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Articles 1 - 23 of 23
Full-Text Articles in Physical Sciences and Mathematics
Peakon, Pseudo-Peakon, And Cuspon Solutions For Two Generalized Camassa- Holm Equations, Jibin Li, Zhijun Qiao
Peakon, Pseudo-Peakon, And Cuspon Solutions For Two Generalized Camassa- Holm Equations, Jibin Li, Zhijun Qiao
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we study peakon, cuspon, and pseudo-peakon solutions for two generalized Camassa-Holm equations. Based on the method of dynamical systems, the two generalized Camassa-Holm equations are shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, pseudo-peakons, and periodic cusp solutions. In particular, the pseudo-peakon solution is for the first time proposed in our paper. Moreover, when a traveling system has a singular straight line and a heteroclinic loop, under some parameter conditions, there must be peaked solitary wave solutions appearing.
The Computation Of Fluid Velocity In A Closed Cavity With A Moving Lid, Daniel A. Montez
The Computation Of Fluid Velocity In A Closed Cavity With A Moving Lid, Daniel A. Montez
Theses and Dissertations - UTB/UTPA
We consider a cavity filled with fluid whose three sides are stationary and the lid at the top is moving at a constant speed. The flow in the cavity is modeled using the conservation of mass and momentum equations with proper boundary conditions. We compute the fluid velocity for the steady state case using the finite element method. We seek the weak formulation and develop a finite element model based on the Galerkin method. Furthermore we use the penalty function method to modify our weak formulation to eliminate the pressure. The Gaussian quadrature method is used to evaluate our integrals …
Optimal Control In The Treatment Of Retinitis Pigmentosa, Erika T. Camacho, Luis A. Melara, Cristina Villalobos, Stephen Wirkus
Optimal Control In The Treatment Of Retinitis Pigmentosa, Erika T. Camacho, Luis A. Melara, Cristina Villalobos, Stephen Wirkus
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Numerous therapies have been implemented in an effort to minimize the debilitating effects of the degenerative eye disease Retinitis Pigmentosa (RP), yet none have provided satisfactory long-term solution. To date there is no treatment that can halt the degeneration of photoreceptors. The recent discovery of the RdCVF protein has provided researchers with a potential therapy that could slow the secondary wave of cone death. In this work, we build on an existing mathematical model of photoreceptor interactions in the presence of RP and incorporate various treatment regiments via RdCVF. Our results show that an optimal control exists for the administration …
On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera
On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera
Theses and Dissertations - UTB/UTPA
The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of …
Traveling Wave Solution To Two-Dimensional Burgers-Korteweg-De Vries Equation, Xiaoqian Gong
Traveling Wave Solution To Two-Dimensional Burgers-Korteweg-De Vries Equation, Xiaoqian Gong
Theses and Dissertations - UTB/UTPA
In this thesis, we study the Two-Dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analyzing the equivalent Abel equation, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded traveling wave solution. By using the theorem of contractive mapping, a traveling wave solution to the 2D-BKdV equation is expressed explicitly. In the end, the behavior of the proper solution of the 2D-BKdV equation is established by applying the comparison theorem of differential equations.
On Cubic Multisections, Andrew Alaniz
On Cubic Multisections, Andrew Alaniz
Theses and Dissertations - UTB/UTPA
In this thesis, a systematic procedure is given for generating cubic multi-sections of Eisenstein series. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. The resulting series are shown to be rational functions of the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations.
Synthetic Aperture Radar With Compressed Sensing, Yufeng Cao
Synthetic Aperture Radar With Compressed Sensing, Yufeng Cao
Theses and Dissertations - UTB/UTPA
A general synthetic aperture radar (SAR) signal model is derived from the Maxwell’s equations, and compressed sensing are introduced to the signal model for SAR image reconstruction. Random Partial Fourier Matrices were applied to prove that compressed sensing can be used to this signal model from the viewpoint of mathematics. In the numerical simulation part, we show that the procedure of basis pursuit can reconstruct SAR image, based on our main results, which is shown efficient in comparison with the matched filter algorithm.
