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Articles 1081 - 1097 of 1097
Full-Text Articles in Mathematics
The Atiyah-Hitchin-Singer Theorem And An 8-Dimensional Generalization, Timothy Ponepal
The Atiyah-Hitchin-Singer Theorem And An 8-Dimensional Generalization, Timothy Ponepal
Theses and Dissertations (Comprehensive)
The Atiyah-Hitchin-Singer theorem states that the twistor almost complex structure on a certain S2 bundle over an oriented Riemannian 4-manifold (M, g) is integrable if and only if the Weyl curvature tensor of g is self-dual. These ideas were developed by Roger Penrose connecting 4-dimensional Riemannian geometry with complex geometry. We present a new approach to the Atiyah-Hitchin-Singer theorem using horizontal lifts and their respective flows, cross products and the quaternions to show that the Nijenhuis tensor vanishes if and only if the Weyl curvature tensor of g is anti-self-dual. An eight dimensional generalization is presented when the …
Recoloring In Hereditary Graph Classes: Structure And Decomposition, Manoj Belavadi
Recoloring In Hereditary Graph Classes: Structure And Decomposition, Manoj Belavadi
Theses and Dissertations (Comprehensive)
In this thesis we study reconfiguration problems in graph theory. A reconfiguration problem is generally defined on the solution space of a problem for which a configuration can be defined as a feasible solution, for example, a coloring of a graph. In Chapters 1 through 4 we study the reconfiguration of vertex colorings. The reconfiguration graph of the k-colorings, denoted Rk(G), is the graph whose vertices are the k-colorings of G and two colorings are adjacent in Rk(G) if they differ on exactly one vertex. The basic question investigated here …
The Coulomb Gauge In Non-Associative Gauge Theory, Sergey Grigorian
The Coulomb Gauge In Non-Associative Gauge Theory, Sergey Grigorian
School of Mathematical & Statistical Sciences Faculty Publications
The aim of this paper is to extend existence results for the Coulomb gauge from standard gauge theory to a non-associative setting. Non-associative gauge theory is based on smooth loops, which are the non-associative analogs of Lie groups. The main components of the theory include a finite-dimensional smooth loop L , its tangent algebra l , a finite-dimensional Lie group Ψ , that is the pseudoautomorphism group of L , a smooth manifold M with a principal Ψ -bundle P , and associated bundles Q and A with fibers L and l , respectively. A configuration in this theory is …
Key Factor Analysis For Base Patterns In Minibridge By Reinforcement Learning, Thanathat Dechakulkamjorn
Key Factor Analysis For Base Patterns In Minibridge By Reinforcement Learning, Thanathat Dechakulkamjorn
Chulalongkorn University Theses and Dissertations (Chula ETD)
No abstract provided.
Specifying The Desired Attributes Of Solutions To Vehicle Routing Problems With Time Windows Using Machine Learning, Teerapong Chaochanglek
Specifying The Desired Attributes Of Solutions To Vehicle Routing Problems With Time Windows Using Machine Learning, Teerapong Chaochanglek
Chulalongkorn University Theses and Dissertations (Chula ETD)
A vehicle routing problem with time windows (VRPTW) has been studied widely in the literature. Most effective methods to find a solution are still heuristics, which are constructed from the inventor’s ideas of how a good solution should be obtained, and their efficiency is quantified only by empirical data. However, these ideas may or may not yield a near-optimal solution. It would be better if we can identify some characteristics of a solution to VRPTW to help guide the heuristic in the right direction. Arnold and Sörensen had proposed a statistical learning model to determine a characteristic of a near-optimal …
Simulation Of Optimal Control Of Vaccination For Svihr Covid-19 Epidemic Model, Kantanop Yimfan
Simulation Of Optimal Control Of Vaccination For Svihr Covid-19 Epidemic Model, Kantanop Yimfan
Chulalongkorn University Theses and Dissertations (Chula ETD)
Infectious disease modeling plays a crucial role in understanding and managing epidemic outbreaks. Mathematical models, combined with control strategies, can help guide effective interventions and policy making. In this study, we examined an epidemic model, so-called SV IHR, which is an extended SIR model with additional states to incorporate vaccination and treatment. Our goal is to determine parameters known as controls; specifically, the vaccination proportion, through the framework of the optimal control problems. We defined an objective function and explored the control strategies that optimize it. Numerical simulations were then performed to illustrate the dynamics of the epidemic both with …
Boundaries Of Overlapping Isosceles Triangles, Kirati Sriamorn
Boundaries Of Overlapping Isosceles Triangles, Kirati Sriamorn
Chulalongkorn University Theses and Dissertations (Chula ETD)
No abstract provided.
