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Analytical Formula For Conditional Moments Of Extended Heston-Cev Hybrid Model With Time-Dependent Parameters, Promsiri Anunak

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis proposes an analytical formula for the conditional moments of the extended Heston-CEV hybrid model, which is the combination of the Heston model and the March-Rosenfeld process, also known as the constant elasticity of variance (CEV) process, to model the price dynamics of the underlying asset. The formula is derived by solving a partial differential equation (PDE) that characterizes a two-dimensional process. This Monte Carlo simulation results to ensure its accuracy. Department formula is practical and more comprehensive than the existing results in the literature. The thesis also includes numerical validations by verifying the analytical formula against

The Lie Algebra Sl2(C) And Krawtchouk Polynomials, Nkosi Alexander

UNF Graduate Theses and Dissertations

The Lie algebra L = sl2(C) consists of the 2 × 2 complex matrices that have trace zero, together with the Lie bracket [y, z] = yz − zy. In this thesis we study a relationship between L and Krawtchouk polynomials. We consider a type of element in L said to be normalized semisimple. Let a, a^∗ be normalized semisimple elements that generate L. We show that a, a^∗ satisfy a pair of relations, called the Askey-Wilson relations. For a positive integer N, we consider an (N + 1)-dimensional irreducible L-module V consisting of the homogeneous polynomials in two variables …

Apparent Contours For Piecewise Smooth Surfaces, Sarah Marie Jackman

UNF Graduate Theses and Dissertations

The set of points on an embedded surface $M$ that are tangent to a set viewing direction $\mathbf{v}$ is called the contour generator of $M$. The projection of those points to an image plane is called a surface's apparent contour. Apparent contours hold certain properties that allow for reconstruction of the original surface using only the information of the apparent contour. In this paper, we explore the structure of the apparent contour through contact classes and singularity types. Additionally we examine the properties of apparent contours that allow for 3 dimensional reconstruction. Our goal is to extend the properties of …

Explorations Of A Topology Constructed On The Maximal Ideals Of A Boolean Algebra, Abbigal Moos

Dissertations and Theses

The primary purpose of this thesis is to construct a topology on the collection of maximal ideals of a distributive and complemented lattice using the hull-kernel methodology. Through the construction of this topological space, we discovered that the space is compact, zero-dimensional, and Hausdorff. Next, we looked at the properties of some lattices, namely the power set of a finite set ordered by inclusion and the set of all positives divisors for some arbitrary integer ordered by divisibility. Whenever these lattices were both distributive and complemented, we constructed a topology on the collection of maximal ideals of the lattices using …

Effects Of Slip On Highly Viscous Thin-Film Flows Inside Vertical Tubes (Constant Radius, Constricted And Flexible), Mark S. Schwitzerlett

Theses and Dissertations

Viscous liquid film flows in a tube arise in numerous industrial and biological applications, including the transport of mucus in human airways. Previous modeling studies have typically used no-slip boundary conditions, but in some applications the effects of slip at the boundary may not be negligible. We derive a long-wave model based on lubrication theory which allows for slippage along the boundary. Linear stability analysis verifies the impact of slip-length on the speed, growth rate, and wavelength of the most unstable mode. Nonlinear simulations demonstrate the impact of slip-length on plug formation and wave dynamics. These simulations are conducted for …

Investigations In The Semi-Strong Product Of Graphs And Bootstrap Percolation, Kevin J. Mccall

Theses and Dissertations

The semi-strong product of graphs G and H is a way of forming a new graph from the graphs G and H. The vertex set of the semi-strong product is the Cartesian product of the vertex sets of G and H, V(G) x V(H). The edges of the semi-strong product are determined as follows: (g₁,h₁)(g₂,h₂) is an edge of the product whenever g₁g₂ is an edge of G and h₁h₂ is an edge of H or g₁ = g₂ and h₁h_{2 …}

Early Termination In Phase Ii Clinical Trials: Admissible Designs Using Decreasingly Informative Priors, Chen Wang

Theses and Dissertations

In Phase II clinical trials, Thall and Simon’s Bayesian posterior probability design is commonly implemented to allow for an early termination to determine whether a new treatment warrants further investigation in a larger-scale Phase III trial; this in turn requires a pre-selected prior distribution based on known clinical opinion or historical information. Moreover, this Bayesian approach can result in an issue of inflating type I error rate by monitoring interim data to inform early termination decisions. Alternatively, a Bayesian approach with the decreasingly informative prior (DIP), which is an informative yet skeptical prior, can be implemented to overcome the contentious …

