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On Quasi-Affinity And Reducing Subspaces Of Multiplication Operator On A Certain Closed Subspace, Yucheng Li, Lina Song, Wenhua Lan
On Quasi-Affinity And Reducing Subspaces Of Multiplication Operator On A Certain Closed Subspace, Yucheng Li, Lina Song, Wenhua Lan
Turkish Journal of Mathematics
Let $H$ denote a certain closed subspace of the Bergman space $A_{\alpha}^{2}({\B}_{n})(\alpha>-1)$ of the unit ball in $\mathbb{C}^{n}$. In this paper, we prove that the operator $\bigoplus\limits_{1}^{m}M_{z^{(s_{1},\cdots,s_{n})}}$ is quasi-affine to the multiplication operator $M_{z^{(ms_{1},\cdot\cdot\cdot,ms_{n})}}$ on $H$. Furthermore, the reducing subspaces of $M_{z^{(ms_{1},\cdots,ms_{n})}}$ are characterized on $H$.
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 …
Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak
Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak
Turkish Journal of Mathematics
This scientific investigation deals with introducing certain basic information relating to the error functions in z-plane, establishing extensive relations between various series expansions of the complex error functions and presenting a number of their implications.
On The Dynamics Of Certain Higher-Order Scalar Difference Equation: Asymptotics, Oscillation, Stability, Pavel Nesterov
On The Dynamics Of Certain Higher-Order Scalar Difference Equation: Asymptotics, Oscillation, Stability, Pavel Nesterov
Turkish Journal of Mathematics
We construct the asymptotics for solutions of the higher-order scalar difference equation that is equivalent to the linear delay difference equation $\Delta y(n)=-g(n)y(n-k)$. We assume that the coefficient of this equation oscillates at the certain level and the oscillation amplitude decreases as $n\to\infty$. Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotic formulae. The obtained results are applied to the oscillation and stability problems for the solutions of the considered equation.
A Note On Simple Trinomial Units In $U_{1}(\Mathbb{Z}C_{P})$, Necat Görentaş
A Note On Simple Trinomial Units In $U_{1}(\Mathbb{Z}C_{P})$, Necat Görentaş
Turkish Journal of Mathematics
In this paper, some new notions are defined about the unit group $U_{1}(\mathbb{Z}G)$ of a finite group G. Especially, notion of simple unit is defined by using the number of elements in its support and absolutely small coefficients of the unit. Units are classified as monomial, binomial, trinomial and k-nomial, level, unit with level $l$ and simple unit. We have shown triviality of monomial units and nonexistence of binomial units in the unit group $U_{1}(\mathbb{Z}G)$ of an arbitrary finite group G. Some basic results and examples are posed about simple units and simple trinomial units in $U_{1}(\mathbb{Z}C_{p})$of a cyclic group …
On The Chromatic Polynomial And The Domination Number Of $K$-Fibonacci Cubes, Ömer Eğeci̇oğlu, Eli̇f Saygi, Zülfükar Saygi
On The Chromatic Polynomial And The Domination Number Of $K$-Fibonacci Cubes, Ömer Eğeci̇oğlu, Eli̇f Saygi, Zülfükar Saygi
Turkish Journal of Mathematics
Fibonacci cubes are defined as subgraphs of hypercubes, where the vertices are those without two consecutive 1's in their binary string representation. $k$-Fibonacci cubes are in turn special subgraphs of Fibonacci cubes obtained by eliminating certain edges. This elimination is carried out at the step analogous to where the fundamental recursion is used to construct Fibonacci cubes themselves from the two previous cubes by link edges. In this work, we calculate the vertex chromatic polynomial of $k$-Fibonacci cubes for $k=1,2$. We also determine the domination number and the total domination number of $k$-Fibonacci cubes for $n,k \leq 12$ by using …
On Symplectic 8-Manifolds Admitting $Spin(7)$-Structure, Eyüp Yalçinkaya, İbrahi̇m Ünal
On Symplectic 8-Manifolds Admitting $Spin(7)$-Structure, Eyüp Yalçinkaya, İbrahi̇m Ünal
Turkish Journal of Mathematics
In this paper we study symplectic 8-manifolds admitting $Spin(7)$- structure. We give examples and show that many of the symplectic 8-manifolds constructed by Pasquotto satisfy the Chern number relations required to admit a $Spin(7)$-structure.
