Mathematics Commons^™

Dimension Reduction For Power System Modeling Using Pca Methods Considering Incomplete Data Readings, Ting Zhao

Dissertations, Master's Theses and Master's Reports - Open

Principal Component Analysis (PCA) is a popular method for dimension reduction that can be used in many fields including data compression, image processing, exploratory data analysis, etc. However, traditional PCA method has several drawbacks, since the traditional PCA method is not efficient for dealing with high dimensional data and cannot be effectively applied to compute accurate enough principal components when handling relatively large portion of missing data. In this report, we propose to use EM-PCA method for dimension reduction of power system measurement with missing data, and provide a comparative study of traditional PCA and EM-PCA methods. Our extensive experimental …

On Binary And Regular Matroids Without Small Minors, Kayla Davis Harville

Electronic Theses and Dissertations

The results of this dissertation consist of excluded-minor results for Binary Matroids and excluded-minor results for Regular Matroids. Structural theorems on the relationship between minors and k-sums of matroids are developed here in order to provide some of these characterizations. Chapter 2 of the dissertation contains excluded-minor results for Binary Matroids. The first main result of this dissertation is a characterization of the internally 4-connected binary matroids with no minor that is isomorphic to the cycle matroid of the prism+e graph. This characterization generalizes results of Mayhew and Royle [18] for binary matroids and results of Dirac [8] and Lovász …

Special Type Of Subset Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we construct special subset topological spaces using subsets from semigroups or groups or rings or semirings. Such study is carried out for the first time and it is both interesting and innovative. Suppose P is a semigroup and S is the collection of all subsets of P together with the empty set, then S can be given three types of topologies and all the three related topological spaces are distinct and results in more types of topological spaces. When the semigroup is finite, S gives more types of finite topological spaces. The same is true in case …

Subset Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the new notion of constructing non associative algebraic structures using subsets of a groupoid. Thus subset groupoids are constructed using groupoids or loops. Even if we use subsets of loops still the algebraic structure we get with it is only a groupoid. However we can get a proper subset of it to be a subset loop which will be isomorphic with the loop which was used in the construction of the subset groupoid. To the best of the authors’ knowledge this is the first time non associative algebraic structures are constructed using subsets. We get …

Indeterminate Masses, Elements And Models In Information Fusion, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper at the beginning, we make a short history of the logics, from the classical Boolean logic to the most general logic of today neutrosophic logic. We define the general logic space and give the definition of the neutrosophic logic. Then we introduce the indeterminate models in information fusion, which are due either to the existence of some indeterminate elements in the fusion space or to some indeterminate masses.

The best approach for dealing with such models is the neutrosophic logic, which is part of neutrosophy. Neutrosophic logic is connected with neutrosophic set and neutrosophic probability and statistics.

Sets Of Discontinuities Of Linearly Continuous Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

The class of linearly continuous functions f:Rⁿ-->R, that is, having continuous restrictions f|L to every straight line L, have been studied since the dawn of the twentieth century. In this paper we refine a description of the form that the sets D(f) of points of discontinuities of such functions can have. It has been proved by Slobodnik that D(f) must be a countable union of isometric copies of the graphs of Lipschitz functions h:K-->R, where K is a compact nowhere dense subset of R^n-1. Since the class Dⁿ of all …

Structure Borne Noise Analysis Using Helmholtz Equation Least Squares Based Forced Vibro Acoustic Components, Logesh Kumar Natarajan

Wayne State University Dissertations

This dissertation presents a structure-borne noise analysis technology that is focused on providing a cost-effective noise reduction strategy. Structure-borne sound is generated or transmitted through structural vibration; however, only a small portion of the vibration can effectively produce sound and radiate it to the far-field. Therefore, cost-effective noise reduction is reliant on identifying and suppressing the critical vibration components that are directly responsible for an undesired sound. However, current technologies cannot successfully identify these critical vibration components from the point of view of direct contribution to sound radiation and hence cannot guarantee the best cost-effective noise reduction.

