Mathematics Commons^™

A Variational Study On A Natural Hamiltonian For Curves, Gözde Özkan Tükel

Turkish Journal of Mathematics

A variational study of finding critical points of the total squared torsion functional for curves in Euclidean 3-spaces is presented. Critical points of this functional also known as one of the natural Hamiltonians of curves are characterized by two Euler-Lagrange equations in terms of curvature and torsion of a curve. To solve these balance equations, the curvature of the critical curve is expressed by its torsion so that equations are completely solved by quadratures. Then two Killing fields along the critical curve are found for integrating the structural equations of the critical curve and this curve is expressed by quadratures …

Approximately Rings In Proximal Relator Spaces, Ebubeki̇r İnan

Turkish Journal of Mathematics

This article introduces approximately rings, approximately ideals, and approximately rings of all approximately cosets by considering new operations on the set of all approximately cosets. Afterwards, some properties of approximately rings and ideals were given.

Conceptualizing And Interpreting Mean And Median With Future Teachers, Eryn M. Stehr, Ha Nguyen, Gregory Chamblee, Sharon Taylor

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of …

Characterizations Of Certain Recently Introduced Discrete Distributions, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of certain recently introduced discrete distributions are presented to complete, in some way, the works cited in the References.

Case–Control Research Study Of Auto-Brewery Syndrome, Barbara Jean Cordell, Anup Kanodia, Gregory K. Miller

Faculty Publications

Background: Auto-brewery syndrome (ABS), also known as Gut Fermentation Syndrome and Endogenous Ethanol Fermentation, is afflicting people worldwide, but little is known about ABS patients’ demographics, health history, lifestyle factors, and diet.

Method: We conducted a broad-based case–control survey study on 52 patients known to have a diagnosis of ABS and their household members. The research compares the symptomatic group (N ¼ 28) to the asymptomatic group (N ¼ 18) regarding lifestyle and health, diet, and medical history.

Results: With a response rate of 88% and using rank-sum tests, the data demonstrate that patients with ABS have …

A Limiting Process To Invert The Gauss-Radon Transform, Jeremy Becnel

Faculty Publications

In this work we extend the finite dimensional Radon transform [23] to the Gaussian measure. We develop an inversion formula for this GaussRadon transform by way of Fourier inversion formula. We then proceed to extend these results to the infinite dimensional setting.

Recovering A Random Variable From Conditional Expectations Using Reconstruction Algorithms For The Gauss Radon Transform, Jeremy Becnel, Daniel Riser-Espinoza

Faculty Publications

The Radon transform maps a function on n-dimensional Euclidean space onto its integral over a hyperplane. The fields of modern computerized tomography and medical imaging are fundamentally based on the Radon transform and the computer implementation of the inversion, or reconstruction, techniques of the Radon transform. In this work we use the Radon transform with a Gaussian measure to recover random variables from their conditional expectations. We derive reconstruction algorithms for random variables of unbounded support from samples of conditional expectations and discuss the error inherent in each algorithm.

Adjustment Of Maximum Likelihood Method For Multivariate Fay-Herriot Model, Annop Angkunsit

Chulalongkorn University Theses and Dissertations (Chula ETD)

The most widely used area-level model in small area estimation is the Fay-Herriot model, proposed by Fay and Herriot. It was used first to estimate average per capita income for small places (population less than 1,000) of the USA. In the context of the Fay-Herriot model, the traditional method in obtaining estimation of the population mean is the empirical best linear unbiased prediction (EBLUP) estimator. The estimate can be expressed as a weighted sum of the direct survey estimator and regression estimator. One problem that has received attention is the estimation of variance of the area random effects in the …

Solving System Of Linear Integro-Differential Equations By Finite Integration Method With Shifted Chebyshev Polynomials, Matinee Juytai

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we modify the finite integration method by using the shifted Chebyshev polynomial (FIM-SCP). The major tool of our FIM-SCP is the shifted Chebyshev integration matrix. It is constructed in order to be a matrix representation for integrating over interpolated points which are generated by the zeros of shifted Chebyshev polynomial of a certain degree. The efficiently numerical algorithms are then created by the modified FIM-SCP for seeking approximate solutions of a system of stiff linear ordinary differential equations, a system of linear Volterra integro-differential equations, and a system of linear Fredholm integro-differential equations under some given boundary …

