Mathematics Commons^™

The Lowest Discriminant Ideal Of Cayley-Hamilton Hopf Algebras, Zhongkai Mi

LSU Doctoral Dissertations

Discriminant ideals are defined for an algebra R with central subalgebra C and trace tr : R → C. They are indexed by positive integers and more general than discriminants. Usually R is required to be a finite module over C. Unlike the abundace of work on discriminants, there is hardly any literature on discriminant ideals. The levels of discriminant ideals relate to the sums of squares of dimensions of irreducible modules over maximal ideals of C containing these discriminant ideals. We study the lowest level when R is a Cayley-Hamilton Hopf algebra, i.e. C is also a Hopf subalgebra, …

Splines On Cayley Graphs Of The Symmetric Group, Nathan Lesnevich

Arts & Sciences Graduate Student Theses and Dissertations

A spline is an assignment of polynomials to the vertices of a graph whose edges are labeled by ideals, where the difference of two polynomials labeling adjacent vertices must belong to the corresponding ideal. The set of splines forms a ring. We consider spline rings where the underlying graph is the Cayley graph of a symmetric group generated by a collection of transpositions. These rings generalize the GKM construction for equivariant cohomology rings of flag, regular semisimple Hessenberg, and permutohedral varieties. These cohomology rings carry two actions of the symmetric group S_n whose graded characters are both of general interest …

Statistics For Iwasawa Invariants Of Elliptic Curves, Ii, Debanjana Kundu, Anwesh Ray

School of Mathematical & Statistical Sciences Faculty Publications

We study the average behavior of the Iwasawa invariants for Selmer groups of elliptic curves. These results lie at the intersection of arithmetic statistics and Iwasawa theory. We obtain lower bounds for the density of rational elliptic curves with prescribed Iwasawa invariants.

“Don’T Call On Me!”: Mediating Preservice Elementary Teachers’ Mathematics Anxiety In A Problem-Based Classroom, Christina Koehne, Wenyen Huang, Nataly Chesky

Excelsior: Leadership in Teaching and Learning

This study aims to understand the ways in which problem-based teaching in a mathematics content course can alleviate pre-service elementary school teachers' mathematics anxiety. The significance of this work is to help increase the content and pedagogical knowledge of mathematics education, as outlined in STEM policies. Using a mixed method approach, the teachers-researchers explore what methods, procedures, and other perhaps unknown variables, helped pre-service elementary teachers decrease their mathematics anxiety during two mathematics content courses. The findings illuminate five major themes the authors discuss, which are illustrated by rich descriptions of students’ narratives and interviews. Given the importance of mathematics …

Faithful Representation Of Free Groups And Congruent Subgroups Of 𝑆𝐿3 (𝑍), Julius Kurian

Thesis/ Dissertation Defenses

This thesis is concerned with the matrix representation of a free non-abelian group by matrices of size ≥ 3. We proceed from defining an equivalence classes and then transitioning to free groups. We discuss in details the group 𝐺𝑛(𝑘) which is the group generated by the matrices filled with first, (second, etc.) column, except for the intersection with the diagonal, and we have ones on the diagonal and zeros at the other places. The filled places are occupied by the same parameter 𝑘. An alternative proof for the known fact that 𝐺𝑛(3) is not free is provided. The main objective …

Extensions Of Algebraic Frames, Papiya Bhattacharjee

Algebra Seminar

A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …

Extensions Of Algebraic Frames, Papiya Bhattacharjee

Mathematics Colloquium Series

A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …

On The Projections And Unitary Groups Of Unital C*-Algebras, Fouzia Shaheen

Thesis/ Dissertation Defenses

H. Dye proved that the unitary group in a factor determines the algebraic type of that factor. Al-Rawashdeh, Booth and Giordano established that, for a large class of simple unital C*- algebras, an isomorphism between the unitary groups, induces an isomorphism between their K0-ordered group and K1-groups. Then using the results of Dadarlat-Elliot-Gong and KirchbergPhillips, the C*-algebras are isomorphic. Dye introduced special projections P{i,j}(a) of the matrix algebra Mn(A), and he used it as a main tool to establish his results in the case of von Neumann factors. Precisely, in case of von Neumann algebra, he proved that if  …

