http://hdl.handle.net/10125/561 Sat, 25 May 2013 03:40:32 GMT 2013-05-25T03:40:32Z http://hdl.handle.net/10125/27418 Thesis (M. A.)--University of Hawaii at Manoa, 1972. Mon, 13 May 2013 00:00:00 GMT http://hdl.handle.net/10125/27418 2013-05-13T00:00:00Z Sox, David Griffiths http://hdl.handle.net/10125/25938 An important and long-standing open problem in universal algebra asks whether every finite lattice is isomorphic to the congruence lattice of a finite algebra. Until this problem is resolved, our understanding of finite algebras is incomplete, since, given an arbitrary finite algebra, we cannot say whether there are any restrictions on the shape of its congruence lattice. If we find a finite lattice that does not occur as the congruence lattice of a finite algebra (as many suspect we will), then we can finally declare that such restrictions do exist. By a well known result of Palfy and Pudlak, the problem would be solved if we could prove the existence of a finite lattice that is not the congruence lattice of a transitive group action or, equivalently, is not an interval in the lattice of subgroups of a finite group. Thus the problem of characterizing congruence lattices of finite algebras is closely related to the problem of characterizing intervals in subgroup lattices. In this work, we review a number of methods for finding a finite algebra with a given congruence lattice, including searching for intervals in subgroup lattices. We also consider methods for proving that algebras with a given congruence lattice exist without actually constructing them. By combining these well known methods with a new method we have developed, and with much help from computer software like the UACalc and GAP, we prove that with one possible exception every lattice with at most seven elements is isomorphic to the congruence lattice of a finite algebra. As such, we have identified the unique smallest lattice for which there is no known representation. We examine this exceptional lattice in detail, and prove results that characterize the class of algebras that could possibly represent this lattice. We conclude with what we feel are the most interesting open questions surrounding this problem and discuss possibilities for future work. Thesis (Ph. D.)--University of Hawaii at Manoa, 2012. Sun, 01 Jan 2012 00:00:00 GMT http://hdl.handle.net/10125/25938 2012-01-01T00:00:00Z DeMeo, William J. http://hdl.handle.net/10125/25937 Ordinary graphs are directed graphs that can be viewed as generalizations of symmetric block designs. They were introduced by Fossorier, Jezek, Nation and Pogel in [2] in an attempt to construct new finite projective planes. In this thesis we investigate some special cases of ordinary graphs, most prominently the case where nonadjacent vertices have no common neighbors. We determine all connected graphs of this type that exist. vii, 65 leaves, bound ; 29 cm.; Thesis (Ph. D.)--University of Hawaii at Manoa, 2005. Sat, 01 Jan 2005 00:00:00 GMT http://hdl.handle.net/10125/25937 2005-01-01T00:00:00Z Kalk, Jonathan W. http://hdl.handle.net/10125/25936 This dissertation introduces triple gluing lattices and proves that a triple gluing lattice is small if the key subcomponents are small. Then attention is turned to triple gluing irreducible small lattices. The triple gluing irreducible [Special characters omitted.] lattices are introduced. The conditions which insure [Special characters omitted.] small are discovered. This dissertation also give some triple gluing irreducible small lattices by gluing [Special characters omitted.] 's. Finally, K-structured lattices are introduced. We prove that a K-structured lattice L is triple gluing irreducible if and only if [Special characters omitted.] . We prove that no 4-element antichain lies in u 1 /v1 of a K-structured small lattice. We also prove that some special lattices with 3-element antichains can not lie in u1 /v1 of a K-structured small lattice. viii, 87 leaves, bound : ill. ; 29 cm.; Thesis (Ph. D.)--University of Hawaii at Manoa, 2000. Sat, 01 Jan 2000 00:00:00 GMT http://hdl.handle.net/10125/25936 2000-01-01T00:00:00Z Heeney, Xiang Xia Huang http://hdl.handle.net/10125/25935 We give a complete characterization of degree two rational maps on P1 with potential good reduction over local fields. We show this happens exactly when the map corresponds to an integral point in the moduli space M2. The proof includes an algorithm by which to conjugate any degree two rational map corresponding to an integral point in M2 into a map with unit resultant. The local fields result is used to solve the same problem for number fields with class number 1. Some additional results are given for degree 2 rational maps over Q. We also give a full description of post-critically finite maps in M2(Q), including the algorithm used to find them. Thesis (Ph. D.)