Mathematics Commons^™

Isar Autofocus Imaging Algorithm For Maneuvering Targets Based On Phase Retrieval And Gabor Wavelet Transform, Hongyin Shi, Ting Yang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The imaging issue of a rotating maneuvering target with a large angle and a high translational speed has been a challenging problem in the area of inverse synthetic aperture radar (ISAR) autofocus imaging, in particular when the target has both radial and angular accelerations. In this paper, on the basis of the phase retrieval algorithm and the Gabor wavelet transform (GWT), we propose a new method for phase error correction. The approach first performs the range compression on ISAR raw data to obtain range profiles, and then carries out the GWT transform as the time-frequency analysis tool for the rotational …

Non-Stationary Platform Inverse Synthetic Aperture Radar Maneuvering Target Imaging Based On Phase Retrieval, Hongyin Shi, Saixue Xia, Qi Qin, Ting Yang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

As a powerful signal processing tool for imaging moving targets, placing radar on a non-stationary platform (such as an aerostat) is a future direction of Inverse Synthetic Aperture Radar (ISAR) systems. However, more phase errors are introduced into the received signal due to the instability of the radar platform, making it difficult for popular algorithms to accurately perform motion compensation, which leads to severe effects in the resultant ISAR images. Moreover, maneuvering targets may have complex motion whose motion parameters are unknown to radar systems. To overcome the issue of non-stationary platform ISAR autofocus imaging, a high-resolution imaging method based …

Solution Of Mathematical Model For Gas Solubility Using Fractional-Order Bhatti Polynomials, Muhammad I. Bhatti, Paul Bracken, Nicholas Dimakis, Armando Herrera

School of Mathematical & Statistical Sciences Faculty Publications

Solutions of a mathematical model for gas solubility in a liquid are attained employing an algorithm based on the generalized Galerkin B-poly basis technique. The algorithm determines a solution of a fractional differential equation in terms of continuous finite number of generalized fractional-order Bhatti polynomial (B-poly) in a closed interval. The procedure uses Galerkin method to calculate the unknown expansion coefficients for constructing a solution to the fractional-order differential equation. Caputo?s fractional derivative is employed to evaluate the derivatives of the fractional B-polys and each term in the differential equation is converted into a matrix problem which is then inverted …

A Formulation Of L-Isothermic Surfaces In Three-Dimensional Minkowski Space, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The Cartan structure equations are used to study space-like and time-like isothermic surfaces in three-dimensional Minkowski space in a unified framework. When the lines of curvature of a surface constitute an isothermal system, the surface is called isothermic. This condition serves to define a system of one-forms such that, by means of the structure equations, the Gauss-Codazzi equations for the surface are determined explicitly. A Lax pair can also be obtained from these one-forms for both cases, and, moreover, a nonhomogeneous Schrödinger equation can be associated with the set of space-like surfaces.

Aluthge Transforms Of 2-Variable Weighted Shifts, Raul E. Curto, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We introduce two natural notions of multivariable Aluthge transforms (toral and spherical), and study their basic properties. In the case of 2-variable weighted shifts, we first prove that the toral Aluthge transform does not preserve (joint) hyponormality, in sharp contrast with the 1-variable case. Second, we identify a large class of 2-variable weighted shifts for which hyponormality is preserved under both transforms. Third, we consider whether these Aluthge transforms are norm-continuous. Fourth, we study how the Taylor and Taylor essential spectra of 2-variable weighted shifts behave under the toral and spherical Aluthge transforms; as a special case, we consider the …

Preconditioning Methods For Thin Scattering Structures Based On Asymptotic Results, Josef A. Sifuentes, Shari Moskow

School of Mathematical & Statistical Sciences Faculty Publications

We present a method to precondition the discretized Lippmann–Schwinger integral equations to model scattering of time-harmonic acoustic waves through a thin inhomogeneous scattering medium. The preconditioner is based on asymptotic results as the thickness of the third component direction goes to zero and requires solving a two dimensional formulation of the problem at the preconditioning step.

Covering A Ball By Smaller Balls, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

We prove that, for any covering of a unit d-dimensional Euclidean ball by smaller balls, the sum of radii of the balls from the covering is greater than d. We also investigate the problem of finding lower and upper bounds for the sum of powers of radii of the balls covering a unit ball.