On The Relation Between Oscillation Of Solutions Of Differential Equations And Corresponding Equations On Time Scales, Olexandr Stanzhytskyi, Roza Uteshova, Victoriia Tsan, Zoia Khaletska

Turkish Journal of Mathematics

This paper studies oscillatory properties of solutions of a dynamic equation on the set of time scales $\mathbf{T}_\lambda$ provided that the graininess function $\mu_\lambda$ approaches zero as $\lambda\to 0$. We derived the conditions under which oscillation of solutions of differential equations implies that of solutions of the corresponding equations defined on time scales with the same initial data, and vice versa.

Notes On Totally Geodesic Foliations Of A Complete Semi-Riemannian Manifold, An Sook Shin, Hyelim Han, Hobum Kim

Turkish Journal of Mathematics

In this paper, we prove that the orthogonal complement $\mathcal{F}^{\perp}$ of a totally geodesic foliation $\mathcal{F}$ on a complete semi-Riemannian manifold $(M,g)$ satisfying a certain inequality between mixed sectional curvatures and the integrability tensor of $\mathcal{F}^{\perp}$ is totally geodesic. We also obtain conditions for the existence of totally geodesic foliations on a complete semi-Riemannian manifold $(M,g)$ with bundle-like metric $g$.

Some Remarks On Parameterized Inequalities Involving Conformable Fractional Operators, Ci̇han Ünal, Fati̇h Hezenci̇, Hüseyi̇n Budak

Turkish Journal of Mathematics

In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using conformable fractional integrals. To be more precise, parameterized inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, previous and new results are presented by using special cases of the obtained theorems.

The Normalized Miller-Ross Function And Its Geometric Properties, Khaled Mehrez

Turkish Journal of Mathematics

The main objective of this paper is to study certain geometric properties (like univalence, starlikeness, convexity, close-to-convexity) for the normalized Miller-Ross function. The various results, which we have established in the present investigation, are believed to be new, and their importance is illustrated by several interesting consequences and examples. Furthermore, some of the main results improve the corresponding results available in the literature [15].

A Calculus For Intuitionistic Fuzzy Values, Enes Yavuz

Turkish Journal of Mathematics

We introduce $^\oplus$calculus and $^\otimes$calculus for intuitionistic fuzzy values and prove some basic theorems by using multiplicative calculus which has useful tools to represent the concepts of introduced calculi. Besides, we construct some isomorphic mappings to interpret the relationships between $^\oplus$calculus and $^\otimes$calculus. This paper reveals also new calculi for fuzzy sets in particular.

Atomic Systems In Krein Spaces, Osmin Ferrer Villar, Edilberto Arroyo Ortiz, José Naranjo Martínez

Turkish Journal of Mathematics

In the present article, we establish a definition of atomic systems in the Krein spaces, specifically, we establish the fundamental tools of the theory of atomic systems in the formalism of the Krein spaces and give a complete characterization of them. We also show that the atomic systems do not depend on the decomposition of the Krein space.

The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales

Turkish Journal of Mathematics

A covariety is a nonempty family $C$ of numerical semigroups that satisfies a certain conditions. In this work we will show that if $F$ is a positive integer, then the set of Arf numerical semigroup with Frobenius number $F$, denoted by $(F)$, is a covatiety. The previous results will be used to give an algorithm which calculates the set $(F).$ Also we will see that if $X\subseteq S\backslash \Delta(F)$ for some $S\in (F),$ then there is the smallest element of $(F)$ containing $X.$

A Note On Half Of Some Med Semigroups Of Maximal Or Almost Maximal Length, Ahmet Çeli̇k

Turkish Journal of Mathematics

In this study, we have shown that numerical semigroups $M=<3,C+1,C+2>$ and $M=<3,C,C+2>$ have maximal or almost maximal length, with conductor $C$, where $C\equiv0(3)$ and $C\equiv2(3),$ respectively. We also examined whether half of these numerical semigroups were of maximal or almost maximal length.

