This thesis is comprised of three main parts: The Hermite-Hadamard inequality on discrete time scales, the fractional Hermite-Hadamard inequality, and Karush-Kuhn- Tucker conditions on higher dimensional discrete domains. In the first part of the thesis, Chapters 2 & 3, we define a convex function on a special time scale T where all the time points are not uniformly distributed on a time line. With the use of the substitution rules of integration we prove the Hermite-Hadamard inequality for convex functions defined on T. In the fourth chapter, we introduce fractional order Hermite-Hadamard inequality and characterize convexity in terms of this inequality. In the fifth chapter, we discuss convexity on n{dimensional discrete time scales T = T1 × T2 × ... × Tn where Ti ⊂ R , i = 1; 2,…,n are discrete time scales which are not necessarily periodic. We introduce the discrete analogues of the fundamental concepts of real convex optimization such as convexity of a function, subgradients, and the Karush-Kuhn-Tucker conditions. We close this thesis by two remarks for the future direction of the research in this area.

This project examines Dr. C. DeLores Tucker’s efforts to abolish the production and distribution of gangsta rap to the American youth. Though her efforts were courageous and daring, they were not sufficient. The thesis will trace Tucker’s crusade beginning in 1992 through the end of the 1990s. It brings together several themes in post-World War II American history, such as the issues of race, gender, popular culture, economics, and the role of government. The first chapter thematically explores Tucker’s crusade, detailing her methodology and highlighting pivotal events throughout the movement. The second chapter discusses how opposition from rap artists, and the music industry, media coverage of Tucker and her followers, and resistance from members of Congress contributed to the failure of her endeavor.

Es werden verschiedene Verfahren zur Lösung verallgemeinerter Nash-Gleichgewichtsprobleme mit dem Schwerpunkt auf deren globaler Konvergenz entwickelt. Ein globalisiertes Newton-Verfahren zur Berechnung normalisierter Lösungen, ein nichtglattes Optimierungsverfahren basierend auf einer unrestringierten Umformulierung des spieltheoretischen Problems, und ein Minimierungsansatz sowei eine Innere-Punkte-Methode zur Lösung der gemeinsamen Karush-Kuhn-Tucker-Bedingungen der Spieler werden theoretisch untersucht und numerisch getestet. Insbesondere das Innere-Punkte Verfahren erweist sich als das zur Zeit wohl beste Verfahren zur Lösung verallgemeinerter Nash-Gleichgewichtsprobleme. / In this thesis different algorithms for the solution of generalized Nash equilibrium problems with the focus on global convergence properties are developed. A globalized Newton method for the computation of normalized solutions, a nonsmooth algorithm based on an optimization reformulation of the game-theoretic problem, and a merit function approach and an interior point method for the solution of the concatenated Karush-Kuhn-Tucker-system are analyzed theoretically and numerically. The interior point method turns out to be one of the best existing methods for the solution of generalized Nash equilibrium problems.

In conventional wireless channel models, there is no control on the gains of different subchannels. In such channels, the transmitted signal undergoes attenuation and phase shift and is subject to multi-path propagation effects. We herein refer to such channels as passive channels. In this dissertation, we study the problem of joint power allocation and channel design for a parallel channel which conveys information from a source to a destination through multiple orthogonal subchannels. In such a link, the power over each subchannel can be adjusted not only at the source but also at each subchannel. We refer to this link as an active parallel channel. For such a channel, we study the problem of sum-rate maximization under the assumption that the source power as well as the energy of the active channel are constrained. This problem is investigated for equal and unequal noise power at different subchannels. For equal noise power over different subchannels, although the sum-rate maximization problem is not convex, we propose a closed-form solution to this maximization problem. An interesting aspect of this solution is that it requires only a subset of the subchannels to be active and the remaining subchannels should be switched off. This is in contrast with passive parallel channels with equal subchannel signal-tonoise- ratios (SNRs), where water-filling solution to the sum-rate maximization under a total source power constraint leads to an equal power allocation among all subchannels. Furthermore, we prove that the number of active channels depends on the product of the source and channel powers. We also prove that if the total power available to the source and to the channel is limited, then in order to maximize the sum-rate via optimal power allocation to the source and to the active channel, half viii ix of the total available power should be allocated to the source and the remaining half should be allocated to the active channel. We extend our analysis to the case where the noise powers are unequal over different subchannels. we show that the sum-rate maximization problem is not convex. Nevertheless, with the aid of Karush-Kuhn-Tucker (KKT) conditions, we propose a computationally efficient algorithm for optimal source and channel power allocation. To this end, first, we obtain the feasible number of active subchannels. Then, we show that the optimal solution can be obtained by comparing a finite number of points in the feasible set and by choosing the best point which yields the best sum-rate performance. The worst-case computational complexity of this solution is linear in terms of number of subchannels. / UOIT

No description available.

Thesis (M.S.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains xii, 170 p. : ill. (some col.), maps (part col.). Includes abstract. Includes bibliographical references (p. 112-116).

