Mathematics Commons^™

Structure Of Colored Complete Graphs Free Of Proper Cycles, Vincent E. Coll, Colton Magnant, Kathleen Ryan

Mathematical Sciences: Faculty Publications

For a fixed integer m, we consider edge colorings of complete graphs which contain no properly edge colored cycle Cm as a subgraph. Within colorings free of these subgraphs, we establish global structure by bounding the number of colors that can induce a spanning and connected subgraph. In the case of smaller cycles, namely C4,C5, and C6, we show that our bounds are sharp.

Full Newton-Step Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Antre M. Drummer, Ljiljana Miletić

Mathematical Sciences: Faculty Publications

In this paper we consider an Infeasible Full Newton-step Interior-Point Method (IFNS-IPM) for monotone Linear Complementarity Problems (LCP). The method does not require a strictly feasible starting point. In addition, the method avoids calculation of the step size and instead takes full Newton-steps at each iteration. Iterates are kept close to the central path by suitable choice of parameters. The algorithm is globally convergent and the iteration bound matches the best known iteration bound for these types of methods.

Rational Approximation On Compact Nowhere Dense Sets, Christopher Mattingly

Theses and Dissertations--Mathematics

For a compact, nowhere dense set X in the complex plane, C, define R^p(X) as the closure of the rational functions with poles off X in L^p(X, dA). It is well known that for 1 ≤ p < 2, R^p(X) = L^p(X) . Although density may not be achieved for p > 2, there exists a set X so that R^p(X) = L^p(X) for p up to a given number greater than 2 but not after. Additionally, when p > 2 we shall establish that the support of the annihiliating and …

Proof-Of-Concept For A Green Energy Linear Program For Optimizing Deployments, James M. Taylor, Betty Love

Mathematics Faculty Proceedings & Presentations

The US military has spent billions of dollars and sacrificed many lives in the effort to bring electrical power services and the fuel that drives the generators to forward-deployed bases in Afghanistan and Iraq over the past 10 years. In an effort to reduce some of these tremendous costs, the US military has considered using alternative energy sources to generate electricity and reduce costs and exposure of fuel truck convoys. While some research [10] has used detailed software packages to model the electrical demand and renewable energy production tradeoffs in this environment, the impact of operational constraints is not readily …

Numerical Ranges Of Composition Operators With Inner Symbols, Valentin Matache

Mathematics Faculty Publications

Operators on function paces acting by composition to the right with a fixed self-map φ of some set are called composition operators with the symbol φ. In this paper, composition operators on the Hilbert Hardy space over the unit disk are considered. The numerical ranges of composition operators with inner symbol of parabolic automorphic type of hyperbolic type are shown to be circular.

High Order Les For Supersonic Ramp Flow Control With Mvg, Yonghua Yan

Mathematics Dissertations - Archive

An implicitly implemented large eddy simulation by using the fifth order bandwidth-optimized WENO scheme is applied to make comprehensive studies on ramp flows with and without control at Mach 2.5 and Re=5760. Flow control in the form of microramp vortex generators (MVG) is applied. The results show that MVG can distinctly reduce the separation zone at the ramp corner and lower the boundary layer shape factor under the condition of the computation. A series of new findings are obtained about the MVG-ramp flow including the three-dimensional vortex structure generated by MVG. The mechanism about the formation vortex ring structure and …

Effects Of Vector Migration On Sylvatic Trypanosoma Cruzi Transmission, Britnee A. Crawford

Mathematics Dissertations - Archive

Vector-borne diseases have had a major impact on global health concerns since their discovery in the 1800's. A vector-borne disease is one transmitted to human or animal host via an invertebrate vector (usually an insect). Chagas' disease, caused by the parasite Trypanosoma cruzi, is transmitted via insect vectors from the Triatoma family. Although human infection with Chagas' is of importance, the disease is maintained in sylvatic (in the wild) transmission cycles. This study examines the effects of vector migration on the spread of T. cruzi in certain sylvatic cycles in the southeastern U.S. and Mexico from several angles. First, a …

Coming Out Of The Dungeon: Mathematics And Role-Playing Games, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

After hiding it for many years, I have a confession to make.

