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Articles 1 - 30 of 2581
Full-Text Articles in Mathematics
Notes On The Geometry Of Electromagnetic Fields And Maxwell’S Equations Along A Nonnull Curves In Nonflat-3d Space Forms MQ3(C), Fatma Almaz, Cumali̇ Eki̇ci̇
Notes On The Geometry Of Electromagnetic Fields And Maxwell’S Equations Along A Nonnull Curves In Nonflat-3d Space Forms MQ3(C), Fatma Almaz, Cumali̇ Eki̇ci̇
Turkish Journal of Mathematics
In this paper, the directional derivatives in accordance with the orthonormal frame {T→, N→, B→} are defined in Mq3(c), the extended Serret-Frenet relations by using Frenet formulas are expressed. Furthermore, we express the bending elastic energy function for the same particle in Mq3(c) according to curve γ(s, ξ, η) and we tried to interpret it from a geometric perspective of the energy for unit vector fields. Also, Maxwell’s equations are expressed for the electric and magnetic field vectors …
Biharmonic Curves In Warped Product Manifolds I ×FMN(C), Şaban Güvenç, Ci̇han Özgür
Biharmonic Curves In Warped Product Manifolds I ×FMN(C), Şaban Güvenç, Ci̇han Özgür
Turkish Journal of Mathematics
We explore the geometric properties of biharmonic curves in warped product manifolds of the form I ×f Mn(c), where I is an open interval and Mn(c) is a space of constant curvature. By establishing a main theorem, we analyze four distinct cases to reveal deeper curvature-related characteristics of these curves, including situations where they are slant. Finally, we construct three examples in I ×f S2(1).
Generalized Submaximality And Paracompactness In Ideal Topological Spaces Via Δβ*-𝔍-Open Sets, Chawalit Boonpok, Areeyuth Sama-Ae
Generalized Submaximality And Paracompactness In Ideal Topological Spaces Via Δβ*-𝔍-Open Sets, Chawalit Boonpok, Areeyuth Sama-Ae
Turkish Journal of Mathematics
This paper explores the notions of δβ*-𝔍-submaximality and δβ*-𝔍-paracompactness within ideal topological spaces, viewing them as natural generalizations of the traditional concepts of submaximality and paracompactness. These concepts arise naturally in the context of ideal topology, where an ideal 𝔍 on a topological space provides additional structure for analyzing topological properties. It focuses on the study of submaximal spaces by employing δβ*-𝔍-open sets, which serve as fundamental building blocks for understanding the topological behavior in ideal spaces. Furthermore, the work provides multiple characterizations of δβ*-𝔍-paracompact spaces and examines how this property behaves …
A Module Theoretic Approach To (B,C)-Invertibility, Tuğba Pakel, Burcu Üngör, Handan Köse, Sai̇t Halicioğlu, Abdullah Harmanci
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.
Ricci Solitons On Manifolds With Norden Golden Structure, Bang-Yen Chen, Foued Aloui, Mohammed Nisar, Majid Ali Choudhary
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.
Comparisons Of Some Weighted Mixed Biased Estimators For The Linear Regression Model, Dünya Karapinar, Murat Polat, Ni̇met Özbay, Selahatti̇n Kaçiranlar
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.
On Sequences Arising From The Action Of Modular Group, Tuncay Köroğlu, Bahadir Özgür Güler
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.
Adaptive Two-Derivative Runge–Kutta–Nyström Method With Trigonometric Fitting Approach, Nur Nabila Huda, Khai Chien Lee, Nurul Huda Abdul Aziz
Adaptive Two-Derivative Runge–Kutta–Nyström Method With Trigonometric Fitting Approach, Nur Nabila Huda, Khai Chien Lee, Nurul Huda Abdul Aziz
Turkish Journal of Mathematics
A fifth-order trigonometrically-fitted explicit two-derivative Runge–Kutta–Nyström method with an adaptive step size strategy, denoted as ATFRKN5, is proposed for efficiently solving second-order ordinary differential equations of the form u″(x) = f(x, u(x)) that exhibit oscillatory behavior. The order conditions of the method are derived using Taylor series expansion, enabling the construction of two-derivative Runge–Kutta–Nyström schemes up to orders four and five. Trigonometric fitting is applied by incorporating the basis functions eiλx and e−iλx, λ ∈ ℝ, allowing the method to adapt naturally to problems with dominant frequencies. …
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
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.
