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Thesis (Ph.D.)--Tufts University, 2003. / Adviser: Joseph P. Noonan. Submitted to the Dept. of Electrical Engineering. Includes bibliographical references (leaves 149-149). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph.D)--Chemistry and Biochemistry, Georgia Institute of Technology, 2010. / Committee Chair: Weck, Marcus; Committee Member: Breedveld, Victor; Committee Member: Fahrni, Christoph; Committee Member: Kelly, Wendy; Committee Member: Lyon, L. Andrew. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (M.S. in Meteorology and Physical Oceanography)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): Patrick Harr. Includes bibliographical references (p. 95-96). Also available online.

A generalization of multigroup energy condensation theory has been developed. The new method generates a solution within the few-group framework which exhibits the energy spectrum characteristic of a many-group transport solution, without the computational time usually associated with such solutions. This is accomplished by expanding the energy dependence of the angular flux in a set of general orthogonal functions. The expansion leads to a set of equations for the angular flux moments in the few-group framework. The 0th moment generates the standard few-group equation while the higher moment equations generate the detailed spectral resolution within the few-group structure. It is shown that by carefully choosing the orthogonal function set (e.g., Legendre polynomials), the higher moment equations are only coupled to the 0th-order equation and not to each other. The decoupling makes the new method highly competitive with the standard few-group method since the computation time associated with determining the higher moments become negligible as a result of the decoupling. The method is verified in several 1-D benchmark problems typical of BWR configurations with mild to high heterogeneity.

WKB procedure is used in the study of asymptotic solutions of differential equations of the hypergeometric type. Hence asymptotic forms of classical orthogonal polynomials associated with the names Jacobi, Laguerre and Hermite have been derived. In particular, the asymptotic expansion of the Jacobi polynomials $P^{(alpha, beta)}_n(x)$ as $n$ tends to infinity is emphasized.

This thesis describes original research aimed at the development of highly efficient polymer functionalization strategies by introducing orthogonal chemistry within polymeric systems. The primary hypothesis of this thesis is that the use of click chemistries or noncovalent interactions can provide new and easy pathways towards the synthesis of highly functionalized polymers thereby addressing the shortcomings of traditional covalent functionalization approaches. To verify the hypothesis, the work presented in the following chapters of this thesis further explores previous methods of either covalent or noncovalent polymer functionalization described in Chapter 1. Chapters 2 and 3 present advanced methods of covalent polymer functionalization based on high-yielding and orthogonal click reactions: 1,3-dipolar cycloaddition, hydrazone formation, and maleimide-thiol coupling. All three click reactions employed can be orthogonal to one another and conversions can be quantitative, leading to the easy and rapid synthesis of highly functionalized polymers without interference among functional handles along the polymer backbones. The next two chapters focus on the noncovalent functionalization strategies for creating supramolecular block copolymers via the main-chain self-assembly of telechelic polymers. Novel synthetic methods to prepare telechelic polymers bearing terminal recognition motifs were developed through a combination of ROMP using functionalized ruthenium initiators and functionalized chain-terminators, and the resulting polymers were self-assembled to form supramolecular block copolymers. Chapter 4 demonstrates the formation of supramolecular multiblock copolymers via self-assembly of symmetrical telechelic polymers using metal coordination, while Chapter 5 demonstrates that supramolecular ABC triblock copolymers can be prepared by the self-assembly of a heterotelechelic polymer as the central block with two other complementary monotelechelic polymers using two orthogonal hydrogen bonding interactions. Chapter 6 presents a unique application of noncovalent functionalization approaches. The ultimate goal of this research is to develop a controlled polymerization method based on noncovalent templation. The initial attempts at the metal coordination-based template polymerization are presented in this chapter. Finally, Chapter 7 summarizes the findings in each chapter and presents the potential extensions of the orthogonal functionalization strategies developed in this thesis.

In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schr&uml / odinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.