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On A Question About Almost Prime Ideals, Esmaeil Rostami, Reza Nekooei
On A Question About Almost Prime Ideals, Esmaeil Rostami, Reza Nekooei
Turkish Journal of Mathematics
In this paper, by giving an example we answer positively the question ``Does there exist a $P$-primary ideal $I$ in a Noetherian domain $R$ such that $PI = I^2$, but $I$ is not almost prime?", asked by S. M. Bhatwadekar and P. K. Sharma. We also investigated conditions under which the answer to the above mentioned question is negative.
The Reversibility Problem For A Family Of Two-Dimensional Cellular Automata, Mehmet Emi̇n Köroğlu, İrfan Şi̇ap, Hasan Akin
The Reversibility Problem For A Family Of Two-Dimensional Cellular Automata, Mehmet Emi̇n Köroğlu, İrfan Şi̇ap, Hasan Akin
Turkish Journal of Mathematics
In this paper the reversibility problem of a family of two-dimensional cellular automata is completely resolved. It is well known that the reversibility problem is a very difficult one in general. In order to determine whether a cellular automaton is reversible or not the reversibility of its rule matrix is studied via linear algebraic tools. However, in this particular study the authors consider a novel approach. By observing the algebraic structures of rule matrices that represent these families and associating them with polynomials in two variables in a quotient ring, the solution to the reversibility problem is simplified greatly. Hence, …
Generalized Bertrand Curves With Spacelike $\Left(1,3\Right) $-Normal Plane In Minkowski Space-Time, Ali̇ Uçum, Osman Keçi̇li̇oğlu, Kazim İlarslan
Generalized Bertrand Curves With Spacelike $\Left(1,3\Right) $-Normal Plane In Minkowski Space-Time, Ali̇ Uçum, Osman Keçi̇li̇oğlu, Kazim İlarslan
Turkish Journal of Mathematics
In this paper, we reconsider the $(1,3)$-Bertrand curves with respect to the casual characters of a $\left( 1,3\right) $-normal plane that is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of $(1,3)$-Bertrand curves to the spacelike $\left( 1,3\right) $-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with spacelike $\left( 1,3\right) $-normal plane to be $(1,3)$-Bertrand curves and we give the related examples for these curves.
Anti-Invariant Riemannian Submersions From Kenmotsu Manifolds Onto Riemannian Manifolds, Ayşe Beri̇, İrem Küpeli̇ Erken, Cengi̇zhan Murathan
Anti-Invariant Riemannian Submersions From Kenmotsu Manifolds Onto Riemannian Manifolds, Ayşe Beri̇, İrem Küpeli̇ Erken, Cengi̇zhan Murathan
Turkish Journal of Mathematics
The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved the nonexistence of (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that the characteristic vector field $\xi $ is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic vector field $\xi $ …
Bounds For The Second Hankel Determinant Of Certain Bi-Univalent Functions, Hali̇t Orhan, Nanjundan Magesh, Jagadeesan Yamini
Bounds For The Second Hankel Determinant Of Certain Bi-Univalent Functions, Hali̇t Orhan, Nanjundan Magesh, Jagadeesan Yamini
Turkish Journal of Mathematics
We investigate the second Hankel determinant inequalities for a certain class of analytic and bi-univalent functions. Some interesting applications of the results presented here are also discussed.
New Inequalities For Fractional Integrals And Their Applications, Hsiow Ru Hwang, Kuei Lin Tseng, Kai Chen Hsu
New Inequalities For Fractional Integrals And Their Applications, Hsiow Ru Hwang, Kuei Lin Tseng, Kai Chen Hsu
Turkish Journal of Mathematics
In this paper, we establish some Hermite--Hadamard-type, Bullen-type, and Simpson-type inequalities for fractional integrals. Some applications for the beta function are also given.
