Mathematics Commons^™

Some Nonparametric And Semiparametric Methods For Discriminant Analysis., Anil Kumar Ghosh Dr.

Doctoral Theses

Discriminant analysis (see e.g., Devijver and Kittler, 1982; Duda, Hart and Stork, 2000; Hastle, Tibahirani and Friedman, 2001) deals with the separation of different groups of obaervationa and allocation of a new oboervation to one of the previously delined grouga. In a J-class discriminant analysis problem, we usually hae a training sample of the form {(xk, ck) : k = 1,2,...,N}, where xk = (Ik1,Ik2,...J) is a d-dimensional measarement vector, and ca € {1,2,...,J} is its class label. On the basis of thia training sample, one aims to form a decision rule d(x) : Rd + (1,2,...,J} for clasifying the …

Set Differential Equations With Causal Operators, Zahia Drici

Mathematics and System Engineering Faculty Publications

We obtain some basic results on existence, uniqueness, and continuous dependence of solutions with respect to initial values for set differential equations with causal operators.

Relative Difference Sets In 2-Groups : A Group Cohomological Viewpoint, Brian Wyman

Honors Theses

No abstract provided.

A Look At The Astrolabe, Emily Storrar

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors program.

Ecological Niching In An Interactive Simulation, Ryan T. Webb

Honors Theses

Our goal is to create a simulation platform for the study of ecological niching that can be extended to suit the needs of biological research. Ecological niching and the accompanying evolutionary process of speciation are difficult to observe in situ, which makes them prime candidates for study via the methods of computer simulation. To this end, we have created an interactive, real-time ecosystem simulation based on the standard predator/prey interaction model, in which interacting populations of organisms exhibit swarming behavior. We hope to provide the basic simulation components necessary to bring about niching and speciation, that may be extended for …

Local Theory Of Almost Split Sequences For Comodules, William Chin, Mark Kleiner, Declan Quinn

Mathematics - All Scholarship

We show that almost split sequences in the category of comodules over a coalgebra with finite-dimensional right-hand term are direct limits of almost split sequences over finite dimensional subcoalgebras. In previous work we showed that such almost split sequences exist if the right hand term has a quasifinitely copresented linear dual. Conversely, taking limits of almost split sequences over finte-dimensional comodule categories, we then show that, for countable-dimensional coalgebras, certain exact sequences exist which satisfy a condition weaker than being almost split, which we call ``finitely almost split''. Under additional assumptions, these sequences are shown to be almost split in …

Lower Bounds For Simplicial Covers And Triangulations Of Cubes, Adam Bliss '03, Francis E. Su

All HMC Faculty Publications and Research

We show that the size of a minimal simplicial cover of a polytope P is a lower bound for the size of a minimal triangulation of P, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their …

A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu

All HMC Faculty Publications and Research

In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …

Actions Of Sl(N,Z) On Homology Spheres, Kamlesh Parwani

Faculty Research and Creative Activity

Any continuous action of SL(n,Z), where n > 2, on a r-dimensional mod 2 homology sphere factors through a finite group action if r < n - 1. In particular, any continuous action of SL(n+2,Z) on the n-dimensional sphere factors through a finite group action.

Actions Of Sl(N,Z) On Homology Spheres, Kamlesh Parwani

Faculty Research and Creative Activity

Any continuous action of SL(n,Z), where n > 2, on a r-dimensional mod 2 homology sphere factors through a finite group action if r < n - 1. In particular, any continuous action of SL(n+2,Z) on the n-dimensional sphere factors through a finite group action.

Double Arrays, Triple Arrays And Balanced Grids, John P. Mcsorley, Nicholas C. Phillips, Walter D. Wallis, Joseph L. Yucas

Articles and Preprints

Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids.

Spaces Of Polygons In The Plane And Morse Theory, Don H. Shimamoto, C. Vanderwaart

Mathematics & Statistics Faculty Works

No abstract provided.

