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2019

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Articles 1201 - 1230 of 1389

Full-Text Articles in Mathematics

What Is The Shape Of A Traditional Rapanui House On Easter Island? A Multicultural Mathematical Activity Involving Ellipses, Cynthia J. Huffman Ph.D. Jan 2019

What Is The Shape Of A Traditional Rapanui House On Easter Island? A Multicultural Mathematical Activity Involving Ellipses, Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

The Rapanui people of the island Rapa Nui, also known as Easter Island, at one time had a system of “writing” called Rongorongo. Unfortunately, the ability to read Rongorongo has since been lost. So currently archaeology and oral tradition are the only available sources for information about the early people of the island. Oral tradition states that the houses originally had upside down canoes for their roofs, and thus they are called hare paenga, or in English, boat-houses. In the literature, these boat-houses are said to be elliptical in shape. In this activity, we will investigate the shape of archaeological …

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The Game Of Ur: An Exercise In Strategic Thinking And Problem Solving And A Fun Math Club Activity, Cynthia J. Huffman Ph.D. Jan 2019

The Game Of Ur: An Exercise In Strategic Thinking And Problem Solving And A Fun Math Club Activity, Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

In this Open Educational Resource activity, students learn a little about the history of the Royal Game of Ur, the first board game, and get to practice critical thinking and problem solving by playing the game. Instructions are given along with a template for the game and game pieces and tetrahedral die.

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Cgi (Computer Generated Imagery) Matrix Multiplication Activity, Cynthia J. Huffman Ph.D. Jan 2019

Cgi (Computer Generated Imagery) Matrix Multiplication Activity, Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

Many students are motivated by real world applications of mathematics, and most students are familiar with the term CGI from watching movies and playing video games. This particular activity ties matrix multiplication to CGI (Computer Generated Imagery). It has been used successfully with high school students in an Algebra II course who had just learned how to do matrix multiplication, middle school and high school students (some of whom were seeing matrix multiplication for the first time) attending a special Math Day on a university campus, and with College Algebra students (during a unit about matrices).

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Kings In The Direct Product Of Digraphs, Morgan Norge Jan 2019

Kings In The Direct Product Of Digraphs, Morgan Norge

Theses and Dissertations

A k-king in a digraph D is a vertex that can reach every other vertex in D by a directed path of length at most k. A king is a vertex that is a k-king for some k. We will look at kings in the direct product of digraphs and characterize a relationship between kings in the product and kings in the factors. This is a continuation of a project in which a similar characterization is found for the cartesian product of digraphs, the strong product of digraphs, and the lexicographic product of digraphs.

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Some Intuition Behind Large Cardinal Axioms, Their Characterization, And Related Results, Philip A. White Jan 2019

Some Intuition Behind Large Cardinal Axioms, Their Characterization, And Related Results, Philip A. White

Theses and Dissertations

We aim to explain the intuition behind several large cardinal axioms, give characterization theorems for these axioms, and then discuss a few of their properties. As a capstone, we hope to introduce a new large cardinal notion and give a similar characterization theorem of this new notion. Our new notion of near strong compactness was inspired by the similar notion of near supercompactness, due to Jason Schanker.

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Gallai-Ramsey Number For Classes Of Brooms, Benjamin J. Hamlin Jan 2019

Gallai-Ramsey Number For Classes Of Brooms, Benjamin J. Hamlin

College of Graduate Studies: Theses & Dissertations

Given a graph $G$, we consider the problem of finding the minimum number $n$ such that any $k$ edge colored complete graph on $n$ vertices contains either a rainbow colored triangle or a monochromatic copy of the graph $G$, denoted $gr_k(K_{3}:G)$. More precisely we consider $G=B_{m,\ell}$ where $B_{m,\ell}$ is a broom graph with $m$ representing the number of vertices on the handle and $\ell$ representing the number of bristle vertices. We develop a technique to reduce the difficulty of finding $gr_{k}(K_{3}:B_{m,\ell})$, and use the technique to prove a few cases with a fixed handle length, but arbitrarily many bristles. Further, …

