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Articles 1  30 of 23851
FullText Articles in Mathematics
Enestr¨OmKakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin
Enestr¨OmKakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin
Electronic Theses and Dissertations
The well known EneströmKakeya Theorem states that: for P(z)=∑_{i=0}^{n} a_{i} z^{i}, a polynomial of degree n with real coefficients satisfying 0 ≤ a_{0} ≤ a_{1} ≤ ⋯≤ 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 …
The Italian Domatic Number On Varying Graph Families, Keith Gallegos
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.
Ramanujan–Sato Series For 1/Π, Timothy Huber, Daniel Schultz, Dongxi Ye
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.
A New Approach To Proper Orthogonal Decomposition With Difference Quotients, Sarah Locke Eskew, John R. Singler
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 …
Euler Archive Spotlight, Erik R. Tou
Euler Archive Spotlight, Erik R. Tou
Euleriana
A survey of two translations posted to the Euler Archive in 2022.
Euler And The Duplication Formula For The GammaFunction, Alexander Aycock
Euler And The Duplication Formula For The GammaFunction, Alexander Aycock
Euleriana
We show how the formulas in Euler’s paper "Variae considerationes circa series
hypergeometricas" [ 4] imply Legendre’s duplication formula for the Γfunction. This
paper can be seen as an Addendum to [2].
Euler Found The First Binary Digit Extraction Formula For Π In 1779, Nick CraigWood
Euler Found The First Binary Digit Extraction Formula For Π In 1779, Nick CraigWood
Euleriana
In 1779 Euler discovered two formulas for π which can be used to calculate any binary digit of π without calculating the previous digits. Up until now it was believed that the first formula with the correct properties (known as a BBPtype formula) for this calculation was published by Bailey, Borwein and Plouffle in 1997.
Analytical Observations (Translation Of E326), Cynthia Huffman Ph.D.
Analytical Observations (Translation Of E326), Cynthia Huffman Ph.D.
Euleriana
Euler, in this publication with Eneström number E326, provides an induction fallacy which arises from analyzing a particular sequence. Euler wrote this work in 1763, one of only two papers he wrote on sequences and/or series in the 1760’s, out of a total of 79 papers on series during his career. His goal in E326 is to investigate the middle terms in the expansion of powers of quadratic trinomial expressions, beginning with the specific simple quadratic , before considering the general quadratic .
The induction fallacy shows up during the analysis of the simple case when Euler first finds an …
Euler's Anticipations, Christopher Goff, Erik Tou
Euler's Anticipations, Christopher Goff, Erik Tou
Euleriana
Welcome to Volume 3 of Euleriana. This issue highlights occasions where Euler's work anticipated future results from other others, sometimes by decades or even centuries!
Problem Of The Week: A StudentLed Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner
Problem Of The Week: A StudentLed 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 realworld 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, Kolby Brink, Tyler Wiles, Nicholas Stergiou, Aaron Likens
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 ndimensional 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 …
Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*Algebras, Khalid Bdarneh
Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*Algebras, Khalid Bdarneh
LSU Doctoral Dissertations
In this thesis we consider the Toeplitz operators on the weighted Bergman spaces and their analytic continuation. We proved the commutativity of the $C^*$algebras generated by the analytic continuation of Toeplitz operators with special class of symbols that are invariant under suitable subgroups of $SU(n,1)$, and we showed that commutative $C^*$algebras with symbols invariant under compact subgroups of $SU(n,1)$ are completely characterized in terms of restriction to multiplicity free representations. Moreover, we extended the restriction principal to the analytic continuation case for suitable maximal abelian subgroups of the universal covering group $\widetilde{SU(n,1)}$, and we obtained the generalized SegalBargmann transform, where …
Modelling Illiquid Stocks Using Quantum Stochastic Calculus, Will Hicks
Modelling Illiquid Stocks Using Quantum Stochastic Calculus, Will Hicks
Journal of Stochastic Analysis
No abstract provided.
