Mathematics Commons^™

On An Asset Model Of Merton Type: Long-Term Observations In Financial Time-Series, Shuya Kanagawa, Narn-Rueih Shieh

Journal of Stochastic Analysis

No abstract provided.

Image Of Mathematics: A Case Study Of Two Women's Early Mathematics Experiences, Lili Zhou, Elizabeth Suazo-Flores, Bima Sapkota, Rose Mbewe, Jill Newton

School of Mathematical & Statistical Sciences Faculty Publications

People often view mathematics as abstract, cold, and irrelevant to real life, and their school experiences likely influence such views. In this case study, we investigated the mathematics experiences of two women who participated in an afterschool girls-only STEM club 30 years ago when they were in fifth and sixth grades. We explored how the participants' early in- and out-of-school experiences informed their images of mathematics. We collected data through a survey, focus group interviews, and individual interviews. We employed oral history methods in interviews to grant participants a significant degree of freedom to retrospectively recount and reconstruct their experiences. …

Artificial Intelligence Meets Quantum, Raul Coto Cabrera

Mathematics Colloquium Series

This talk will provide an overview of the ubiquitous field of artificial intelligence, the growing field of quantum computers, and their intersection, quantum machine learning. This new branch harnesses the combined potential of its predecessors to unlock groundbreaking applications. I will briefly introduce the paradigms of AI and fundamental concepts around it. We will discuss algorithms that learn and make decisions based on data, as well as neural networks that are data-free, that is, learned from models.

Maximum Spread Of KS,T - Minor-Free Graphs, William Linz, Linyuan Li, Zhiyu Wang

Faculty Publications

The spread of a graph G is the difference between the largest and smallest eigenvalue of the adjacency matrix of G. In this paper, we consider the family of graphs which contain no K_s,t-minor. We show that for any t ≥ s ≥ 2 and sufficiently large n, there is an integer ξ_t such that the extremal n-vertex K_s,t-minor-free graph attaining the maximum spread is the graph obtained by joining a graph L on (s − 1) vertices to the disjoint union of ⌊(2n + ξ …

Two Families Of Graceful Cacti, Christian Barrientos

Communications on Number Theory and Combinatorial Theory

We present a graceful labeling for each member of a subfamily of quadrangular cacti whose underlying graph correspond to the subclass of rooted binary trees where every level has at most two vertices. We also prove the existence of an $\alpha$-labeling (the most restricted type of graceful labeling) for all cyclic snakes, i.e., those cacti whose blocks are copies of the cycle $C_{4n}$ and its maximum degree is four.

The Frequency Of Elliptic Curves Over $\Mathbb{Q}[I]$ With Fixed Torsion, Alan S. Zhao

Rose-Hulman Undergraduate Mathematics Journal

Mazur\textsc{\char13}s Theorem states that there are precisely 15 possibilities for the torsion subgroup of an elliptic curve defined over the rational numbers. It was previously shown by Harron and Snowden that the number of isomorphism classes of elliptic curves of height up to $X$ that have a specific torsion subgroup $G$ is on the order of $X^{1/{d(G)}}$, for some positive $d(G)$ depending on $G$. We compute $d(G)$ for these groups over $\Qi$. Furthermore, in a collection of recent papers it was proven that there are 9 more possibilities for the torsion subgroup in the base field $\Qi$. We compute the …

Model-Theoretic Properties Of Nilpotent Groups And Lie Algebras, Christian D'Elbée, Isabel Müller, Nicholas Ramsey, Daoud Siniora

Faculty Journal Articles

We give a systematic study of the model theory of generic nilpotent groups and Lie algebras. We show that the Fraïssé limit of 2-nilpotent groups of exponent p studied by Baudisch is 2-dependent and NSOP1. We prove that the class of c-nilpotent Lie algebras over an arbitrary field, in a language with predicates for a Lazard series, is closed under free amalgamation. We show that for 2c.

