Physical Sciences and Mathematics Commons^™

A Class Of Transformations Of A Quadratic Integral Generating Dynamical Systems, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A class of transformation is investigated which maps a quadratic integral back to its original form but under a redefinition of free parameters. When this process is iterated, a dynamical system is generated in the form of recursive sequences which involve the parameters of the integrand.

The creation of this dynamical system and some of its convergence properties are investigated.

MR3724632

A Geometric Formulation Of Lax Integrability For Nonlinear Equationsin Two Independent Variables, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A geometric formulation of Lax integrability is introduced which makes use of a Pfaffan formulation of Lax integrability. The Frobenius theorem gives a necessary and suffcient condition for the complete integrability of a distribution, and provides a powerful way to study nonlinear evolution equations. This permits an examination of the relation between complete integrability and Lax integrability. The prolongation method is formulated in this context and gauge transformations can be examined in terms of differential forms as well as the Frobenius theorem.

Yang Mills Theories, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Yang-Mills gauge theories have become an important way in which to describe matter at a fundamental level. This book explores some of the aspects of their structure, quantization applications and formalism in detail. The subject matter is approached from a number of different points of view. The path integral technique is used to study and quantize the theory. Some solvable low dimensional models are introduced as well.

On The Finite W-Algebra For The Lie Superalgebra Q(N) In The Non-Regular Case, Elena Poletaeva, Vera Serganova

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we study the finite W-algebra for the queer Lie superalgebra Q(N) associated with the non-regular even nilpotent coadjoint orbits in the case when N = nl, and the corresponding nilpotent element has Jordan blocks each of size l. We prove that this finite W-algebra is isomorphic to a quotient of the super-Yangian of Q(n).

Multi-Type Branching Processes Modeling Of Nosocomial Epidemics, Zeinab Mohamed, Tamer Oraby

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Nosocomial epidemics are infectious diseases which spread among different types of susceptible individuals in a health-care facility. To model this type of epidemics, we use a multi-type branching process with a multivariate negative binomial offspring distribution. In particular, we estimate the basic reproduction number R0 and study its relationship with the parameters of the offspring distribution. in case of a single-type epidemic, we investigate the effect of contact tracing on the estimates for R0.

Cybersecurity: Time Series Predictive Modeling Of Vulnerabilities Of Desktop Operating System Using Linear And Non-Linear Approach, Nawa Raj Pokhrel, Hansapani Rodrigo, Chris P. Tsokos

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Vulnerability forecasting models help us to predict the number of vulnerabilities that may occur in the future for a given Operating System (OS). There exist few models that focus on quantifying future vulnerabilities without consideration of trend, level, seasonality and non linear components of vulnerabilities. Unlike traditional ones, we propose a vulnerability analytic prediction model based on linear and non-linear approaches via time series analysis. We have developed the models based on Auto Regressive Moving Average (ARIMA), Artificial Neural Network (ANN), and Support Vector Machine (SVM) settings. The best model which provides the minimum error rate is selected for prediction …

Applications Of The Lichnerowicz Laplacian To Stress Energy Tensors, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A generalization of the Laplacian for p-forms to arbitrary tensors due to Lichnerowicz will be applied to a 2-tensor which has physical applications. It is natural to associate a divergencefree symmetric 2-tensor to a critical point of a specific variational problem and it is this 2-tensor that is studied. Numerous results are obtained for the stress-energy tensor, such as its divergence and Laplacian. A remarkable integral formula involving a symmetric 2-tensor and a conformal vector field is obtained as well

Assessment Of The Effects Of Azimuthal Mode Number Perturbations Upon The Implosion Processes Of Fluids In Cylinders, Michael R. Lindstrom

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Highlights

• Implosion instabilities are studied by linearizing about a symmetric implosion.

• This suggests azimuthal instabilities decrease with time and mode number.

• Numerics capture the delta functions from linearized solutions of conservation laws.

• The mass of these delta functions is used to estimate perturbations in shock fronts.

• The linear Klein–Gordon equation in one dimension is solved via formal asymptotics.