Throughout middle school and high school my friends and I would gather almost every weekend, spending hours using numbers, probability, and optimization to build models that we could use to simulate almost anything.

That’s right. My big secret is simple. I was a high school mathematical modeler.

Of course, our weekend mathematical models didn’t bear any direct relationship to the models we explored in our mathematics and science classes. You would probably not even recognize our regular gatherings as mathematical exercises. If you looked into the room, you’d …

Minimality And Duality Of Tail-Biting Trellises For Linear Codes, Elizabeth A. Weaver

Theses and Dissertations--Mathematics

Codes can be represented by edge-labeled directed graphs called trellises, which are used in decoding with the Viterbi algorithm. We will first examine the well-known product construction for trellises and present an algorithm for recovering the factors of a given trellis. To maximize efficiency, trellises that are minimal in a certain sense are desired. It was shown by Koetter and Vardy that one can produce all minimal tail-biting trellises for a code by looking at a special set of generators for a code. These generators along with a set of spans comprise what is called a characteristic pair, and we …

Hilbert Polynomials And Strongly Stable Ideals, Dennis Moore

Theses and Dissertations--Mathematics

Strongly stable ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers among saturated ideals with a given Hilbert polynomial, three algorithms are presented. Each of these algorithms produces all strongly stable ideals with some prescribed property: the saturated strongly stable ideals with a given Hilbert polynomial, the almost lexsegment ideals with a given Hilbert polynomial, and the saturated strongly stable ideals with a given Hilbert function. Bounds for the complexity of our algorithms are included. Also included are some applications for …

Analytic And Topological Combinatorics Of Partition Posets And Permutations, Jiyoon Jung

Theses and Dissertations--Mathematics

In this dissertation we first study partition posets and their topology. For each composition c we show that the order complex of the poset of pointed set partitions is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module of a border strip associated to the composition. We also study the filter of pointed set partitions generated by knapsack integer partitions. In the second half of this dissertation we study descent …

The Hydrodynamic Flow Of Nematic Liquid Crystals In R3, Jay Lawrence Hineman

Theses and Dissertations--Mathematics

This manuscript demonstrates the well-posedness (existence, uniqueness, and regularity of solutions) of the Cauchy problem for simplified equations of nematic liquid crystal hydrodynamic flow in three dimensions for initial data that is uniformly locally L³(R³) integrable (L³_U(R³)). The equations examined are a simplified version of the equations derived by Ericksen and Leslie. Background on the continuum theory of nematic liquid crystals and their flow is provided as are explanations of the related mathematical literature for nematic liquid crystals and the Navier–Stokes equations.

2012 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman

Mathematics Faculty Publications

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.

Existence And Uniqueness Conditions For A Class Of (K+4j)-Point N-Th Order Boundary Value Problems, Paul W. Eloe, Johnny Henderson, Rahmat Ali Khan

Mathematics Faculty Publications

No abstract provided.

A Leggett-Williams Type Theorem Applied To A Fourth Order Problem, Richard Avery, Paul Eloe, Johnny Henderson

Mathematics Faculty Publications

We apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a fourth order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach spstce. Inequalities that extend the notion of concavity to fourth order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.

Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold.

Creating Macroscopes With Technology And Analytics: New Possibilities In Our Lives – The Important Role Of Tomorrow’S Mathematics Professionals (Abstract), Lilian S. Wu

Kenneth C. Schraut Memorial Lectures

Our world is increasingly computerized, interconnected, and instrumented with sensors. Massive amounts of data are being captured in computer systems about our natural environment and man-made engineered structures, processes, and systems. But it is necessary to make sense out of all this data. With new computer methods computers can in effect become macroscopes, enabling us to see the world portrayed by our data.

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Vortex Patterns Beyond Hypergeometric, Andrei Ludu

Publications

We prove that loop vortices are created by a point-like magnetic dipole in an infinite superconductor space. The geometry of the vortex system is obtained through analytic solutions of the linearized Ginzburg-Landau equation described in terms of Heun functions, generalizing the traditional hypergeometric behavior of such magnetic singularity.