Mathematics ThesesCopyright (c) 2024 University of Texas at Arlington All rights reserved.
https://mavmatrix.uta.edu/math_theses
Recent documents in Mathematics Thesesen-usThu, 12 Sep 2024 02:54:50 PDT3600A SNAPSHOT OF THE ALIGNMENT OF UNIVERSITY STUDENTS’ MATHEMATICAL PROBLEM SOLVING PRACTICES TO A LIKERT SCALE ASSESSMENT OF MATHEMATICAL PROBLEM SOLVING
https://mavmatrix.uta.edu/math_theses/26
https://mavmatrix.uta.edu/math_theses/26Tue, 10 Sep 2024 12:59:18 PDT
This study investigates the alignment of students' actual problem-solving practices and compares them to the outcomes on a Likert scale mathematical problem solving (MPS) assessment. The Likert scale survey items developed by the Mathematical Problem Solving Item Development Project (MPSI) to gather information on undergraduate's MPS in five domains: sense-making, representing/connecting, reviewing, justifying, and challenge (Epperson, Rhoads, and Campbell, 2016). This snapshot investigation analyzes two individual undergraduate student interviews to characterize the students' MPS practices. Data analysis suggests a promising alignment between the MPSI survey results and students' actual practices. The analysis also establishes preliminary reliability of the MPSI survey items and their links to the MPS domains from observations and responses during the student interviews. In addition, the relationship between the undergraduate students' subject-matter domain knowledge in algebra, their MPS behaviors, and their responses on the MPSI survey items is explored to determine what effects subject-matter domain knowledge may have on the MPSI survey results.
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Duy PhanUSE OF GENERALIZED GAMMA DISTRIBUTION IN MODELING
https://mavmatrix.uta.edu/math_theses/25
https://mavmatrix.uta.edu/math_theses/25Tue, 10 Sep 2024 12:59:17 PDT
In this study, we have considered analysis of lifetime or survival data with right censoring, which is the most common form of censoring encountered in practice. Assuming a fully parametric setup, the main objective is to consider a wider family of distributions for the lifetime and then find the maximum likelihood estimates of the model parameters using some optimization technique available in R statistical software. In this work, the generalized gamma distribution is considered as the distribution for the lifetime which is flexible in the sense that it contains some of the commonly used lifetime distributions, such as Weibull, gamma, and lognormal, as its special case. This flexibility allows us to carry out a formal test of hypothesis to determine a particular distribution within this family that provides an adequate fit to the data. Another objective is to carry out an extensive Monte Carlo simulation study to demonstrate the performance of the estimation method and the flexibility of the generalized gamma family. To demonstrate the flexibility of the generalized gamma family, we carried out a model discrimination using the likelihood ratio test and information-based criteria. Finally, we illustrate the estimation method and the flexibility of the generalized gamma family using a real data.
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Hongbo YuPredictive Model For Bigheaded Carps In Mississippi River
https://mavmatrix.uta.edu/math_theses/24
https://mavmatrix.uta.edu/math_theses/24Tue, 10 Sep 2024 12:59:17 PDT
Bigheaded carps refer to two species of fish called Silver carp and Bigheaded carp which have invaded the Upper Mississippi River System and are causing nuisance to the native fish like catfish, paddlefish and gizzard Shad by encroaching their habitat. The exponential growth of their population due to their overwhelming reproduction capability and adaptation features calls for a careful study of their population dynamics. In this study, we offer a mathematical model with artificial excessive fishing effort to reduce the population of Bigheaded carps. We numerically observe the correlation among growth rate, fishing rate and the future population of the Bigheaded carps.
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Jitendra K. ShresthaOptimal Control Methods for Chagas Disease
https://mavmatrix.uta.edu/math_theses/23
https://mavmatrix.uta.edu/math_theses/23Tue, 10 Sep 2024 12:59:16 PDT
Chagas disease is the world's most neglected tropical disease. Having a lack of cure makes the primary focus on the disease preventing it and controlling it. This study takes into account three different control measures: bed nets, low-volume insecticide spraying, and improving housing conditions, analyzes their cost effectiveness compared to each other, and determines which combination of the three control measures prevents the most T. cruzi infections in a rural Latin American village over a decade. It was shown that there is a a hierarchical importance in the control measures when preventing the spread of Chagas disease. In order of highest effectiveness, they are bed nets, low-volume insecticide spraying, and improving overall housing conditions. It was found that the most cost-effective scenario occurs when full coverage for bed nets and low-volume insecticide spraying is obtained, followed by devoting the remaining portion of the budget towards improving overall housing conditions. It was shown that if at least 36.30 USD per month is devoted to bed nets, then R₀ < 1.
