Mathematics Department
http://hdl.handle.net/10125/23249
Mon, 06 Jul 2015 15:51:53 GMT2015-07-06T15:51:53ZGeneralized Analytic Continuation
http://hdl.handle.net/10125/29513
Analytic continuation is the extension of the domain of a given analytic function in the complex plane, to a larger domain of the complex plane. This process has been utilized in many other areas of mathematics, and has given mathematicians new insight into some of the world’s hardest problems. This paper will cover more general forms of analytic continuation, which will be referred to as generalized analytic continuations. The paper will closely follow William Ross’ and Harold Shapiro’s book “Generalized Analytic Continuation” [14], with the proofs worked out with more detail, and a few generalizations are made regarding the Poincare example in Section 3.3.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/295132012-01-01T00:00:00ZToyofuku, JustinInformation Processing and Energy Dissipation in Neurons
http://hdl.handle.net/10125/29510
We investigate the relationship between thermodynamic and information theoretic inefficiencies in an individual neuron model, the adaptive exponential integrate-and-fire neuron. Recent work has revealed that minimization of energy dissipation is tightly related to optimal information processing, in the sense that a system has to compute a maximally predictive model. In this thesis we justify the extension of these results to the neuron and quantify the neuron’s thermodynamic and information processing inefficiencies.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/295102012-01-01T00:00:00ZMcIntosh, LaneAn Iterated Version of the Generalized Singular Value Decomposition for the Joint Analysis of Two High-Dimensional Data Sets
http://hdl.handle.net/10125/29508
In this work, we developed a new computational algorithm for the integrated analysis of high-dimensional data sets based on the Generalized Singular Value Decomposition(GSVD). We developed an iterative version of the Generalized Singular Value Decomposition (IGSVD) that jointly analyzes two data matrices to identify signals that correlate the rows of two matrices. The IGSVD has been validated on simulated and real genomic data sets and results on simulated show that the algorithm is able to sequentially detect multiple simulated signals that were embedded in high levels of background noise. Results on real DNA microarray data from normal and tumor tissue samples indicate that the IGSVD detects signals that are biologically relevant to the initiation and progression of liver cancer.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10125/295082013-01-01T00:00:00ZZeinalzadeh, AshkanNondeterministic Finite State Complexity
http://hdl.handle.net/10125/29507
We define a new measure of complexity for finite strings using nondeterministic finite automata, called nondeterministic automatic complexity and denoted AN(x). In this paper we prove some basic results for AN(x), give upper and lower bounds, estimate it for some specific strings, begin to classify types of strings with small complexities, and provide AN(x) for |x| ≤ 8.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10125/295072013-01-01T00:00:00ZHyde, KayleighValidating a Food Frequency Questionnaire for Guam
http://hdl.handle.net/10125/29506
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/295062012-01-01T00:00:00ZChong, Marie Q.Geometric Path Planning for a Lego AUV
http://hdl.handle.net/10125/29504
For the last thirty years or so, differential geometry and control theory have merged and grown together to produce extraordinary results. When applied to mechanical systems, one sees a system waiting to be exploited for its inherent geometric properties. In this paper, we present the equations of motion for a submerged rigid body from a geometric point of view and use tools from differential geometry to provide solutions to the motion planning problem for an autonomous underwater vehicle. Specifically, the geometry allows us to deduce permissible motions for a vehicle that is underactuated purely from the available degrees of freedom. The geometric equations of motion are then used to path plan for a cost-effective Lego vehicle through simulations and actual implementation as providing a proof of concept.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/295042012-01-01T00:00:00ZAndonian, MichaelLinear 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, LukaszEquations implying congruence n-permutability and semidistributivity
http://hdl.handle.net/10125/25949
T. Dent, K. Kearnes and A. Szendrei de ne the derivative, 0, of a
set of equations and show, for idempotent , that implies congruence modularity
if 0 is inconsistent ( 0 j= x y). In this paper we investigate other types of
derivatives that give similar results for congruence n-permutable for some n, and for
congruence semidistributivity.
