Rayleigh matroids are a class of matroids with sets of bases that satisfy a strong negative correlation property. Interesting characteristics include the existence of an efficient algorithm for sampling the bases of a Rayleigh matroid [7]. It has been conjectured that the class of Rayleigh matroids satisfies Mason’s conjecture [14]. Though many elementary properties of Rayleigh matroids have been established, it is not known if this class has a finite set of minimal excluded minors. At this time, it seems unlikely that this is the case. It has been shown that there is a single minimal excluded minor for the smaller class of binary Rayleigh matroids [5]. The aim of this thesis is to detail our search for the set of minimal excluded minors for ternary Rayleigh matroids. We have found several minimal excluded minors for the above class of matroids. However, our search is incomplete. It is unclear whether the set of excluded minors for this set of matroids is finite or not, and, if finite, what the complete set of minimal excluded minors is. For our method to answer this question definitively will require a new computer program. This program would automate a step in our process that we have done by hand: writing polynomials in at least ten indeterminates as a sum with many terms, squared.

Carbon nanotubes (CNTs) are advanced materials that have numerous novel and useful properties. Controlling the synthesis and properties of CNTs is the major challenge toward their future applications. This thesis addresses this challenge with several contributions. This thesis begins with the brief introduction of CNTs, including the history of their discovery, their geometric structure, unique properties and potential applications. Then focus is laid on the subsequent three sections: characterization, synthesis, and manipulation of CNTs. Chapter 2 describes three characterization tools: AFM, SEM and Raman, which are commonly used to analyze CNTs and other nanomaterials. They offer both qualitative and quantitative information on many physical properties including size, morphology, surface texture and roughness. Also, they can be used to determine the structure of CNTS. Chapter 3 addresses the synthesis of CNTS, because synthesis is an important and indispensible process to study CNTs experimentally. Specifically, two controllable synthesis techniques are realized, which are capable to produce iron catalyst nanoparticles for single-walled carbon nanotube (SWNT) growth. Iron nanoparicles of different sizes obtained from both wet chemistry and electrodeposition can be used for diameter-controlled synthesis of SWNTs. Following synthesis, two manipulation methods of CNTs are discussed in Chapter 4. Firstly, effort of electrical breakdown of CNTs is introduced. Both SWNTs and MWNTs (Multi-walled carbon nanotubes) are cut using this method. Moreover, SWNT kink is shown using AFM tip manipulation. These two manipulation methods provide us a possibility to fabricate large cavity from a MWNT for our purposes. In the end of this thesis, conclusions on my master work in research field of CNTs are drawn and future research directions are proposed.

Polyolefins are the most important commodity polymers today. Their end use properties polymers depend primarily on their molecular weight (MWD) and chemical composition (CCD) distributions. Several characterization techniques are used to analyze the microstructures of the polyolefins. High-temperature gel permeation chromatography (GPC) is the most widely used technique for MWD determination. Temperature rising elution fractionation (TREF) and crystallization analysis fractionation (CRYSTAF) are routinely used for CCD measurement. There have been significant improvements over the last few years on CCD characterization techniques for polyolefins with the introduction of crystallization elution fractionation (CEF) and high-temperature thermal gradient interaction chromatography (HT-TGIC). The main objective of this thesis was to conduct systematic studies on HT-TGIC and CEF to provide a better understanding on the separation mechanism of these new techniques and to find out operational conditions that enhance the resolution of the measured CCDs. The effects of cooling rate, adsorption/desorption temperature range, heating rate and sample size on HT-TGIC fractionation were investigated using polyethylene and ethylene/1-octene copolymers made with metallocene catalyst. It was found out that HT-TGIC was relatively insensitive to the cooling rate within the range investigated in this study. However, the obtained profiles depended strongly on the heating rate applied during the desorption cycle. Chromatograms measured under faster heating rates were broader and had lower resolutions, supposedly due to co-desorption effects. Analysis of polyolefin blends by HT-TGIC showed that sample volume was a very important parameter affecting peak separation of the blend components; reducing the volume of the injected sample can be used to minimize the degree of co-adsorption and co-desorption effects. The effect of solvent type on HT-TGIC analysis was investigated using o-dichlorobenzene (ODCB), 1,2,4-trichlorobenzene (TCB), and chloronaphthalene (CN). Polyolefin blends were analyzed using these solvents and the best resolution was obtained iv when ODCB was used as the mobile phase. The profiles obtained using TCB and CN were similar and both were strongly affected by the co-adsorption and co-desorption phenomena. HT-TGIC profiles of ethylene homopolymers and ethylene/1-octene copolymers were also compared with the equivalent CEF profiles. Interestingly, it was found out that the differences between the profiles measured by these techniques decreased as the comonomer content increased, with CEF systematically measuring sharper profiles for samples with low 1-olefin comonomer content. A new method was also developed to quantify the degree of co-crystallization of polyolefin blends analyzed by CEF and was used to quantify operating conditions that influenced co-crystallization. The results showed that co-crystallization can be minimized using slower cooling rates, but heating rates play a less important role. A detailed study on the effect of CEF operating conditions on CCD resolution was also conducted using industrial LLDPE resins that have broad MWDs and CCDs. Cooling rate and solvent flow rate during the cooling cycle significantly affect the degree of co-crystallization of CEF profiles. However, varying the heating rate does not have a marked impact on these separations. The CEF profiles of these resins were compared with the equivalent HT-TGIC profiles, showing that CEF provided better peak separation than HT-TGIC. Finally, a new mathematical model was developed to simultaneously deconvolute the MWD and CCD of polyolefins made with multiple site-type catalysts such as Ziegler-Natta catalysts. The model was applied to several industrial linear low-density polyethylene (LLDPE) resins to estimate the minimum number of active site types, the number average molecular weight, the average comonomer mole fraction, and the mass fraction of soluble and non-soluble polymer made on each site type.

