Applied Mathematics Commons^™

Goppa Codes And Their Use In The Mceliece Cryptosystems, Ashley Valentijn

Renée Crown University Honors Thesis Projects - All

We explore the topic of Goppa codes and how they are used in the McEliece Cryptosystem. We first cover basic terminology that is needed to understand the rest of the paper. Then we explore the definition and limitations of a Goppa code along with how such codes can be used in a general cryptosystem. Then we go in depth on the McEliece Cryptosystem in particular and explain how the security of this method works.

The Minimal Zn-Symmetric Graphs That Are Not Zn-Spherical, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a graph G equipped with faithful and fixed-point-free Γ-action (Γ a finite group) we define an orbit minor H of G to be a minor of G for which the deletion and contraction sets are closed under the Γ-action. The orbit minor H inherits a Γ-symmetry from G, and when the contraction set is acyclic the action inherited by H remains faithful and fixed-point free. When G embeds in the sphere and the Γ-action on G extends to a Γ-action on the entire sphere, we say that G is Γ-spherical. In this paper we determine for every odd value …

On Mikhailov's Reduction Group, Tihomir Valchev

Articles

We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal $S$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.

The Effect Of Noise On The Response Of A Vertical Cantilever Beam Energy Harvester, Michael I. Friswell, Onur Bilgen, S. Faruque Ali, Grzegorz Litak, Sondipon Adhikari

Mechanical & Aerospace Engineering Faculty Publications

An energy harvesting concept has been proposed comprising a piezoelectric patch on a vertical cantilever beam with a tip mass. The cantilever beam is excited in the transverse direction at its base. This device is highly nonlinear with two potential wells for large tip masses, when the beam is buckled. For the pre-buckled case considered here, the stiffness is low and hence the displacement response is large, leading to multiple solutions to harmonic excitation that are exploited in the harvesting device. To maximise the energy harvested in systems with multiple solutions the higher amplitude response should be preferred. This paper …

On The 3-Dimensional Fluid-Structure Interaction Of Flexible Fibers In A Flow, Ryan Howard Allaire

Theses, Dissertations and Culminating Projects

We discuss the equilibrium configurations of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s. Experimental results are presented with both two-dimensional and three-dimensional numerical simulations used to model this problem. We present the effects of flow speed and initial configuration angle between the fiber and the direction of the flow. Investigations reveal that both the orientation of the fiber and the fiber length have a significant impact on the deformation of the fiber as well as on the forces it experiences. Specifically, we …

Improved Self-Consistency For Sced-Lcao., Lyle C. Smith

Electronic Theses and Dissertations

In this document I describe a novel implementation of the generalized bisection method for finding roots of highly non-linear functions of several variables. Several techniques were optimized to reduce computation time. The implementation of the bisection method allows for the calculation of heterogeneous systems with SCED-LCAO, since derivative-based methods often fail for these systems. Systems composed of Gallium and Nitrogen are currently receiving much interest due to their behavior as semi-conductors and their ability to form nano-wires. The methods developed here were employed to create a set of SCED-LCAO parameters for homogeneous Gallium and heterogeneous Gallium Nitride systems. These parameters …

Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, Brittney Keel

Department of Mathematics: Dissertations, Theses, and Student Research

The exact evolutionary history of any set of biological sequences is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this dissertation we propose a game-theoretic approach to clustering biological sequences and analyzing their evolutionary histories. In this context we use the term evolution as a broad descriptor for the entire set of mechanisms driving the inherited characteristics of a population. The key assumption in our development is that evolution tries to accommodate the competing forces of selection, of which the conservation force seeks to …

Time Integration Methods Of Fundamental Solutions And Approximate Fundamental Solutions For Nonlinear Elliptic Partial Differential Equations, Corey Leon Jones

Dissertations

A time-dependent method is coupled with the Method of Approximate Particular Solutions (MAPS) of Delta-shaped basis functions, the Method of Fundamental Solutions (MFS), and the Method of Approximate Fundamental Solutions (MAFS) to solve a second order nonlinear elliptic partial differential equation (PDE) on regular and irregular shaped domains. The nonlinear PDE boundary value problem is first transformed into a time-dependent quasilinear problem by introducing a fictitious time. Forward Euler integration is then used to ultimately convert the problem into a sequence of time-dependent linear nonhomogeneous modified Helmholtz boundary value problems on which the superposition principle is applied to split the …

