Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Articles 1 - 9 of 9

Full-Text Articles in Physical Sciences and Mathematics

General Factoring Algorithms For Polynomials Over Finite Fields, Wade Combs Jan 2015

General Factoring Algorithms For Polynomials Over Finite Fields, Wade Combs

Online Theses and Dissertations

In this paper, we generate algorithms for factoring polynomials with coefficients in finite fields. In particular, we develop one deterministic algorithm due to Elwyn Berlekamp and one probabilistic algorithm due to David Cantor and Hans Zassenhaus. While some authors present versions of the algorithms that can only factor polynomials of a certain form, the algorithms we give are able to factor any polynomial over any finite field. Hence, the algorithms we give are the most general algorithms available for this factorization problem. After formulating the algorithms, we look at various ways they can be applied to more specialized inquiries. For …


Vegetation-Based Metrics Of Biotic Integrity For Assessing The Ecological Condition Of Wetlands Of Kentucky, Tanner Matthew Morris Jan 2015

Vegetation-Based Metrics Of Biotic Integrity For Assessing The Ecological Condition Of Wetlands Of Kentucky, Tanner Matthew Morris

Online Theses and Dissertations

Over the last two centuries, wetland acreage across the world has significantly declined due to human disturbances. It has been estimated that Kentucky has lost over 80% of its wetland area. In response to these losses occurring across the United States, the Clean Water Act was passed to halt this dramatic decline and to restore the ecological integrity of waters of the United States. To enforce the Clean Water Act, a number of ecological assessment techniques have been developed to quantify the ecological quality of the waters of the United States. Kentucky recently adopted a rapid method for assessing the …


A Comparison Of Management Strategies For The Federally Endangered Running Buffalo Clover (Trifolium Stoloniferum) On The Blue Grass Army Depot, Ky, Alexi David Dart-Padover Jan 2015

A Comparison Of Management Strategies For The Federally Endangered Running Buffalo Clover (Trifolium Stoloniferum) On The Blue Grass Army Depot, Ky, Alexi David Dart-Padover

Online Theses and Dissertations

Running buffalo clover (Trifolium stoloniferum) is a federally endangered plant that appears to depend on habitat disturbance, although proposed management strategies such as cattle grazing, mowing, and herbicide application have never been compared in a controlled study. We evaluate the efficacy of these techniques on the Blue Grass Army Depot (BGAD) in Madison County, KY, where one of T. stoloniferum’s largest populations occurs. Fifty-nine patches of T. stoloniferum on the BGAD were treated annually between 2012 and 2014 with combinations of mowing and grass-specific herbicide. Patches of T. stoloniferum also were exposed to one of three types of cattle exposure …


A Thorough And Accessible Proof Of The Erdo˝S-Kac Theorem Following Granville And Soundararajan, Thomas John Scheithauer Jan 2015

A Thorough And Accessible Proof Of The Erdo˝S-Kac Theorem Following Granville And Soundararajan, Thomas John Scheithauer

Online Theses and Dissertations

The Erd\H{o}-Kac Theorem states that, as $n$ tends to infinity, the distribution of $\omega(n)$, the number of distinct prime divisors of $n$, becomes normally distributed with mean and variance $\log\log n$. Granville and Soundararajan gave a proof of the Erd\H{o}s-Kac Theorem that avoided many of the specialized techniques present in several earlier approaches. This thesis includes considerable detail, prerequisite theorems, and instructive background in order to provide a self-contained exposition of the proof of Granville and Soundararajan.


