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Physical Sciences and Mathematics Commons™

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Theses/Dissertations

2016

Mathematics

University of Texas Rio Grande Valley

Articles 1 - 8 of 8

Full-Text Articles in Physical Sciences and Mathematics

Numerical Simulations Of Shock Waves Reflection And Interaction, Ligang Sun Dec 2016

Numerical Simulations Of Shock Waves Reflection And Interaction, Ligang Sun

Theses and Dissertations

The main objective of this dissertation is to detect and study the phenomena of reflection of one shock wave and interaction of two shock waves using numerical methods. In theory, solutions of non-linear Euler equations of compressive inviscid gas dynamics in two dimensions can display various features including shock waves and rarefaction waves. To capture the shock waves properly, highly accurate numerical schemes are designed according to second order Lax-Wendroff method. In this thesis, three numerical experiments were designed to show the reflection and interaction phenomena. Firstly, one shock was formed due to the encounter of two high speed gas …

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Sparse Representation For The Isar Image Reconstruction, Mengqi Hu Aug 2016

Sparse Representation For The Isar Image Reconstruction, Mengqi Hu

Theses and Dissertations

In this paper, a sparse representation for the data form a multi-input multi-output based inverse synthetic aperture radar (ISAR) system is derived for two dimensions. The proposed sparse representation motivates the use a of a Convex Optimization directly that recovers the image without the loss information of the image with far less samples that that is required by Nyquist–Shannon sampling theorem, which increases the efficiency and decrease the cost of calculation in radar imaging.

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Lie Symmetry To Second-Order Nonlinear Differential Equations And Its First Integrals, Pengfei Gu Aug 2016

Lie Symmetry To Second-Order Nonlinear Differential Equations And Its First Integrals, Pengfei Gu

Theses and Dissertations

There are many well-known techniques for obtaining exact solutions of differential equations, but most of them are merely special cases of a few powerful symmetry methods. In this paper, we focus our attention on a second-order nonlinear ordinary differential equation of special forms with arbitrary parameters, which is a combination of Liénard-type equation and equation with quadratic friction. With the help of Lie Symmetry methods, we identify several integrable cases of this equation. And for each case, we use the Lie Symmetry method to derive the associated determining system, and apply it further to find infinitesimal generators under …

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A Comparative Study And Data Analysis For The Ultimate Fighting Championship, Victor Villalpando Aug 2016

A Comparative Study And Data Analysis For The Ultimate Fighting Championship, Victor Villalpando

Theses and Dissertations

Mixed Martial Arts is the fastest growing sport with many organizations worldwide. The biggest stage or biggest organization for Mixed Martial Arts is the Ultimate Fighting Championship (UFC). There are eight weight classes for men. The website: http://www.foxsports.com/ufc/stats provides data on fighters in all these categories. This data measures Striking Accuracy, Take downs, Reversals, Knockdowns, etc. in each category. It is interesting to understand and interpret all these numbers and study their relationships. Statistical tools like both parametric and nonparametric inference may give rise to such interpretations and provide explanations how the weight classes differ from one another. In this …

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Compressive Sensing And Radar Imaging, John Montalbo Jul 2016

Compressive Sensing And Radar Imaging, John Montalbo

Theses and Dissertations

The field of remote sensing contains many unique and practical problems. Radar imaging, in all of its many forms, lies within this field of study. One problem is the need to acquire high-resolution images and store them on-board the system acquisition vessel . For some systems this could mean storing very high amounts of data, depending on the scene in question [3]. So a very natural goal is to store only what is absolutely necessary and nothing more. We investigate methods to compress signals into their most important components so that other parties can recover the original data completely or …

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On Hypergroups Of Order At Most 6, Jordy C. Lopez May 2016

On Hypergroups Of Order At Most 6, Jordy C. Lopez

Theses and Dissertations

This thesis surveys recent results on hypergroups as defined by Frédéric Marty in [3] and [4] and their relation to association schemes as presented in [5]. We show that every association scheme is a hypergroup. Then, we compile a few general results on hypergroups needed for our investigation of hypergroups with three, four and six elements. From [1] and [7], we give examples of hypergroups that do not come from finite schemes and from no scheme at all. Our main result occurs when considering hypergroups S with six elements that have a non-normal closed subset T of order 2 with …

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Opinion Formation About Childhood Immunization And Disease Spread On Networks, Shan Shan Zhao May 2016

Opinion Formation About Childhood Immunization And Disease Spread On Networks, Shan Shan Zhao

Theses and Dissertations

People are physically and socially connected with each other. Those connections between people represent two, probably overlapping, networks: biological networks, through which physical contacts occur, or social network, through which information diffuse. In my thesis research, I am trying to answer that question in the context of pediatric disease spread on the biological network between households as well as within them and its relationship with information sharing on the social network of households (parents in that case) via "Information Cascades." I mainly focus on the Erdos-Renyi network model. In particular, I use two different but overlapping Erdos-Renyi networks for the …

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Lie Symmetry To Nonlinear Oscillator Systems And Applications, Xiaoyan Li May 2016

Lie Symmetry To Nonlinear Oscillator Systems And Applications, Xiaoyan Li

Theses and Dissertations

In this paper, we apply the theory of Lie symmetry to study a generalized second-order nonlinear differential equation, which includes several physical nonlinear oscillators such as force-free Helmholtz oscillator, force-free Duffing and Duffing-van der Pol oscillators, modified Emden-type equation and its hierarchy etc, and investigate the dynamical properties of this rather general equation. We identify and classify several new integrable cases for arbitrary values of exponents, which determine the tangent vector as well as the infinitesimal generator. Using the Lie point symmetry, we find the useful infinitesimal generators and canonical coordinates, and obtain the first integrals of the second-order nonlinear …

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