Existence Results Of Positive Solutions For Kirchhoff Type Biharmonic Equation Via Bifurcation Methods*, Jinxiang Wang, Dabin Wang
Existence Results Of Positive Solutions For Kirchhoff Type Biharmonic Equation Via Bifurcation Methods*, Jinxiang Wang, Dabin Wang
Turkish Journal of Mathematics
This paper is concerned with the existence of positive solutions for the fourth order Kirchhoff type problem $$ \left\{\begin{array}{ll} \Delta^{2}u-(a+b\int_\Omega \nabla u ^2dx)\triangle u=\lambda f(u(x)),\ \ \text{in}\ \Omega,\\ u=\triangle u=0,\ \ \text{on}\ \partial\Omega,\\ \end{array} \right. $$ where $\Omega\subset \mathbb{R}^{N}$($N\geq 1$) is a bounded domain with smooth boundary $\partial \Omega$, $a>0, b\geq 0$ are constants, $\lambda\in \mathbb{R}$ is a parameter. For the case $f(u)\equiv u$, we use an argument based on the linear eigenvalue problems of fourth order elliptic equations to show that there exists a unique positive solution for all $\lambda>\Lambda_{1,a}$, here $\Lambda_{1,a}$ is the first eigenvalue of …
New Criteria For The Oscillation And Asymptotic Behavior Of Second-Order Neutral Differential Equations With Several Delays, Başak Karpuz, Shyam Sundar Santra
New Criteria For The Oscillation And Asymptotic Behavior Of Second-Order Neutral Differential Equations With Several Delays, Başak Karpuz, Shyam Sundar Santra
Turkish Journal of Mathematics
In this paper, necessary and sufficient conditions for asymptotic behavior are established of the solutions to second-order neutral delay differential equations of the form \begin{equation} \frac{d}{d{}t}\Biggl(r(t)\biggl(\frac{d}{d{}t}[x(t)-p(t)x(\tau(t))]\biggr)^{\gamma}\Biggr)+\sum_{i=1}^{m}q_{i}(t)f_{i}\bigl(x(\sigma_{i}(t))\bigr)=0 \quad\text{for}\ t\geq{}t_{0}.\nonumber \end{equation} We consider two cases when $f_{i}(u)/u^{\beta}$ is nonincreasing for $\gamma>\beta$, and nondecreasing for $\beta>\gamma$, where $\beta$ and $\gamma$ are quotients of two positive odd integers. Our main tool is Lebesgue's dominated convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.
Some Results On A System Of Multiterm Fractional Integro-Differential Equations, Shahram Rezapour, Fethi̇ye Müge Sakar, Seher Meli̇ke Aydoğan, Elahe Ravash
Some Results On A System Of Multiterm Fractional Integro-Differential Equations, Shahram Rezapour, Fethi̇ye Müge Sakar, Seher Meli̇ke Aydoğan, Elahe Ravash
Turkish Journal of Mathematics
In present study, we investigate the existence of solution for a multiterm fractional integro-differential system with special boundary conditions under some different conditions. In this way, we provide different results for the existence of solutions for the system and also for obtaining unique solution for the system under different conditions. We also present three numerical examplesin which by using the Legendre multiwavelet method, we approximate solutions of the system. These examples illustrate our main results.
Lerch Matrix Collocation Method For 2d And 3d Volterra Type Integral And Second Order Partial Integro Differential Equations Together With An Alternative Error Analysis And Convergence Criterion Based On Residual Functions, Seda Çayan, Mehmet Sezer
Lerch Matrix Collocation Method For 2d And 3d Volterra Type Integral And Second Order Partial Integro Differential Equations Together With An Alternative Error Analysis And Convergence Criterion Based On Residual Functions, Seda Çayan, Mehmet Sezer
Turkish Journal of Mathematics
In this study, second order linear Volterra partial integro-differential equation with two- and three-dimensional are solved by collocation method based on Lerch polynomials. This method is composed of the operational matrix and collocation methods, which are based upon the matrix forms of the Lerch polynomials with the parameter $\lambda$ and Taylor polynomials, and their derivatives and integrals. The approximate solutions of the mentioned equations are investigated in terms of the Lerch polynomials the different values of $\lambda$. Also, to verify the accuracy and efficiency of the present method, an alternative convergence criterion along with error analysis depending on residual function …
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)
Mixed Boundary Value Problem For A Class Of Quasi-Linear Elliptic Operators Containing $P$-Laplacian, Junichi Aramaki
Mixed Boundary Value Problem For A Class Of Quasi-Linear Elliptic Operators Containing $P$-Laplacian, Junichi Aramaki
Turkish Journal of Mathematics
In this paper, we consider a mixed boundary value problem to a class of quasi-linear elliptic operators containing a $p$-Laplace operator. We show the existence of a unique weak solution and an estimate. We also demonstrate the continuity of the solution on the given data. Moreover, we consider the dual problem.
