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Articles 391 - 420 of 2595
Full-Text Articles in Mathematics
Structure Of Annihilators Of Powers, Jongwook Baeck, Nam Kyun Kim, Tai Keun Kwak, Yang Lee
Structure Of Annihilators Of Powers, Jongwook Baeck, Nam Kyun Kim, Tai Keun Kwak, Yang Lee
Turkish Journal of Mathematics
We study the following two conditions in rings: (i) the right annihilator of some power of any element is an ideal, and (ii) the right annihilator of any nonzero element $a$ contains an ideal generated by some power of any right zero-divisor of the element $a$. We investigate the structure of rings in relation to these conditions; especially, a ring with the condition (ii) is called right APIP. These conditions are shown to be not right-left symmetric. For a prime two-sided APIP ring $R$ we prove that every element of $R$ is either nilpotent or regular, and that if $R$ …
On Central Polynomials And Codimension Growth, Fabrizio Martino
On Central Polynomials And Codimension Growth, Fabrizio Martino
Turkish Journal of Mathematics
Let $A$ be an associative algebra over a field of characteristic zero. A central polynomial is a polynomial of the free associative algebra that takes central values of $A.$ In this survey, we present some recent results about the exponential growth of the central codimension sequence and the proper central codimension sequence in the setting of algebras with involution and algebras graded by a finite group.
Codimensions Of Algebras With Additional Structures, Daniela La Mattina
Codimensions Of Algebras With Additional Structures, Daniela La Mattina
Turkish Journal of Mathematics
Let $A$ be an associative algebra endowed with an automorphism or an antiautomorphism $\varphi$ of order $\leq 2.$ One associates to $A,$ in a natural way, a numerical sequence $c^\varphi_n(A),$ $n=1, 2, \ldots$, called the sequence of $\varphi$-codimensions of $A$ which is the main tool for the quantitative investigation of the polynomial identities satisfied by $A$. In \cite{GLM} it was proved that such a sequence is eventually nondecreasing in case $\varphi$ is an antiautomorphism. Here we prove that it still holds in case $\varphi$ is an automorphism and present some recent results about the asymptotics of $c^\varphi_n(A)$.
On $(A,D)$-Edge Local Antimagic Coloring Number Of Graphs, Rajkumar Sundaramoorthy, Nalliah Moviri Chettiar
On $(A,D)$-Edge Local Antimagic Coloring Number Of Graphs, Rajkumar Sundaramoorthy, Nalliah Moviri Chettiar
Turkish Journal of Mathematics
For any graph $G=(V,E),$ the order and size of G are $p$ and $q$. A bijection $l$ from $V(G)$ to $\{1,2,..,p\}$ is called $(a,d)$-edge local antimagic labeling if for any two adjacent edges are not received the same edge-weight (color) and the set of all edge-weights are formed an arithmetic progression $\{a,a+d,a+2d,\dots,a+(c-1)d\}$, for some integers $a,d>0$ and $c$ is the number of distinct colors used in the proper coloring.} An edge-weight (color) $w(uv)$ is the sum of two end vertices labels, $w(uv)=f(u)+f(v),uv\in E(G).$ The $(a,d)$-edge local antimagic coloring number is the least color (edge-weight) used in any $(a,d)$-edge local …
A New Approach To Word Standardization And Some Of Its Applications, Wesam Talab
A New Approach To Word Standardization And Some Of Its Applications, Wesam Talab
Turkish Journal of Mathematics
