Physical Sciences and Mathematics Commons^™

Hydro-Thermal Convective Solutions For An Aquifer System Heated From Below, Dambaru Bhatta

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We investigate the effect of hydro-thermal convection in an aquifer system. It is assumed that the aquifer is bounded below and above by impermeable boundaries and it is heated from below. The solution of the governing system is expressed in terms of the basic steady state solution and perturbed solution. We obtain the critical Rayleigh number and critical wavenumber using Runge-Kutta method in combination of shooting method and present the marginal stability curve. The amplitude equation is derived by introducing the adjoint system. After amplitude is obtained, we compute the linear solutions for super-critical and sub-critical cases. Numerical results for …

Algebro-Geometric Solutions For The Degasperis--Procesi Hierarchy, Yu Hou, Peng Zhao, Engui Fan, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Though the completely integrable Camassa--Holm (CH) equation and Degasperis--Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the …

Generalized Local Test For Local Extrema In Single-Variable Functions, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We give a detailed derivation of a generalization of the second derivative test of single-variable calculus which can classify critical points as local minima or local maxima (or neither), whenever the traditional second derivative test fails, by considering the values of higher-order derivatives evaluated at the critical points. The enhanced test is local, in the sense that it is only necessary to evaluate all relevant derivatives at the critical point itself, and it is reasonably robust. We illustrate an application of the generalized test on a trigonometric function where the second derivative test fails to classify some of the critical …

The Schwinger Action Principle And Its Applications To Quantum Mechanics, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

No abstract provided.

The Two-Phase Arterial Blood Flow With Or Without A Catheter And In The Presence Of A Single Or Multi Stenosis, Ani E. Garcia, Daniel N. Riahi

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We consider the problem of blood flow in an artery with or without a catheter and in the presence of single or multi stenosis whose shape is based on the available experimental data for the stenosis in a human’s artery. The presence of stenosis in the artery, which locally narrows portion of the artery, can be a result of fatty materials such as cholesterol in the blood. The use of catheter is important as a standard tool for diagnosis and treatment in patience whose blood flow passage in the artery is affected adversely by the presence of the stenosis within …

Characterizations Of Exponential Distribution Based On Sample Of Size Three, George Yanev, Santanu Chakraborty

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Two characterizations of the exponential distribution based on equalities among order statistics in a random sample of size three are proved. This proves two conjectures stated recently in Arnold and Villasenor [4].

Analytic Matrix Elements Of The Schrödinger Equation, Muhammad I. Bhatti

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A previously defined analytic technique of constructing matrix elements from the Bernstein-polynomials (B-poly) has been applied to Schr¨odinger equation. This method after solving generalized eigenvalue problem yields very accurate eigenenergies and eigenvectors. The numerical eigenvectors and eigenvalues obtained from this process agree well with exact results of the hydrogen-like systems. Furthermore, accuracy of the numerical spectrum of hydrogen equation depends on the number of B-polys being used to construct the analytical matrix elements. Validity of eigenvalues and quality of the constructed wavefunctions is verified by evaluating the Thomas-Reiche-Kuhn (TRK) sum rules. Excellent numerical agreement is seen with exact results of …

On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.

On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Distributional relations of the form Y d= X +T where X, Y, and T are record values or order statistics and the random translator T is independent from X are considered. Characterizations of the exponential distribution when the ordered random variables are non-neighboring are proved. Corollaries for Pareto and power function distributions are also derived.

Zero-Bounded Limits As A Special Case Of The Squeeze Theorem For Evaluating Single-Variable And Multivariable Limits, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Many limits, typically taught as examples of applying the ‘squeeze’ theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful for both single-variable limits and multidimensional limits. A comprehensive treatment of multidimensional limits and continuity is also outlined.

High Prevalence Of Subclinical Atherosclerosis By Carotid Ultrasound Among Mexican Americans: Discordance With 10-Year Risk Assessment Using The Framingham Risk Score, Susan T. Laing, Beverly Smulevitz, Kristina Vatcheva, Anne R. Rentfro, David D. Mcpherson, Susan P. Fisher-Hoch, Joseph B. Mccormick

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Background: Framingham risk scores (FRS) were validated in a mostly Caucasian population. Evaluation of subclinical atherosclerosis by carotid ultrasound may improve ascertainment of risk in nonwhite populations. This study aimed to evaluate carotid intima-media thickness (cIMT) and carotid plaquing among Mexican Americans, and to correlate these markers with coronary risk factors and the FRS.

