Mathematics Commons^™

Positive Solutions Of Nonlocal Boundary Value Problem For Higher Order Fractional Differential System, Mujeeb Ur Rehman, Rahmat Ali Khan, Paul W. Eloe

Mathematics Faculty Publications

In this paper, we study existence and multiplicity results for a coupled system of nonlinear nonlocal boundary value problems for higher order fractional differential equations of the type (see PDF) where (see PDF) is Caputo fractional derivative. We employ the Guo-Krasnosel’skii fixed point theorem to establish existence and multiplicity results for positive solutions. We derive explicit intervals for the parameters _ and μ for which the system possess the positive solutions or multiple positive solutions. Examples are included to show the applicability of the main results.

Platonic Solids In Z3, Eugen J. Ionascu

Faculty Bibliography

Extending previous results on a characterization of all equilateral triangle in space having vertices with integer coordinates (“in Z 3 ”), we look at the problem of characterizing all regular polyhedra (Platonic Solids) with the same property. To summarize, we show first that there is no regular icosahedron/ dodecahedron in Z 3 . On the other hand, there is a finite (6 or 12) class of regular tetrahedra in Z 3 , associated naturally to each nontrivial solution (a, b, c, d) of the Diophantine equation a 2 + b 2 + c 2 = 3d 2 and for every …

Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luís, Henrique Oliveira

Mathematics Faculty Research

This survey contains the most updated results on the dynamics of periodic difference equations or discrete dynamical systems this time. Our focus will be on stability theory, bifurcation theory, and on the effect of periodic forcing on the welfare of the population (attenuance versus resonance). Moreover, the survey alludes to two more types of dynamical systems, namely, almost periodic difference equations and stochastic di®erence equations.

Minimax And Maximin Fitting Of Geometric Objects To Sets Of Points, Yan B. Mayster

Electronic Theses and Dissertations

This thesis addresses several problems in the facility location sub-area of computational geometry. Let S be a set of n points in the plane. We derive algorithms for approximating S by a step function curve of size k < n, i.e., by an x-monotone orthogonal polyline ℜ with k < n horizontal segments. We use the vertical distance to measure the quality of the approximation, i.e., the maximum distance from a point in S to the horizontal segment directly above or below it. We consider two types of problems: min-ε, where the goal is to minimize the error for a …

Approximate Transversals Of Latin Squares, Jon Kyle Pula

Electronic Theses and Dissertations

A latin square of order n is an n by n array whose entries are drawn from an n-set of symbols such that each symbol appears precisely once in each row and column. A transversal of a latin square is a subset of cells that meets each row, column, and symbol precisely once.

There are many open and difficult questions about the existence and prevalence of transversals. We undertake a systematic study of collections of cells that exhibit regularity properties similar to those of transversals and prove numerous theorems about their existence and structure. We hope that our results …

A Comparison Of Category And Lebesgue Measure, Adam Matthew Moore

Theses Digitization Project

This study, Lebesgue measure and category have proved to be useful tools in describing the size of sets. The notions of category and Lebesgue measure are commonly used to describe the size of a set of real numbers (or of a subset of Rn). Although cardinality is also a measure of the size of a set, category and measure are often the more important gauges of size when studying properties of classes of real functions, such as the space of continuous functions or the space of derivatives.

Symmetric Generation Of M₂₂, Bronson Cade Lim

Theses Digitization Project

This study will prove the Mathieu group M₂₂ contains two symmetric generating sets with control grougp L₃ (2). The first generating set consists of order 3 elements while the second consists of involutions.

A Study On The Modular Structures Of Z₂S₃ And Z₅S₃, Bethany Michelle Tasaka

Theses Digitization Project

This project is a study of the properties of the modules Z₂S₃ and Z₅S₃, which are examined both as modules over themselves and as modules over their respective integer fields. Each module is examined separately since they each hold distinct properties. The overall goal is to determine the simplicity and semisimplicity of each module.

Symmetric Presentation Of Finite Groups, Thuy Nguyen

Theses Digitization Project

The main goal of this project is to construct finite homomorphic images of monomial infinite semi-direct products which are called progenitors. In this thesis, we provide an alternative convenient and efficient method. This method can be applied to many groups, including all finite non-abelian simple groups.

Monitoring Radiation Use In Cardiac Fluoroscopy Imaging Procedures, Nathaniel Stevens, S H. Steiner, I R. Smith, R J. Mackay

Mathematics

Objective: Timely identification of systematic changes in radiation delivery of an imaging system can lead to a reduction in risk for the patients involved. However, existing quality assurance programs involving the routine testing of equipment performance using phantoms are limited in their ability to effectively carry out this task. To address this issue we propose the implementation of an ongoing monitoring process that utilizes procedural data to identify unexpected large or small radiation exposures for individual patients, as well as to detect persistent changes in the radiation output of imaging platforms.

Methods: Data used in this study were obtained from …

Planning And Analysis Of Measurement Reliability Studies, S H. Steiner, Nathaniel Stevens, R Browne, R J. Mackay

Mathematics

In the traditional plan for assessing the reliability of a measurement system, a number of raters each measure the same group of subjects. If the system has a large number of raters, we recommend a new set of plans that have two advantages over the traditional plan. First, the proposed plans provide greater precision for estimating the intraclass correlation coefficient with the same total number of measurements. Second, the plans are flexible and can be adapted to constraints on the number of times any subject can be assessed or the number of times any rater can make an assessment. We …

A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved

Theses Digitization Project

This project demonstrates how an elliptic curve f defined by invariance under two involutions can be represented by the locus of circumcenters of isosceles triangles in the hyperbolic plane, using inversive model.

