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.
Conditional Constrained And Unconstrained Quantization For Probability Distributions,
2024
The University of Texas Rio Grande Valley
Conditional Constrained And Unconstrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we present the idea of conditional quantization for a Borel probability measure P on a normed space Rk. We introduce the concept of conditional quantization in both constrained and unconstrained scenarios, along with defining the conditional quantization errors, dimensions, and coefficients in each case. We then calculate these values for specific probability distributions. Additionally, we demonstrate that for a Borel probability measure, the lower and upper quantization dimensions and coefficients do not depend on the conditional set of the conditional quantization in both constrained and unconstrained quantization.
Brillouin Zones Of Integer Lattices And Their Perturbations,
2024
The University of Texas Rio Grande Valley
Brillouin Zones Of Integer Lattices And Their Perturbations, Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian, Mathijs Wintraecken
School of Mathematical & Statistical Sciences Faculty Publications
For a locally finite set, 𝐴⊆ℝ𝑑 , the 𝑘 th Brillouin zone of 𝑎∈𝐴 is the region of points 𝑥∈ℝ𝑑 for which ‖𝑥−𝑎‖ is the 𝑘 th smallest among the Euclidean distances between 𝑥 and the points in 𝐴 . If 𝐴 is a lattice, the 𝑘 th Brillouin zones of the points in 𝐴 are translates of each other, and together they tile space. Depending on the value of 𝑘 , they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our …
Heuristics For Anti-Cyclotomic ℤp-Extensions,
2024
The University of Texas Rio Grande Valley
Heuristics For Anti-Cyclotomic ℤp-Extensions, Debanjana Kundu, Lawrence C. Washington
School of Mathematical & Statistical Sciences Faculty Publications
This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model “how often” the p-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent. Second we propose the Invariants Heuristics: these predict that the Iwasawa invariants 𝜆 and 𝜇 usually vanish for imaginary quadratic fields where p is non-split.
Decompositions Of Nonlinear Input-Output Systems To Zero The Output,
2024
Old Dominion University
Decompositions Of Nonlinear Input-Output Systems To Zero The Output, W. Steven Gray, Kurusch Ebrahimi-Fard, Alexander Schmeding
Electrical & Computer Engineering Faculty Publications
Consider an input–output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact solution, that is, the tracking error is exactly the zero function. If the system has a well defined relative degree and the zero function is in the range of the input–output map, then it is well known that the system is locally left invertible, and thus, the problem has a unique exact solution. A system will fail to have relative degree when more than one exact solution exists. The general goal …
Generalized Functions In The Study Of Signals And Systems,
2024
Georgia Institute of Technology
Generalized Functions In The Study Of Signals And Systems, Erik I. Verriest, Gunther Dirr, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
We collect three instances where the theory of generalized functions may still make contributions to the study of signals and systems. In the first, a purely algebraic approach is presented for LTI-ODE's, in terms of two operators, D and T, respectively the differentiation operator and the multiplication-by-the-independent-variable operator. This formalism adds simplicity, a duality theory, and nicely generalizes to other classes of operator equations and their solutions. In the second part we extend the classical bilateral Laplace transform to include Bohl functions with support in ℝ by invoking Sato's hyperfunctions. Finally, in the third case we use the Colombeau algebra …
A Little More On Ideals Associated With Sublocales,
2024
Chapman University
A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen
Mathematics, Physics, and Computer Science Faculty Articles and Research
As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let βL and λL denote the Stone- Čech compactification of L and the Lindelöf coreflection of L, respectively. There is a natural way of associating with each sublocale of βL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of βL. The intent in this paper …
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 …
