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Articles 1 - 30 of 169
Full-Text Articles in Physical Sciences and Mathematics
Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç
Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç
Turkish Journal of Mathematics
The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric. We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.
Solvability And Maximal Regularity Results For A Differential Equation With Diffusion Coefficient, Kordan Ospanov, Adilet Yesbayev
Solvability And Maximal Regularity Results For A Differential Equation With Diffusion Coefficient, Kordan Ospanov, Adilet Yesbayev
Turkish Journal of Mathematics
We consider a second-order differential equation with rapidly growing intermediate coefficients. We obtain a solvability result in the cases that the diffusion coefficient of equation is unbounded or it tends to zero at the infinity. Under additional conditions, we prove the $L_p - $ maximal regularity estimate for the solution of this equation.
Bilateral-Type Solutions To The Fixed-Circle Problem With Rectified Linear Units Application, Ni̇hal Taş
Bilateral-Type Solutions To The Fixed-Circle Problem With Rectified Linear Units Application, Ni̇hal Taş
Turkish Journal of Mathematics
In this paper, we prove new fixed-circle (resp. fixed-disc) results using the bilateral type contractions on a metric space. To do this, we modify some known contractive conditions called the Jaggi-type bilateral contraction and the Dass-Gupta type bilateral contraction. We give some examples to show the validity of our obtained results. Also, we construct an application to rectified linear units activation functions used in the neural networks. This application shows the importance of studying "fixed-circle problem".
Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam
Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the $n$th$~(n\geq 3)$ Taylor-Maclaurin coefficients $\left\vert a_{n}\right\vert $ of functions belong to these new subclasses with $a_{k}=0$ for $2\leq k\leq n-1$, also we find non-sharp estimates on the first two coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $. The results, which are presented in this paper, would generalize those in related earlier works of several authors.
Some Results On Top Generalized Local Cohomology Modules With Respect To A System Of Ideals, Nguyen Minh Tri
Some Results On Top Generalized Local Cohomology Modules With Respect To A System Of Ideals, Nguyen Minh Tri
Turkish Journal of Mathematics
Let $R$ be a commutative Noetherian ring and $\Phi$ be a system of ideals of $R.$ In this paper, we study the annihilators and the set of attached prime ideals of top generalized local cohomology modules with respect to a system of ideals.
Some Characterizations Of Kb-Operators On Banach Lattices And Ordered Banach Spaces, Bi̇rol Altin, Nabil Machrafi
Some Characterizations Of Kb-Operators On Banach Lattices And Ordered Banach Spaces, Bi̇rol Altin, Nabil Machrafi
Turkish Journal of Mathematics
We determine that two recent classes of KB-operators and weak KB-operators and the well-known class of b-weakly compact operators, from a Banach lattice into a Banach space, are the same. We extend our study to the ordered Banach space setting by showing that a weak chain-preserving operator between two ordered Banach spaces is a KB-operator if and only if it is a weak KB-operator.
On Hausdorff-Young Inequalities In Generalized Lebesgue Spaces, Miqdad Ismailov
On Hausdorff-Young Inequalities In Generalized Lebesgue Spaces, Miqdad Ismailov
Turkish Journal of Mathematics
Lebesgue spaces with the variable rate of summability are considered in this work. Generalizations of Riesz and Paley theorems are proved in these spaces. The obtained results are applied, in particular, to a classical exponential system.
On $\Mathcal{X}$-Gorenstein Projective Dimensions And Precovers, Bin Yu
On $\Mathcal{X}$-Gorenstein Projective Dimensions And Precovers, Bin Yu
Turkish Journal of Mathematics
For a class of $R$-modules $\mathcal{X}$ containing all projective $R$-modules, the $\mathcal{X}$-Gorenstein projective $R$-modules vary from projective to Gorenstein projective $R$-modules. We characterize the rings over which the left global $\mathcal{X}$-Gorenstein projective dimensions are finite. If further $\mathcal{Y}$ contains all injective $R$-modules, we show the existence of a new left global Gorenstein dimension of $R$ with respect to $\mathcal{X}$ and $\mathcal{Y}$ satisfying proper conditions. As an application we characterize Ding-Chen rings by this new global Gorenstein dimension and show the existence of Ding-Chen rings with infinite global Gorenstein dimension. We also show the existence of $\mathcal{X}$-Gorenstein projective precovers for a …
Asymptotic Theory For A Critical Class Of Third-Order Differential Equations, Aziz S. A. Alhammadi
Asymptotic Theory For A Critical Class Of Third-Order Differential Equations, Aziz S. A. Alhammadi
Turkish Journal of Mathematics
An asymptotic theory is developed for a class of third-order differential equations. We identify a critical case to obtain the asymptotic form of three linearly independent solutions for large $x$.
Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er
Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er
Turkish Journal of Mathematics
In this paper, we introduce almost symmetric Arf partitions (for short, ASA-partitions) and using properties of partitions of positive integers, we give the number of almost symmetric Arf semigroups of genus $g$.
$Q-$Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
$Q-$Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this paper, we develop the basic theory of linear $q-$ Hamiltonian systems. In this context, we establish an existence and uniqueness result. Regular spectral problems are studied. Later, we introduce the corresponding maximal and minimal operators for this system. Finally, we give a spectral resolution.
Polarization Of Neural Codes, Katie Christensen, Hamid Kulosman
Polarization Of Neural Codes, Katie Christensen, Hamid Kulosman
Turkish Journal of Mathematics
The neural rings and ideals as an algebraic tool for analyzing the intrinsic structure of neural codes were introduced by C. Curto, V. Itskov, A. Veliz-Cuba, and N. Youngs in 2013. Since then they were investigated in several papers, including the 2017 paper by S. Güntürkün, J. Jeffries, and J. Sun, in which the notion of polarization of neural ideals was introduced. In our paper we extend their ideas by introducing the notions of polarization of motifs and neural codes. We show that the notions that we introduce have very nice properties which allow the studying of the intrinsic structure …
The Existence And Compactness Of The Set Of Solutions For A Nonlinear Integrodifferential Equation In N Variables In A Banach Space, Huynh Thi Hoang Dung, Le Thi Phuong Ngoc, Nguyen Thanh Long
The Existence And Compactness Of The Set Of Solutions For A Nonlinear Integrodifferential Equation In N Variables In A Banach Space, Huynh Thi Hoang Dung, Le Thi Phuong Ngoc, Nguyen Thanh Long
Turkish Journal of Mathematics
The paper is devoted to the study of a nonlinear integrodifferential equation in N variables with values in a general Banach space. By applying fixed point theorems in a suitable Banach space under appropriate conditions for subsets to be relatively compact, we prove the existence and the compactness of theset of solutions.Inorder to illustrate the results,we give two examples.
Higher-Order Sturm-Liouville Problems With The Same Eigenvalues, Hanif Mirzaei
Higher-Order Sturm-Liouville Problems With The Same Eigenvalues, Hanif Mirzaei
Turkish Journal of Mathematics
In this paper, we consider self-adjoint Sturm?Liouville problem (SLP) of higher-order. We define an equivalence relation between second- and higher-order SLP. Using the Darboux lemma and equivalence relation we obtain the closed form of a family of SLP which have the same eigenvalues. Also, some spectral properties of this family of Sturm?Liouville problems are investigated.
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.
Inverse Problem For Sturm-Liouville Differential Operators With Finite Number Of Constant Delays, Mohammad Shahriari
Inverse Problem For Sturm-Liouville Differential Operators With Finite Number Of Constant Delays, Mohammad Shahriari
Turkish Journal of Mathematics
In this manuscript,we study nonself-adjoint second-order differential operators with finite number of constant delays. We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from their spectra. An inverse spectral problem is studied for recovering differential operator from the potential from spectra of two boundary value problems with one common boundary condition.The uniqueness theorem is proved for this inverse problem.
Inverse Problems For Differential Operators With Two Delays Larger Than Half The Length Of The Interval And Dirichlet Conditions, Biljana Vojvodic, Milenko Pikula, Vladimir Vladicic, Fatma Ayça Çeti̇nkaya
Inverse Problems For Differential Operators With Two Delays Larger Than Half The Length Of The Interval And Dirichlet Conditions, Biljana Vojvodic, Milenko Pikula, Vladimir Vladicic, Fatma Ayça Çeti̇nkaya
Turkish Journal of Mathematics
This paper deals with nonself-adjoint second-order differential operators with two constant delays from $\left[\frac{\pi}{2}, \pi\right)$ and two real-valued potentials from $L_{2} [0,\pi]$. An inverse spectral problem of recovering operators from the spectra of four boundary value problems is studied.