The Hewitt Realcompactification Of An Orbit Space, Sadik Eyi̇doğan, Mehmet Onat
The Hewitt Realcompactification Of An Orbit Space, Sadik Eyi̇doğan, Mehmet Onat
Turkish Journal of Mathematics
In this paper, we show that the statement in the study of Srivastava (1987) holds also for the Hewitt realcompactification. The mentioned statement showed that when the action of a finite topological group on a Tychonoff space is given, the Stone-Cech compactification of the orbit space of the action is the orbit space of the Stone-Cech compactification of the space. As an application, we show that Srivastava's result can be obtained using the main theorem of the present study.
Introduction To $N$-Soft Algebraic Structures, Hüseyi̇n Kamaci
Introduction To $N$-Soft Algebraic Structures, Hüseyi̇n Kamaci
Turkish Journal of Mathematics
This paper is dedicated to two main objectives. The first of these is to develop some new operations on $N$-soft set, which is the generalization of soft set. The second is to highlight the concepts of $N$-soft group, $N$-soft ring, $N$-soft ideal, completely semiprime $N$-soft ideal, $N$-soft field and $N$-soft lattice. Moreover, in this study, it is attempted to derive certain properties for these concepts and to analyze the relations between them.
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 …
Unimodality And Linear Recurrences Associated With Rays In The Delannoy Triangle, Said Amrouche, Hacene Belbachir
Unimodality And Linear Recurrences Associated With Rays In The Delannoy Triangle, Said Amrouche, Hacene Belbachir
Turkish Journal of Mathematics
In this paper, we study the unimodality of sequences located in the infinite transversals of the Delannoy triangle. We establish recurrence relations associated with the sum of elements laying along the finite transversals of the cited triangle and we give the generating function of the established sum. Moreover, new identities for the odd and even terms of the Tribonacci sequence are given. Finally, we define a $q$-analogue for the Delannoy numbers and we propose a $q$-deformation of the Tribonacci sequence.
On The Product Of Dilation Of Truncated Toeplitz Operators, Zohra Bendaoud, Nafissa Saouli
On The Product Of Dilation Of Truncated Toeplitz Operators, Zohra Bendaoud, Nafissa Saouli
Turkish Journal of Mathematics
In this paper we study when the product of two dilations of truncated Toeplitz operators gives a dilation of a truncated Toeplitz operator. We will use an approach established in a recent paper written by Ko and Lee. This approach allows us to represent the dilation of the truncated Toeplitz operator via a 2 $\times$ 2 block operator.
Sensitivity Analysis In Parametric Vector Optimization In Banach Spaces Via ${\Tau}^W$-Contingent Derivatives, Thanh Tung Le, Thanh Hung Pham
Sensitivity Analysis In Parametric Vector Optimization In Banach Spaces Via ${\Tau}^W$-Contingent Derivatives, Thanh Tung Le, Thanh Hung Pham
Turkish Journal of Mathematics
This paper is concerned with sensitivity analysis in parametric vector optimization problems via ${\tau}^w$-contingent derivatives. Firstly, relationships between the ${\tau}^w$-contingent derivative of the Borwein proper perturbation map and the ${\tau}^w$-contingent derivative of feasible map in objective space are considered. Then, the formulas for estimating the ${\tau}^w$-contingent derivative of the Borwein proper perturbation map via the ${\tau}^w$-contingent of the constraint map and the Hadamard derivative of the objective map are obtained.
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 …
Ruled Surfaces Obtained By Bending Of Curves, Uğur Gözütok, Hüsnü Anil Çoban, Yasemi̇n Sağiroğlu
Ruled Surfaces Obtained By Bending Of Curves, Uğur Gözütok, Hüsnü Anil Çoban, Yasemi̇n Sağiroğlu
Turkish Journal of Mathematics
We consider a first-order infinitesimal bending of a curve in $\mathbb{R}^3$ to obtain a ruled surface. This paper investigates this kind of ruled surfaces and their properties. Also, we obtain conditions for ruled surfaces obtained by bending to be developable.
