Mathematics Commons^™

Discrete-Time Risk Model Based On Zero Inflated Poisson Time Series, Siwarak Sawongnam

Chulalongkorn University Theses and Dissertations (Chula ETD)

An important goal of actuary is to develop models for company portfolio and insurance products. Risk measurement is one of the essential measures that inform actuaries and risk managers about the degree to which the risk bearing entity. To have precise risk measure, we require an appropriate claim count process. The common claim count processes are usually constructed from the Poisson distribution. However, insurance data have generally excess zeros which causes the overdispersion. This violates the assumption of the Poisson distribution. Therefore, alternative distributions accommodating zero count are explored in literature. The zero inflated Poisson distribution is one of the …

Quaternion Algebras Over Some Extensions Of Function Fields, Silipong Thongmeepun

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study quaternion algebras over rational function fields over finite fields of odd order. [It is known that a quaternion algebra is either the algebra of 2x2- matrices or a division algebra.] We determine conditions for quaternion algebras of the form(symbol) to be division algebras and conditions for quaternion algebras to split after the constant quadratic field extension.

Strict Stability Of Fixed Points And Iteration Schemes, Kittisak Tontan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we introduce the concept of a strictly stable fixed point of a selfmap and investigate the relationship among various types of fixed point stability. We prove that all fixed point of a quasi-nonexpansive map is strictly stable and extend the concept of a strictly stable fixed point of a selfmap to an iteration scheme. We introduce the concept of convexly strictly stable fixed points of selfmaps and apply it to obtain virtual stability of some well-known iteration schemes in a convex subset of a Banach space.

Generalized Factorizability Of Certain Implicit Dependence Copulas, Peerapong Panyasakulwong

Chulalongkorn University Theses and Dissertations (Chula ETD)

The copula CX,Y of random variables X and Y that are uniformly distributed on [0,1] is called an implicit dependence copula if f(X)=g(Y) almost surely for some Borel functions f and g on [0,1]. Via a generalized Markov product, we give a one-to-one correspondence between the implicit dependence copulas and the parametric classes of subcopulas on a corresponding domain for the cases that f=g=Λθ, the tent function whose top is at (θ,1). We also show in the case f=g=α, a simple measure-preserving function, that implicit dependence copulas are generalized factorizable.

Harmonic Analysis Of Riesz-Type Transforms Arising In Nonlocal Partial Differential Equations, Sasikarn Yeepo

Chulalongkorn University Theses and Dissertations (Chula ETD)

where s ∈ (0, 1) and g is a given function, has been widely studied under different assumptions on the kernel K. In this work, we introduce an operator associated to the above nonlocal equation via Riesz potential. Under assumptions that K is measurable, symmetric and elliptic, we obtain that such an operator is a CalderónZygmund operator

Convergence Of Trinomial Formula For Call Option Prices, Yuttana Ratibenyakool

Chulalongkorn University Theses and Dissertations (Chula ETD)

The binomial formula given by Cox, Ross and Rubinstein (1979) is a tool for valuating the call option price. It is well known that the price from binomial formula converges to the price from Black-Scholes formula which was given by Black, Scholes and Merton (1973) as the number of periods (n) converges to infinity. In 1988, Boyle introduced the trinomial formula which is another tool for calculating call option price. He considered the trinomial formula in the case that the rising rate of a stock price is u = e λσ√T n and the falling rate of the stock price …

Reduced Dataset Neural Network Model For Manuscript Character Recognition, Mohammad Anwarul Islam

College of Graduate Studies: Theses & Dissertations

The automatic character recognition task has been of practical interest for a long time. Nowadays, there are well-established technologies and software to perform character recognition accurately from scanned documents. Although handwritten character recognition from the manuscript image is challenging, the advancement of modern machine learning techniques makes it astonishingly manageable. The problem of accurately recognizing handwritten character remains of high practical interest since a large number of manuscripts are currently not digitized, and hence inaccessible to the public. We create our repository of the datasets by cropping each letter image manually from the manuscript images. The availability of datasets is …

Middle-School Mathematics Teachers' Use Of Formative Assessment Data, Shawana T. Green

Walden Dissertations and Doctoral Studies

A school district located in the southeastern United States uses benchmark tests as formative assessment to provide teachers with data to differentiate their instruction to meet the individual needs of students in their classrooms. Despite this effort, student achievement in mathematics in this school district has not improved. The purpose of this study was to gain an understanding of how middle-grade mathematics teachers used the benchmark results as formative data to guide instruction and meet student needs. The conceptual framework that grounded this study was the model of formative assessment developed by Black and Wiliam. For this basic qualitative study, …

