Mathematics Commons^™

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.

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.

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 …

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.

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.

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.

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 …

Counting Rotational Subsets Of The Circle $\Mathbb{R}/ \Mathbb{Z}$ Under The Angle-Multiplying Map $T\Mapsto Dt$, Ian Tan

Rose-Hulman Undergraduate Mathematics Journal

A rotational set is a finite subset $A$ of the unit circle $\mathbb{R}/ \mathbb{Z}$ such that the angle-multiplying map $\sigma_{d}:t\mapsto dt$ maps $A$ onto itself by a cyclic permutation of its elements. Each rotational set has a geometric rotation number $p/q$. Lisa Goldberg introduced these sets to study the dynamics of complex polynomial maps. In this paper, we provide a necessary and sufficient condition for a set to be $\sigma_{d}$-rotational with rotation number $p/q$. As applications of our condition, we recover two classical results and enumerate $\sigma_d$-rotational sets with rotation number $p/q$ that consist of a given number of orbits.

Mathematics In Everyday Life: Exploring Practical Applications And Real-World Impact, Priyant Banerjee, Arshad Bhat

Himalayan Research Papers Archive

Mathematics is an essential part of daily life and influences decisions and problem-solving in various aspects of life. This study explores how mathematical concepts are embedded in daily activities such as financial management, cooking, travel planning, and technological interactions. We will show how arithmetic, algebra, geometry, and statistics are applied in real life to improve decision-making, efficiency, and productivity. Findings indicate that people with higher mathematical literacy solve problems more efficiently, especially in budgeting, as accurate calculations minimize financial mistakes and facilitate long-term financial planning. In cooking, proportional reasoning ensures the accuracy of recipes, thus providing consistent culinary results. Travel …

Impartial Geodetic Building Games On Graphs, Bret J. Benesh, Dana C. Ernst, Marie Meyer, Sarah K. Salmon, Nándor Sieben

Mathematics Faculty Publications

A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the set. The convex hull of a set of vertices is the smallest convex set containing the set. We study variations of two games introduced by Buckley and Harary, where two players take turns selecting previously-unselected vertices of a graph until the convex hull of the jointly-selected vertices becomes too large. The last player to move is the winner. The achievement game ends when the convex hull contains every vertex. In the avoidance game, the …

Malliavin Calculus On The Clifford Algebra, Takayoshi Watanabe

Journal of Stochastic Analysis

No abstract provided.

Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary Vs Non-Unitary Time Evolution, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Supplementary Files For: "Structure Identification For High-Dimensional Data In The Vicinity Of Bear Lake", Ben Shaw, Haley Burger, Brennan Bean, Kevin Moon

Browse all Datasets

This report focuses on seven water quality measurements taken at 43 different depths on the Bear Lake for the months of June - November in the years 2018 - 2023. These measurements create a high-dimensional dataset on which we apply state-of-the-art machine learning (ML) techniques to look for low-dimensional structure in the data. A similar effort was made for weather measurements taken near the lake. Our analysis revealed that water quality measurements tend to cluster (i.e., group together) by year, while weather measurements tend to cluster by time of the year. This suggests that the structure observed in the water …