Mathematics Commons^™

Tolerance-Localized And Control-Localized Solutions To System Of Interval Linear Equations, Kanokwan Burimas

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we are interested in a system of interval linear equations Ax=b whose coefficient A and right hand side b vary in some real intervals. We study two types of solutions called tolerance--localized and control--localized solutions of interval linear equations system. The characterizations of each solution are proposed in two main theorems. First, the proposed theorem is stated in terms of center and radius matrices which is directly proved by following their definitions. The other theorem is presented as magnitude sense with new notation. Based on the second theorem, the closed form of all solution sets is released. …

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 …

Tropical Cyclone Hazards In Relation To Propagation Speed, Jiehao Huang

Dissertations and Theses

As the population and infrastructure along the US East Coast increase, it becomes increasingly important to study the characteristics of tropical cyclones that can impact the coast. A recent study shows that the propagation speed of tropical cyclones has slowed over the past 60 years, which can lead to greater accumulation of precipitation and greater storm surge impacts. The study presented herein is meant to examine and analyze the relationships that exist between the propagation speed of tropical cyclones, their surface wind strength, displacement angles, and cyclone averaged winds. This analysis is focused on tropical cyclones spanning from 1950-2015 in …

Symmetry Algebras Of The Canonical Lie Group Geodesic Equations In Dimension Five, Hassan Almusawa

Theses and Dissertations

Nowadays, there is much interest in constructing exact analytical solutions of differential equations using Lie symmetry methods. Lie devised the method in the 1880s. These methods were substantially developed utilizing modern mathematical language in the 1960s and 1970s by several different groups of authors such as L.V. Ovsiannikov, G. Bluman, and P. J. Olver, and have since been implemented as a software package for symbolic computation on commonly used platforms such as Mathematica and MAPLE.

In this work, we first develop an algorithmic scheme using the MAPLE platform to perform a Lie symmetry algebra identification and validate it on nonlinear …

The Special Atom Space And Haar Wavelets In Higher Dimensions, Eddy Kwessi, G. De Souza, N. Djitte, M. Ndiaye

Mathematics Faculty Research

In this note, we will revisit the special atom space introduced in the early 1980s by Geraldo De Souza and Richard O'Neil. In their introductory work and in later additions, the space was mostly studied on the real line. Interesting properties and connections to spaces such as Orlicz, Lipschitz, Lebesgue, and Lorentz spaces made these spaces ripe for exploration in higher dimensions. In this article, we extend this definition to the plane and space and show that almost all the interesting properties such as their Banach structure, Hölder's-type inequalities, and duality are preserved. In particular, dual spaces of special atom …

Definable Modules Over Definable Rings Without Zero Divisors In O-Minimal Structures, Jaruwat Rodbanjong

Chulalongkorn University Theses and Dissertations (Chula ETD)

In an o-minimal structure, every definable group admits a definable group manifold. Moreover, one can also show an analogue of this statement for definable rings. In this work, we prove that every definable module over definable ring without zero divisors admits a definable module manifold. In addition, we also give the classification of definable modules over definable rings without zero divisors in o-minimal structures

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.

Greybody Factors For Perfect Fluid Black Hole, Kunlapat Sansuk

Chulalongkorn University Theses and Dissertations (Chula ETD)

The Einstein equation is a field equation which describes gravity in terms of the curvature of spacetime. It states how matter curves spacetime. The solutions of the Einstein field equation are the metrics of spacetime from which the curvature of spacetime can be found. The field equations are non-linear, which are complicated to solve. Therefore, some assumptions are needed to reduce the complexity of the Einstein equation. One of these assumptions is a perfect fluid sphere. Perfect fluid sphere satisfies the following: no viscosity, no heat conduction, and isotropy. Perfect fluid black holes are black hole solutions of the Einstein …

A Two-Stage Model For Balancing Instructor Workload And Teaching Preference In University Course Timetabling, Nipitta Burana

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis focuses on balancing instructor workload and maximizing preferences by using the data in the first semester of 2019 from Department of Mathematics and Computer Science,Faculty of Science, Chulalongkorn University as a case study. Since there are many instructors with over-workload in the department which directly affect their research qualities, balancing teaching workload is the main objective of this study. The proposed approach to balance workload is to split some basic courses into two parts: before midterm and after midterm and then assign each course to two instructors. Moreover, the preferences or the requests of teaching a course are …

Building Detection From Remote Sensing Images Using Yolo, Noppadon Pumpong

Chulalongkorn University Theses and Dissertations (Chula ETD)

Building detection system through the remote sensing of images has been widely studied. In this thesis, we propose a model for detecting buildings at airports in Asia through different levels of remote sensing image. The proposed model is improved using the You Only Look Once (YOLO) algorithm based on the convolutional neural network (CNN). We also adjust an inputted image to our model using the Jet Saliency Map. The buildings to be detected in this study are the passenger terminals, the control towers, the cargo buildings, and the hangars. The data set has been collected from 322 different airports in …

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.

