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Articles 1081 - 1110 of 2494
Full-Text Articles in Physical Sciences and Mathematics
Pythagorean Triples Containing Generalized Lucas Numbers, Zafer Şi̇ar, Refi̇k Keski̇n
Pythagorean Triples Containing Generalized Lucas Numbers, Zafer Şi̇ar, Refi̇k Keski̇n
Turkish Journal of Mathematics
Let $P$ and $Q$ be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: $U_{0}(P,Q)=0,U_{1}(P,Q)=1,$ and $ U_{n+1}(P,Q)=PU_{n}(P,Q)+QU_{n-1}(P,Q)$ for $n\geq 1$ and $ V_{0}(P,Q)=2,V_{1}(P,Q)=P,$ and $V_{n+1}(P,Q)=PV_{n}(P,Q)+QV_{n-1}(P,Q)$ for $n\geq 1,$ respectively. In this paper, we assume that $P$ and $Q$ are relatively prime odd positive integers and $P^{2}+4Q>0.$ We determine all indices $n$ such that $U_{n}=(P^{2}+4Q)x^{2}.$ Moreover, we determine all indices $n$ such that $(P^{2}+4Q)U_{n}=x^{2}.$ As a result, we show that the equation $V_{n}^{2}(P,1)+V_{n+1}^{2}(P,1)=x^{2}$ has solution only for $n=2,$ $P=1,$ $x=5$ and $V_{n+1}^{2}(P,-1)=V_{n}^{2}(P,-1)+x^{2}$ has no solutions. Moreover, we solve some Diophantine equations.
$R$-Submodules And $Sr$-Submodules, Suat Koç, Ünsal Teki̇r
$R$-Submodules And $Sr$-Submodules, Suat Koç, Ünsal Teki̇r
Turkish Journal of Mathematics
In this article, we introduce new classes of submodules called $r$-submodule and special $r$-submodule, which are two different generalizations of $r$-ideals. Let $M $be an $R$-module, where $R $is a commutative ring$. $We call a proper submodule $N\ $of $M$ an $r$-submodule (resp., special $r$-submodule) if the condition $am\in N$ with $ann_{M}(a)=0_{M} $(resp., $ann_{R}(m)=0$) implies that $m\in N$ (resp., $a\in(N:_{R} M)$) for each $a\in R $and $m\in M. $ We also give various results and examples concerning $r$-submodules and special $r$-submodules.
Bounded Solutions And Asymptotic Stability Of Nonlinear Second-Order Neutral Difference Equations With Quasi-Differences, Magdalena Nockowska Rosiak
Bounded Solutions And Asymptotic Stability Of Nonlinear Second-Order Neutral Difference Equations With Quasi-Differences, Magdalena Nockowska Rosiak
Turkish Journal of Mathematics
This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n $$ with respect to $(q_n)$. For $q_n\to1$, $q_n\in(0,1)$ the standard fixed point approach is insufficient to get the existence of the bounded solution, so we combine this method with an approximation technique to achieve our goal. Moreover, for $p\ge 1$ and $\sup q_n
On The Rank Of Transformation Semigroup $T_{(N,M)}$, Kemal Toker, Hayrullah Ayik
On The Rank Of Transformation Semigroup $T_{(N,M)}$, Kemal Toker, Hayrullah Ayik
Turkish Journal of Mathematics
Let $T_{n}$ and $S_{n}$ be the full transformation semigroup and the symmetric group on $X_{n}=\{1,\ldots,n\}$, respectively. For $n,m\in \mathbb{Z}^{+}$ with $m\le n-1$ let $$T_{(n,m)}=\{ \alpha \in T_{n} : X_{m} \alpha = X_{m}\} .$$ In this paper we research generating sets and the rank of $T_{(n,m)}$. In particular, we prove that $$rank(T_{(n,m)})=\left\{ \begin{array}{lll} 2 & \mbox{ if }\, (n,m)=(2,1) \mbox{ or }(3,2)\\ 3 & \mbox{ if }\, (n,m)=(3,1) \mbox{ or } 4\leq n \mbox{ and } m=n-1\\ 4 & \mbox{ if }\, 4\leq n \mbox{ and } 1\leq m\leq n-2. \end{array}\right. $$ for $1\leq m\leq n-1$.