In this article, we study word standardization in comparison to Young tableau standardization. We count the number of words (respectively Young tableau) standardized to a given permutation (respectively to a given standard Young tableau). We prove that both rectification and standardization applications commute and show that the standardization commutes with the insertion of Robinson--Schensted. We show that the standardizations of Knuth-equivalent two words are also Knuth equivalent. Finally, using word standardization we establish a proof for the following well-known equality: $$ \forall l \in \left\lbrace 0,1,\ldots,n-1\right\rbrace ,~~\left \langle {n\atop l} \right \rangle=d_{n,l}=a_{n,l}= \sum_{0\leq k \leq l}(-1)^k { n+1 \choose k …
On $ Mj $-Clean Ring And Strongly $ Mj $-Clean Ring, Gülşen Ulucak, Arda Kör
On $ Mj $-Clean Ring And Strongly $ Mj $-Clean Ring, Gülşen Ulucak, Arda Kör
Turkish Journal of Mathematics
In this paper, we introduce the concepts of $ mj $-clean and strongly $ mj $-clean rings which are generalizations of $ j $-clean ring and strongly $ j $-clean ring, respectively. Let $ R $ be a ring with a nonzero identity and $ m\geq 2 $ a positive integer. We call the ring $ R $ as $ mj $-clean if each element of $ R$ can be written as a sum of an $ m $-potent and an element of $J(R)$ and also if these elements are commute, then we call $R$ as strongly $ mj $-clean …
Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko
Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko
Turkish Journal of Mathematics
We deal with varieties of nonassociative algebras having polynomial growth of codimensions. We describe some results obtained in recent years in the class of left nilpotent algebras of index two. Recently the authors established a correspondence between the growth rates for left nilpotent algebras of index two and the growth rates for commutative or anticommutative metabelian algebras that allows to transfer the results concerning varieties of left nilpotent algebras of index two to varieties of commutative or anticommutative metabelian algebras.
On $S$-Comultiplication Modules, Eda Yildiz, Ünsal Teki̇r, Suat Koç
On $S$-Comultiplication Modules, Eda Yildiz, Ünsal Teki̇r, Suat Koç
Turkish Journal of Mathematics
Let $R\ $be a commutative ring with $1\neq0$ and $M$ be an $R$-module. Suppose that $S\subseteq R\ $is a multiplicatively closed set of $R.\ $Recently Sevim et al. in \cite{SenArTeKo} introduced the notion of an $S$-prime submodule which is a generalization of a prime submodule and used them to characterize certain classes of rings/modules such as prime submodules, simple modules, torsion free modules,\ $S$-Noetherian modules and etc. Afterwards, in \cite{AnArTeKo}, Anderson et al. defined the concepts of $S$-multiplication modules and $S$-cyclic modules which are $S$-versions of multiplication and cyclic modules and extended many results on multiplication and cyclic modules to …
Analyzing Bifurcation, Stability, And Chaos Control For A Discrete-Time Prey-Predator Model With Allee Effect, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Ni̇hal Öztürk
Analyzing Bifurcation, Stability, And Chaos Control For A Discrete-Time Prey-Predator Model With Allee Effect, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Ni̇hal Öztürk
Turkish Journal of Mathematics
In this paper, the qualitative behavior of a discrete-time prey-predator model with Allee effect in prey population is discussed. Firstly, the existence of the fixed points and their topological classification are analyzed algebraically. Then, the conditions of existence for both period-doubling and Neimark--Sacker bifurcations arising from coexistence fixed point with the help of the center manifold theorem and bifurcation theory are investigated. OGY feedback control method is implemented to control chaos in the proposed model due to the emergence of bifurcations. Finally, numerical simulations are performed to support the theoretical findings.