Rupert Property Of Some Solids In Higher Dimensions, Pongbunthit Tonpho
Rupert Property Of Some Solids In Higher Dimensions, Pongbunthit Tonpho
Chulalongkorn University Theses and Dissertations (Chula ETD)
We say that a solidS has the Rupert property if a hole could be cut into one copy of S so that another copy of S can be passed through this hole. In recent years, many solids in R$ have been shown to have the Rupert property. However, not much is known about the Rupert property in higher dimensions. This dissertation investigates the Rupert property for some solids in R". We introduce lemmas that help to verify this property. In particular, we prove that some particular n-simplices, the generalized n-octahedrons/and the two-way cones in In have the Rupert property.
Certain Incident Matrices For Lines Intersecting On Plane, Anawin Chongaumklang
Certain Incident Matrices For Lines Intersecting On Plane, Anawin Chongaumklang
Chulalongkorn University Theses and Dissertations (Chula ETD)
This work studies arrangements of lines on the plane, focusing on Fourier’s 17 lines problem, which involves constructing 101 intersection points with 17 lines. We use code notation and incident matrices to classify possible configurations and develop algorithms to determine which codes are drawable. Special attention is given to the role of multiple points and parallel families in these arrangements. Out of 924 possible codes, 658 are confirmed drawable using a combination of theoretical analysis and computer verification. For the remaining cases, new lemmas are proposed to construct additional intersection points. Our findings offer both theoretical insights and practical algorithms …
Splitness Of The Characteristic Polynomial Of 2×2 Normal Matrices Over A Finite Field, Sarawut Therdchanthuk
Splitness Of The Characteristic Polynomial Of 2×2 Normal Matrices Over A Finite Field, Sarawut Therdchanthuk
Chulalongkorn University Theses and Dissertations (Chula ETD)
เราได้ทฤษฎีบทสเปกตรัมสำหรับเมทริกซ์ขนาด 2x2 เหนือฟีลด์จำกัดที่มีลักษณะเฉพาะเท่ากับ 2 โดยการตรวจสอบการแตกตัวของพหุนามลักษณะเฉพาะเหนือฟีลด์ดังกล่าว ซึ่งใช้ข้อเท็จจริงเสริมบางประการเกี่ยวกับพหุนามกำลังสองและเมทริกซ์เหนือฟีลด์ดังกล่าว พหุนามลักษณะเฉพาะจะสะท้อนให้เห็นถึงรูปแบบบัญญัติของเมทริกซ์เหล่านี้ เป็นผลให้สามารถแยกชั้นความคล้ายของเมทริกซ์ปรกติได้ และสำหรับเมทริกซ์ปรกติที่แปลงเป็นทแยงมุมได้ เราให้ข้อความที่สมมูลกับการทำให้เป็นเมทริกซ์ที่แปลงเป็นทแยงมุมแบบยูนิแทรีได้
Developing Test Statistics For Familial Dna Searches Through Multinomial Logistic Regression Model, Akaraphon Jantaraphum
Developing Test Statistics For Familial Dna Searches Through Multinomial Logistic Regression Model, Akaraphon Jantaraphum
Chulalongkorn University Theses and Dissertations (Chula ETD)
In hypothesis testing for familial DNA searches, the likelihood ratio (LR) is a commonly used statistic that requires allele frequency distributions. However, since the population background of a forensic sample is generally unknown, the appropriate allele frequency distribution is uncertain. To address this issue, various LR-based methods—such as those using local allele frequencies (LRLAF), or selecting maximum, minimum, or average LRs (LRMAX, LRMIN, LRAVG), and Naive Bayes classification (LRNB)—have been developed. In this study, we introduce a family of LR-based statistics incorporating multinomial logistic regression classification (LRMLR). DNA samples are classified into subpopulations using multinomial logistic regression, and the likelihood …