Regular $\Mathscr{D}$-Classes Of The Semigroup Of $N\Times N$ Tropical Matrices, Lin Yang
Regular $\Mathscr{D}$-Classes Of The Semigroup Of $N\Times N$ Tropical Matrices, Lin Yang
Turkish Journal of Mathematics
In this paper we give the characterizations of Green's relations $\mathscr{R}$, $\mathscr{L}$, and $\mathscr{D}$ on the set of matrices with entries in a tropical semiring. An $m\times n$ tropical matrix $A$ is called regular if there exists an $n\times m$ tropical matrix $X$ satisfying $AXA = A$. Furthermore, we study the regular $\mathscr{D}$-classes of the semigroup of all $n\times n$ tropical matrices under multiplication and give a partition of a nonsingular regular $\mathscr{D}$-class.
Existence Of Maximal Ideals In Leavitt Path Algebras, Songül Esi̇n, Müge Kanuni̇ Er
Existence Of Maximal Ideals In Leavitt Path Algebras, Songül Esi̇n, Müge Kanuni̇ Er
Turkish Journal of Mathematics
Let $E$ be an arbitrary directed graph and let $L$ be the Leavitt path algebra of the graph $E$ over a field $K$. The necessary and sufficient conditions are given to assure the existence of a maximal ideal in $L$ and also the necessary and sufficient conditions on the graph that assure that every ideal is contained in a maximal ideal are given. It is shown that if a maximal ideal $M$ of $L$ is nongraded, then the largest graded ideal in $M$, namely $gr(M)$, is also maximal among the graded ideals of $L$. Moreover, if $L$ has a unique …
On One Bvp For A Thermo-Microstretch Elastic Space With Spherical Cavity, Lamara Bitsadze
On One Bvp For A Thermo-Microstretch Elastic Space With Spherical Cavity, Lamara Bitsadze
Turkish Journal of Mathematics
The present paper considers the equilibrium theory of thermo-microstretch elastic solids with microtemperatures. The method to solve the Neumann-type boundary value problem (BVP) for the whole space with spherical cavity is presented. The solution of this BVP in the form of absolutely and uniformly convergent series is obtained.
Convolution And Jackson Inequalities In Musielak--Orlicz Spaces, Ramazan Akgün, Yunus Emre Yildirir
Convolution And Jackson Inequalities In Musielak--Orlicz Spaces, Ramazan Akgün, Yunus Emre Yildirir
Turkish Journal of Mathematics
In the present work we prove some direct and inverse theorems for approximation by trigonometric polynomials in Musielak-Orlicz spaces. Furthermore, we get a constructive characterization of the Lipschitz classes in these spaces.
Chordality Of Graphs Associated To Commutative Rings, Ashkan Nikseresht
Chordality Of Graphs Associated To Commutative Rings, Ashkan Nikseresht
Turkish Journal of Mathematics
We investigate when different graphs associated to commutative rings are chordal. In particular, we characterize commutative rings $R$ with each of the following conditions: the total graph of $R$ is chordal; the total dot product or the zero-divisor dot product graph of $R$ is chordal; the comaximal graph of $R$ is chordal; $R$ is semilocal; and the unit graph or the Jacobson graph of $R$ is chordal. Moreover, we state an equivalent condition for the chordality of the zero-divisor graph of an indecomposable ring and classify decomposable rings that have a chordal zero-divisor graph.
Congruences Modulo 9 For Bipartitions Withdesignated Summands, Robert Xiaojian Hao, Erin Yiying Shen
Congruences Modulo 9 For Bipartitions Withdesignated Summands, Robert Xiaojian Hao, Erin Yiying Shen
Turkish Journal of Mathematics
Andrews, Lewis, and Lovejoy studied arithmetic properties of partitions with designated summands that are defined on ordinary partitions by tagging exactly one part among parts with equal size. A bipartition of $n$ is an ordered pair of partitions $(\pi_1, \pi_2)$ with the sum of all of the parts being $n$. In this paper, we investigate arithmetic properties of bipartitions with designated summands. Let $PD_{-2}(n)$ denote the number of bipartitions of $n$ with designated summands. We establish several Ramanujan-like congruences and an infinite family of congruences modulo $9$ satisfied by $PD_{-2}(n)$.
