No / This paper presents a new approach to estimate the unknown frequencies of the constituent sinusoids in a noiseless signal. The signal comprising of unknown number of sinusoids of unknown amplitudes and unknown phases is measured in the time domain. The Hankel matrix of measured samples is used as a basis for further analysis in the Pisarenko harmonic decomposition. A new constraint, the Existence Factor (EF), has been introduced in the methodology based on the relationship between the frequencies of the unknown sinusoids and the eigenspace of Hankel matrix of signal's samples. The accuracy of the method has been tested through multiple simulations on different signals with an unknown number of sinusoidal components. Results showed that the proposed method has efficiently estimated all the unknown frequencies.

This dissertation explores the persistent gap between rural and urban areas in the percentage of households that access the Internet at home (a discrepancy commonly known as the "digital divide"). The theoretical framework underlying a household's Internet adoption decision is examined, with emphasis on the roles that household characteristics, network externalities, and digital communication technology (DCT) infrastructure potentially play. This framework is transferred into a statistical model of household Internet access, where non-linear decomposition techniques are employed to estimate the contributions of these variables to the digital divide in a given year. Differences in Internet access rates between years are also analyzed to understand the importance of temporal resistance to the continuing digital divide. The increasing prevalence of "high-speed" or broadband access is also taken into account by modeling a decision process where households that choose to have Internet access must decide between dial-up and high-speed access. This nested process is also decomposed in order to estimate the contributions of household characteristics, network externalities, DCT infrastructure, and temporal resistance to the high-speed digital divide. The results suggest that public policies designed to alleviate digital divides in both general and high-speed access should focus more on the broader income and education inequities between rural and urban areas. The results also imply that the current policy environment of encouraging DCT infrastructure investment in rural areas may not be the most effective way to close the digital divide in both general and high-speed Internet access. / Ph. D.

Forest plantations in the southeastern U.S. are fertilized to increase growth on infertile, sandy soils. Nitrogen (N) and phosphorus (P) are the most common growth limiting nutrients. A key question that arises following fertilization of these soils is whether the applied fertilizer benefits only the current trees in the stand or also improves long-term site quality. The objectives of this study were to compare accumulation of N and P in the forest floor and mineral soil among unfertilized and fertilized plantations, determine soluble and residual N and P fractions and soluble carbohydrate and phenol fractions in foliage and litter, determine whether higher N in the forest floor from fertilization resulted in increased release of N from the forest floor and increased mineral soil N availability, and determine loblolly pine forest floor decomposition rate and release of nutrients in a simulated disturbance environment. Research was conducted at a 25-year old loblolly pine (Pinus taeda L.) plantation in NC (SETRES) and 13-year old loblolly pine and sweetgum (Liquidambar styraciflua L.) plantations in GA (Mt. Pleasant). Fertilization resulted in increases in mineral soil N that were likely to be temporary and not sustained following cessation of fertilization N applications. This was likely due to an inability of acidic, sandy mineral soils to retain NH4-N and NO3-N. The forest floor accumulated N due to slow release of N during decomposition. Fertilization with N results in only temporary increases in mineral soil N availability that occur during fertilizer application and from forest floor decomposition. Future changes in N availability are primarily determined by decomposition of the forest floor following a disturbance that accelerates decomposition. In contrast to N, fertilization of loblolly pine and sweetgum with P results in a long-term increase in site P availability. Fertilization with P has lasting effects by increasing mineral soil P in stable forms that can be made available for plant uptake over time suggesting increased supply of P to trees in the next rotation. Retention of P in the mineral soil was likely due to the tendency of acidic, sandy mineral soils to accumulate P in Al- and Fe-phosphates. / Ph. D.