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Turkish Journal of Mathematics
In this paper the second-order difference equations of the form \[ \Delta^2 x_n=a_nf(n,x_{\sigma(n)})+b_n \] are considered. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. In particular, we present conditions under which there exists an asymptotically linear solution. Moreover, we study the asymptotic behavior of solutions.
On ${\Bf H}$-Curvature Of $(\Alpha,\Beta)$-Metrics, Akbar Tayebi, Masoome Razgordani
On ${\Bf H}$-Curvature Of $(\Alpha,\Beta)$-Metrics, Akbar Tayebi, Masoome Razgordani
Turkish Journal of Mathematics
The non-Riemannian quantity ${\bf H}$ was introduced by Akbar-Zadeh to characterization of Finsler metrics of constant flag curvature. In this paper, we study two important subclasses of Finsler metrics in the class of so-called $(\alpha,\beta)$-metrics, which are defined by $F=\alpha\phi(s)$, $s=\beta/\alpha$, where $\alpha$ is a Riemannian metric and $\beta$ is a closed 1-form on a manifold. We prove that every polynomial metric of degree $k\geq 3$ and exponential metric has almost vanishing ${\bf H}$-curvature if and only if ${\bf H}=0$. In this case, $F$ reduces to a Berwald metric. Then we prove that every Einstein polynomial metric of degree $k\geq …
Direct And Inverse Approximation Theorems In The Weighted Orlicz-Type Spaces With A Variable Exponent, Fahreddi̇n Abdullayev, Stanislav Chaichenko, Meerim Imash Kyzy, Andrii Shidlich
Direct And Inverse Approximation Theorems In The Weighted Orlicz-Type Spaces With A Variable Exponent, Fahreddi̇n Abdullayev, Stanislav Chaichenko, Meerim Imash Kyzy, Andrii Shidlich
Turkish Journal of Mathematics
In weighted Orlicz-type spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre $K$-functionals is shown in the spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$.
Faber-Laurent Series In Variable Smirnov Classes, Dani̇yal İsrafi̇lzade, Eli̇fe Gürsel
Faber-Laurent Series In Variable Smirnov Classes, Dani̇yal İsrafi̇lzade, Eli̇fe Gürsel
Turkish Journal of Mathematics
In this work, the maximal convergence properties of partial sums of Faber-Laurent series in the variable exponent Smirnov classes of analytic functions defined on a doubly connected domain of the complex plane are investigated.
Existence And Uniqueness Of Solutions For Nonlinear Caputo Fractional Difference Equations, Churong Chen, Martin Bohner, Baoguo Jia
Existence And Uniqueness Of Solutions For Nonlinear Caputo Fractional Difference Equations, Churong Chen, Martin Bohner, Baoguo Jia
Turkish Journal of Mathematics
We study two cases of nabla fractional Caputo difference equations. Our main tool used is a Banach fixed pointtheorem, which allows us to give some existence and uniqueness theorems of solutions for discrete fractional Caputo equations. In addition, we develop the existence results for delta fractional Caputo difference equations, which correct ones obtained in Chen and Zhou. We present two examples to illustrate our main results.
Bertrand And Mannheim Curves Of Framed Curves In The 3-Dimensional Euclidean Space, Shun'ichi Honda, Masatomo Takahashi
Bertrand And Mannheim Curves Of Framed Curves In The 3-Dimensional Euclidean Space, Shun'ichi Honda, Masatomo Takahashi
Turkish Journal of Mathematics
A Bertrand curve is a space curve whose principal normal line is the same as the principal normal line of another curve. On the other hand, a Mannheim curve is a space curve whose principal normal line is the same as the binormal line of another curve. By definitions, another curve is a parallel curve with respect to the direction of the principal normal vector. Even if that is the regular case, the existence conditions of the Bertrand and Mannheim curves seem to be wrong in some previous research. Moreover, parallel curves may have singular points. As smooth curves with …
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy
Turkish Journal of Mathematics
In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its applications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when the order m is odd.