Classification Of Main Components In Airports From Remote Sensing Images By Efficient Network, Pimpisa Charoenchittang

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we classify the type of main components in airports from the remote sensing images. This datasets is considered as an interesting information since the same type of component may have different shape, size, and color. EfficientNet architecture is the deep learning architecture to use in this research due to the small number of parameters and computational time compared to the other architectures with similar accuracy. In our experiment, we apply the EfficientNet in versions B0, B1, B2, B3, and B4 to classify four types of components in the airport; the passenger terminal, the radio tower, the runway, …

Cops And Robbers On Hypergraphs, Pinkaew Siriwong

Chulalongkorn University Theses and Dissertations (Chula ETD)

Cops and robbers game is a game usually played on a finite connected graphwith two players, cop and robber. Recently, cops and robbers game played on hypergraphs was introduced. To give a better chance to a cop by allowing morethan one cop and at least one cop has to move, the cop-number, the least numberof cops to guarantee that they win the game, on graphs and hypergraphs is studied.This thesis provides (i) a characterization of a cop-win hypergraph (ii) some results on the products of hypergraphs and (iii) the cop-number of complete k-partite hypergraphs and n-prisms over a hypergraph. Moreover, …

Graph And Number Theoretic Properties Of Certain Maps Over Finite Field, Pratchayaporn Doemlim

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study the graph over a finite field $\mathbb{F}_q$, where $q$ is a prime power, obtained by iterations of the map $g(x)=x^p$, where $p$ is a prime number. Some properties of the graphs such as a characterization of their vertices and the number of cycles with specific length are showed. Moreover, some statistical estimates about the tail and cycle lengths of the related graphs are established.

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

Graph Grabbing Games And Toucher-Isolator Games, Sopon Boriboon

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this research, we study the graph grabbing game and the Toucher-Isolator game. In the graph grabbing game, we partially confirm a conjecture of Seacrest and Seacrest which states that Alice wins the game on every weighted connected bipartite even graph. In the Toucher-Isolator game, we give a simple alternative proof of a result of Räty that determines the most suitable tree on n vertices for Toucher which answers a question of Dowden, Kang, Mikalački and Stojaković.

Stochastic Differential Equation Models On Sphere For Animal Migration, Viput Puttanugool

Chulalongkorn University Theses and Dissertations (Chula ETD)

Animal migration is a seasonal movement of a bundle of animals from place to place. A migration cycle is often annually and closely linked with the cyclic pattern of seasons. A short-distance migration can be modeled on a planar surface, but most animals have long-distance migrations, e.g., Arctic terns migrate from the North Pole to the South Pole; thus, their migration should be modeled on a spherical surface. In addition, the Brownian motion term is included in a model to represent noises and randomness of movements. This work aims to simulate their migration routes using stochastic differential equations (SDEs) on …

Improved Adaptive Fractional Order Differential Method For Medical Image Enhancement, Wasin Tranghiranyathorn

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this work, we propose a construction of a new 5x5 fractional order differential mask that uses sixteen directions of gradient operator and weights each pixel in the mask by the Euclidean distance from the center of the mask. Then, we apply this new mask to the Adaptive Fractional Differential Algorithm (AFDA). The AFDA allows the optimal fractional order of each pixel to be obtained using an adaptive function constructed based on the area feature of image. Experimental results for medical images, show that the AFDA with the new mask gives better image enhancement than the original AFDA. It makes …

Knight's Tours On Ringboards, Deficient 4 X N Chessboards And Some L-Boards, Wasupol Srichote

Chulalongkorn University Theses and Dissertations (Chula ETD)

A (legal) knight's move is the result of moving the knight two squares horizontally or vertically on the board and then turning and moving one square in a perpendicular direction. A closed knight's tour is a sequence of knight's moves that visits every square on a given chessboard exactly once and returns to its start square. A closed knight's tour and its variations are studied widely over the rectangular chessboard or a three-dimensional rectangular box. For m,n > 2r, an (m,n,r)-ringboard or RB(m,n,r) is defined to be an m x n chessboard, denoted by CB(m x n), with the middle part …