Electronic commerce servers have a significant presence in today's Internet. Corporations want to maintain high availability, sufficient capacity, and satisfactory performance for their E-commerce Web systems, and want to provide satisfactory services to customers. Workload characterization and the analysis of customers' interactions with Web sites are the bases upon which to analyze server performance, plan system capacity, manage system resources, and personalize services at the Web site. To date, little empirical evidence has been discovered that identifies the characteristics for Web workloads of E-commerce systems and the behaviours of customers. This thesis analyzes the Web access logs at public Web sites for three organizations: a car rental company, an IT company, and the Computer Science department of the University of Saskatchewan. In these case studies, the characteristics of Web workloads are explored at the request level, functionlevel, resource level, and session level; customers' interactions with Web sites are analyzed by identifying and characterizing session groups. The main E-commerce Web workload characteristics and performance implications are: i) The requests for dynamic Web objects are an important part of the workload. These requests should be characterized separately since the system processes them differently; ii) Some popular image files, which are embedded in the same Web page, are always requested together. If these files are requested and sent in a bundle, a system will greatly reduce the overheads in processing requests for these files; iii) The percentage of requests for each Web page category tends to be stable in the workload when the time scale is large enough. This observation is helpful in forecasting workload composition; iv) the Secure Socket Layer protocol (SSL) is heavily used and most Web objects are either requested primarily through SSL or primarily not through SSL; and v) Session groups of different characteristics are identified for all logs. The analysis of session groups may be helpful in improving system performance, maximizing revenue throughput of the system, providing better services to customers, and managing and planning system resources. A hybrid clustering algorithm, which is a combination of the minimum spanning tree method and k-means clustering algorithm, is proposed to identify session clusters. Session clusters obtained using the three session representations Pages Requested, Navigation Pattern, and Resource Usage are similar enough so that it is possible to use different session representations interchangeably to produce similar groupings. The grouping based on one session representation is believed to be sufficient to answer questions in server performance, resource management, capacity planning and Web site personalization, which previously would have required multiple different groupings. Grouping by Pages Requested is recommended since it is the simplest and data on Web pages requested is relatively easy to obtain in HTTP logs.

