Mathematics Commons^™

2014 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2014 Fall Colloquium.

The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle

Mathematics Faculty Publications

Since the 1970’s, great interest has been taken in the study of pure O-sequences, which are in bijective correspondence to the Hilbert functions of Artinian level monomial algebras. Much progress has been made in classifying these by their shape. It has been shown that all monomial complete intersections, Artinian algebras in two variables and Artinian level monomial algebras with type two in both three and four variables have unimodal Hilbert functions. This paper proves that Artinian level monomial algebras of type three in three variables have unimodal Hilbert functions. We will also discuss the licciness of these algebras.

Configuration Spaces Of Convex And Embedded Polygons In The Plane, Don H. Shimamoto, Mary K. Wootters , '08

Mathematics & Statistics Faculty Works

This paper concerns the topology of configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that, modulo translations and rotations, each component of the space of convex configurations is homeomorphic to a closed Euclidean ball and each component of the space of embedded configurations is homeomorphic to a Euclidean space. This represents an elaboration on the topological information that follows from the convexification theorem of Connelly, Demaine, and Rote.

Prognostic Value Of Estimated Functional Capacity Incremental To Cardiac Biomarkers In Stable Cardiac Patients, W.H. Wilson Tang, Eric J. Topol, Yiying Fan, Yuping Wu, Leslie Cho, Cindy Stevenson, Stephen G. Ellis, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background: Few studies have investigated functional capacity self-assessment tools in either prediction of future major adverse cardiac outcomes beyond all-cause mortality or direct comparisons with clinically available biomarkers. Methods and Results: We estimated functional capacity using the Duke Activity Status Index (DASI) questionnaire in 8987 sequential stable patients without acute coronary syndrome who were undergoing elective diagnostic coronary angiography with 3-year follow-up of major adverse cardiac events (death, nonfatal myocardial infarction, or stroke). A low DASI score provided independent prediction of a 4.8-fold increase in future risk of incident major adverse cardiac events at 3 years (quartiles 1 versus 4 …

Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. …

Relatively Congruence-Free Regular Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

Yu, Wang, Wu and Ye call a semigroup S τ -congruence-free, where τ is an equivalence relation on S, if any congruence ρ on S is either disjoint from τ or contains τ . A congruence-free semigroup is then just an ω-congruence-free semigroup, where ω is the universal relation. They determined the completely regular semigroups that are τ -congruence-free with respect to each of the Green’s relations. The goal of this paper is to extend their results to all regular semigroups. Such a semigroup is J –congruence-free if and only if it is either a semilattice or has …

Generalized Exponentiated Moment Exponential Distribution, Zafar Iqbal, Syed Anwer Hasnain, Muhammad Salman, Munir Ahmad, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Moment distributions have a vital role in mathematics and statistics, in particular in probability theory, in the perspective research related to ecology, reliability, biomedical field, econometrics, survey sampling and in life-testing. Hasnain (2013) developed an exponentiated moment exponential (EME) distribution and discussed some of its important properties. In the present work, we propose a generalization of EME distribution which we call it generalized EME (GEME) distribution and develop various properties of the distribution. We also present characterizations of the distribution in terms of conditional expectation as well as based on hazard function of the GEME random variable.

Some Remarks On Recent Characterizations Of Continuous Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We would closely look at two recent published papers dealing with characterizations of certain univariate continuous distributions. We shall explain that the main results reported lack important assumptions. These results nevertheless are based on the conditional expectations of monotone functions of the generalized order statistics. We will also mention that similar results have recently been reported without the assumption of monotonicity of the functions of the generalized order statistics.

Martingales For Uniformly Quasisymmetric Circle Endomorphisms, Yunchun Hu

Dissertations, Theses, and Capstone Projects

The main subject studied in this thesis is the space of all uniformly quasisymmetric circle endomorphisms preserving the Lebesgue measure. Although many of our arguments work for any degree d≥2, our proof will be mainly written for degree 2 maps.

We will introduce a sequence of Markov partitions of the unit circle by using preimages of the fixed point of such circle endomorphism f. The uniform quasisymmetry condition is equivalent to the bounded nearby geometry condition of the Markov partitions. In Chapter 2 of this thesis, for each f, we use the Lebesgue invariant condition and the …

An Algorithmic Approach To The Differential Galois Theory Of Second-Order Linear Differential Equations With Differential Parameters, Carlos Eduardo Arreche Aguayo

Dissertations, Theses, and Capstone Projects

We present algorithms to compute the differential Galois group G associated via the parameterized Picard-Vessiot theory to a parameterized second-order linear differential equation with respect to d/dx, with coefficients in the field of rational functions F(x) over a differential field F, where we think of the derivations on F as being derivations with respect to parameters. We build on an earlier procedure, developed by Dreyfus, that computes G when the equation is unimodular, assuming either that G is reductive, or else that its maximal reductive quotient is differentially constant. We first show how to modify the space of parametric derivations …

Combinatorial Properties Of Polyiamonds, Christopher Larson

Dissertations, Theses, and Capstone Projects

Polyiamonds are plane geometric figures constructed by pasting together equilateral triangles edge-to-edge. It is shown that a diophantine equation involving vertices of degrees 2, 3, 5 and 6 holds for all polyiamonds; then an Eberhard-type theorem is proved, showing that any four-tuple of non-negative integers that satisfies the diophantine equation can be realized geometrically by a polyiamond. Further combinatorial and graph-theoretic aspects of polyiamonds are discussed, including a characterization of those polyiamonds that are three-connected and so three-polytopal, a result on Hamiltonicity, and constructions that use minimal numbers of triangles in realizing four-vectors.