Fri, 08 Feb 2013 00:00:00 GMThttp://hdl.handle.net/10125/259492013-02-08T00:00:00ZFreese, RalphCongruence 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 A.Linear 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, AndrzejThe snowflake decoding algorithm
http://hdl.handle.net/10125/25931
This paper describes an automated algorithm for generating a group code using any unitary group, initial vector, and generating set that satisfy a necessary condition. Examples with exceptional complex reflection groups, as well as an analysis of the decoding complexity, are also included.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2012
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/259312012-01-01T00:00:00ZWalker, CatherineExtending lp--decoding for permutation codes from euclidean to Kendall tau metric
http://hdl.handle.net/10125/25930
Invented in the 1960’s, permutation codes have reemerged in recent years as a topic of great interest because of properties making them attractive for certain modern technological applications. In 2011 a decoding method called LP (linear programming) decoding was introduced for a class of permutation codes with a Euclidean distance induced metric. In this paper we comparatively analyze the Euclidean and Kendall tau metrics, ultimately providing conditions and examples for which LP-decoding methods can be extended to permutation codes with the Kendall tau metric. This is significant since contemporary research in permutation codes and their promising applications has incorporated the Kendall tau metric.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2012
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/259302012-01-01T00:00:00ZKong, JustinOn Kaneko congruences
http://hdl.handle.net/10125/25929
We present a proof of certain congruences modulo powers of an odd prime for the coefficients of a series produced by repeated application of U -operator to a certain weakly holomorphic modular form. This kind of congruences were first observed by Kaneko as a result of numerical experiments, and later proved in a different (but similar) case by Guerzhoy [6]. It is interesting to note that, in our case, the congruences become different, both experimentally and theoretically, depending on whether the prime is congruent to 1 or 3 modulo 4.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2012
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/259292012-01-01T00:00:00ZChi, MingjingMultimetric continuous model theory
http://hdl.handle.net/10125/25928
In this paper, we study metric structures with a finite number of metrics by extending the model theory developed by Ben Yaacov et al. in themonograph Model theory for metric structures. We first define a metric structure with finitely many metrics, develop the theory of ultraproducts of multimetric structures, and prove some classical model-theoretic theorems about saturation for structures with multiple metrics. Next, we give a characterization of axiomatizability of certain classes of multimetric structures. Finally, we discuss potential avenues of research regarding structures with multiple metrics.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2012
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10125/259282012-01-01T00:00:00ZCaulfield, ErinRiemann, Hurwitz, and branched covering spaces: an exposition in mathematics
http://hdl.handle.net/10125/25927
We will consider spaces with nice connectedness properties, and the groups that act on them in such a way that the topology is preserved; we consider looking at the symmetry groups of a surface of genus g. Restricting our view to nite groups, we will develop the concept of covering spaces and illustrate its usefulness to the study of these group actions by generalizing this development to the theory of branched coverings. This theory lets us develop the famous Riemann-Hurwitz Relation, which will in turn allow us to develop Hurwitz's Inequality, an upper bound on the order of a symmetry group of a given surface. We then follow Kulkarni and use the Riemann-Hurwitz Relation to construct a congruence relating the genus g of a surface to the cyclic deciencies of the symmetry groups that can act on it. These developments will then be applied to study a special case of branched coverings, those in which there is only one branch point, yielding a lower bound on the genus of both surfaces involved.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10125/259272011-01-01T00:00:00ZTurner, Wm. Pitt V.A brief survey of the discrete logarithm problem
http://hdl.handle.net/10125/25926
The Discrete Logarithm Problem (DLP) has been the subject of interest among many mathematicians and cryptographers in recent times because of its computational di¢ culty. For the former, the enormity of the mathematics involved and the intellectual challenge that it entails are certainly motivating factors; for the latter, its usefulness in the ...eld of cryptography. Cryptosystems rest their security on some assumptions that certain mathematical problems are dificult to solve. The ElGamal cryptosystem, for instance, is considered secure because of the computational assumption that it is di¢ cult to solve the Discrete Logarithm Problem. The di¢ culty of the DLP lies in the fact that it has a “one-way” property. Its computational complexity is roughly measured by the computing time of the algorithm used to solve this mathematical problem. This paper is a brief survey of some of the best known algorithms for solving the DLP, examines their computing time, and considers the DLP over two particular ...nite groups.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10125/259262011-01-01T00:00:00ZSia, Gretel S.A-T-menability of groups