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Francis MastromeTensor Products of a Finite-Dimensional Representation and an Infinite-Dimensional Representation
https://mavmatrix.uta.edu/math_theses/22
https://mavmatrix.uta.edu/math_theses/22Tue, 10 Sep 2024 12:59:16 PDT
In this project, we explicitly find the decomposition of the tensor product of a Verma module $Z(\lambda)$ and the standard module ${\mathbb C}^n$ of the Lie algebras $\mathfrak{sl}(n)$, $n=2,3$. The result provides an explicit description of the translation functor introduced by Bernstein and Gelfand.
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Felicia DewanagaA Mathematical Model of Hepatitis C Virus Infection Incorporating Immune Responses and Cell Proliferation
https://mavmatrix.uta.edu/math_theses/20
https://mavmatrix.uta.edu/math_theses/20Tue, 10 Sep 2024 12:59:15 PDT
This thesis introduces a mathematical model of differential equations for the chronic hepatitis C virus (HCV) infection, which is a contagious disease that infects the liver cells. Firstly, we present the early mathematical models for the basic dynamics of virus infection that developed and analyzed to understand the dynamics of human immunodeficiency virus (HIV), hepatitis B virus (HBV), and some other viruses. Next, we present the extended model of the basic HCV virus dynamics that incorporate the effectiveness of a treatment. After that, the mathematical model that includes proliferation terms for both infected and uninfected hepatocytes is discussed. Lastly, the mathematical model that is considering the interaction between HCV virus and immune responses in a host is introduced. In this thesis, we formulate an ordinary differential equations (ODE) model to describe the interactions between the hepatitis C (HCV) virus and the immune system in a human body under treatment, taking into consideration the proliferation for both infected and uninfected hepatocytes. Analysis of the model reveals the existence of multiple equilibrium states: the disease-free steady state in which no virus is present, an infected state with no immune responses, an infected steady state with immune responses in which virus and infected cells are present, an infected steady state with dominant CTLs responses in which no antibody (B-cell) is present, an infected steady state with dominant antibody responses in which no CTLs is present, and an infected steady state with coexistence responses in which all are present. Finally, we run simulations and compare our model to other models in the literature. In addition, several different scenarios were numerically simulated to demonstrate the practical applications of the mathematical model.
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Huda Amer HadiNUMBER SENSE IN HIGH SCHOOL MATHEMATICS STUDENTS
https://mavmatrix.uta.edu/math_theses/21
https://mavmatrix.uta.edu/math_theses/21Tue, 10 Sep 2024 12:59:15 PDT
Understanding the real number system plays a very important role in each student’s mathematical achievement. The Texas Essential Knowledge and Skills (TEKS) for Mathematics Subchapter A. Elementary states, “For students to become fluent in mathematics, students must develop a robust sense of number” (TEKS Subchapter A Elementary, 2012). Knowledge of the real number system and number sense develops over several years. Once students get to high school, they are expected to have a large amount of knowledge about the real number system and number sense in order to effectively start and complete their high school math courses. However, many high school students struggle with real numbers concepts and operations. The purpose of this project is to investigate the area(s) of number sense that high school students need to understand in order to be successful in mathematics. A number sense assessment tool was developed specific to students at the secondary level. The tool was used to evaluate that number sense of 124 high school students in varied mathematics courses.The outcomes of the number sense assessment were compared with the students’ most recent standardized math score, as well as the grade of the first quarter of the highest common level high school math class. The result shows a positive correlation between secondary students’ number sense knowledge and their mathematic ability.
