Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions,
2024
The University of Texas Rio Grande Valley
Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions, Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai
School of Mathematical & Statistical Sciences Faculty Publications
This paper studies fine Selmer groups of elliptic curves in abelian p -adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Z p -extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg's Conjecture is clarified.
Key Factor Analysis For Base Patterns In Minibridge By Reinforcement Learning,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
คณะวิทยาศาสตร์
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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 …
Creating A Positive Learning Environment: Preliminary Results,
2024
University of Texas at El Paso
Creating A Positive Learning Environment: Preliminary Results, Kien H. Lim, Hilda Y. Sotelo
Departmental Papers (Math)
No abstract provided.
Counting Conjugates Of Colored Compositions,
2024
Georgia Southern University
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Honors College Theses
The properties of n-color compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.
Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property,
2024
Georgia Southern University
Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property, Samuel A. Aguilar
Honors College Theses
Zeckendorf's Theorem states that every natural number can be expressed uniquely as the sum of distinct non-consecutive terms of the shifted Fibonacci sequence (i.e. 1, 2, 3, 5, ...). This theorem has motivated the study of representation of integers by the sum of non-adjacent terms of Nth order Fibonacci sequences, including the characterization of the uniqueness of Zeckendorf representation based on the initial terms of the sequence. Moreover, when this uniqueness property is satisfied for third order Fibonacci sequences, the ratio of integers less than a given number X that have a Zeckendorf representation has been estimated by Dr. Sungkon …
Enumeration Of Increasing Trees,
2024
Georgia Southern University
Enumeration Of Increasing Trees, Garrett M. Southwood
Honors College Theses
We consider the generating function for increasingly labelled trees. By generalizing the proof through symbolic method, we are able to study various statistics regarding binary increasing trees with respect to height restrictions. We then apply our approach to special colorings of increasing trees in order to obtain their generating functions and, from there, derive the counting sequence for (ak+a)-colored recursive trees. We also present some interesting bijections between colored and non-colored increasing trees.
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders,
2024
Wilfrid Laurier University
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen
Theses and Dissertations (Comprehensive)
The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …
Self-Exciting Point Processes In Real Estate,
2024
Wilfrid Laurier University
Self-Exciting Point Processes In Real Estate, Ian Fraser
Theses and Dissertations (Comprehensive)
This thesis introduces a novel approach to analyzing residential property sales through the lens of stochastic processes by employing point processes. Herein, property sales are treated as point patterns, using self-exciting point process models and a variety of statistical tools to uncover underlying patterns in the data. Key findings include the identification and explanation of clustering in both space and time, and the efficacy of a temporal Hawkes process with a sinusoidal background in predicting home sale occurrences. The temporal analysis starts by employing the state of art techniques for time series data like regression, autoregressive, and autoregressive integrated moving …
The Atiyah-Hitchin-Singer Theorem And An 8-Dimensional Generalization,
2024
Wilfrid Laurier University
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,
2024
Wilfrid Laurier University
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 …
A Corona Theorem For Multipliers On The Dirichlet Space,
2024
University at Albany, State University of New York
A Corona Theorem For Multipliers On The Dirichlet Space, Alea Wittig
Electronic Theses & Dissertations (2024 - present)
An analogue to Wolff's ideal problem for the multiplier algebra of the Dirichlet space, the main theorem provides sufficient conditions to classify membership of an arbitrary function in an infinitely generated ideal of the multiplier algebra.