Linear Mappings Satisfying Some Recursive Sequences, Amin Hosseini, Mehdi Mohammadzadeh Karizaki
Linear Mappings Satisfying Some Recursive Sequences, Amin Hosseini, Mehdi Mohammadzadeh Karizaki
Turkish Journal of Mathematics
Let $\mathcal{A}$ be a unital, complex normed $\ast$-algebra with the identity element $\textbf{e}$ such that the set of all algebraic elements of $\mathcal{A}$ is norm dense in the set of all self-adjoint elements of $\mathcal{A}$ and let $\{D_n\}_{n = 0}^{\infty}$ and $\{\Delta_n\}_{n = 0}^{\infty}$ be sequences of continuous linear mappings on $\mathcal{A}$ satisfying \[ \left\lbrace \begin{array}{c l} D_{n + 1}(p) = \sum_{k = 0}^{n}D_{n - k}(p)D_k(p),\\ \\ \Delta_{n + 1}(p) = \sum_{k = 0}^{n}\Delta_{n - k}(p)D_k(p), \end{array} \right. \] for all projections $p$ of $\mathcal{A}$ and all nonnegative integers $n$. Moreover, suppose that $D_0(p) = D_0(p)^2$ holds for all projections …
4-Generated Pseudo Symmetric Monomial Curves With Not Cohen-Macaulay Tangent Cones, Ni̇l Şahi̇n
4-Generated Pseudo Symmetric Monomial Curves With Not Cohen-Macaulay Tangent Cones, Ni̇l Şahi̇n
Turkish Journal of Mathematics
In this article, standard bases of some toric ideals associated to 4-generated pseudo symmetric semigroups with not Cohen-Macaulay tangent cones at the origin are computed. As the tangent cones are not Cohen-Macaulay, nondecreasingness of the Hilbert function of the local ring was not guaranteed. Therefore, using these standard bases, Hilbert functions are explicitly computed as a step towards the characterization of Hilbert function. In addition, when the smallest integer satisfying $k(\alpha_2+1)
Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü
Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü
Turkish Journal of Mathematics
In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additionally, we prove some fixed point …
A Reduced Computational Matrix Approach With Convergence Estimation For Solving Model Differential Equations Involving Specific Nonlinearities Of Quartic Type, Ömür Kivanç Kürkçü
A Reduced Computational Matrix Approach With Convergence Estimation For Solving Model Differential Equations Involving Specific Nonlinearities Of Quartic Type, Ömür Kivanç Kürkçü
Turkish Journal of Mathematics
This study aims to efficiently solve model differential equations involving specific nonlinearities of quartic type by proposing a reduced computational matrix approach based on the generalized Mott polynomial. This method presents a reduced matrix expansion of the generalized Mott polynomial with the parameter-$\alpha$, matrix equations, and Chebyshev--Lobatto collocation points. The simplicity of the method provides fast computation while eliminating an algebraic system of nonlinear equations, which arises from the matrix equation. The method also scrutinizes the consistency of the solutions due to the parameter-$\alpha$. The oscillatory behavior of the obtained solutions on long time intervals is simulated via a coupled …
Continuous Dependence Of Solutions For Damped Improved Boussinesq Equation, Sema Bayraktar, Şevket Gür
Continuous Dependence Of Solutions For Damped Improved Boussinesq Equation, Sema Bayraktar, Şevket Gür
Turkish Journal of Mathematics
In this paper, the initial-boundary value problem for a damped nonlinear improved Boussinesq equation is studied. A priori estimates for the solution of the equation are obtained in terms of initial data and coefficients of the problem. The continuous dependence of solutions on dispersive $(\delta)$ and $(r)$ and dissipative $(b)$ coefficients are established by multiplier method.
Prolongations Of Isometric Actions To Vector Bundles, Hülya Kadioğlu
Prolongations Of Isometric Actions To Vector Bundles, Hülya Kadioğlu
Turkish Journal of Mathematics
In this paper, we define an isometry on a total space of a vector bundle $\mathbb{E}$ by using a given isometry on the base manifold $\mathbb{M}$. For this definition, we assume that the total space of the bundle is equipped with a special metric which has been introduced in one of our previous papers. We prove that the set of these derived isometries on $\mathbb{E}$ form an imbedded Lie subgroup $\tilde{G}$ of the isometry group $I(E)$. Using this new subgroup, we construct two different principal bundle structures based one on $\mathbb{E}$ and the other on the orbit space $\mathbb{E}/\tilde{G}$.