Some Properties Of $E$-Symmetric Rings, F M, Junchao Wei
Some Properties Of $E$-Symmetric Rings, F M, Junchao Wei
Turkish Journal of Mathematics
In this paper, we first give some characterizations of $e$-symmetric rings. We prove that $R$ is an $e$-symmetric ring if and only if $a_{1}a_{2}a_{3}=0$ implies that $a_{\sigma(1)}a_{\sigma(2)}a_{\sigma(3)}e=0$, where $\sigma $ is any transformation of $\{1,2,3\}$. With the help of the Bott--Duffin inverse, we show that for $e\in ME_{l}(R)$, $R$ is an $e$-symmetric ring if and only if for any $a\in R$ and $g\in E(R)$, if $a$ has a Bott--Duffin $(e,g)$-inverse, then $g=eg$. Using the solution of the equation $axe=c$, we show that for $e\in ME_{l}(R)$, $R$ is an $e$-symmetric ring if and only if for any $a,c \in R$, if …
Conformal Riemannian Maps From Almost Hermitian Manifolds, Bayram Şahi̇n, Şener Yanan
Conformal Riemannian Maps From Almost Hermitian Manifolds, Bayram Şahi̇n, Şener Yanan
Turkish Journal of Mathematics
Conformal Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, namely conformal invariant Riemannian maps, holomorphic conformal Riemannian maps, and conformal antiinvariant Riemannian maps, are introduced. We mainly focus on conformal antiinvariant Riemannian maps from Kaehlerian manifolds. We give proper examples of conformal antiinvariant Riemannian maps, obtain the integrability of certain distributions, and investigate the geometry of leaves of these distributions. We also obtain various conditions for such maps to be horizontally homothetic maps.
Limit Behaviors Of Nonoscillatory Solutions Of Three-Dimensional Time Scale Systems, Özkan Öztürk, Raegan Higgins
Limit Behaviors Of Nonoscillatory Solutions Of Three-Dimensional Time Scale Systems, Özkan Öztürk, Raegan Higgins
Turkish Journal of Mathematics
In this article, we investigate the oscillatory behavior of a three-dimensional system of dynamic equations on an unbounded time scale. A time scale $\T$ is a nonempty closed subset of real numbers. An example is given to illustrate some of the results.
3-Class Groups Of Cubic Cyclic Function Fields, Zhengjun Zhao
3-Class Groups Of Cubic Cyclic Function Fields, Zhengjun Zhao
Turkish Journal of Mathematics
Let $F$ be a global function field over the finite constant field $\mathbb{F}_q$ with $3\mid q-1$, and let $K/F$ be a cubic cyclic function fields extension with Galois group $G=$Gal$(K/F)=$. Denote by $\mathcal{C}(K)$ and $\mathcal{C}(K)_3$ the ideal class group of $K$ and its Sylow 3-subgroup, respectively. Let $\mathcal{C}(K)_3^G=\{[\fa]\in \mathcal{C}(K)_3 \ \sigma[\fa]=[\fa]\}$ and $\mathcal{C}(K)_3^{1-\sigma}=\{[\fa](\sigma[\fa])^{-1} \ [\fa]\in \mathcal{C}(K)_3\}$. In this paper, we present a method for computing the 3-rank of the quotient group $\mathcal{C}(K)_3^G\mathcal{C}(K)_3^{1-\sigma}/\mathcal{C}(K)_3^{1-\sigma}$. Specifically, when $K$ is a cubic Kummer extension of $\mathbb{F}_q(T)$, we determine explicitly the key factors $t$, $x_1,\cdots, x_t$, and $[\mathfrak{A}_1],\cdots, [\mathfrak{A}_t]$ in the process of computing the …
On Matrix Rings With The Sip And The Ads, Fi̇gen Takil Mutlu
On Matrix Rings With The Sip And The Ads, Fi̇gen Takil Mutlu
Turkish Journal of Mathematics
In this paper, matrix rings with the summand intersection property (SIP) and the absolute direct summand (ads) property (briefly, $SA$) are studied. A ring $R$ has the right SIP if the intersection of two direct summands of $R$ is also a direct summand. A right $R$-module $M$ has the ads property if for every decomposition $M=A\oplus B$ of $M$ and every complement $C$ of $A$ in $M$, we have $M=A\oplus C$. It is shown that the trivial extension of $R$ by $M$ has the SA if and only if $R$ has the SA, $M$ has the ads, and $(1-e)Me=0$ for …
Derivations, Generalized Derivations, And *-Derivations Of Period $2$ In Rings, Hesham Nabiel
Derivations, Generalized Derivations, And *-Derivations Of Period $2$ In Rings, Hesham Nabiel
Turkish Journal of Mathematics
The aim of this article is to discuss the existence of certain kinds of derivations and *-derivations that are of period 2. Moreover, we obtain the form of generalized reverse derivations and generalized left derivations of period $2$.