Developing A B -Tagging Algorithm Using Soft Muons At Level-3 For The Dø Detector At Fermilab, Mayukh Das

Doctoral Dissertations

The current data-taking phase of the DØ detector at Fermilab, called Run II, is designed to aid the search for the Higgs Boson. The neutral Higgs is postulated to have a mass of 117 GeV. One of the channels promising the presence of this hypothetical particle is through the decay of b-quark into a muon. The process of identifying a b-quark in a jet using muon as a reference is b-tagging with a muon tag.

At the current data taking and analysis rate, it will take long to reach the process of identifying valid events. The triggering mechanism of the …

Obstruction Sets For Classes Of Cubic Graphs, Joshua Hughes

Doctoral Dissertations

This dissertation establishes two theorems which characterize the set of minimal obstructions for two classes of graphs. A minimal obstruction for a class of graphs is a graph that is not in the class but every graph that it properly contains, under some containment relation, is in the class. In Chapter 2, we provide a characterization of the class of cubic outer-planar graphs in terms of its minimal obstructions which are also called cubic obstructions in this setting. To do this, we first show that all the obstructions containing loops can be obtained from the complete set of loopless obstructions …

A Preface To Gutstein Generalized: A Philosophical Debate, Johnny W. Lott

The Mathematics Enthusiast

The National Council of Teachers of Mathematics (NCTM) has taken a very firm stand on the issue of equity in mathematics education. Not only is equity incorporated in the Curriculum and Evaluation Standards for School Mathematics (1989) and Principles and Standards for School Mathematics (2000), equity is the first plank of NCTM’s legislative platform.

Response To Gutstein Generalized- A Philosophical Debate, Eric Gutstein

The Mathematics Enthusiast

It is a pleasure, challenge, and an honor to respond to the thoughtful and innovative debate started by Braver, Micklus, Bradley, van Spronsen, Allen, & Campbell on teaching mathematics for social justice. They take seriously the issues in, and raise many interesting views about, my article, Teaching and Learning Mathematics for Social Justice in an Urban Latino School (JRME, January, 2003). I would like to respond to (connected) two points in particular: the relationship of functional to critical literacies, and the relationship of “critical thinking” in mathematics to learning mathematics for social justice. However, I would first like to clarify …

Taxi Cab Geometry: History And Applications!, Chip Reinhardt

The Mathematics Enthusiast

We will explore three real life situations proposed in Eugene F. Kraus e's book Taxicab Geometry. First a dispatcher for Ideal City Police Department receives a report of an accident at X = (-1,4). There are two police cars located in the area. Car C is at (2,1) and car D is at (-1,-1). Which car should be sent? Second there are three high schools in Ideal city. Roosevelt at (2,1), Franklin at ( -3,-3) and Jefferson at (-6,-1). Draw in school district boundaries so that each student in Ideal City attends the school closet to them. For the third …

Tme Volume 2, Number 1

The Mathematics Enthusiast

No abstract provided.

A Numerical Method For Obtaining An Optimal Temperature Distribution In A 3d Triple-Layered Cylindrical Skin Structure, Le Zhang

Doctoral Dissertations

In recent years, it has been interesting to research hyperthermia combined with radiation and cytotoxic drugs to enhance the killing of tumors. The crucial problem is that when heating the tumor tissues, one needs to keep the surrounding normal tissue below a temperature that will produce harm. Thus, it is important to obtain the temperature field of the entire treatment region. The objective of this dissertation is to develop a numerical model for obtaining an optimal temperature distribution in a 3D triple-layered cylindrical skin structure. To this end, we pre-specify the temperatures to be obtained at the center and perimeter …

Cardano's Solution To The Cubic: A Mathematical Soap Opera, Kacee Ballou

The Mathematics Enthusiast

Through this research into the solution of the cubic, I hope to learn the thoughts of mathematicians during this period of history. This knowledge must be conveyed in a way that is historically and mathematically accurate, yet comprehensible and readily available to use in a class of eighth grade math students. It is my wish that as we begin to delve into the world of algebraic and graphical solutions to the problems in the eighth grade text, students will be able to make a connection with this information to that they are currently using to solve their problems. They should …

