Physical Sciences and Mathematics Commons^™

Covering Of Objects Related To Rupert Property, Pongbunthit Tonpho

Chulalongkorn University Theses and Dissertations (Chula ETD)

One problem related to covering problem is whether one object has Rupert property. An object K in R³ has the Rupert property if a hole could be cut through one copy of K with the same size to permit another copy to pass through it. There are objects in R³ which have Rupert property, such as a cube. But not all of objects in R³ has Rupert property, such as a sphere. It is interesting to check that a given object has Rupert property. In this work, we construct useful lemmas for studying this problem. Furthermore, we apply these lemmas …

Generalized Symplectic Graphs And Generalized Orthogonal Graphs Over Finite Commutative Rings, Siripong Sirisuk

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let R be a finite commutative ring with identity, n ∈ N and β a bilinear form on Rⁿ. In this dissertation, we count the numbers of free submodules and totally isotropic free submodules of Rⁿ of rank s by using the lifting idea. We define the generalized bilinear form graph whose vertex set is the set of totally isotropic free submodules of Rⁿ of rank s and the adjacency condition is given by some rank conditions. We study this graph when (Rⁿ, β) is a symplectic space and an orthogonal space. We can determine the degree of each vertex …

Variant Of D'Alembert Functional Equation On Compact Homogeneous Space, Sorawit Viwanthananut

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this work, we introduce a new functional equation on compact homogeneous spaces based on the d'Alembert functional equation on compact groups. We solve the functional equation by using tools from harmonic analysis.

Closed-Form Formula For Pricing Discretely-Sampled Moment Swaps On One-Dimensional Ito Process, Kittisak Chumpong

Chulalongkorn University Theses and Dissertations (Chula ETD)

Moment swaps are essentially forward contracts on realized higher moments of log-returns of a specified underlying asset, which play an important role in protection against different kinds of market shocks. Variance, skewness, and kurtosis swaps are examples of moment swaps currently traded in markets. To facilitate market practitioners, this work provides a simple and easy-to-use pricing formula of moment swaps on discrete sampling under the Ito process, extended Black-Scholes model for stock prices and Schwartz model for commodity prices. Furthermore, the interesting topics of the fair prices are also investigated. Finally, Monte Carlo simulations are performed to support the accuracy …

Cyclic Clique Decompositions Of Powerof Cycles, Apiwat Peereeyaphat

Chulalongkorn University Theses and Dissertations (Chula ETD)

A clique decomposition P of a graph G is a collection of cliques of G such that each edge of G belongs to exactly one clique in the collection. We say that P is cyclic if there is an isomorphism : V (G)→ V (G) such that Kk{α (v₁), α (v₂), α (v₃), ... , α (vk)g is a clique in P whenever Kk{v₁; v₂; v₃; :::; vk} is. The k-power of an n-cycle, Ck n, is the graph having the same vertex set as Cn and uv is an edge in Ck n if and only if dCn(u; v) …

Defective Colorings On Complete Bipartite And Multipartite K-Uniform Hypergraphs, Artchariya Muaengwaeng

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we modify the definition of a defective coloring and a defective chromatic number on graphs to a defective coloring and a defective chromatic number on hypergraphs. First, we find the defective chromatic number on a complete bipartite k-uniform hypergraph and the defective chromatic number on a complete bipartite k-uniform hypergraph of which each color class is acyclic. Second, we determine the defective chromatic number and the defective chromatic number of which each color class is acyclic on a complete k-partite k-uniform hypergraph whose each edge has k vertices from k different partite sets. Finally, we determine the …

Critical Exponent For Nonlinear Nonlocal Equations, Auttawich Manui

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study the nonlinear nonlocal equation ∂t u=J*u-u+u¹+p where p>0 and J is nonnegative, bounded, and radially symmetric with unit integral. The Fourier transform of J satisfies J ̂(ξ)=1-A|ξ|^β (ln1/|ξ| 〗 )^μ+o(〖|ξ|〗^β (ln〖1/(|ξ|)〗 )^μ ) as ξ→0, for 0<β≤2, μ∈R, and A>0. In this study, we establish the local existence, uniqueness, and the comparison principle of solutions. Furthermore, we show that the Fujita critical exponent for this equation is β/n when μ<0. For the case μ>1, we discover that the critical exponent is β/n , and the solutions belong to the global to the small initial data regime.

Finite Integration Method Using Chebyshev Polynomials For Solving Time-Dependent Linear Partial Differential Equations And Linear Fractional Order Differential Equations, Arnont Saengsiritongchai

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we devise numerical algorithms base on the finite integration method (FIM) using Chebyshev polynomial to find numerical solutions of time-dependent linear partial differential equations and linear fractional order differential equations. The results show that for time-dependent linear partial differential equations, our algorithm gives a lot better accuracy than the traditional FIMs. Several examples illustrate that our algorithm for linear fractional order differential equations gives good approximate solution as well.

