Department: Department of Mathematics and Statistics ![[clear]](close-x.png "Remove this limiter")
32 matches in the database.
These are records: 1 - 30.
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1.
Adovasio, Ben.
A Character Theory Free Proof of Burnside's paqb Theorem.
Degree: MS, Department of Mathematics and Statistics, 2012, Youngstown State University
► In 1904, George Burnside [2] proved that any group G with |G|…
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▼ In 1904, George Burnside [2] proved that any group G with |G| = paqb where p and q are primes and a and b are positive integers is solvable. Burnside accomplished this through the use of character theory, i.e., the interaction between a group and a vector space. Since then, group theorists began to try to prove this theorem without the use of character theory. They wanted a proof that relied only on group theoretical principles. This was finally achieved in 1972 by Helmut Bender [1]. However, in 1970, David M. Goldschmidt [3] supplied a group theoretic proof of Burnside's Theorem but only when the order of the group, G, was odd. Then in 1972, Hiroshi Matsuyama [4] supplied a group theoretic proof of Burnside's Theorem when the order of the group, G, was even. Ironically, Bender's and Matsuyama's results occurred independently and simultaneously. Therefore, both papers were published even though Bender's proof was more general. The goal of this paper is to present the background knowledge and the more general proof of Burnside's Theorem.
Advisors/Committee Members: Flowers, Neil.
Subjects: Mathematics
Keywords: Burnsides Theorem; Abstract Algebra; Group Theory; Mathematics
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2.
Agbeko, Joseph D.K.M.A.
Evaluation and Application of Bloom Filters in Computer Network Security.
Degree: MS, Department of Mathematics and Statistics, 2009, Youngstown State University
► Unstructured Peer-to-Peer (P2P) networks for content distribution are decentralized and robust. Searching…
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▼ Unstructured Peer-to-Peer (P2P) networks for content distribution are decentralized and robust. Searching for content in the network is based on the Gnutella Protocol. Broadcast Updates Look-up Search Protocol (BULLS) reverses Gnutella and enables a local look-up search at the cost of storing all the files shared in the network. In this thesis we introduce the use of bloom filters in the design and evaluation of a data structure that reduces space and search time in P2P networks based on BULLS. We also discuss the main ideas of a new Space Efficient Local Look-up Search (SELLS) protocol that is based on BULLS and uses this new data structure. The new data structured is called the Inverse Bloom Filter (IBF) and uses bloom filters. A bloom filter is a space efficient probabilistic structure for membership queries. That is,they can be used to efficiently determine if a file is stored at a host. The cost is a small probability of error called false positive. The challenge is to evaluate the search efficiency (i.e., remember searches that have not been successful) of bloom filters as the primary data structure of SELLS. The empirical evaluation can be achieved using real file names from a P2P network and determining the false positive rate of the bloom filter. Novel applications of SELLS could possibly include secure key distribution; building block towards securing P2P networks
Advisors/Committee Members: Perera, Graciela.
Subjects: Computer science
Keywords: Bloom filters; computer network security; space efficient; protocol
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3.
Agyemang, Perpetual O.
Modeling the Preference of Wine Quality Using Logistic Regression Techniques Based on Physicochemical Properties.
Degree: MS, Department of Mathematics and Statistics, 2010, Youngstown State University
► Wine quality is attributed to many different factors of the wine working…
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▼ Wine quality is attributed to many different factors of the wine working collectively to bear a sensory experience that is not apparent from considering these components in isolation. The various chemical components in wine give the wine its distinct taste and aroma. Appreciation of wine quality involves moving beyond our innate preferences. Currently, about 1300 components relating to wine quality have been identified in wine and new components continue to be found. These physicochemical properties can be used to model wine quality. This review presents an analysis to extend what P. Cortez, A. Cerdeira, F. Almeida, T. Matos and J. Reis accomplished using support vector machine and neural network methods for modeling wine preferences by data mining from physicochemical properties. Two logistic regression approaches are used to predict human wine taste preferences with the goal of better predictions. The data were subject to the logistic regression analysis to develop suitable equations to predict which components were significant in the determination of quality of wine. Since ordering exists in the dependent variable, we first considered using ordinal logistic regression. Ordinal logistic regression is a statistical technique whose dependent variable is the order response category variable and the independent variables may be categorical, interval or ration scale. An order response variable is useful for subjective assessment of quality, importance or relevance. After applying this technique, we realized that sulphate, which improves the scent of wine, and citric acid were significant as an indication of quality in both red and white wine. As some of the assumptions of the ordinal logistic model were violated, we employed multinomial logistic regression as well. Multinomial logistic regression is used when the dependent (response) variable in question is nominal, i.e. a set of categories which cannot be ordered in any meaningful way (for example, societal class) and consists of more than two categories. It assumes that data are case specific (each independent variable has a single value for each case), independent of inappropriate options. Using this technique, alcohol was statistically significant and had a negative effect throughout the various quality levels of red wine. pH was statistically significant and had a negative effect throughout the various quality levels of white wine. This research provides a useful basis for assessing the various chemical components in wine that give wine its quality, using two regression approaches. The model built for wine quality in this analysis is anticipated to be of great use because of its dependence on only seven components for red wine and eight components for white wine.