The technology developed …

Evaluation, Adaptation And Validation Of A Model To Predict Grass Growth In Ireland, Christina Hurtado Uria

Theses

Budgeting grass supply allows producers to minimise the quantity of purchased feed required in the diet of grazing livestock. One tool for managing grass supply could be a mathematical model that can simulate grass growth. The development of such a model would allow better management around the variability of feed supply and help identify feed surpluses and deficits, and therefore increase the accuracy of management decisions. This would be a key feature of profitable milk and meat production systems in the future which will be hugely important as global food demand increases due to population growth. It is forecasted that …

Gaussian Amicable Pairs, Ranthony Ashley Clark

Online Theses and Dissertations

Amicable pairs are two integers where the sum of the proper divisors of one is the other and vice versa. Since the Gaussian integers have many of the properties of the regular integers, we sought to discover whether there exist any pairs of Gaussian integers with the same property. It turns out that they do exist. In fact, some of the normal amicable pairs carry over as Gaussian amicable pairs. Also discovered are pairs that have a complex part.

Applications Of Leggett Williams Type Fixed Point Theorems To A Second Order Difference Equation, Charley Lockhart Seelbach

Online Theses and Dissertations

Using extensions of the Leggett-Williams fixed-point theorem, we prove the existence of solutions for a class of second-order difference equations with Dirichlet boundary conditions. We present these fixed point theorems and then show what conditions have to be met in order to satisfy the theorem. Finally, we provide specific examples to show the hypotheses of the theorems do not contradict one another.

Effective Methods Of Formative Assessment, Chelse Rae Bugg

Online Theses and Dissertations

The purpose of this research is to explore the implementation of formative assessment in the mathematics classroom. Formative assessment is considered to be any data-driven activity that an educator uses to help guide and improve instruction. While there is an abundance of research that concludes that formative assessment does indeed improve student achievement, practical methods of implementation are not thoroughly discussed. To partially determine which methods of formative assessment most positively impact student achievement, a study was conducted at Lafayette High School. The researcher compared two popular methods of formative assessment: daily exit slips and unit probing (pre-, middle-, and …

Increasing Automaticity, Sara Burns

Online Theses and Dissertations

Automaticity is defined as the process of developing fluency in mathematics and the ability to answer a basic math problem routinely. Automaticity is one of the most important skills that a student can possess in mathematics. While there are many ways that an educator can implement strategies to increase automaticity in the classroom, the purpose of this study was to determine which of these methods of implementation is more effective: requiring students to practice automaticity three times per week or requiring students to practice automaticity five times per week.

Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem, Sarah Schulz King`

Online Theses and Dissertations

The existence of smallest positive eigenvalues is established for the linear differential equations $u^{(4)}+\lambda_{1} q(t)u=0$ and $u^{(4)}+\lambda_{2} r(t)u=0$, $0\leq t \leq 1$, with each satisfying the boundary conditions $u(0)=u'(p)=u''(1)=u'''(1)=0$ where $1-\frac{\sqrt{3}}{3}\le p < 1$. A comparison theorem for smallest positive eigenvalues is then obtained. Using the same theorems, we will extend the problem to the fifth order via the Green's Function and again via Substitution. Applying the comparison theorems and the properties of $u_0$-positive operators to determine the existence of smallest eigenvalues. The existence of these smallest eigenvalues is then applied to characterize extremal points of the differential equation $u^{(4)} + q(t)u = 0$ satisfying boundary conditions $u(0) = u'(p) = u''(b) = u'''(b)= 0$ where $1-\frac{

Machine Learning And The Perceptron Algorithm, John Travis Shrontz

Summer Community of Scholars Posters (RCEU and HCR Combined Programs)

No abstract provided.

Counting Links And Knots In Complete Graphs, Loren Abrams, Blake Mellor, Lowell Trott

Mathematics, Statistics and Data Science Faculty Works

We investigate the minimal number of links and knots in embeddings of complete partite graphs in S³. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links in an embedding of K_4,4,1 is 74. We also provide exact values or bounds on the minimal number of knots for all complete partite graphs with 8 vertices.