http://hdl.handle.net/10125/25925
This paper presents a detailed study of a-T-menable discrete groups. Starting with several conditions required for a-T-menability, we prove that they are equivalent and hence charaterize a class of a-T-menable discrete groups. We then show that the free groups on two generators is a-T-menable. Using the infnite cyclic group, we succesfully draw a rigid connection –from the perspective of affine isometric actions –between amenable groups and a-T-menable groups. We also prove that the quotient of an a-T-menable group by a finite normal subgroup is a-T-menable. We conclude with a new proof that the free product of two a-T-menable groups is a-T-menable.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10125/259252011-01-01T00:00:00ZLu, Ni YenZeros of the modular parametrization of rational elliptic curves
http://hdl.handle.net/10125/25924
Some Rational elliptic curves whose modular parametrization is given by an Eichler integral were considered. The points, other than cusps, that map to zero under modular parametrization were studied computationally. Surprisingly, these zeros appear to be CM-points.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10125/259242011-01-01T00:00:00ZKodgis, LisaComplex reflection group coding
http://hdl.handle.net/10125/25923
This paper considers complex reflection groups for which the generalization of subgroup decoding method does not work at all are considered in this paper. A new method of decoding is introduced to effectively encode and decode the exceptional complex reflection groups. A general decoding algorithm is devised and the results of analysis are presented. Discussion of future research is presented as well.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10125/259232011-01-01T00:00:00ZKim, Hye JungA generalization of Euler's constant
http://hdl.handle.net/10125/25922
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10125/259222011-01-01T00:00:00ZHedley, MarkCore and no-treat equilibrium in tournament games with externalities
http://hdl.handle.net/10125/25921
We consider a situation where coalitions are formed to divide a resource. As in real life, the value of a payoff to a given agent is allowed to depend on the payoff to other agents with whom he shares a common interest. There are various notions of equilibrium for this type of game, including the core and no-treat equilibrium. These stabilities may exist or not, depending on the power structure and the rule for allocating the resource. It is shown that under certain conditions, the no-treat equilibrium can exist even though the core is empty.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2010
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10125/259212010-01-01T00:00:00ZMizuno, RyoPolynomial-clone reducibility
http://hdl.handle.net/10125/25920
Polynomial-clone reducibilities are generalizations of the truth-table reducibilities. A polynomial clone is a set of functions over a finite set X that is closed under composition and contains all the constant and projection functions. For a fixed polynomial clone C, a sequence B ∈ X ω is C-reducible to A ∈ X ω if there is an algorithm that computes B from A using only effectively selected functions from C. We show that if A is a Kurtz random sequence and C1 C2 are distinct polynomial clones, then there is a sequence B that is C1 -reducible to A but not C2 -reducible to A. This implies a generalization of a result first proved by Lachlan for the case |X| = 2. We also show that the same result holds if Kurtz random is replaced by Kolmogorov-Loveland stochastic.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2010
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10125/259202010-01-01T00:00:00ZCulver, QuinnAlmost global feedack control of autonomous underwater vehicles
http://hdl.handle.net/10125/25919
An Autonomous Underwater Vehicle (AUV) is expected to operate in an aquatic environment and compensate for poorly known disturbance forces and moments. Due to uncertain environment, it is difficult to apply an open-loop control scheme for tracking the desired trajectory. The objective of this thesis is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2009
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10125/259192009-01-01T00:00:00ZSingh, Shashi BhushanOmega function: a theoretical introduction
http://hdl.handle.net/10125/25918
This paper investigates the theory behind a new universal performance measure (the so called Omega function), which was frst introduced by Con Keating and William F. Shadwick in 2002 (see [1]). In the frst section, we review some rudimentary probability. We then defne the Omega function, introduce some of its properties, and prove these properties without continuity assumptions. We also defne the standard dispersion, a new statistic derived from the Omega function. We prove one new theorem about the range of the standard dispersion for a fnite sample. The structure of the second section on the Omega function follows closely that of a recent talk given by Ana Cascon and William Shadwick in [4]. In the last section, we demonstrate these properties with real-life data.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2009
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10125/259182009-01-01T00:00:00ZNguyen, Vu NgocSatellite orbital control
http://hdl.handle.net/10125/25917