Constructible Numbers: Euclid And Beyond, Joshua Scott Marcy

Theses Digitization Project

The purpose of this project is to demonstrate first why trisection for an arbitrary angle is impossible with compass and straightedge and second how trisection does become possible if a marked ruler is used instead.

Geodesics Of Surface Of Revolution, Wenli Chang

Theses Digitization Project

The purpose of this project was to study the differential geometry of curves and surfaces in three-dimensional Euclidean space. Some important concepts such as, Curvature, Fundamental Form, Christoffel symbols, and Geodesic Curvature and equations are explored.

Fixed Block Configuration Gdds With Block Size 6 And (3, R)-Regular Graphs , Melanie R. Laffin

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

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis.

In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ₁; λ₂). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s …

Twelfth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Imaginary Numbers, Unsolvable Equations, And Newton's Method (Abstract), Jeffrey Diller

Kenneth C. Schraut Memorial Lectures

You might have been led to believe that math is all about solving equations. Sadly, however, most equations can't actually be solved. The best one can do is to try to approximate their solutions.

Flipping The Winner Of A Poset Game, Adam O. Kalinich '12

Student Publications & Research

Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element and all elements greater than it, and whoever takes the last element wins. Examples of poset games include Nim and Chomp. We investigate the complexity of computing which player of a poset game has a winning strategy. We give an inductive procedure that modifies poset games to change the nim-value which informally captures the winning strategies in the game. For a generic …

Semi-Direct Galois Covers Of The Affine Line, Linda Gruendken, Laura L. Hall-Seelig, Bo-Hae Im, Ekin Ozman, Rachel Pries, Katherine Stevenson

Mathematics Faculty Publications

Let k be an algebraically closed field of characteristic p > 0. Let G be a semi-direct product of the form (Z/`Z) b o Z/pZ where b is a positive integer and ` is a prime distinct from p. In this paper, we study Galois covers ψ : Z → P 1 k ramified only over ∞ with Galois group G. We find the minimal genus of a curve Z which admits a covering map of this form and we give an explicit formula for this genus in terms of ` and p. The minimal genus occurs when b equals the …

Another Proof Of The Existence A Dedekind Complete Totally Ordered Field, James F. Hall, Todor D. Todorov

Mathematics

We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind complete totally ordered field or, equivalently, to another proof of the consistency of the axioms of the real numbers. We believe that our construction is simpler and shorter than the classical Dedekind construction and Cantor construction of such fields assuming some basic familiarity with non-standard analysis.

Tilings, Patterns And Technology, Ma. Louise Antonette N. De Las Peñas, Angela Fatima H. Guzon

Mathematics Faculty Publications

In this paper we discuss various situations where tilings and patterns, with the aid of technology, facilitate the teaching of mathematics and serve as tools in understanding and developing new mathematical ideas. We also illustrate how technology makes possible cultural connections in the study of mathematics using Islamic tilings and patterns.

Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu

Pomona Faculty Publications and Research

The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their …

Review: Nearly Invariant Subspaces For Backwards Shifts On Vector-Valued Hardy Spaces, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Review: Massey Products On Cycles Of Projective Lines And Trigonometric Solutions Of The Yang-Baxter Equations, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Unitary Equivalence To A Complex Symmetric Matrix: A Modulus Criterion, Stephan Ramon Garcia, Daniel E. Poore '11, Madeline K. Wyse '11

Pomona Faculty Publications and Research

We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We compare our approach to several existing methods [1, 19, 20] and present a number of examples.

Nilpotent Elements And Reduced Rings, Junchao Wei, Libin Li

Turkish Journal of Mathematics

In this paper, we show the following results: (1) R is a min-leftsemicentral ring if and only if eR(1-e)Re=0 for all e \in ME_l(R); (2) Quasi-normal rings, NI rings and weakly reversible rings are all min-leftsemicentral ring; (3) R is left MC2 ring if and only if aRe=0 implies eRa=0 for all e \in ME_l(R) and a \in R if and only if every projective simple left R-module is MUP-injective; (4) R is reduced if and only if R is n-regular and quasi-normal if and only if R is n-regular and weakly reversible; (5) R is strongly regular if and …

The Cyclicity Of The Period Annulus Of A Quadratic Reversible System With One Center Of Genus One, Linping Peng, Yannan Sun

Turkish Journal of Mathematics

This paper is concerned with a quadratic reversible and non-Hamiltonian system with one center of genus one. By using the properties of related elliptic integrals and the geometry of some planar curves defined by them, we prove that the cyclicity of the period annulus of the considered system under small quadratic perturbations is two. This verifies Gautier's conjecture about the cyclicity of the related period annulus.

2011 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

Geologic Map Of The Ganiki Planitia Quadrangle (V–14), Venus, Eric B. Grosfils, Sylvan M. Long, Elizabeth M. Venechuk, Debra M. Hurwitz, Joseph W. Richards, Brian Kastl, Dorothy E. Drury, Johanna S. Hardin

Pomona Faculty Publications and Research

Our current research focuses on addressing four specific questions. Has the dominant style of volcanic expression within the quadrangle varied in a systematic fashion over time? Does the tectonic deformation within the quadrangle record significant regional patterns that vary spatially or temporally, and if so what are the scales, orientations and sources of the stress fields driving this deformation? If mantle upwelling and downwelling have played a significant role in the formation of Atla Regio and Atalanta Planitia as has been proposed, does the geology of Ganiki Planitia record evidence of northwest-directed lateral mantle flow connecting the two sites? Finally, …

Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis

Mathematics Faculty Publications

During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the …