Advisors/Committee Members: Wakefield, Thomas.
Subjects: Mathematics; Statistics
Keywords: Wine quality; Logistic regression; Physicochemical; Properties
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4.
Alam, Mohammad Tanveer.
Image Classification for Remote Sensing Using Data-Mining Techniques.
Degree: MS, Department of Mathematics and Statistics, 2011, Youngstown State University
► Remote Sensing engages electromagnetic sensors to measure and monitor changes in the…
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▼ Remote Sensing engages electromagnetic sensors to measure and monitor changes in the earth's surface and atmosphere. Remote Sensing Satellites are currently the fastest growing source of geographical area. Using data-mining techniques enables more opportunistic use of data banks of remote sensing satellite images. This thesis focuses on supervised and unsupervised classification, the two data mining techniques on the high resolution satellite Imagery from satellite IKONOS and satellite LANDSAT taken of the area around Kent State University, Ohio. The image was classified into ten distinct class: 1) Water, 2) Forested, 3) Agriculture, 4) Urban Development, 5) Vegetation1, 6) Vegetation2, 7) Vegetation3, 8) Vegetation4, 9) Grass, 10)Road. ERDAS Imagine was used in manipulating the images and creating the classification and analysis. The result obtained in form of accuracy helps to decide which image and classification technique is better to identify geographical patterns related to land use.
Advisors/Committee Members: Sullins, John.
Subjects: Computer Science; Geographic Information Science; Remote Sensing
Keywords: Image Classification; Remote Sensing; Datamining; unsupervised classification; supervised classification; LANDSAT; IKONOS
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5.
Ballone, Frank.
On Volterra Spaces.
Degree: MS, Department of Mathematics and Statistics, 2010, Youngstown State University
► Continuity is one of the most important concepts in Mathematics. A. Cauchy…
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▼ Continuity is one of the most important concepts in Mathematics. A. Cauchy was one of the first to define the continuity of a function. Here is Cauchy's condition of the continuity of a function: " ... We also say that the function f(x) is a continuous function of x in the neighborhood of a particular value assigned to the variable x as long as it (the function) is continuous between those two limits of x, no matter how close together, which enclose the value in question ... "(see [31]). This concept was refined by K. Weierstrass, which is the definition of continuity that we use today. For a historical account on how the notation of continuity has evolved see [31]. The study of continuity usually begins in calculus, where we study continuous functions. Questions on how a set of points of continuity of a given real-valued function of real variable look are very important. I will discuss these sets for real-valued functions of real variable in chapter 1. In chapter 2, I will continue to look at real-valued functions and examine their points of continuity. This time, the functions will be defined on metric spaces. Furthermore, I will examine the set of points of continuity of real-valued functions defined on topological spaces in chapter 4. In chapter 3, important topological concepts are introduced that will be used from chapters 4 through 6. The analysis of the existing proofs on the Volterra theorem, which I will begin to discuss in chapter 1, led to the class of spaces known as Volterra spaces. In chapter 5, I will explain the concept of a Volterra space and explain various properties of these spaces. Finally, in chapter 6, I will list original and recent research results from various articles to illustrate the progress on Volterra spaces since their introduction in [15]. Throughout my thesis, I will illustrate various concepts with the help of diagrams and examples, some of I created. In addition, I will further explain topics from classical sources in detail to make the material easy to follow and more understandable to the reader.
Advisors/Committee Members: Piotrowski, Zbigniew.
Subjects: Mathematics
Keywords: Volterra; Volterra spaces; Volterra's theorem
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6.