On The Diophantine Equation $((C+1)M^{2}+1)^{X}+(Cm^{2}-1)^{Y}=(Am)^Z$, Eli̇f Kizildere, Takafumi Miyazaki, Gökhan Soydan
On The Diophantine Equation $((C+1)M^{2}+1)^{X}+(Cm^{2}-1)^{Y}=(Am)^Z$, Eli̇f Kizildere, Takafumi Miyazaki, Gökhan Soydan
Turkish Journal of Mathematics
Suppose that $c$, $m$, and $a$ are positive integers with $a \equiv 11,\,13 \pmod{24}$. In this work, we prove that when $2c+1=a^{2}$, the Diophantine equation in the title has only solution $(x, y, z)=(1,1,2)$ where $m \equiv \pm 1 \pmod{a}$ and $m>a^2$ in positive integers. The main tools of the proofs are elementary methods and Baker's theory.
Bargraphs In Bargraphs, Toufik Mansour, Armend Shabani
Bargraphs In Bargraphs, Toufik Mansour, Armend Shabani
Turkish Journal of Mathematics
Bargraphs are lattice paths in $\mathbb{N}_0^2$ that start at the origin and end upon their first return to the $x$-axis. Each bargraph is represented by a sequence of column heights $\pi_1\pi_2\cdots\pi_m$ such that column $j$ contains $\pi_j$ cells. In this paper, we study the number of bargraphs with $n$ cells and $m$ columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.
A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao
A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao
Turkish Journal of Mathematics
Let $R$ be a regular local ring. In this note, we prove that $Ass_RH^2_I(R)$ is finite for any ideal $I$ of $R$. We also give a sufficient condition for $Ass_RH^3_{(x,y,z)}(R)$ to be finite for $x, y$ an $R$-regular sequence and $z\in R$, which would imply that Lyubeznik's conjecture is true in the regular local rings case.
Natural Mates Of Frenet Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Azeb Alghanemi
Natural Mates Of Frenet Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Azeb Alghanemi
Turkish Journal of Mathematics
For each Frenet curve $\alpha $ in the Euclidean 3-space $\mathbb{E}^{3}$, there exists a unique unit speed curve $\beta$ tangent to the principal normal vector field of $\alpha $. We simply call this curve $\beta $ the natural mate of $\alpha$. The main purpose of this paper is to prove some relationships between a Frenet curve and its natural mate. In particular, we obtain some necessary and sufficient conditions for the natural mate of a Frenet curve to be a helix, a spherical curve, or a curve of constant curvature. Several applications of our main results are also presented.
Strongly $Cm$-Semicommutative Rings, Liang Zhao, Jiaqun Wei
Strongly $Cm$-Semicommutative Rings, Liang Zhao, Jiaqun Wei
Turkish Journal of Mathematics
We study the strongly semicommutative properties relative to a monoid crossed product. The concept of strongly $CM$-semicommutative rings is introduced and investigated. Many results related to semicommutative properties over polynomial rings, skew polynomial rings, monoid rings, and skew monoid rings are extended and unified.
On The Growth Of Meromorphic Solutions Of Some Higher Order Linear Differential Equations, Farid Mesbout, Tahar Zerzaihi
On The Growth Of Meromorphic Solutions Of Some Higher Order Linear Differential Equations, Farid Mesbout, Tahar Zerzaihi
Turkish Journal of Mathematics
Let $k,m,n $ be integers such that $k\geq 1$, $n\geq 2$ and $1\leq m\leq n$. In this article we study the order $\rho(f)$ and the hyperorder $\rho_2(f)$ of nonzero meromorphic solutions $f$ of the differential equation $$\sum_{j=1,j\ne m}^{n}A_j(z)f^{(j)}(z)+A_m(z)e^{p_m(z)}f^{(m)}(z)+\left(A_0(z)e^{p(z)}+B_0(z)e^{q(z)}\right)f(z)=0,$$ where $B_0(z)$, $A_0(z), \cdots, A_n(z)$ are meromorphic functions such that $A_0A_mA_nB_0\not\equiv 0$, $\max\{\rho(B_0), \rho(A_0), \cdots,\rho(A_n)\}
Bound States And Spectral Singularities Of An Impulsive Schrödinger Equation, Emel Yildirim
Bound States And Spectral Singularities Of An Impulsive Schrödinger Equation, Emel Yildirim
Turkish Journal of Mathematics
In this paper, we study the analytical properties of the Jost function of an impulsive Schrödinger equation. We also investigate the bound states and spectral singularities of this equation. We present some conditions on the potential function that guarantee that the impulsive Schrödinger equation has a finite number of bound states and spectral singularities with finite multiplicities.