We give a projective resolution of a finite dimensional 𝛫-algebra 𝛬 over its enveloping algebra 𝛬<SUP>𝑒</SUP> = 𝛬<SUP>𝑜𝑝</SUP> ⨂<SUB>𝛫</SUB>𝛬. The description of this resolution is related to decompositions of the first syzygy module of 𝛬 as an 𝛬<SUP>𝑒</SUP> module. Resolutions of right 𝛬 modules 𝑀<SUB>𝛬</SUB> may be obtained by tensoring 𝑀 over 𝛬 with this bimodule resoution. We describe how to obtain such a resolution when 𝑀 is simple or when 𝑀 is given in the form of a projective presentation. Computations of <I>𝐸𝑥𝑡</I><SUB>𝛬</SUB><SUP>𝑛</SUP>(𝑆<SUB>𝑣</SUB>,𝑆<SUB>𝑤</SUB>) for certain classes of algebras 𝛬 are made using these resolutions, and applied to obtain results on global dimension. / Ph. D.

Estimation of covariance matrix and its inverse is of great importance in multivariate statistics with broad applications such as dimension reduction, portfolio optimization, linear discriminant analysis and gene expression analysis. However, accurate estimation of covariance or inverse covariance matrices is challenging due to the positive definiteness constraint and large number of parameters, especially in the high-dimensional cases. In this thesis, I develop several approaches for estimating large covariance and inverse covariance matrices with different applications. In Chapter 2, I consider an estimation of time-varying covariance matrices in the analysis of multivariate financial data. An order-invariant Cholesky-log-GARCH model is developed for estimating the time-varying covariance matrices based on the modified Cholesky decomposition. This decomposition provides a statistically interpretable parametrization of the covariance matrix. The key idea of the proposed model is to consider an ensemble estimation of covariance matrix based on the multiple permutations of variables. Chapter 3 investigates the sparse estimation of inverse covariance matrix for the highdimensional data. This problem has attracted wide attention, since zero entries in the inverse covariance matrix imply the conditional independence among variables. I propose an orderinvariant sparse estimator based on the modified Cholesky decomposition. The proposed estimator is obtained by assembling a set of estimates from the multiple permutations of variables. Hard thresholding is imposed on the ensemble Cholesky factor to encourage the sparsity in the estimated inverse covariance matrix. The proposed method is able to catch the correct sparse structure of the inverse covariance matrix. Chapter 4 focuses on the sparse estimation of large covariance matrix. Traditional estimation approach is known to perform poorly in the high dimensions. I propose a positive-definite estimator for the covariance matrix using the modified Cholesky decomposition. Such a decomposition provides a exibility to obtain a set of covariance matrix estimates. The proposed method considers an ensemble estimator as the center" of these available estimates with respect to Frobenius norm. The proposed estimator is not only guaranteed to be positive definite, but also able to catch the underlying sparse structure of the true matrix. / Ph. D.

This thesis discusses the problem of decomposing rectilinear regions, with or without holes, into a minimum number of rectangles. There are two different types of decomposition considered here : decomposing a figure into non-overlapping parts, called partitioning, and decomposing a figure into possibly overlapping parts, called covering. A method is outlined and proved for solving the above two problems, and algorithms for the solutions of these problems are presented. The partitioning problem can be solved in time O(n⁵ ²), where n is the number of vertices of the figure, whereas the covering problem is exponential in its time complexity. / M.S.

Bandwidth enhancement of low-profile omnidirectional, electrically-small antennas has evolved from the design and construction of AM transmitter towers eighty years ago to current market demand for battery-powered personal communication devices. Electrically-small antenna theory developed with well-known approximations for characterizing radiation properties of antenna structures that are fractions of the radiansphere. Current state-of-the-art wideband small antennas near kaH1 have achieved multiple-octave impedance bandwidths when utilizing volume-efficient designs. Significant advances in both the power and miniaturization of microelectronics have created a second possible approach to enhance bandwidth. Frequency agility, via switch tuning of reconfigurable structures, offers the possibility of the direct integration of high-speed electronics to the antenna structure. The potential result would provide a means to translate a narrow instantaneous bandwidth across a wider operating bandwidth. One objective of the research was to create a direct comparison of the passive- multi-resonant and active-reconfigurable approaches to enhance bandwidth. Typically, volume-efficient, wideband antennas are unattractive candidates for low-profile applications and conversely, active electronics integrated directly antenna elements continue to introduce problematic loss mechanisms at the proof-of-concept level The dissertation presents an analysis method for wide bandwidth self-resonant antennas that exist in the 0.5dkad1.0 range. The combined approach utilizes the quality factor extracted directly from impedance response data in addition to near-and-far field modal analyses. Examples from several classes of antennas investigated are presented with practical boundary conditions. The resultant radiation properties of these antenna-finite ground plane systems are characterized by an appreciable percentage of radiated power outside the lowest-order mode. Volume-efficient structures and non-omnidirectional radiation characteristics are generally not viable for portable devices. Several examples of passive structures, representing different antenna classes are investigated. A PIN diode, switch-tuned low-profile antenna prototype was also developed for the comparison which demonstrated excessive loss in the physical prototype. Lastly, a passive, low-profile multi-resonant antenna element with monopole radiation is introduced. The structure is an extension of the planar inverted-F antenna with the addition of a capacitance-coupled parasitic to enhance reliable operation in unknown environments. / Ph. D.