Pricing Asian Options During Crises With The Impact Of Exogenous Events, Moath Ali Bakour

Thesis/ Dissertation Defenses

Asian options are path-dependent options since their payoff is built on the prices of the underlying asset over a time period. The Asian option pricing problem is primarily subject to the prediction model for asset prices. The pioneer Black Scholes paper suggests a GBM- Geometric Brownian motion. The Black-Scholes formula suffers from several shortcomings. For instance, the GBM does not take into consideration crises. Another problem with the Black-Scholes model is that it does not deal with the impact of external events. This work aims at a suggested model that encompasses the impacts of crises and external events together. It …

On Properties Of Pair Operations, Sarah Jane Poiani

Mathematics & Statistics ETDs

For any closure operation $\cl$ and interior operation $\ri$ on a class of $R$-modules, we develop the theory of $\cl$-prereductions and $\ri$-postexpansions. A pair operation is a generalization of closure and interior operations. Using Epstein, R.G. and Vassilev's duality \cite{ERGV-nonres}, we show that these notions are in fact dual to each other. We discuss the relationship between the core and hull and prereductions and postexpansions. We further the thematic notion of duality and seek to understand how it arises in the context of properties pair operations can be endowed with and focus on inner product spaces and properties demonstrated by …

Generalized Q-Fock Spaces And Structural Identities, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using 𝑞-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their 𝑞-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative.

Hgs-3 The Influence Of A Tandem Cycling Program In The Community On Physical And Functional Health, Therapeutic Bonds, And Quality Of Life For Individuals And Care Partners Coping With Parkinson’S Disease, Leila Djerdjour, Jennifer L. Trilk

SC Upstate Research Symposium

Purpose Statement: Several studies have shown that aerobic exercise can have a positive impact on alleviating symptoms experienced by individuals with Parkinson's disease (PD). Despite this evidence, the potential benefits of exercise for both PD patients and their care partners (PD dyad) remain unexplored. This research project investigates the effectiveness, therapeutic collaborations, and physical outcomes of a virtual reality (VR) tandem cycling program specifically designed for PD dyads.

Methods: Following approval from the Prisma Health Institutional Review Board, individuals with PD were identified and screened by clinical neurologists. The pre-testing measures for PD dyads (N=9) included emotional and cognitive status …

Towards Erasing The Distinction Between The Computational And Syntactic Accounts Of Scientific Theories, Timothy Luft

Theses

One of the main goals of philosophy of science is to give a proper account of scientific theories and their structure. One way that accounts of the structure of scientific theories can be distinguished is by the mathematical or logical structures that they involve. For instance, syntactic accounts of scientific theories hold that theories are axioms in a logical framework, whereas semantic accounts are more liberal in the range of mathematical and logical structures they take as pertinent to the structure of scientific theories. Paul Thagard (1988) offers a computational account of scientific theories, which holds that theories are complex …

Identity Development Among Pre-Health Students During The Covid-19 Pandemic, Anya Kapitula, Anna Tyshka

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

Many sociology studies have been published regarding the experiences and development of medical school students, but there is a gap in research observing undergraduate students on pre-health professions tracks. Specifically, studies have been published noting a significant decrease in the empathy of medical school students during their third year, but no research has been conducted to identify development patterns of these students during their undergraduate years. This study aims to identify groups of undergraduate students on pre-health professions tracks based on typologies formed from longitudinal survey responses, and also to identify any significant transitions between these groups over time. Because …

On Axially Rational Regular Functions And Schur Analysis In The Clifford-Appell Setting, Daniel Alpay, Fabrizio Colombo, Antonino De Martino, Kamal Diki, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we start the study of Schur analysis for Cauchy–Fueter regular quaternionic-valued functions, i.e. null solutions of the Cauchy–Fueter operator in . The novelty of the approach developed in this paper is that we consider axially regular functions, i.e. functions spanned by the so-called Clifford-Appell polynomials. This type of functions arises naturally from two well-known extension results in hypercomplex analysis: the Fueter mapping theorem and the generalized Cauchy–Kovalevskaya (GCK) extension. These results allow one to obtain axially regular functions starting from analytic functions of one real or complex variable. Precisely, in the Fueter theorem two operators play a …