Eddy, Scott M.
Lie Groups and Lie Algebras.
Degree: MS, Department of Mathematics and Statistics, 2011, Youngstown State University
► The subject of Lie groups is one that slips by many a…
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▼ The subject of Lie groups is one that slips by many a mathematician. Many claim that the topic is not accessible to undergraduate research. The book Lie Groups by Harriet Pollatsek came out a few years ago, and it was meant to be a new way to be introduced to the topic. However, the book does not quite get far enough to give a formal definition of a Lie group. The goal of this project is to “bridge the gap.” The objective of this thesis is to include all the introductory material required to get to where the definition of a Lie group is no longer something so complicated. We will illustrate the major concepts by examples. Many matrix groups are Lie groups. Matrix groups are well-known, and they are an ideal place to start learning about what a Lie group can do. We then look at tangent spaces of the matrix groups, or the Lie algebra that is associated with each Lie group. After some motivation behind Lie algebras, we finally get to the feature presentation: a group and a differentiable manifold, put together into one super structure known as a Lie group.
Advisors/Committee Members: Goldthwait, Richard.
Subjects: Mathematics
Keywords: Lie groups; Lie algebras; Tangent spaces
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7.
Eynon, James R.
Comparison of Logistic Force of Mortality Models for Predicting Life Table Probabilities of Death: A Simulation-Based Approach.
Degree: MS, Department of Mathematics and Statistics, 2011, Youngstown State University
► A program was written in the statistical software package R for conducting…
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▼ A program was written in the statistical software package R for conducting Monte Carlo studies based on simulated life tables, and then used in a study to compare two different models for predicting life table probabilities of death. A parametric probability model was used by the program to generate the cohort distribution of deaths, based on supplied life table data. For the present study a cohort life table was constructed using mortality data from the Social Security Death Index, Master File. The models evaluated in the present Monte Carlo study are alternative three-parameter versions of the logistic force of mortality model. The models were fit to simulated life table data for ages 80 to 99, and then used to make probability of death predictions for ages 80 to 105. The Monte Carlo simulations were used to obtain the average values and standard deviations of the probability of death predictions generated by the two models, which were then compared to one another and to the actual probabilities of death based on the probability model that generated the simulated life table data. Results of the simulations showed that the mean probabilities of death predicted by the two models were very similar over the range of ages considered, but usually deviated somewhat from the actual probabilities of death. In the age range of 80-99, the average percentage deviation was less than 2% for each model, while in the age range of 100-105, the average percentage deviation for the models was around 5-6%. In the age range of 100-105, both models always underestimated the true probability of death.
Advisors/Committee Members: Wakefield, Thomas.
Subjects: Aging; Applied Mathematics; Demographics; Statistics
Keywords: Logistic force of mortality models; Monte Carlo simulation; Life table probability of death; Social Security Death Index
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8.
Hamilton, Jeremy.
An Exploration of the Erdös-Mordell Inequality.
Degree: MS, Department of Mathematics and Statistics, 2010, Youngstown State University
► We investigate the Erdös-Mordell Inequality for triangles through the literature: proving the…
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▼ We investigate the Erdös-Mordell Inequality for triangles through the literature: proving the result in its original form, modifying the result, looking at applications of the result, providing other inequalities resembling the Erdös-Mordell Inequality, and finding a comparable inequality for quadrilaterals.
Advisors/Committee Members: Smotzer, Thomas.
Subjects: Mathematics
Keywords: Mathematics; Erdös-Mordell Inequality; triangle inequalities
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9.
Harris, Miles J.
Assessing the Impact of Developmental Mathematics on College Students.
Degree: MS, Department of Mathematics and Statistics, 2008, Youngstown State University
► A study was performed to assess the effectiveness of the developmental mathematics…
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▼ A study was performed to assess the effectiveness of the developmental mathematics program at Youngstown State University. For this study, two cohort groups of developmental mathematics students were selected, and the success rate of both groups in their developmental and subsequent college-level courses was tracked. The results of the cohort study was compared to the success rates found in a population study, to check if the developmental students performed as well in their college-level courses as the population. For every college-level course tracked in this study, there was no statistically significant difference in the passing rate of the cohort groups and the population group.
Advisors/Committee Members: Goldthwait, R. G.
Subjects: Mathematics education
Keywords: developmental mathematics
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10.