--University of Hawaii at Manoa, 2012. Sun, 01 Jan 2012 00:00:00 GMT http://hdl.handle.net/10125/25935 2012-01-01T00:00:00Z Yap, Diane http://hdl.handle.net/10125/25934 A mock modular form f+ is the holomorphic part of a harmonic Maass form f. The non-holomorphic part of f is a period integral of a cusp form g, which we call the shadow of f+. The study of mock modular forms and mock theta functions is one of the most active areas in number theory with important works by Bringmann, Ono, Zagier, Zwegers, among many others. The theory has many wide-ranging applications: additive number theory, elliptic curves, mathematical physics, representation theory, and many others. We consider arithmetic properties of mock modular forms in three different settings: zeros of a certain family of modular forms, coupling the Fourier coefficients of mock modular forms and their shadows, and critical values of modular L-functions. For a prime p > 3, we consider j-zeros of a certain family of modular forms called Eisenstein series. When the weight of the Eisenstein series is p - 1, the j-zeros are j-invariants of elliptic curves with supersingular reduction modulo p. We lift these j-zeros to a p-adic field, and show that when the weights of two Eisenstein series are p-adically close, then there are j-zeros of both series that are p-adically close. A direct method for relating the coefficients of shadows and mock modular forms is not known. This is considered to be among the first of Ono's Fundamental Problems for mock modular forms. The fact that a shadow can be cast by infinitely many mock modular forms, and the expected transcendence of generic mock modular forms pose serious obstructions to this problem. We solve these problems when the shadow is an integer weight cusp form. Our solution is p-adic, and it relies on our definition of an algebraic regularized mock modular form. We use mock modular forms to compute generating functions for the critical values of modular L-functions. To obtain this result we derive an Eichler-Shimura theory for weakly holomorphic modular forms and mock modular forms. This includes an "Eichler-Shimura isomorphism", a "multiplicity two" Hecke theory, a correspondence between mock modular periods and classical periods, and a "Haberland-type" formula which expresses Petersson's inner product and a related antisymmetric inner product on M!k in terms of periods. 87 leaves, bound ; 29 cm.; Thesis (Ph. D.)--University of Hawaii at Manoa, 2010. Sat, 01 Jan 2011 00:00:00 GMT http://hdl.handle.net/10125/25934 2011-01-01T00:00:00Z Kent, Zachary A http://hdl.handle.net/10125/25933 Let T : R [x] → R [x] be a linear operator such that T[ xk] = gammakxk for all k = 0, 1, 2, ..., where gamma k ∈ R . The real sequence gkinfinity k=0 is called a multiplier sequence if for any p ∈ R [x], having only real zeros, T[ p] also has only real zeros. A characterization of all multiplier sequences that can be interpolated by rational functions is given. This partially solves a problem of G. Csordas and T. Craven, who asked for a characterization of all the meromorphic functions, Y(k), such that Yk infinityk=0 is a multiplier sequence. An eight-year-old conjecture of I. Krasikov is proved. Several discrete analogues of classical inequalities for polynomials with only real zeros are obtained, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-Polya class. A study of finite difference operators which preserve reality of zeros is initiated, and new results are proved. Composition theorems and inequalities for polynomials having their zeros in a sector are obtained. These are analogs of classical results by Polya, Schur, and Turan. In addition, a result of Obreschkoff is used to show that the Jensen polynomials related to the Riemann xi-function have only real zeros up to degree 1017. Sufficient conditions are established for a linear transformation to map polynomials having zeros only in a sector to polynomials of the same type, and some multivariate extensions of these results are presented. A complete characterization is given for linear operators which preserve closed ("strict") half-plane stability in the univariate Weyl algebra. These results provide new information about a general stability problem posed formally by G. Csordas and T. Craven. In his 2011 AMS Bulletin article, D. G. Wagner describes recent activity in multivariate stable polynomial theory as "exciting work---elementary but subtle, and with spectacular consequences." Wagner points out that many of the recent advancements in the theory of multivariate stable polynomials are due to the pioneering work of J. Borcea and P. Branden. These results play an important role in the investigation of linear stability preservers in this dissertation. Several different approaches to characterizing linear transformations which map polynomials having zeros only in one region of the complex plane to polynomials of the same type are explored. In addition, an open problem of S. Fisk is solved, and several partial results pertaining to open problems from the 2007 AIM workshop "Polya-Schur-Lax problems: hyperbolicity and stability preservers" are obtained. Thesis (Ph. D.)