Mathematics Commons^™

Volatility Modelling In Garch Frameworks: A Comparative Analysis Of Non-Gaussian Error Distributions With Skewed Parameters., Olatunbosun Adewale Akanbi, Timothy Olabisi Olatayo, Abass Ishola Taiwo

Al-Bahir

Forecasting volatility in financial time series remains challenging due to their asymmetric nature and excess kurtosis. This study evaluates and compares the performance of four variant of GARCH models incorporating skewed non-Gaussian error innovation distribution. The performances of these GARCH family of models under the skewed error innovation distributions were evaluated for three different unique data sets to have a more robust assessment of the performance of these skewed error innovation distributions. This study leverage on daily closing prices of Bitcoin, Naira to Dollar Exchange rates and daily Nigeria All Share Index between January 1, 2015 and January 26, 2024. …

Non-Orientable Surfaces Bounded By Knots, Megan K. Fairchild

LSU Doctoral Dissertations

The non-orientable 4-genus of a knot $K$ in $S^{3}$ is defined to be the minimum first Betti number of a non-orientable surface $F$ in $B^{4}$ so that $K$ bounds $F$. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots, torus knots, and Whitehead doubles. We also will view obstructions to a knot bounding a M\"{o}bius band given by the double branched cover of $S^{3}$ branched over $K$. Additionally, we discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used …

On Examples And Classification Of Frobenius Objects In Rel, Ivan Contreras, Adele Long, Sophia Marx, Rajan Amit Mehta

Mathematics Sciences: Faculty Books

This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology, Geometry, and Physics, held virtually on March 26–27, 2022.

The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories. There is an intricate interplay between geometry, topology, and algebra which captures these theories. The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background on which the theories are formulated. The higher structures considered in the volume are generalizations of operads, models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, …

Voronoi Conjecture For Five-Dimensional Parallelohedra, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

We prove the Voronoi conjecture for five-dimensional parallelohedra. Namely, we show that if a convex five-dimensional polytope P tiles ℝ5 with translations, then P is an affine image of the Dirichlet-Voronoi polytope for a five-dimensional lattice.
/="/">Our proof is based on an exhaustive combinatorial analysis of possible dual 3-cells and incident dual 4-cells encoding local structures around two-dimensional faces of five-dimensional parallelohedron P and their edges aiming to prove existence of a free direction for P paired with new properties established for parallelohedra (in any dimension) that have a free direction that guarantee the Voronoi conjecture for P.

Group Approach To Geometric Quantization Of Two Physical Groups, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Physical systems as a rule are associated with a symmetry group. One way of quantizing the system is to use this symmetry group to construct a geometric form of quantization procedure. This group quantization procedure is discussed and illustrated here on two different systems. Group cohomology and extensions of groups play a key role. Many important groups in physics can be extended by the local U(1) group. The process is introduced here and applied to two nontrivial systems.

Hypergraph Association With Lie Algebra Of Upper Triangular Matrices And Its Application To Wireless Networks, Supriya S

Theses and Dissertations

A hypergraph is a generalized graph characterized by edges spanning more than one vertices describing multiple relationships among them. It provides a mathematical framework for comprehending and learning about a wide range of real-world challenges. On the other side, the theory of non-associative algebras, such as Jordan, Octonions, Malcev, and Lie, has found significant impetus in recent years. These structures proved intriguing from an algebraic standpoint; they generated novel concepts and approaches that aided in solving specific classic algebraic problems, also progressing towards application.

