Ph.D. Dissertations- Mathematics Department
http://hdl.handle.net/10125/23255
Fri, 18 Apr 2014 09:51:40 GMT2014-04-18T09:51:40ZLinear and non-linear operators, and the distribution of zeros of entire functions
http://hdl.handle.net/10125/29455
An important chapter in the theory of distribution of zeros of entire functions pertains to the study of linear operators acting on entire functions. This dissertation presents new results involving not only linear, but also some non-linear operators.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10125/294552013-01-01T00:00:00ZYoshida, RintaroOn-linear coefficient-wise stability and hyperbolicity preserving transformations
http://hdl.handle.net/10125/29454
We study the operation of replacing the coefficients of a real function with a non-linear combination of its coefficients. We are particularly interested in the coefficient-wise transformations that preserve the location of zeros in a prescribed region.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/294542012-01-01T00:00:00ZGrabarek, LukaszCongruence Lattices of Finite Algebras
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 GMThttp://hdl.handle.net/10125/259382012-01-01T00:00:00ZDeMeo, William J.Sparse ordinary graphs
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 GMThttp://hdl.handle.net/10125/259372005-01-01T00:00:00ZKalk, Jonathan W.Small lattices
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 GMThttp://hdl.handle.net/10125/259362000-01-01T00:00:00ZHeeney, Xiang Xia HuangPotential Good Reduction of Degree 2 Rational Maps
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 GMThttp://hdl.handle.net/10125/259352012-01-01T00:00:00ZYap, DianeP-adic analysis and mock modular forms
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 GMThttp://hdl.handle.net/10125/259342011-01-01T00:00:00ZKent, Zachary ALinear preservers and entire functions with restricted zero loci
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 GMThttp://hdl.handle.net/10125/259332011-01-01T00:00:00ZChasse, Matthew NegusLinear Operators and the Distribution of Zeros of Entire Functions
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 GMThttp://hdl.handle.net/10125/259322007-01-01T00:00:00ZPiotrowski, AndrzejGeneralized Gelfand triples
http://hdl.handle.net/10125/11728
Typescript.; Thesis (Ph. D.)--University of Hawaii, 1971.; Bibliography: leaves 73-74.; vi, 74 l
Fri, 01 Jan 1971 00:00:00 GMThttp://hdl.handle.net/10125/117281971-01-01T00:00:00ZCasteren, J. A. vanDual linear spaces generated by a non-Desarguesian configuration
http://hdl.handle.net/10125/11727
Mode of access: World Wide Web.; Thesis (Ph. D.)--University of Hawaii at Manoa, 2005.; Includes bibliographical references (leaves 160-161).; Electronic reproduction.; Also available by subscription via World Wide Web; viii, 161 leaves, bound ill. 29 cm
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10125/117272005-01-01T00:00:00ZSeffrood, Jiajia Yang GarciaGeometry and singularities of spatial and spherical curves
http://hdl.handle.net/10125/11726
Mode of access: World Wide Web.; Thesis (Ph. D.)--University of Hawaii at Manoa, 2004.; Includes bibliographical references (leaves 113-114).; Electronic reproduction.; Also available by subscription via World Wide Web; vii, 114 leaves, bound ill. 29 cm
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10125/117262004-01-01T00:00:00ZXiong, JianfeiFinite group graded lie algebraic extensions and trefoil symmetric relativity, standard model, yang mills and gravity theories
http://hdl.handle.net/10125/11725
Mode of access: World Wide Web.; Thesis (Ph. D.)--University of Hawaii at Manoa, 2004.; Includes bibliographical references (leaves 159-164).; Electronic reproduction.; Also available by subscription via World Wide Web; x, 164 leaves, bound ill. 29 cm
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10125/117252008-01-01T00:00:00ZWills, Luis AlbertoAutomated reasoning and machine learning
http://hdl.handle.net/10125/9963
Thesis (Ph. D.)--University of Hawaii at Manoa, 1996.; Includes bibliographical references (leaves 140-144).; Microfiche.; x, 144 leaves, bound ill. 29 cm
Mon, 01 Jan 1996 00:00:00 GMThttp://hdl.handle.net/10125/99631996-01-01T00:00:00ZHuang, GuoxiangCombinatorial remedies
http://hdl.handle.net/10125/9962
Thesis (Ph. D.)--University of Hawaii at Manoa, 1994.; Includes bibliographical references (leaves 29-30); Microfiche.; 30 leaves, bound ill. 29 cm
Sat, 01 Jan 1994 00:00:00 GMThttp://hdl.handle.net/10125/99621994-01-01T00:00:00ZMackey, John FletcherProblems in hyperbolic geometry
http://hdl.handle.net/10125/9961
Thesis (Ph. D.)--University of Hawaii at Manoa, 1993.; Includes bibliographical references (leaf 124); Microfiche.; vii, 124 leaves, bound ill. 29 cm
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/10125/99611993-01-01T00:00:00ZReiser, Edward JAlmost completely decomposable groups with two critical types and their endomorphism rings
http://hdl.handle.net/10125/9960
Thesis (Ph. D.)--University of Hawaii at Manoa, 1992.; Includes bibliographical references (leaves 48-49); Microfiche.; iv, 49 leaves, bound 29 cm
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/10125/99601992-01-01T00:00:00ZLewis, WayneA covering space approach to (d,k) constrained codes
http://hdl.handle.net/10125/9959
Thesis (Ph. D.)--University of Hawaii at Manoa, 1992.; Includes bibliographical references (leaves 102-104); Microfiche.; ix, 104 leaves, bound ill. 29 cm
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/10125/99591992-01-01T00:00:00ZPerry, Patrick NeilMaximum principles and Liouville theorems for elliptic partial differential equations
http://hdl.handle.net/10125/9958
Typescript.; Thesis (Ph. D.)--University of Hawaii at Manoa, 1990.; Includes bibliographical references.; Microfiche.; vi, 96 leaves, bound ill. 29 cm
Mon, 01 Jan 1990 00:00:00 GMThttp://hdl.handle.net/10125/99581990-01-01T00:00:00ZZhou, ChipingNew classes of finite commutative rings
http://hdl.handle.net/10125/3076
This dissertation introduces the concept of Q-Witt rings and SQ-Witt rings. A Q-Witt ring is defined as a finite quotient of a torsion free abstract Witt ring for an elementary 2-group G. Local Q-Witt rings are characterized using topological and ring theoretic tools. Q-Witt rings of the integral group ring Z[Z2] are classified and several properties are shown. An SQ-Witt ring is formed as a finite quotient of torsion free Witt rings of a formally real field. Recursive construction can be used to locate all SQ-Witt rings.
Thesis (Ph. D.)--University of Hawaii at Manoa, 2003.; Includes bibliographical references (leaves 51-52).; Mode of access: World Wide Web.; Also available by subscription via World Wide Web; vi, 52 leaves, bound 29 cm
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10125/30762003-01-01T00:00:00ZVo, Monika