Mathematics Commons^™

2014 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

Conjugate Points For Fractional Differential Equations, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

Let b > 0. Let 1 < α ≤ 2. The theory of u 0-positive operators with respect to a cone in a Banach space is applied to study the conjugate boundary value problem for Riemann-Liouville fractional linear differential equations D 0+α u + λp(t)u = 0, 0 < t < b, satisfying the conjugate boundary conditions u(0) = u(b) = 0. The first extremal point, or conjugate point, of the conjugate boundary value problem is defined and criteria are established to characterize the conjugate point. As an application, a fixed point theorem is applied to give sufficient conditions for existence of a solution of a related boundary value problem for a nonlinear fractional differential equation.

Existence And Comparison Of Smallest Eigenvalues For A Fractional Boundary-Value Problem, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

The theory of u0-positive operators with respect to a cone in a Banach space is applied to the fractional linear differential equations

(see PDF)

0 < t < 1, with each satisfying the boundary conditions u(0) = u(1) = 0. The existence of smallest positive eigenvalues is established, and a comparison theorem for smallest positive eigenvalues is obtained.

Data Stories And Pictures; Discovering Lessons And Principles For Statistics And For Life (Abstract), Rafe Donahue

Kenneth C. Schraut Memorial Lectures

Our world is full of data and of analyses of these data. Why are we doing to our data what we are doing to our data?

2013 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2013 Fall Colloquium.

Every Scattered Space Is Subcompact, William Fleissner, Vladimir Tkachuk, Lynne Yengulalp

Mathematics Faculty Publications

We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every Čech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense G_δ-subsets of Cantor cubes are subcompact.

2013 (Summer), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2013 Summer Colloquium.

2013 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2013 Spring Colloquium.

A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn

Mathematics Faculty Publications

In this paper we extend the spectral order of Coecke and Martin to infinite-dimensional quantum states. Many properties present in the finite-dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analysed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and that part is not a closed subset of the model. The finite parts of the lattices used by Birkhoff and von Neumann as models for classical and quantum logic appear as subsets of the models for infinite …

Concavity Of Solutions Of A 2n-Th Order Problem With Symmetry, Abdulmalik Altwaty, Paul W. Eloe

Mathematics Faculty Publications

In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a 2n-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to 2n-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.

The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman

Mathematics Faculty Publications

The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are …

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

When Cp(X) Is Domain Representable, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

Let M be a metrizable group. Let G be a dense subgroup of M^X . If G is domain representable, then G = MX . The following corollaries answer open questions. If X is completely regular and C_p(X) is domain representable, then X is discrete. If X is zero-dimensional, T₂ , and C_p(X;D) is subcompact, then X is discrete.

An Implicit Interface Boundary Integral Method For Poisson’S Equation On Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, Richard Tsai

Mathematics Faculty Publications

We propose a simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with smooth boundaries defined through their signed distance function. Our formulation is based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain, where the integrations are carried out in the level set framework using an appropriate Jacobian. By the coarea formula, the algorithm operates in the Euclidean space and does not require any explicit parameterization of the boundaries. We present numerical results in two and three dimensions.

An Example Employing Convexity In Functional Fixed Point Arguments, Richard I. Avery, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

This paper illustrates a convexity technique to be employed with functional fixed point theorems in proving the existence of solutions to boundary value problems.

2012 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2012 Fall Colloquium.

2012 (Summer), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2012 Summer Colloquium.

2012 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2012 Spring Colloquium.

A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman

Mathematics Faculty Publications

We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.

The Role Of Concavity In Applications Of Avery Type Fixed Point Theorems To Higher Order Differential Equations, Abdulmalik A. Altwaty, Paul W. Eloe

Mathematics Faculty Publications

In this article we apply an extension of an Avery type fixed point theorem to a family of boundary value problems for higher order ordinary differential equations. The theorem employs concave and convex functionals defined on a cone in a Banach space. We begin by extending a known application to a right focal boundary value problem for a second order problem to a conjugate boundary value problem for a second order problem. We then extend inductively to a two point boundary value problem for a higher order equation. Concavity of differentiable functions plays a key role in the application to …

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.

2011 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2011 Fall Colloquium.

A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh

Mathematics Faculty Publications

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …

2011 (Summer), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2011 Summer Colloquium.