Mathematics Commons^™

An Algorithm To Determine All Odd Primitive Abundant Numbers With D Prime Divisors, Jacob Liddy

Williams Honors College, Honors Research Projects

An abundant number is said to be primitive if none of its proper divisors are abundant. Dickson proved that for an arbitrary positive integer d there exists only finitely many odd primitive abundant numbers having exactly d prime divisors. In this paper we describe a fast algorithm that finds all primitive odd numbers with d unique prime divisors. We use this algorithm to find all the number of odd primitive abundant numbers with 6 unique Divisors. We use this algorithm to prove that an odd weird number must have at least 6 prime divisors.

Group Rings, Christopher Wrenn

Masters Essays

No abstract provided.

Mathematical Curves In The High School Classroom, Magdalena Zook

Masters Essays

No abstract provided.

Advanced Enrichment Topics In An Honors Geometry Course, Kayla Woods

Masters Essays

No abstract provided.

On A Pseudodifferential Calculus With Modest Boundary Decay Condition, Binbin Huang

Graduate Dissertations and Theses

A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the b-calculus of Melrose, is proposed based on this modest decay condition. The mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented.

The Kumaraswamy Weibull Geometric Distribution With Applications, Mahdi Rasekhi, Morad Alizadeh, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this work, we study the kumaraswamy weibull geometric (Kw-WG) distribution which includes as special cases, several models such as the kumaraswamy weibull distribution, kumaraswamy exponential distribution, weibull geometric distribution, exponential geometric distribution, to name a few. This distribution was monotone and non-monotone hazard rate functions, which are useful in lifetime data analysis and reliability. We derive some basic properties of the Kw-WG distribution including non-central rth-moments, skewness, kurtosis, generating functions, mean deviations, mean residual life, entropy, order statistics and certain characterizations of our distribution. The method of maximum likelihood is used for estimating the model parameters and a simulation …

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

Quick Trips: On The Oriented Diameter Of Graphs, Garner Paul Cochran

Theses and Dissertations

In this dissertation, I will discuss two results on the oriented diameter of graphs with certain properties. In the first problem, I studied the oriented diameter of a graph G. Erdos et al. in 1989 showed that for any graph with |V | = n and δ(G) = δ the maximum the diameter could possibly be was 3 n/ δ+1. I considered whether there exists an orientation on a given graph with |G| = n and δ(G) = δ that has a small diameter. Bau and Dankelmann (2015) showed that there is an orientation of diameter 11 n/ δ+1 + …

Local Rings And Golod Homomorphisms, Thomas Schnibben

Theses and Dissertations

The Poincaré series of a local ring is the generating function of the Betti numbers for the residue field. The question of when this series represents a rational function is a classical problem in commutative algebra. Golod rings were introduced by Golod in 1962 and are one example of a class of rings that have rational Poincaré series. The idea was generalized to Golod homomorphisms by Levin in 1975.

In this paper we prove two homomorphisms are Golod. The first is a class of ideals such that the natural projection to the quotient ring is a Golod homomorphism. The second …

Special Fiber Rings Of Certain Height Four Gorenstein Ideals, Jaree Hudson

Theses and Dissertations

Let S be a set of four variables, k a field of characteristic not equal to two such that k contains all square roots, and I a height four Gorenstein ideal of k[S] generated by nine quadratics so that I has a Gorenstein-linear resolution. We define a complex X• so that each module of X• is the tensor product of a certain polynomial ring Q in nine variables and a direct sum of indecomposable k[Sym(S)]-modules and the differential maps are Q- and k[Sym(S)]-module homomorphisms. Work with the Macaulay2 software suggests that H0(X•) is the special fiber ring of I and …

Logic -> Proof -> Rest, Maxwell Taylor

Senior Independent Study Theses

REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.

Active Calculus Multivariable: 2018 Edition, Steven Schlicker, David Austin, Matthew Boelkins

Open Textbooks

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are freely readable online in HTML format (new in this version of Active Calculus Multivariable) and are also available for in PDF; in the electronic format, graphics are in full color; the texts are open source, and interested instructors can gain access to the original source files on GitHub; the style of the texts requires students to be active learners — there are very few worked examples in the …

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.

กลยุทธ์การลงทุนส่วนบุคคลบนพื้นฐานเกณฑ์การจัดเก็บภาษีเงินได้, ปิยวดี สุขชาติ

Chulalongkorn University Theses and Dissertations (Chula ETD)