The Local Theory For Regular Systems In The Context Of T-Bonded Sets, Mikhail M. Bouniaev, Nikolay Dolbilin

School of Mathematical & Statistical Sciences Faculty Publications

The main goal of the local theory for crystals developed in the last quarter of the 20th Century by a geometry group of Delone (Delaunay) at the Steklov Mathematical Institute is to find and prove the correct statements rigorously explaining why the crystalline structure follows from the pair-wise identity of local arrangements around each atom. Originally, the local theory for regular and multiregular systems was developed with the assumption that all point sets under consideration are (r,R)" role="presentation">(r,R) -systems or, in other words, Delone sets of type (r,R)" role="presentation">(r,R) in d-dimensional Euclidean space. In this paper, we will …

Using Restrictions To Accept Or Reject Solutions Of Radical Equations, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original equation. We propose alternative solution procedures that are rigorous and simple to execute where the extraneous solutions can be identified without verification against the original equation. In this article, we review previous literature, establish and illustrate rigorous solution procedures for radical equations of depth 1 (i.e. equations …

Optimal Quantizers For Some Absolutely Continuous Probability Measures, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of n-means and the nth quantization errors are calculated for some positive integers n.

Cartan Frames And Algebras With Links To Integrable Systems Differential Equations And Surfaces, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Moving frames and Clifford algebras will be used to illustrate an interconnected approach to the study of integrable systems, their surfaces, and methods for producing integrable partial differential equations. After a system of one-forms is defined, moving frame equations can be integrated and the resulting equations for the surface can be obtained. Other differential equations which involve quantities relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case of constant mean curvature, they can be expressed in terms of Jacobi elliptic functions.

The Development Of Secondary Mathematics Teachers’ Pedagogical Identities In The Social Context Of Classroom Interactions, Hyung Won Kim

School of Mathematical & Statistical Sciences Faculty Publications

Research demonstrates a disjuncture between the practices encouraged by teacher education programs and what teachers actually do in the classroom. It also informs us that the cognitive and social characteristics of individual teachers such as their attitudes, beliefs and knowledge contribute to their classroom practices. This qualitative study investigates how the teacher identity of mathematics teachers – the person’s sense of who he/she is as a mathematics teacher – is related to the disjuncture between encouraged and actual classroom practices. Specifically, the study looks into how mathematics teachers form their teaching practices in the social context of their classroom interactions, …

Linear Stability Analysis With Solution Patterns Due To Varying Thermal Diffusivity For A Convective Flow In A Porous Medium, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

Here we investigate the effect of the vertical rate of change in thermal diffusivity due to a hydrothermal convective flow in a horizontal porous medium. The continuity equation, the heat equation and the momentum-Darcy equation constitute the governing system for the flow in a porous medium. Assuming a vertically varying basic state, we derive the linear system and from this linear system, we compute the critical Rayleigh and wave numbers. Using fourth-order Runge-Kutta and shooting methods, we obtain the marginal stability curves and linear solutions to analyze the solution pattern for different diffusivity parameters.

Exchanging Deficit For Affordance: Developing Preservice Teachers’ Capacity To See Emergent Bilingual Students’ Resources, Aaron T. Wilson, Hyung Won Kim, M. Alejandra Sorto

School of Mathematical & Statistical Sciences Faculty Publications

We present a Scholarship of Teaching and Learning (SoTL) research project aimed at helping pre-service teachers to grasp the importance of their emergent bilingual students' bilingualism and cultural backgrounds as resources to serve them in apprehending mathematics instruction and explaining their mathematics to others.

Wavelet Neural Network Model For Yield Spread Forecasting, Firdous Ahmad Shah, Lokenath Debnath

School of Mathematical & Statistical Sciences Faculty Publications

In this study, a hybrid method based on coupling discrete wavelet transforms (DWTs) and artificial neural network (ANN) for yield spread forecasting is proposed. The discrete wavelet transform (DWT) using five different wavelet families is applied to decompose the five different yield spreads constructed at shorter end, longer end, and policy relevant area of the yield curve to eliminate noise from them. The wavelet coefficients are then used as inputs into Levenberg-Marquardt (LM) ANN models to forecast the predictive power of each of these spreads for output growth. We find that the yield spreads constructed at the shorter end and …

An Answer To A Question Of A. Lubin: The Lifting Problem For Commuting Subnormals, Sang Hoon Lee, Woo Young Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we give an answer to a long-standing open question on the lifting problem for commuting subnormals (due to A. Lubin): The subnormality for the sum of commuting subnormal operators does not guarantee the existence of commuting normal extensions.

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

School of Mathematical & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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.

Convective Flow In An Aquifer Layer, Dambaru Bhatta, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

Here, we investigate weakly nonlinear hydrothermal two-dimensional convective flow in a horizontal aquifer layer with horizontal isothermal and rigid boundaries. We treat such a layer as a porous medium, where Darcy’s law holds, subjected to the conditions that the porous layer’s permeability and the thermal conductivity are variable in the vertical direction. This analysis is restricted to the case that the subsequent hydraulic resistivity and diffusivity have a small rate of change with respect to the vertical variable. Applying the weakly nonlinear approach, we derive various order systems and express their solutions. The solutions for convective flow quantities such as …

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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 & Statistical Sciences Faculty Publications

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.

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

School of Mathematical & Statistical Sciences Faculty Publications

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 …