Solvability In The Small Of $M$-Th Order Elliptic Equations In Weighted Grand Sobolev Spaces, Bilal Bilalov, Yusuf Zeren, Sabina Sadigova, Şeyma Çeti̇n
Solvability In The Small Of $M$-Th Order Elliptic Equations In Weighted Grand Sobolev Spaces, Bilal Bilalov, Yusuf Zeren, Sabina Sadigova, Şeyma Çeti̇n
Turkish Journal of Mathematics
In this work we consider the Sobolev spaces generated by the norm of the power weighted grand Lebesgue spaces. It is considered $m$-th order elliptic equation with nonsmooth coefficients on bounded domain in $R^{n} $. This space is nonseparable and by using shift operator we define the separable subspace of it, in which infinitely differentiable functions are dense. The investigation needs to establish boundedness property of convolution regarding weighted grand Lebesgue spaces. Then on scheme of nonweighted case we establish solvability (strong sense) in the small of $m$-th order elliptic equations in power weighted grand Sobolev spaces. Note that in …
Distortion Bound And Growth Theorems For A Subclass Of Analytic Functions Defined By $Q$-Derivative, Osman Altintaş, Ni̇zami̇ Mustafa
Distortion Bound And Growth Theorems For A Subclass Of Analytic Functions Defined By $Q$-Derivative, Osman Altintaş, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this study, we introduce and examine a subclasses of analytic and univalent functions defined by $q$-derivative. Here, we give necessary conditions for the functions to belong to these subclasses, and distortion bound and growth theorems for the functions belonging to these classes.
On The Geodesics Of Deformed Sasaki Metric, Nour Elhouda Djaa, Abderrahim Zagane
On The Geodesics Of Deformed Sasaki Metric, Nour Elhouda Djaa, Abderrahim Zagane
Turkish Journal of Mathematics
We define in this note a natural metric over the tangent bundle $TM$ by using a vertical deformation of Sasaki metric. First we present the geometric result concerning the Levi-Civita connection and all forms of Riemannian curvature tensors of this metric. Secondly, we study the geodesics on the tangent bundle $TM$ and unit tangent bundle $T_{1}M$. Finally, we characterize the geodesic curvatures on $T_{1}M$.
Vanishing Ideals Of Parameterized Subgroups In A Toric Variety, Esma Baran Özkan
Vanishing Ideals Of Parameterized Subgroups In A Toric Variety, Esma Baran Özkan
Turkish Journal of Mathematics
Let $K$ be a finite field and $X$ be a complete simplicial toric variety over $K$ with split torus $T_X\cong (K^*)^n$. We give an algorithm relying on elimination theory for finding generators of the vanishing ideal of a subgroup $Y_Q$ parameterized by a matrix $Q$ which can be used to study algebraic geometric codes arising from $Y_Q$. We give a method to compute the lattice $L$ whose ideal $I_L$ is exactly $I(Y_Q)$ under a mild condition. As applications, we give precise descriptions for the lattices corresponding to some special subgroups. We also prove a Nullstellensatz type theorem valid over finite …
A New Kind Of $F$-Contraction And Some Best Proximity Point Results For Such Mappings With An Application, Hakan Şahi̇n
A New Kind Of $F$-Contraction And Some Best Proximity Point Results For Such Mappings With An Application, Hakan Şahi̇n
Turkish Journal of Mathematics
In this paper, we aim to present a new and unified way, including the previously mentioned solution methods, to overcome the problem in [7] for closed and bounded valued $F$-contraction mappings. We also want to obtain a real generalization of fixed point results existing in the literature by using best proximity point theory. Further, considering the strong relationship between homotopy theory and various branches of mathematics such as category theory, topological spaces, and Hamiltonian manifolds in quantum mechanics, our objective is to present an application to homotopy theory of our best proximity point results obtained in the paper. In this …
Inverse Nodal Problem For Sturm-Liouville Operator On A Star Graph With Nonequal Edges, Sevi̇m Durak
Inverse Nodal Problem For Sturm-Liouville Operator On A Star Graph With Nonequal Edges, Sevi̇m Durak
Turkish Journal of Mathematics
In this study, Sturm-Liouville operator was investigated on a star graph with nonequal edges. First, the behaviors of sufficiently large eigenvalues were learned, then the solution of the inverse problem was given to determine the potantial functions and parameters of the boundary condition on the star graph with the help of a dense set of nodal points and obtain a constructive solution to the inverse problems of this class.
