Mathematics Commons^™

Laplacian Spectra Of Kneser-Like Bipartite Graphs, Cesar Iram Vazquez

Open Access Theses & Dissertations

Given a,b ∈N such that a > b we define a Kneser-like bipartite graph G(a,b), whose two bipartite sets of vertices represent the a-subsets and b-subsets of S = {1,...,a + b + 1}, and whose edges are pairs of vertices X and Y such that X ∩Y = ∅. We prove that the eigenvalues of the Laplacian matrix of graphs G(a,1) are all nonnegative integers. In fact, we describe these eigenvalues, and their respective multiplicities.

Mathematical Modeling Of Microemulsification Processes, Numerical Simulations And Applications To Drug Delivery, Ogochukwu Nneka Ifeacho

Open Access Theses & Dissertations

Microemulsion systems are a great pharmaceutical tool for the delivery of formulations containing multiple hydrophilic and hydrophobic ingredients of varying physicochemical properties. These systems are gaining popularity because of its long shelf life, improved drug solubilisation capacity, easy preparation and improvement of bioavailability. Despite the advantages associated with the use of microemulsion systems in pharmaceutical industries, the major challenge impeding their use has been and continues to be the lack of understanding of these systems.

Microemulsions can be mathematically modeled by an initial boundary value problem involving a sixth order nonlinear time dependent equation. In this Thesis, we present a …

Using Machine Learning On An Imbalanced Cancer Dataset, James Ekow Arthur

Open Access Theses & Dissertations

With an estimated 1.4 million cancer diagnosis worldwide and the increasing death of cancer patients. It is prudent to investigate methods, approaches and smarter ways of predicting and diagnosing of cancer so that a holistic techniques can be used to curb or reduce false predictions , increase exact predictions and also meticulos prognosis information .

Can a feasible technique be developed for the general problem of prognosis and diagnosis of cancer be developed ?

We will show here that this problem of cancer prognosis and diagnosis can be efficiently tackled with the aid of machine learning techniques and the best, …

Planar Motion Control Of A Cube Satellite Using Cold Gas Thrusters, Christian Lozoya

Open Access Theses & Dissertations

This Thesis presents a mathematical model developed for the computational simulation ofCubeSat movement using four thrusters that permit uniaxial translation and rotation. Arbitrary functions are fit to boundary conditions to simulate the force, acceleration, velocity, and displacement of the CubeSat along a plane. The model is used to derive a motion control algorithm assuming constant pressure and mass. A single model describes both translation and rotation. This Thesis also explores the relationship between propellant consumption and the time required to complete a displacement implied by the model.

Extrinsic Ricci Flow On Surfaces Of Revolution, Vincent E. Coll, Jeff Dodd, David L. Johnson

Research, Publications & Creative Work

An extrinsic representation of a Ricci flow on a differentiable n-manifold M is a family of submanifolds S(t), each smoothly embedded in Rn+k, evolving as a function of time t such that the metrics induced on the submanifolds S(t) by the ambient Euclidean metric yield the Ricci flow on M. When does such a representation exist? We formulate this question precisely and describe a new, comprehensive way of addressing it for surfaces of revolution in R3. Our approach is to build the desired embedded surfaces of revolution S(t) in R3 into the flow at the outset by rewriting the Ricci …

A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler

Senior Independent Study Theses

Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.

Poisson Approximation For Locally Dependent Collateralized Debt Obligation, Nat Yonghint

Chulalongkorn University Theses and Dissertations (Chula ETD)

A collateralized debt obligation (CDO) is a type of structured asset-backed security. The assets are pooled together and divided into tranches to be sold to investors. Each tranche has a substantially different credit quality and risk level. Jaio and Kaouri (2009), Neammanee and Yonghint (2020) used Poisson approximation to approximate a percentage loss for each tranche in CDO where all reference assets are independent. However, in the real world, each asset may not have the independent structure. In this thesis, we consider reference assets without assuming independence. If a default of reference asset may affect to some asset then we …

Improvement Of Error Bounds Of Local Limit Theorems For Sums Of Independent Integer-Valued Random Variables, Tatpon Siripraparat

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Smooth Approximations Of Continuous Functions Definable In D-Minimal Structures, Phaphontee Yamchote

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

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.