Methods Of Analysis For Fermentation Science Products Using Various Analytical Techniques, Casey Jay Howdieshell Jan 2015

Methods Of Analysis For Fermentation Science Products Using Various Analytical Techniques, Casey Jay Howdieshell

Online Theses and Dissertations

Fermentation science, the study of microorganisms as they digest food sources to produce usable products for consumption, has been around since the dawn of modern civilization. Historically, the fermentation process has been utilized for the production of alcoholic beverages. More recently, however, the production of bioethanol and biodiesel as a fuel source alternative to classical fossil fuels has gained increased popularity. As with any synthetic process, derivations and optimizations for ideal production are needed. As such, analytical techniques must be implemented to ensure quality control and pinnacle efficiency. This body of work describes analytical techniques providing key qualitative and quantitative …


Existence Of Positive Solutions To A Family Of Fractional Two-Point Boundary Value Problems, Christina Ashley Hollon Jan 2015

Existence Of Positive Solutions To A Family Of Fractional Two-Point Boundary Value Problems, Christina Ashley Hollon

Online Theses and Dissertations

In this paper we will consider an nth order fractional boundary value problem with boundary conditions that include a fractional derivative at 1. We will develop properties of the Green's Function for this boundary value problem and use these properties along with the Contraction Mapping Principle, and the Schuader's, Krasnozel'skii's, and Legget-Williams fixed point theorems to prove the existence of positive solutions under different conditions.


Validating A Kentucky Wetland Rapid Assessment Method For Forested Riverine Wetlands Using Vegetation, Bird Surveys, And Landscape Analysis, Johnryan Andrew Polascik Jan 2015

Validating A Kentucky Wetland Rapid Assessment Method For Forested Riverine Wetlands Using Vegetation, Bird Surveys, And Landscape Analysis, Johnryan Andrew Polascik

Online Theses and Dissertations

Within the last two centuries, Kentucky has undergone wetland losses exceeding 80 percent (approximately 500,000 hectares). As a response to these losses, the Kentucky Division of Water (KDOW) and Eastern Kentucky University (EKU) developed the Kentucky Wetland Rapid Assessment Method (KY-WRAM) to evaluate the condition of Kentucky's remaining wetlands. The goal of this study was to validate the KY-WRAM for forested riverine wetlands using a vegetation index of biotic integrity (VIBI), bird surveys, and landscape development index (LDI). Specific objectives of this study were to: 1) determine the correlation between bird species richness, VIBI, and LDI with the KY-WRAM in …


Preparation And Characterization Of Self-Assembled Monolayers And Mesoscale Protein Patterning, Panae Noomuna Jan 2015

Preparation And Characterization Of Self-Assembled Monolayers And Mesoscale Protein Patterning, Panae Noomuna

Online Theses and Dissertations

Bottom-up approach was used to develop self-assembled monolayers of octadecyltrichlorosilane (OTS) and undecenyltrichlorosilane(UTS) on Si(100) wafer. Undecenyltrichlorosilane monolayer was oxidized at the vinyl terminal to generate a carboxylic acid group. Lysozyme protein was immobilized on the polar carboxylic acid group. The developed protein patterns were investigated using fluorescence microscopy. Lysozyme has an isoelectronic point of 11.35. At a pH below this value the protein is positively charged making it a good candidate for electrostatic adsorption on the negatively charge -COO- group. Fluorescence images confirm formation of lysozyme across the silicon wafer. The patterned Si(100) wafer can be used as a …


Examining The Impacts Of Valley Fills In Stream Ecosystems On Amphibian And Aquatic Insect Communities In Southeastern Kentucky, John Clayton Bourne Jan 2015

Examining The Impacts Of Valley Fills In Stream Ecosystems On Amphibian And Aquatic Insect Communities In Southeastern Kentucky, John Clayton Bourne

Online Theses and Dissertations

Chapter 1. Abstract: Biodiversity is not evenly distributed, and understanding factors that determine spatial patterns of species diversity remains a key question in ecology. Because of their relatively high abundance and complex life cycles, stream salamanders and aquatic insects are important trophic links and serve a critical role in transferring energy. Despite this importance little research has examined their community structure simultaneously in aquatic ecosystems. The primary objective of this research was to determine the structure of these communities across natural areas of southeastern Kentucky and understand what factors impact their abundances and distributions. To address this, we sampled eight …