ตามที่กรมสรรพากรได้ระบุไว้ใน แบบแสดงรายการภาษีเงินได้บุคคลธรรมดา ปีภาษี 2559 สำหรับผู้มีเงินได้ตามมาตรา 40 (1) - (8) แห่งประมวลรัษฎากร (ภ.ง.ด.90) จะสามารถนำเงินไปลงทุนในแหล่งต่าง ๆ เพื่อลดเงินได้สุทธิก่อนที่จะนำไปคำนวณภาษี ในที่นี้ผู้ทำวิจัยสนใจการวางแผนการลงทุนเพื่อจะได้รับประโยชน์ทางภาษีและผลตอบแทนสูงสุดโดยการนำเงินไปลงทุนใน 3 แหล่ง ประกอบด้วย ประกันชีวิต (Life insurance) กองทุนรวมเพื่อการเลี้ยงชีพ (Retirement Mutual Fund : RMF) และกองทุนรวมหุ้นระยะยาว (Long Term Equity Fund : LTF) โดยการหากลยุทธ์การลงทุนเพื่อแนะนำแหล่งลงทุนและหาสัดส่วนจำนวนเงินที่เหมาะสมที่ใช้ในการลงทุนในแหล่งต่าง ๆ ที่สอดคล้องกับแผนการลงทุนที่มีอยู่ในตลาดและนำเสนอแผนการลงทุนที่เหมาะสมสำหรับแต่ละบุคคล โดยที่ผู้ลงทุนไม่เสียสภาพคล่องทางการเงิน อีกทั้งยังได้รับประโยชน์ทางภาษีและผลตอบแทน นั่นคือการเสียภาษีน้อยลงจากเดิมและได้ผลตอบแทนจากการลงทุนสูงสุด เริ่มจากการหาแหล่งลงทุนที่เหมาะสมสำหรับแต่ละบุคคลตามระดับความเสี่ยงที่รับได้ สร้างตัวแบบทางคณิตศาสตร์เพื่อทำนายราคากองทุนต่าง ๆ แล้วทำนายผลตอบแทนกองทุนต่าง ๆ ตามแหล่งลงทุนที่เหมาะสมนั้นเพื่อหาว่ากองทุนใดให้ผลตอบแทนที่เหมาะสมที่สุดที่เหมาะกับบางช่วงของรายได้ เพื่อคำนวณสัดส่วนจำนวนเงินที่เหมาะสมสำหรับแต่ละบุคคลที่จะต้องใช้ในการลงทุนในแหล่งต่าง ๆ และนำเสนอแผนการลงทุนที่ให้ผลตอบแทนสูงสุดสามอันดับของแต่ละแหล่งลงทุน เพื่อให้ผู้ลงทุนใช้ประกอบการตัดสินใจ เมื่อผู้มีเงินได้นำเงินได้สุทธิไปลงทุนแล้วนั้น จะเป็นการลดเงินได้สุทธิให้น้อยลงหรือปรับลดขั้นเงินได้สุทธิ ทำให้อัตราภาษีที่จะต้องเสียในปีนั้น ๆ ลดลงและได้ผลตอบแทนสูงสุด

Thin Cloud Removal Using Local Minimization And Image Transformation In Hsi Color Space, Thanet Markchom

Chulalongkorn University Theses and Dissertations (Chula ETD)

In the use of satellite images, clouds can be an obstacle due to their opacity property that can block the visibility of ground objects in case of thick clouds and can also be blended with the underlying details in case of thin clouds. In this research, we propose a novel method to remove thin clouds and retrieve the actual information by taking the advantage of HSI color space instead of RGB color space. The proposed method aims to estimate the cloud appearance called the scattering light, remove thin clouds from intensity channel to avoid an effect to the original color, …

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) …

Preceding-Jump Simplex Method, Natdanai Kafakthong

Chulalongkorn University Theses and Dissertations (Chula ETD)

A practical linear programming solver uses the simplex method to identify the optimal solution by iteratively searching among adjacent feasible vertices. It may visit numerous vertices before finding the optimal one for a large linear programming problem taking a long time to succeed. This research proposes a heuristic method to alleviate this issue by jumping to a new vertex close to the optimal one before performing the simplex method. The new vertex is identified by first jumping from the initial vertex along the gradient vector of the objective function or alternative direction if the objective direction points out of the …

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 …

Streaming Data Classification Method Using Scalable Hyper-Ellipsoids With Linear Discriminant Projection Distance Ratio, Perasut Rungcharassang

Chulalongkorn University Theses and Dissertations (Chula ETD)

Learning streaming data with limited size of memory storage becomes an interesting problem. Although there have been several learning methods recently proposed, based on the interesting concept of discard-after-learn, the performance of these issues: the learning speed, number of redundant neurons, and classification accuracy of these methods can be further improved in terms of faster speed, less number of neurons, and higher accuracy. The following new four concepts and approaches were proposed in this dissertation: (1) a more generic structure of hyper-ellipsoidal function called Scalable Hyper-Ellipsoidal Function (SHEF) capable of handling the problem of curse of dimensionality by introducing a …

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 …

Geometry Of Derived Categories On Noncommutative Projective Schemes, Blake Alexander Farman

Theses and Dissertations

Noncommutative Projective Schemes were introduced by Michael Artin and J.J. Zhang in their 1994 paper of the same name as a generalization of projective schemes to the setting of not necessarily commutative algebras over a commutative ring. In this work, we study the derived category of quasi-coherent sheaves associated to a noncommutative projective scheme with a primary emphasis on the triangulated equivalences between two such categories.

