Abstract For a set D of positive integers, the integral distance graph G(Z, D) is the graph with vertex set Z and edge set { xy : x, y 2 Z and | x − y | 2 D } . An integral distance graph G(Z, D) is called ¡§locally dense¡¨ if the clique size of G(Z, D) is not less to | D | . This paper acterizes locally dense integral distance graphs and determine their chromatic numbers.

This thesis discusses the game chromatic number of Halin graphs. We shall prove that with a few exceptions, all Halin graphs have game chromatic number 4.

The electroreflectance spectra(ER) have been measured on InxGa1-xAs film under various bias(Vbias), and they have exhibited many Franz-Keldysh Oscillations(FKOs) above band-gap energy. Their strength of field in the film can be obtained by the periods of FKOs. Due to many oscillations of FKOs, the Fast Fourier transform can be applied to separate heavy- and light-hole transitions. The relation between F and Vbias was nearly linear. FKOs were observable at a large range of photon energy(£_E). The mean free path of carriers can be estimated from the relation between £_E and F. It was compared with the range of order obtained from X-ray diffraction.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 57-59).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Low Reynolds Number; Micro Air Vehicle; Low Aspect Ratio; Spanwise pressure measurements; Spanwise Lift Distributions. Includes bibliographical references (p. 84-85).

Thesis (M.S.)--University of Central Florida, 2008. / Adviser: Larry Chew. Includes bibliographical references (p. 146-148).

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Let K be a quadratic imaginary number field, let Kp^(infinity) the top of its p-class field tower for p an odd prime, and let G=Gal(Kp^(infinity)/K). It is known, due to a tremendous collection of work ranging from the principal results of class field theory to the famous Golod-Shafarevich inequality, that G is finite if the p-rank of the class group of K is 0 or 1, and is infinite if this rank is at least 3. This leaves the rank 2 case as the only remaining unsolved case. In this case, while finiteness is still a mystery, much is still known about G: It is a 2-generated, 2-related pro-p-group equipped with an involution that acts as the inverse modulo commutators, and is of one of three possible Zassenhaus types (defined in the paper). If such a group is finite, we will call it an interesting p-tower group. We further the knowledge on such groups by showing that one particular Zassenhaus type can occur as an interesting p-tower group only if the group has order at least p^24 (Proposition 8.1), and by proving a succinct cohomological condition (Proposition 4.7) for a p-tower group to be infinite. More generally, we prove a Golod-Shafarevich equality (Theorem 5.2), refining the famous Golod-Shafarevich inequality, and obtaining as a corollary a strict strengthening of previous Golod-Shafarevich inequalities (Corollary 5.5). Of interest is that this equality applies not only to finite p-groups but also to p-adic analytic pro-p-groups, a class of groups of particular relevance due to their prominent appearance in the Fontaine-Mazur conjecture. This refined version admits as a consequence that the sizes of the first few modular dimension subgroups of an interesting p-tower group G are completely determined by p and its Zassenhaus type, and we compute these sizes. As another application, we prove a new formula (Corollary 5.3) for the Fp-dimensions of the successive quotients of dimension subgroups of free pro-p-groups.