We provide an exposition of J. Milnor's proof of the h-Cobordism Theorem. This theorem states that a smooth, compact, simply connected n-dimensional manifold W with n greater than or equal to 6, whose boundary boundaryW consists of a pair of closed simply connected (n-1)-dimensional manifolds M0 and M1 and whose relative integral homology groups H(W,M0) are all trivial, is diffeomorphic to the cylinder M0 x [0, 1]. The proof makes heavy use of Morse Theory and in particular the cancellation of certain pairs of Morse critical points of a smooth function. We pay special attention to this cancellation and provide some explicit examples. An important application of this theorem concerns the generalized Poincare conjecture, which states that a closed simply connected n-dimensional manifold with the integral homology of the n-dimensional sphere is homeomorphic to the sphere. We discuss the proof of this conjecture in dimension n greater than or equal to 6, which is a consequence of the h-Cobordism Theorem. / Thesis (M.S.)--Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics

Query privacy is a critical concern to users of location-based services. A majority of existing query privacy protection techniques are based on the notion of k-anonymity, wherein a user's exact location is obfuscated into a spatial range containing at least k users, called the cloaking region. Thus, the user who issues the query cannot be distinguished from k-1 other users. However, when mobile users issue continuous queries using such a k-anonymity scheme, an adversary can exploit the overlapped areas of the corresponding cloaking regions to determine the query issuer with a significantly higher probability. This thesis proposes a query-based memorizing algorithm to specifically address this issue. The main idea in this thesis is to memorize the identity of the users in an anonymity set or cloaking region. When a user issues sequential location-based queries, the cloaking regions are determined such that they include a maximum number of users that have appeared in the past cloaking regions. The query-based memorizing approach is empirically evaluated by means of simulation experiments and a detailed comparative analysis with three other popular privacy protection algorithms using standard privacy metrics is performed. The results show that the proposed algorithm efficiently protects users' query privacy against the overlapped area attack, especially when users are highly mobile. / Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science

The search for alternative energy generation methods requires development for new energy storage methods as well. The ability to use nanotechnology to achieve high surface area, which is correlated to increased energy storage, brought advancements in supercapacitor applications. Supercapacitors have the potential to charge and discharge quickly and hold as much energy as batteries and other chemical storage devices. By having a completely solid-state supercapacitor, problems with leakage and decay could be avoided. Supercapacitors were assembled from electrodes made by reducing graphene oxide in a computer disc drive and adhering two electrodes with composite electrolytes having various concentrations of PVA/CNT. Tests were performed on the completed supercapacitors, as well as the individual components. The analysis of the different concentrations of carbon nanotubes in PVA electrolytes showed the lowest resistivity for 0.5wt% CNT (294 Omega cm) and the highest specific capacitance for 1.0wt% CNT (123.5 F/g). This specific capacitance is a 27% improvement on an electrolyte without CNT. The electrolyte with pure PVA has similar capacitance to other solid-state supercapacitors in the literature. Electrolytes with higher percentages of CNT (0.5%) show higher resistivity because of the decreased carbon solubility or agglomerations. The final product supercapacitors, thin, flexible, and environmentally friendly, can be used in wide temperature ranges, and have a theoretically long lifespan. They can charge more quickly than batteries, and hold more energy than capacitors. This study shows promising enhancements in solid-state supercapacitors, making them an even more plausible replacement for batteries in the near future. The improvements made on the specific capacitance with the different electrolytes could lead to greater efficiency and lower cost in many unique applications requiring absence of liquid components. / Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Mechanical Engineering