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Vi Le NguyenEvaluating Factors Influencing Wound Healing: A Mixture Cure Rate Model Approach
https://mavmatrix.uta.edu/math_theses/19
https://mavmatrix.uta.edu/math_theses/19Tue, 13 Aug 2024 16:05:10 PDT
The study focuses on healing of chronic wound. A cure rate and probabilities of patients are calculated and visualized byusing Proportional Hazards Mixture Cure (PHMC) Model. This study reveals that alkaline wounds tend to heal slower than non-alkaline wounds, with significant differences between male and female patients. To be specific, males generally exhibit slower wound healing in both alkaline and non-alkaline conditions compared to females. This study also reveals the need for future research into biological, environmental and social factors, such as hormonal imbalance, living conditions and caregiver support among the patients.
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Anoushka KhayarHigh Order Weighted Compact Boundary Condition
https://mavmatrix.uta.edu/math_theses/18
https://mavmatrix.uta.edu/math_theses/18Mon, 08 Jul 2024 09:15:14 PDT
In multi-dimension flows, we expect to have problems at the boundaries when a shock hits or reflects at the boundary wall the remedy to this would be to develop weighted boundary conditions similar to the Weighted Compact Scheme for the interior nodes, by choosing candidate stencils around the boundary nodes and assigning weights to each of these stencils with the ENO reconstruction. This would avoid spurious oscillations when shocks are encountered at the boundaries. This thesis investigates higher order weighted compact boundary conditions for Weighted Compact Scheme (WCS). WCS is a combination of Essentially Non Oscillatory Scheme and Weighted Compact Finite Difference Schemes with Spectral-like Resolution. Implicit higher order schemes for spatial derivatives are derived for nodes in the neighborhood of the boundaries for the existing WCS scheme, which is used for the interior nodes. The objective is to achieve a higher weighted algorithm at the boundary, by using a compact stencil. To obtain this target, a combination of the spatial nodes' derivatives and values is going to be used. Several higher order schemes for the boundaries are derived and tested for both sine function and exponential function under 1st, 2nd and 3rd Boundary Condition. This new boundary scheme not only preserves the characteristic of standard compact schemes and achieves high order accuracy and high resolution using compact stencils, but also has the potential ability to accurately capture shock waves and discontinuities without oscillation. Numerical examples show the scheme is very promising and successful.
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Zhengjie WangNonlinear Dynamics And Stochasticity Of Core Genetic Regulation
https://mavmatrix.uta.edu/math_theses/15
https://mavmatrix.uta.edu/math_theses/15Mon, 08 Jul 2024 09:15:13 PDT
Bacillus subtilis is one of the very well-studied organisms in biology. Recent results show that an alternative competence regulation circuit for this bacterium, differing only in the order of the composite negative feedback loop onto the master competence regulator gene comK, despite presenting equivalent functionality, exhibits physiologically important differences.It is not clear why Nature only selects a specific gene regulation circuit other than a plethora of equivalent others. Here, we hope, from the point of view of reverse engineering, to discover the fundamental reasons for natural selection of a particular circuit structure over another. Based on the wild-type Bacillus subtilis circuit, we add a positive autoregulation feedback loop to the intermediate gene comS in the composite negative feedback loop onto ComK. Since positive feedback loops are most frequently observed in biology, this hypothetical modification of the original circuit is evolutionarily plausible.We use bifurcation theory to study the dynamical features of the hypothetical gene circuit vs. the feedback strength of the added positive autoregulation loop, and we rely on stochastic simulations to perform in silico experiments. We discover the existence of a bistable system: a stable limit cycle and a stable fixed point separated by an unstable limit cycle with a varying height of underlying stochastic potential. This structure is absent from the wild type. The coexistence of the unstable limit cycle and stochastic noise endows the circuit with an ability to trap, shield or switch between its two stable attractors. We study the implications for competence. By calculating the probability of entering competence, we conclude that the hypothetical circuit possesses less ability, compared to the wild-type circuit, to survive the severe environmental stresses. This provides some insight into the natural selection of a particular circuit structure by Evolution.