Hermite-Hadamard-Mercer Type Inclusions For Interval-Valued Functions Via Riemann-Liouville Fractional Integrals, Hasan Kara, Muhammad Aamir Ali, Hüseyi̇n Budak
Hermite-Hadamard-Mercer Type Inclusions For Interval-Valued Functions Via Riemann-Liouville Fractional Integrals, Hasan Kara, Muhammad Aamir Ali, Hüseyi̇n Budak
Turkish Journal of Mathematics
In this research, we first establish some inclusions of fractional Hermite-Hadamard-Mercer type for interval-valued functions. Moreover, by special cases of our main results, we show that our main results reduce several inclusions obtained in the earlier works.
Global Differential Invariants Of Nondegenerate Hypersurfaces, Yasemi̇n Sağiroğlu, Uğur Gözütok
Global Differential Invariants Of Nondegenerate Hypersurfaces, Yasemi̇n Sağiroğlu, Uğur Gözütok
Turkish Journal of Mathematics
Let $\{g_{ij}(x)\}_{i, j=1}^n$ and $\{L_{ij}(x)\}_{i, j=1}^n$ be the sets of all coefficients of the first and second fundamental forms of a hypersurface $x$ in $R^{n+1}$. For a connected open subset $U\subset R^{n}$ and a $C^{\infty }$-mapping $x:U\rightarrow R^{n+1}$ the hypersurface $x$ is said to be $d$-\textit{nondegenerate}, where $d\in \left\{1, 2, \ldots n\right\}$, if $L_{dd}(x)\neq 0$ for all $u\in U$. Let $M(n)=\{F:R^{n}\longrightarrow R^{n}\mid Fx=gx+b, \; g\in O(n), \; b\in R^{n}\}$, where $O(n)$ is the group of all real orthogonal $n\times n$-matrices, and $SM(n)=\{F\in M(n)\mid g\in SO(n)\}$, where $SO(n)=\left\{g\in O(n)\mid \det(g)=1\right\}$. In the present paper, it is proved that the set $\left\{g_{ij}(x), …
On A Class Of Nonlocal Porous Medium Equations Of Kirchhoff Type, Uğur Sert
On A Class Of Nonlocal Porous Medium Equations Of Kirchhoff Type, Uğur Sert
Turkish Journal of Mathematics
We study the Dirichlet problem for the degenerate parabolic equation of the Kirchhoff type \[ u_{t}-a\left(\ u\ _{L^{p}(\Omega)}^{p}\right)\sum\limits_{i=1}^{n}D_{i}\left( \left\vert u\right\vert ^{p-2}D_{i}u\right) +b\left( x,t,u\right)=f\left( x,t\right) \quad \text{in $Q_T=\Omega \times (0,T)$}, \] where $p\geq2$, $T>0$, $\Omega \subset \mathbb{R}^{n}$, $n\geq 2$, is a smooth bounded domain. The coefficient $a(\cdot)$ is real-valued function defined on $\mathbb{R}_+$ and $b(\cdot,\cdot,\tau)$ is a measurable function with variable nonlinearity in $\tau$. We prove existence of weak solutions of the considered problem under appropriate and general conditions on $a$ and $b$. Sufficient conditions for uniqueness are found and in the case $f\equiv0$ the decay rates for $\ u\ …
On The Extended Zero-Divisor Graph Of Strictly Partial Transformation Semigroup, Emrah Korkmaz
On The Extended Zero-Divisor Graph Of Strictly Partial Transformation Semigroup, Emrah Korkmaz
Turkish Journal of Mathematics
Given a commutative ring $R$, the zero-divisor graph of $R$ is an undirected simple graph with vertices the nonzero zero-divisors of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0$. In [8], Redmond presented different versions of zero-divisor graphs of noncommutative rings. The main aim of this paper is to analyse these graphs for the semigroup $\mathcal{SP}_{n}$ of all strictly partial transformations on the set $X_{n}=\{1,2,\dots,n\}$.