Most promising implementations in quantum computing are based on Linear Nearest Neighbor (LNN) architectures, where qubits only interact with neighbors. Multi-control Toffoli gates are used in many quantum applications such as error correction and algorithms like Shor's factorization. Typically, to implement a multi-control Toffoli gate in an LNN architecture, additional operations called swap gates are required to bring the qubits adjacent to each other. This may increase the total number of quantum gates and computational overhead of the circuit. Here, we propose a new method to implement multi-control Toffoli gates in LNN arrays without using swap gates. The circuit reduction techniques discussed here are based on 3 lemmas. Using the lemmas, we show how to implement multi-control Toffoli gates in LNN arrays with different separations between the control and target qubits. The key feature of our scheme is to involve qubits other than control and target qubits to take part in gate operations. We call these qubits auxiliary" qubits and they are used in our gate decomposition protocols. Auxiliary qubits can be in any arbitrary states, a|0>+beta|1> , and are always restored back to their original states. Since we do not use swap gates to bring qubits adjacent to each other, compared to circuits using swap gates, the total number of gate operations used in our method is decreased, and the quantum cost is lowered. In addition, for implementing multi-control Toffoli gate operations efficiently in LNN arrays, we also show how to extend our protocols to 2D arrays. Here, in addition to translating our gate reduction techniques, directly from 1D to 2D, we use further simplification techniques for particular arrangements of qubits. / Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science

This study investigates the stratal relationships of a pure microbolite within the Upper Jurassic strata at the Little Cedar Creek, and Brooklyn Fields, or complex, for the development of a refined exploration model of Smackover reefal buildups in the eastern Gulf Coast. During the Jurassic, southwestern Alabama was divided by Appalachian ridges into three sub-basins: the Conecuh Embayment, Manila Embayment, and the eastern extension of the Mississippi Interior Salt Basin. The complex is located in the Conecuh Embayment of southeastern Conecuh County, Alabama, and is the largest accumulation of hydrocarbons discovered in the state of Alabama. As of January of 2014 hydrocarbon production is currently over 31 million barrels of oil and over 34 billion cubic feet of gas. The microbolite buildups formed in an inner ramp setting of the Upper Jurassic (Oxfordian) Smackover Formation.The Little Cedar Creek and Brooklyn Fields are anomalous discoveries compared to other oil and gas fields in the region. Previous studies observed that microbial nucleation occurred on Paleozoic crystalline basement highs where depositional fabrics were heavily modified by dolomitization. Instead, the complex's microbolite buildups developed on mudstones, have no apparent association with paleo-highs, and have retained a large percentage of original depositional fabrics.This study found thrombolitic reefs develop on paleotopographic highs that were indicated by a thinning of underlying transgressive lime mudstones. / Thesis (M.S.)--Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Geology

This report presents the development of a nanocomposite coating using nano graphene platelets associated with an epoxy primer to improve the coating resistance against corrosion and weathering. It was hypothesized that coatings containing nanoadditives would be more resistant to degradation than coatings without nanoadditives; but also that by modifying the graphene particles through a surface modification technique called 'silanization' before inclusion in the coating, the stability of the graphene particles would be improved and hence improve the resistance of the polymer coating against degradation to a greater extent than if unmodified graphene was used. The performance of the nanocomposite coating was assessed by exposing it to UV light and salt fog for different time spans. The specimens were alternatively placed in the corrosion and UV chamber in intervals of 24 hours for 20 days. The coating performance analyses were carried out using atomic force microscopy, Fourier transform infrared spectrometer, thickness measurements, water contact angle, and electro-chemical impedance spectroscopy testing. It was found that after 20 days' exposure to UV and salt fog degradation, a 17.15% reduction in coating thickness is observed for coating containing silanized graphene, while for coating with unmodified graphene a 20.60% reduction is seen. Contact angle values showed that in the case of silanized graphene, the addition of a higher percentage of the nanoadditives significantly improved the performance of the coating, while for unmodified graphene up to 6% can be added to the coating to see improvement. EIS studies showed that nanocomposite coatings containing unmodified graphene had a higher corrosion rate (38.71E-06 mpy), and a lower impedance value (75,040 ohms) than nanocomposite coatings containing silanized graphene boasting a corrosion rate of 12.11E-06 mpy and an impedance value of 140,000 ohms, hence confirming the positive effects of silanization of graphene. / Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Mechanical Engineering

Thesis (M.M.)--Wichita State University, College of Fine Arts, Dept. of Music Theory/Composition