Methods/results: Participants (n = 141) were drawn from the Cameron County Hispanic Cohort. Carotid artery ultrasound was performed and cIMT measured. Carotid plaque was defined as areas of thickening >50% of the thickness of the surrounding walls. Mean age was 53.1 ± 11.7 years (73.8% female). …

Missed Opportunities For Diagnosis And Treatment Of Diabetes, Hypertension, And Hypercholesterolemia In A Mexican American Population, Cameron County Hispanic Cohort, 2003-2008, Susan P. Fisher-Hoch, Kristina Vatcheva, Susan T. Laing, Monir Hossain, M Hossein Rahbar, Craig Hanis, H Shelton Brown, Anne R. Rentfro, Belinda M. Reininger, Joseph B. Mccormick

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Introduction

Diabetes, hypertension, and hypercholesterolemia are common chronic diseases among Hispanics, a group projected to comprise 30% of the US population by 2050. Mexican Americans are the largest ethnically distinct subgroup among Hispanics. We assessed the prevalence of and risk factors for undiagnosed and untreated diabetes, hypertension, and hypercholesterolemia among Mexican Americans in Cameron County, Texas.

Methods

We analyzed cross-sectional baseline data collected from 2003 to 2008 in the Cameron County Hispanic Cohort, a randomly selected, community-recruited cohort of 2,000 Mexican American adults aged 18 or older, to assess prevalence of diabetes, hypertension, and hypercholesterolemia; to assess the extent to …

Negative-Order Korteweg–De Vries Equations, Zhijun Qiao, Engui Fan

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, based on the regular Korteweg–de Vries (KdV) system, we study negative-order KdV (NKdV) equations, particularly their Hamiltonian structures, Lax pairs, conservation laws, and explicit multisoliton and multikink wave solutions thorough bilinear B¨acklund transformations. The NKdV equations studied in our paper are differential and actually derived from the first member in the negative-order KdV hierarchy. The NKdV equations are not only gauge equivalent to the Camassa-Holm equation through reciprocal transformations but also closely related to the Ermakov-Pinney systems and the Kupershmidt deformation. The bi-Hamiltonian structures and a Darboux transformation of the NKdV equations are constructed with the aid …

Electrocardiographic Abnormalities Among Mexican Americans: Correlations With Diabetes, Obesity, And The Metabolic Syndrome, Saulette R. Queen, Beverly Smulevitz, Anne R. Rentfro, Kristina Vatcheva, David D. Mcpherson, Susan P. Fisher-Hoch, Joseph B. Mccormick, Susan T. Laing

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Background: Resting ischemic electrocardiographic abnormalities have been associated with cardiovascular mortality. Simple markers of abnormal autonomic tone have also been associated with diabetes, obesity, and the metabolic syndrome in some populations. Data on these electrocardiographic abnormalities and correlations with coronary risk factors are lacking among Mexican Americans wherein these conditions are prevalent.

Objective: This study aimed to evaluate the prevalent resting electrocardiographic abnormalities among community-dwelling Mexican Americans, and correlate these findings with coronary risk factors, particularly diabetes, obesity, and the metabolic syndrome.

Methods: Study subjects (n=1280) were drawn from the Cameron County Hispanic Cohort comprised of community-dwelling Mexican Americans living …

Quantum Mechanics Entropy And A Quantum Version Of The H-Theorem, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

No abstract provided.

Geometry Of Partial Differential Equations, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The study of partial differential equations has been the object of much investigation and seen a great many advances recently. This is primarily due to the fact that certain classes of these equations fall under the category of being integrable. These kinds of equations have many useful properties such as the existence of Lax pairs, Backlund transformations, explicit solutions and the existence of a correspondence with geometric manifolds. There have also been many applications of solutions to these equations in the study of solitons and other objects which have seen applications in physics. It is the objective here to study …

Characterizations Of Logistic Distribution Through Order Statistics With Independent Exponential Shifts, M. Ahsanullah, George Yanev, Constantin Onica

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Distributional properties of logistic order statistics subject to independent exponential one-sided and two-sided shifts are established. Utilizing these properties, we extend several known results and obtain new characterizations of the logistic distribution.