Two-Step-Change Pivot Rule For Simplex Method, Rawit Chaiareekij
Two-Step-Change Pivot Rule For Simplex Method, Rawit Chaiareekij
Chulalongkorn University Theses and Dissertations (Chula ETD)
The simplex method is a fundamental method for solving linear programming problems proposed by George B. Dantzig in 1963. The simplex method’s efficiency hinges on the choice of the entering variable, determined by the pivot rule. Dantzig’s original pivot rule, while effective in many cases, can exhibit exponential behavior on certain problems. To address this problem, this thesis proposes a new pivot rule for the simplex method, called the two-step-change pivot rule. The idea is to obtain the two-step-change improvement from the objective value by computing the direction of change for each entering variable to determine the cost per unit. …
Closed-Form Formulas For Conditional Moments Of Stochastic Volatility Markovswitching Model And Applications, Supavit Kiatteerarat
Closed-Form Formulas For Conditional Moments Of Stochastic Volatility Markovswitching Model And Applications, Supavit Kiatteerarat
Chulalongkorn University Theses and Dissertations (Chula ETD)
In the present day, the regime-switching model plays a crucial role in the financial world. This thesis studies a stochastic volatility model with regime switching, specifically examining a Markovian regime-switching process known as Cox-Ingersoll-Ross. Analytical formulas for the conditional moment generation function of the process are developed, presenting both a linearly closed-form and an exponentially closed-form. The formulas are derived by solving a partial differential equation (PDE) that obtains the Feynman-Kac Theorem. We also present the relationship between these two closed-forms, demonstrated by using the formula by Faà Bruno. Additionally, a numerical validation, the Monte Carlo method, is employed to …
Quotients Of The Curve Complex, Joseph Maher, Hidetoshi Masai, Saul Schleimer
Quotients Of The Curve Complex, Joseph Maher, Hidetoshi Masai, Saul Schleimer
Publications and Research
We consider three kinds of quotients of the curve complex, which are obtained by coning off uniformly quasiconvex subspaces: symmetric curve sets, non-maximal train track sets, and compression body disc sets. We show that the actions of the mapping class group on those quotients are strongly weakly properly discontinuously (WPD), which implies that the actions are non-elementary and those quotients are of infinite diameter.
Instances Of Undecidability In The Semigroup Word Problem, Timothy C. Grosky
Instances Of Undecidability In The Semigroup Word Problem, Timothy C. Grosky
Honors Theses and Capstones
We will examine the decidability of the word problem in semigroups, which is a yes/no question. We will examine tools that have been developed to help answer it, and then look at some examples where the word problem is decidable or undecidable.
Creating A Positive Learning Environment: Preliminary Results, Kien H. Lim, Hilda Y. Sotelo
Creating A Positive Learning Environment: Preliminary Results, Kien H. Lim, Hilda Y. Sotelo
Departmental Papers (Math)
No abstract provided.
Extending Natural Mates In Euclidean 3-Space And Applications To Bertrand Pairs, Yun Myung Oh, Alexander Navarro
Extending Natural Mates In Euclidean 3-Space And Applications To Bertrand Pairs, Yun Myung Oh, Alexander Navarro
Faculty Publications
In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate. A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.