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Homological Constructions Over A Ring Of Characteristic 2, Michael S. Nelson Jan 2019

Homological Constructions Over A Ring Of Characteristic 2, Michael S. Nelson

College of Graduate Studies: Theses & Dissertations

We study various homological constructions over a ring $R$ of characteristic $2$. We construct chain complexes over a field $K$ of characteristic $2$ using polynomials rings and partial derivatives. We also provide a link from the homology of these chain complexes to the simplicial homology of simplicial complexes. We end by showing how to construct all finitely-generated commutative differential graded $R$-algebras using polynomial rings and partial derivatives.

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Inverse Problems Related To The Wiener And Steiner-Wiener Indices, Matthew Gentry Jan 2019

Inverse Problems Related To The Wiener And Steiner-Wiener Indices, Matthew Gentry

College of Graduate Studies: Theses & Dissertations

In a graph, the generalized distance between multiple vertices is the minimum number of edges in a connected subgraph that contains these vertices. When we consider such distances between all subsets of $k$ vertices and take the sum, it is called the Steiner $k$-Wiener index and has important applications in Chemical Graph Theory. In this thesis we consider the inverse problems related to the Steiner Wiener index, i.e. for what positive integers is there a graph with Steiner Wiener index of that value?

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Cardinal Characteristics Associated With Families Of Functions And Permutations, Nattapon Sonpanow Jan 2019

Cardinal Characteristics Associated With Families Of Functions And Permutations, Nattapon Sonpanow

Chulalongkorn University Theses and Dissertations (Chula ETD)

The Continuum Hypothesis (CH) states that the size of the set of real numbers c is the least uncountable cardinal, i.e. c = N₁. In the absence of CH, it is possible that there are cardinals that lie between N₁ and c. Many of them are cardinals of infinite families related to some concepts in infinite combinatorics, called cardinal characteristics. Most of these cardinals are defined on families of infinite sets of natural numbers. We study families of functions and permutations on the set of natural numbers with some combinatorial properties and associated cardinal characteristics. We give relations among these …

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A Statistical Investigation Of Stock Market Activity And Instances Of Financial Crime, Elizabeth G. Biggs Jan 2019

A Statistical Investigation Of Stock Market Activity And Instances Of Financial Crime, Elizabeth G. Biggs

Theses and Dissertations

This project aims to identify a possible statistical relationship between the stock market and incidences of financial crime in Illinois, Texas, and Utah through big data analysis techniques using data from the FBI’s Federal Bureau of Investigation’s National Incident-Based Reporting System (NIBRS) database. By analyzing the occurrences of financial crime by location, year, and type in relation to the S&P 500’s percent change in close price on the first day of the calendar year, it will be possible to determine if a statistical relationship exists between the two. In addition, regression analysis was performed in order to predict financial crime …

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Spectral Properties Of The Finite Hilbert Transform On Two Adjacent Intervals Via The Method Of Riemann-Hilbert Problem, Elliot Blackstone Jan 2019

Spectral Properties Of The Finite Hilbert Transform On Two Adjacent Intervals Via The Method Of Riemann-Hilbert Problem, Elliot Blackstone

Electronic Theses and Dissertations

In this dissertation, we study a self-adjoint integral operator $\hat{K}$ which is defined in terms of finite Hilbert transforms on two adjacent intervals. These types of transforms arise when one studies the interior problem of tomography. The operator $\hat{K}$ possesses a so-called "integrable kernel'' and it is known that the spectral properties of $\hat{K}$ are intimately related to a $2\times2$ matrix function $\Gamma(z;\lambda)$ which is the solution to a particular Riemann-Hilbert problem (in the $z$ plane). We express $\Gamma(z;\lambda)$ explicitly in terms of hypergeometric functions and find the small $\lambda$ asymptotics of $\Gamma(z;\lambda)$. This asymptotic analysis is necessary for the …