Congruence Classes Of 2-Adic Valuations Of Stirling Numbers Of The Second Kind, Curtis Bennett, Edward Mosteig

Mathematics, Statistics and Data Science Faculty Works

We analyze congruence classes of S(n,k), the Stirling numbers of the second kind, modulo powers of 2. This analysis provides insight into a conjecture posed by Amdeberhan, Manna and Moll, which those authors established for k at most 5. We provide a framework that can be used to justify the conjecture by computational means, which we then complete for values of k between 5 and 20.

Twisted Alexander Polynomials Of 2-Bridge Knots, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

We investigate the twisted Alexander polynomial of a 2-bridge knot associated to a Fox coloring. For several families of 2-bridge knots, including but not limited to, torus knots and genus-one knots, we derive formulae for these twisted Alexander polynomials. We use these formulae to confirm a conjecture of Hirasawa and Murasugi for these knots.

Torsion In One-Term Distributive Homology, Alissa S. Crans, Józef H. Przytycki, Krzysztof K. Putyra

Mathematics, Statistics and Data Science Faculty Works

The one-term distributive homology was introduced by J.H.Przytycki as an atomic replacement of rack and quandle homology, which was first introduced and developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and M.Saito. This homology was initially suspected to be torsion-free, but we show in this paper that the one-term homology of a finite spindle can have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their homology precisely. In addition, we show that any finite group can appear as the torsion subgroup of the first homology of some finite spindle. Finally, …

Cohomology Of Frobenius Algebras And The Yang-Baxter Equation, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Enver Karadayi, Masahico Saito

Mathematics, Statistics and Data Science Faculty Works

A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions in analogy with Hochschild cohomology of bialgebras based on deformation theory. Concrete computations are provided for key examples. Skein theoretic constructions give rise to solutions to the Yang-Baxter equation using multiplications and comultiplications of Frobenius algebras, and 2-cocycles are used to obtain deformations of R-matrices thus obtained.

A Method Based On Total Variation For Network Modularity Optimization Using The Mbo Scheme, Huiyi Hu, Thomas Laurent, Mason A. Porter, Andrea L. Bertozzi

Mathematics, Statistics and Data Science Faculty Works

The study of network structure is pervasive in sociology, biology, computer science, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups of nodes called “communities.” One popular approach to finding communities is to maximize a quality function known as modularity to achieve some sort of optimal clustering of nodes. In this paper, we interpret the modularity function from a novel perspective: we reformulate modularity optimization as a minimization problem of an energy functional that consists of a total variation term and an $\ell_2$ balance term. By employing numerical techniques …

How Ideas Grow: Critical Mass In The Linear Threshold Model, Hossein Alidaee

Mathematics, Statistics, and Computer Science Honors Projects

We study how ideas spread through a social network using the Linear Threshold Model. Each node i on the complete graph K_n is given a threshold Ɵ_i chosen uniformly at random from (0, 1]. This threshold indicates the fraction of the social network that must be active (or believe the idea) prior to node i becoming active. We start with an activated group of early adopters, called the seed set. Considering various scenarios, we use the probabilistic method to find lower bounds on size of a seed set which guarantees that all nodes become active with high …

Students' Development And Use Of Internal Representations When Solving Algebraic Tasks, Laban J. Cross

Theses and Dissertations

The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for examining the internalization patterns of school-aged children, gain a deeper understanding of how these internal representations are developed and used, and search for internalization patterns associated with successful generalizations.

Semi-structured interviews were conducted with six sixth-grade students and six tenth-grade students. During these interviews the students were asked to solve a series of …

The Mc-Dagum Distribution And Its Statistical Properties With Applications, Broderick O. Oluyede, Sasith Rajasooriya

Mathematical Sciences: Faculty Publications

In this paper, a new class of distributions called Mc-Dagum distribution is proposed. This class of distributions contains several distributions such as beta-Dagum, beta-Burr III, beta-Fisk, Dagum, Burr III and Fisk distributions as special cases. The hazard function, reverse hazard function, moments, mean residual life function, Renyi entropy and Fisher information are obtained. Lorenz, Bonferroni and Zenga curves are derived. Maximum likelihood estimates of the model parameters and numerical examples are given to illustrate the usefulness of the proposed class of distributions.