Thesis (M.S.)--West Virginia University, 2005 / Title from document title page. Document formatted into pages; contains viii, 138 p. : ill. (some col.), col. map. Includes abstract. Includes bibliographical references (p. 81-85).

Thesis (M.S.)--Marshall University, 2004. / Title from document title page. Includes abstract. Document formatted into pages; contains vii, 120 p. including illustrations. Includes bibliographical references (p. 110-114).

Thesis (M.S.)--West Virginia University, 2004. / Title from document title page. Document formatted into pages; contains viii, 89 p. : ill. (some col.), maps (some col.). Includes abstract. Includes bibliographical references (p. 79-81).

The United States (US) witnessed remarkable growth in annual long distance travel over the past few decades. Over half of the long distance travel in the US is made for pleasure, including visiting friends and relatives (VFR) and leisure activities. This trend could continue with increased use of information and communication technologies for socialization, and enhanced mobility being achieved using fuel-efficient (electric/hybrid) and technology enhanced vehicles. Despite these developments, and recent interest to implement alternate mass transit options to serve this market, not much exists on the measurement, analysis and modeling of long distance pleasure travel in the U.S. Statewide and national models are used to estimate long distance travel, but these are predominantly trip-based models, making it difficult to understand long distance trips as collection of household-level travel behavior. This form of travel behavior has been studied a lot in tourism, but in a piecemeal manner, such as to (from) a specific destination. Further, most of these studies are confined to analyzing leisure market, with VFR market gaining recognition only recently. In essence, annual household long distance pleasure travel behavior needs to be studied in a comprehensive manner rather than as isolated trips. This is because, most of these household travel decisions are undertaken considering their annual time and monetary budget, and their perceived cost to travel to one (or more) destination for given pleasure purpose on one (or more) occasion using a given mode of travel. Thus, the main objective of this dissertation is to develop a comprehensive behavioral model framework to analyze the above-discussed annual household long distance pleasure travel choices. To start the above effort, it is first required to collect detailed annual household travel data, last collected over two decades ago (e.g.: ATS, 1995). No such recent effort has been pursued due to the significant labor and economic resource required to undertake it. There exist recent surveys (NHTS, 2001), but collected over a shorter (four week) period, and require significant processing even to arrive at aggregate annual travel estimates. Second, besides surveys, there is a need for additional data to estimate households’ annual pleasure travel budget, and their cost to travel and stay at each of their potential destination choices, which are not readily available. Thus, as the first goal, this dissertation analyzes long distance travel reported across historical surveys (NPTS; ATS; NHTS), to understand the differences in their definition, enumeration of purpose and collection methods. The intent here is twofold, first to conceive a method to estimate annual travel from surveys with shorter collection period. Further, the second intent is to gather travel patterns from these historical datasets such that it informs the second goal of this dissertation, i.e. development of a behavioral framework to analyze annual household pleasure travel. To this effect, this research also analyzes pleasure expenditures using Consumer Expenditure Survey (CEX, BLS) data. Interestingly, the analysis reveals CEX pleasure travel expenditure pattern to be similar to the travel pattern reported for the same market segments in travel survey (ATS). Importantly, the above analysis informs the development of behavioral models, pursued as two distinct tasks to achieve the second goal. As the first task, a novel econometric model and forecasting procedure is developed to analyze a household’s annual long distance leisure travel decisions. Specifically, a households’ time spent across one (or more) destination and travel mode to such destination for leisure is modeled subject to time and money budget constraints. In this methodological framework, the destination choice is modeled as a continuous variable (time at destination) using Multiple-Discrete Continuous Extreme Value model (MDCEV). While, travel mode choice to these destination(s) are modeled as a discrete choice, through a nested Multinomial Logit Model (MNL), with price variation introduced across the above choice of destination(s) and travel modes (air/ground). This required estimating annual monetary budgets, travel cost and per night lodging cost for each sample household, with each of them having 210 potential destinations and 2 travel mode choices respectively. The second task, involved the development of a broader national model system to analyze households’ annual pleasure travel decisions such as: choice (duration) at destination(s), travel purpose (VFR or leisure), mode (airplane or auto) choice and trip frequencies to these destination(s) using the same dataset. It was modeled in two stages, with the first stage estimating households’ annual pleasure time budget using a stochastic frontier model. This budget was then used as constraint to analyze households’ annual choice of destination and purpose using a nested MDCEV-MNL model in the second stage. A log sum variable from a nested joint multinomial logit model of trip frequency and mode choice for each purpose (VFR or leisure) is also introduced as input at this stage. This model was then validated using a prediction procedure, and further applied to test a policy scenario (increase in travel cost). The above national pleasure travel demand model could be further enhanced by including monetary constraints and price variation as in the first task. Overall, the model system proposed in this dissertation forms the foundation for a national comprehensive long distance travel model. This could be achieved through inclusion of other prominent travel purpose such as business and commuting to the national travel demand model presented in this research.