First Order Self-Adjoint Multipoint Quasi-Differential Operators, Ruki̇ye Öztürk Mert, Bülent Yilmaz, Zameddi̇n İsmai̇lov
First Order Self-Adjoint Multipoint Quasi-Differential Operators, Ruki̇ye Öztürk Mert, Bülent Yilmaz, Zameddi̇n İsmai̇lov
Turkish Journal of Mathematics
In this paper, using the Calkin-Gorbachuk method, the general form of all self-adjoint operators generated by first order linear singular multipoint quasi-differential expressions in the direct sum of weighted Hilbert spaces of vector functions has been found. Later on, the geometry of the spectrum set of these type extensions was researched.
Parametric Nondifferentiable Multiobjective Fractional Programmingunder $(B,\Psi ,\Phi ,\Rho )$-Univexity, Tadeusz Antczak, Ram Verma
Parametric Nondifferentiable Multiobjective Fractional Programmingunder $(B,\Psi ,\Phi ,\Rho )$-Univexity, Tadeusz Antczak, Ram Verma
Turkish Journal of Mathematics
In this paper, we are concerned with optimality conditions and duality results for nondifferentiable multiobjective fractional programming problems. Parametric necessary optimality conditions are established for such vector optimization problems in which each component of the involved functions is locally Lipschitz. Further, under the introduced concept of nondifferentiable $(b,\Psi ,\Phi ,\rho )$-univexity, the parametric sufficient optimality conditions are established for a new class of nonconvex multiobjective fractional programming problems. Furthermore, for the considered multiobjective fractional programming problem, its parametric vector dual problem in the sense of Schaible is defined. Then several duality theorems are also established under $(b,\Psi ,\Phi ,\rho )$% …
Coefficients Inequalities For Classes Of Meromorphic Functions, Jacek Dziok, Maslina Darus, Janusz Sokol
Coefficients Inequalities For Classes Of Meromorphic Functions, Jacek Dziok, Maslina Darus, Janusz Sokol
Turkish Journal of Mathematics
A typical problem in the theory of analytic functions is to study a functional made up of combinations of coefficients of the original function. Usually, there is a parameter over which the extremal value of the functional is needed. One of the important functionals of this type is the Fekete-Szegö functional defined on the class of analytic functions. In this paper we transfer the Fekete-Szegö problem to some classes of meromorphic functions.
Global Attractors For The Semilinear Beam Equationwith Localized Viscosity, Sema Yayla
Global Attractors For The Semilinear Beam Equationwith Localized Viscosity, Sema Yayla
Turkish Journal of Mathematics
In this paper, we deal with the semilinear beam equation with localized viscosity. Under mild conditions on the viscous coefficient, we establish the well-posedness and boundedness of the weak solutions. Then we prove that the semigroup generated by this problem has a smooth global attractor in $H^{3}\left( 0,1\right) \times H_{0}^{1}\left( 0,1\right) $.
Symmetry Of Numerical Range And Semigroup Generation Of Infinite Dimensional Hamiltonian Operators, Junjie Huang, Jie Liu, Alatancang Chen
Symmetry Of Numerical Range And Semigroup Generation Of Infinite Dimensional Hamiltonian Operators, Junjie Huang, Jie Liu, Alatancang Chen
Turkish Journal of Mathematics
This paper deals with the infinite dimensional Hamiltonian operator with unbounded entries. Using the core of its entries, we obtain the conditions under which the numerical range of such an operator is symmetric with respect to the imaginary axis. Based on the symmetry above, a necessary and sufficient condition for generating $C_0$ semigroups is further given.
A Coanalytic Menger Group That Is Not $\Sigma$-Compact, Seçi̇l Tokgöz
A Coanalytic Menger Group That Is Not $\Sigma$-Compact, Seçi̇l Tokgöz
Turkish Journal of Mathematics
Under $V=L$ we construct coanalytic topological subgroups of reals, demonstrating that even for definable groups of reals, selection principles may differ.
Analysis Of Periodic And Asymptotically Periodic Solutions In Nonlinear Coupled Volterra Integro-Differential Systems, Youssef Raffoul
Analysis Of Periodic And Asymptotically Periodic Solutions In Nonlinear Coupled Volterra Integro-Differential Systems, Youssef Raffoul
Turkish Journal of Mathematics
In this note, we investigate the existence of periodic and asymptotically periodic solutions of a system of coupled nonlinear Volterra integro-differential equations with infinite delay. We will make use of Schauder fixed point theorem to prove our maps have fixed points.