Neumann Boundary Value Problem For The Beltrami Equation In A Ring Domain, İlker Gençtürk

Turkish Journal of Mathematics

In this paper, the Neumann boundary value problem for the Beltrami operator is explicitly solved in a circular ring domain, solvability conditions for this problem are also given in explicit forms. Moreover, the Neumann problem for second-order operators with the Bitsadze/Laplace operator as the main part as combinations of the Cauchy-Riemann and the Beltrami operators is investigated.

Strong Homotopy Lie Algebras And Hypergraphs, Samuel J. Bevins, Marco Aldi

UROP Posters

We study hypergraphs by attaching a nilpotent strong homotopy Lie algebra. We especially focus on hypergraph theoretic information that is encoded in the cohomology of the resulting strong homotopy Lie algebra.

The Multiset Partition Algebra: Diagram-Like Bases And Representations, Alexander N. Wilson

Dartmouth College Ph.D Dissertations

There is a classical connection between the representation theory of the symmetric group and the general linear group called Schur--Weyl Duality. Variations on this principle yield analogous connections between the symmetric group and other objects such as the partition algebra and more recently the multiset partition algebra. The partition algebra has a well-known basis indexed by graph-theoretic diagrams which allows the multiplication in the algebra to be understood visually as combinations of these diagrams. My thesis begins with a construction of an analogous basis for the multiset partition algebra. It continues with applications of this basis to constructing the irreducible …

Elliptic Functions And Iterative Algorithms For Π, Eduardo Jose Evans

UNF Graduate Theses and Dissertations

Preliminary identities in the theory of basic hypergeometric series, or `q-series', are proven. These include q-analogues of the exponential function, which lead to a fairly simple proof of Jacobi's celebrated triple product identity due to Andrews. The Dedekind eta function is introduced and a few identities of it derived. Euler's pentagonal number theorem is shown as a special case of Ramanujan's theta function and Watson's quintuple product identity is proved in a manner given by Carlitz and Subbarao. The Jacobian theta functions are introduced as special kinds of basic hypergeometric series and various relations between them derived using the triple …

Adapted Metrics For A Modified Coulomb/Newton’S Potential, Lucian M. Ionescu, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae

Faculty Publications – Mathematics

Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the …

The Relationships Between Flow, Mathematics Self-Efficacy, And Mathematics Anxiety Among International Undergraduate Students In The United States, Samah Abduljabbar

Dissertations

Problem

A worldwide problem, math anxiety is defined as an anxious state with an unpleasant feeling of tension characterized by fear of failing to achieve mathematics targets. Psychologically, math anxiety involves anxiety, tension, discomfort, nervousness, fear, shock, and insecurity. Math anxiety has been perceived as a key influencer of reduced math achievement, and avoidance of math-related careers. On the other hand, abilities, flow, interests, and psychological conditions contribute to student mathematics success. Belief in one's ability to perform a specific task boosts self-efficacy, which has been studied widely as a predictor of student academic performance. When students are interested in, …

Mathematical Analysis Of Convolutional Neural Networks, Daniel Mccarter

Dissertations and Theses

In this thesis, the main topic is convolution as a mathematical operation and Convolutional Neural Networks (CNN’s). While convolution is classically defined as a function, it can also be defined as an operator from Lp(R) to itself for 1 ≤ p ≤ 2 where Tw(f ) = f ∗ w given some w ∈ L1(R). CNN’s use convolution in its convolutional layers. Defining a neural network to be the composition of layer maps, we find that the neural network is, by necessity, Lipschitz. While CNN’s can be very powerful for image classification, slight changes to an image can completely fool …

An Exploratory Study On Methods For Interpolating And Extrapolating Baseball Win-Loss Percentage, Giselle Palacios

All Student Theses and Dissertations

The 2020 Major League Baseball season was shortened by a few months due to travel restrictions implemented in response to Coronavirus pandemic. When baseball began in mid-July, the schedule had been changed so that teams were mostly playing against division opponents. This left some fans wondering how different the 2020 season would have looked if the original schedule of 162 games were played. A website called Strat-O-Matic used the Monte Carlo method to simulate a full 2020 season. This paper proposes and explores other possible models for predicting the outcome of the season. The first model we present is a …