Haught, Damon.
On the Existence of Solutions to Discrete, Two Point, Non-linear Boundary Value Problems.
Degree: MS, Department of Mathematics and Statistics, 2010, Youngstown State University
► Within this treatise we establish conditions for the existence of solutions to…
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▼ Within this treatise we establish conditions for the existence of solutions to two-point, discrete, non-linear boundary value problems. We will be examining two different variations of the problem. First, we will be examining generalized discrete nonlinear systems of the form x(t + 1) = Ax(t) + f(x(t)), t ∈ {0, 1, ..., N – 1} subject to Bx(0) + Dx(N) = 0. We demonstrate the existence of solutions to this type of problem when the associated linear, homogeneous boundary value problem has only the trivial solution, and the nonlinear element exhibits sublinear growth. Next, we will consider scalar, two-point, nonlinear boundary value problems of the form y(t + n) + an–1y(t + n – 1) + ··· + a0y(t) = g(y(t)), for t ∈ {0, 1, ..., N – 1}, subject to n∑j=1bijy(j – 1) + n∑j=1dijy(j + N – 1) = 0, for i = 1, 2, ..., n. In this case, we assume the associated linear homogeneous boundary value problem has a one-dimensional solution space and establish criteria that guarantee the existence of solutions by analyzing the relationship between the nonlinear element and the solution space of the associated linear boundary value problem through a projection scheme.
Advisors/Committee Members: Taylor, Padraic.
Subjects: Mathematics
Keywords: Boundary value problems; Solutions; Non-linear
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11.
Kolat, Alycia M.
Topological Function Spaces.
Degree: MS, Department of Mathematics and Statistics, 2011, Youngstown State University
► This thesis is an introduction to function spaces endowed with the topology…
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▼ This thesis is an introduction to function spaces endowed with the topology of pointwise convergence, abbreviated Cp-theory, and a look at a small portion of the open questions in the field. In the introductory chapters, several different cardinal functions are presented and then used to characterize properties of Cp-spaces. The final chapters explore several open questions pertaining to Lindelöfness and metacompactness of Cp-spaces.
Advisors/Committee Members: Tartir, Jamal.
Subjects: Mathematics
Keywords: topology; function spaces; Cp-theory
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12.
Kolenick, Joseph F Jr.
On Exponentially Perfect Numbers Relatively Prime to 15.
Degree: MS, Department of Mathematics and Statistics, 2007, Youngstown State University
► If the natural number n has the canonical form p1a1p2a2⋯prar, then we…
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▼ If the natural number n has the canonical form p1a1p2a2⋯prar, then we say that an exponential divisor of n has the form d = p1b1p2b2⋯prbr, where bi|ai for i = 1, 2, … r. We denote the sum of the exponential divisors of n by σ(e)(n). A natural number n is said to be exponentially perfect (or e-perfect) if σ(e)(n) = 2n. The purpose of this thesis is to investigate the existence of e-perfect numbers relatively prime to 15. In particular, if such numbers exist, are they bounded below? How many distinct prime divisors must they have? Several lemmas are utilized throughout the paper on route to answering these questions. Also, computer programs written in Maple are used for numerical estimates.
Advisors/Committee Members: Fabrykowski, Jacek.
Subjects: Mathematics
Keywords: exponential divisor function; exponentially perfect numbers
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13.
Lazaj, Klotilda.
Metric Preserving Functions.
Degree: MS, Department of Mathematics and Statistics, 2009, Youngstown State University
► The primary topic of this paper is distance (or "metric") preserving functions.…
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▼ The primary topic of this paper is distance (or "metric") preserving functions. In particular, the paper will focus on the least integer function - a step function, also referred to as the ceiling function. Herein, the author will provide information about the ceiling function, as well as a proof that it is indeed metric preserving, supported by Wilson's Theorem and the Borsik-Dobos Theorem. In addition, the paper will show that the amenable condition and triangle triplet condition guarantee that a function is distance preserving.
Advisors/Committee Members: Piotrowski, Zbigniew.
Subjects: Mathematics
Keywords: least integer function; metric preserving function; triangle triplets
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14.
Lester, Jeremy W.
The Elliptic Curve Group Over Finite Fields: Applications in Cryptography.