The Inclusion Theorems For Variable Exponent Lorentz Spaces, Öznur Kulak
The Inclusion Theorems For Variable Exponent Lorentz Spaces, Öznur Kulak
Turkish Journal of Mathematics
Let $\left( \text{X,}\Sigma ,\mu \right) $ and $\left( \text{X,}\Sigma ,\nu \right) $ be measure spaces. Assume that $L^{p_{1}\left( .\right) ,q_{1}\left( .\right) }\left( X,\mu \right) $ and $L^{p_{2}\left( .\right) ,q_{2}\left( .\right) }\left( X,\nu \right) $ are two variable exponent Lorentz spaces where $p,q\in P_{0}\left( \left[ 0,l\right] \right) $. In this paper we investigated the existence of the inclusion $L^{p_{1}\left( .\right) ,q_{1}\left( .\right) }\left( X,\mu \right) $ $\subset L^{p_{2}\left( .\right) ,q_{2}\left( .\right) }\left( X,\nu \right) $ under what conditions for two measures $\mu $ and $\nu $ on $\left( X,\Sigma \right) .$
Point-Wise Slant Submanifolds In Almost Contact Geometry, Mohammad Bagher Kazemi Balgeshir
Point-Wise Slant Submanifolds In Almost Contact Geometry, Mohammad Bagher Kazemi Balgeshir
Turkish Journal of Mathematics
In this paper, we introduce point-wise slant submanifolds of almost contact and almost contact 3-structure manifolds. We characterize them, give some examples, and obtain necessary and sufficient conditions for a point-wise slant submanifold of a 3-Sasakian manifold to be a slant submanifold. Moreover, we show that there exist no proper Sasakian point-wise 3-slant submanifolds.
Projective Crossed Modules Of Algebras And Cyclic Homology, Eli̇f Ilgaz
Projective Crossed Modules Of Algebras And Cyclic Homology, Eli̇f Ilgaz
Turkish Journal of Mathematics
In this work, we give a characterization of free crossed modules and also get a relation between projective crossed modules and the cyclic homology of associative algebras by using Hopf-type formulas.
Harmonic Functions And Quadratic Harmonic Morphisms On Walker Spaces, Cornelia-Livia Bejan, Simona-Luiza Druta-Romaniuc
Harmonic Functions And Quadratic Harmonic Morphisms On Walker Spaces, Cornelia-Livia Bejan, Simona-Luiza Druta-Romaniuc
Turkish Journal of Mathematics
Let $(W,q, \mathcal{D})$ be a 4-dimensional Walker manifold. After providing a characterization and some examples for several special $(1,1)$-tensor fields on $(W,q, \mathcal{D})$, we prove that the proper almost complex structure $J$, introduced by Matsushita, is harmonic in the sense of Garcia-Rio et al. if and only if the almost Hermitian structure $(J,q)$ is almost Kahler. We classify all harmonic functions locally defined on $(W,q, \mathcal{D})$. We deal with the harmonicity of quadratic maps defined on $\mathbb{R}^4$ (endowed with a Walker metric $q$) to the $n$-dimensional semi-Euclidean space of index $r$, and then between local charts of two 4-dimensional Walker …
A Characterization Of Derivations On Uniformly Mean Value Banach Algebras, Amin Hosseini
A Characterization Of Derivations On Uniformly Mean Value Banach Algebras, Amin Hosseini
Turkish Journal of Mathematics
In this paper, a uniformly mean value Banach algebra (briefly UMV-Banach algebra) is defined as a new class of Banach algebras, and we characterize derivations on this class of Banach algebras. Indeed, it is proved that if $\mathcal{A}$ is a unital UMV-Banach algebra such that either $a = 0$ or $b = 0$ whenever $ab = 0$ in $\mathcal{A}$, and if $\delta:\mathcal{A} \rightarrow \mathcal{A}$ is a derivation such that $a \delta(a) = \delta(a)a$ for all $a \in \mathcal{A}$, then the following assertions are equivalent:\\ (i) $\delta$ is continuous; \\(ii) $\delta(e^a) = e^a\delta(a)$ for all $a \in \mathcal{A}$; \\(iii) $\delta$ is …
A New Approach To Soft Uniform Spaces, Taha Yasi̇n Öztürk
A New Approach To Soft Uniform Spaces, Taha Yasi̇n Öztürk
Turkish Journal of Mathematics
The purpose of this paper is to introduce the concept of soft uniform spaces and the relationships between soft uniform spaces and uniform spaces. The notions of soft uniform structure, soft uniform continious function, and operations on soft uniform space are introduced and their basic properties are investigated.
