Mathematics Commons^™

Boolean Modeling Of Biochemical Networks, Tomáš Helikar, Naomi Kochi, John Konvalina, Jim A. Rogers

Mathematics Faculty Publications

The use of modeling to observe and analyze the mechanisms of complex biochemical network function is becoming an important methodological tool in the systems biology era. Number of different approaches to model these networks have been utilized-- they range from analysis of static connection graphs to dynamical models based on kinetic interaction data. Dynamical models have a distinct appeal in that they make it possible to observe these networks in action, but they also pose a distinct challenge in that they require detailed information describing how the individual components of these networks interact in living cells. Because this level of …

Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman

Mathematics Faculty Publications

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti

Mathematics Faculty Publications

This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.

Non-Normality Points Of Β X\X, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

We seek conditions implying that (β X\X) \ {y} is not normal. Our main theorem: Assume GCH and all uniform ultrafilters are regular. If X is a locally compact metrizable space without isolated points, then (β X\X) \ {y} is not normal for all y ∈ β X\X. In preparing to prove this theorem, we generalize the notions “uniform”, “regular”, and “good” from set ultrafilters to z-ultrafilters. We discuss non-normality points of the product of a discrete space and the real line. We topologically embed a nonstandard real line into the remainder of this product space.

Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler

Mathematics Faculty Publications

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.

Upper And Lower Solutions For Regime-Switching Diffusions With Applications In Financial Mathematics, Paul W. Eloe, R. H. Liu

Mathematics Faculty Publications

This paper develops a method of upper and lower solutions for a general system of second-order ordinary differential equations with two-point boundary conditions. Our motivation of study stems from a class of financial mathematics problems under regime-switching diffusion models. Two examples are double barrier option valuation and optimal selling rules in asset trading. We establish the existence of a unique C2 solution of the two-point boundary value problem. We construct monotone sequences of upper and lower solutions that are shown to converge to the unique solution of the boundary value problem. This construction provides a feasible numerical method to compute …

Optimal Intervals For Uniqueness Of Solutions For Nonlocal Boundary Value Problems, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

For the nth order differential equation (see PDF for equation) we obtain optimal bounds on the length of intervals on which solutions are unique for certain nonlocal three point boundary value problems. These bounds are obtained through an application of the Pontryagin Maximum Principle from the theory of optimal control.

2011 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Program and abstracts of papers presented at the 2011 Undergraduate Mathematics Day held at the University of Dayton.

Perfect And Abundant Numbers - A Perfect And Abundant Source For Undergraduate Research Projects (Abstract), Judy Holdener

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

In June of 2009, the 47th perfect number was discovered by the Great Internet Mersenne Prime Search (GIMPS), a collaborative computing project involving volunteers from all over the world. Like all known perfect numbers before it, this number is even. Does an odd perfect number exist? Are there infinitely many perfect numbers?

Personal And Professional Numeracy: A Unit For Pre-Service Teachers At The University Of Tasmania, Jane M. Watson

Numeracy

This paper addresses issues associated with the development of a unit preparing pre-service teachers to be quantitatively literate in three respects. These issues surround (i) the need to be aware of numeracy demands across the curriculum, (ii) the need to model numerate behavior in all interactions of teachers, and (iii) the need to be able to interpret and use system data provided from local and national testing programs. The context for the unit described is Australia, where a national testing program for literacy and numeracy requires teachers to analyze extensive data on their students, a national curriculum requires teachers of …

Go Figure: Calculus Students' Use Of Figures And Graphs In Technical Report Writing, Thomas J. Pfaff, Michael Rogers, Ali Erkan, Jason G. Hamilton

Numeracy

Understanding how to read and use graphs to communicate scientific and mathematical information is critical for STEM majors, as well as an important part of quantitative literacy. Our study suggests that first-semester calculus students do not know how to use graphs in a technical report without explicit instruction. Although not a surprising result, it leaves us wondering about when such skills are developed, and if calculus I is a place to start. Our work is now exploring the potential benefit on students' use of graphs by having them formally evaluate other students' reports.