Degree: MS, Department of Mathematics and Statistics, 2012, Youngstown State University
► It is the intent of this thesis to study the mathematics, and…
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▼ It is the intent of this thesis to study the mathematics, and applications behind the elliptic curve group over Fp. Beginning with the definition of the '+' operation,under which the points on the elliptic curves form an abelian group. Then moving to a brief introduction to both public, and private key cryptography. This will lead into an explanation of the discrete logarithm problem along with an implementation using the elliptic curve group over Fp. This thesis will conclude with an exploration Lenstra's factoring algorithm using the elliptic curve group.
Advisors/Committee Members: Fabrykowski, Jacek.
Keywords: Elliptic Curve Group; Cryptography
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15.
McMillen, Brandon.
The Knapsack Problem, Cryptography, and the Presidential Election.
Degree: MS, Department of Mathematics and Statistics, 2012, Youngstown State University
► The 0-1 Knapsack Problem is an NP-hard optimization problem that has been…
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▼ The 0-1 Knapsack Problem is an NP-hard optimization problem that has been studied extensively since the 1950s, due to its real world significance. The basic problem is that a knapsack with a weight capacity c is to be filled with a subset of n items. Each item i, has a weight value wi and a profit value pi. The goal is to maximize total profit value without the having the total weight exceed the capacity. In this thesis, the 0-1 Knapsack Problem is introduced and some of the research and applications of the problem are given. Pisinger's branch-and-bound algorithm that will converge to an optimal solution is presented. One of the earliest applications of the knapsack problem, the knapsack cryptosystems, is then discussed. The earliest knapsack cryptosystem, the Merkle-Hellman Cryptosystem, is described along with how Adi Shamir broke this cryptosystem. Generating functions are then used to provide a number of solutions to a knapsack problem. Using the generating function of the knapsack problem, the paper concludes with an application on the Electoral College.
Advisors/Committee Members: Ritchey, Nathan.
Subjects: Mathematics
Keywords: Knapsack Problem; Cryptography; Generating Functions
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16.
Mohammed, Zakiyah.
Carter Subgroups and Carter's Theorem.
Degree: MS, Department of Mathematics and Statistics, 2011, Youngstown State University
► In 1961 Roger W. Carter proved a theorem about solvable groups similar…
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▼ In 1961 Roger W. Carter proved a theorem about solvable groups similar to Sylow's theorem. He proved that if a group is solvable then it always contains a nilpotent, self-normalizing subgroup called a Carter subgroup, and that all such subgroups are conjugate to each other by an element of the group. The objective of this thesis is to present a proof of Carter's theorem.
Advisors/Committee Members: Flowers, Neil.
Subjects: Mathematics
Keywords: Carter Subgroups; Carter's theorem; Nilpotent Groups; Solvable groups
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17.
Moore, Theresa Lynn.
Seasonal Time Series Model Comparison for Nonstationary Passenger Flight Data.
Degree: MS, Department of Mathematics and Statistics, 2007, Youngstown State University
► The objective of this paper is to analyze the number of passengers…
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▼ The objective of this paper is to analyze the number of passengers flying a sample of three airlines before and after 9/11 to discover whether there has been a recovery. The three airlines were modeled using simple linear regression and time series analysis. Dummy variables and trigonometric functions were used to mimic the seasonal variation and additive decomposition was used to remove the seasonal component and model the trend. The additive decomposition quadratic models were deemed the best fits. From the quadratic models is concluded that the three airlines chosen for this paper have recovered from the effects of 9/11.
Advisors/Committee Members: Kerns, G. Jay.
Subjects: Statistics; Mathematics
Keywords: Passenger Flight Data; Statistics; Mathematics; Time Series; Nonstationary
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18.
Ogbonna, Antoine I.
Eccentricity Sequence of 2.
Degree: MS, Department of Mathematics and Statistics, 2010, Youngstown State University
► We attempt to construct graphs with eccentricity sequence of 2. By looking…
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▼ We attempt to construct graphs with eccentricity sequence of 2. By looking at the degree sequence of a graph, it is shown that some properties can be found that describe graphs with eccentricity sequence of 2. The main result of this research is that the minimum graph with eccentricity sequence of 2 has degree sum of 2(2n-5). This enables us to count the number of degree sums of graphs with eccentricity sequence of 2.
Advisors/Committee Members: O'Mellan, Anita C.
Subjects: Mathematics
Keywords: Graphs; Eccentricity; Eccentricity sequence; Degree sequence; Degree sums; AO-Graphs; Connected graphs
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19.