On The Solvability Of The Riemann Boundary Value Problem In Morrey--Hardy Classes, Bilal Bilalov, Telman Gasymov, Aida Guliyeva
On The Solvability Of The Riemann Boundary Value Problem In Morrey--Hardy Classes, Bilal Bilalov, Telman Gasymov, Aida Guliyeva
Turkish Journal of Mathematics
This work considers the Riemann boundary value problem with the piecewise continuous coefficient in Morrey-Hardy classes. Under some conditions on the coefficient, the Fredholmness of this problem is studied and the general solution of homogeneous and nonhomogeneous problems in Morrey-Hardy classes is constructed.
Some Results Concerning The Summability Of Spliced Sequences, Tuğba Yurdakadi̇m, Mehmet Ünver
Some Results Concerning The Summability Of Spliced Sequences, Tuğba Yurdakadi̇m, Mehmet Ünver
Turkish Journal of Mathematics
A spliced sequence is formed by combining all of the terms of two or more convergent sequences, in their original order, into a new spliced sequence. In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transformation of these sequences by a summability matrix. We also present some further results via the Lebesgue integral.
Numerical Approach For Solving Space Fractional Orderdiffusion Equations Using Shifted Chebyshev Polynomials Of The Fourth Kind, Nasser Hassan Swielam, Abd Elhameed Mohamed Nagy, Adel Abd Elaziz El Sayed
Numerical Approach For Solving Space Fractional Orderdiffusion Equations Using Shifted Chebyshev Polynomials Of The Fourth Kind, Nasser Hassan Swielam, Abd Elhameed Mohamed Nagy, Adel Abd Elaziz El Sayed
Turkish Journal of Mathematics
In this paper, a new approach for solving space fractional order diffusion equations is proposed. The fractional derivative in this problem is in the Caputo sense. This approach is based on shifted Chebyshev polynomials of the fourth kind with the collocation method. The finite difference method is used to reduce the equations obtained by our approach for a system of algebraic equations that can be efficiently solved. Numerical results obtained with our approach are presented and compared with the results obtained by other numerical methods. The numerical results show the efficiency of the proposed approach.
Derivation-Homomorphisms, Lingyue Li, Xiaowei Xu
Derivation-Homomorphisms, Lingyue Li, Xiaowei Xu
Turkish Journal of Mathematics
In this paper, we introduce notions of $(n,m)$-derivation-homomorphisms and Boolean $n$-derivations. Using Boolean $n$-derivations and $m$-homomorphisms, we describe structures of $(n, m)$-derivation-homomorphisms.
Conformal Anti-Invariant Submersions From Almost Hermitian Manifolds, Mehmet Aki̇f Akyol, Bayram Şahi̇n
Conformal Anti-Invariant Submersions From Almost Hermitian Manifolds, Mehmet Aki̇f Akyol, Bayram Şahi̇n
Turkish Journal of Mathematics
We introduce conformal anti-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arose from the definition of a conformal submersion, and find necessary and sufficient conditions for a conformal anti-invariant submersion to be totally geodesic. We also check the harmonicity of such submersions and show that the total space has certain product structures. Moreover, we obtain curvature relations between the base space and the total space, and find geometric implications of these relations.