We adapt Artin and Zhang’s noncommutative projective schemes for the language of differential graded categories and work in Ho (dgcatk), the homotopy category of differential graded categories, making extensive use of Bertrand Toën’s Derived …

States And The Numerical Range In The Regular Algebra, James Patrick Sweeney

Theses and Dissertations

In this dissertation we investigate the algebra numerical range defined by the Banach algebra of regular operators on a Dedekind complete complex Banach lattice, i.e., V (Lr(E), T) = {Φ(T) : Φ ∈ Lr(E)∗, ||Φ|| = 1 = Φ(I)}. For T in the center Z(E) of E we prove that V (Lr(E), T) = co(σ(T)). For T ⊥ I we prove that V (Lr(E), T) is a disk centered at the origin. We then consider the part of V (Lr(E), T) obtained by restricting ourselves to positive states Φ ∈ Lr(E)∗. In this case we show that we get a …

Theory, Computation, And Modeling Of Cancerous Systems, Sameed Ahmed

Theses and Dissertations

This dissertation focuses on three projects. In Chapter 1, we derive and implement the compact implicit integration factor method for numerically solving partial differential equations. In Chapters 2 and 3, we generalize and analyze a mathematical model for the nonlinear growth kinetics of breast cancer stem cells. And in Chapter 4, we develop a novel mathematical model for the HER2 signaling pathway to understand and predict breast cancer treatment. Due to the high order spatial derivatives and stiff reactions, severe temporal stability constraints on the time step are generally required when developing numerical methods for solving high order partial differential …

Sparse Trees With A Given Degree Sequence, Ao Shen

College of Graduate Studies: Theses & Dissertations

In this thesis, we consider the properties of sparse trees and summarized a certain class of trees under some constraint (including with a given degree sequence, with given number of leaves, with given maximum degree, etc.) which have maximum Wiener index and the minimum number of subtrees at the same time. Wiener index is one of the most important topological indices in chemical graph theory. Steiner k�� Wiener index can be regarded as the generalization of Wiener index, when k = 2, Steiner Wiener index is the same as Wiener index. Steiner k�� Wiener index of a tree T is …

A Journey To The Adic World, Fayadh Kadhem

College of Graduate Studies: Theses & Dissertations

The first idea of this research was to study a topic that is related to both Algebra and Topology and explore a tool that connects them together. That was the entrance for me to the “adic world”. What was needed were some important concepts from Algebra and Topology, and so they are treated in the first two chapters.

The reader is assumed to be familiar with Abstract Algebra and Topology, especially with Ring theory and basics of Point-set Topology.

The thesis consists of a motivation and four chapters, the third and the fourth being the main ones. In the third …

Survey Of Results On The Schrodinger Operator With Inverse Square Potential, Richardson Saint Bonheur

College of Graduate Studies: Theses & Dissertations

In this paper we present a survey of results on the Schrodinger operator with Inverse ¨ Square potential, L_a= −∆ + a/|x|^2 , a ≥ −( d−2/2 )^2. We briefly discuss the long-time behavior of solutions to the inter-critical focusing NLS with an inverse square potential(proof not provided). Later we present spectral multiplier theorems for the operator. For the case when a ≥ 0, we present the multiplier theorem from Hebisch [12]. The case when 0 > a ≥ −( d−2/2 )^2 was explored in [1], and their proof will be presented for completeness. No improvements on the sharpness …

The Beauty Of Numbers In Nature: Mathematical Patterns And Principles From The Natural World [Book Review], John A. Adam

Mathematics & Statistics Faculty Publications

(First paragraph) It came as quite a shock at the time. I cannot recall exactly when it happened, but it certainly caught me by surprise. For most of my life, and certainly from elementary school (or “primary” school in the UK) through high school I had become used to seeing posters and books illustrating the “standard” map of the world: the Mercator projection. Of course, Greenwich, London, sat at longitude 0◦ (and still does!). And certainly I knew that planet Earth is spheroidal and that this flat projection distorted the shapes and areas (especially near the polar regions), but somehow …

Dimensional Analysis: Physical Insight Gained Through Algebra, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Stationary Automata, Anaam Mutar Bidhan

Graduate Theses, Dissertations, and Problem Reports (ETD)

In this dissertation, we investigate new automata, we call it stationary automata or ST-automata. This concept is based on the definition of TF-automaton by Wojciechowski [Woj2]. What is new in our approach is that we incorporate stationary subsets of limit ordinals of uncountable cofinality. The first objective of the thesis is to motivate the new construction of automata. This concept of ST-automata allows us to make a connection with infinite graph theory. Aharoni, Nash-Williams, and Shelah [AhNaSh] formulated a condition that is necessary and sufficient for a bipartite graph to have a matching. For a bipartite …