Pace, Dennis.
Axiom of Choice: Equivalences and Applications.
Degree: MS, Department of Mathematics and Statistics, 2012, Youngstown State University
► This paper proves the equivalences of the Axiom of Choice and 7…
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▼ This paper proves the equivalences of the Axiom of Choice and 7 other well known formulations. It then proves a few notable applications of the Axiom of Choice and discusses its importance in modern mathematics.
Advisors/Committee Members: Tartir, Jamal.
Subjects: Mathematics
Keywords: Axiom of choice; Well ordering principle; Set theory
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20.
Panta, Purushottam.
Web Design, Development and Security.
Degree: MS, Department of Mathematics and Statistics, 2009, Youngstown State University
► Websites are the most convenient way to present and disseminate information to…
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▼ Websites are the most convenient way to present and disseminate information to the maximum number of people in the world. The web browsers are the means to render the information on web page, the basic building blocks of a website, and web programming is the basic structure (architecture) of each web page.The thesis on "Web Design, Development and Security" is a complete analysis of website design and development. Web sites should be able to present abundant information to a visitor in well organized manner. In addition, there must be a reliable transfer of secure information between server and client. There exist other major factors such as user friendliness, layout, simplicity, ease of rendering in the browser and so on that are closely related with the quality of website. This thesis will elaborate on a number of issues that are related with web design and development. These principles will be illustrated and demonstrated in the design of some websites that I have designed so far.
Advisors/Committee Members: Sullins, John.
Subjects: Computer science
Keywords: web design; web server security; web development; security; web information system; SQL injection
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21.
Paris, Lisa.
Existence and Uniqueness of Solutions to Positive Bounded Below Operator Equations.
Degree: MS, Department of Mathematics and Statistics, 2011, Youngstown State University
► We investigate solving a differential equation boundary value problem. Using "variational" or…
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▼ We investigate solving a differential equation boundary value problem. Using "variational" or "energy" methods, we transform the problem into one of minimizing the value of a certain functional expression involving a definite integral. Finally, we show the existence and uniqueness of solutions to positive bounded below operator equations.
Advisors/Committee Members: Goldthwait, Richard.
Subjects: Materials Science; Mathematics; Mechanical Engineering
Keywords: Positive bounded below operator; L 2 space, boundary value problem; Minimum functional theorem
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22.
Pirilla, Patrick Brian.
On the Trajectories of Particles in Solitary Waves.
Degree: MS, Department of Mathematics and Statistics, 2011, Youngstown State University
► Across the country, school students learn that ocean waves cause water particles…
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▼ Across the country, school students learn that ocean waves cause water particles to form looping paths, traveling in circles which become smaller as you look deeper underwater. In this paper, we investigate the approximations which are used to make this claim. Furthermore, we investigate closer approximation techniques which show that these looping paths actually propogate forward with the wave's motion. Finally, we investigate the specific case of the soliton, which causes particles underneath to travel in a forward-moving arc, with no looping motion at all. With this background, we examine the recent work of A. Constantin and collaborators, specifically his conclusion that our results for the soliton hold for any solitary wave.
Advisors/Committee Members: Yates, George T.
Subjects: Applied Mathematics; Fluid Dynamics; Mathematics; Physics
Keywords: Solitons; Fluid dynamics; Water waves; Euler equation; KdV equation; Differential equations
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23.
Richardson, Robert.
On the Number of Integers Expressible as the Sum of Two Squares.
Degree: MS, Department of Mathematics and Statistics, 2009, Youngstown State University
► We attempt to provide a reasonably complete work concerning the estimation of…
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▼ We attempt to provide a reasonably complete work concerning the estimation of the number of integers expressible as the sum of two squares. We begin with some basic concepts from number theory, and progress rapidly through the theory necessary for Landau's theorem before presenting two proofs of his theorem.
Advisors/Committee Members: Fabrykowski, Jacek.
Subjects: Mathematics
Keywords: sum of two squares; prime number theorem; generalized Wiener-Ikehara theorem; Landau
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24.
Sajja, Sunitha.
Data Mining of Medical Datasets with Missing Attributes from Different Sources.
