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On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara
On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara
Turkish Journal of Mathematics
In this paper we consider the following higher-order nonlinear difference equation $$ x_{n}=\alpha x_{n-k}+\frac{\delta x_{n-k}x_{n-\left( k+l\right) }}{\beta x_{n-\left( k+l\right) }+\gamma x_{n-l}},\ n\in \mathbb{N} _{0}, $$ where $k$ and $l$ are fixed natural numbers, and the parameters $\alpha $, $ \beta $, $\gamma $, $\delta $ and the initial values $x_{-i}$, $i=\overline{ 1,k+l}$, are real numbers such that $\beta ^{2}+\gamma ^{2}\neq 0$. We solve the above-mentioned equation in closed form and considerably extend some results in the literature. We also determine the asymptotic behavior of solutions and the forbidden set of the initial values using the obtained formulae for the case …
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.
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.
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 $PD_{-2}(n)$.
Positive Solutions Of Neumann Problems For A Discrete System Coming From Models Of House Burglary, Tianlan Chen, Ruyun Ma, Yongwen Liang
Positive Solutions Of Neumann Problems For A Discrete System Coming From Models Of House Burglary, Tianlan Chen, Ruyun Ma, Yongwen Liang
Turkish Journal of Mathematics
We show existence results of positive solutions of Neumann problems for a discrete system: $$\aligned &\eta\Delta^2(A_{k-1}-A^0_{k-1})-A_{k}+A^0_{k}+N_kA_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta\big(\Delta N_{k-1}-2N_k\frac{\Delta A_{k-1}}{A_{k}}\big)-N_kA_{k}+A^1_{k}-A^0_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned $$ where the assumptions on $\eta,\ A_k^0$, and $A_k^1$ are motivated by some mathematics models for house burglary. Our results are based on the topological degree theory.
On The Type And Generators Of Monomial Curves, Nguyen Thi Dung
On The Type And Generators Of Monomial Curves, Nguyen Thi Dung
Turkish Journal of Mathematics
Let $n_1, n_2,\ldots, n_d$ be positive integers and $H $ be the numerical semigroup generated by $n_1,n_2, \ldots, n_d$. Let $A:=k[H]:=k[t^{n_1}, t^{n_2},\ldots, t^{n_d}]\cong k[x_1,x_2,\ldots,x_d]/I$ be the numerical semigroup ring of $H $ over $k.$ In this paper we give a condition $(*)$ that implies that the minimal number of generators of the defining ideal $I$ is bounded explicitly by its type. As a consequence for semigroups with $d=4$ satisfying the condition $(*)$ we have $\mu ({\rm in}(I))\leq 2(t(H))+1$.
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and necessary and sufficient, conditions for the functions belonging to these classes, respectively, are also given. Furthermore, various properties like order of starlikeness and radius of convexity of the subclasses of these classes and radii of starlikeness and convexity of these subclasses are examined.
Difference Uniqueness Theorems On Meromorphic Functions In Several Variables, Zhixue Liu, Qingcai Zhang
Difference Uniqueness Theorems On Meromorphic Functions In Several Variables, Zhixue Liu, Qingcai Zhang
Turkish Journal of Mathematics
In this paper, we mainly investigate the uniqueness problem on meromorphic functions in $\mathbb{C}^m$ sharing small functions with their difference operators or shifts, and we obtain some interesting results that act as some extensions of previous results from one complex variable to several complex variables.
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.
Olsen-Type Inequalities For The Generalized Commutator Of Multilinear Fractional Integrals, Xiao Yu, Shanzhen Lu
Olsen-Type Inequalities For The Generalized Commutator Of Multilinear Fractional Integrals, Xiao Yu, Shanzhen Lu
Turkish Journal of Mathematics
In this paper, we study certain multilinear operators of fractional integral type defined by \[ I^{\vec{A}}_{\alpha}\vec{f}(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion (\mathbb{R} %EndExpansion ^{n})^m}\frac{f_1(y_1)\cdots f_m(y_m)}{ (x-y_1,\cdots,x-y_m) ^{mn-\alpha+\sum\limits_{i=1}^m(N_i-1)}}\prod\limits_{i=1}^mR_{N_i}(A_i;x,y_i)d\vec{y}, \] where $0< \alpha
Delta-Shocks And Vacuums As Limits Of Flux Approximation For The Pressureless Type System, Jinjing Liu, Hanchun Yang
Delta-Shocks And Vacuums As Limits Of Flux Approximation For The Pressureless Type System, Jinjing Liu, Hanchun Yang
Turkish Journal of Mathematics
In this paper, we investigate the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions of the pressureless type system with flux approximation. First, the Riemann problem of the pressureless type system with a flux perturbation is considered. A parameterized delta-shock and generalized constant density solution are obtained. Then we rigorously prove that, as the flux perturbation vanishes, they converge to the delta-shock and vacuum state of the pressureless type system, respectively. Secondly, by adding an artificial pressure term in the pressureless type system, we solve the Riemann problem of the system with a …
Quasinilpotents In Rings And Their Applications, Jian Cui
Quasinilpotents In Rings And Their Applications, Jian Cui
Turkish Journal of Mathematics
An element $a$ of an associative ring $R$ is said to be quasinilpotent if $1-ax$ is invertible for every $x\in R$ with $xa=ax$. Nilpotents and elements in the Jacobson radical of a ring are well-known examples of quasinilpotents. In this paper, properties and examples of quasinilpotents in a ring are provided, and the set of quasinilpotents is applied to characterize rings with some certain properties.
