Physical Sciences and Mathematics Commons^™

Extensions Of The Cayley-Hamilton Theorem With Applications To Elliptic Operators And Frames., Alberto Mokak Teguia

Electronic Theses and Dissertations

The Cayley-Hamilton Theorem is an important result in the study of linear transformations over finite dimensional vector spaces. In this thesis, we show that the Cayley-Hamilton Theorem can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.

Cell Toxicology Study Of Rrr-Alpha-Tocopheryl Polyethylene Glycol 1000 Succinate (Tpgs)., Clarisse Sornsay Muenyi

Electronic Theses and Dissertations

This research focused on the cytotoxic properties of RRR-alpha-tocopheryl polyethylene glycol 1000 succinate (TPGS) in transformed and cancerous cell lines. We used RAW264.7 macrophage and prostate cancer (LNCaP) cell lines in this study. TPGS caused cell death and decreased cell viability in a dose and time dependent manner. Cell death was evaluated fluorimetrically by employing the nucleic acid-binding fluorophore; propidium iodide. A colorimetric 3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyl tetrazolium bromide (MTT) assay was used to evaluate cell viability. Cell death can occur through necrosis or apoptosis. Our results suggested that TPGS triggered apoptotic cell death. Induction of apoptosis, as measured by caspase …

The Interquartile Range: Theory And Estimation., Dewey Lonzo Whaley

Electronic Theses and Dissertations

The interquartile range (IQR) is used to describe the spread of a distribution. In an introductory statistics course, the IQR might be introduced as simply the “range within which the middle half of the data points lie.” In other words, it is the distance between the two quartiles, IQR = Q₃ - Q₁. We will compute the population IQR, the expected value, and the variance of the sample IQR for various continuous distributions. In addition, a bootstrap confidence interval for the population IQR will be evaluated.

Potential Energy Surface Around The Tropylium Ion., Kenneth Wayne Bullins

Electronic Theses and Dissertations

The formation of the tropylium ion, C₇H₇⁺, in the mass spectrum of toluene is a chemical process that has been studied extensively in the past. The advances in computational power of personal computers have made the investigation of the pathway to form this ion and its subsequent decomposition feasible at a fairly high level of theory. The calculations that we performed were at the HF/6-31G (d, p) and the B3LYP/6-311++G (2d) levels. This work will show areas of the potential energy surface around the highly symmetric tropylium ion to give a glance of possible mechanisms …

Bicyclic Mixed Triple Systems., Benkam Benedict Bobga

Electronic Theses and Dissertations

In the study of triple systems, one question faced is that of finding for what order a decomposition exists. We state and prove a necessary and sufficient condition for the existence of a bicyclic mixed triple system based on the three possible partial orientations of the 3-cycle with twice as many arcs as edges. We also explore the existence of rotational and reverse mixed triple systems. Our principal proof technique applied is the difference method. Finally, this work contains a result on packing of complete mixed graphs on v vertices, M_v, with isomorphic copies of two …

Evaluating The Effectiveness Of A Company's Online Health And Safety Training Program By Assessing Its Employees Perceptions And Knowledge., Jo Nell Maynard Mullins

Electronic Theses and Dissertations

A cross-sectional study was conducted to evaluate a company’s online H & S training program. The ABC Company’s online 8-hr HAZWOPER refresher course is based on current OSHA standard topics required for certification and principles flexible to fit site- or task-specific situations and conditions.

An 18-question survey was used to evaluate employee perceptions of online training compared to traditional classroom training. Perceptions were compared by demographic variables (e.g. gender, position, race, age and longevity with the ABC Company), which suggested that only age had an influence on employee response. Fifty-five percent of the employees surveyed preferred online training as compared …

The Challenges Of Network Security Remediation At A Regional University., William R. Simons

Electronic Theses and Dissertations

This thesis describes challenges encountered during a year-long effort to improve the security of the 3,300 node administrative computer network at East Tennessee State University. The key remediation strategies used included employing the vulnerability scanner Nessus to profile the network, analyzing the scan results, and attempting to remove the most critical vulnerabilities found. The project succeeded in decreasing known “high” criticality vulnerabilities on campus by 26.1%, and confirmed four standard observations about the challenges of network administration:

• Vulnerability scanning is a lengthy task best performed in parallel and supported by automated data analysis.
• Securing a network is like trying to …

Survival Model And Estimation For Lung Cancer Patients., Xingchen Yuan

Electronic Theses and Dissertations

Lung cancer is the most frequent fatal cancer in the United States. Following the notion in actuarial math analysis, we assume an exponential form for the baseline hazard function and combine Cox proportional hazard regression for the survival study of a group of lung cancer patients. The covariates in the hazard function are estimated by maximum likelihood estimation following the proportional hazards regression analysis. Although the proportional hazards model does not give an explicit baseline hazard function, the baseline hazard function can be estimated by fitting the data with a non-linear least square technique. The survival model is then examined …

Extending The Abstract Data Model., Matthew Bryston Winegar

Electronic Theses and Dissertations

The Abstract Data Model (ADM) was developed by Sanderson [19] to model and predict semantic loss in data translation between computer languages. In this work, the ADM was applied to eight languages that were not considered as part of the original work. Some of the languages were found to support semantic features, such as the restriction semantics for inheritance found in languages like XML Schemas and Java, which could not be represented in the ADM. A proposal was made to extend the ADM to support these semantic features, and the requirements and implications of implementing that proposal were considered.

Graph Theory For The Secondary School Classroom., Dayna Brown Smithers

Electronic Theses and Dissertations

After recognizing the beauty and the utility of Graph Theory in solving a variety of problems, the author decided that it would be a good idea to make the subject available for students earlier in their educational experience. In this thesis, the author developed four units in Graph Theory, namely Vertex Coloring, Minimum Spanning Tree, Domination, and Hamiltonian Paths and Cycles, which are appropriate for high school level.

Using Domination To Analyze Rna Structures., Travis Reves Coake

Electronic Theses and Dissertations

Understanding RNA molecules is important to genomics research. Recently researchers at the Courant Institute of Mathematical Sciences used graph theory to model RNA molecules and provided a database of trees representing possible secondary RNA structures. In this thesis we use domination parameters to predict which trees are more likely to exist in nature as RNA structures. This approach appears to have promise in graph theory applications in genomics research.