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 …

Positive Labeled And Unlabeled Learning Methods Of Meta-Path Based Functional Profiles For Predicting Drug-Disease Associations, Thitipong Kawichai

Chulalongkorn University Theses and Dissertations (Chula ETD)

Drug repositioning, discovering new indications for existing drugs, is a competent strategy to reduce time, costs, and risk in drug discovery and development. Many computational methods have been developed to identify new drug-disease associations for further validation and drug development. A recent approach showing superior performance with less required data is a meta-path based approach, which derives network-based information using path patterns from drug to disease nodes. However, existing meta-path based methods discard information of intermediate nodes along paths, which are important indicators for describing relationships between drugs and diseases. With known (positive) and unknown (unlabeled) drug-disease associations, this research …

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.

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 …

The Poisson Topp Leone Generator Of Distributions For Lifetime Data: Theory, Characterizations And Applications, Faton Merovci, Haitham M. Yousof, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al., (2016)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Some special models of the new family are discussed. An application is carried out on real data set applications sets to show the potentiality of the proposed family.

Projective Splitting Methods For Maximal Monotone Mappings In Hilbert Spaces, Oday Hazaimah

Graduate Research Theses & Dissertations

In this dissertation, novel approaches for solving convex nonsmooth optimization, variational inequalities and inclusion problems are studied. The main contributions of the dissertation are given in Chapter 4 and Chapter 5. The two proposed iterations in Chapter 4, Half-Extragradient algorithm (HEG) and its accelerated version, are a natural modification of the classical Extragradient algorithm (EG)

when the composite objective function is a sum of three convex functions. EG evaluates the smooth operator twice per iteration via proximal mappings, and also, it allows larger step sizes. One of the main advantages of the proposed scheme is to avoid evaluating an

extragradient …

A Computational Study Of Binary Linear And Quadratic Programming And Solvers, William Cody Mackelfresh

Graduate Research Theses & Dissertations

In this thesis we study and compare computational capability of two solvers, Gurobi and BiqCrunch, and their capabilities to solve various binary quadratic and linear programming problems. We review two types of programming models for three types of combinatorial optimization problems, namely Max-Cut, Max Independent Set, and Max-$k$-Cluster. We also review the Reformulation-Linearization Technique (RLT) and Semidefinite Programming (SDP) approaches for solving these models, go over the software and hardware used to solve these problems, and finally review the numerical results obtained by solving the problems.

The Effect Of Self-Reflection On Relative Student Success In Undergraduate Calculus 1, Kevin Shryock

Graduate Research Theses & Dissertations

This thesis examines the effect of completion and self-reflection credit on multiple aspects of undergraduate student success in Calculus 1. Specifically, this study assessed the validity of a plug-and-play classroom framework utilizing a combination of a holistic rubric and corresponding worksheets to direct students’ attention towards their conceptual understanding of material and written work, all while removing the pressure of performance grades on all but four summative assessments. By comparing students’ relative performance on these summative assessments, as well as students’ responses on regular surveys, this study found that students who chose to forego performance grades in favor of completion …

A Spider's Web Of Doughnuts, Daniel Stoertz

Graduate Research Theses & Dissertations

This dissertation studies an interplay between the dynamics of iterated quasiregular map-

pings and certain topological structures. In particular, the relationship between the Julia set

of a uniformly quasiregular mapping f : R 3 → R 3 and the fast escaping set of its associated

Poincaré linearizer is explored. It is shown that, if the former is a Cantor set, then the latter

is a spider’s web. A new class of uniformly quasiregular maps is constructed to which this

result applies. Toward this, a geometrically self-similar Cantor set of genus 2 is constructed.

It is also shown that for any …

Digital Hurewicz Theorem And Digital Homology Theory, Samira Sahar Jamil, Danish Ali

Turkish Journal of Mathematics

In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we obtain two main results that make this homology different from already existing homologies of digital images. We prove digital analog of Hurewicz theorem for digital cubical singular homology. We also show that the homology functors developed in this paper satisfy properties that resemble the Eilenberg-Steenrod axioms of homology theory, in particular, the homotopy and the excision axioms. We finally define axioms of digital homology theory.

$Q$-Analogues Of Five Difficult Hypergeometric Evaluations, Xiaojing Chen, Wenchang Chu

Turkish Journal of Mathematics

A nonterminating balanced $q$-series is examined by means of the modified Abel lemma on summation by parts that leads to $q$-analogues of five difficult identities for classical hypergeometric series, including three formulae conjectured by Gosper in 1977.