Proportion Of Nilpotent Subgroups In Finite Groups And Their Properties, João Victor Monteiros De Andrade, Leonardo Santos Da Cruz
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
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.
Oscillation Properties Of First-Order Difference Equations With Nonmonotone Delays: New Insights And Criteria, Emad Attia, George Chatzarakis
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 …
Close-To-Convexity Properties Of Inverse Hypergeometric Functions, Ijlal Hussain, Wasim Ul Haq, Janusz Sokol
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 …
Improved Oscillation Criteria For A Class Of Neutral Differential Equations In The Canonical Case, Abdulaziz Khalid Alsharidi, Ali Muhib
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 The Number Of Exact Factorization Of Finite Groups, Jesus Alonso Ochoa Arango, Maria Angelica Umbarila Martin
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 .
The Degree Of Nondensifiability In Hausdorff Locally Convex Topological Vector Spaces And Applications, Gonzalo Garcia
The Degree Of Nondensifiability In Hausdorff Locally Convex Topological Vector Spaces And Applications, Gonzalo Garcia
Turkish Journal of Mathematics
The so called degree of nondensifiability, DND, has been studied in Banach spaces through several studies, and some fixed point results using the DND have been proved. In the present paper, we extend the concept of DND to a Hausdorff locally convex topological vector space (LCTVS). Its main properties, as well as the differences between the DND in Banach spaces and the DND in a LCTVS, are analyzed. Furthermore, under suitable conditions, we provide some fixed point results in a LCTVS by using the DND, and as an application, we prove the existence of solutions of certain Volterra integral equations.
Existence Of Positive Periodic Solutions For A First-Order Semilinear Functional Differential Equation With An Iterative Source Term, Ahlème Bouakkaz, Rabah Khemis
Existence Of Positive Periodic Solutions For A First-Order Semilinear Functional Differential Equation With An Iterative Source Term, Ahlème Bouakkaz, Rabah Khemis
Turkish Journal of Mathematics
In this paper, we will establish the existence of positive periodic solutions for a class of first order iterative functional differential equations by using a powerful and effective technique based on the Krasnoselskii fixed point theorem together with some useful properties of a Green's function. The obtained results that complement some previous works, are illustrated with an example.
Simplicity In Le-Semigroups Via Partitions Of Full Words, And Its Applications To Regularity Conditions Induced By Linear Inequalities, Nareupanat Lekkoksung
Simplicity In Le-Semigroups Via Partitions Of Full Words, And Its Applications To Regularity Conditions Induced By Linear Inequalities, Nareupanat Lekkoksung
Turkish Journal of Mathematics
The concept of simplicity in le-semigroups has been used to characterize the coincidence of ideal elements and to study Khayopulu–Green’s relations. Several types of simplicities are known, including two-sided simplicity, left simplicity, right simplicity, bisimplicity, quasisimplicity, and biinterior simplicity. A natural question arises: are there further notions of simplicity for le-semigroups? If so, how are they related? By employing the notion of partition ideal elements, we observe that several potential simplicities have not yet been explored. In this paper, we introduce new forms of simplicity in le-semigroups defined via partitions of full words, and we investigate the …
On The Semigroups Of Order-Preserving And Orientation-Preserving Full Contraction Mappings On A Finite Chain, Gonca Ayik, Hayrullah Ayik
On The Semigroups Of Order-Preserving And Orientation-Preserving Full Contraction Mappings On A Finite Chain, Gonca Ayik, Hayrullah Ayik
Turkish Journal of Mathematics
Let OPCTn (OCTn) denote the semigroup consisting of all orientation-preserving (order-preserving) full contraction mappings on the finite chain Xn = {1 < ··· < n}, and let OPDCTn (ODCTn) denote the subsemigroup of OPCTn (OCTn) consisting of all order-decreasing transformations. The purpose of this paper is to determine the cardinalities of OPCTn, OPDCTn, N(ODCTn), and N(OPDCTn), and to identify generating sets of minimal size, thereby determining their ranks. Moreover, the number of idempotents of OPDCTn is determined.