Surface water reservoirs in rural areas of the Canadian prairies often have poor water quality due to contamination by dissolved organic carbon (DOC). DOC can activate growth of microorganisms in water distribution systems and form disinfection by-products (DBPs) in water treatment. The presence of microbiological contaminants and DBPs are potentially harmful to human health. Therefore, rapid and simple methods for DOC characterization are needed to evaluate potential water sources and to assist in understanding how best to remove DOC. The first objective of this project was to develop a sample preparation and analysis procedure utilizing Fourier Transform Infrared Spectroscopy (FTIR) to characterize the DOC content of water samples. The second objective was to compare FTIR analysis results for fractionated and un-fractionated water samples to more convention DOC characterization methods (such as UV, SUVA and specific THMFP). The third objective was to demonstrate the application of the procedure to source water assessment and water treatment process evaluation by characterizing the DOC content of several typical treated and un-treated prairie water samples at several locations in Saskatchewan.<p> In the first phase of the study prepared samples of known DOC concentration were separated into six fractions (hydrophobic acid (HPOA), hydrophobic neutral (HPON) and hydrophobic base (HPOB); and hydrophilic acid (HPIA), hydrophilic neutral (HPIN) and hydrophilic base (HPIB)) using resin fractionation techniques. FTIR and conventional UV spectroscopic measurements, DOC concentration, and trihalomethane formation potential (THMFP) measurements were taken on the un-fractionated samples and their fractions. A water matrix interference problem in the FTIR measurements was overcome by depositing a residue of dry solids from the aqueous solution containing the DOC on a flat, organic compound free and non-infrared absorptive gold plated slide before analysis. This simple evaporation procedure developed for concentrating water samples successfully deposited a solid residue for FTIR scanning. Scanning of the solid residue of each sample at multiple locations successfully produced a spectrum of average results suitable for interpretation.<p> Each organic fraction separated from the prepared samples of known DOC was then assessed using FTIR analysis. Comparison of the spectra from the resin adsorption fractions gave an indication of the relationship between functional groups and the hydrophobic/hydrophilic nature of the DOC. The results suggest that the hydrophobic fractions contain more aromatic functional groups. This demonstrates that the FTIR spectra can provide information regarding the hydrophobic/hydrophilic nature of the DOC as an alternative to the resin separation procedure. The sample preparation and FTIR analysis procedure was then used to characterize the DOC content of source and treated waters at several locations within Saskatchewan. The results of these initial investigations indicate the method can effectively identify the major organic functional groups present in source waters and the changes in the major functional groups that occur as the water is subjected to water treatment unit operations and processes. Further, the presence of several key functional groups is related to an increase in THMFP.

This thesis reports on a new design of photonic crystal waveguides (PCWs) to achieve large guiding bandwidth, linear dispersion, single-mode behavior, good coupling efficiency to dielectric waveguides, and small loss. The design is based on using the linear dispersion region of one PCW in the photonic bandgap (PBG) of another PCW. While perturbing the period can result in a PCW with linear dispersion and large guiding bandwidth, it introduces an odd mode at those frequencies, as well. By using another perturbation scheme, it is shown that single-mode behavior can also be achieved. The linear dispersion of these waveguides and their operation at lower frequencies of the PBG, where the density of states of radiation modes is smaller, gives rise to very small loss coefficients as verified experimentally. Full characterization of a waveguide requires the measurement of not only the transmission coefficient, but also the dispersion and spectral phase. We have developed a real-time characterization technique based on spectral interferometry with femtosecond laser pulses at optical communication wavelengths to measure the spectral phase of waveguides. This haracterization technique can be used to study fast dynamics in timevarying structures and makes the alignment easy.

Engineering industries usually require nondestructive evaluation (NDE) methods to ensure quality control, safety, and optimized use of resources. Among potential NDE techniques, ultrasonic wave methods are widely used because of their versatility and affordability. For applications to layered structures, ultrasonic guided waves are naturally excited and detected, so these guided waves are the preferred choice when compared to conventional bulk waves. The main advantage of guided waves over bulk waves for layered structures is that these guided waves can propagate a much farther distance, and thus they enable long range inspection. It is important to note that guided waves are multi-mode, so a preferred mode can be selectively used, although it is sometimes more efficient to use multiple wave modes. The characteristics of guided waves, namely dispersive propagation and attenuation, are directly related to the properties of the system in which they are propagating, so the measurement of these wave characteristics can be used for material characterization and condition monitoring. Despite a number of successful techniques to experimentally measure propagation characteristics of guided waves, there is a lack of a standard procedure to obtain attenuation characteristics. This research develops such a quantitative and systematic procedure to extract attenuation characteristics from real guided wave time-domain signals. This research considers multiple wave-modes, and focuses on broadband attenuation measurements with laser ultrasonic techniques. The analytical model of guided waves with attenuation is studied in general cases, and a numerical simulation is developed to model the point source/receiver laser measurement system. The attenuation extraction technique is developed using synthetic signals generated by the simulation. Finally, this research demonstrates the use of experimentally-measured attenuation data for material characterization and condition monitoring by developing an inversion scheme to back-calculate material properties for a number of practical cases.