There are two critical research needs for the study of hydrocarbon combustion in high speed flows: 1) combustion diagnostics with adequate temporal and spatial resolution, and 2) mathematical techniques that can extract key information from large datasets. The goal of this work is to address these needs, respectively, by the use of high speed and multi-perspective chemiluminescence and advanced mathematical algorithms. To obtain the measurements, this work explored the application of high speed chemiluminescence diagnostics and the use of fiber-based endoscopes (FBEs) for non-intrusive and multi-perspective chemiluminescence imaging up to 20 kHz. Non-intrusive and full-field imaging measurements provide a wealth of information for model validation and design optimization of propulsion systems. However, it is challenging to obtain such measurements due to various implementation difficulties such as optical access, thermal management, and equipment cost. This work therefore explores the application of FBEs for non-intrusive imaging to supersonic propulsion systems. The FBEs used in this work are demonstrated to overcome many of the aforementioned difficulties and provided datasets from multiple angular positions up to 20 kHz in a supersonic combustor. The combustor operated on ethylene fuel at Mach 2 with an inlet stagnation temperature and pressure of approximately 640 degrees Fahrenheit and 70 psia, respectively. The imaging measurements were obtained from eight perspectives simultaneously, providing full-field datasets under such flow conditions for the first time, allowing the possibility of inferring multi-dimensional measurements. Due to the high speed and multi-perspective nature, such new diagnostic capability generates a large volume of data and calls for analysis algorithms that can process the data and extract key physics effectively. To extract the key combustion dynamics from the measurements, three mathematical methods were investigated in this work: Fourier analysis, proper orthogonal decomposition (POD), and wavelet analysis (WA). These algorithms were first demonstrated and tested on imaging measurements obtained from one perspective in a sub-sonic combustor (up to Mach 0.2). The results show that these algorithms are effective in extracting the key physics from large datasets, including the characteristic frequencies of flow—flame interactions especially during transient processes such as lean blow off and ignition. After these relatively simple tests and demonstrations, these algorithms were applied to process the measurements obtained from multi-perspective in the supersonic combustor. compared to past analyses (which have been limited to data obtained from one perspective only), the availability of data at multiple perspective provide further insights into the flame and flow structures in high speed flows. In summary, this work shows that high speed chemiluminescence is a simple yet powerful combustion diagnostic. Especially when combined with FBEs and the analyses algorithms described in this work, such diagnostics provide full-field imaging at high repetition rate in challenging flows. Based on such measurements, a wealth of information can be obtained from proper analysis algorithms, including characteristic frequency, dominating flame modes, and even multi-dimensional flame and flow structures. / Ph. D.