Characterization Of Exponential Polynomial As Solution Of Certain Type Of Nonlinear Delay-Differential Equation, Abhijit Banerjee, Tania Biswas
Characterization Of Exponential Polynomial As Solution Of Certain Type Of Nonlinear Delay-Differential Equation, Abhijit Banerjee, Tania Biswas
Turkish Journal of Mathematics
In this paper, we have characterized the nature and form of solutions of the following nonlinear delay-differential equation: $$f^{n}(z)+\sum_{i=1}^{n-1}b_{i}f^{i}(z)+q(z)e^{Q(z)}L(z,f)=P(z),$$ where $b_i\in\mathbb{C}$, $L(z,f)$ are a linear delay-differential polynomial of $f$; $n$ is positive integers; $q$, $Q$ and $P$ respectively are nonzero, nonconstant and any polynomials. Different special cases of our result will accommodate all the results of [J. Math. Anal. Appl., 452(2017), 1128-1144; Mediterr. J. Math., 13(2016), 3015-3027; Open Math., 18(2020), 1292-1301]. Thus our result can be considered as an improvement of all of them. We have also illustrated a handful number of examples to show that all the cases as …
On Minimal Absolutely Pure Domain Of Rd-Flat Modules, Yusuf Alagöz
On Minimal Absolutely Pure Domain Of Rd-Flat Modules, Yusuf Alagöz
Turkish Journal of Mathematics
Given modules $A_{R}$ and $_{R}B$, $_{R}B$ is called absolutely $A_{R}$-pure if for every extension $_{R}C$ of $_{R}B$, $A\otimes B\rightarrow A\otimes C$ is a monomorphism. The class $\underline{\mathfrak{Fl}}^{-1}(A_{R})=$\{$_{R}B$ : $_{R}B$ is absolutely $A_{R}$-pure\} is called the absolutely pure domain of a module $A_{R}$. If $_{R}B$ is divisible, then all short exact sequences starting with $B$ is RD-pure, whence $B$ is absolutey $A$-pure for every $RD$-flat module $A_{R}$. Thus the class of divisible modules is the smallest possible absolutely pure domain of an $RD$-flat module. In this paper, we consider $RD$-flat modules whose absolutely pure domains contain only divisible modules, and we …
Matrix Mappings And Compact Operators For Schröder Sequence Spaces, Muhammet Ci̇hat Dağli
Matrix Mappings And Compact Operators For Schröder Sequence Spaces, Muhammet Ci̇hat Dağli
Turkish Journal of Mathematics
In this paper, we discuss the domain of a recently defined conservative matrix, constructed by means of the Schröder numbers in the spaces of $p-$absolutely summable sequences and bounded sequences. We determine the $\beta-$duals of the Banach spaces, introduced here, and present characterization of some matrix operators. Moreover, we give the characterization of certain compact operators via the Hausdorff measure of noncompactness.
On Properties Of The Reeb Vector Field Of $(\Alpha,\Beta)$ Trans-Sasakian Structure, Alexander Yampolsky
On Properties Of The Reeb Vector Field Of $(\Alpha,\Beta)$ Trans-Sasakian Structure, Alexander Yampolsky
Turkish Journal of Mathematics
The paper focused on the mean curvature and totally geodesic property of the Reeb vector field $\xi$ on $(\alpha,\beta)$ trans-Sasakian manifold $M$ of dimension $(2n+1)$ as a submanifold in the unit tangent bundle $T_1M$ with Sasaki metric $g_S$. We give an explicit formula for the norm of mean curvature vector of the submanifold $\xi(M)\subset (T_1M,g_S)$. As a byproduct, for the Reeb vector field, we get some known results concerning its minimality, harmonicity and the property to define a harmonic map. We prove that on connected proper trans-Sasakian manifold the Reeb vector field does not give rise to totally geodesic submanifold …
On A Generalization Of Szasz-Mirakyan Operators Including Dunkl-Appell Polynomials, Serdal Yazici, Fatma Taşdelen Yeşi̇ldal, Bayram Çeki̇m
On A Generalization Of Szasz-Mirakyan Operators Including Dunkl-Appell Polynomials, Serdal Yazici, Fatma Taşdelen Yeşi̇ldal, Bayram Çeki̇m
Turkish Journal of Mathematics
In this study, we have introduced a generalization of Szasz-Mirakyan operators including Dunkl-Appell polynomials with help of sequences satisfying certain conditions and have derived some approximation properties of this generalization.
