Proportion Of Nilpotent Subgroups In Finite Groups And Their Properties,
2026
TÜBİTAK
Proportion Of Nilpotent Subgroups In Finite Groups And Their Properties, João Victor Monteiros De Andrade, Leonardo Santos Da Cruz
Turkish Journal of Mathematics
This work introduces and investigates the function J(G) = Nil(G) / L(G) , where Nil(G) denotes the number of nilpotent subgroups and L(G) the total number of subgroups of a finite group G. The function J(G), defined on the interval (0,1], represents the proportion of nilpotent subgroups relative to the total number of subgroups, including trivial ones. It serves as a tool for analyzing structural patterns in finite groups, particularly in nonnilpotent families such as supersolvable and dihedral groups. Analytical results reveal the distribution of J(G) values across products of dihedral groups, emphasizing its density over (0,1]. Additionally, a probabilistic …
Optimal Control Of An Inverse Two-Point Boundary Value Problem For A Pseudoparabolic Equation With Samarskii–Ionkin-Type Boundary Conditions, Khanlar R. Mamedov, Tursun K. Yuldashev, Zholdoshbek Zh. Shermamatov
Turkish Journal of Mathematics
This paper investigates an inverse optimal control problem for a pseudoparabolic equation governed by nonlinear control function in a two-point boundary condition. The differential equation is considered under Samarskii Ionkin-type boundary value conditions with respect to the spatial variable x. Necessary optimality conditions are derived, and the associated nonlinear functional equations are analyzed. Using the contraction mapping principle, the existence and uniqueness of the control function are established. Subsequently, the redefinition function and the state function are determined. The convergence of their respective Fourier series representations is rigorously proven.
Close-To-Convexity Properties Of Inverse Hypergeometric Functions,
2026
University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba, 260-0808, Japan
Close-To-Convexity Properties Of Inverse Hypergeometric Functions, Ijlal Hussain, Wasim Ul Haq, Janusz Sokol
Turkish Journal of Mathematics
The normalized inverse hypergeometric function zFν−1(d, e, f; z) = ∑s=0∞ Aszs+1 is considered, where As = (f)s(ν + 1)s / (d)s(e)s. We aim to provide constraints on d, e, f, and ν under which zFν−1(d, e, f; z) belongs to various subclasses of the class of close-to-convex functions. Coefficient characterizations of these families are derived under additional conditions. Some associated operators …
Existence Results And Uniqueness For Some Caputo-Hadamard Fractional Differential Equations Via The Measures Of Noncompactness,
2026
Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, 65080, Van, Turkey
Existence Results And Uniqueness For Some Caputo-Hadamard Fractional Differential Equations Via The Measures Of Noncompactness, Manochehr Kazemi, Mohammad Esmael Samei, Hamid Reza Sahebi, Osman Tunç
Turkish Journal of Mathematics
In this paper, the existence of solutions to Caputo–Hadamard fractional differential equations is investigated using measures of noncompactness and the Petryshyn fixed point theorem. Several new results are established, recovering certain earlier results under weaker conditions. Finally, two illustrative examples are presented.
Improved Oscillation Criteria For A Class Of Neutral Differential Equations In The Canonical Case,
2026
Ibb university
Improved Oscillation Criteria For A Class Of Neutral Differential Equations In The Canonical Case, Abdulaziz Khalid Alsharidi, Ali Muhib
Turkish Journal of Mathematics
This paper develops an analytical framework based on comparison with first-order equations to derive new oscillation criteria for all solutions of a class of second-order differential equations with multiple delays. These criteria extend and improve upon previously published results. Illustrative examples are provided to validate the theoretical findings and to demonstrate the significance and applicability of the proposed criteria.
On Sequences Arising From The Action Of Modular Group,
2026
TÜBİTAK
On Sequences Arising From The Action Of Modular Group, Tuncay Köroğlu, Bahadir Özgür Güler
Turkish Journal of Mathematics
This paper examines the sequences produced by the natural action of specific elements of the modular group on extended rational numbers. The polynomial sequences Pr(c) and Qr(c) are derived from the orbit of the point at infinity under a specific modular transformation. These sequences satisfy linear recurrence relations, which are analyzed using generating functions. The polynomials encode k-Fibonacci numbers, and studying their behavior modulo a fixed integer m reveals notable arithmetic and combinatorial properties. We also explore the connection between these modular actions and Farey graphs, illustrating the hyperbolic transformations as nested geodesic paths in the upper half-plane.
A Module Theoretic Approach To (B,C)-Invertibility,
2026
Ankara University
A Module Theoretic Approach To (B,C)-Invertibility, Tuğba Pakel, Burcu Üngör, Handan Köse, Sai̇t Halicioğlu, Abdullah Harmanci
Turkish Journal of Mathematics
In this paper, we introduce and investigate the concept of an (r, f)-inverse in the context of modules, drawing inspiration from the (b, c)-inverse, which is the analogous notion in ring theory. We demonstrate the uniqueness of (r, f)-inverses in modules whenever they exist. We provide some necessary and sufficient conditions for the existence of (r, f)-inverses in modules.