Motivic Integration Over Nilpotent Structures, Andrew Ryan Stout

Dissertations, Theses, and Capstone Projects

This thesis concerns developing the notion of Motivic Integration in such a way that it captures infinitesimal information yet reduces to the classical notion of motivic integration for reduced schemes. Moreover, I extend the notion of Motivic Integration from a discrete valuation ring to any complete Noetherian ring with residue field $\kappa$, where $\kappa$ is any field. Schoutens' functorial approach (as opposed to the traditional model theoretic approach) allows for some very general notions of motivic integration. However, the central focus is on using this general framework to study generically smooth schemes, then non-reduced schemes, and then, finally, formal schemes. …

A Mentoring Program For Inquiry-Based Teaching In A College Geometry Class, Nathaniel Miller, Nathan Wakefield

Department of Mathematics: Faculty Publications

This paper describes a mentoring program designed to prepare novice instructors to teach a college geometry class using inquiry-based methods. The mentoring program was used in a medium-sized public university with approximately 12,000 undergraduate students and 1,500 graduate students. The authors worked together to implement a mentoring program for the first time. One author was an associate professor and experienced using inquiry-based learning. The other author was a graduate student in mathematics education. During the course of the year the graduate student first observed and then taught a college level inquiry-based geometry course for pre-service teachers. This article describes the …

Self-Referentiality In Constructive Semantics Of Intuitionistic And Modal Logics, Junhua Yu

Dissertations, Theses, and Capstone Projects

This thesis explores self-referentiality in the framework of justification logic. In this framework initialed by Artemov, the language has formulas of the form t:F, which means "the term t is a justification of the formula F." Moreover, terms can occur inside formulas and hence it is legal to have t:F(t), which means "the term t is a justification of the formula F about t itself." Expressions like this is not only interesting in the semantics of justification logic, but also, as we will see, necessary in applications of justification logic in formalizing constructive contents implicitly carried by modal and intuitionistic …

Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities …

The Scientific Theories Of Michael Faraday And James Clerk Maxwell, Shannon P. Israelsen

The Purdue Historian

This paper explores the role of mathematical formalism in physics theories through an analysis of the work of physicists Michael Faraday and James Clerk Maxwell in the field of electromagnetism. After a brief description of the educational backgrounds of each scientist, their views on the nature of physics theory and its relationship to mathematics are contrasted. Faraday sought a mathematics-free theory to describe the results of his experiments, producing a family of concepts that became the roots of electromagnetic field theory. Maxwell built upon these concepts, giving them robust mathematical expression and incorporating them into one unified theoretical picture. An …

Proximinality Properties Of Subspaces And Intersection Properties Of Balls In Banach Spaces., Jayanarayanan C. R. Dr.

Doctoral Theses

In this chapter, we explain the background and the main theme of this thesis and provide a chapter-wise summary of its principal results. We introduce some notations and preliminaries that will be used in the subsequent chapters.Study of proximinality related properties and ball intersection related properties of Banach spaces have been an active area of research in the field of geometry of Banach spaces. In this thesis, we mainly study these two classes of Banach space theoretic properties.We consider only Banach spaces over the real field R and all subspaces we consider are assumed to be closed.1.1 PreliminariesFor a Banach …

Performance Comparison Of Projective Elliptic-Curve Point Multiplication In 64-Bit X86 Runtime Environment, Ninh Winson

CCAC Theses and Dissertations

For over two decades, mathematicians and cryptologists have evaluated and presented the theoretical performance of Elliptic-curve scalar point-multiplication in projective geometry. Because computation in projective domain is composed of a wide array of formulations and computing optimizations, there is not a comprehensive performance comparison of point-multiplication using projective transformation available to verify its realistic efficiency in 64-bit x86 computing platforms. Today, research on explicit mathematical formulations in projective domain continues to excel by seeking higher computational efficiency and ease of realization. An explicit performance evaluation will help implementers choose better implementation methods and improve Elliptic-curve scalar point-multiplication. This paper was …

Synthetic Lethality As A Promising Approach For Targeted Cancer Prevention, Wei Tu, Hua Wang, Guang Peng

Mathematical Sciences: Faculty Publications

Carcinogenesis is recognized as a multistep process. It occurs over a relative long span of time, which offers intervention opportunities for cancer prevention [1] . Using drugs to prevent cancer rather than treat cancer is the major research goal in the field of ‘chemoprevention’. Tremendous research efforts have been devoted toward using natural, synthetic or biological agents to prevent, suppress or delay the initiation and or the progression of premalignant cells to cancer [1] . However a big challenge for effective cancer prevention is to identify chemoprevention agents with demonstrable efficacy and safety for healthy general …

An Optimal Three-Way Stable And Monotonic Spectrum Of Bounds On Quantiles: A Spectrum Of Coherent Measures Of Financial Risk And Economic Inequality, Iosif Pinelis

Michigan Tech Publications, Part 1

A spectrum of upper bounds (Q_α(X ; p) _αε[0,∞] on the (largest) (1-p)-quantile Q(X;p) of an arbitrary random variable X is introduced and shown to be stable and monotonic in α, p, and X , with Q₀(X ;p) = Q(X;p). If p is small enough and the distribution of X is regular enough, then Q_α(X ; p) is rather close to Q(X ; p). Moreover, these quantile bounds are coherent measures of risk. Furthermore, Q_α(X ; p) is the optimal value in a certain minimization problem, the minimizers in which are described …