Mathematics Cognitive And Content Abilities Across The Vincentian Student Population, Brendalee Rorena Cato

Walden Dissertations and Doctoral Studies

Mathematics achievement is a key component of student overall academic achievement. However, many students from Saint Vincent and the Grenadines (Vincentian students) continue to perform poorly on the regional Caribbean Secondary Examination Certificate (CSEC) mathematics examination. This poor mathematics performance is a concern for education stakeholders. The purpose of this quantitative, nonexperimental study was to explore the extent to which the CSEC mathematics scores of high-scoring Vincentian students versus low-scoring Vincentian students in the cognitive domains of knowledge, comprehension, and reasoning differ across the content domains of algebra; geometry; measurement; statistics; and relations, functions, and graphs (RFG). The theoretical foundation …

Comparative Survival Of Asian And White Metastatic Castration-Resistant Prostate Cancer Men Treated With Docetaxel, Susan Halabi, Sandipan Dutta, Catherine M. Tangen, Mark Rosenthal, Daniel P. Petrylak, Ian M. Thompson Jr., Kim N. Chi, Johann S. De Bono, John C. Araujo, Christopher Logothetis, Mario A. Eisenberger, David I. Quinn, Karim Fizazi, Michael J. Morris, Celestia S. Higano, Ian F. Tannock, Eric J. Small, William Kevin Kelly

Mathematics & Statistics Faculty Publications

There are few data regarding disparities in overall survival (OS) between Asian and white men with metastatic castration-resistant prostate cancer (mCRPC). We compared OS of Asian and white mCRPC men treated in phase III clinical trials with docetaxel and prednisone (DP) or a DP-containing regimen. Individual participant data from 8820 men with mCRPC randomly assigned on nine phase III trials to receive DP or a DP-containing regimen were combined. Men enrolled in these trials had a diagnosis of prostate adenocarcinoma. The median overall survival was 18.8 months (95% confidence interval [CI] = 17.4 to 22.1 months) and 21.2 months (95% …

Residual Control Chart For Binary Response With Multicollinearity Covariates By Neural Network Model, Jong-Min Kim, Ning Wang, Yumin Liu, Kayoung Park

Mathematics & Statistics Faculty Publications

Quality control studies have dealt with symmetrical data having the same shape with respect to left and right. In this research, we propose the residual (r) control chart for binary asymmetrical (non-symmetric) data with multicollinearity between input variables via combining principal component analysis (PCA), functional PCA (FPCA) and the generalized linear model with probit and logit link functions, and neural network regression model. The motivation in this research is that the proposed control chart method can deal with both high-dimensional correlated multivariate data and high frequency functional multivariate data by neural network model and FPCA. We show that the neural …

Investigating The Numerical Stability Of Using An Impedance Boundary Condition To Model Broadband Noise Scattering With Acoustic Liners, Michelle E. Rodio, Fang Q. Hu, Douglas M. Nark

Mathematics & Statistics Faculty Publications

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for achieving aircraft noise reduction and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model will be discussed in which the liner impedance …

What's Your Sphericity Index? Rationalizing Surface Area And Volume, John A. Adam

Mathematics & Statistics Faculty Publications

Virginia Standards of Learning include mathematical content related to the surface area and the volume of various geometric objects. In the seventh grade, “Students... solve problems involving volume and surface area” In the eighth grade, “Proportional reasoning is expounded upon as students solve a variety of problems. Students find the volume and surface area of more complex three dimensional figures”. In high school geometry, “The student... use[s] surface area and volume of three-dimensional objects to solve practical problems” (Virginia Department of Education, 2016). The challenge is to find scenarios that are engaging to students and keep them interested in the …

Computing The Newton Potential In The Boundary Integral Equation For The Dirichlet Problem Of The Poisson Equation, Wenchao Guan, Ying Jiang, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Evaluating the Newton potential is crucial for efficiently solving the boundary integral equation of the Dirichlet boundary value problem of the Poisson equation. In the context of the Fourier-Garlerkin method for solving the boundary integral equation, we propose a fast algorithm for evaluating Fourier coefficients of the Newton potential by using a sparse grid approximation. When the forcing function of the Poisson equation expressed in the polar coordinates has mth-order bounded mixed derivatives, the proposed algorithm achieves an accuracy of order 𝒪(n^-m log³ n), with requiring 𝒪(n log² n) number of arithmetics for …