In this project we will be looking at the change in control required to transfer a satellite between two elliptic Keplerian orbits. We will first derive the equations of motion for our satellite and then study the controllability properties of our system. We will introduce a simple feedback controller and prove local asymptotic stability of the target orbit. The goal of this paper is to prove stability using both geometric control theory as well as stabilization methods and thus link prior work done on orbital control in both fields.Our primary tool to accomplish this will be LaSalle’s invariance principle.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2009
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10125/259172009-01-01T00:00:00ZEvans, Regina M.Time optimal control of a right invariant system on a compact Lie group
http://hdl.handle.net/10125/25916
In this paper we will study the pulse sequences in NMR spectroscopy and quantum computing as a time control problem. Radio frequency pulses are used to execute a unitary transfer of state. Sequences of pulses should be as short as possible to minimize decoherence. We model the problem as a controllable right invariant system on a compact Lie group. We investigate the minimum time required to steer the system from an initial point to a specified final point.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2008
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10125/259162008-01-01T00:00:00ZStorm, Jody LynnLinear differential operators and the distribution of zeros of polynomials
http://hdl.handle.net/10125/25915
The purpose of this paper is fourfold: (1) to survey some classical and recent results in the theory of distribution of zeros of entire functions, (2) to demonstrate a novel proof answering a question of Raitchinov, (3) to present some new results in the theory of complex zero decreasing operators, and (4) to initiate the study of the location of zeros of complex polynomials under the action of certain linear operators. In addition, several open problems are given.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2008
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10125/259152008-01-01T00:00:00ZSo, EugeneStabilization of a cart and double pendulum system
http://hdl.handle.net/10125/25914
This Master’s Plan B report for the University of Hawai‘i at M ̄noa is the result of Daniel Langdon’s examination of methods of modeling and stabilizing a cart and double-pendulum system against small disturbances. The Euler-Lagrange Equations, a fundamental result of the calculus of variations, combined with the Principle of Least Action and the Lagrange D’Alembert Principle are used to describe the equations of motion for a cart and double-pendulum system in terms of the kinetic and potential energy of the system, which is in turn described in terms of the positions and velocities of the cart and two pendulum bobs. Theorems from differential equations are combined with a linear approximation of the equations of motion and the notion of feedback to compute an algorithm for stabilization, whose action of stabilization against a sample small disturbance is demonstrated.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2007
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10125/259142007-01-01T00:00:00ZLangdon, Daniel AllenSolving the Dirichlet problem via Brownian motion
http://hdl.handle.net/10125/25913
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2007
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10125/259132007-01-01T00:00:00ZKrot, TatianaSymmetry group solutions to differential equations
http://hdl.handle.net/10125/25912
In this project we will be looking at Sophus Lie’s desire (his so called idee fixe) to apply Contact Transformations (what would eventually develop into the modern idea of a Lie Algebra) in order to arrive at symmetries of differential equations, and thus certain solutions. Our goal—as well as Lie’s—is to develop a more universal method for solving differential equations than the familiar cook-book methods we learn in an introductory ordinary or partial differential equations class. We answer three questions. What was the historical underpinning of Sophus Lie’s theory? How do we find the symmetry Lie algebras? How do we use the symmetry Lie algebras to find solutions to the differential equation? (In order to answer these questions we will need to fill in some background material and our answers will also result in a novel derivation of the “Fundamental Source Solution.”) Our second objective will be to establish a connection between solvability in Galois Theory and in Differential Equations. We will assume a familiarity with certain concepts from Abstract Algebra.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2007
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10125/259122007-01-01T00:00:00ZBurkman, Jacob HarryNormality of stock prices
http://hdl.handle.net/10125/25911
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2006
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10125/259112006-01-01T00:00:00ZShi, BoThe Laguerre inequality and the distribution of zeros of entire functions
http://hdl.handle.net/10125/25910
The purpose of this paper is fourfold: (1) to survey some classical and recent results in the theory of distribution of zeros of entire functions, (2) to generalize the Laguerre inequality, (3) to establish several special cases of the Hawai‘i Conjecture, and (4) to present some new results dealing with the polar derivatives of polynomials. In addition, applications of the extended Laguerre inequalities are given. The paper concludes with several open problems.