Mathematically Rigorous Deep Learning Paradigms For Data-Driven Scientific Modeling, Owen Nicholas Davis

Mathematics & Statistics ETDs

This dissertation explores the crucial role of data-driven modeling in science and engineering, with a focus on developing surrogate models to accelerate large-scale computational tasks, aiding in both outer-loop functions like uncertainty quantification and expensive inner-loop tasks within broader computational frameworks. Challenges arise with increased problem dimension and sparse, noisy training data, particularly significant when constructing surrogates for very expensive computational models where acquiring sufficient high-fidelity training data is unfeasible. In such scenarios, training surrogates from an ensemble of multifidelity information sources of varying accuracy and cost becomes essential. We emphasize neural network-based modeling paradigms, which are flexible in integrating …

Optimal Control Of Coefficients For The Second Order Parabolic Free Boundary Problems, Ali Hagverdiyev

Mathematics Colloquium Series

In this talk I will discuss Inverse Stefan type free boundary problem for the second order parabolic equation arising for instance, in modeling of laser ablation of biomedical tissues, where the information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the temperature and free boundary. New PDE constrained optimal control framework is employed, where the missing data and the free boundary are components of the control vector, and optimality criteria are based on the final moment measurement of the temperature and position of the free boundary. …

Gender And The Billboard Top 40 Charts Between 1958 And 2023, Brileigh Cates, Justin W. Pope

Undergraduate Research Conference at Missouri S&T

Is there an inherent bias towards male artists in the music industry? Evidence has been shown in previous studies, the most recent being from 2017, that there may be bias towards male artists appearing in Billboard Magazine s Hot 100 list. This study not only updates previous data to include 2017 through 2023, but also looks at the top 40 charts on a week-by-week bias as opposed to the year-end charts that other studies used for their data. We coded each song so as to indicate the gender of the artist(s) as well as whether or not the artists appeared …

The History Of The Billboard Hot 100 And Its Process, Brileigh Cates

Undergraduate Research Conference at Missouri S&T

The Billboard Hot 100 has been around for decades, and it is believed without much accreditation. What really is Billboard, and why is it so popular? Why have other charting companies not taken up as much popularity? How does Billboard determine the popularity of artists? How has this changed with the introduction of the internet? This research project addresses all of these question, allowing the validity of the data collection to be addressed.

Numerical Studies On Bose-Einstein Condensates, Megan Benkendorf

Undergraduate Research Conference at Missouri S&T

Bose-Einstein condensate (BEC) is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent "super-wave". The superfluidity of BEC has been the focus of active research since the first experimental realization of BEC in 1995. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018, has once again drawn spotlights to these fascinating properties of BEC. In this project, we will carry out numerical studies to understand the behavior of exciton-polariton BECs. A modified Gross-Pitaevskii equation is used to model the dynamics …

Numerical Studies On Bose–Einstein Condensates, Megan Benkendorf

Undergraduate Research Conference at Missouri S&T

Bose-Einstein condensate (BEC) is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent "super-wave". The superfluidity of BEC has been the focus of active research since the first experimental realization of BEC in 1995. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018, has once again drawn spotlights to these fascinating properties of BEC. In this project, we will carry out numerical studies to understand the behavior of exciton-polariton BECs. A modified Gross-Pitaevskii equation is used to model the dynamics …

Towards Fast, Realistic Gas Plume Simulation For Lwir Hyperspectral Images To Improve Deep Learning Identification Models, Scout Jarman

Student Research Symposium

• Longwave infrared (LWIR) hyperspectral images (HSI) are taken from airborne platforms and can be used to find gas plumes.
• Detection and identification of gas plumes has applications in environmental monitoring, disaster response, and national security
• Deep learning can be used to identify gases from a large library of materials,  but can be difficult to apply in practice

Structure Of A Class Of Ordinary Differential Equations, Letao Chang

SACAD: Scholarly Activities

In the realm of mathematics, an ordinary differential equation (ODE) denotes a particular type of differential equation contingent solely upon a single independent variable. Similar to other differential equations, an ODE involves one or more functions as its unknowns and encompasses derivatives of these functions. The designation "ordinary" serves to distinguish these equations from partial differential equations, which may pertain to multiple independent variables.