Oscillation Properties Of First-Order Difference Equations With Nonmonotone Delays: New Insights And Criteria,
2026
School of Pedagogical and Technological Education (ASPETE), Department of Electrical and Electronic Engineering Educators, N. Heraklio, Athens, 14121, Greece.
Oscillation Properties Of First-Order Difference Equations With Nonmonotone Delays: New Insights And Criteria, Emad Attia, George Chatzarakis
Turkish Journal of Mathematics
In this paper, we examine the oscillatory behavior of the first-order linear delay difference equation Δy(n) + p(n) y(τ(n)) = 0, n ∈ ℕ0. It is known in the literature that, for any C > 0, the condition lim supn→∞ ∑i=τ(n)n p(i) > C, with τ(n) nonmonotone, is not, in general, sufficient to establish the oscillation of the difference equation. We prove that, for certain classes of difference equations, the aforementioned condition is sufficient to ensure the …
Ricci Solitons On Manifolds With Norden Golden Structure,
2026
Maulana Azad National Urdu University
Ricci Solitons On Manifolds With Norden Golden Structure, Bang-Yen Chen, Foued Aloui, Mohammed Nisar, Majid Ali Choudhary
Turkish Journal of Mathematics
The concept of golden structure is a compelling area with wide-ranging applications. In this paper, we introduce and investigate the notion of Norden golden Ricci solitons. In particular, we investigate Ricci solitons on a Norden golden Riemannian manifold of constant sectional curvature. Furthermore, we explore Ricci solitons and Norden golden Ricci solitons on Norden golden Riemannian manifolds whose potential vector fields are killing, conformal killing, concurrent, or homothetic.
On The Number Of Exact Factorization Of Finite Groups,
2026
TÜBİTAK
On The Number Of Exact Factorization Of Finite Groups, Jesus Alonso Ochoa Arango, Maria Angelica Umbarila Martin
Turkish Journal of Mathematics
In this work, the function f2(G), which counts the number of exact factorizations of a finite group G, is studied. The value of f2(G) is computed for several well-known families of finite groups, and an asymptotic expression is derived for the number of exact factorizations of the alternating group A2n .
Comparisons Of Some Weighted Mixed Biased Estimators For The Linear Regression Model,
2026
TÜBİTAK
Comparisons Of Some Weighted Mixed Biased Estimators For The Linear Regression Model, Dünya Karapinar, Murat Polat, Ni̇met Özbay, Selahatti̇n Kaçiranlar
Turkish Journal of Mathematics
This paper presents comparative results on the two-parameter weighted mixed estimator, which is a distinct class of estimator defined to address the problem of multicollinearity. The two-parameter weighted mixed estimator is a general estimator that includes the weighted mixed estimator, the weighted mixed Liu estimator, and the weighted mixed ridge estimator. Detailed comparisons among the mentioned estimators are carried out based on the matrix mean square error. Theoretical findings are supported by two numerical examples in addition to a Monte Carlo simulation study.
Λ-Fold Near-Factorizations Of Groups,
2026
Michigan Technological University
Λ-Fold Near-Factorizations Of Groups, Donald L. Kreher, Shuxing Li, Douglas R. Stinson
Michigan Tech Publications
We initiate the study of λ-fold near-factorizations of groups with λ>1. While λ-fold near-factorizations of groups with λ=1 have been studied in numerous papers, this is the first detailed treatment for λ>1. We establish fundamental properties of λ-fold near-factorizations and introduce the notion of equivalence. We prove various necessary conditions of λ-fold near-factorizations, including upper bounds on λ. We present three constructions of infinite families of λ-fold near-factorizations, highlighting the characterization of two subfamilies of λ-fold near-factorizations. We discuss a computational approach to λ-fold near-factorizations and tabulate computational results for abelian groups of small order.
Relation Subspaces In Vertex Operator Algebras: Residue Generators For O_N^\Circ(V) And Intersections With (L(−1) +L(0))V,
2026
University of Nebraska at Kearney
Relation Subspaces In Vertex Operator Algebras: Residue Generators For O_N^\Circ(V) And Intersections With (L(−1) +L(0))V, Junghyun Kim
Undergraduate Research Journal
We study the relation subspace 𝑂◦𝑛 (𝑉) that appears in the definition o f the level-𝑛 Zhu algebra 𝐴𝑛 (𝑉) = 𝑉/𝑂𝑛 (𝑉), where 𝑂𝑛 (𝑉) = 𝑂𝐿 (𝑉) + 𝑂◦𝑛 (𝑉) and 𝑂𝐿 (𝑉) =(𝐿(−1) + 𝐿(0))𝑉. Using residue calculus, we introduce operators 𝑅𝑛,𝑘 that encode the circle products 𝑢◦𝑛 𝑣 and prove explicit change-of-generators formulas between the standard generators (𝑢−𝑚1)◦𝑛 𝑣 and the residue generators 𝑢 𝑅𝑛,0𝑣, together with a binomial inversion. These identities provide a practical framework for computing 𝑂◦𝑛 (𝑉), especially in strongly generated VOAs. As progress toward understanding the overlap 𝑂◦𝑛 (𝑉) ∩ 𝑂𝐿 (𝑉), …
Identifiability, Sequentiality And Infinity,
2026
Wayne State University
Identifiability, Sequentiality And Infinity, Jose L. Menaldi
Mathematics Faculty Research Publications
Abstract: A definition of identifiable-sets is used with sequential analysis to establish a realm of mathematics. Within this imaginary world, a specific consonant between infinite sets and sequentiality is reached. This consonant allows some mathematical constructions to model pieces of the reality, based on dual philosophy and physics itself. There is an effort made to render this understandable for the scientific community.
Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene,
2026
Louisiana State University and Agricultural and Mechanical College
Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard
LSU Doctoral Dissertations
Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be …
Global Invertibility Of Sobolev Mappings And Energy Minimizers With Prescribed Jacobian,
2026
Syracuse University
Global Invertibility Of Sobolev Mappings And Energy Minimizers With Prescribed Jacobian, Sabrina Traver
Dissertations - ALL
We prove two main results at the intersection of Geometric Function Theory and Nonlinear Elasticity. The first is a Sobolev variant of the Inverse Function Theorem, which generalizes a famous result of John Ball. It uses Classical Sobolev Theory as well as the Degree Function, which was initially a topological tool. The second result is the existence and uniqueness (up to rotation) of a radially-symmetric minimizer for Sobolev mappings with prescribed Jacobian. This result generalizes recent work of André Guerra, Lukas Koch, and Sauli Lindberg.
Dg Algebra Techniques For Tor Algebras And Edge Ideals,
2026
Syracuse University
Dg Algebra Techniques For Tor Algebras And Edge Ideals, Desiree Martin
Dissertations - ALL
This thesis is comprised of two projects. The first is individual work where I use semifree Gamma-extensions to show, for an ideal I with infinite projective dimension over a Noetherian local ring R, there exists a splitting morphism from a Tor algebra Tor(R/I,R/I) to the exterior algebra of the R/I-free summands of the conormal module. In particular, when the conormal module is free over R/I, we see that the exterior algebra of the conormal module splits completely from Tor(R/I,R/I) as algebras. For the second project my collaborators, Hugh Geller and Henry Potts-Rubin, and I completely classify all trees and cycle …
On Compact Quasi-Einstein Metrics Of Constant Scalar Curvature,
2026
Syracuse University
On Compact Quasi-Einstein Metrics Of Constant Scalar Curvature, Eric Morgan Cochran
Dissertations - ALL
This thesis concerns a generalization of Einstein manifolds called quasi-Einstein manifolds. These manifolds are a triple $(M,g,X)$ where $(M,g)$ is a Riemannian manifold, and $X$ is a smooth vector field on $M$. Quasi-Einstein manifolds are of interest in general relativity, where a special class of quasi-Einstein manifolds are known as near horizon geometries. They are also related to Ricci solitons, which are self-similar solutions of the Ricci flow. In the first set of results in this thesis, we study the existence of Killing fields on compact quasi-Einstein manifolds. In particular, we prove an equivalence between compact quasi-Einstein manifolds of constant …
Quasi-Einstein Metrics And Homogeneous Conformally Einstein Manifolds,
2026
Syracuse University
Quasi-Einstein Metrics And Homogeneous Conformally Einstein Manifolds, Nazia Valiyakath
Dissertations - ALL
This thesis investigates a classic question in Riemannian geometry: What is the best metric to put on a Riemannian manifold? It combines two projects that explore different aspects of this question. The first project studies nilpotent and unimodular solvable Lie groups that admit m-quasi-Einstein metrics (M,g,X) with X a left-invariant vector field, which we call totally left-invariant quasi-Einstein metrics. We give a complete classification of nilpotent Lie groups admitting such metrics, showing that this occurs if and only if the group is isomorphic to Heisenberg Lie group. For unimodular solvable Lie groups S, we prove that the existence of a …
Greedy Algorithms And Matroids,
2026
Louisiana State University and Agricultural and Mechanical College
Greedy Algorithms And Matroids, Kiri M. Strack
LSU Master's Theses
In a connected graph with weights on the edges, a minimum-weight spanning tree can be obtained by repeatedly choosing minimum-weight edges while avoiding choosing the edge set of any cycle. This algorithm is known as Kruskal’s Algorithm, although it was first introduced by Boruvka in 1926. Prim introduced an alternative algorithm in which, at each step, the chosen set of edges forms a connected graph. Both of these algorithms make locally optimal choices that eventually yield a global optimum. This thesis considers how these algorithms can be extended to matroids. In particular, it is shown that matroids are exactly the …