Optimal Orientations Of VertexMultiplications Of Trees With Diameter 4, Willie Han Wah Wong, Eng Guan Tay
Optimal Orientations Of VertexMultiplications 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 $G$ vertexmultiplications into three classes $\mathscr{C}_0, \mathscr{C}_1$ and $\mathscr{C}_2$. They also showed that any vertexmultiplication of a tree with diameter at least 3 does not belong to the class $\mathscr{C}_2$. Of interest, $G$ vertexmultiplications 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 vertexmultiplications 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, Philip Feinsilver
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, Ellen Veomett
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, Ruma Dutta, Gabriela Popa, Aurel Stan
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, Jimmie D. Lawson
Something, Gerhard Gierz
Mastery Based Grading For Secondary Mathematics, Anderson Trimm
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, Nelson Carella
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, Leonardo Digiosia, Jahangir Habib, Jack Hirsch, Lea Kenigsberg, Kevin Li, Dylanger Pittman, Jackson Petty, Christopher Xue, Weitao Zhu
Optimal Monohedral Tilings Of Hyperbolic Surfaces, Leonardo Digiosia, Jahangir Habib, Jack Hirsch, Lea Kenigsberg, Kevin Li, Dylanger Pittman, Jackson Petty, Christopher Xue, Weitao Zhu
RoseHulman Undergraduate Mathematics Journal
The hexagon is the leastperimeter 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 kgonal tile with 120degree angles is isoperimetric. For area π/3, the regular heptagon has 120degree 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 7gon is the optimal ngonal tile of …
The Determining Number And Cost Of 2Distinguishing Of Select Kneser Graphs, James E. Garrison
The Determining Number And Cost Of 2Distinguishing Of Select Kneser Graphs, James E. Garrison
RoseHulman Undergraduate Mathematics Journal
A graph $G$ is said to be \emph{ddistinguishable} if there exists a notnecessarily proper coloring with $d$ colors such that only the trivial automorphism preserves the color classes. For a 2distinguishing 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 PostNewtonian England (Book Review), Calvin Jongsma
Generations Of Reason: A Family’S Search For Meaning In PostNewtonian England (Book Review), Calvin Jongsma
Faculty Work Comprehensive List
Reviewed Title: Generations of Reason: A Family's Search for Meaning in PostNewtonian England by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.
Pricing MultiAsset Contingent Claims In A MultiDimensional Binomial Market, Jarek Kedra, Assaf Libman, Victoria Steblovskaya
Pricing MultiAsset Contingent Claims In A MultiDimensional 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., 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, Fran Herr, Legrand Jones Ii
Iterated Jump Graphs, Fran Herr, Legrand Jones Ii
RoseHulman 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 nontrivial repeating sequences of jump …
The Chromatic Index Of Ring Graphs, Lilian Shaffer
The Chromatic Index Of Ring Graphs, Lilian Shaffer
RoseHulman Undergraduate Mathematics Journal
The goal of graph edge coloring is to color a graph G with as few colors as possible such that each edge receives a color and that adjacent edges, that is, different edges incident to a common vertex, receive different colors. The chromatic index, denoted χ′(G), is the minimum number of colors required for such a coloring to be possible. There are two important lower bounds for χ′(G) on every graph: maximum degree, denoted ∆(G), and density, denoted ω(G). Combining these two lower bounds, we know that every graph’s chromatic index must be at least ∆(G) or …
Richard Whately's Revitalization Of Syllogistic Logic, Calvin Jongsma
Richard Whately's Revitalization Of Syllogistic Logic, Calvin Jongsma
Faculty Work Comprehensive List
This is an expanded version of the first chapter Richard Whately’s Revitalization of Syllogistic Logic in Aristotle’s Syllogism and the Creation of Modern Logic edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author’s 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/ ) and more current scholarship, this essay traces the critical historical background to Whately’s work in more detail than could be done in the published version.
The MalliavinStein Method For Normal Random Walks With Dependent Increments, Ian Flint, Nicolas Privault, Giovanni Luca Torrisi
The MalliavinStein Method For Normal Random Walks With Dependent Increments, Ian Flint, Nicolas Privault, Giovanni Luca Torrisi
Journal of Stochastic Analysis
No abstract provided.