Mathematics Commons^™

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.

Higher Order Dynamic Equations On Measure Chains: Wronskians, Disconjugacy, And Interpolating Families Of Functions, Martin Bohner, Paul Eloe

Paul W. Eloe

This paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations, which cover simultaneously as special cases (among others) both differential equations and difference equations. We also define Markov, Fekete, and Descartes interpolating systems of functions. The main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator. The results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference …

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.

Exponential Stability In Functional Dynamic Equations On Time Scales, Elvan Akin, Youssef Raffoul, Christopher Tisdell

Youssef N. Raffoul

We are interested in the exponential stability of the zero solution of a functional dynamic equation on a time scale, a nonempty closed subset of real numbers. The approach is based on suitable Lyapunov functionals and certain inequalities. We apply our results to obtain exponential stability in Volterra integrodynamic equations on time scales.

The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen Bansal, Gholamhossein Hamedani, Hans Volkmer

Naveen Bansal

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X₁,X₂,…,X_n)(X1,X2,…,Xn) without the assumption of continuity and symmetry for each component X_iXi:

P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,

where allαi≥0 are special weights with∑i=1nαi=1.

Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen Bansal, Gholamhossein Hamedani, Ru Sheng

Naveen Bansal

We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the …

Creating Composite Age Groups To Smooth Percentile Rank Distributions Of Small Samples, Francesca Lopez, Amy Olson, Naveen Bansal

Naveen Bansal

Individually administered tests are often normed on small samples, a process that may result in irregularities within and across various age or grade distributions. Test users often smooth distributions guided by Thurstone assumptions (normality and linearity) to result in norms that adhere to assumptions made about how the data should look. Test users, however, may come across particular tests or sets of data in which the Thurstone assumptions are untenable. When users expect deviations from normality within age or grade, an alternate method is desirable. The authors present a relatively simple procedure that allows the user to treat observed raw …

Bounds On The Generating Functions Of Certain Smoothing Operations, William F. Trench

William F. Trench

No abstract provided.