Mathematics Commons^™

A Classification Of Real Indecomposable Solvable Lie Algebras Of Small Dimension With Codimension One Nilradicals, Alan R. Parry

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters.

In the first, we described the necessary concepts and definitions about Lie algebras as well as a few helpful theorems that are necessary to understand the project. We also reviewed many concepts from linear algebra that are essential to the research.

The second chapter was occupied with a description of how we went about classifying the Lie algebras. In particular, it outlined the basic premise of the classification: that we can use …

Use Of Logic Game To Improve High School Students' Logical Reasoning Skills : Results Of A Teaching Experiment, Frank Forte

Theses, Dissertations and Culminating Projects

High school students often struggle with the concept of logical reasoning. A study conducted with 37 ninth grade geometry students involved a teaching experiment. This study documented whether instruction on a logic game called the Color of the Board Game helped students’ logical reasoning skills, and if those skills could be reflected in a “‘pencil and paper” test. Each student in a control and treatment group received a pre-test with 25 multiple-choice logic questions and an open-ended question. Multiple-choice questions were based on geometry and contextual logic. The treatment group received the Color of the Board Instructional Unit between the …

Ets (Efficient, Transparent, And Secured) Self-Healing Service For Pervasive Computing Applications, Shameem Ahmed, Moushumi Sharmin, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

To ensure smooth functioning of numerous handheld devices anywhere anytime, the importance of self-healing mechanism cannot be overlooked. Incorporation of efficient fault detection and recovery in device itself is the quest for long but there is no existing self-healing scheme for devices running in pervasive computing environments that can be claimed as the ultimate solution. Moreover, the highest degree of transparency, security and privacy attainability should also be maintained. ETS Self-healing service, an integral part of our developing middleware named MARKS (Middleware Adaptability for Resource discovery, Knowledge usability, and Self-healing), holds promise for offering all of those functionalities.

Clinical Experience And Examination Performance: Is There A Correlation?, Gary L. Beck, Mihaela Teodora Matache, Carrie Riha, Katherine Kerber, Frederick A. Mccurdy

Mathematics Faculty Publications

Context  The Liaison Committee on Medical Education (LCME) requires there to be: ‘…comparable educational experiences and equivalent methods of evaluation across all alternative instructional sites within a given discipline’. It is an LCME accreditation requirement that students encounter similar numbers of patients with similar diagnoses. However, previous empirical studies have not shown a correlation between the numbers of patients seen by students and performance on multiple-choice examinations.

Objective  This study examined whether student exposure to patients with specific diagnoses predicts performance on multiple-choice examination questions pertaining to those diagnoses.

Methods  The Department of Pediatrics at the University of Nebraska Medical …

A Study To Ascertain The Effects Of The Connected Mathematics Project On Student Achievement In The Buffalo Public Schools, Darryl A. King

Mathematics Education Theses

This study examines the impact of The Connected Mathematics Project (CMP) on student achievement in the Buffalo School District. Student scores were compared for the Grade 8 2005 and 2006 NY State Assessments and the Grade 7 2006 NY State Assessment. Students taught with NY State Math Standards were the control group. Students taught with CMP curriculum were the experimental group. This study found mixed results in favor of the standards group.

Products Of Characters With Few Irreducible Constituents, Edith Adan-Bante

Faculty Publications

We study the solvable groups G that have an irreducible character χ ∈ Irr(G) such that χ^--χ has at most two nonprincipal irreducible constituents.

Local Effective Potential Theory: Nonuniqueness Of Potential And Wave Function, Viraht Sahni, Marlina Slamet, Xiao-Yin Pan

Physics Faculty Publications

In local effective potential energy theories such as the Hohenberg-Kohn-Sham density functional theory (HKS-DFT) and quantal density functional theory (Q-DFT) electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and in the mapping to a model …

Decomposing Vector Space Representations Of The Lie Algebras S[2c And S[2r, Brian W. Gleason

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

It is known that any finite-dimensional representation of a semi-simple Lie algebra is decomposable into a direct sum of irreducible representations. Here we prove some theoretical results that allow us to construct an efficient algorithm for computing such a decomposition for representations of s[2C and s[2R. We then implement this algorithm in a procedure for the computer algebra system Maple that will quickly and easily perform the decomposition. We also give several examples of this decomposition performed by the procedure in order to illustrate its advantages over calculations done ‘by hand'.

Dynamics Of Spatial Pattern Formation: Cases Of Spikes And Droplets, Yuya Sasaki

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis studies the gradient system that forms spatial patterns such that the minimum distances of pairs among various points are maximized in the end. As this problem innately involves singularity issues, an extended system of the gradient system is proposed. Motivated by the spatial pattern suggested by a numerical example, this extended system is applied to a three-point problem and then to a two-point problem in a quotient space of ℝ² modulo a lattice.