Global Optimality Conditions In Mathematical Programming And Optimal Control, Pariwat Pacheenburawana

Dissertations

We derive new first-order necessary and sufficient optimality conditions characterizing global minimizers in mathematical programming and optimal controlproblems. These conditions are based on level sets of an objective functional and they do not assume special structure of a problem (convexity, linearity, etc.). For a mathematical programming problem of minimization of a smooth functional on some compact convex set with equality nonlinear constraints, we derive first-order optimality conditions in the form of a generalized Lagrange multiplier rule. This rule should hold for any point from the level set of the objective functional corresponding to a global minimizer. We demonstrate that these …

An Excel Application For Valuing European Options With Monte Carlo Analysis, Tom Arnold, Stephen C. Henry

Finance Faculty Publications

By developing the basic intuition of how Monte Carlo simulation works within an Excel spreadsheet framework, this paper allows the undergraduate student to use Monte Carlo simulation techniques to price European style options without additional sophisticated software. Further, the skills and intuition developed provide the basis for much more complex simulation techniques.

Structure Preserving Algorithms For Computing The Symplectic Singular Value Decom Position, Archara Chaiyakarn

Dissertations

In this thesis we develop two types of structure preserving Jacobi algorithms for com puting the symplectic singular value decomposition of real symplectic matrices and complex symplectic matrices. Unlike general purpose algorithms, these algorithms produce symplectic structure in all factors of the singular value decomposition.

Our first algorithm uses the relation between the singular value decomposition and the polar decomposition to reduce the problem of finding the symplectic singular value decomposition to th a t of calculating the structured spectral decomposition of a doubly structured m atrix. A Jacobi-like m ethod is developed to compute this doubly structured spectral decomposition. …

Stratification And Domination In Graphs And Digraphs, Ralucca M. Gera

Dissertations

In this thesis we combine the idea of stratification with the one of domination in graphs and digraphs, respectively.

A graph is 2-stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2-stratified graph rooted at some blue vertex v . An F -coloring of a graph G is a red-blue coloring of the vertices of G in which every blue vertexu belongs to a copy of F rooted at u . The F -domination number γ …

Nonautonomous Beverton-Holt Equations And The Cushing-Henson Conjectures, Saber Elaydi, Robert J. Sacker

Mathematics Faculty Research

In [3] Jim Cushing and Shandelle Henson published two conjectures (see Section 3) related to the Beverton-Holt difference equation (with growth parameter exceeding one), which said that the B-H equation with periodically varying coefficients (a) will have a globally asymptotically stable periodic solution and (b) the average of the state variable along the periodic orbit will be strictly less than the average of the carrying capacities of the individual maps. They had previously [2] proved both statements for period 2.

Editorial, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Action: Tell Me More Albert!, Jerry T. Baty, Virginia A.H. Mcclendon

The Mathematics Enthusiast

The new school year opens with the instructor cheerfully announcing to the students on the first day, “Good morning, class! Welcome to the fun of a new language called algebra”. He continues, “Today we are going to have a conversation about your success in this classroom. First, is the area of mathematics called algebra, necessary for your future?"

None of the students responds.

Gutstein Generalized- A Philosophical Debate: A Critical Commentary On Gutstein's (2003) Thesis For The Incorporation Of Social Justice In The Mathematics Curriculum, Seth Braver, Jane Micklus, Sheila Bradley, Hillary Van Spronsen, Samantha Allen, Vicki Campbell

The Mathematics Enthusiast

The Scene: A Courtroom
The Year: 2004 (old style), 15 (new style - After Standards)

The Grand Inquisitor mounts the podium, and addresses the Debaters standing silently before him. A large crowd fills the hall.

Inquisitor:
Ladies and Gentlemen! You have been summoned here today to present the final arguments for and against these propositions which have so vexed our society in recent months. Each of you represents a vision of the future of mathematics education. Ere the sun sets we shall fix our resolve to one vision or the other. The victors, I doubt not, shall lead us into …

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

Call For Papers

The Mathematics Enthusiast

No abstract provided.