A New Integrable Two-Component System With Cubic Nonlinearity, Junfeng Song, Changzheng Qu, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, a new integrable two-component system, mt=[m(uxvx−uv+uvx−uxv)]x,nt=[n(uxvx−uv+uvx−uxv)]x, where m=u−uxx and n=v−vxx, is proposed. Our system is a generalized version of the integrable system mt=[m(u2x−u2)]x, which was shown having cusped solution (cuspon) and W/M-shape soliton solutions by Qiao [J. Math. Phys. 47, 112701 (2006). The new system is proven integrable not only in the sense of Lax-pair but also in the sense of geometry, namely, it describes pseudospherical surfaces. Accordingly, infinitely many conservation laws are derived through recursion relations. Furthermore, exact solutions such as cuspons and W/M-shape solitons are also obtained.

When Is Hyponormality For 2-Variable Weighted Shifts Invariant Under Powers?, Raul E. Curto, Jasang Yoon

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Abstract. For 2-variable weighted shifts W(α,β) ≡ (T1, T2) we study the invariance of (joint) khyponormality under the action (h, ℓ) 7→ W (h,ℓ) (α,β) := (T h 1 , T ℓ 2 ) (h, ℓ ≥ 1). We show that for every k ≥ 1 there exists W(α,β) such that W (h,ℓ) (α,β) is k-hyponormal (all h ≥ 2, ℓ ≥ 1) but W(α,β) is not k-hyponormal. On the positive side, for a class of 2-variable weighted shifts with tensor core we find a computable necessary condition for invariance. Next, we exhibit a large nontrivial class for which hyponormality …

Mathematical Modeling And Computation Of Channel Flow Over Discrete Structures, Rolando J. Olivares, Daniel N. Riahi

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper mathematical modeling and computation of channel flow over small discrete structures are carried out under some reasonable conditions. A mathematical model for such a flow problem, which is based on a relevant system of partial differential equations and Fourier analysis, is studied using perturbation and nonlinear stability methods, and the resulting flow solutions over two types of discrete structures are computed under both stable and unstable conditions. It was found, in particular, that for a subcritical domain with the Reynolds number R slightly less than its critical value Rc, which is defined as the value below which …

Characterizations Of Exponential Distribution Via Conditional Expectations Of Record Values, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We prove that the exponential distribution is the only one which satisfies a regression identity. This identity involves conditional expectation of the sample mean of record values given two record values outside of the sample.

Dissipation Scales And Anomalous Sinks In Steady Two-Dimensional Turbulence, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In previous papers I have argued that the fusion rules hypothesis, which was originally introduced by L’vov and Procaccia in the context of the problem of three-dimensional turbulence, can be used to gain a deeper insight in understanding the enstrophy cascade and inverse energy cascade of two-dimensional turbulence. In the present paper, we show that the fusion rules hypothesis, combined with nonperturbative locality, itself a consequence of the fusion rules hypothesis, dictates the location of the boundary separating the inertial range from the dissipation range. In so doing, the hypothesis that there may be an anomalous enstrophy sink …

Bifurcations Of Traveling Wave Solutions For An Integrable Equation, Jibin Li, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper deals with the following equation mt= 1/2 1/mk xxx− 1/2 1/mk x, which is proposed by Z. J. Qiao J. Math. Phys. 48, 082701 2007 and Qiao and Liu Chaos, Solitons Fractals 41, 587 2009. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the …

Spatial Instability Of Electrically Driven Jets With Finite Conductivity And Under Constant Or Variable Applied Field, Saulo Orizaga, Daniel N. Riahi

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We investigate the problem of spatial instability of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton’s method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One of these modes is enhanced by the strength Ω of …

Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We consider the problem of steady flow around a growing protein crystal in a medium of its solution in a normal gravity environment. The whole flow system is assumed to be rotating with a constant angular velocity about a vertical axis which is anti-parallel to the gravity vector. Convective flow takes place due to the solute depletion around the growing crystal which leads to a buoyancy driven flow. Such convective flow can produce inhomogeneous solute concentration, which subsequently generate non-uniformities in the crystal’s structure finalizing lower quality protein crystal. Using scaling analysis within a diffusion boundary layer around the crystal, …

Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L’vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of nonperturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that …

Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we discuss some interesting applications of Dirac's delta function in Statistics. We have tried to extend some of the existing results to the more than one variable case. While doing that, we particularly concentrate on the bivariate case.

Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. …

An Action For A Classical String, The Equation Of Motion And Group Invariant Classical Solutions, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.

Quantum Phases For A Generalized Harmonic Oscillator, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.