In this thesis we conduct a numerical study of the 1D viscous Burgers' equation and several Reduced Order Models (ROMs) over a range of parameter values. This study is motivated by the need for robust reduced order models that can be used both for design and control. Thus the model should first, allow for selection of optimal parameter values in a trade space and second, identify impacts from changes of parameter values that occur during development, production and sustainment of the designs. To facilitate this study we apply a Finite Element Method (FEM) and where applicable, the Group Finite Element Method (GFE) due its demonstrated stability and reduced complexity over the standard FEM. We also utilize Proper Orthogonal Decomposition (POD) as a model reduction technique and modifications of POD that include Global POD, and the sensitivity based modifications Extrapolated POD and Expanded POD. We then use a single baseline parameter in the parameter range to develop a ROM basis for each method above and investigate the error of each ROM method against a full order "truth" solution for the full parameter range. / Master of Science

This thesis presents results of the application of energy-based large-scale optimization of a two-subsystem (propulsion subsystem (PS) and airframe subsystem-aerodynamics (AFS-A)) air-to-air fighter (AAF) with two types of AFS-A models: a fixed-wing AFS-A and a morphing-wing AFS-A. The AAF flies 19 mission segments of a supersonic fighter aircraft mission and the results of the study show that for very large structural weight penalties and fuel penalties applied to account for the morphing technology, the morphing-wing aircraft can significantly outperform a fixed-wing AAF counterpart in terms of fuel burned over the mission. The optimization drives the fixed-wing AAF wing-geometry design to be at its best flying the supersonic mission segment, while the morphing-wing AFS-A wing design is able to effectively adapt to different flight conditions, cruising at subsonic speeds much more efficiently than the fixed-wing AAF and, thus yielding significant fuel savings. Also presented in this thesis are partially optimized results of the application of a decomposition strategy for large-scale optimization applied to a nine-subsystem AAF consisting of a morphing-wing AFS-A, turbofan propulsion subsystem (PS), environmental controls subsystem (ECS), fuel loop subsystem (FLS), vapor compression/polyalphaolefin loop subsystem (VC/PAOS), electrical subsystem (ES), central hydraulics subsystem (CHS), oil loop subsystem (OLS), and flight controls subsystem (FCS). The decomposition strategy called Iterative Local-Global Optimization (ILGO) is incorporated into a new engineering aircraft simulation and optimization software called iSCRIPT™ which also incorporates the models developed as part of this thesis work for the nine-subsystem AAF. The AAF flies 21 mission segments of a supersonic fighter aircraft mission with a payload drop simulating a combat situation. The partially optimized results are extrapolated to a synthesis/design which is believed to be close to the system-level optimum using previously published results of the application of ILGO to a five-subsystem AAF to which the partially optimized results of the nine-subsystem AAF compare relatively well. In addition to the optimization results, a parametric study of the morphing AFS-A geometry is conducted. Three mission segments are studied: subsonic climb, subsonic cruise, and supersonic cruise. Four wing geometry parameters are studied: leading-edge wing sweep angle, wing aspect ratio, wing thickness-to-chord ratio, and wing taper ratio. The partially optimized AAF is used as the baseline, and the values for these geometric parameters are increased or decreased up to 20% relative to an established baseline to see the effect, if any, on AAF fuel consumption for these mission segments. The only significant effects seen in any of the mission segments arise from changes in the leading-edge sweep angle and wing aspect ratio. The wing thickness-to-chord ratio shows some effect during the subsonic climb segment, but otherwise shows no effect along with the taper ratio in any of the three mission segments studied. It should be emphasized, however, that these changes are made about a point (i.e. synthesis/design), which is already optimal or nearly so. Thus, the conclusions drawn cannot be generalized to syntheses/designs, which may be far from optimal. Also note that the results upon which these conclusions are based may very likely highlight a weakness in the conceptual-level drag-buildup method used in this thesis work. Further optimization studies using this drag-buildup method may warrant setting the thickness-to-chord ratios and taper ratios rather than having them participate in the optimization as degrees of freedom (DOF). The final set of results is a parametric study conducted to highlight the correlation between the fuel consumption and the total exergy destruction in the AFS-A. The results for the subsonic cruise and supersonic cruise mission segments show that at least for the case when the AFS-A is optimized by itself for a fixed specific fuel consumption that there is a direct correlation between the fuel burned and total exergy destruction. However, as shown in earlier work where a three-subsystem AAF with AFS-A, PS, and ECS is optimized, this may not always be the case. Furthermore, based on the results presented in this thesis, there is a smoothing effect observed in the exergy response curves compared to the fuel-burned response curves to changes in AFS-A geometry. This indicates that the exergy destruction is slightly less sensitive to such changes. / Master of Science