Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, 2023 East Tennessee State University

#### 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=0}^{n} a_{i} z^{i}*, a polynomial of degree

*n*with real coefficients satisfying

*0 ≤ a*, all zeros of

_{0}≤ a_{1}≤ ⋯≤ a_{n}*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 …

A New Approach To Proper Orthogonal Decomposition With Difference Quotients, 2023 Missouri University of Science and Technology

#### A New Approach To Proper Orthogonal Decomposition With Difference Quotients, Sarah Locke Eskew, John R. Singler

*Mathematics and Statistics Faculty Research & Creative Works*

In a Recent Work (Koc Et Al., SIAM J. Numer. Anal. 59(4), 2163–2196, 2021), the Authors Showed that Including Difference Quotients (DQs) is Necessary in Order to Prove Optimal Pointwise in Time Error Bounds for Proper Orthogonal Decomposition (POD) Reduced Order Models of the Heat Equation. in This Work, We Introduce a New Approach to Including DQs in the POD Procedure. Instead of Computing the POD Modes using All of the Snapshot Data and DQs, We Only Use the First Snapshot Along with All of the DQs and Special POD Weights. We Show that This Approach Retains All of the …

Ramanujan–Sato Series For 1/Π, 2023 The University of Texas Rio Grande Valley

#### 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.

Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, 2023 University of Nebraska at Omaha

#### Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner

*UNO Student Research and Creative Activity Fair*

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …

Time Evolution Is A Source Of Bias In The Wolf Algorithm For Largest Lyapunov Exponents, 2023 University of Nebraska at Omaha

#### Time Evolution Is A Source Of Bias In The Wolf Algorithm For Largest Lyapunov Exponents, Kolby Brink, Tyler Wiles, Nicholas Stergiou, Aaron Likens

*UNO Student Research and Creative Activity Fair*

Human movement is inherently variable by nature. One of the most common analytical tools for assessing movement variability is the largest Lyapunov exponent (LyE) which quantifies the rate of trajectory divergence or convergence in an *n*-dimensional state space. One popular method for assessing LyE is the Wolf algorithm. Many studies have investigated how Wolf’s calculation of the LyE changes due to sampling frequency, filtering, data normalization, and stride normalization. However, a surprisingly understudied parameter needed for LyE computation is evolution time. The purpose of this study is to investigate how the LyE changes as a function of evolution time …

Modelling Illiquid Stocks Using Quantum Stochastic Calculus, 2023 Memorial University of Newfoundland, St Johns, NL A1C 5S7, Canada

#### Modelling Illiquid Stocks Using Quantum Stochastic Calculus, Will Hicks

*Journal of Stochastic Analysis*

No abstract provided.

Optimal Orientations Of Vertex-Multiplications Of Trees With Diameter 4, 2023 National Institute of Education, Nanyang Technological University of Singapore

#### Optimal Orientations Of Vertex-Multiplications Of Trees With Diameter 4, Willie Han Wah Wong, Eng Guan Tay

*Theory and Applications of Graphs*

\noindent Koh and Tay proved a fundamental classification of $G$ vertex-multiplications into three classes $\mathscr{C}_0, \mathscr{C}_1$ and $\mathscr{C}_2$. They also showed that any vertex-multiplication of a tree with diameter at least 3 does not belong to the class $\mathscr{C}_2$. Of interest, $G$ vertex-multiplications are extensions of complete $n$-partite graphs and Gutin characterised complete bipartite graphs with orientation number 3 (or 4 resp.) via an ingenious use of Sperner's theorem. In this paper, we investigate vertex-multiplications of trees with diameter $4$ in $\mathscr{C}_0$ (or $\mathscr{C}_1$) and exhibit its intricate connections with problems in Sperner Theory, thereby extending Gutin's approach. Let $s$ …

Symmetric Functions Algebras I: Introduction And Basic Features, 2023 Southern Illinois University, Carbondale, Illinois 62901, USA

#### Symmetric Functions Algebras I: Introduction And Basic Features, Philip Feinsilver

*Journal of Stochastic Analysis*

No abstract provided.

A Dialogue With Professor Ellen Veomett: The Intersections Of Mathematics & Gerrymandering, 2023 Saint Mary's College of California

#### A Dialogue With Professor Ellen Veomett: The Intersections Of Mathematics & Gerrymandering, Ellen Veomett

*SMC Community Engagement*

No abstract provided.

Random Variables With Overlapping Number And Weyl Algebras I, 2023 Missouri State University, Springfield, MO 65897, U.S.A.

#### Random Variables With Overlapping Number And Weyl Algebras I, Ruma Dutta, Gabriela Popa, Aurel Stan

*Journal of Stochastic Analysis*

No abstract provided.

