Physical Sciences and Mathematics Commons^™

On Some Aspects Of The Arens-Hoffman Extension Of Banach Algebras, David Brown

David C. Brown

In this dissertation, we will refer to any commutative algebra over the complex field which possesses an identity e simply as an algebra... This dissertaion deals primarily with algebraic aspects of the Arens-Hoffman extension of a Banach Algebra A and thus builds upon the work of G. A. Heuer, J.A. Lindberg, and Heuer and Lidberg...

Pixley-Roy Hyperspaces Of Ω-Graphs, Joe Mashburn

Joe D. Mashburn

The techniques developed by Wage and Norden are used to show that the Pixley-Roy hyperspaces of any two ω-graphs are homeomorphic. The Pixley-Roy hyperspaces of several subsets of Rn are also shown to be homeomorphic.

Countable Covers Of Spaces By Migrant Sets, Zoltan Balogh, Joe Mashburn, Peter Nyikos

Joe D. Mashburn

The motivation for this note is a paper by Hidenori Tanaka in which he shows that the Pixley-Roy hyperspace of a metric space X is normal if and only if X is an almost strong q-set.

Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn

Joe D. Mashburn

It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.

A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn

Joe D. Mashburn

We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very different if the set is not continuous. The basic properties of these three topologies are compared. We will show that while domain representable spaces must be Baire, this is not the case with the new topologies.

Propagating Lyapunov Functions To Prove Noise-Induced Stabilization, Tiffany Kolba, Avanti Athreya, Jonathan Mattingly

Tiffany N Kolba

No abstract provided.

Project-Based Collaborative Innovation For The Igeneration, James Gerry, Carl Heine

Carl Heine

Social media provides powerful opportunities to create new learning communities. Online, project-based activities reach today's iGen students in ways they learn best, maximizing interaction and individualization through the use of free Web technologies such as CoolHub.IMSA. Discover ways to use networing tools to transform teaching and learning at your school.

Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori Ziegelmeier, Tom Halverson

Chad M. Topaz

Bifurcations In Steady State Solutions Of A Class Of Nonlinear Dispersive Wave Equation, Paul Eloe, Muhammad Usman

Paul W. Eloe

We consider the damped externally excited KdV and BBM equations and use an asymptotic perturbation method to analyze the stability of solutions. We consider the primary resonance by defining the detuning parameter. External-excitation and frequency-response curves are shown to exhibit jump and hysteresis phenomena (dis-continuous transitions between two stable solutions) for both KdV and BBM equations.

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

Muhammad Usman

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 …

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

Muhammad Usman

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.

Forced Oscillations Of A Class Of Nonlinear Dispersive Wave Equations And Their Stability, Muhammad Usman, Bingyu Zhang

Muhammad Usman

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Korteweg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a finite domain. Consideration is given to the initial-boundary-value problem * {ut+ux=uux+u(0,t)=h(t),uxxx=0,u(x,0)=ϕ(x),u(1,t)=0,ux(1,t)=0,00,t>0. It is shown that if the boundary …

Modified Homotopy Perturbation Transform Method: A Paradigm For Nonlinear Boundary Layer Problems, Yasir Khan, Muhammad Usman

Muhammad Usman

This paper suggests a novel modified homotopy perturbation transform method (MHPTM) for a nonlinear boundary layer problem by suitable choice of an initial solution. The steady Navier–Stokes equations are reduced to nonlinear ordinary differential equations by using similarity variables. The governing nonlinear differential equations are solved by means of MHPTM. The equations are Laplace transformed and the nonlinear terms represented by He's polynomials. The series solution of the nonlinear boundary layer problem is obtained. For such a boundary layer problem, the second derivative at zero is an important point of function, so we have computed f″(0) and compared it …

Bifurcations In Steady State Solutions Of A Class Of Nonlinear Dispersive Wave Equation, Paul Eloe, Muhammad Usman

Muhammad Usman

We consider the damped externally excited KdV and BBM equations and use an asymptotic perturbation method to analyze the stability of solutions. We consider the primary resonance by defining the detuning parameter. External-excitation and frequency-response curves are shown to exhibit jump and hysteresis phenomena (dis-continuous transitions between two stable solutions) for both KdV and BBM equations.

Wavelet Analysis And Applications In Economics And Finance, Tian-Xiao He, Tung Nguyen, '15

Tian-Xiao He