The Red Top Model: A Landscape-Scale Integrodifference Equation Model Of The Mountain Pine Beetle-Lodgepole Pine Forest Interaction, Justin Heavilin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Under normative conditions the mountain pine beetle (Dendroctonus ponderosae Hopkins) has played a regulating role in healthy lodgepole pine (Pinus contorta) forests. However, recently eruptive outbreaks that result from large pine beetle populations have destroyed vast tracts of valuable forest. The outbreaks in North America have received a great deal of attention from both the timber industry and government agencies as well as biologists and ecologists.

In this dissertation we develop a landscape-scaled integrodifference equation model describing the mountain pine beetle and its effect on a lodgepole pine forest. The model is built upon a stage-structured model …

Structural Properties Of Formal Polynomial Algebras In Noncommuting Or Nonassociating Indeterminates, Serge C. Ballif

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In order to enlarge the class of equations provided by traditional polynomials over a binary algebra A to a more useful class of equations, we introduce polynomials in noncommuting or nonassociating indeterminates. We discuss algebraic properties of these formal polynomial algebras and their accompanying polynomial function algebras. We present certain basis results for polynomial algebras, which are used to address the question of zero divisors in a polynomial algebra. We give an analog of the remainder theorem and the factor theorem for polynomials. Particular emphasis is placed on showing the difference between polynomials and polynomial functions. We also provide a …

A Method For Finding Standard Error Estimates For Rma Expression Levels Using Bootstrap, Gabriel Nicholas

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Oligonucleotide arrays are used in many applications. Affymetrix GeneChip arrays are widely used. Before researchers can use the information from these arrays, the raw data must be transformed and summarized into a more meaningful and usable form. One of the more popular methods for doing so is RMA (Robust Multi-array Analysis).

A problem with RMA is that the end result (estimated gene expression levels) is based on a fairly complicated process that is unusual. Specifically, there is no closed-form estimate of standard errors for the estimated gene expression levels. The current recommendation is to use a naive estimate for the …

Black-Scholes And Extended Black-Scholes Models: A Comparative Statistical Analysis, Bradley Thomas Bush

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Much research has been done on options pricing. Black and Scholes [12] set the benchmark in 1973 with their model for arbitrage-free, risk-neutral options valuation. Arbitrage-free refers to a market environment where prices are such that trading opportunities with no risk do not exist and risk-neutral commodities earn a risk free interest rate. Since then the literature has seen a multitude of models improving the fit of the traditional Black -Scholes (BS) model. A brief overview of options and these models is given. A derivation and discussion of BS is followed by a derivation and discussion of the Extended Black-Scholes …

The Effects Of Using The Geometer’S Sketchpad On Student Learning Of Transformations In The Coordinate Plane, Leeann Elizabeth Gennett

Theses, Dissertations and Culminating Projects

The primary purpose of this study was to investigate how grade nine honors geometry students and grade ten regular geometry students learn and retain information about three basic rigid geometric transformations with the support of the software package The Geometer’s Sketchpad in comparison to the traditional, non-software supported method of instruction.

The study was conducted in a high school with two tenth grade regular geometry classes and two ninth grade honors geometry classes. The researcher and another teacher each conducted a one-week instructional unit on the three basic, isometric transformations. Thirty-four students agreed to participate in the study. Nineteen students …

Reality Properties Of Conjugacy Classes In Algebraic Groups., Anupam Kumar Singh Dr.

Doctoral Theses

In this thesis we denote a field by k. We consider fields of characteristic not 2 unless stated otherwise. The notation ¯k and ks denotes an algebraic closure and separable closure of k respectively. The symbols Q, R, C will denote fields of rational, real, complex numbers respectively. The symbol Z will denote the set of integers. We denote by cd(k) the cohomological dimension of k.We use G to denote an algebraic group and G(k) to denote the group of k rational points of G. Sometimes we abuse notation and denote the group of ¯k points of G by G. …

2007 Sonia Kovalevsky Math For Girls Day Featured Workshop: Knot Theory, Association For Women In Mathematics, Lincoln University Of Missouri

Math for Girls Day Documents

2nd Annual Lincoln University Sonia Kovalevsky Math for Girls Day featured workshop by Mrs. Bernadette Turner on the topic of knot theory.

Anisotropic Diffusion Techniques On Synthetic Aperture Radar Data, Josef Vaughn De Allen, Emile Ganthier, Gnana Bhaskar Tenali

Mathematics and System Engineering Faculty Publications

Speckle in SAR imagery is a by-product of constructive and destructive interference between scatterers within a resolution cell. This speckle phenomenon gives SAR imagery a "noise-like" appearance and is often exploited in near angle and/or coherent stereo pairs. However, in many cases, this speckle is unwanted and can be considered noise or interference. We use partial differential equation (PDE) methods for speckle mitigation in detected imagery and the collected complex image data. In particular, we study the effects of non-linear anisotropic diffusion filters on collected SAR image data. In the past, anisotropic diffusion (AD) techniques have been successfully used in …

Anticipating Semilinear Spdes (International Conference Stochastic Analysis And Stochastic Geometry), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

Ua66 2007 Student Awards Ceremony, Wku Ogden College Of Science & Engineering

WKU Administration Documents

Program recognizing Ogden College students with brief list of activities for each student.