Connecting Number Theory With High School Mathematics, Andre Richmond

All Student Theses and Dissertations

Number theory is the study of natural numbers and one of the oldest branches of mathematics. Elementary number theory concepts are integrated into K-12 learning experience. This paper will identify ideas and methods in elementary number theory that could be connected to K-12 education and taught in high school classrooms. In fact, Common Core Standards in Mathematics include some basic concepts and skills in elementary number theory. In this study, we will focus on the greatest common divisor, Euclid's algorithm, least common multiple, factorization and divisibility criteria (divisible by 2, 3, 4, 5, 6, 8, 9, and 11). We hope …

Mixture Sutoregressive Models For Thai Stock Market Data, Apicha Suthichayapipat

Chulalongkorn University Theses and Dissertations (Chula ETD)

The autoregressive (AR) model is one of the most widely used time series forecasting models. The standard AR model was established using the normal distribution, which is violated in some datasets, notably financial data. Therefore, alternative distributions are proposed in the literature, such as the concept of mixture distributions. This concept is also applied to time series modeling in the family of mixture autoregressive models that combine different autoregressive components. Specifically, we consider both the univariate mixture autoregressive model and the multivariate mixture autoregressive model based on the normal and t distributions. In this study, we construct the EM algorithm …

Dynamic Nearest Neighbor Classifier Using Mass-Ratio-Variance Outlier Factors For Class Imbalance Problem, Patcharasiri Fuangfoo

Chulalongkorn University Theses and Dissertations (Chula ETD)

The objective of classifcation is to assign a class to a given data instance. One well-recognized classifer is the k-NN model, where the class of an instance is determined by considering the majority class among its k nearest neighbors. However, k-NN’s performance weakens in imbalanced datasets. To address this, adjusting k for each instance based on factors like its position relative to clusters or isolation, and integrating density-based scores from a parameterfree Mass-ratio-variance Outlier Factor (MOF) into the k-NN process, helps determine suitable nearest neighbors. Our research focuses on the development of a dynamic nearest neighbor classifer tailored specifcally to …

Co-Designing Elementary-Level Computer Science And Mathematics Lessons: An Expansive Framing Approach, Umar Shehzad, Jody Clarke-Midura, Kimberly Beck, Jessica Shumway, Mimi Recker

Publications

This study examines how a rural-serving school district aimed to provide elementary-level computer science (CS) by offering instruction during students’ computer lab time. As part of a research-practice partnership, cross-context mathematics and CS lessons were co-designed to expansively frame and highlight connections across – as opposed to integration within – the two subjects. Findings indicated that most students who engaged with the lessons across the lab and classroom contexts reported finding the lessons interesting, seeing connections to their mathematics classes, and understanding the programming. In contrast, a three-level logistic regression model showed that students who only learned about mathematics connections …

Introduction To Contemporary Mathematics Syllabus (Spring 2023), Heather Nunnally

Open Textbooks and Course Materials

This syllabus was used in the Spring of 2023 for MATH 131: Introduction to Contemporary Mathematics. There were no textbook costs for this course; instead, MyOpenMath was used for the textbook and homework.

Approximations Of Practice And Equity: Surveying The Spaces, Bima Sapkota, Carrie Lee, Liza Bondurant, Heather Howell

School of Mathematical & Statistical Sciences Faculty Publications

After three years of meeting as a working group at PME-NA, we will be editing a book on how several models of approximations of practice support or hinder the creation of equitable mathematics learning and thinking spaces. Participants and working group leaders will serve as critical friends as we use a fishbowl format and small groups to provide spaces for refinement and challenge. Participants will leave with a network of thought partners and a draft chapter. At the end of the working group, we will identify overarching themes about affordances and limitations of several models of digital and non-digital forms …

Supporting Spatial Reasoning: Identifying Aspects Of Length, Area, And Volume In Textbook Definitions, Eryn M. Stehr Maher, Jia He

Mathematical Sciences: Faculty Publications

Length, area, and volume share structural similarities enabling flexibility in reasoning for real-world applications. Deep understanding of structures can help teachers connect these concepts to support their students’ mathematical reasoning and practices involving real-world situations. In mathematics textbooks designed for future teachers, definitions of length, area, and volume vary from procedural (e.g., use a ruler to measure side lengths, use formulas to calculate measures) to conceptual (e.g., construct appropriate n-dimensional units that tessellate the n-dimensional space) to formal (e.g., construct a function mapping qualitative size to a quantity of appropriate units). Most textbooks describe length, area, and volume …