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Semi-Analytical Solutions Of Non-Linear Differential Equations Arising In Science And Engineering, Mangalagama Dewasurendra Jan 2019

Semi-Analytical Solutions Of Non-Linear Differential Equations Arising In Science And Engineering, Mangalagama Dewasurendra

Electronic Theses and Dissertations

Systems of coupled non-linear differential equations arise in science and engineering are inherently nonlinear and difficult to find exact solutions. However, in the late nineties, Liao introduced Optimal Homotopy Analysis Method (OHAM), and it allows us to construct accurate approximations to the systems of coupled nonlinear differential equations. The drawback of OHAM is, we must first choose the proper auxiliary linear operator and then solve the linear higher-order deformation equation by spending lots of CPU time. However, in the latest innovation of Liao's "Method of Directly Defining inverse Mapping (MDDiM)" which he introduced to solve a single nonlinear ordinary differential …

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Mathematical Investigation Of The Spatial Spread Of An Infectious Disease In A Heterogeneous Environment, Arielle Gaudiello Jan 2019

Mathematical Investigation Of The Spatial Spread Of An Infectious Disease In A Heterogeneous Environment, Arielle Gaudiello

Electronic Theses and Dissertations

Outbreaks of infectious diseases can devastate a population. Researchers thus study the spread of an infection in a habitat to learn methods of control. In mathematical epidemiology, disease transmission is often assumed to adhere to the law of mass action, yet there are numerous other incidence terms existing in the literature. With recent global outbreaks and epidemics, spatial heterogeneity has been at the forefront of these epidemiological models. We formulate and analyze a model for humans in a homogeneous population with a nonlinear incidence function and demographics of birth and death. We allow for the combination of host immunity after …

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Frames And Phase Retrieval, Ted Juste Jan 2019

Frames And Phase Retrieval, Ted Juste

Electronic Theses and Dissertations

Phase retrieval tackles the problem of recovering a signal after loss of phase. The phase problem shows up in many different settings such as X-ray crystallography, speech recognition, quantum information theory, and coherent diffraction imaging. In this dissertation we present some results relating to three topics on phase retrieval. Chapters 1 and 2 contain the relevant background materials. In chapter 3, we introduce the notion of exact phase-retrievable frames as a way of measuring a frame's redundancy with respect to its phase retrieval property. We show that, in the d-dimensional real Hilbert space case, exact phase-retrievable frames can be of …

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Effects Of Cell Morphology And Attachment To A Surface On The Hydrodynamic Performance Of Unicellular Choanoflagellates, Hoa Nguyen, M. A. R. Koehl, Christian Oakes, G. Bustamente, L. Fauci Jan 2019

Effects Of Cell Morphology And Attachment To A Surface On The Hydrodynamic Performance Of Unicellular Choanoflagellates, Hoa Nguyen, M. A. R. Koehl, Christian Oakes, G. Bustamente, L. Fauci

Mathematics Faculty Research

Choanoflagellates, eukaryotes that are important predators on bacteria in aquatic ecosystems, are closely related to animals and are used as a model system to study the evolution of animals from protozoan ancestors. The choanoflagellate Salpingoeca rosetta has a complex life cycle with different morphotypes, some unicellular and some multicellular. Here we use computational fluid dynamics to study the hydrodynamics of swimming and feeding by different unicellular stages of S. rosetta: a swimming cell with a collar of prey-capturing microvilli surrounding a single flagellum, a thecate cell attached to a surface and a dispersal-stage cell with a slender body, long …

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Finite Integration Method With Chebyshev Expansion For Finding Numerical Solution Of Nonlinear And Fractional Order Differential Equations, Ampol Duangpan Jan 2019