Homothetic Motions With Dual Octonions In Dual $8-$Space, Hesna Kabadayi
Homothetic Motions With Dual Octonions In Dual $8-$Space, Hesna Kabadayi
Turkish Journal of Mathematics
In this study, for dual octonions in dual $8-$space $D^{8}$ over the domain of coefficients $D,$ we give a matrix that is similar to a Hamilton operator. By means of this matrix a new motion is defined and this motion is proven to be homothetic. For this one parameter dual homothetic motion, we prove some theorems about dual velocities, dual pole points, and dual pole curves. Furthermore, after defining dual accelerations, we show that the motion defined by the regular order $m$ dual curve, at every $t$-instant, has only one acceleration center of order $\left( m-1\right) .$
Gorenstein Homological Dimensions Of Modules Over Triangular Matrix Rings, Rongmin Zhu, Zhongkui Liu, Zhanping Wang
Gorenstein Homological Dimensions Of Modules Over Triangular Matrix Rings, Rongmin Zhu, Zhongkui Liu, Zhanping Wang
Turkish Journal of Mathematics
Let $A$ and $B$ be rings, $U$ a $(B, A)$-bimodule, and $T=\left(\begin{smallmatrix} A & 0 \\ U & B \\\end{smallmatrix}\right)$ the triangular matrix ring. In this paper, we characterize the Gorenstein homological dimensions of modules over $T$, and discuss when a left $T$-module is a strongly Gorenstein projective or strongly Gorenstein injective module.
A Presentation And Some Finiteness Conditions For A New Version Of The Schützenberger Product Of Monoids, Eylem Güzel Karpuz, Firat Ateş, Ahmet Si̇nan Çevi̇k, İsmai̇l Naci̇ Cangül
A Presentation And Some Finiteness Conditions For A New Version Of The Schützenberger Product Of Monoids, Eylem Güzel Karpuz, Firat Ateş, Ahmet Si̇nan Çevi̇k, İsmai̇l Naci̇ Cangül
Turkish Journal of Mathematics
In this paper we first define a \textit{new version} of the Sch\"{u}tzenberger product for any two monoids $A$ and $B$, and then, by defining a generating and relator set, we present some finite and infinite consequences of the main result. In the final part of this paper, we give necessary and sufficient conditions for this new version to be periodic and locally finite.
On The Finite $P$-Groups With Unique Cyclic Subgroup Of Given Order, Libo Zhao, Yangming Li, Lu Gong
On The Finite $P$-Groups With Unique Cyclic Subgroup Of Given Order, Libo Zhao, Yangming Li, Lu Gong
Turkish Journal of Mathematics
In this paper, we prove that if $G$ is nonabelian and $ G >p^4$, then $G$ has a unique cyclic subgroup of order $p^m$ with $m\geq 3$ if and only if $G$ has a unique abelian subgroup of order $p^3$ if and only if $G$ is a $2$-group of maximal class.
Sparse Sums With Bases Of Chebyshev Polynomials Of The Third And Fourth Kind, Maryam Shams Solary
Sparse Sums With Bases Of Chebyshev Polynomials Of The Third And Fourth Kind, Maryam Shams Solary
Turkish Journal of Mathematics
We derive a generalization for the reconstruction of $M$-sparse sums in Chebyshev bases of the third and fourth kind. This work is used for a polynomial with Chebyshev sparsity and samples on a Chebyshev grid of $[-1,1]$. Further, fundamental reconstruction algorithms can be a way for getting M-sparse expansions of Chebyshev polynomials of the third and fourth kind. The numerical results for these algorithms are designed to compare the time effects of doing them.
The Dual Generalized Chernoff Inequality For Star-Shaped Curves, Deyan Zhang, Yunlong Yang
The Dual Generalized Chernoff Inequality For Star-Shaped Curves, Deyan Zhang, Yunlong Yang
Turkish Journal of Mathematics
In this paper, we first introduce the $k$-order radial function $\rho_k(\theta)$ for star-shaped curves in $\mathbb{R}^2$ and then prove a geometric inequality involving $\rho_k(\theta)$ and the area $A$ enclosed by a star-shaped curve, which can be looked upon as the dual Chernoff--Ou--Pan inequality. As a by-product, we get a new proof of the classical dual isoperimetric inequality. We also prove that $\frac{C^2}{k^2}\leq A
Weakly $2$-Absorbing Submodules Of Modules, Sedigheh Moradi, Abdulrasool Azizi
Weakly $2$-Absorbing Submodules Of Modules, Sedigheh Moradi, Abdulrasool Azizi
Turkish Journal of Mathematics
Let $M$ be a module over a commutative ring $R.$ A proper submodule $N$ of $M$ is called weakly $2$-absorbing, if for $r,s\in R$ and $x\in M$ with $0\neq rsx\in N,$ either $rs\in (N:M)$ or $rx\in N$ or $sx\in N.$ We study the behavior of $(N:M)$ and $\sqrt{(N:M)},$ when $N$ is weakly $2$-absorbing. The weakly $2$-absorbing submodules when $R=R_1\oplus R_2$ are characterized. Moreover we characterize the faithful modules whose proper submodules are all weakly $2$-absorbing.