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Hongguang XiSolving The Optimization Control Problem For Lunar Soft Landing Using Minimization Technique
https://mavmatrix.uta.edu/math_theses/13
https://mavmatrix.uta.edu/math_theses/13Mon, 08 Jul 2024 09:15:12 PDT
Minimizing fuel consumption in lunar missions has been a well studied and documented optimization problem. In this paper two cases of the lunar Lander are studied. The first case is the one dimensional problem where the objective is to make a vertical soft landing using the minimum amount of fuel. The second case has the same objective but an initial tangential velocity greater than zero is given making it a two dimensional problem. The first case is solved using Newton's shooting method, finite difference method (using MATLAB's embedded function bvp4c), and solving it explicitly. For the second case, a minimization technique is proposed for cases where the above methods fail to provide a solution.
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Lizeth Patricia OcampoOn The Image Of The Totalling Functor
https://mavmatrix.uta.edu/math_theses/12
https://mavmatrix.uta.edu/math_theses/12Mon, 08 Jul 2024 09:15:11 PDT
Let A denote a DG algebra and k a field. The totalling functor, from the category of chain complexes over the graded A-modules to the catagory of DG modules over A, can be extended to one between their derived categories. If this extension were onto, the derived category of the category of DG modules would be superfluous. This paper investigates the image of the extension of Tot in the fundamental case when A is the polynomial ring in d variables over k. When d is at least 2, there are semifree DG modules of rank n, where n is at least 4, that are not obtained from the totalling of any complex of graded A-modules. However, when A=k[x], every rank n semifree DG module over A is in the image of Tot. Moreover, for a polynomial ring of arbitrary size, we will define a special class of rank n semifree DG modules over A which are always in the image of Tot.
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Kristen Ann BeckAn Investigation Of The Conceptual Understanding Of Continuity And Derivatives In Calculus Of Emerging Scholars Versus Non-emerging Scholars Program Students
https://mavmatrix.uta.edu/math_theses/9
https://mavmatrix.uta.edu/math_theses/9Mon, 08 Jul 2024 09:15:09 PDT
The Emerging Scholars Program (ESP) has been adapted at colleges and universities across the nation in efforts to increase student access to Science, Technology, Engineering and Mathematics (STEM) disciplines. This study uses a written assessment to gain insight regarding conceptual knowledge on continuity and derivatives for ESP students versus non-ESP students in the same lecture course in first semester calculus at large urban university in the southwest. We analyze the assessment results of 22 ESP and 48 non-ESP students and discuss findings, particularly, those that indicate statistically significant differences regarding continuity over an interval.
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Susan Lai ChanA Mathematical Model For Swine Flu 2009 With Vaccination
https://mavmatrix.uta.edu/math_theses/6
https://mavmatrix.uta.edu/math_theses/6Mon, 08 Jul 2024 09:15:08 PDT
H1N1 influenza is one of the deadliest diseases in human's history. Swine Flu 2009 is the same virus and it was named in 2009. Vaccination is of the most common ways to control a disease. We offer a new vaccination model with recommendations from the US Centers for Disease Control and Prevention (CDC). The entire population is divided into 4 different age groups: one group with no vaccination, one group with 2 doses of vaccination, and two groups with 1 dose of vaccination. We establish that higher levels of vaccination lead to greater savings of life. We also consider the effects of vaccination on the economy by comparing the number of infected people to different vaccination rates. We also consider a special case for office workers and nursing home persons to look at the aspects of the above mentioned effects. A set of numerical simulations is also presented to show these outcomes.
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Irfan TurkMultiple Linear Regression Model Of Visceral Leishmaniasis In Bihar, India
https://mavmatrix.uta.edu/math_theses/7
https://mavmatrix.uta.edu/math_theses/7Mon, 08 Jul 2024 09:15:08 PDT
Visceral Leishmaniasis (VL) is one of the world's worst parasitic killers, second only to Malaria, claiming nearly 500,000 lives each year. The disease attacks the spleen, liver, and bone marrow, and if left untreated is nearly always fatal. Whilst the disease is found all around the world, it is primarily prevalent in developing countries, in particular India. The most affected state in India is Bihar, where the disease is endemic. While other research has been conducted with emphasis on the effect of climate variables on the disease incidence rate, this analysis focuses on socio-economic variables such as literacy rate, housing structure, and working environment, to study their roles on the incidence rate. A Multiple linear regression model that includes these socio-economic factors as independent variables was initially developed and it explained 92% of the observed variance. The model was then reduced via stepwise regression and two models that explained 81% and 63% of the observed variance were used to help determine the most significant variables, such as housing and literacy rates. Modest comments are made on possible measures that could be taken to decrease the VL incidence rate, along with limitations of the model and suggestions for further research on this topic.
