Mathematics Commons^™

On Trinomial Units Of The Group Ring RcN, César A. Hernandez Melo, Fernanda Diniz De Melo Hernandez, Patricia Massae Kitani

Turkish Journal of Mathematics

Let R be an associative ring with identity, C_n be the cyclic group of order n, and g be a generator of C_n. In this manuscript, for i ∈ N such that 1 ≤ i < n and gcd(i, n) = 1, the algebraic properties of the trinomial elements h_i = -1 + g + g^-i in the group ring RC_n are investigated. More precisely, necessary and sufficient conditions are given for an element h_i to be a unit in RC_n. When h_i is a unit, explicit formulas for computing …

End-Regular Flower Graphs CR,S, Joerg Koppitz, Suparat Phantukang, Phurinut Srisawad, Somnuek Worawiset

Turkish Journal of Mathematics

In the present paper, we study the regularity of the endomorphism monoid of a class of graphs, which generalizes the cycle graph. We give a complete list of all end-regular r × s flower graphs. In particular, for an odd integer s ≥ 3, the s × s flower graph Cs,s has a regular endomorphism monoid, i.e., Cs,s is end-regular. For Cs,s, s ≥ 3 odd, we determine the cardinality and the rank of its endomorphism monoid (including a generating set of minimal size).

Generalized Szász–Mirakyan Operators In The Variation Seminorm, Sare Yumruçali, Harun Karsli, Fatma Taşdelen Yeşi̇ldal

Turkish Journal of Mathematics

The aim of the present paper is to introduce generalized Szász–Mirakyan operators. This article studies the property of variation seminorm and some approximation properties of generalized Szász–Mirakyan operators not only in normed spaces but also in variation seminorm. We obtain convergence properties of our operators using of Korovkin’s theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetre’s K functional. We also give asymptotic formula and the convergence of the derivatives for these operators. We investigate the variation detracting property of generalized Szász–Mirakyan operators. We show the convergence of generalized Szász–Mirakyan operators …

Some Properties Of Nabla Laplace Transform On Isolated Time Scales, Müfi̇t Şan, Huri̇ye Dağ, Manuel D. Ortigueira

Turkish Journal of Mathematics

This study presents the properties of the bilateral and unilateral nabla Laplace transform, defined on isolated time scales. Furthermore, it explores the nabla Laplace transforms of several elementary functions, employing various proof techniques from real and complex analysis. The findings are illustrated with examples, demonstrating the applicability of these definitions.

From Rough Categories To Rough Groupoids, Mehmet Mustafa Beydaği, Abdullah Fati̇h Özcan, İlhan İçen

Turkish Journal of Mathematics

In this study, we introduce the concepts of rough category and rough groupoid by combining the concepts of category theory and groupoid with rough set theory. We present some properties and examples of these concepts, which are discussed for the first time. Additionally, by defining a rough functor among the rough categories, the category of rough categories were created. Moreover, rough groupoid homomorphism, rough action groupoid, and category of the rough groupoids have been examined algebraically and introduced to the literature.

An Investigation Of New Associated Curves Of A Frenet Curve In Euclidean N-Space, Bedi̇a Meri̇h Özçeti̇n

Turkish Journal of Mathematics

In this study, we introduce the V2-direction curve, Vn−1-direction curve and Vn-direction curve of a Frenet curve in n-dimensional Euclidean space. We provide characterizations and investigate the relationships between the Frenet apparatus of the principal curve and the corresponding apparatus of the direction curves. We also present an application for all direction curves with the results shown using computer code implemented in MATLAB.

New Structures Of Golden Type On The Tangent Bundle, Simona-Luiza Druta-Romaniuc, Cristina-Elena Hretcanu, Aydin Gezer

Turkish Journal of Mathematics

The aim of our paper is to prove the existence of some types of almost (α, p)–golden structures, obtained as general natural lifts of the Riemannian metric from the base manifold M to the total space TM of the tangent bundle. We show that TM, endowed with a general natural almost (α, p)–golden structure (which is a generalisation of the golden structure) and with a general natural metric, is an almost (α, p)–golden Riemannian manifold if and only if the function coefficients of the almost (α, p)–golden structure are related to …

Corrigendum To “ Improved Berezin Radius Inequalities For Functional Hilbert Space Operators” [Turkish Journal Of Mathematics 49 (5) 2025 545-561], Mojtaba Bakherad, Ulaş Yamanci, Mohammad W. Alomari

Turkish Journal of Mathematics

In the article entitled Improved Berezin radius inequalities for functional Hilbert space operators, published in the Turkish Journal of Mathematics, [49 (5): 545-561. https://doi.org/10.55730/1300-0098.3607], the affiliation of the author MOHAMMAD W. ALOMARI was published incorrectly due to an error at the submission stage. The incorrect affiliation was Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid, Jordan T he correct affiliation is Department of Mathematics, Faculty of Science, Jadara University, Irbid, Jordan T he authors apologize for any inconvenience caused.