Unitary Equivalence To Truncated Hankel Operators, Xi Zhao, Tao Yu
Unitary Equivalence To Truncated Hankel Operators, Xi Zhao, Tao Yu
Turkish Journal of Mathematics
In this paper, we characterize the operators which are unitarily equivalent to truncated Hankel operators. We show that every rank one operator and every $2\times 2$ matrix is unitarily equivalent to a truncated Hankel operator. Furthermore, we get that certain sum of tenser products of truncated Hankel operators is unitarily equivalent to a truncated Hankel operator.
Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo
Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo
Turkish Journal of Mathematics
In this paper, we introduce new notions of symmetric operators such as semisymmetric shape operator and structure Jacobi operator in complex hyperbolic two-plane Grassmannians. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with such notions.
Equicontinuity And Sensitivity On Countable Amenable Semigroup, Nader Asadi Karam, Mohammad Kbari Tootkaboni, Abbas Sahleh
Equicontinuity And Sensitivity On Countable Amenable Semigroup, Nader Asadi Karam, Mohammad Kbari Tootkaboni, Abbas Sahleh
Turkish Journal of Mathematics
In this paper, we obtain the classification of topological dynamical systems with a discrete action. The equicontinuity and sensitivity for amenable discrete countable semigroup action are shown by the left Følner sequence. We consider the notion of uniquely ergodic and mean equicontinuous on amenable discrete countable semigroup action and develop the notion of density with respect to the Følner sequence on equicontinuous and sensitivity.
$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus
$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus
Turkish Journal of Mathematics
In the present article, making use of the $(p,q)$-Hurwitz zeta function, we provide and investigate a new integral operator. Also, we define two families ${\mathcal{S}\mathcal{M}}_{p,q}\left(\xi ,\zeta,\delta,u,\tau \right)$ and ${\mathcal{S}\mathcal{C}}_{p,q}\left(\lambda, \zeta,\vartheta,u,\tau \right)$ of biunivalent and holomorphic functions in the unit disc connected with $(p,q)$-Chebyshev Polynomials. Then we find coefficient estimates $\left a_2\right $ and $\left a_3\right .$ Finally, we obtain Fekete-Szeg$\ddot{\mathrm{o}}$ inequalities for these families.
Inverse Nodal Problems For Dirac Type Integro Differential System With A Nonlocal Boundary Condition, Baki̇ Keski̇n
Inverse Nodal Problems For Dirac Type Integro Differential System With A Nonlocal Boundary Condition, Baki̇ Keski̇n
Turkish Journal of Mathematics
In this paper, the Dirac type integro differential system\ with a nonlocal integral boundary condition is considered. First, we derive the asymptotic expressions for the solutions and large eigenvalues. Second, we provide asymptotic expressions for the nodal points and prove that a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered differential system. We also provide an effective procedure for solving the inverse nodal problem.
The Dual Spaces Of Variable Anisotropic Hardy-Lorentz Spaces And Continuity Of A Class Of Linear Operators, Wenhua Wang, Aiting Wang
The Dual Spaces Of Variable Anisotropic Hardy-Lorentz Spaces And Continuity Of A Class Of Linear Operators, Wenhua Wang, Aiting Wang
Turkish Journal of Mathematics
In this paper, the authors obtain the continuity of a class of linear operators on variable anisotropic Hardy--Lorentz spaces. In addition, the authors also obtain that the dual space of variable anisotropic Hardy-Lorentz spaces is the anisotropic BMO-type spaces with variable exponents. This result is still new even when the exponent function $p(\cdot)$ is $p$.