A Geometric Property Characterizing The 3d-Generalized Clothoids, Pascual Lucas, José-Antonio Ortega-Yagües
A Geometric Property Characterizing The 3d-Generalized Clothoids, Pascual Lucas, José-Antonio Ortega-Yagües
Turkish Journal of Mathematics
In this paper, we study 3D-generalized clothoids, defined as curves for which there exists another distinct curve, with proportional arclength parameter, such that the Darboux lines of both curves at corresponding points are the same. We prove that these curves are those for which the ratio of torsion and curvature τ/κ is a linear rational function of the arclength. We also show that any 3D-generalized clothoid can be constructed from a rectifying curve, which is of constant curvature in the case of a 3D-clothoid.
Multiplicative Lorentz Matrix Multiplication And The Motion On Multiplicative Lorentz Plane, Osman Keçi̇li̇oğlu, İlayda Durmaz, Hali̇t Gündoğan
Multiplicative Lorentz Matrix Multiplication And The Motion On Multiplicative Lorentz Plane, Osman Keçi̇li̇oğlu, İlayda Durmaz, Hali̇t Gündoğan
Turkish Journal of Mathematics
In this paper, we define the multiplicative determinant for general n×n matrices, extending previous studies that were limited to lower-dimensional cases. Additionally, we introduce a novel matrix multiplication operation based on the multiplicative Lorentz inner product and conduct a thorough investigation of its algebraic properties. Furthermore, we explore rotational and reflectional transformations in the two-dimensional multiplicative Lorentz space L*2, supported by illustrative examples of these geometric motions.
Investigation Of The Behavior Of Biparametric Potentials Associated With The Laplace-Bessel Differential Operator In Weighted Lebesgue Spaces, Çağla Seki̇n
Turkish Journal of Mathematics
In this article, we investigate the mapping properties of potential-type operators of the form Jαβ = (E + (−Δν)β/2)−α/β, (β, α > 0), where Δν is the Laplace-Bessel differential operator. We establish norm inequalities that describe the boundedness of the operator Jαβ from Lp,ν to Lq,ν under suitable conditions on α, β, p and q. The results extend and unify the known estimates for classical potential operators. In particular, the cases β = 1 and β = 2 correspond to the modified Flett and Bessel potentials, respectively.
On Fredholm Type Integral Equations In H\"{O}Der Spaces: Existence Of Solutions, Yasemi̇n Başci, Adi̇l Misir, Süleyman Öğrekçi̇
On Fredholm Type Integral Equations In H\"{O}Der Spaces: Existence Of Solutions, Yasemi̇n Başci, Adi̇l Misir, Süleyman Öğrekçi̇
Turkish Journal of Mathematics
In this study, we investigate the existence of solutions for a quadratic integral equation of the Fredholm type. The analysis is conducted on a finite interval bounded by two arbitrary constants, where the unknown function is associated with a prescribed kernel and two operators satisfying specific regularity and boundedness conditions. The methodological framework of this work is built upon the classical Schauder fixed point theorem, complemented by the structural properties of Hölder spaces. The results obtained not only encompass but also extend several previous contributions in the literature, as the discussion is carried out within a generalized setting over the …
Exploring Topological And Game-Theoretic Properties Of Selective Covering Bispaces, Selma Özçağ
Exploring Topological And Game-Theoretic Properties Of Selective Covering Bispaces, Selma Özçağ
Turkish Journal of Mathematics
This paper considers set selectively star countable chain condition in a bitopological setting, exploring its fundamental topological properties and its relationships with the existing selective covering properties. Furthermore we investigate a game-theoretic characterizations of the selectively countable chain condition property in bitopological spaces.
