What constitutes an adequate solution to a mathematical problem? When is an adequate solution a 'good' solution? In this thesis I consider these questions in relation to two Diophantine equations, namely, x$ sp2$ + k = y$ sp3$ and 6y$ sp2$ = x(x + 1)(2x + 1). The first dates back to Diophantus himself (c. 250 AD) while the second can be traced to a puzzle proposed by Edouard Lucas in 1875. Each of these equations has attracted a number of solutions and each solution reveals something about its era. An examination and comparison of these solutions will give us an opportunity to reflect on some of the criteria used for judging proofs in mathematics. In particular, we shall see that contemporary computer technology has made a certain kind of solution to these equations acceptable which might have seemed pointless, incomplete or inelegant to the mathematicians who first studied them. Included among these 'computer solutions' is my own solution to 6y$ sp2$ = x(x + 1)(2x + 1).

This thesis investigates the function of number marking in Persian, within the framework of principles and parameters (P&P), and its relationship to inflectional and derivational number marking. Following the assumption in Distributed Morphology that inflectional and derivational morphology are not distinct, the distribution and properties of number marking in Persian provide evidence for both inflectional and derivational number marking. Assuming the two parameters of number marking (Wiltschko, 2007, 2008), number marking as a functional head and number marking as a modifier, I propose that number marking in Persian is mainly inflectional while number functions as a functional head; moreover, I propose that number marking in Persian can be derivational while number functions as a modifier. This explains that number morphology in Persian is not split to either inflectional or derivational. Rather, following Booij’s (1993, 1995) claim that inflectional morphology can be used contextually as well as inherently, I propose that number morphology in Persian is inflectional while number is a functional head; however, it has inherent residues as a modifier. Considering the functions of inflectional plural morphology in Persian, I argue that the functional category Number Phrase (NumP) is projected in Persian, and number is generated in the head of this functional category. Besides, Persian is a classifier language in which classifiers are in complementary distribution with plural marking. Following Borer’s (2005) discussion of the complementary distribution of plural marking and classifiers in Armenian, I argue that the head of NumP in Persian is either occupied by the plural maker or by full/empty classifiers. Moreover, I show that the presence of bare singulars/plurals in certain syntactic positions in Persian is related to the projection/non-projection of NumP.

No description available.

Let $F$ be a non-Archimedean local field and $G$ be the general linear group $\mathrm{GL}_n$ over $F$. Bushnell and Henniart described the essentially tame local Langlands correspondence of $G(F)$ using rectifiers, which are certain characters defined on tamely ramified elliptic maximal tori of $G(F)$. They obtained such result by studying the automorphic induction character identity. We relate this formula to the spectral transfer character identity, based on the theory of twisted endoscopy of Kottwitz, Langlands, and Shelstad. In this article, we establish the following two main results. (i) To show that the automorphic induction character identity is equal to the spectral transfer character identity when both are normalized by the same Whittaker data. (ii) To express the essentially tame local Langlands correspondence using admissible embeddings constructed by Langlands-Shelstad $\chi$-data and to relate Bushnell-Henniart's rectifiers to certain transfer factors.

No description available.

Thesis (M. Ed.)--University of Hong Kong, 2007. / Also available in print.

Thesis--University of Florida. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 103-105).

Thesis (Ph. D.)--University of Kentucky, 2004. / Title from document title page (viewed Jan. 7, 2005). Document formatted into pages; contains x, 180p. : ill. Includes abstract and vita. Includes bibliographical references (p. 173-178).

Thesis--Copenhagen.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.