Examine Participant Dropout, Undiagnosed Diabetes And Undiagnosed Prediabetes In A Chronic Disease Prevention Education Program, Yiwen Cao
Theses and Dissertations - UTB/UTPA
There were 2768 participants enrolled in a chronic disease prevention education program. Survey and health measurements were obtained at three time points. We examine potential factors that might contribute to participant dropout, undiagnosed diabetes and undiagnosed prediabetes respectively. Logistic regression was used to examine the association between participant dropout and predictors, and to compare the odds of being undiagnosed with diabetes and prediabetes. We found that the potential predictors for participant dropout included age, employment, insurance, diabetes, self-reported health status, session type, program duration and curriculum. Factors affecting undiagnosed diabetes and prediabetes were age, self-reported health status birth country, limited …
Lax Pairs For Some Nonlinear Equations, Ana Castillo
Lax Pairs For Some Nonlinear Equations, Ana Castillo
Theses and Dissertations - UTB/UTPA
Several methods have been proposed to approach the topic of integrable systems of nonlinear partial differential equations. One of these methods is called the Lax pair. The Lax pair is a pair of matrices or operators, that depend on time and satisfy the Lax equation. Based on the inverse scattering method introduced by Gardner, Greene, Kruskal and Miura (1967), Peter Lax introduced the Lax pair to derive soliton equations from the Lax equation. This thesis provides with a brief background on soliton theory, inverse scattering theory, and Lax pairs. The details missing in the work published by Ablowitz, Kaup, Newell, …
Distributed Sparse Matrix Solver And Pivoting Algorithms For Large Linear Equations, Esteban Torres
Distributed Sparse Matrix Solver And Pivoting Algorithms For Large Linear Equations, Esteban Torres
Theses and Dissertations - UTB/UTPA
This thesis presents a distributed sparse direct solver and pivoting strategies for distributed sparse LU factorization. In Chapter I, we introduce some background concepts in linear algebra. In Chapter II, we discuss parallel hardware architectures and introduce our problem for discussion. In Chapter III, we describe the implementation of our sparse direct solver and our pivoting algorithms. Next, we present our simulation methodology and results in Chapter IV and we show that our pivoting algorithm yields up to 50% more accurate results than a current state-of-the-art solver, SuperLU_DIST. Finally, in Chapter V, we present some ideas to further improve the …
Hydro-Thermal Convective Solutions For An Aquifer System Heated From Below, Dambaru Bhatta
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 …
Generalized Local Test For Local Extrema In Single-Variable Functions, Eleftherios Gkioulekas
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 …
Algebro-Geometric Solutions For The Degasperis--Procesi Hierarchy, Yu Hou, Peng Zhao, Engui Fan, Zhijun Qiao
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 …
Compressed Sensing For Multiple Input-Multiple Output Radar Imaging, Juan F. Lopez Jr.
Compressed Sensing For Multiple Input-Multiple Output Radar Imaging, Juan F. Lopez Jr.
Theses and Dissertations - UTB/UTPA
Multiple input - multiple output (MIMO) radar utilizes the transmission of spatially diverse waveforms from a static antenna array to gather information about the desired scene. We will demonstrate how techniques from compressed sensing can be applied to image formation in MIMO radar when in the presence of undersampling. We analyze the problem under the general theoretical framework of inverse scattering.
A Model For The Micro-Doppler Effect Of The Quadrupedal Body Motion, Noe Pena
A Model For The Micro-Doppler Effect Of The Quadrupedal Body Motion, Noe Pena
Theses and Dissertations - UTB/UTPA
In radar returns from quadrupedal body motion the micro-Doppler effect is present. This effect can be used to identify and distinguish this motion from others. In this work the model for the micro-Doppler effect due to quadrupedal motion is developed from Maxwell’s equations. The common gait for all quadrupedal mammal motion is described and analyzed. The radar crossection of quadrupedal motion backscattering is discussed. Quadrupedal motion is simulated and the radar returns are analyzed. The micro-Doppler signatures are decomposed and kinematic parameters are extracted
Mathematical Modeling Of Two-Phase Arterial Blood Flow, Ani Emire Garcia Escorcia
Mathematical Modeling Of Two-Phase Arterial Blood Flow, Ani Emire Garcia Escorcia
Theses and Dissertations - UTB/UTPA
Problem of blood flow in an artery with or without catheter and in the presence of single or multi stenosis will be considered. The presence of stenosis locally thickens the artery wall and the use of catheter in the affected area is very important to the diagnostic and treatment of the patient. The blood flow in the arterial tube is represented by a two-phase model composing a suspension of erythrocytes in plasma. The governing equations for both fluid and particles are solved subjected to reasonable modeling and approximations. The important quantities such as blood speed, blood pressure force, impedance (blood …
The Schwinger Action Principle And Its Applications To Quantum Mechanics, Paul Bracken
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.
On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev
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.
On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas
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.
Analytic Matrix Elements Of The Schrödinger Equation, Muhammad I. Bhatti
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 …
Zero-Bounded Limits As A Special Case Of The Squeeze Theorem For Evaluating Single-Variable And Multivariable Limits, Eleftherios Gkioulekas
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.
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
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
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].