Zero Triple Product Determined Generalized Matrix Algebras, Dong Han
Zero Triple Product Determined Generalized Matrix Algebras, Dong Han
Turkish Journal of Mathematics
In this paper, we prove that the generalized matrix algebra G = \left[ A M N B \right] is a zero triple product (resp. zero Jordan triple product) determined if and only if A and B are zero triple products (resp. zero Jordan triple products) determined under certain conditions. Then the main results are applied to triangular algebras and full matrix algebras.
Stability Of Perturbed Dynamic System On Time Scales With Initial Time Difference, Coşkun Yakar, Bülent Oğur
Stability Of Perturbed Dynamic System On Time Scales With Initial Time Difference, Coşkun Yakar, Bülent Oğur
Turkish Journal of Mathematics
The behavior of solutions of a perturbed dynamic system with respect to an original unperturbed dynamic system, which have initial time difference, are investigated on arbitrary time scales. Notions of stability, asymptotic stability, and instability with initial time difference are introduced. Sufficient conditions of stability properties are given with the help of Lyapunov-like functions.
Spherically Symmetric Finsler Metrics With Scalar Flag Curvature, Weidong Song, Fen Zhou
Spherically Symmetric Finsler Metrics With Scalar Flag Curvature, Weidong Song, Fen Zhou
Turkish Journal of Mathematics
In this paper, we study spherically symmetric Finsler metrics F= y \phi( x ,\frac{}{ y }), where x \in B^n(r) \subset R^n, y \in T_xB^n(r)\{0} and \phi:[0,r)\times R \rightarrow R. By investigating a PDE equivalent to these metrics being locally projectively flat, we manufacture projectively flat spherically symmetric Finsler metrics in terms of error functions and, using Shen's result, we give its flag curvature.
Rings With Finite Ding Homological Dimensions, Chunxia Zhang, Zhongkui Liu
Rings With Finite Ding Homological Dimensions, Chunxia Zhang, Zhongkui Liu
Turkish Journal of Mathematics
In this paper, we study Ding homological dimensions of complexes. Special attention is paid to the dimensions of homologically bounded complexes that have nice functorial descriptions. These results are applied to give new characterizations of rings R such that l.Ggldim(R) < \infty and quasi-Frobenius rings.
A Note On Infinite Groups Whose Subgroups Are Close To Be Normal-By-Finite, Francesco De Giovanni, Federica Saccomanno
A Note On Infinite Groups Whose Subgroups Are Close To Be Normal-By-Finite, Francesco De Giovanni, Federica Saccomanno
Turkish Journal of Mathematics
A group G is said to have the CF-property if the index X:X_G is finite for every subgroup X of G. Extending previous results by Buckley, Lennox, Neumann, Smith, and Wiegold, it is proven here that if G is a locally graded group whose proper subgroups have the CF-property, then G is abelian-by-finite, provided that all its periodic sections are locally finite. Groups in which all proper subgroups of infinite rank have the CF-property are also studied.
Bifurcation And Dynamics Of A Normal Form Map, Reza Khoshsiar Ghaziani
Bifurcation And Dynamics Of A Normal Form Map, Reza Khoshsiar Ghaziani
Turkish Journal of Mathematics
This paper investigates the dynamics and stability properties of a so-called planar truncated normal form map. This kind of map is widely used in the applied context, especially in normal form coefficients of n-dimensional maps. We determine analytically the border collision bifurcation curves that characterize the dynamic behaviors of the system. We first analyze stability of the fixed points and the existence of local bifurcations. Our analysis shows the presence of a rich variety of local bifurcations, namely stable fixed points, periodic cycles, quasiperiodic cycles that are constraints to stable attractors called invariant closed curves, and chaos, where dynamics of …