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.
The Local And Semilocal Convergence Analysis Of New Newton-Like Iteration Methods, Vatan Karakaya, Kadri̇ Doğan, Yunus Atalan, Nour El Houda Bouzara
The Local And Semilocal Convergence Analysis Of New Newton-Like Iteration Methods, Vatan Karakaya, Kadri̇ Doğan, Yunus Atalan, Nour El Houda Bouzara
Turkish Journal of Mathematics
The aim of this paper is to find new iterative Newton-like schemes inspired by the modified Newton iterative algorithm and prove that these iterations are faster than the existing ones in the literature. We further investigate their behavior and finally illustrate the results by numerical examples.
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 Biquaternion Algebras With Orthogonal Involution, Amir Hossein Nokhodkar
On Biquaternion Algebras With Orthogonal Involution, Amir Hossein Nokhodkar
Turkish Journal of Mathematics
We investigate the Pfaffians of decomposable biquaternion algebras with involution of orthogonal type. In characteristic two, a classification of these algebras in terms of their Pfaffians and some other related invariants is studied. Also, in arbitrary characteristic, a criterion is obtained for an orthogonal involution on a biquaternion algebra to be metabolic.
Existence Of Positive Periodic Solution Of Second-Order Neutral Differential Equations, Tuncay Candan
Existence Of Positive Periodic Solution Of Second-Order Neutral Differential Equations, Tuncay Candan
Turkish Journal of Mathematics
In this work, we consider two types of second-order neutral differential equations and we obtain sufficient conditions for the existence of positive $\om$-periodic solutions for these equations. We employ Krasnoselskii's fixed point theorem for the sum of a completely continuous and a contraction mapping. An example is included to illustrate our results.
Characterizations Of *-Dmp Matrices Over Rings, Yuefeng Gao, Jianlong Chen
Characterizations Of *-Dmp Matrices Over Rings, Yuefeng Gao, Jianlong Chen
Turkish Journal of Mathematics
Let $R$ be a ring with involution $*$. $R^{m\times n}$ denotes the set of all $m\times n$ matrices over $R$. In this paper, we give a characterization of the pseudo core inverse of $A\in R^{n\times n}$ in the form of $A=GDH$, $N_r(G)=0$, $N_l(H)=0$, $D^2=D=D^*$, where $N_l(A)=\{x\in R^{1\times m} xA=0\}$ and $N_r(A)=\{x\in R^{n\times 1}~ ~Ax=0\}.$ Then we obtain necessary and sufficient conditions for $A\in R^{n\times n}$, in the form of $A=GDH$, $N_r(G)=0$, $N_l(H)=0$, $D^2=D=D^*$, to be *-DMP. If $R$ is a principal ideal domain (resp. semisimple Artinian ring), then matrices expressed as that form include all $n\times n$ matrices over $R$.
Stability Of Abstract Dynamic Equations On Time Scales By Lyapunov's Second Method, Alaa Hamza, Karima Oraby
Stability Of Abstract Dynamic Equations On Time Scales By Lyapunov's Second Method, Alaa Hamza, Karima Oraby
Turkish Journal of Mathematics
In this paper, we use the Lyapunov's second method to obtain new sufficient conditions for many types of stability like exponential stability, uniform exponential stability, $h$-stability, and uniform $h$-stability of the nonlinear dynamic equation \begin{equation*} x^{\Delta}(t)=A(t)x(t)+f(t,x),\;t\in \mathbb{T}^+_\tau:=[\tau,\infty)_{\mathbb T}, \end{equation*} on a time scale $\mathbb T$, where $A\in C_{rd}(\mathbb T,L(X))$ and $f:\mathbb T\times X\to X$ is rd-continuous in the first argument with $f(t,0)=0.$ Here $X$ is a Banach space. We also establish sufficient conditions for the nonhomogeneous particular dynamic equation \begin{equation*} x^{\Delta}(t)=A(t)x(t)+f(t),\,t\in\mathbb{T}^+_{\tau}, \end{equation*} to be uniformly exponentially stable or uniformly $h$-stable, where $f\in C_{rd}(\mathbb T,X)$, the space of rd-continuous functions from …
On The Hilbert Formulas And Of Change Of Integration Order For Some Singular Integrals In The Unit Circle, Juan Bory Reyes, Ricardo Abreu Blaya, Marco Antonio Perez De La Rosa, Baruch Schneider
On The Hilbert Formulas And Of Change Of Integration Order For Some Singular Integrals In The Unit Circle, Juan Bory Reyes, Ricardo Abreu Blaya, Marco Antonio Perez De La Rosa, Baruch Schneider
Turkish Journal of Mathematics
We obtain some analogues of the Hilbert formulas on the unit circle for $\alpha$-hy\-per\-ho\-lo\-mor\-phic function theory when $\alpha$ is a complex number. Such formulas relate a pair of components of the boundary value of an $\alpha$-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincaré-Bertrand formula for the $\alpha$-hyperholomorphic singular integrals in the unit circle is presented.