Review Of Sex, Drugs And Body Counts: The Politics Of Numbers In Global Crime And Conflict, Edited By Peter Andreas And Kelly M. Greenhill, Aaron G. Montgomery

Numeracy

Andreas, Peter, and Greenhill, Kelly M. (Eds.). Sex, Drugs, and Body Counts: The Politics of Numbers in Global Crime and Conflict, (Ithaca, NY: Cornell University Press, 2010). 287 pp. ISBN 978-0-8014-4861-4 (cloth); ISBN 978-0-8014-7618-1 (pbk).

The ten scholarly papers in Sex, Drugs and Body Counts explore the generation and propagation of numbers that drive policy decisions in the U.S. government regarding human trafficking, drug trade, and armed conflict (including the war on terror). Each of these papers, written by different authors, provides an illuminating insight into how some of the numbers we hear or read in the news are derived. …

Twisted Virtual Biracks, Jessica Ceniceros

CMC Senior Theses

This thesis will take a look at a branch of topology called knot theory. We will first look at what started the study of this field, classical knot theory. Knot invariants such as the Bracket polynomial and the Jones polynomial will be introduced and studied. We will then explore racks and biracks along with the axioms obtained from the Reidemeister moves. We will then move on to generalize classical knot theory to what is now known as virtual knot theory which was first introduced by Louis Kauffman. Finally, we take a look at a newer aspect of knot theory, twisted …

The Mathematical Landscape, Antonio Collazo

CMC Senior Theses

The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject.  By no means is the following a complete formulation of any of the topics covered.  I want to give the reader a tour of the mathematical landscape.  There are plenty of further details to explore in each section, I have just touched the tip the iceberg.  The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math.  The first sections are a exposition into the mathematical objects and their …

Determining A Patient Recovery From A Total Knee Replacement Using Fuzzy Logic And Active Databases, Robert Azarbod

All Graduate Theses, Dissertations, and Other Capstone Projects

The purpose of the knowledge-based system is to predict the rehabilitation timeline of a patient in physical therapy for a total knee replacement. All patients have various attributes that contribute to their rehabilitation rate such as: weight, gender, smoking habit, medications, physical ability, or other medical problems. A combination of any one or several of these attributes will affect the recovery process. The proposed FRTP (Fuzzy Rehabilitation Timeline Predictor) is a fuzzy data mining model that can predict the recovery length of a patient in physical therapy for a total knee replacement and provide feedback to experts for revision of …

Polynomial Extension Operators. Part Iii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

Mathematics and Statistics Faculty Publications and Presentations

In this concluding part of a series of papers on tetrahedral polynomial extension operators, the existence of a polynomial extension operator in the Sobolev space H(div) is proven constructively. Specifically, on any tetrahedron K, given a function w on the boundary ∂K that is a polynomial on each face, the extension operator applied to w gives a vector function whose components are polynomials of at most the same degree in the tetrahedron. The vector function is an extension in the sense that the trace of its normal component on the boundary ∂K coincides with w. Furthermore, the extension operator is …

On The Singular Weyl-Titchmarsh Function Of Perturbed Spherical Schrödinger Operators, Aleksey Kostenko, Gerald Teschl

Articles

We investigate the singular Weyl–Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x) ∈ L1(0, 1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular mfunction belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations.

On The (Non)-Integrability Of Kdv Hierarchy With Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov

Articles

Nonholonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called “squared solutions” (squared eigenfunctions). Such deformations are equivalent to a perturbed model with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV6 equation are analysed. This allows for a formulation of conditions on the perturbation terms that preserve its integrability. The perturbation corrections to the scattering data and to the corresponding action-angle (canonical) variables are studied. The analysis shows …

Rational Bundles And Recursion Operators For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valtchev

Articles

We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan’s classification and having additional reductions.

Polynomial Bundles And Generalised Fourier Transforms For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander V. Mikhailov, Tihomir Valchev

Articles

A certain class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions is analysed via the Inverse Scattering Method (ISM). The class contains systems of nonlinear evolution equations (NLEEs) associated with a Lax operator (for the time-evolution) polynomial in the spectral parameter. Using the Wronskian relations, the mapping between the potential and the minimal sets of scattering data is constructed. Furthermore, completeness relations for the `squared solutions' (generalised exponentials) are derived. Next, expansions of Q and its variation are obtained. This demonstrates that the interpretation of the inverse scattering method as a generalized Fourier transform …