On Orthomorphism Elements In Ordered Algebra, Bahri̇ Turan, Hüma Gürkök
On Orthomorphism Elements In Ordered Algebra, Bahri̇ Turan, Hüma Gürkök
Turkish Journal of Mathematics
Let C be an ordered algebra with a unit e. The class of orthomorphism elements Orthe(C) of C was introduced and studied by Alekhno in "The order continuity in ordered algebras". If C = L(G), where G is a Dedekind complete Riesz space, this class coincides with the band Orth(G) of all orthomorphism operators on G. In this study, the properties of orthomorphism elements similar to properties of orthomorphism operators are obtained. Firstly, it is shown that if C is an ordered algebra such that $C_r$, the set of all regular elements of C, is a Riesz space with the …
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.
Wirtinger Type Inequalities For Higher Order Differentiable Functions, Samet Erden
Wirtinger Type Inequalities For Higher Order Differentiable Functions, Samet Erden
Turkish Journal of Mathematics
Inthiswork,we establish a Wirtinger type inequality which gives the relation between the integral of square of its any order derivative via Taylor's formula. Then,we provide a similar inequality for mappings that are elements of Lr space with r > 1. Also, we indicate that special cases of these inequalities give some results presented in the earlier works.
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.
Oscillatory And Asymptotic Behavior Of Third-Order Nonlinear Differential Equations With A Superlinear Neutral Term, Said R. Grace, Iren Jadlovska, Ercan Tunç
Oscillatory And Asymptotic Behavior Of Third-Order Nonlinear Differential Equations With A Superlinear Neutral Term, Said R. Grace, Iren Jadlovska, Ercan Tunç
Turkish Journal of Mathematics
Sufficient conditions are derived for all solutions of a class of third-order nonlinear differential equations with a superlinear neutral term to be either oscillatory or convergent to zero asymptotically. Examples illustrating the results are included and some suggestions for further research are indicated.
A Unique Solution To A Fourth-Order Three-Point Boundary Value Problem, Vedat Suat Ertürk
A Unique Solution To A Fourth-Order Three-Point Boundary Value Problem, Vedat Suat Ertürk
Turkish Journal of Mathematics
In this study, it is aimed to examine the solutions of the following nonlocal boundary value problem \begin{equation*} y^{(4)}+g(x,y)=0,x\in [{c,d}], y(c)=y'(c)=y''(c)=0,y(d)=\lambda y(\xi). \end{equation*} Here, $\xi\in ({c,d}),\lambda \in \mathbb{R},g\in C([{c,d}]\times \mathbb{R},\mathbb{R})$ and $g(x,0)\neq 0.$ It is concentrated on applications of Green's function that corresponds to the above problem to derive existence and uniqueness results for the solutions. One example is also given to demonstrate the results.
From Ordered Semigroups To Ordered Hypersemigroups, Niovi Kehayopulu
From Ordered Semigroups To Ordered Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
In an attempt to show the way we pass from ordered semigroups to ordered hypersemigroups, we examine some well known results of regular and intraregular ordered semigroups in case of ordered hypersemigroups. The corresponding results on hypersemigroups (without order) can also be obtained as application of the results of the present paper. The sets we use in our investigation shows the pointless character of the results.
On A Pair Of Ramanujan's Modular Equations And $P$-$Q$ Theta Functions Of Level 35, K. R. Vasuki, Anusha T
On A Pair Of Ramanujan's Modular Equations And $P$-$Q$ Theta Functions Of Level 35, K. R. Vasuki, Anusha T
Turkish Journal of Mathematics
S. Ramanujan recorded several modular equations and $P$-$Q$ theta function identities in his notebooks and lost notebook without recording the proofs. In this paper, we provide an elementary proof of two modular equations and two $P$-$Q$ theta function identities of level 35, which have been proved by B.C. Berndt using the theory of modular forms.
Eta Quotients Of Level $\Mathbf{12}$ And Weight $\Mathbf{1}$, Ayşe Alaca, Şaban Alaca, Zafer Selcuk Aygin
Eta Quotients Of Level $\Mathbf{12}$ And Weight $\Mathbf{1}$, Ayşe Alaca, Şaban Alaca, Zafer Selcuk Aygin
Turkish Journal of Mathematics
We find all the eta quotients in the spaces $M_1 \Big(\Gamma_0(12), \left(\frac{d}{\cdot}\right) \Big)$ ($d=-3, -4$) of modular forms and determine their Fourier coefficients, where $\left(\frac{d}{\cdot}\right)$ is the Legendre-Jacobi-Kronecker symbol.