Multiplicative Noise Removal: Nonlocal Low-Rank Model And It's Proximal Alternating Reweighted Minimization Algorithm, Xiaoxia Liu, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to multiplicative noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex …

Maximality And Applications Of Subword-Closed Languages, Rhys Davis Jones

UNF Graduate Theses and Dissertations

Characterizing languages D that are maximal with the property that D^* ⊆ S^⊗ is an important problem in formal language theory with applications to coding theory and DNA codewords. Given a finite set of words of a fixed length S, the constraint, we consider its subword closure, S^⊗, the set of words whose subwords of that fixed length are all in the constraint. We investigate these maximal languages and present characterizations for them. These characterizations use strongly connected components of deterministic finite automata and lead to polynomial time algorithms for generating such languages. We prove that …

Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick

Senior Honors Theses

Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow …

Cosmic: Us-Based Conversion Master's Degree In Computing, Gary S. Krenz, Thomas Kaczmarek

Mathematical and Statistical Science Faculty Research and Publications

COSMIC is an NSF S-STEM graduate curriculum initiative/conversion program that strives to provide an accelerated pathway to a Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over into the computing field. The structure of our conversion program, the context that motivated it, and insights from conversion students' instructors are presented. Program successes with students from under-represented populations and the limitations that are also experienced are discussed. Our conversion program is based on a highly focused summer bridge course, combined with a customized curriculum pathway that enables people …

Perfect 2-Colorings Of The Grassmann Graph Of Planes, Stefaan Dewinter, Klaus Metsch

Michigan Tech Publications, Part 1

We construct an infinite family of intriguing sets, or equivalently perfect 2-colorings, that are not tight in the Grassmann graph of planes of PG(n, q), n ≥ 5 odd, and show that the members of the family are the smallest possible examples if n ≥ 9 or q ≥ 25.

Weighted Modulo Orientations Of Graphs, Jianbing Liu

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation focuses on the subject of nowhere-zero flow problems on graphs. Tutte's 5-Flow Conjecture (1954) states that every bridgeless graph admits a nowhere-zero 5-flow, and Tutte's 3-Flow Conjecture (1972) states that every 4-edge-connected graph admits a nowhere-zero 3-flow. Extending Tutte's flows conjectures, Jaeger's Circular Flow Conjecture (1981) says every 4k-edge-connected graph admits a modulo (2k+1)-orientation, that is, an orientation such that the indegree is congruent to outdegree modulo (2k+1) at every vertex. Note that the k=1 case of Circular Flow Conjecture coincides with the 3-Flow Conjecture, and the case of k=2 implies the 5-Flow Conjecture. This work is devoted …

Circuits And Cycles In Graphs And Matroids, Yang Wu

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation mainly focuses on characterizing cycles and circuits in graphs, line graphs and matroids. We obtain the following advances.

1. Results in graphs and line graphs. For a connected graph G not isomorphic to a path, a cycle or a K1,3, let pc(G) denote the smallest integer n such that the nth iterated line graph Ln(G) is panconnected. A path P is a divalent path of G if the internal vertices of P are of degree 2 in G. If every edge of P is a cut edge of G, then P is a bridge divalent path of G; …

Theory And Techniques Of Convergence Of Topological Transformation Group Actions, Murtadha Jaber Sarray

Graduate Theses, Dissertations, and Problem Reports (ETD)

n this dissertation, we present new set functions called strongly limit and strongly prolongation limit sets. We show the new sets, especially strongly prolongation limit sets, characterize proper action under an arbitrary setting. That is, we characterize proper action for wider class of proper ܩ-spaces. Also, we show the new version of the sets could be derived from strongly exceptional sets which have been used as a good technique for the characterization of a proper maps. Moreover, we review properties of well-known limit sets and prolongations and properties for the new version of limit sets under an arbitrary setting on …

Forced (2 + 1)-Dimensional Discrete Three-Wave Equation, Junyi Zhu, Sishou Zhou, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

We generalize the ∂-dressing method to investigate a (2 + 1)-dimensional lattice, which can be regarded as a forced (2 + 1)-dimensional discrete three-wave equation. The soliton solutions to the (2 + 1)-dimensional lattice are given through constructing different symmetry conditions. The asymptotic analysis of one-soliton solution is discussed. For the soliton solution, the forces are zero.