The Role Of Α-Inequalities In Examining The Singular Version Of The Big Bang Model, Samane Ijadi, S. Mansour Vaezpour, Mehdi Shabibi, Shahram Rezapour

Turkish Journal of Mathematics

In this article, by extending Friedmann's equation, we propose a singular fractional differential system for the Big Bang model. In this model, the rate of increase in the size of the universe tends to infinity at time near to zero and causes the emergence of a singular differential equation,which physically justifies the near-infinity energy of the universe in the near-zero volume of the universe in the early moments of the Big Bang. Then, we investigate this type of strong singular boundary value problem, by using $\alpha$-inequalities. In the sequel, some examples, describe the main results. Moreover, we present numerical and …

Asymptotic Behavior Of The Kirchhoff Index For Square Lattice With Boundary Conditions, Fati̇h Ecevi̇t, Arzu Boysal

Turkish Journal of Mathematics

We determine leading asymptotic behavior of the Kirchhoff index for the square lattice under free, cylindrical and toroidal boundary conditions. Our results provide correct forms of the eleven false theorems/results published in the following papers: L. Ye, On the Kirchhoff index of some toroidal lattices, Linear Multilinear Algebra, 59:6 (2011), 645--650; J.-B. Liu, X.-F. Pan, J. Cao, X. Huang, The Kirchhoff index of toroidal meshes and variant networks, Math. Probl. Eng., Article ID 286876, 8 pages (2014); J.-B. Liu, X.-F. Pan, A unified approach to the asymptotic topological indices of various lattices, Appl. Math. Comput., 270 (2015), 62--73.

Properties Of Frontier, Exterior And Border In Picture Topological Spaces, Shanmugasundharam Durga, Lakshmanadas Vidyarani, Mandarasalam Vigneshwaran, Tomasz Witczak

Turkish Journal of Mathematics

The paper is dedicated to picture sets. They are crisp version of Cuong's picture fuzzy sets (just like intuitionistic sets introduced by Coker are crisp version of intuitionistic fuzzy sets). We have already defined several basic topological notions in this framework and we have analyzed its algebra. Now we continue our research. We introduce the notions of border, frontier and exterior. Many properties are studied. Moreover, we point out that there are some important differences between classical and non-classical approach.

Inverse Ordered Semigroups, Michael Tsingelis

Turkish Journal of Mathematics

Ένα στοιχείο x μιας διατεταγμένης ημιομάδας [[EQUATION]] ονομάζεται αντίστροφο στοιχείο του [[EQUATION]]if [[EQUATION]]και [[EQUATION]]. Μια αντίστροφη διατεταγμένη ημιομάδα είναι μια διατεταγμένη ημιομάδα S για την οποία κάθε στοιχείο του S έχει ένα αντίστροφο στοιχείο και τα αντίστροφα στοιχεία οποιουδήποτε στοιχείου του S βρίσκονται στην ίδια συνδεδεμένη συνιστώσα του διαγράμματος Hasse της σχέσης τάξης του. Παρουσιάζουμε ιδιότητες που ικανοποιούνται από αντίστροφα διατεταγμένες ημιομάδες και χαρακτηρίζουμε αντίστροφα διατεταγμένες ημιομάδες με βάση την έννοια της κανονικότητας των διατεταγμένων ημιομάδων, το σύνολο των αδυναμιών τους και τις σχέσεις του Green. Επίσης αποδεικνύουμε ότι η αντιστρεψιμότητα των διατεταγμένων ημιομάδων διατηρείται από ομομορφισμούς.

On Minimal Hypersurfaces In Euclidean Spaces And Riemannian Manifolds, Josef Mikeš, Sergey Stepanov, Irina Tsyganok

Turkish Journal of Mathematics

In this paper, we present the conditions under which minimal and stable minimal hypersurfaces are as hyperplanes in Euclidean spaces ands a totally geodesic submanifolds in Riemannian manifolds.

Local Dynamic Analysis Of The Covid-19 Mathematical Model Based On Discrete-Time Predator-Prey Population Model, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Özge Kuzucu

Turkish Journal of Mathematics

In this article, the local dynamics of a discrete-time Covid-19 pandemic model based on the Lotka Volterra model with topological classifications, bifurcation analysis and chaos control are investigated. It is shown that under some parametric conditions, the discrete-time Covid-19 pandemic model has two equilibrium points. With linear stability theory, local dynamics are investigated with topological classifications about the equilibrium points of the discrete-time Covid-19 epidemic model. In addition, the existence of a Neimark-Sacker bifurcation at the internal equilibrium point is proved and this bifurcation is analysed using explicit criteria. Furthermore, the chaos in the discrete Covid-19 pandemic model is also …

Generalization Of Dual Numbers And Dual Euclidean 3-Space, Şükran Duygu Soylu, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r

Turkish Journal of Mathematics

In this study, we consider the generalized dual numbers and determine their algebraic and geometric properties. Then we generalize the well-known D3 module and introduce the generalized dual Euclidean 3-space with its scalar product and norm. After determining the conditions for being a unit generalized dual Euclidean vector, we derive the generalized Euclidean Study map, which states that there is a bijective correspondence between directed lines of the space and the elements of the unit generalized dual Euclidean sphere. Finally, we define the dual Euclidean angle between two generalized dual Euclidean vectors.