Abstract

Fluid instabilities arise in a variety of contexts and are often unwanted results of engineering imperfections. In one particular model for a magnetized target fusion reactor, a pressure wave is propagated in a cylindrical annulus comprised of a dense fluid before …

Frequency Of Nonalcoholic Fatty Liver Disease And Subclinical Atherosclerosis Among Young Mexican Americans, Clarence Gill, Kristina Vatcheva, Jen-Jung Pan, Beverly Smulevitz, David D. Mcpherson, Michael Fallon, Joseph B. Mccormick, Susan P. Fisher-Hoch, Susan T. Laing

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Non-alcoholic fatty liver disease (NAFLD) is considered the hepatic manifestation of the metabolic syndrome, whose criteria are risk factors for atherosclerotic cardiovascular disease. We aimed to evaluate the prevalence of NAFLD, its association with subclinical atherosclerosis, and factors that may account for this association in Mexican Americans. In a population based cross-sectional sample drawn from the Cameron County Hispanic Cohort in Texas, carotid intima media thickness (cIMT), an indicator of subclinical atherosclerosis, was measured. Abnormal carotid ultrasound study was defined as mean cIMT >75th percentile for age and gender and/or plaque presence. NAFLD was defined as steatosis by ultrasound in …

On The Denesting Of Nested Square Roots, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is rewritten as a sum of fourth-order roots of rational numbers. The theory is illustrated with several solved examples.

A Refined Approach For Non-Negative Entire Solutions Of Δ U + Up = 0 With Subcritical Sobolev Growth, John Villavert

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Let N≥2and 1uis a non-negative classical solution of the Lane–Emden equation, thenu≡0. The method of moving planes combined with the Kelvin transform provides an elegant proof of this theorem. A classical approach of Serrin and Zou, originally used for the Lane–Emden system, yields another proof but only in lower dimensions. Motivated by this, we further refine this approach to find an alternative proof of the Liouville type theorem in all dimensions.

Spectral Theory Of Operators On Manifolds, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Differential operators that are defined on a differentiable manifold can be used to study various properties of manifolds. The spectrum and eigenfunctions play a very significant role in this process. The objective of this chapter is to develop the heat equation method and to describe how it can be used to prove the Hodge Theorem. The Minakshisundaram-Pleijel parametrix and asymptotic expansion are then derived. The heat equation asymptotics can be used to give a development of the Gauss-Bonnet theorem for two-dimensional manifolds.

An Introduction To Ricci Flow For Two-Dimensional Manifolds, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The study of diferentiable manifolds is a deep an extensive area of mathematics. A technique such as the study of the Ricci flow turns out to be a very useful tool in this regard. This flow is an evolution of a Riemannian metric driven by a parabolic type of partial differential equation. It has attracted great interest recently due to its important achievements in geometry such as Perelman's proof of the geometrization conjecture and Brendle-Schoen's proof of the differentiable sphere theorem. It is the purpose here to give a comprehensive introduction to the Ricci flow on manifolds of dimension two …

Electric Ion Dispersion As A New Type Of Mass Spectrometer, Michael R. Lindstrom, Iain Moyles, Kevin Ryczko

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

At the 2014 Fields-MPrime Industrial Problem Solving Workshop, PerkinElmer presented a design problem for mass spectrometry. Traditionally, mass spectrometry is done via three methods: using magnetic fields to deflect charged particles whereby different masses bend differently; using a time-of-flight procedure where particles of different mass arrive at different times at a target; and using an electric quadrupole that filters out all masses except for one very narrow band. The challenge posed in the problem was to come up with a new design for mass spectrometry that did not involve magnetic fields and where mass fractions could be measured in an …

Using Technology To Determine Factorability Or Non-Factorability Of Quadratic Algebraic Trinomials, John E. T. Bernard, Olga Ramirez, Cristina Villalobos

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper is aimed for mathematics educators who teach algebra, more specifically, the factoring of quadratic algebraic expressions, and who want to enhance student learning of this topic using technology in conjunction with the Middle Term Splitting Method (Donnell, 2010; MTSM 2016a; MTSM 2016b). We will use technology-based algebra and geometry connections to help determine factorability or nonfactorability of quadratic algebraic trinomials over the integers, over the real numbers, and over the complex numbers, both with clarity, certainty and with understanding by using two equations, one derived from the coefficients of the outer terms and the other from the middle …

An Intrinsic Characterization Of Bonnet Surfaces Based On A Closed Differential Ideal, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The structure equations for a two-dimensional manifold are introduced and two results based on the Codazzi equations pertinent to the study of isometric surfaces are obtained from them. Important theorems pertaining to isometric surfaces are stated and a theorem due to Bonnet is obtained. A transformation for the connection forms is developed. It is proved that the angle of deformation must be harmonic, and that the differentials of many of the important variables generate a closed differential ideal. This implies that a coordinate system exists in which many of the variables satisfy particular ordinary differential equations, and these results can …