Molecular Dynamics simulations have been carried out to investigate the dynamics of horse heart Cytochrome C and associated crystallographic water molecules in different water-methanol systems. The 100 ns simulation predicts that hh-CytC undergoes different dynamical transitions with some common conformations in different solvents. With increase of methanol concentration in solvents, hh-CytC has increased flexibility, fluctuating its hydrophobic solvent accessible surface area (SASA), and number of persistent internal hydrogen bonds with long hydrogen-bond-lifetime. The protein became more liquid-like in mixed solvents compared to pure solvents; flexibility increases in the absence of the crystallographic water. Similarly, the number of hydrogen bonds between solvent molecules and hh-CytC decreased with increasing of methanol concentration. Water-protein and methanol-protein hydrogen bond lifetimes were computed 11.5 and 16.6 picoseconds, respectively, in pure solvents. However, in mixtures, solvent-protein hydrogen bond lifetime was higher in twenty percent methanol than in fourty percent in water. The surface crystallographic water molecules diffused easily in bulk solvents within 1 nanosecond and protein surface is stabilized by hydrogen bonds with a solvation layer. The two crystallographic water molecules which are buried internally in hh-CytC have 5 to more than 100 nanoseconds residence time in the conserved sites with 100's of picoseconds of hydrogen bond lifetime depending on the solvent compositions. The residence time might depend on the mechanism of conformational transition of protein in simulation. Solvent water molecules exchange these buried water molecules but exchange is less frequent than that in hydration layer. Even though methanol has succeeded to reside into these conserved sites in pure methanol solvent but its distance with hydrogen bonding partners more than 5 A with labile hydrogen bonding state. / Thesis (M.S.)--Wichita State University, Fairmount College of Liberal Arts, Dept. of Chemistry

Carbon fiber is extensively used in aircraft components and structures, where its superior strength-to weight ratio far exceeds that of any metal. Thirty percent of all carbon fiber is used in the aerospace industry. The purpose of this research was to determine the influence of material properties on the impact response of a laminate, whereby specimens were fabricated and cured under a vacuum and high temperature using three types of pre-impregnated (prepreg), carbon fibers, namely unidirectional fiber, plain weave woven fiber, and non-crimp fiber. Each carbon fiber panel, usually known for its low-impact properties, with respective type of prepregs, of 16 plies underwent impact testing using a low-velocity impactor and visual damage inspection by C-scan in order to measure the damage area and depth, before and after impact testing. These panels were treated with UV exposure and moisture conditioning for 20 days each. Water contact angles were taken into consideration to determine the hydrophobicity and hydrophillicity of the respective prepreg material. Experimental results and damage analysis show that UV exposure and moisture conditioning showcased the variation in impact response and behavior, such as load-carrying capacity, absorbed energy, and impact energy of the carbon fiber panels. This study illustrates that non-crimp carbon fiber laminates were far more superior relative to load capacity than woven and unidirectional laminates, with the NCF-AS laminate exhibiting the highest load capacity of 17,244 lb/in (pre-UV) with only 0.89% decrease after UV exposure. This same laminate also had a 1.54% decrease in sustaining impact and 31.4% increase in wettability of the panel. Moreover, the study shows how symmetric and asymmetric stacking sequences affect the impact behavior of non-crimp fiber laminates. These results may be useful for expanding the capacity of carbon fiber, lowering costs, and growing new markets, thus turning carbon fiber into a viable commercial product. / Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Mechanical Engineering

The purpose of this thesis was to extend the quasi-steady-state approximation and matrix block diagonalization methods utilized in the work of Shim and Sawan [1]. These authors showed that an approximate controller solution could be developed by relocating only the slow poles for two-time-scale aircraft dynamics. In addition, they showed that the difference between approximate solutions and exact solutions was bounded within limits as O(epsilon) and O(epsilon2). This technique was successfully applied to the lateral dynamics of the de Haviland Canada DHC-2 Beaver aircraft. In this thesis, the same technique was applied to the NASA F-8 aircraft dynamics in order to show that the method is not unique to the Beaver and can be applied to other aircraft models. It also extended the method to consider the singularly perturbed stochastic system and showed that a finite solution to the Lyapunov equation existed as a result of the stability. / Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science