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2003
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10125/259102003-01-01T00:00:00ZMuranaka, BrandonSymmetric algebras over rings and fields
http://hdl.handle.net/10125/25489
Connections between annihilators and ideals in Frobenius and symmet-
ric algebras are used to provide a new proof of a result of Nakayama on quotient
algebras and an application is given to central symmetric algebras.
Thu, 03 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10125/254892013-01-03T00:00:00ZCraven, Thomas; Smith, TaraThe “Lillie Transition”: Models of the Onset of Saltatory Conduction in Myelinating Axons
http://hdl.handle.net/10125/24451
Almost 90 years ago, Lillie reported that rapid saltatory conduction arose in an iron wire model of nerve impulse propagation when he covered the wire with insulating sections of glass tubing equivalent to myelinated internodes. This led to his suggestion of a similar mechanism explaining rapid conduction in myelinated nerve. In both their evolution and their development, myelinating axons must make a similar transition between continuous and saltatory conduction. Achieving a smooth transition is a potential challenge that we examined in computer models simulating a segmented insulating sheath surrounding an axon having Hodgkin-Huxley squid parameters. With a wide gap under the sheath, conduction was continuous. As the gap was reduced, conduction initially slowed, owing to the increased extra-axonal resistance, then increased (the “rise”) up to several times that of the unmyelinated fiber, as saltatory conduction set in. The conduction velocity slowdown was little affected by the number of myelin layers or modest changes in the size of the “node,” but strongly affected by the size of the “internode” and axon diameter. The steepness of the rise of rapid conduction was greatly affected by the number of myelin layers, and axon diameter, variably affected by internode length and little affected by node length. The transition to saltatory conduction occurred at surprisingly wide gaps and the improvement in conduction speed persisted to surprisingly small gaps. The study demonstrates that the specialized paranodal seals between myelin and axon, and indeed even the clustering of sodium channels at the nodes, are not necessary for saltatory conduction.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10125/244512013-01-01T00:00:00ZCastelfranco, Ann M.; Young, Robert G.; Hartline, Daniel K.How much randomness is needed for statistics?
http://hdl.handle.net/10125/24285
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure λ, a choice needs to be made. One approach is to allow randomness tests to access the measure λ as an oracle
(which we call the \classical approach"). The other approach is the opposite one, where the randomness tests are completely effective and do not have access to the information contained in λ (we call this approach \Hippocratic"). While the Hippocratic approach is in general much more restrictive, there are cases
where the two coincide. The first author showed in 2010 that in the particular case where the notion of randomness considered is Martin-Löf randomness and the measure λ is a Bernoulli measure, classical randomness and Hippocratic randomness coincide. In this paper, we prove that this result no longer holds for
other notions of randomness, namely computable randomness and stochasticity.
Mon, 05 Nov 2012 00:00:00 GMThttp://hdl.handle.net/10125/242852012-11-05T00:00:00ZKjos-Hanssen, BjoernRiemann, Hurwitz, and Branched Covering Spaces: An Exposition in Mathematics
http://hdl.handle.net/10125/23260
We will consider spaces with nice connectedness properties, and the groups that act on them in such a way that the topology is preserved; we consider looking at the symmetry groups of a surface of genus g. Restricting our view to nite groups, we will develop the concept of covering spaces and illustrate its usefulness to the study of these group actions by generalizing this development to the theory of branched coverings. This theory lets us develop the famous Riemann-Hurwitz Relation, which will in turn allow us to develop Hurwitz's Inequality, an upper bound on the order of a symmetry group of a given surface. We then follow Kulkarni and use the Riemann-Hurwitz Relation to construct a congruence relating the genus g of a surface to the cyclic de ciencies of the symmetry groups that can act on it. These developments will then be applied to study a special case of branched coverings, those in which there is only one branch point, yielding a lower bound on the genus of both surfaces involved.