Situational Assessment Using Graph Comparison, Pavan Kumar Pallapunidi

UNLV Theses, Dissertations, Professional Papers, and Capstones

In strategic operations, the assessment of any given situation is very important and may trigger the development of a mission plan. The mission plan consists of various actions that should be executed in order to successfully mitigate the situation. For a new mission plan to be designed or implemented, the effect of the previous mission plan should be accessed. These mission plans use various sensors to collect the data which can be very large and aggregate them to obtain detailed information of the situation. In order to implement an effective mission plan the current situation has to be assessed effectively. …

A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

Electronic Theses and Dissertations

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2. …

Random Walks On Random Lattices And Their Applications, Ryan Tyler White

Theses and Dissertations

This work studies a class of continuous-time, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary are studied extensively by stochastic analysis and operational calculus. Further, information on the process can be ascertained only upon observations occurring according to a delayed renewal process, rather than in real time. Passage times are thus obscured and results are first derived pertaining to the pre-passage and post-passage observations. Two distinct strategies are developed to combat the crudeness of delayed observations in order to derive more refined information about the …

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

An Experimental Analysis Of Adaptive Learning In A Multi-Subject Economy, David Martin

Business and Economics Honors Papers

The rational expectations hypothesis (REH) has long served as a foundation in macroeconomic laws of motion. However, the assumptions of REH are likely too powerful to be representative of economic actors. This research evaluates adaptive learning, a developing alternative to rational expectations, using a multi-agent macroeconomic prediction “game.” Data was gathered from a group of students, each predicting the outcome of a single economy over time. Each agent was asked to forecast output (GDP) and inflation in each period based on historic levels of output, inflation, and interest rates. These data were then analyzed under various theoretical models of adaptive …

Modeling Traffic At An Intersection, Kaleigh L. Mulkey, Saniita K. Fasenntao

Symposium of Student Scholars

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program …

A Seasonal Analysis Of Extreme Precipitation Trends In The Contiguous United States, Rachael Balstad, Jaechoul Lee

College of Arts and Sciences Presentations

The purpose of this paper is to examine extreme precipitation trends in the United States. The National Climate Assessment estimated that average precipitation in the United States has increased in the last 100 years, with variation occurring regionally. Some regions have experienced larger increases in average precipitation, while others have experienced decreases. However, this aggregate increase in average precipitation does not necessarily indicate an analogous trend in extreme precipitation. Statistically, average and extreme values are nearly independent. In this paper, a changepoint technique and extreme value statistical models will be used for estimation of trend and its uncertainty. A changepoint …

Helping A Microfinance Institution Select Its Clients: A Risk Analysis Using Social Networks, Sayantan Mitra, Varunavi Newar

Black & Gold

This paper formulates an objective mathematical model for a Microfinance Institution (MFI) to measure the credit worthiness associated with a potential client. We use concepts from network theory to determine the credit worthiness of an individual in relation to other households in the community. We use the concept of eigenvector centrality to evaluate the relative credit worthiness in the network. The latter part of the model focuses on the absolute measures of credit worthiness such as income, ownership of assets and risk of the proposed investment. This model would help MFIs reduce the risk of borrowing by ensuring that there …

Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate

Senior Honors Theses

Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a …

Primes And Zeros: A Million Dollar Mystery, Brian Conrey

Dalrymple Lecture Series

A prime number is an integer greater than one whose only positive divisors are 1 and itself. In 1859 G. F. B. Riemann proposed a way to understand how the prime numbers are distributed among the natural numbers. More than 150 years later mathematicians still have not proven Riemann's Hypothesis. The stature of this problem has continued to rise so that today it is widely regarded as the most important unsolved problem in all of mathematics. In this talk I will describe some of the colorful history that surrounds this question.

The Kerzman–Stein Operator For Piecewise Continuously Differentiable Regions, Michael Bolt, Andrew Raich

University Faculty Publications and Creative Works

The Kerzman–Stein operator is the skew-hermitian part of the Cauchy operator defined with respect to an unweighted hermitian inner product on a rectifiable curve. If the curve is continuously differentiable, the Kerzman–Stein operator is compact on the Hilbert space of square integrable functions; when there is a corner, the operator is noncompact. Here, we give a complete description of the spectrum for a finite symmetric wedge and we show how this reveals the essential spectrum for curves that are piecewise continuously differentiable. We also give an explicit construction for a smooth curve whose Kerzman–Stein operator has large norm.

Bootstrapping Vs. Asymptotic Theory In Property And Casualty Loss Reserving, Andrew J. Difronzo Jr.

Honors Projects in Mathematics

One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling …