Mathematics Commons^™

Computing Brain Networks With Complex Dynamics, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Gap Junctions And Synchronization Clusters In The Thalamic Reticular Nuclei, Anca R. Radulescu, Michael Anderson

Biology and Medicine Through Mathematics Conference

No abstract provided.

Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin

Electronic Theses and Dissertations

The well known Eneström-Kakeya Theorem states that: for P(z)=∑_i=0ⁿ a_i zⁱ, a polynomial of degree n with real coefficients satisfying 0 ≤ a₀ ≤ a₁ ≤ ⋯≤ a_n, all zeros of P(z) lie in |z|≤1 in the complex plane. In this thesis, we will find inner and outer bounds in which the zeros of complex and quaternionic polynomials lie. We will do this by imposing restrictions on the real and imaginary parts, and on the moduli, of the complex and quaternionic coefficients. We also apply similar restrictions on complex polynomials with …

Symmetric Functions Algebras (Sfa) Ii: Induced Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

The Italian Domatic Number On Varying Graph Families, Keith Gallegos

Scholar Week 2016 - present

See file download option for presentation.

.pdf of abstract, which contains mathematical formulas, is available as a "Supplemental File" below.

Bridging The Chasm Between Fundamental, Momentum, And Quantitative Investing, Allen Hoskins, Jeff Reed, Robert Slater

SMU Data Science Review

A chasm exists between the active public equity investment management industry's fundamental, momentum, and quantitative styles. In this study, the researchers explore ways to bridge this gap by leveraging domain knowledge, fundamental analysis, momentum, crowdsourcing, and data science methods. This research also seeks to test the developed tools and strategies during the volatile time period of 2020 and 2021.

It Application Administrator Internship, Payton Simmons

Research & Creative Achievement Day

This presentation is a focus on my internship with Fastenal as an IT Application Administrator. I'll talk about some of my daily tasks as well as the CMDB installation that will take place in the future. I am incredibly grateful to everyone who helped make this position possible because it gave me a wealth of knowledge that I will use in the near future.

An Analysis Of Major League Baseball Sabermetrics, Zack O. Fuller

Research & Creative Achievement Day

With baseball becoming an increasingly competitive sport, professional baseball teams are looking to the statistical side of the sport to find ways to win more games. With my analysis, I studied baseball statistics to look for interesting patterns and relationships. For example, I investigated the effect of a trade on a player's performance (both batters and pitchers) and analyzed the relationship between a player's performance and salary. My analysis also determined the statistics teams should utilize to win more games. To effectively analyze these patterns and relationships, visualizations were made in Tableau, and linear models were fit with R. Overall, …

Translation Of: Sur Des Familles D’Hypersurfaces Isoparamétriques Des Espaces Sphériques À 5 Et À 9 Dimensions By Èlie Cartan, Thomas E. Cecil

Mathematics Department Faculty Scholarship

English title: On Families of Isoparametric Hypersurfaces in Spherical Spaces of 5 and 9 Dimensions

This is an English translation of the article "Sur des familles de surfaces isoparamétriques des espaces sphériques à 5 et à 9 dimensions" which was originally published in Revista Univ. Tucumen, Serie A, 1, pp. 5-22 (1940), by Élie Cartan.

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in French. All references should be made to the original paper.

Mathematics Subject Classification Numbers: 53B25, 53C40, 53C42

Volume 14, Ireland Seagle, Dalton C. Whitby, Cassandra Poole, Rachel Cannon, Heidi Parker-Combes, Devon G. Shifflett, Antonio Harvey

Incite: The Journal of Undergraduate Scholarship

Table of Contents:

• Introduction: Dr. Amorette Barber
• From the Editor: Dr. Larissa "Kat" Tracy
• From the Designers: Rachel English, Rachel Hanson
• Hungry Like the Wolf: The Wolf as Metaphor in Paramount Network’s Yellowstone: Ireland Seagle
• “Floating Cities”: Illustrating the Commercial and Conservation Conflict of Alaskan Cruise Ship Tourism: Dalton C. Whitby
• What Can You Do When Your Genes are the Enemy? Current Applications of Gene Manipulation and the Associated Ethical Considerations: Cassandra Poole
• La doble cara: un tema romántico en las obras de Larra y Hawthorne: Rachel Cannon
• Resolving a Conflict: How to …

Translation Of: Sur Quelque Familles Remarquables D’Hypersurfaces, C.R. Congrès Math. Liège, 1939, Pp. 30–41, By Élie Cartan., Thomas E. Cecil

Mathematics Department Faculty Scholarship

English title: On some remarkable families of hypersurfaces

This is an English translation of the article "Sur quelque familles remarquables d’hypersurfaces" which was originally published in C.R. Congrès Math. Liège, pp. 30–41 (1939), by Élie Cartan.

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in French. All references should be made to the original paper.

Mathematics Subject Classification Numbers: 53B25, 53C40, 53C42

Optimal Control Problems For Stochastic Processes With Absorbing Regime, Yaacov Kopeliovich

Journal of Stochastic Analysis

No abstract provided.

Bounds For The Augmented Zagreb Index, Ren Qingcuo, Li Wen, Suonan Renqian, Yang Chenxu

Theory and Applications of Graphs

The augmented Zagreb index (\rm{AZI} for short) of a graph $G$, introduced by Furtula et al. in 2010, is defined as ${\rm AZI}(G)=\sum\limits_{v_iv_j\in E(G)}{\left(\frac{d(v_i)d(v_j)}{d(v_i)+d(v_j)-2}\right)}^3$, where $E(G)$ is the edge set of $G$, and $d(v_i)$ denotes the degree of the vertex $v_i$. In this paper, we give some new bounds on general connected graphs, molecular trees and triangle-free graphs. \\[2mm] {\bf Keywords:} Agumented Zagreb index; molecular trees; Triangle-free graph

New Diagonal Graph Ramsey Numbers Of Unicyclic Graphs, Richard M. Low, Ardak Kapbasov

Theory and Applications of Graphs

Grossman conjectured that $R(G, G) = 2 \cdot |V(G)| - 1$, for all simple connected unicyclic graphs $G$ of odd girth and $|V(G)| \geq 4$. In this note, we prove his conjecture for various classes of $G$ containing a triangle. In addition, new diagonal graph Ramsey numbers are calculated for some classes of simple connected unicyclic graphs of even girth.

Ts-Reconfiguration Of $K$-Path Vertex Covers In Caterpillars For $K \Geq 4$, Duc A. Hoang

Theory and Applications of Graphs

A $k$-path vertex cover ($k$-PVC) of a graph $G$ is a vertex subset $I$ such that each path on $k$ vertices in $G$ contains at least one member of $I$. Imagine that a token is placed on each vertex of a $k$-PVC. Given two $k$-PVCs $I, J$ of a graph $G$, the \textsc{$k$-Path Vertex Cover Reconfiguration ($k$-PVCR)} under Token Sliding ($\mathsf{TS}$) problem asks if there is a sequence of $k$-PVCs between $I$ and $J$ where each intermediate member is obtained from its predecessor by sliding a token from some vertex to one of its unoccupied neighbors. This problem is known …

Ramsey Numbers For Connected 2-Colorings Of Complete Graphs, Mark Budden

Theory and Applications of Graphs

In 1978, David Sumner introduced a variation of Ramsey numbers by restricting to $2$-colorings in which the subgraphs spanned by edges in each color are connected. This paper continues the study of connected Ramsey numbers, including the evaluation of several cases of trees versus complete graphs.

Over-Determined Control Systems On Time Scales, Danian Castillo, Drew Barnes, Nick Wintz

2023 Student Academic Showcase

Control theory is a branch of mathematics focused on observing or controlling a process governed by a dynamic equation. We use state-space notation to represent all meaningful information about our process. This means our processes are expressed in vector form. Typically, the state matrix is square. In this project, we consider a control system where the corresponding state is over-determined, meaning there are more rows than columns. In addition, our state equation is on a time scale T, which allows us to consider discrete, continuous, or hybrid measurements. Here, we offer two methods to solve the dynamic system. Finally, we …

Matroid Generalizations Of Some Graph Results, Cameron Crenshaw

LSU Doctoral Dissertations

The edges of a graph have natural cyclic orderings. We investigate the matroids for which a similar cyclic ordering of the circuits is possible. A full characterization of the non-binary matroids with this property is given. Evidence of the difficulty of this problem for binary matroids is presented, along with a partial result for binary orderable matroids.

For a graph G, the ratio of |E(G)| to the minimum degree of G has a natural lower bound. For a matroid M that is representable over a finite field, we generalize this to a lower bound on …

Sl(2,Z) Representations And 2-Semiregular Modular Categories, Samuel Nathan Wilson

LSU Doctoral Dissertations

We address the open question of which representations of the modular group SL(2,Z) can be realized by a modular category. In order to investigate this problem, we introduce the concept of a symmetrizable representation of SL(2,Z) and show that this property is necessary for the representation to be realized. We then prove that all congruence representations of SL(2,Z) are symmetrizable. The proof involves constructing a symmetric basis, which greatly aids in further calculation. We apply this result to the reconstruction of modular category data from representations, as well as to the classification of semiregular categories, which are defined via an …

Ramanujan–Sato Series For 1/Π, Timothy Huber, Daniel Schultz, Dongxi Ye

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equations. A complete list of rational and quadratic series corresponding to singular values of the parameters is derived.