The original article can be accessed at: https://doi.org/10.55730/1300-0098.3607

Monotone Positive Solutions Of Impulsive Differential Equations Asymptotic To Nonprincipal Solutions, Si̇bel Doğru Akgöl, Ağacik Zafer

Turkish Journal of Mathematics

This study investigates the asymptotic behavior of monotone positive solutions for a general class of nonlinear second-order impulsive differential equations. By employing the principal and nonprincipal solutions of the associated homogeneous equation, we establish the existence of a monotone positive solution asymptotic to a nonprincipal solution at infinity. To achieve this, we also prove a compactness criterion for an effective use of Schauder’s fixed-point theorem. Under suitable conditions, similarly to the classical case, it is demonstrated that a monotone positive solution asymptotic to a nonprincipal solution exists. A concrete example is given to illustrate the results.

Exploratory Study Of Semiconductor Nanomembranes In Em Applications, Grant D. Heileman

Electrical and Computer Engineering ETDs

Antenna systems are a cornerstone of modern technologies, playing an increasingly vital role in their advancement. As demand for compact, high-performance, and adaptable communication platforms grows reconfigurable antenna technologies are becoming essential. This research explores a novel front-end reconfigurable antenna system (FERAS) architecture that leverages the mechanical flexibility and photoconductive behavior of semiconductor nanomembrane (SNM) devices. By exploiting the emergent properties of ultra-thin silicon (Si) or gallium arsenide (GaAs) nanomaterials and optically exciting these samples using vertical-cavity surface-emitting laser (VCSEL) arrays, this study develops lightweight, low-cost, deployable antenna structures for satellite communications, remote sensing, GPS, and radar. Despite their significant …

Problems In Extremal Graph Theory And Spectral Graph Theory, Fareeha Jamal

Thesis/ Dissertation Defenses

Spectral graph theory is a subfield of algebraic graph theory that studies the matrices associated with graphs. It lives at the nexus of Linear Algebra and Combinatorics. Many intriguing results in the domains of Matrix Theory and Combinatorics have come from studying the eigenvalues of graph matrices; in fact, several open problems in both areas have been resolved. Beyond its theoretical appeal, spectral graph theory has found meaningful applications in theoretical chemistry, particularly in the mathematical classification of chemical graphs. These classifications underpin quantitative structure–property relationships (QSPRs), facilitating the prediction of physicochemical properties such as enthalpy of vaporization, molar refractivity, …

Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread, Michelle Marfo, Dr. Padmanabhan Seshaiyer, Alonso Ogueda-Oliva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Cancer Cell Growth Predictions Based On Classical Mathematical Models With Physics-Informed Neural Network, Widodo Samyono

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Invitation To Polynomiography Via Chatgpt: For Teachers, Students And Artists, Bahman Kalantari

LASER Journal

Teachers, students, and artists in the United States and abroad who have encountered polynomiography, in lectures, demos, or software, consistently appreciate its educational value and artistic potential. While dedicated polynomiography programs require upkeep as systems evolve, AI chatbots now offer a practical, accessible alternative. This article invites readers to explore polynomiography with ChatGPT, broadening access beyond specialized tools. While the approach will not match the full range or polish of advanced software, it provides a powerful and flexible entry point with many possibilities.

At its core, polynomiography transforms polynomial equations, each encoding a finite set of points in the complex …

Turning Papers And Class Notes Into Books, Olcay Akman, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Kadel] Parameter Personalization Of Medical Digital Twins, Logan Rose

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Deep-Shallow Mindset Through Student-Instructor Interactions Within The Classroom, David Chan, Kaden Sadler, Charles Ibitamuno, Oyita Udiani, Rani Satyam, Miriah Dudley, Ajay Manohar, Indranil Sahoo, Yanjun Qian, Nick Wong

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Untitled Unmastered: Initial Conditions And Emergent Properties Of The Mathematics Classroom, Reginald L. Mcgee

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Probability Of N Clonal Rosettes In A Bromeliaceae Genetic Individual, Erin N. Bodine, Layla K. Lammers

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Infographic: Pisa Insights – Encouraging Mathematical Thinking, Dominique Russell

Teacher infographics

Each cycle of the global Programme for International Student Assessment (PISA) includes a teacher questionnaire. One questionnaire topic – encouraging mathematical thinking – can help foster critical thinking, enhance problem-solving skills and allow students to see the relevance and connectedness of mathematics in their lives.