--University of Hawaii at Manoa, 2011. Sat, 01 Jan 2011 00:00:00 GMT http://hdl.handle.net/10125/25933 2011-01-01T00:00:00Z Chasse, Matthew Negus http://hdl.handle.net/10125/25932 Motivated by the work of Pólya, Schur, and Turán, a complete characterization of multiplier sequences for the Hermite polynomial basis is given. Laguerre's theorem and a remarkable curve theorem due to Pólya are generalized. Sufficient conditions for the location of zeros in certain strips in the complex plane are determined. Results pertaining to multiplier sequences and complex zero decreasing sequences for other polynomial sets are established. viii, 178 leaves, bound ; 29 cm.; Thesis (Ph. D.)--University of Hawaii at Manoa, 2007. Mon, 01 Jan 2007 00:00:00 GMT http://hdl.handle.net/10125/25932 2007-01-01T00:00:00Z Piotrowski, Andrzej http://hdl.handle.net/10125/25805 The stress-buffering model was used as a framework to explore the ways in which perceptions of social support are related to student-athletes’ stress, self-efficacy, and performance in their academic and athletic lives. Ninety-seven student-athletes were asked to complete a survey that measured these constructs with regard to a specific academic and athletic event. Results showed a significant negative relationship between stress and self-efficacy in an academic context and a significant positive relationship between self-efficacy and performance in both an academic and athletic context. Received social support was not significantly related to self-efficacy. The overall results showed moderate support for the stress-buffering model. Future research should explore the harmful and beneficial effects of stress for SAs, whether received or perceived availability of social support is helpful to SAs, and where social support rests in the stress-coping process. A thesis to be submitted to the graduate division of the University of Hawaiʻi at Mānoa in partial fulfillment of the requirements for the degree of Master of Arts in Communicology August 2012. Tue, 29 Jan 2013 00:00:00 GMT http://hdl.handle.net/10125/25805 2013-01-29T00:00:00Z van Raalte, Lisa http://hdl.handle.net/10125/25584 Beginning with Palauan perspectives and worldviews, this thesis traces the genealogy of the modern-day court system in Palau. It ends with an analysis of cases showing how the return of public lands in Palau has been largely impeded by the nature of a court system that came from a different set of interests than that of Palauans’ interests. The court system embodies ideologies in place that do not necessarily fit well with Palauan needs and interests. Many problems may be seen in the land cases analyzed in this thesis. As a result, it is argued that there is no better time than now for Palauans to reassess not only the way they choose to resolve conflicts, but also which ideology governs the way they decide to operate. Pacific Island Studies Sun, 01 Jan 2012 00:00:00 GMT http://hdl.handle.net/10125/25584 2012-01-01T00:00:00Z Matsutaro, Ebil http://hdl.handle.net/10125/24330 Sat, 01 Jan 1977 00:00:00 GMT http://hdl.handle.net/10125/24330 1977-01-01T00:00:00Z Kwok, Madeline http://hdl.handle.net/10125/24273 plan A; Pacific Islands Studies Sat, 01 Jan 2011 00:00:00 GMT http://hdl.handle.net/10125/24273 2011-01-01T00:00:00Z Wilson, Dorah http://hdl.handle.net/10125/24272 plan B; Pacific Islands Studies Sat, 01 Jan 2011 00:00:00 GMT http://hdl.handle.net/10125/24272 2011-01-01T00:00:00Z Tabe, Tammy http://hdl.handle.net/10125/24271 plan B; Pacific Islands Studies Fri, 01 Jan 2010 00:00:00 GMT http://hdl.handle.net/10125/24271 2010-01-01T00:00:00Z Nishida, Junko http://hdl.handle.net/10125/24270 plan A; Pacific Islands Studies Fri, 01 Jan 2010 00:00:00 GMT http://hdl.handle.net/10125/24270 2010-01-01T00:00:00Z Masterson, Ian http://hdl.handle.net/10125/24269 plan A; Pacific Islands Studies Fri, 01 Jan 2010 00:00:00 GMT http://hdl.handle.net/10125/24269 2010-01-01T00:00:00Z Lee, Louisa http://hdl.handle.net/10125/24268 plan A; Pacific Islands Studies Sat, 01 Jan 2011 00:00:00 GMT http://hdl.handle.net/10125/24268 2011-01-01T00:00:00Z Kaiku, Patrick http://hdl.handle.net/10125/24267 plan B; Pacific Islands Studies Fri, 01 Jan 2010 00:00:00 GMT http://hdl.handle.net/10125/24267 2010-01-01T00:00:00Z Hoppe-Cruz, Anghet; Borja-Kicho'cho', Kisha http://hdl.handle.net/10125/24266 plan A; Pacific Islands Studies Sat, 01 Jan 2011 00:00:00 GMT http://hdl.handle.net/10125/24266 2011-01-01T00:00:00Z Hirabe, Aska http://hdl.handle.net/10125/24265 plan B; Pacific Islands Studies Sun, 01 Jan 2012 00:00:00 GMT http://hdl.handle.net/10125/24265 2012-01-01T00:00:00Z Diaz, Keola K.