Degree: MS, Department of Mathematics and Statistics, 2010, Youngstown State University
► Two major problems in data mining are 1) dealing with missing values…
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▼ Two major problems in data mining are 1) dealing with missing values in the datasets used for knowledge discovery, and 2) using one data set as a predictor of other datasets. We explore this problem using four different datasets from the UCI Machine learning repository, from four different sources with different missing values. Each dataset contains 13 attributes and one class attribute which denotes the presence of heart disease and the absence of heart disease. Missing values were replaced in a number of ways; first by using normal mean and mode method, secondly by removing the attributes that contains missing values, thirdly by removing the records that contains more than 60 percent of values missing and filling the remaining missing values. We also experimented with different classification techniques, including Decision tree, Naive Bayes, and MultiLayerPerceptron, using Medical Datasets. Rapid Miner and Weka tools. The consistency of the datasets was found by combining the datasets together and comparing the results of this datasets with the classification error of different datasets. It can be seen from the results that if fewer number of missing values are present, the normal mean and mode method is good. If larger amount of missing values are present than removing instances that contain 60% of missing values and replacing with remaining along with different preprocessing steps works better, and using one dataset as a predictor of other dataset produced moderate accuracy.
Advisors/Committee Members: Sullins, John.
Subjects: Computer Science
Keywords: data mining; missing attributes; data classification; outliers
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25.
Shakeel, Mohammad Danish.
Land Cover Classification Using Linear Support Vector Machines.
Degree: MS, Department of Mathematics and Statistics, 2008, Youngstown State University
► GIS has been an effective tool in identifying and recognizing urban patterns.…
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▼ GIS has been an effective tool in identifying and recognizing urban patterns. Various techniques like Support Vector Machines, artificial neural networks have been used with GIS to classify the patterns for urban analysis. Liblinear has emerged as another effective tool which produces results in much lesser time without compromising the accuracy. In this thesis the datasets used were extracted using GIS. The datasets were from the Ohio state counties namely the Delaware, Holmes, Mahoning and Medina counties. Each had over a million records and contained seven independent variables related to urban development and a class label which denotes the urban areas versus the rural areas. Using Liblinear, Libsvm, Rapid Miner and Weka some experiments were carried out over smaller datasets and the results have been shown. It can be seen that Liblinear is as effective as Libsvm while the latter takes much longer time for producing the results. The results can help indentify geographical patterns related to urban land use.
Advisors/Committee Members: Lazar, Alina.
Subjects: Computer science; Geography
Keywords: support vector machines; data mining; geographic information systems; urban pattern recognition
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26.
Shoaib, Naveed.
A Portable and Improved Implementation of the Diffie-Hellman Protocol for Wireless Sensor Networks.
Degree: MS, Department of Mathematics and Statistics, 2009, Youngstown State University
► Wireless sensor nodes generally face serious limitations in terms of computational power,…
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▼ Wireless sensor nodes generally face serious limitations in terms of computational power, energy supply, and network bandwidth. One of the biggest challenges faced by researches today is to provide effective and secure techniques for establishing cryptographic keys between wireless sensor networks. Public-key algorithms (such as the Diffie-Hellman key-exchange protocol) generally have high energy requirements because they require computational expensive operations. So far, due to the limited computation power of the wireless sensor devices, the Diffie-Hellman protocol is considered to be beyond the capabilities of today's sensor networks. We analyzed existing methods of implementing Diffie-Hellman and proposed a new improved method of implementing the Diffie-Hellman key-exchange protocol for establishing secure keys between wireless sensor nodes. We also provide an easy-to-use implementation of the Elliptic Curve Diffie-Hellman key-exchange protocol for use in wireless sensor networks.
Advisors/Committee Members: Perera, Graciela.
Subjects: Communication; Computer science; Information Systems; Mathematics
Keywords: Wireless Sensor Networks; Sun SPOTS; Diffie-Hellman Key-Exchange Protocol; Elliptic Curve Cryptography; Elliptic Curve Diffie-Hellman; Portable Diffie-Hellman
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27.
Stiles, Megan E.
The Mathieu Groups.