Text Localization And Extraction From Background With Texture And Noise In Digital Images Using Adaptive Thresholding And Convolutional Neural Network, Pukjira Pattaranuprawat

Chulalongkorn University Theses and Dissertations (Chula ETD)

For the past few years, research topics on finding position of text have received more and more attention from researchers because there are still lots of problems that are needed to be solven. We propose a novel method to find the position of text in an image. The first step of the proposed method is to adjust an image by converting a color image to a gray scale image and then use an average filter to improve an image. An average filter is used to make the background smooth and reduce noise. After that an adaptive thresholding is used to …

Some Results On Partial Difference Sets And Partial Geometries, Eric J. Neubert Jr

Dissertations, Master's Theses and Master's Reports

This thesis shows results on 3 different problems involving partial difference sets (PDS) in abelian groups, and uses PDS to study partial geometries with an abelian Singer group. First, the last two undetermined cases of PDS on abelian groups with k ≤ 100, both of order 216, were shown not to exist. Second, new parameter bounds for k and ∆ were found for PDS on abelian groups of order p^n , p an odd prime, n odd. A parameter search on p^5 in particular was conducted, and only 5 possible such cases remain for p < 250. Lastly, the existence of rigid type partial geometries with an abelian Singer group are examined; existence is left undetermined for 11 cases with α ≤ 200. This final study led to the determination of nonexistence for an infinite class of cases which impose a negative Latin type PDS.

Uniform Distribution Of Fractional Parts Of Average Of Kth Power Of Prime Divisors, Chitpanu Chairatanagul

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we prove that for every positive integer k greater than or equal to two, the sequence of the fractional parts of the arithmetic mean of the kth power of prime divisors of n counted with or without multiplicity, as n runs through all positive integers, is uniformly distributed modulo one.

Parameter-Free Outlier Scoring Using Acute Angle Ordered Difference Distance, Pollaton Pumruckthum

Chulalongkorn University Theses and Dissertations (Chula ETD)

An anomaly scoring algorithm assigns a score to an instance that provides a large value for an outlier in order to help detecting anomalies within a dataset. In 2013, one of the parameter-free techniques called the order difference distance outlier factor was proposed (OOF). OOF was computed using the ordered difference distance derived from the distance matrix sorted in each row, before calculating the difference. The minimum distance was included to avoid false detection but it also decreased the score of anomalies forming a small cluster. To avoid the use of the minimum distance, the new technique is proposed base …

Normal Approximation For Locally Dependent Collateralized Debt Obligation, Suporn Jongpreechaharn

Chulalongkorn University Theses and Dissertations (Chula ETD)

This dissertation sheds light on a collateralized debt obligation (CDO) since it resulted in the financial crisis between 2007 and 2008. Because of damage of this crisis, several authors have attempted to approximate loss on a tranche of a CDO. For instance, in 2009, Karoui and Jiao used a normal random variable to approximate the loss on a tranche of a CDO containing independent assets. However, in this work, we are attentive to dependence structure among assets in a CDO. We present two types of dependent condition: local dependence (LD) and disjoint local dependence (DLD). They roughly mean that defaults …

Boundaries Of Overlapping Reuleaux Triangles, Jirapat Kaewkam

Chulalongkorn University Theses and Dissertations (Chula ETD)

where R1 and R2 are two congruent Reuleaux triangle such that Int(R1)∩Int(R2) ̸= ∅. Denote ∂Ri and Int(Ri) the boundary and the interior of Ri , respectively. We finish the proof when R2 is a translated copy R1 and we obtain some interesting results when R1 and R2 intersect in general position.

Numerical Methods For Jump-Extended Cox-Ingersoll-Ross And Constant Elasticity Of Variance Models, Purin Klunklar

Chulalongkorn University Theses and Dissertations (Chula ETD)

The jump-extended Cox-Ingersoll-Ross and jump-extended constant elasticity of variance models are stochastic differential equations (SDEs) used to forecast interest rates or stock prices. We simulate these SDEs directly by eight numerical methods: Euler Maruyama method, simplified Euler method, jump-adapted Euler method, jumpadapted simplified Euler method, jump-adapted order two weak method, jump-adapted simplified order two weak method, jump-adapted order two derivative free method and jump-adapted simplified order two derivative free method. The transformed approach is also applied with these eight numerical methods. We compare their performance by testing the positivity preserving of numerical solutions and finding their weak orders of convergence …