Incremental Proper Orthogonal Decomposition For Pde Simulation Data: Algorithms And Analysis, Hiba Fareed

Doctoral Dissertations

"We propose an incremental algorithm to compute the proper orthogonal decomposition (POD) of simulation data for a partial differential equation. Specifically, we modify an incremental matrix SVD algorithm of Brand to accommodate data arising from Galerkin-type simulation methods for time dependent PDEs. We introduce an incremental SVD algorithm with respect to a weighted inner product to compute the proper orthogonal decomposition (POD). The algorithm is applicable to data generated by many numerical methods for PDEs, including finite element and discontinuous Galerkin methods. We also modify the algorithm to initialize and incrementally update both the SVDand an error bound during the …

Cox-Type Model Validation With Recurrent Event Data, Muna Mohamed Hammuda

Doctoral Dissertations

"Recurrent event data occurs in many disciplines such as actuarial science, biomedical studies, sociology, and environment to name a few. It is therefore important to develop models that describe the dynamic evolution of the event occurrences. One major problem of interest to researchers with these types of data is models for the distribution function of the time between events occurrences, especially in the presence of covariates that play a major role in having a better understanding of time to events.

This work pertains to statistical inference of the regression parameter and the baseline hazard function in a Cox-type model for …

Hdg Methods For Dirichlet Boundary Control Of Pdes, Yangwen Zhang

Doctoral Dissertations

"We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems for PDEs. These problems can involve atypical variational formulations, and often have solutions with low regularity on polyhedral domains. These issues can provide challenges for numerical methods and the associated numerical analysis. In this thesis, we use an existing HDG method for a Dirichlet boundary control problem for the Poisson equation, and obtain optimal a priori error estimates for the control in the high regularity case. We also propose a new HDG method to approximate the solution of a Dirichlet boundary …

Automating The Calculation Of Hilbert-Kunz Multiplicities And F-Signatures, Gabriel Johnson

Honors Theses

We describe an application written to automate a calculation for the mathematical research of Dr. Spiroff of University of Mississippi & Dr. Enescu of Georgia State University. This work represents a way to overcome the barriers of the mathematical calculations in obtaining theoretical results.

Some Results On A Class Of Functional Optimization Problems, David Rushing Dewhurst

Graduate College Dissertations and Theses

We first describe a general class of optimization problems that describe many natu- ral, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances of these problems in statistical physics, facility allocation, and machine learning. A dynamic description and statement of a partial inverse problem follow. When attempting to optimize the state of a system governed by the generalized equipartitioning princi- ple, it is vital to understand the nature of the governing probability distribution. We show that optimiziation for the incorrect probability distribution can have catas- trophic results, e.g., …

Novelty Detection Of Machinery Using A Non-Parametric Machine Learning Approach, Enrique Angola

Graduate College Dissertations and Theses

A novelty detection algorithm inspired by human audio pattern recognition is conceptualized and experimentally tested. This anomaly detection technique can be used to monitor the health of a machine or could also be coupled with a current state of the art system to enhance its fault detection capabilities. Time-domain data obtained from a microphone is processed by applying a short-time FFT, which returns time-frequency patterns. Such patterns are fed to a machine learning algorithm, which is designed to detect novel signals and identify windows in the frequency domain where such novelties occur. The algorithm presented in this paper uses one-dimensional …

Nonlinear Coupled Effects In Nanomaterials, Sia Bhowmick

Theses and Dissertations (Comprehensive)

Materials at the nanoscale have different chemical, structural, and optoelectrical properties compared to their bulk counterparts. As a result, such materials, called nanomaterials, exhibit observable differences in certain physical phenomena. One such resulting phenomenon called the piezoelectric effect has played a crucial role in miniature self-powering electronic devices called nanogenerators which are fabricated by using nanostructures, such as nanowires, nanorods, and nanofilms. These devices are capable of harvesting electrical energy by inducing mechanical strain on the individual nanostructures. Electrical energy created in this manner does not have environmental limitations. In this thesis, important coupled effects, such as the nonlinear piezoelectric …

Abelian Subalgebras Of Maximal Dimension In Euclidean Lie Algebras, Mark Curro

Theses and Dissertations (Comprehensive)

In this paper we define, discuss and prove the uniqueness of the abelian subalgebra of maximal dimension of the Euclidean Lie algebra. We also construct a family of maximal abelian subalgebras and prove that they are maximal.