Inferring Inertial Navigation Errors From Sar Image Distortions Using A Convolutional Neural Network, Teresa White

Student Research Symposium

Precise navigation data is necessary for autonomous vehicles. In normal circumstances: GPS is typically used.

Optimal Control For Delayed Nanoparticle Dosing Models Using Conformable Derivatives, Drew Barnes, Micah Duffield, Abi Waters

2024 Student Academic Showcase

Previously, a research group used a theoretical state-space framework to study the effects nanoparticles had on cancerous tumors in mice. Since sensors are used to determine the number of nanoparticles found in the bloodstream, it is natural for a time delay to occur when making adjustments to the dosage. Here, an equal time delay has been put on the state and control to study the effects of multiple dosage strategies. However, these researchers did not consider how the absorption of these nanoparticles would affect treatment. In this project, we construct a model using a conformable derivative first introduced by Khalil …

Crash Analysis For Lake St. Louis Police Department, Anna Carter, Melisa Murillo, Joseph E. Smith, Mackenzie Holmes

2024 Student Academic Showcase

Lake Saint Louis is a small city of just under 17,000 people in the same county as Lindenwood University. Originally a planned community, it is easily accessible by Interstate 64 and Interstate 70. It also contains two large lakes and shopping centers that attracts visitors to the area. As a result, there has been a number of traffic accidents in the area. The Police Department has requested that Lindenwood’s PIC Math group review data from 2018-2023 to identify patterns. The group has reviewed the crash data at several locations and under multiple conditions and has uncovered some noticeable trends. The …

Youth In Need Data Analysis, Drew Barnes, Ryan Eckman, Abi Waters

2024 Student Academic Showcase

Youth In Need is a nonprofit that offers mental and physical health resources to kids under the age of 19 in the St. Charles area. They have been in operation for 50 years. Youth In Need is concerned that their services may have been negatively impacted by the pandemic. They have asked Lindenwood’s PIC Math group to review their data over 2015-2023 and identify trends. Identifying these trends may help the client optimize their resources. So far, the group has identified trends when the intake of new clients occurs as well as trends between the counselors’ client-scores and clients’ self-scores …

Quandle Rings, Idempotents And Cocycle Invariants Of Knots, Dipali Swain

USF Tampa Graduate Theses and Dissertations

Quandles are sets with self-distributive binary operations that axiomatize the three Reidemeister movesin classical knot theory. In an attempt to bring ring theoretic techniques to the study of quandles, a theory of quandle rings analogous to the classical theory of group rings where several interconnections between quandles and their associated quandle rings have been explored. Functoriality of the construction implies that morphisms of quandle rings give a natural enhancement of the well-known quandle coloring and quandle 2 cocycle invariant of knots and links.

The dissertation is structured into two main parts. In the first part, we delve into quandle rings …

Game 'Make 24', Seunghyeok Jang

SACAD: Scholarly Activities

• Basic numerical skills are a must-have in today’s world. However, children are not picking up the four basic numerical skills adequately.

• To improve their mathematical skills, they need a way to learn the numerical skills easily.

• "Make 24" is a game for young children who are having a difficult time with basic numerical operations. The game helps children improve their numerical skills by playing this game.

Finite Monodromy And Artin Representations, Emma Lien

LSU Doctoral Dissertations

Artin representations, which are complex representations of finite Galois groups, appear in many contexts in number theory. The Langlands program predicts that Galois representations like these should arise from automorphic representations and many examples of this correspondence have been found such as in the proof of Fermat's Last Theorem. This dissertation aims to make an analysis of explicitly computable examples of Artin representations from both sides of this correspondence. On the automorphic side, certain weight 1 modular forms have been shown to be related to Artin representations and an explicit analysis of their Fourier coefficients allows us to identify the …