Decomposition Of 2-Soliton Solutions For The Good Boussinesq Equations, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

We consider decompositions of two-soliton solutions for the good Boussinesq equation obtained by the Hirota method and the Wronskian technique. The explicit forms of the components are used to study the dynamics of 2-soliton solutions. An interpretation in the context of eigenvalue problems arising from KdV type equations and transport equations is considered. Numerical examples are included.

Flows Of Co-Closed G_{2}-Structures, Sergey Grigorian

School of Mathematical & Statistical Sciences Faculty Publications

We survey recent progress in the study of G_{2}-structure Laplacian coflows, that is, heat flows of co-closed G_{2}-structures. We introduce the properties of the original Laplacian coflow of G_{2}-structures as well as the modified coflow, reviewing short-time existence and uniqueness results for the modified coflow and well as recent Shi-type estimates that apply to a more general class of G_{2}-structure flows.

Bayesian Modelling Of Nonlinear Poisson Regression With Artificial Neural Networks, Hansapani Rodrigo, Chris P. Tsokos

School of Mathematical & Statistical Sciences Faculty Publications

Modelling and prediction of count and rate responses have substantial usage in many fields, including health, finance, social, etc. Conventionally, linear Poisson regression models have been widely used to model these responses. However, the linearity assumption of the systematic component of linear Poisson regression models restricts their capability of handling complex data patterns. In this regard, it is important to develop nonlinear Poisson regression models to capture the inherent variability within the count data. In this study, we introduce a probabilistically driven nonlinear Poisson regression model with Bayesian artificial neural networks (ANN) to model count and rate data. This new …

On Cohen-Macaulay Hopf Monoids In Species, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We study Cohen-Macaulay Hopf monoids in the category of species. The goal is to apply techniques from topological combinatorics to the study of polynomial invariants arising from combinatorial Hopf algebras. Given a polynomial invariant arising from a linearized Hopf monoid, we show that under certain conditions it is the Hilbert polynomial of a relative simplicial complex. If the Hopf monoid is Cohen- Macaulay, we give necessary and sufficient conditions for the corresponding relative simplicial complex to be relatively Cohen-Macaulay, which implies that the polynomial has a nonnegative h-vector. We apply our results to the weak and strong chromatic polynomials of …

Screening Potential Citrus Rootstocks For Phytophthora Nicotianae Tolerance, Madhurababu Kunta, Sandy Chavez, Zenaida Viloria, Hilda S. Del Rio, Madhavi Devanaboina, George Yanev, Jong-Won Park, Eliezer S. Louzada

School of Mathematical & Statistical Sciences Faculty Publications

Seeds from four citrus rootstocks including sour orange, Bitters-C22 citrandarin, Sarawak pummelo 3 Rio Red grapefruit, and Sarawak pummelo 3Bower mandarin were exposed to high inoculum levels of Phytophthora nicotianae to screen for tolerance. Inoculation of pregerminated seeds (PGIS) and non-PGIS was carried out. The average P. nicotianae propagule counts from the soil samples where these seedlings were raised ranged from 424 to 1361 colony forming units/cm3. The proportion of live to dead plants was recorded at 11months postinoculation, which showed that Sarawak3Bower performed significantly better than other rootstocks. Evaluation of the rootstocks 18 months postinoculation resulted in only one …

Finite Lifespan Of Solutions Of The Semilinear Wave Equation In The Einstein–De Sitter Spacetime, Anahit Galstian, Karen Yagdjian

School of Mathematical & Statistical Sciences Faculty Publications

We examine the solutions of the semilinear wave equation, and, in particular, of the φq model of quantum field theory in the curved space-time. More exactly, for 1 < q < 4 we prove that the solution of the massless self-interacting scalar field equation in the Einstein-de Sitter universe has finite lifespan.

The Quantization Of The Standard Triadic Cantor Distribution, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. For a given k ≥ 2, let {Sj : 1 ≤ j ≤ k} be a set of k contractive similarity mappings such that Sj(x) = 1 2k−1x + 2(j−1) 2k−1 for all x ∈ R, and let P = 1 k Pk j=1 P ◦ S−1 j . Then, P is a unique Borel probability measure on R such that P has support the Cantor set generated by the similarity mappings …