Identifying Requirements For The Invasion Of A Tick Species And Tick-Borne Pathogen Through Ticksim, Holly Gaff, Robyn Nadolny

Biological Sciences Faculty Publications

Ticks and tick-borne diseases have been on the move throughout the United State over the past twenty years. We use an agent-based model, TICKSIM, to identify the key parameters that determine the success of invasion of the tick and if that is successful, the success of the tick-borne pathogen. We find that if an area has competent hosts, an initial population of ten ticks is predicted to always establish a new population. The establishment of the tick-borne pathogen depends on three parameters: the initial prevalence in the ten founding ticks, the probability that a tick infects the longer-lived hosts and …

A Comparison Of Two Teaching Methods For Pediatric Medication Administration: Multimedia And Text-Based Modules, Renee Granados

Doctoral Dissertations

A Comparison of Two Teaching Methods for Pediatrics: Multimedia and Text-based Modules to Teach Pediatric Medication Administration

Nurse educators are in a position to design and develop effective methods that consider the cognitive structures and how the mind processes information to teach pediatric medication content to nursing students. The majority of methods teaching medication administration use only one mode: the visual mode. One mode to present leaning material does not take advantage of the additive effects of using two modes to present learning material.

The purpose of the study was to compare the effectiveness of two teaching methods to present …

Pressure Poisson Method For The Incompressible Navier-Stokes Equations Using Galerkin Finite Elements, John Cornthwaite

College of Graduate Studies: Theses & Dissertations

In this thesis we examine the Navier-Stokes equations (NSE) with the continuity equation replaced by a pressure Poisson equation (PPE). Appropriate boundary conditions are developed for the PPE, which allow for a fully decoupled numerical scheme to recover the pressure. The variational form of the NSE with PPE is derived and used in the Galerkin Finite Element discretization. The Galerkin finite element method is then used to solve the NSE with PPE. Moderate accuracy is shown.

Simplicial Complexes Obtained From Qualitative Probability Orders, Paul H. Edelman, Tatiana Gvozdeva, Arkadii Slinko

Vanderbilt Law School Faculty Publications

The goal of this paper is to introduce a new class of simplicial complexes that naturally generalize the threshold complexes. These will be derived from qualitative probability orders on subsets of a finite set that generalize subset orders induced by probability measures. We show that this new class strictly contains the threshold complexes and is strictly contained in the shifted complexes. We conjecture that this class of complexes is exactly the set of strongly acyclic complexes, a class that has previously appeared in the context of cooperative games. Beyond the results themselves, this new class of complexes allows us to …

Optimization Problem In Single Period Markets, Tian Jiang

Electronic Theses and Dissertations

There had been a number of researches that investigated on the security market without transaction costs. The focus of this research is in the area that when the security market with transaction costs is fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal. The research approach adopted in this thesis includes linear algebra and elementary probability. The thesis provides evidence that we can maximize expected utility function to achieve our goal (maximize expected return under certain risk tolerance). The main conclusions drawn from this study are under certain conditions the security market …

Nonparametric And Empirical Bayes Estimation Methods, Rida Benhaddou

Electronic Theses and Dissertations

In the present dissertation, we investigate two different nonparametric models; empirical Bayes model and functional deconvolution model. In the case of the nonparametric empirical Bayes estimation, we carried out a complete minimax study. In particular, we derive minimax lower bounds for the risk of the nonparametric empirical Bayes estimator for a general conditional distribution. This result has never been obtained previously. In order to attain optimal convergence rates, we use a wavelet series based empirical Bayes estimator constructed in Pensky and Alotaibi (2005). We propose an adaptive version of this estimator using Lepski’s method and show that the estimator attains …

Extensions Of S-Spaces, Bernd Losert

Electronic Theses and Dissertations

Given a convergence space X, a continuous action of a convergence semigroup S on X and a compactification Y of X, under what conditions on X and the action on X is it possible to extend the action to a continuous action on Y . Similarly, given a Cauchy space X, a Cauchy continuous action of a Cauchy semigroup S on X and a completion Y of X, under what conditions on X and the action on X is it possible to extend the action to a Cauchy continuous action on Y . We answer the first question for some …