Odds And Ends, 2023 Louisiana State University, Baton Rouge, LA 70803 USA

Something, 2023 University of California, Riverside, CA 92521

Mastery Based Grading For Secondary Mathematics, 2023 Illinois Mathematics and Science Academy

#### Mastery Based Grading For Secondary Mathematics, Anderson Trimm

*Professional Learning Day*

Dr. Trimm will discuss in detail his design and implementation of a mastery grading system in calculus at IMSA and how it offers many benefits over traditional grading. Dr. Trimm will also explain how it makes creating assessments and grading easier and less work for the teacher, while being more accurate.

A Result In The Theory Of Twin Primes, 2023 CUNY Bronx Community College

#### A Result In The Theory Of Twin Primes, Nelson Carella

*Publications and Research*

This article determines a lower bound for the number of twin primes $p$ and $p+2$ up to a large number $x$.

Optimal Monohedral Tilings Of Hyperbolic Surfaces, 2023 Rice University

#### Optimal Monohedral Tilings Of Hyperbolic Surfaces, Leonardo Digiosia, Jahangir Habib, Jack Hirsch, Lea Kenigsberg, Kevin Li, Dylanger Pittman, Jackson Petty, Christopher Xue, Weitao Zhu

*Rose-Hulman Undergraduate Mathematics Journal*

The hexagon is the least-perimeter tile in the Euclidean plane for any given area. On hyperbolic surfaces, this "isoperimetric" problem differs for every given area, as solutions do not scale. Cox conjectured that a regular k-gonal tile with 120-degree angles is isoperimetric. For area π/3, the regular heptagon has 120-degree angles and therefore tiles many hyperbolic surfaces. For other areas, we show the existence of many tiles but provide no conjectured optima. On closed hyperbolic surfaces, we verify via a reduction argument using cutting and pasting transformations and convex hulls that the regular 7-gon is the optimal n-gonal tile of …

The Determining Number And Cost Of 2-Distinguishing Of Select Kneser Graphs, 2023 Hampden-Sydney College

#### The Determining Number And Cost Of 2-Distinguishing Of Select Kneser Graphs, James E. Garrison

*Rose-Hulman Undergraduate Mathematics Journal*

A graph $G$ is said to be \emph{d-distinguishable} if there exists a not-necessarily proper coloring with $d$ colors such that only the trivial automorphism preserves the color classes. For a 2-distinguishing labeling, the \emph{ cost of $2$-distinguishing}, denoted $\rho(G),$ is defined as the minimum size of a color class over all $2$-distinguishing colorings of $G$. Our work also utilizes \emph{determining sets} of $G, $ sets of vertices $S \subseteq G$ such that every automorphism of $G$ is uniquely determined by its action on $S.$ The \emph{determining number} of a graph is the size of a smallest determining set. We investigate …

Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), 2023 Dordt University

#### Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), Calvin Jongsma

*Faculty Work Comprehensive List*

Reviewed Title: *Generations of Reason: A Family's Search for Meaning in Post-Newtonian England *by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.

Pricing Multi-Asset Contingent Claims In A Multi-Dimensional Binomial Market, 2023 University of Aberdeen, AB24 3UE Aberdeen, Scotland, UK

#### Pricing Multi-Asset Contingent Claims In A Multi-Dimensional Binomial Market, Jarek Kedra, Assaf Libman, Victoria Steblovskaya

*Journal of Stochastic Analysis*

No abstract provided.

Translation Of: Sur Des Familles Remarquables D’Hypersurfaces Isoparamétriques Dans Les Espaces Sphériques, Mathematische Zeitschrift 45, 335–367 (1939), By Élie Cartan., 2023 College of the Holy Cross

#### Translation Of: Sur Des Familles Remarquables D’Hypersurfaces Isoparamétriques Dans Les Espaces Sphériques, Mathematische Zeitschrift 45, 335–367 (1939), By Élie Cartan., Thomas E. Cecil

*Mathematics Department Faculty Scholarship*

This is an English translation of the article "Sur des familles remarquables d’hypersurfaces isoparamétriques dans les espaces sphériques," which was originally published in Mathematische Zeitschrift 45, 335–367 (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**

Iterated Jump Graphs, 2023 University of Washington, Seattle

#### Iterated Jump Graphs, Fran Herr, Legrand Jones Ii

*Rose-Hulman Undergraduate Mathematics Journal*

The jump graph J(G) of a simple graph G has vertices which represent edges in G where two vertices in J(G) are adjacent if and only if the corresponding edges in G do not share an endpoint. In this paper, we examine sequences of graphs generated by iterating the jump graph operation and characterize the behavior of this sequence for all initial graphs. We build on work by Chartrand et al. who showed that a handful of jump graph sequences terminate and two sequences converge. We extend these results by showing that there are no non-trivial repeating sequences of jump …