Finite Integration Method With Chebyshev Expansion For Finding Numerical Solution Of Nonlinear And Fractional Order Differential Equations, Ampol Duangpan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we develop the finite integration method by using Chebyshev polynomial expansion (FIM-CPE) for solving one- and two-dimensional nonlinear differential equations. The developed FIM-CPE can be used on any domains. Then, we utilize our FIM-CPE to deal with the spatial variable and the forward difference quotient to handle the derivative involving temporal variable. Thus, the numerical algorithms based on this idea are devised to overcome three nonlinear problems including one-dimensional Burgers' equation with shock wave, time-fractional Benjamin-Bona-Mahony-Burgers' equation and two-dimensional nonlinear Poisson equation over irregular domains. Moreover, we examine our algorithms with several experimental examples by comparing the …

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Adjustment Of Maximum Likelihood Method For Multivariate Fay-Herriot Model, Annop Angkunsit Jan 2019

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 …

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Bayesian Models For Poverty Mapping In Thailand, Sarasinee Somjettana Jan 2019

Bayesian Models For Poverty Mapping In Thailand, Sarasinee Somjettana

Chulalongkorn University Theses and Dissertations (Chula ETD)

Poverty maps are important sources of information for solving social, economic, and environmental problems. Initially, the World Bank used the ELL method to produce poverty maps for used in designing, targeting, prioritizing interventions and allocating the budgets for underdeveloped countries. Even though the ELL method has been shown to have many advantages in poverty mapping, it does not use a survey for the most benefit. Therefore, the Empirical Bayes (EB) method and the hierarchical Bayes (HB) method were proposed in literature. In another aspect, Louis shows that the usual Bayes has a limitation. Therefore, he proposed a new method called …

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Stochastic Differential Equation With Jumps For Tilapia Population, Kanitin Sukchum Jan 2019

Stochastic Differential Equation With Jumps For Tilapia Population, Kanitin Sukchum

Chulalongkorn University Theses and Dissertations (Chula ETD)

Tilapia population with harvesting in the tilapia farm can be modeled by an ordinary differential equation (ODE). In real life, tilapia population can be affected by many factors. To make the model for tilapia population more realistic, we develop the ODE into the stochastic differential equation (SDE) together with jumps that represent the epidemic occuring for tilapia. Furthermore, we study the effect of some important parameters in the model to the number of tilapia in the tilapia farm via simulation. Both SDEs for tilapia population with and without jumps are simulated by using Euler-Maruyama and jump-adapted Euler methods.

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Integer-Valued Time Series Risk Model With Surrender And Investment, Nuntanut Foosarmpok Jan 2019

Integer-Valued Time Series Risk Model With Surrender And Investment, Nuntanut Foosarmpok

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this study, we construct the discrete-time risk models based on integer-valued time series models by incorporating the concepts of surrender and investment. The surrender considered in this study is the situation that the policyholder decides to exit the policy before maturity date. In our study, we provide the probabilistic properties of the model. Moreover, we derive approximation of ruin probabilities of the constructed risk model. Finally, we discuss the trends of the ruin probability and the value at risk of the model by numerical simulations.

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Text Localization And Extraction From Background With Texture And Noise In Digital Images Using Adaptive Thresholding And Convolutional Neural Network, Pukjira Pattaranuprawat Jan 2019

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 …

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Iterative Jump To Binding Point For Simplex Method, Rujira Visuthirattanamanee Jan 2019

Iterative Jump To Binding Point For Simplex Method, Rujira Visuthirattanamanee

Chulalongkorn University Theses and Dissertations (Chula ETD)

The basic idea of an iterative jump method is moving a feasible point along the direction that improves the objective value maintaining the feasibility. It is applied for solving a linear programming (LP) model without artificial variables by applying the iterative jump on the LP relaxation having only acute constraints with respect to the objective direction and reinsert all non-acute constraints to find the optimal solution which is named SAJS. However, it may cause the last jump point to locate far away from the optimal solution so another approach for initially finding a suitable starting point is proposed. The new …

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First Order Integer-Valued Autoregressive Model With A Two-Parameter Generalized Poisson-Lindley Distribution, Suchiraporn Bunyaris Jan 2019

First Order Integer-Valued Autoregressive Model With A Two-Parameter Generalized Poisson-Lindley Distribution, Suchiraporn Bunyaris

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this study, we introduce the first order integer-valued autoregressive models for count data with the two-parameter generalized Poisson-Lindley distribution. The thinning operators considered in this study are the binomial and negative binomial thinning operators. Some important probabilistic and statistical properties such as moments, stationarity and autocorrelation functions are derived. Moreover, parameter estimations and numerical simulations to examine the constructed model are performed. Finally, applications of the models for real data sets are also discussed.

