of pure hydrocarbons, and thermo-kinetic values; (ii) Estimating flammability limits of binary hydrocarbon mixtures through CFT-V modeling prediction (calculated flame temperature at constant volume), which is based on a comprehensive consideration of energy conservation. For the experimental part, thermal detection was used in this experiment. The experimental results indicate that the experimental results fit Le Chatelier’s Law within experimental uncertainty at the lower flammability limit condition. At the upper flammability limit condition, Le Chatelier’s Law roughly fits the saturated hydrocarbon mixture data, while with mixtures that contain one or more unsaturated components, a modification of Le Chatelier’s is preferred to fit the experimental data. The easy and efficient way to modify Le Chatelier’s Law is to power the molar percentage concentrations of hydrocarbon components. For modeling prediction part, the CFT-V modeling is an extended modification of CAFT modeling at constant volume and is significantly related to the reaction vessel configuration. This modeling prediction is consistent with experimental observation and Le Chatelier’s Law at the concentrations of lower flammability limits. When the quenching effect is negligible, this model can be simplified by ignoring heat loss from the reaction vessel to the external surroundings. Specifically, when the total mole changes in chemical reactions can be neglected and the quenching effect is small, CFTV modeling can be simplified to CAFT modeling.

In this dissertation, we consider various aspects of the boundary behavior of holomorphic functions of several complex variables. In dimension one, a characterization of the radial limit zero sets of nonconstant holomorphic functions on the disc has been given by Lusin, Privalov, McMillan, and Berman. In higher dimensions, no such characterization is known for holomorphic functions on the unit ball B. Rudin posed the question as to the existence of nonconstant holomorphic functions on the ball with radial limit zero almost everywhere. Hakim, Sibony, and Dupain showed that such functions exist. Because the characterization in dimension one involves both Lebesgue measure and Baire category, it is natural to also ask whether there exist nonconstant holomorphic functions on the ball having residual radial limit zero sets. We show here that such functions exist. We also prove a higher dimensional version of the Lusin-Privalov Radial Uniqueness Theorem, but we show that, in contrast to what is the case in dimension one, the converse does not hold. We show that any characterization of radial limit zero sets on the ball must take into account the "complex structure" on the ball by giving an example that shows that the family of these sets is not closed under orthogonal transformations of the underlying real coordinates. In dimension one, using the theorem of McMillan and Berman, it is easy to see that radial limit zero sets are not closed under unions (even finite unions). Since there is no analogous result in higher dimensions of the McMillan and Berman result, it is not obvious whether the radial limit zero sets in higher dimensions are closed under finite unions. However, we show that, as is the case in dimension one, these sets are not closed under finite unions. Finally, we show that there are smooth curves of finite length in S that are non-tangential limit uniqueness sets for holomorphic functions on B. This strengthens a result of M. Tsuji.