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Turkish Journal of Mathematics
In this paper, on one hand, we propose a new type of symmetric function to interpret the bi$^{s}$nomial coefficients and their analogs. On other hand, according to this function, we give an interpretation of these coefficients by lattice paths and tiling. Some identities of these coefficients are also established. This work is an extension of the results of Belbachir and Benmezai's ''A $\mathit{q}$-analogue for bi$^{\mathit{s}}$nomial coefficients and generalized Fibonacci sequences".
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Turkish Journal of Mathematics
The iterative equation $f^{q}(x)=g(x)$, $x\in X$ for a given function $g$ and a positive integer $q$ is solved in the following two main cases: (i) $X=\mathbb{Z}$, $g(x)=ax+b$, ($a,b\in\mathbb{Z}$; $a\neq0,1$); (ii) $X=\mathbb{N}\cup\left\{ 0\right\} $, $g$ is increasing with no fixed point.
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Turkish Journal of Mathematics
A variant of Weyl- and Horn-type inequalities for cyclically compact operators on Kaplansky-Hilbert modules is given.
Three Binomial Sums Weighted By Falling And Rising Factorials, Emrah Kiliç
Three Binomial Sums Weighted By Falling And Rising Factorials, Emrah Kiliç
Turkish Journal of Mathematics
In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial coefficients. Then we rewrite the claimed identities in terms of generalized hypergeometric functions to prove the claimed results.
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
Turkish Journal of Mathematics
Using generalized hypergeometric functions to perform symbolic manipulations of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, that function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new …
Continuous Dependence Of Solutions To The Strongly Damped Nonlinear Klein-Gordon Equation, Şevket Gür, Mesude Eli̇f Uysal
Continuous Dependence Of Solutions To The Strongly Damped Nonlinear Klein-Gordon Equation, Şevket Gür, Mesude Eli̇f Uysal
Turkish Journal of Mathematics
This article is devoted to the study of the initial-boundary value problem for the strongly damped nonlinear Klein-Gordon equation. It is proved that the solution depends continuously on changes in the damping terms, diffusion, mass, and nonlinearity effect term in the $H^1$ norm.
Nearly Kahler And Nearly Kenmotsu Manifolds, Nikrooz Heidari, Niloufar Hoseein Pour Kashani, Behzad Najafi
Nearly Kahler And Nearly Kenmotsu Manifolds, Nikrooz Heidari, Niloufar Hoseein Pour Kashani, Behzad Najafi
Turkish Journal of Mathematics
We study the class of strict nearly Kenmotsu manifolds and prove that there is no Einstein manifold or locally symmetric or locally $\phi$-symmetric in this class of manifolds. We describe strict nearly Kenmotsu manifolds in low dimensions. Finally, we obtain a relation between the curvature of nearly Kenmotsu manifolds and nearly Kahler manifolds.
A New Formula For Hyper-Fibonacci Numbers, And The Number Of Occurrences, Takao Komatsu, Laszlo Szalay
A New Formula For Hyper-Fibonacci Numbers, And The Number Of Occurrences, Takao Komatsu, Laszlo Szalay
Turkish Journal of Mathematics
In this paper, we develop a new formula for hyper-Fibonacci numbers $F_n^{[k]}$, wherein the coefficients (related to Stirling numbers of the first kind) of the polynomial ingredient $p_k(n)$ are determined. As an application we investigate the number of occurrences of positive integers among $F_n^{[k]}$ and determine all the solutions in nonnegative integers $x$ and $y$ to the Diophantine equation $F_x^{[k]}=F_y^{[\ell]}$, where $0\le k
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Turkish Journal of Mathematics
Let $E$ be a Banach space, $\lambda$ a perfect sequence space, and $M$ an Orlicz function. Denote by $\lambda \left(E, M\right)_{r}$ the space of all weakly $(M, \lambda)$-summable sequences from $E$ that are the limit of their finite sections. In this paper, we describe the continuous linear functionals on $\lambda \left(E, M\right)_{r}$ in terms of strongly $(N, \lambda^{\ast})$-summable sequences in the dual $E^{*}$ of $E$, and then we give a characterization of the reflexivity of $\lambda \left(E, M\right)$ in terms of that of $\lambda$ and of $E$ and the AK-property.