A preeminent observation that galvanizes this thesis is that hypergraph association is still unexplored in Lie …

Stochastic Games Of Parental Vaccination Decision Making And Bounded Rationality, Andras Balogh, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

Vaccination is an effective strategy to prevent the spread of diseases. However, hesitancy and rejection of vaccines, particularly in childhood immunizations, pose challenges to vaccination efforts. In that case, according to rational decision-making and classical utility theory, parents weigh the costs of vaccination against the costs of not vaccinating their children. Social norms influence these parental decision-making outcomes, deviating their decisions from rationality. Additionally, variability in values of utilities stemming from stochasticity in parents' perceptions over time can lead to further deviations from rationality. In this paper, we employ independent white noises to represent stochastic fluctuations in parental perceptions of …

Asymptotic Matrix Behaviors And Iterative Algorithms, Tin-Yau Tam

Mathematics Colloquium Series

This presentation examines the asymptotic behavior of matrix iterations, focusing on the QR and LR algorithms and their significance in eigenvalue computation. It highlights foundational developments by Rutishauser, Francis, and Kublanovskaya and modern refinements by Huang and Tam, particularly on matrix decompositions and spectral properties. Extensions of Yamamoto’s theorem, including recent works by Nayak and Shekhawat, and Huang and Tam, are discussed, connecting iterative processes to spectral radius formulas and Jordan decompositions. This is a joint work with Huajun Huang of Auburn University.

Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar

Journal of Stochastic Analysis

No abstract provided.

Differentiating Contact With Symptomatic And Asymptomatic Infectious Individuals In A Seir Epidemic Model, Victoria Chebotaeva, Anish Srinivasan, Paula A. Vasquez

Faculty Publications

This manuscript introduces a new Erlang-distributed SEIR model. The model incorporates asymptomatic spread through a subdivided exposed class, distinguishing between asymptomatic (E_a) and symptomatic (E_s) cases. The model identifies two key parameters: relative infectiousness, β_SA, and the percentage of people who become asymptomatic after being infected by a symptomatic individual, κ. Lower values of these parameters reduce the peak magnitude and duration of the infectious period, highlighting the importance of isolation measures. Additionally, the model underscores the need for strategies addressing both symptomatic and asymptomatic transmissions.

Optimized Hiv/Aids Resource Allocation In Ohio: A Linear Programming Approach, Godfred Ahenkroa Kesse

Data Science and Data Mining

This study employs a linear and integer programming approach to optimize HIV resource allocation in Ohio, aiming to minimize new infections and enhance the impact of limited resources. With the advances in HIV prevention and treatment, Ohio faces challenges in addressing disparities in access to healthcare, particularly among high-risk populations. The proposed model integrates data on infection rates, transmission patterns, demographic factors, and cost-effectiveness to provide a decision-support framework for policymakers. Using epidemiological data and equity constraints, the model prioritizes high-risk regions and populations while ensuring fair resource distribution. Results indicate that increased funding allocations significantly enhance the potential to …

Ultrathin-Layer Strain-Based Electronic Devices: From-First-Principles Derivation Of The Corresponding Equation, Julio C. Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

Most information about the world comes from sensors -- and from the results of processing sensor data. In many practical situations -- e.g., in biomedical applications -- it is desirable to make sure that the sensors are as "invisible" as possible, in particular, that they are as small as possible. One way to achieve such small size is to use ultrathin-layer materials such as graphene. It is known that for such materials, strain causes electromagnetic effects -- which can be used to detect small strains. Interestingly, it turned out that the same equation describes the relation between strain and electric …

A Natural Extension Of F-Transform To Triangular And Triangulated Domains Necessitates The Use Of Triangular Membership Functions, Hana Zámečiková, Irina Perfilieva, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations when we process 1-D data, the method of F-transform turned out to be very useful. In this method, we can use either triangular membership functions or more complex ones. Because this method has been so successful in 1-D applications, a natural idea is to extend it to functions defined on 2-D and higher-dimensional domains -- e.g., to images. This method allows natural generalization to rectangular domains, where it indeed turned out to be very effective. A recent paper showed that it can extended to more general domains -- e.g., to triangular domains and to more general …

Fourier Series For Singular Measures In Higher Dimensions, Chad Berner, John E. Herr, Palle E.T. Jorgensen, Eric S. Weber