Covers For Leo Moser's Worm Problem, Thitipong Kanchai

Chulalongkorn University Theses and Dissertations (Chula ETD)

Leo Moser’s worm problem was posted in 1966 stating that “What is the region of the smallest area that can cover every unit are?”. In 2018, N. Ploymaklam and W. Wichiramala illustrated a new cover, which is currently smallest. Their cover was adapted from the cover of R. Norwood and G. Poole. In this work, we modify the region from the work of R. Norwood and G. Poole and the work of N. Ploymaklam and W. Wichiramala. Our regions are modified by changing their upper boundary. However, the regions remain satisfying properties in the work of R. Norwood and G. …

Stationary Test For First Order Autoregressive Model Subject To Sampling Errors, Weerapat Rattanachadjan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In 1979, Dickey and Fuller introduced a stationary test on the first order autoregressive model, AR(1), and limitting distribution of the estimator of autoregressive coefficient and the test statistics. The method has been applied to test the stationarity of the first order autoregressive time series model. However, the method has been applied regardless of sampling errors which usually occurs in data collection. autoregressive model subject to sampling errors.

On A Generalization Of Lucas Numbers, Skylyn Olyvia Irby

Honors Theses

In this paper, we consider a generalization of Lucas numbers. Recall that Lucas numbers are the sequence of integers defined by the recurrence relation: L_n = L_{n−1} + L_{n−2} with the initial conditions L_1 = 1 and L_2 = 3(or L_0 = 1 and L_1 = 3 if the first subscript is zero). That is, the classical Lucas number sequence is 1, 3, 4, 7, 11, 18, .... The goal of the present paper is to study properties of certain generalizations of the Lucas sequence. In particular, we consider the following generalizations of the sequence: l_n = al_{n−1} + l_{n−2} …

6th-12th Grade Math Teachers And Their Experiences With The Mississippi College- And Career-Readiness Standards, Dorothy Reid

Honors Theses

This thesis identifies and describes 6th-12th grade math teachers and their experiences with the Mississippi College- and Career- Readiness Standards. There are two parts to this thesis: 1) a survey distributed to public school math teachers across the state and 2) the written thesis. In my thesis, I craft teacher narratives from the quantitative and qualitative results of the survey. Listening to the teachers’ narratives provides beneficial insights to the implementation of the MCCRS at the classroom level. Teachers have many different experiences. My thesis offers policy recommendations, based on the teacher narratives, to three levels of education: teachers, schools …

Upper Bounds For Constant Slope P-Adic Families Of Modular Forms, John Bergdall

Mathematics Faculty Research and Scholarship

We study p-adic families of eigenforms for which the p-th Hecke eigenvalue 𝑎𝑝 a p has constant p-adic valuation (“constant slope families”). We prove two separate upper bounds for the size of such families. The first is in terms of the logarithmic derivative of 𝑎𝑝 a p while the second depends only on the slope of the family. We also investigate the numerical relationship between our results and the former Gouvêa–Mazur conjecture.

Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives, Ramunas Garunkstis

Turkish Journal of Mathematics

Levinson and Montgomery proved that the Riemann zeta-function ζ(s) and its derivative have approximately the same number of nonreal zeros left of the critical line. Spira showed that ζ'(1/2+it) = 0 implies that ζ(1/2+it) = 0. Here we obtain that in small areas located to the left of the critical line and near it the functions ζ(s) and ζ'(s) have the same number of zeros. We prove our result for more general zeta-functions from the extended Selberg class S. We also consider zero trajectories of a certain family of zeta-functions from S.

A First-Year Teacher’S Implementation Of Short-Cycle Formative Assessment Through The Use Of A Classroom Response System And Flexible Grouping, Adrienne Irving Dumas

Electronic Theses and Dissertations

As teachers we are tasked with ensuring that our students are equipped with the skills necessary to not only perform with proficiency on local state and national assessments but also to provide our students with opportunities to develop confidence and competence as learners of mathematics through meaningful challenging and worthwhile activities. As such many teachers have turned to technology and cooperative groups as staples in the classroom. The purpose of this study was to understand how one first-year teacher implemented what she was taught in her undergraduate coursework in teaching two specific units of instruction in two sections of high …