Degree: MS, Department of Mathematics and Statistics, 2011, Youngstown State University
► The Classification of Finite Simple Groups was a prominent goal of algebraists.…
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▼ The Classification of Finite Simple Groups was a prominent goal of algebraists. The Classification Theorem was complete in 1983 and many textbooks from the 1980s include detailed proofs and explorations of many aspects of this subject. For example, J.J. Rotman devotes an entire chapter to the Mathieu groups [13]. It seems that there is still disagreement amongst mathematicians as to whether the Classification Theorem should be deemed thorough or without major error. Looking into the entire Classification Theorem would be a huge undertaking, so in this paper we are discussing only the five sporadic Mathieu groups. Looking at these small sporadic simple groups opened up a discussion of transitivity and k-transitivity. In addition to traditional abstract algebra material, this paper explores a relationship between the five sporadic Mathieu groups and the combinatorial Steiner Systems. Included in this discussion is the relationship of M24 with the Binary Golay Code. This thesis ends in a proof of the simplicity of the Mathieu Groups. The proof of the simplicity of M11 and M23 which was developed by R. Chapman in his note, An elementary proof of the Mathieu groups M11 and M23 makes the preliminary theorems to the simplicity proof in J.J. Rotman's book look much less perfunctory [2],[13]. This raises the question of whether there could possibly be a more succinct proof of the simplicity of M12, M22 and M24.
Advisors/Committee Members: Wakefield, Thomas.
Subjects: Mathematics
Keywords: Mathieu Groups; Transitive Groups; Abstract Algebra
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28.
Talukdar, Shahidur R.
Social, Political, and Institutional Determinants of Investment and Economic Growth: A Cross-Country Study.
Degree: MS, Department of Mathematics and Statistics, 2009, Youngstown State University
► Investment and economic growth are affected by many factors such as physical…
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▼ Investment and economic growth are affected by many factors such as physical and human capital, geography, social, and political factors. The aim of this paper is to study how social, political and institutional factors affect investment and economic growth. Specifically, this thesis aims to study the relationship between socio-political indicators such as law and order, democratic accountability, ethnic tension, government stability, and corruption in government and economic indicators like the investment, GDP and growth rate. The analysis of the impact of socio-political indicators on the investment provides a mechanism through which these affect the GDP and hence the growth rate. Employing multivariate regression on panel data with a cross-section of 141 countries over a period of 24 years ranging from 1984 to 2007, the study finds that the institutional indicators such as law and order, democratic accountability and government stability have positive relationship with growth while indicators like ethnic tension and corruption affect growth negatively, although the effect of ethnic tension and corruption are not robust in some specifications.
Advisors/Committee Members: Uppal, Yogesh.
Subjects: Economics
Keywords: economic growth; political stability; corruption; foreign direct investment
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29.
Thomas, Teri M.
A Generalization of Sylow’s Theorem.
Degree: MS, Department of Mathematics and Statistics, 2009, Youngstown State University
► In the study of group theory, it is common to break up…
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▼ In the study of group theory, it is common to break up a complex group into simpler subgroups in order to arrive at a structure that is easier to analyze and understand. It is also sometimes possible to reconstruct the original group from these subgroups. Although this is not always possible, we can apply this process to finite solvable groups and derive some theorems regarding these groups. Sylow’s Theorem and Hall’s Theorem are among the most famous results. Hall’s Theorem, which is regarded as an extension of Sylow’s Theorem, states that if a group G is solvable and is of some order mn, where m is prime to n, then G has a subgroup of order m and all subgroups of this order are conjugate. When p = π, a Hall π-subgroup is simply a Sylow p-subgroup. While Sylow’s Theorem is valid for any finite group, Hall subgroups need not exist in nonsolvable groups. For example, A5 has order 60 = 3 ⋅ 20, but it has no subgroups of order 20. This is demonstrated within the paper. Hall’s Theorem has been the starting point for the theory of finite solvable groups developed over the past seventy years, although those results are not given here.
Advisors/Committee Members: Flowers, Neil.
Subjects: Mathematics
Keywords: Hall’s theorem; Sylow’s theorem; group theory; abstract algebra
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30.
Waller, Russell.
Strong Continuity on Product Spaces.
Degree: MS, Department of Mathematics and Statistics, 2009, Youngstown State University
► Strong continuity as defined by O. Dzagnidze is explored. Strong continuity with…
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▼ Strong continuity as defined by O. Dzagnidze is explored. Strong continuity with respect to a variable is demonstrated to be continuity with respect to a variable in terms of A.L. Cauchy. New results concerning the relation between strong continuity and near continuity, quasicontinuity, and somewhat continuity on product spaces are given.
Advisors/Committee Members: Piotrowski, Zbigniew.
Subjects: Mathematics
Keywords: strong continuity; quasi-continuity; near continuity; somewhat continuity
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