Turbidite reservoirs in deep-water depositional systems, such as the oil fields in the offshore Gulf of Mexico and North Sea, are becoming an important exploration target in the petroleum industry. Accurate seismic reservoir characterization, however, is complicated by the heterogeneous of the sand and shale distribution and also by the lack of resolution when imaging thin channel deposits. Amplitude variation with offset (AVO) is a very important technique that is widely applied to locate hydrocarbons. Inaccurate estimates of seismic reflection amplitudes may result in misleading interpretations because of these problems in application to turbidite reservoirs. Therefore, an efficient, accurate, and robust method of modeling seismic responses for such complex reservoirs is crucial and necessary to reduce exploration risk. A fast and accurate approach generating synthetic seismograms for such reservoir models combines wavefront construction ray tracing with composite reflection coefficients in a hybrid modeling algorithm. The wavefront construction approach is a modern, fast implementation of ray tracing that I have extended to model quasishear wave propagation in anisotropic media. Composite reflection coefficients, which are computed using propagator matrix methods, provide the exact seismic reflection amplitude for a stratified reservoir model. This is a distinct improvement over conventional AVO analysis based on a model with only two homogeneous half spaces. I combine the two methods to compute synthetic seismograms for test models of turbidite reservoirs in the Ursa field, Gulf of Mexico, validating the new results against exact calculations using the discrete wavenumber method. The new method, however, can also be used to generate synthetic seismograms for the laterally heterogeneous, complex stratified reservoir models. The results show important frequency dependence that may be useful for exploration. Because turbidite channel systems often display complex vertical and lateral heterogeneity that is difficult to measure directly, stochastic modeling is often used to predict the range of possible seismic responses. Though binary models containing mixtures of sands and shales have been proposed in previous work, log measurements show that these are not good representations of real seismic properties. Therefore, I develop a new approach for generating stochastic turbidite models (STM) from a combination of geological interpretation and well log measurements that are more realistic. Calculations of the composite reflection coefficient and synthetic seismograms predict direct hydrocarbon indicators associated with such turbidite sequences. The STMs provide important insights to predict the seismic responses for the complexity of turbidite reservoirs. Results of AVO responses predict the presence of gas saturation in the sand beds. For example, as the source frequency increases, the uncertainty in AVO responses for brine and gas sands predict the possibility of false interpretation in AVO analysis.

Information on the locations for feeding, reproductions, and resting, are essential to effectively protect sea turtle populations and implement conservation efforts. This type of ecological information is critically important for hawksbill turtle conservation in Los Roques Archipelago National Park (LRANP) where turtles have been declining in spite of habitat protection efforts. The goal of this research was to produce a benthic habitat map of LRANP employing in situ visual surveys, remote sensing and geographic information system techniques, and to spatially characterize sea turtle occupancy and patterns of usage by habitat type. Between June and August of 2008, turtle behavior and habitat use were recorded during 159 h of observation, comprising 46 sighting events (n = 20 juveniles, n = 26 female adults). Observed activities were grouped into 4 categories: foraging, resting, swimming, and reproductive behavior. The benthic habitat at each turtle sighting was recorded as one of three categories: coral reef, sand or marine vegetation. Results suggest that the population of turtles within LRANP is comprised primarily of female adults and juvenile individuals and that coral reef is the most important habitat for this species. The most important foraging area in the atoll is a coral patch reef that connects Dos Mosquises Sur and Dos Mosquises Norte. The data in this thesis have been made available in digital and map form to the managers of LRANP for management purposes.

This study explored different chemical characterization methods of agricultural and urban airborne particulate matter. Three different field campaigns are discussed. For the agricultural aerosols, measurement of the chemical composition of size-resolved agricultural aerosols collected from a ground site at the nominally downwind and upwind edge of a feedlot in West Texas were reported. High volume cascade impactor samplers were used for the collection of the particles, and two major analytical methods were applied to characterize different components of the aerosols, ion chromatography (IC ) was used to measure ionic composition with the main targets being ammonium (NH4 ), nitrate (NO3 -), and sulfate (SO4 2-), direct thermal desorption gas chromatography-mass spectrometry/flame ionization detection (GC-MS/FID) methodology was used to identify and quantify organic compounds in the aerosol particles. For the urban aerosols, I report the measurement of mass, and the chemical composition of size-resolved aerosols collected from two different locations in Houston, analyzed by the thermal desorption GC-MS/FID method. The investigation of single particle composition using RM is reported as well: RM and chemical mapping techniques have been applied for the qualitative analysis of components in the samples of air particulate matter collected in downtown Houston.