Beta Invariant And Variations Of Chain Theorems For Matroids, Sooyeon Lee

Electronic Theses and Dissertations

The beta invariant of a matroid was introduced by Crapo in 1967. We first find the lower bound of the beta invariant of 3-connected matroids with rank r and the matroids which attain the lower bound. Second we characterize the matroids with beta invariant 5 and 6. For binary matroids we characterize matroids with beta invariant 7. These results extend earlier work of Oxley. Lastly we partially answer an open question of chromatic uniqueness of wheels and prove a splitting formula for the beta invariant of generalized parallel connection of two matroids. Tutte's Wheel-and-Whirl theorem and Seymour's Splitter theorem give …

Quadratic Reciprocity: Proofs And Applications, Awatef Noweafa Almuteri

Electronic Theses and Dissertations

The law of quadratic reciprocity is an important result in number theory. The purpose of this thesis is to present several proofs as well as applications of the law of quadratic reciprocity. I will present three proofs of the quadratic reciprocity. We begin with a proof that depends on Gauss's lemma and Eisenstein's lemma. We then describe another proof due to Eisentein using the $n$th roots of unity. Then we provide a modern proof published in 1991 by Rousseau. In the second part of the thesis, we present two applications of quadratic reciprocity. These include special cases of Dirichlet's theorem …

Procuring Pediatric Vaccines In A Two-Economy Duopoly, Seongeun Lee, Susan E. Martonosi

Scripps Senior Theses

In this work, we aim to present an optimization model for vaccine pricing in a two-economy duopoly. This model observes the price dynamics between a high income country and a low income country that procure vaccinations through PAHO. This model is formulated to provide insights on optimal pricing strategy for PAHO to ultimately increase vaccine accessibility to low income countries. The objective is to satisfy the public demand at the lowest price possible, while providing enough profit for the vaccine manufacturers to stay in business. Using non-linear integer programming, the model results show that cross-subsidization occurs in PAHO vaccine procurement.

Formulation And Implementation Of Iterative Method For Generating Spatially-Variant Lattices, Manuel Fernando Martinez

Open Access Theses & Dissertations

The use of a matrix-free, memory-efficient approach to generate large-scale spatially variant lattices (SVL) was explored. A matrix-free iterative SVL generation algorithm was formulated and then implemented with a tremendous memory reduction observed. The algorithm consists of solving first-order central finite-differences along the entirety of the problem space point-by-point to obtain the grating phase function Φ(𝑠⃗) to which all desired spatially variant lattice properties are applied to. The algorithm was studied to identify key areas of data and task parallelism to exploit in heterogeneous computing systems consisting of clusters of central processing units (CPU) and graphics processing units (GPU) combinations. …

Cantor Sets, Cantorvals, And Their Topological Structure, Ángel Adrián Agüero

Open Access Theses & Dissertations

With interesting topological properties, the Cantor set is worth studying for itself. In other areas, topological structures arise that are in fact homeomorphic to the Cantor set. In particular, we see sets that are homeomorphic to the Cantor set which result from the subsums of particular series, as well as linear combinations of algebraic sums of Cantor sets. These also result in what has been termed a Cantorval, which we also investigate.

Improving Student Achievement Through The Implementation Of A Classroom Performance System, Stacy Maria Artis

Theses and Dissertations

This applied dissertation was designed to implement and examine the impact of a classroom performance system (CPS) on student achievement for Grade 9 mathematics students. Seventy-five students in 4 Coordinate Algebra classes were observed during the regular school day for 9 weeks. The treatment group received CPS-based instruction, and the control group received traditional mathematics instruction without the use of a CPS. The teacher was the same for all classes.

Data from benchmark assessments as well as quarterly grade reports were compared for both groups. The findings of this study showed mixed results in relation to the impact of CPS-based …

Robust Statistical Inference For The Gaussian Distribution, Andrews Tawiah Anum

Open Access Theses & Dissertations

The aim of robust statistics is to develop statistical procedures which are not unduly influenced by outliers or observations that are not representative of the underlying "true" data generating process. This thesis focuses on an estimator with this characteristic. The divergence function is introduced in Chapter 2 with the sole aim of taking the function f to be the univariate normal distribution and α - [0, 1]. The estimator fails when we rely on the classic Newton's method to converge to the minimum of the density power divergence (MDPD) function. There is a tendency of such estimator never to approach …