M.A. Plan B Theses- Mathematics Department

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Almost global feedack control of autonomous underwater vehicles

Singh, Shashi Bhushan (University of Hawaii at Manoa, 2009)

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 ...
A-T-menability of groups

Lu, Ni Yen (University of Hawaii at Manoa, 2011)

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 ...
A brief survey of the discrete logarithm problem

Sia, Gretel S. (University of Hawaii at Manoa, 2011)

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 ...
Complex reflection group coding

Kim, Hye Jung (University of Hawaii at Manoa, 2011)

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 ...
Core and no-treat equilibrium in tournament games with externalities

Mizuno, Ryo (University of Hawaii at Manoa, 2010)

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. ...
Extending lp--decoding for permutation codes from euclidean to Kendall tau metric

Kong, Justin (University of Hawaii at Manoa, 2012)

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 ...
A generalization of Euler's constant

Hedley, Mark (University of Hawaii at Manoa, 2011)
Generalized Analytic Continuation

Toyofuku, Justin (University of Hawaii at Manoa, 2012)

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 ...
Geometric Path Planning for a Lego AUV

Andonian, Michael (University of Hawaii at Manoa, 2012)

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 ...
Information Processing and Energy Dissipation in Neurons

McIntosh, Lane (University of Hawaii at Manoa, 2012)

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 ...
An Iterated Version of the Generalized Singular Value Decomposition for the Joint Analysis of Two High-Dimensional Data Sets

Zeinalzadeh, Ashkan (University of Hawaii at Manoa, 2013)

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 ...
The Laguerre inequality and the distribution of zeros of entire functions

Muranaka, Brandon (University of Hawaii at Manoa, 2003)

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 ...
Linear differential operators and the distribution of zeros of polynomials

So, Eugene (University of Hawaii at Manoa, 2008)

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) ...
Multimetric continuous model theory

Caulfield, Erin (University of Hawaii at Manoa, 2012)

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 ...
Nondeterministic Finite State Complexity

Hyde, Kayleigh (University of Hawaii at Manoa, 2013)

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 ...
Normality of stock prices

Shi, Bo (University of Hawaii at Manoa, 2006)
Omega function: a theoretical introduction

Nguyen, Vu Ngoc (University of Hawaii at Manoa, 2009)

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 ...
On Kaneko congruences

Chi, Mingjing (University of Hawaii at Manoa, 2012)

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 ...
Polynomial-clone reducibility

Culver, Quinn (University of Hawaii at Manoa, 2010)

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 ...
Riemann, Hurwitz, and branched covering spaces: an exposition in mathematics

Turner, Wm. Pitt V (University of Hawaii at Manoa, 2011)

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 ...