Mon, 23 Jul 2012 00:00:00 GMThttp://hdl.handle.net/10125/232602012-07-23T00:00:00ZTurner, Wm. Pitt V.Differential Equations
http://hdl.handle.net/10125/21735
Mon, 01 Jan 1962 00:00:00 GMThttp://hdl.handle.net/10125/217351962-01-01T00:00:00ZBear, H.S. Jr.Generalized 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
A dual linear space is a partial projective plane which contains the intersection of every pair of its lines. Every dual linear space can be extended to a projective plane, usually infinite, by a sequence of one line extensions. Moreover, one may describe necessary conditions for the sequence of one line extensions to terminate after finitely many steps with a finite projective plane. A computer program that attempts to construct a finite projective plane from a given dual linear space by a sequence of one line extension has been written by Dr. Nation. In particular, one would like to extend a dual linear space containing a non-Desarguesian configuration to a finite projective plane of nonprime- power order. This dissertation studies the initial dual linear spaces to be used in this algorithm. The main result is that there are 105 non-isomorphic initial dual linear spaces containing the basic non-Desarguesian configuration.
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
In the first part of this dissertation the spherical evolute, the spherical involute, the spherical orthotomic and the spherical antiorthotomic are investigated and their local diffeomorphic types are determined. The concept of the spherical conic is introduced. It is proven that the incident angle and reflection angle are equal for the spherical conic. The necessary and sufficient conditions for the spherical conic to be a circle are given. In the second part of this dissertation the ruled surfaces of normals and binormals of a regular space curve are locally classified under the left-right action according to the types of the curve. For this purpose some results are obtained on the relationship of the powers of terms in the Taylor series of an invertible function and its inverse.
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
We introduce the Quotient Group Graded Lie algebras, which involve graded structure constants. This structure is then used to obtain a graded extension of supersymmetry where diverse features of the Standard Model of elementary particles arise naturally. For the Minimal Vector Clover Extension of the symmetries of special relativity, we develop the extended superspace formalism in differential geometric language. We construct connections, curvature, and prove Bianchi identities both in coordinate and in symmetry covariant bases. We study also a connection making the Lorentz symmetry point dependent, its torsion and curvature. Moreover, we examine a transformation that removes noncommutativity from the Minimal Vector Clover Extension.
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
This dissertation introduces new theorem-proving strategies and uses these strategies to solve a wide variety of difficult problems requiring logical reasoning. It also shows how to use theorem-proving to solve the problem of learning mathematical concepts. Our first algorithm constructs formulas called Craig interpolants from the refutation proofs generated by contemporary theorem-provers using binary resolution, paramodulation, and factoring. This algorithm can construct the formulas needed to learn concepts expressible in the full first-order logic from examples of the concept. It can also find sentences which distinguish pairs of nonisomorphic finite structures. We then apply case analysis to solve hard problems such as the zebra problem, the pigeonhole problem, and the stable marriage problem. The case analysis technique we use is the first to be fully compatible with resolution and rewriting and powerful enough to solve these problems. Our primary new theorem-proving strategies generate subgoals and efficient sets of rules. We show how to divide problems into smaller parts with intermediate goals by reversing logical implications. We solve these subdivided parts by discovering efficient subsets of rules or by generating efficient new rules. We apply these and other new search strategies to solve difficult problems such as the 15-puzzle, central solitaire, TopSpin, Rubik's cube, and masterball. Our strategies apply universally to all such problems and can solve them quite efficiently: the 15-puzzle, Rubik's cube and masterball can all be done in 300 seconds. Finally we apply our search strategies to solve real-world problems such as sorting, solving equations and inverting nonsingular matrices.