Squares Of Characters And Finite Groups, Edith Adan-Bante

Faculty Publications

Let G be a finite group and χ be an irreducible complex character. We study the character χ² in the case that χ(1) is a prime power.

Stable Algebras Of Entire Functions, Dan Coman, Evgeny A. Poletsky

Mathematics - All Scholarship

Suppose that h and g belong to the algebra B generated by the rational functions and an entire function f of finite order on Cⁿ and that h/g has algebraic polar variety. We show that either h/g in B or f = q₁e^p +q₂, where p is a polynomial and q¹, q² are rational functions. In the latter case, h/g belongs to the algebra generated by the rational functions, e^p and e^−p.

Anticipating Semilinear Spdes (International Conference Modern Perpspectives In Real And Stochastic Analysis), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

Complete Shrinking Ricci Solitons Have Finite Fundamental Group, William Wylie

Mathematics - All Scholarship

We show that if a complete Riemannian manifold supports a vector field such that the Ricci tensor plus the Lie derivative of the metric with respect to the vector field has a positive lower bound, then the fundamental group is finite. In particular, it follows that complete shrinking Ricci solitons and complete smooth metric measure spaces with a positive lower bound on the Bakry-Emery tensor have finite fundamental group. The method of proof is to generalize arguments of Garcia-Rio and Fernandez-Lopez in the compact case.

Suboptimal Minimax Design Of Constrained Parabolic Systems With Mixed Boundary Control, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in mixed (Robin) boundary conditions. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We design and justify an easily implemented suboptimal structure of the feedback boundary regulator and compute its optimal parameters ensuring the required state performance and robust stability of the nonlinear closed-loop control system on the infinite horizon.

An Assembly Language I.D.E. To Engage Students Of All Levels: Tutorial Presentation, Pete Sanderson, Kenneth Vollmar

Mathematics Faculty Scholarship

MIPS assembly language is widely taught in computer organization and related courses due to its elegant design and ease of learning. In this workshop, participants will explore varied uses of the MARS integrated development environment (IDE) and simulator for MIPS assembly language programming. Basic exploration is guided by a set of MIPS programming exercises to illustrate MARS use and its extensive and intuitive interactive debugging capabilities. The next level of exploration will introduce MARS "tools", applications that can interact with executing MIPS programs by observing the simulated MIPS memory and registers. Exercises will demonstrate how currently-available MARS tools can be …

A Combinatorial Proof Of Vandermonde's Determinant, Arthur T. Benjamin, Gregory P. Dresden

All HMC Faculty Publications and Research

No abstract provided in this article.

Rationalized Evaluation Subgroups Of A Map Ii: Quillen Models And Adjoint Maps, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

We identify the long exact sequence induced on rational homotopy groups by the evaluation map ω: map(X, Y ; f)→Y and in particular the rationalization of the evaluation subgroups off, in terms of derivations of Quillen models and adjoint maps. We consider a generalization of a question of Gottlieb within the context of rational homotopytheory. We also study the rationalization of the G-sequence of a map. In a separate result of independent interest, we give an explicit Quillen minimal model of a product A×X, in the case in which A is a rational co-H-space.

A Variational Principle For Discontinuous Potentials, Anna Mummert

Mathematics Faculty Research

Let $X$ be a compact space, $f\colon X \to X$ a continuous map, and $\Lambda \subset X$ be any $f$-invariant subset. Assume that there exists a nested family of subsets $\{\Lambda_l\}_{l \geq 1}$ that exhaust $\Lambda$, that is $\Lambda_l \subset\Lambda_{l+1}$ and $\Lambda =\bigcup_{l \geq 1} \Lambda_l$. Assume that the potential $\varphi \colon X \to \mathbb{R}$ is continuous on the closure of each $\Lambda_l$ but not necessarily continuous on $\Lambda$. We define the topological pressure of $\varphi$ on $\Lambda$. This definition is shown to have a corresponding variational principle. We apply the topological pressure and variational principle to systems with non-zero …

Existence To Singular Boundary Value Problems With Sign Changing Nonlinearities Using An Approximation Method Approach, Haishen Lu, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

This paper studies the existence of solutions to the singular boundary value problem {−u′′=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), {−u″=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), , where g: (0, 1) × (0, ∞) → ℝ and h: (0, 1) × [0, ∞) → [0, ∞) are continuous. So our nonlinearity may be singular at t = 0, 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.

Preface

Communications on Stochastic Analysis

No abstract provided.