The Killing Magnetic Curves In The Anti-De Sitter Space H31, Uğur Dursun
The Killing Magnetic Curves In The Anti-De Sitter Space H31, Uğur Dursun
Turkish Journal of Mathematics
In this paper, we study space-like, time-like and light-like Killing magnetic curves derived from Killing magnetic vector fields of the anti-de Sitter space H31 by using the half-space model H31 of H31. We find the first integrals of the system of nonlinear differential equations that describe the Killing magnetic curves corresponding to some Killing vector fields of H31, and then we give some particular solutions to obtain space-like, time-like and light-like magnetic curves of H31. Also, we calculate the curvature and torsion of some space-like and time-like …
A Non-Newtonian Approach To Screw Motion And Dual Numbers, Esra Parlak, Zehra Özdemi̇r
A Non-Newtonian Approach To Screw Motion And Dual Numbers, Esra Parlak, Zehra Özdemi̇r
Turkish Journal of Mathematics
In this paper, we define multiplicative dual numbers, multiplicative dual vectors, scalars, and vector products associated with the multiplicative dual numbers. We give the base elements of multiplicative dual elliptic quaternions and their operational properties. We explain the rotation and translation motions in multiplicative dual elliptical quaternions. We provide the matrix representations of the screw motion using multiplicative dual elliptical quaternions. Thanks to these multiplicative dual elliptical quaternions, we explain the screw motion along with rotation and translation with theorems and proofs. We visualize this screw motion with mathematical programs by applying screw-ruled surfaces.
ℤ3-Graded Cartan Calculus On 𝒪(ℂQ1|1|1), Sultan Çeli̇k, Sali̇h Çeli̇k
ℤ3-Graded Cartan Calculus On 𝒪(ℂQ1|1|1), Sultan Çeli̇k, Sali̇h Çeli̇k
Turkish Journal of Mathematics
After a brief introduction of the basic concepts of ℤ3-grading, the paper continues by introducing ℤ3-graded differential calculus and ℤ3-graded Cartan calculus. Then, using a matrix R which is a solution of the Yang-Baxter equation, a new ℤ3-graded quantum group and a ℤ3-graded quantum space are introduced. The scheme of the ℤ3-graded differential calculus developed on the algebra of functions on this quantum space is extended to the ℤ3-graded Cartan calculus and all the results obtained are formulated using the matrix R.
G-Topological Groupoids, Osman Mucuk
G-Topological Groupoids, Osman Mucuk
Turkish Journal of Mathematics
In the groupoid theory, it is unclear that a topological groupoid's quotient groupoid with the quotient topology is topological. In this paper, we approach this problem considering G-methods and G-convergence. We define G-topological groupoid, which agrees with the sequential version of a topological groupoid in the particular case G=lim, and give some counterexamples. Then, we extend the usual properties of topological groupoids to the G-topological groupoids. We also prove that a G-topological groupoid's quotient groupoid is G-topological groupoid when a normal subgroupoid is suitably chosen. This result enables us to obtain examples of topological quotient groupoids in a particular case.
The Derivative Of Spectral Function Of The Problem With The Boundary Condition Dependent On Spectral Parameter, Eli̇f Başkaya, Haskiz Coşkun
The Derivative Of Spectral Function Of The Problem With The Boundary Condition Dependent On Spectral Parameter, Eli̇f Başkaya, Haskiz Coşkun
Turkish Journal of Mathematics
In this study, the computation of the derivative of the spectral function for Sturm-Liouville problem with eigenvalue dependent boundary condition at the finite left end is considered.