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Graph Representation For Room Layout Matching Using Spectral Embedding, Thamonwan Sa-Ngawong Jan 2019

Graph Representation For Room Layout Matching Using Spectral Embedding, Thamonwan Sa-Ngawong

Chulalongkorn University Theses and Dissertations (Chula ETD)

Graph matching is efficient to search similar layout when the architectural floor plan data size is increasing. Because the computational time of floor plan matching using spectral embedding is only in seconds, so it is one of the popular methods. However, the isomorphism of each floor plan leads to low accuracy in the matching process and it becomes the weakness of this method. Therefore, we propose a graph representation for room layout matching using spectral embedding. Normally, graph representations of the floor plan define nodes as rooms and edges as connections between rooms. Besides, the graph spectral embedding is to …

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Cubic Rank Transmuted Modified Burr Iii Pareto Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Wenhui Sheng, Munir Ahmad Jan 2019

Cubic Rank Transmuted Modified Burr Iii Pareto Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Wenhui Sheng, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. …

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On Burr Iii Marshal Olkin Family: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Gauss M. Cordeiro, Haitham M. Yousof, Munir Ahmad Jan 2019

On Burr Iii Marshal Olkin Family: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Gauss M. Cordeiro, Haitham M. Yousof, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the …

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On The Modified Burr Xii-Power Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad Jan 2019

On The Modified Burr Xii-Power Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see …

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The Nested Joint Clustering Via Dirichlet Process Mixture Model, Shengtong Han, Hongmei Zhang, Wenhui Sheng, Hasan Arshad Jan 2019

The Nested Joint Clustering Via Dirichlet Process Mixture Model, Shengtong Han, Hongmei Zhang, Wenhui Sheng, Hasan Arshad

Mathematical and Statistical Science Faculty Research and Publications

This article focuses on the clustering problem based on Dirichlet process (DP) mixtures. To model both time invariant and temporal patterns, different from other existing clustering methods, the proposed semi-parametric model is flexible in that both the common and unique patterns are taken into account simultaneously. Furthermore, by jointly clustering subjects and the associated variables, the intrinsic complex shared patterns among subjects and among variables are expected to be captured. The number of clusters and cluster assignments are directly inferred with the use of DP. Simulation studies illustrate the effectiveness of the proposed method. An application to wheal size data …

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Group Presentations As A Site For Collective Modeling Activity, Corey Brady, Hyunyi Jung Jan 2019

Group Presentations As A Site For Collective Modeling Activity, Corey Brady, Hyunyi Jung

Mathematical and Statistical Science Faculty Research and Publications

We approach student presentations of solutions to modeling tasks as occasions for whole-class reflection on the rich conceptual work that small-group teams have done in parallel. Analyzing and interpreting these interactions can offer insights into how a classroom group negotiates a shared sense of what they have learned and what they collectively view as “newsworthy” across groups from their recent (and ongoing) model-building. We describe analytical tools to interpret a classroom’s work during presentations, and we illustrate their use in a single case. This work offers a foothold for design-based research to harness presentations to improve learning, drive instructional decisions, …

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Mathematical Modeling And Classroom Discourse: A Case For Modeling-Specific Discussion Strategies, Ashley Dorlack, Hyunyi Jung, Sarah Brand, Samuel Franklin Gailliot Jan 2019

Mathematical Modeling And Classroom Discourse: A Case For Modeling-Specific Discussion Strategies, Ashley Dorlack, Hyunyi Jung, Sarah Brand, Samuel Franklin Gailliot

Mathematical and Statistical Science Faculty Research and Publications

No abstract provided.

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