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
This dissertation consists of 3 chapters which consider distinct combinatorial problems. In the first chapter we consider objects known as groupies. A non-isolated vertex of a graph G is called a groupie if the average degree of the vertices connected to it is larger than or equal to the average degree of the vertices in G. An isolated vertex is a groupie only if all vertices of G are isolated. It is well known that every graph must contain at least one groupie. The graph Kn - e contains precisely 2 groupie vertices for n ≥2. In this chapter we derive a lower bound for the number of groupies in terms of the number of vertices of each particular degree. This shows, in particular, that any graph with 2 or more vertices must contain at least 2 groupies. In chapter 2 we show that, for a prime number p+n+1 , the number of pth powers in Sn+1 is n+1 times the number of pth powers in Sn. Here Sn denotes the symmetric group on n objects. Our technique also yields a recursion for calculating the number of r": powers in Sn+1. An analogous identity, and corresponding recursion, for pth powers containing a specified number of pi-cycles is also obtained. This generalizes work of Blum in the case p = 2, and Chernoff's work for general p. Finally, in chapter 3, we use techniques introduced by Giraud to obtain lower bounds for certain Ramsey Numbers. The Ramsey Number R(k,j) is defined to be the least positive integer n such that every n-vertex graph contains either a clique of order k or an independent set of order j. In particular we show that R (6, 6) ≤ 165, R (7, 7) ≤ 540, R (8, 8) ≤ 1870, R (9, 9) ≤ 6625, and R (10, 10) ≤ 23854 . These estimates replace bounds of 166, 574, 1982, 7042, and 25082, respectively.
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
In this thesis, we discuss the proof that all convex polyhedral metrics can be realized in euclidean and hyperbolic 3-space. This result is accredited to A.D. Alexandrov and is fundamental in modern synthetic differential geometry. Nevertheless, gaps appear in currently acknowledged proofs: (1) It is necessary to prove that strictly convex metrics with 4 real vertices can be realized. (2) It must be shown that, within manifolds of convex polyhedra in E3 or H3, there exist submanifolds of degenerate polyhedra which are "thin" when mapped into manifolds of (abstract) strictly convex metrics. In this thesis we prove these statements. The remainder of the thesis is devoted to general hyperbolic geometry with emphasis on the synthetic point of view. We first construct horocyclic coordinates and use these to derive the Poincare model for the hyperbolic plane. Then we compute useful formulas for the curvature of a surface, and use these formulas to study C2 surfaces in H3, infinitesimal deformations of the horosphere, and curves of constant curvature in H2. Finally, we also prove that certain surfaces of rotation in E3 isometrically imbed in H3. These results, some of which are new, provide a background for synthetic methods underlying the theorem of Alexandrov.
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 J.Almost completely decomposable groups with two critical types and their endomorphism rings
http://hdl.handle.net/10125/9960
An almost completely decomposable group with two critical types is a direct sum of rank-one groups and indecomposable rank-two groups. A complete set of near isomorphism invariants for an acd group with two critical types is the isomorphism class of the regulator and the isomorphism class of the regulator quotient; with one additional invariant, namely an element of a certain quotient group of (Ζ/m Ζ)^x , a complete set of isomorphism invariants for an acd group with two critical types is obtained. Finally, the endomorphism ring of an acd group with two critical types is computed and the resulting structure is used to give an example of two nearly isomorphic groups with non-isomorphic endomorphism rings.
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
The capacity of the (d, k) constrained codes and of the (d, k) L level charge constrained codes is considered. The case of rational capacity is examined. and an error in the literature is corrected. This leads to an interesting (0.3)L = 4 level charge constrained code. The error control for this code is done using the finite field GF(3). A table of the ternary convolutional codes of greatest free distance is given for possible applications. The topological properties of the (d, k) constraint graphs are examined. The fundamental group of a constraint graph and covering spaces of a constraint graph are discussed. A constructive process for building a covering space of a constraint graph is given. The construction of (d, k) constrained block codes from covering spaces of the (d, k) constraint graph is examined. Several types of block codes are introduced. The base point codes consist of the (d, k) constrained sequences whose associated edge paths in the covering space are loops at a specified vertex. The parity point codes consist of the (d, k) constrained sequences whose associated edge paths in the covering space conned two specified vertices. It is shown that an [n, k] cyclic code can be constructed as a base point code for a 2^(n-k) fold covering of the (0,∞) constraint graph. Systematic (d, k) constrained block codes are constructed for detecting all single shift errors, drop in errors, and drop out errors. The average probability of an undetected error for the systematic (d, k) constrained block codes is shown to decrease exponentially with the parity length times the capacity of a (d, k) constrained code.
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