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Darren SheetsA Snapshot Of Advanced High School Students' Understanding Of Continuity
https://mavmatrix.uta.edu/math_theses/5
https://mavmatrix.uta.edu/math_theses/5Mon, 08 Jul 2024 09:15:07 PDT
We report on a study of sixteen high school calculus and seven precalculus students' concept image and concept definition of continuity after one-trimester of instruction at a large suburban high school in the southwestern United States. The researchers developed a questionnaire based upon the work of Tall and Vinner (1981) to determine if calculus students had developed a more sophisticated concept image and concept definition of continuity than students in pre-calculus after a typical treatment in both courses. Using data from the written assessment it was not evident that calculus students demonstrated a more sophisticated concept image and concept definition than pre-calculus students. However, findings suggest that a weak concept image or concept definition of continuity reflects practices in precalculus and calculus instruction.
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Melissa Jo VelaThe Impact Of Vaccination And Multiple Types Of HPV On Cervical Cancer
https://mavmatrix.uta.edu/math_theses/4
https://mavmatrix.uta.edu/math_theses/4Mon, 08 Jul 2024 09:15:07 PDT
Understanding the relationship between multiple strains of human papillomavirus and cervical cancer may play a key role in vaccination strategies for the virus. In this article we formulate a model with two strains of infection and vaccination for one of the strains in order to investigate how multiple strains of HPV and vaccination may aect the number of cervical cancer cases and deaths due to infections with both types of HPV. We calculate the basic reproductive number for both strains independently as well as the basic reproductive number for the system based on R1 and R2. We also compute the invasion reproductive number R~i for strain i when strain j is at equilibrium (i 6= j). We show that the disease-free equilibrium is locally stable when R0 = maxfR1;R2g < 1 and each single strain endemic equilibrium Ei exists when Ri > 1. We determine stability of the single strain equilibrium using the invasion reproductive numbers. The R1;R2 parameter space is partitioned into 4 regions by the curves R1 = 1;R2 = 1;R~1 = 1, and R~2 = 1. In each region a dierent equilibrium is dominant. The presence of strain 2 can increase strain 1 related cancer deaths by more than 100 percent, but can be reduced by more than 90 percent with 50 percent vaccination coverage. Under certain conditions, we show that vaccination against strain 1 can actually eradicate strain 2.
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Britnee A. CrawfordComparative Analysis Of Various Continuous-time Deterministic Models Of Tumor-immune Interactions
https://mavmatrix.uta.edu/math_theses/2
https://mavmatrix.uta.edu/math_theses/2Mon, 08 Jul 2024 09:15:05 PDT
Cancer is historically a leading cause of death in the United States. In 2013,cancer was the second leading cause of death with 584,881 deaths \cite{CDC}.Having solely been responsible for 22.5\% of all deaths in 2013 alone \cite{CDC},obtaining as complete an understanding as possible of cancer is obviously necessitated.I investigate deterministic ordinary differential equation models of increasingcomplexity simulating avascular tumor growth and interactions with the innate immuneresponse. After first establishing a baseline of tumor growth limited only by theavailability of local nutrients, I compare the effects on said growth of the nativeimmune system response, chemotherapy, immunotherapy, and various combinations ofthe aforementioned treatment options and responses. These efforts focus onincreasing the understanding of tumor-immune interactions under various conditionsand scenarios in hopes of identifying the most effective approach in combatingsimilar cancerous tumors.
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Robert Paul ChildressCuspidal Modules Of The Lie Superalgebras Osp(1|2n)
https://mavmatrix.uta.edu/math_theses/1
https://mavmatrix.uta.edu/math_theses/1Mon, 08 Jul 2024 09:15:05 PDT
The classification of all bounded weight modules for the classical Lie superalgebras is an open question. Only recently, in fact, has the question been closed for the Lie algebras (see Mathieu). We give a differential algebra isomorphic to osp(1|2n), which is one of the remaining Lie superalgebras to have its modules classified. We also conjecture, following the results for the Lie algebra sp(2n), a method to finalize the classification for osp(1|2n).
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Alekzander J. Malcom