Estimates Of The Numerical Radius Utilizing Various Function Properties, Vuk Stojiljkovic, Mehmet Gürdal

Turkish Journal of Mathematics

Numerous inequalities of the vector and numerical radius types have been found. We achieved several extensions of the well-known numerical radius type inequalities by using the function [[EQUATION]] described in the publication by Stojiljkovi\'{c} and Dragomir in [30] and convexity characteristics with standard operator theory approaches. In particular, the following integral type numerical radius inequality has been obtained, that is [[EQUATION]]

Nearly Toric Varieties Of Type A, Mahi̇r Bi̇len Can, Nestor Fernando Diaz Morera

Turkish Journal of Mathematics

A notion of a nearly toric variety is introduced. The examples of nearly toric varieties in the context of Schubert varieties are discussed. In particular, combinatorial characterizations of the smooth and singular nearly toric Schubert varieties are found. Furthermore, the counts and generating series are determined. Additionally, a connection between Dyck paths and a certain family of nearly toric Schubert varieties is established.

Face-Magic Labelings Of Polygonal Graphs, Wai Chee Shiu, Richard M. Low, Andy K. Liu

Theory & Applications of Graphs

For a plane graph $G = (V, E)$ embedded in $\mathbb{R}^2$, let $\mathcal{F}(G)$ denote the set of faces of $G$. Then, $G$ is called a \textit{$C_n$-face-magic graph} if there exists a bijection $f: V(G) \to \{1, 2, \dots, |V(G)|\}$ such that for any $F \in \mathcal{F}(G)$ with $F \cong C_n$, the sum of all the vertex labels along $C_n$ is a constant $c$. In this paper, we investigate face-magic labelings of polygonal graphs.

A Characterization Of Chordal Graph Without Sun And Co-Rising Sun As Convex Geometry, Silvia B. Tondato

Theory & Applications of Graphs

In this paper we introduce the notion of $t_3$ \textit{convexity}, a natural restriction of triangle convexity. A \textit{triangle path} is a path allowing just short chords. A triangle path $P$ between two non-adjacent vertices in a graph $G$ is called $t_3$ \textit{path} if the first vertex of $P$ is among vertices from $P$ adjacent only to the second vertex of $P$, and the last vertex of $P$ is among vertices from $P$ adjacent only to the second-last vertex of $P$. A set $S \subseteq V(G)$ is $t_3$ \textit{convex} if for any two non-adjacent vertices $x, y \in S$ any vertex …

Failed Zero Forcing Numbers Of Trees And Circulant Graphs, Luis Gomez, Karla Rubi, Jorden Terrazas, Rigoberto Florez, Darren A. Narayan

Theory & Applications of Graphs

Given a graph $G$, the zero forcing number of $G$, $Z(G)$, is the smallest cardinality of any set $S$ of vertices on which repeated applications of the forcing rule (described below) results in all vertices being in $S$. The forcing rule is as follows: if a vertex $v$ is in $S$, and exactly one neighbor $u$ of $v$ is not in $S$, then $u$ is added to $S$ in the next iteration. Zero forcing numbers have attracted great interest over the past 15 years and have been well studied. The zero forcing number is used to study the maximum nullity/minimum …

Kroger Post-Pandemic Customer Segmentation, Mario Mata, Joey Truitt, Renn Spigelmyer, Dhanuja Kasturiratna, Lisa Holden, Nitish Baidya, Hanna Tafari

Posters-at-the-Capitol

The grocery retail industry landscape has changed greatly in the wake of the pandemic. Specifically, delivery and pickup services have become more popular and customer buying habits have evolved. At the same time, improvements in data collection and analysis have allowed grocery marketing strategies to become highly individualized.

We worked with 84.51, an analytics firm, to identify customer segments for the Kroger Company based on data from 2023. Using clustering techniques, we organized customers into groups, or segments, based on similar characteristics. We identified and profiled four distinct groups of customers. Three segments were characterized by high frequency and spending …