Mathematics and Statistics Faculty Research & Creative Works

For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal L2 Fourier expansions. Our results hold for probability measures μ with finite support in Rd that satisfy a certain disintegration condition that we refer to as "slice-singular". In this general framework, we present explicit L2(μ)-Fourier expansions, with Fourier exponentials having positive Fourier frequencies in each of the d coordinates. Our Fourier representations apply to every f∈L2(μ), are based on an extended Kaczmarz algorithm, and use a new recursive μ Rokhlin disintegration representation. In detail, our Fourier series expansion for f is in terms of the …

Unconditionally Optimal Convergent Zero-Energy-Contribution Scheme For Two Phase Mhd Model, Jinjin Yang, Shipeng Mao, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

This paper focuses on the unconditionally optimal error estimates of a fully discrete decoupled scheme for two-phase magnetohydrodynamic (MHD) model with different viscosities and electric conductivities, by using the zero-energy-contribution (ZEC) method for the temporal discretization and mixed finite elements for the spatial discretization. Based on the ZEC property of the nonlinear and coupled terms of the model, an ordinary differential equation is designed to introduce a nonlocal scalar auxiliary variable which will play a key role in the design and the energy stability of the decoupled scheme. Combining fully explicit treatment on the nonlinear and coupled terms with the …

The Effects Of Functional Moves In Teacher Questioning On Students’ Contextualization Of Mathematical Word Problem Solving, Yi-Jung Lee

Curriculum and Instruction Faculty Publications and Presentations

Posing purposeful questions is one of the most effective teaching practices (NCTM in Principles to actions: Ensuring mathematics success for all. National Council of Teachers of Mathematics, 2014). Although the types and functions of teacher questioning have been abundantly studied, research on the role of teacher questioning in students’ contextualization process as they solve word problems is rather scarce. This study was conducted to investigate the function of six elementary preservice teachers’ questioning, its impact on students’ contextualization, as well as the successes and difficulties of enacting questioning. The collected data were analyzed using thematic analysis. The findings indicated that …

Analytical Method For Solving Systems Of Fractional Initial Value Problems Using The Modified Atangana-Baleanu Derivative, Lana Mohammad Aref

Theses

This thesis presents an analytical method to solve systems of fractional initial value problems using the Modified Atangana-Baleanu Fractional Derivative. The proposed approach leverages an improved operational matrix method, incorporating an iterative, direct computation technique to simplify the solution process and reduce computational costs. Foundational concepts in fractional calculus and block pulse functions are introduced, followed by the derivation of operational matrices tailored for fractional systems. Theoretical analysis establishes the existence and uniqueness of solutions, along with uniform convergence and error estimates. Practical examples and applications are presented that demonstrate the efficiency, accuracy, and versatility of the method in solving …

Project Title: Maximizing The Volume Of A Cardboard Box To Save Trees– An Application Of Polynomial Functions To Address Global Issues [Mathematics], Lucie Mingla

Open Educational Resources

MAT 115 College Algebra & Trigonometry/Precalculus

Project Title: Maximizing the Volume of a Cardboard Box to Save Trees– An Application of Polynomial Functions to Address Global Issues

Reflective Narrative:

This project was inspired by my participation in the "Designing and Implementation of STEM Co-Curricular Activities" CTL seminar in Spring 2023. I am grateful to Drs. Bukurie Gjoci, Daniel Gertner, Ingrid Veras, and Midas Tsai, along with fellow participants, for their invaluable feedback that helped shape its development. The project was implemented in two College Algebra and Trigonometry courses. I participated in two seminars to further develop this project. The Community …

Order-2 Delaunay Triangulations Optimize Angles, Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

School of Mathematical & Statistical Sciences Faculty Publications

The local angle property of the (order-1) Delaunay triangulations of a generic set in R2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">R2R2 asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">R2R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations …

For Chow Variety Try This New Dessert Recipe, Jane P. Sheldon

Journal of Humanistic Mathematics

A positive addition to any dinner table or social function, this baked good can be served plane or à la mode.