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An Effective Prediction Method For Network State Information In Sd-Wan, Erdal Akin, Ferdi̇ Saraç, Ömer Aslan
An Effective Prediction Method For Network State Information In Sd-Wan, Erdal Akin, Ferdi̇ Saraç, Ömer Aslan
Turkish Journal of Electrical Engineering and Computer Sciences
In a software-defined wide area network (SD-WAN), a logically centralized controller is responsible for computing and installing paths in order to transfer packets among geographically distributed locations and remote users. Accordingly, this would necessitate obtaining the global view and dynamic network state information (NSI) of the network. Therefore, the centralized controller periodically collects link-state information from each port of each switch at fixed time periods. While collecting NSI in short periods causes protocol overhead on the controller, collecting in longer periods leads to obtaining inaccurate NSI. In both cases, packet losses are inevitable, which is not preferred for quality of …
Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren
Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren
Turkish Journal of Mathematics
In this paper, we present some relationships between statistical boundedness and statistical monotonicity of a given sequence and its subsequences. The results concerning statistical boundedness and monotonicity presented here are also closely related to earlier results regarding statistical convergence and are dealing with the Lebesgue measure and with the Baire category.
Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan
Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan
Turkish Journal of Mathematics
We study hyperelastic curves known as a generalization of elastic curves in $3-$dimensional lightlike cone which is a degenerate hypersurface in Minkowski $4-$space as critical points of the cone curvature energy functional constructed with the $r-$th power of the cone curvature depending on the given boundary conditions for the natural number $r \geq 2$. We derive the Euler-Lagrange equations for the critical points of this functional that is namely the hyperelastic curves and solve completely the Euler-Lagrange equations by quadratures. Then, we construct Killing vector fields along the hyperelastic curves. Lastly, we give explicitly the hyperelastic curves by integral according …
Hyers-Ulam Stability Of A Certain Fredholm Integral Equation, Alberto Simões, Ponmana Selvan
Hyers-Ulam Stability Of A Certain Fredholm Integral Equation, Alberto Simões, Ponmana Selvan
Turkish Journal of Mathematics
In this paper, by using fixed point theorem we establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of certain homogeneous Fredholm Integral equation of the second kind $$ \phi(x) = \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ and the nonhomogeneous equation $$ \phi(x) = x + \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ for all $x \in [0,1]$ and $0
Examination Of Eigenvalues And Spectral Singularities Of A Discrete Dirac Operator With An Interaction Point, Şeri̇fenur Cebesoy
Examination Of Eigenvalues And Spectral Singularities Of A Discrete Dirac Operator With An Interaction Point, Şeri̇fenur Cebesoy
Turkish Journal of Mathematics
In this paper, the main content is the consideration of the concepts of eigenvalues and spectral singularities of an operator generated by a discrete Dirac system in $\ell_{2}(\mathbb{Z},\mathbb{C}^{2})$ with an interior interaction point. Defining a transfer matrix $ M $ enables us to present a relationship between the $ M_{22} $ component of this matrix and Jost functions of mentioned Dirac operator so that its eigenvalues and spectral properties can be studied. Finally, some special cases are examined where the impulsive condition possesses certain symmetries.
To The Solution Of Integro-Differential Equations With Nonlocal Conditions, Kamil R. Aida-Zade, Vagif M. Abdullayev
To The Solution Of Integro-Differential Equations With Nonlocal Conditions, Kamil R. Aida-Zade, Vagif M. Abdullayev
Turkish Journal of Mathematics
We investigate linear integro-differential equations with ordinary derivatives. The kernels of the integrands depend only on the variable of integration, and the conditions involve the terms with the point and integral values of the unknown function. We drive necessary and sufficient conditions for the existence and uniqueness of the solution of the problem, which can be used both for analytical and numerical solutions. We present the results of solving an illustrative test problem.
Upper And Lower Bounds Of The $A$-Berezin Number Of Operators, Mualla Bi̇rgül Huban
Upper And Lower Bounds Of The $A$-Berezin Number Of Operators, Mualla Bi̇rgül Huban
Turkish Journal of Mathematics
Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\mathcal{H}$. Any positive operator $A$ induces a semiinner product on $\mathcal{H}$ defined by $\left\langle x,y\right\rangle _{A}:=\left\langle Ax,y\right\rangle _{\mathcal{H}},$ $\forall x,y\in\mathcal{H}.$ For any $T\in\mathcal{B}\left( \mathcal{H}\left( \Omega\right) \right) $, its $A$-Berezin symbol $\widetilde{T}^{_{A}}$ is defined on $\Omega$ by $\widetilde{T}^{_{A}% }:=\left\langle T\widehat{K}_{\lambda},\widehat{K}_{\lambda}\right\rangle _{A},$ $\lambda\in\Omega,$where $\widehat{K}_{\lambda}$ is the normalized reproducing kernel of $\mathcal{H}$. In this paper, we introduce the notions $\left( A,r\right) $-adjoint of operators and $A$-Berezin number of operators on the reproducing kernel Hilbert space and prove some upper and lower bounds of the $A$-Berezin numbers of operators. In …
Commutativity Degree Of Crossed Modules, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan, Alper Odabaş
Commutativity Degree Of Crossed Modules, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan, Alper Odabaş
Turkish Journal of Mathematics
In this work, we define the notion of commutativity degree of crossed modules and find some bounds on commutativity degree for special types of crossed modules. Also, we give a function for finding commutativity degree of crossed modules in GAP and classify crossed modules by using this function.
Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad
Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad
Turkish Journal of Mathematics
In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales $$ \begin{aligned} &\mathcal{T}_α^{\Delta}\big[\mathcal{T}_β^{\Delta}\big(\vartheta_\mathtt{n}(t)\big)\big]=\varphi(t)\mathtt{f}_\mathtt{n}\left(\vartheta_{\mathtt{n}+1}(t)\right),~t\in(0,1)_\mathbb{T},~1
Uniformly Convergent Finite Difference Method For Reaction-Diffusion Type Third Order Singularly Perturbed Delay Differential Equation, Rajendran Mahendran, Veerasamy Subburayan
Uniformly Convergent Finite Difference Method For Reaction-Diffusion Type Third Order Singularly Perturbed Delay Differential Equation, Rajendran Mahendran, Veerasamy Subburayan
Turkish Journal of Mathematics
A class of third order reaction-diffusion type singularly perturbed ordinary delay differential equations is considered in this article. A fitted finite difference method on Shishkin mesh is suggested to solve the problem. Moreover, we present a class of nonlinear problems. An error estimation is obtained based on the maximum norm and it is of almost first order convergence. Numerical results are given to support theoretical claims.
Determination Of A Differential Pencil Frominterior Spectral Data On A Union Of Two Closed Intervals, İbrahi̇m Adalar
Determination Of A Differential Pencil Frominterior Spectral Data On A Union Of Two Closed Intervals, İbrahi̇m Adalar
Turkish Journal of Mathematics
In this paper, we consider a quadratic pencil of Sturm-Liouville operator on closed sets. We study an interior-inverse problem for this kind operator and give a uniqueness theorem with an appropriate example.
Discrete Impulsive Sturm-Liouville Equation With Hyperboliceigenparameter, Turhan Köprübaşi, Yelda Aygar Küçükevci̇li̇oğlu
Discrete Impulsive Sturm-Liouville Equation With Hyperboliceigenparameter, Turhan Köprübaşi, Yelda Aygar Küçükevci̇li̇oğlu
Turkish Journal of Mathematics
Let $L$ denote the selfadjoint difference operator of second order with boundary and impulsive conditions generated in $\ell _{2}\left( %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion \right) $ by \begin{equation*} a_{n-1}y_{n-1}+b_{n}y_{n}+a_{n}y_{n+1}=\left( 2\cosh z\right) y_{n}\text{ },% \text{ }n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion \setminus \left\{ k-1,k,k+1\right\} , \end{equation*}% \begin{equation*} \begin{array}{c} y_{0}=0\text{ }, \\ \left\{ \begin{array}{c} y_{k+1}=\theta _{1}y_{k-1} \\ \bigtriangleup y_{k+1}=\theta _{2}\bigtriangledown y_{k-1} \end{array}% \right. ,\text{ }\theta _{1},\theta _{2}\in %TCIMACRO{\U{211d}}% %BeginExpansion \mathbb{R}, %EndExpansion \end{array}% \end{equation*} where $\left\{ a_{n}\right\} _{n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion },$ $\left\{ b_{n}\right\} _{n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion }$ are real sequences and $\bigtriangleup ,\bigtriangledown $ are respectively forward …
Limited Frequency Band Diffusive Representation For Nabla Fractional Order Transfer Functions, Yiheng Wei, Yingdong Wei, Yuqing Hou, Xuan Zhao
Limited Frequency Band Diffusive Representation For Nabla Fractional Order Transfer Functions, Yiheng Wei, Yingdong Wei, Yuqing Hou, Xuan Zhao
Turkish Journal of Mathematics
Though infinite-dimensional characteristic is the natural property of nabla fractional order systems and it is the foundation of stability analysis, controller synthesis and numerical realization, there are few research focusing on this topic. Under this background, this paper concerns the diffusive representation of nabla fractional order systems. Firstly, several variants are developed for the elementary equality in frequency domain, i.e. $\frac{1}{s^\alpha} = \int_0^{ + \infty } {\frac{{{\mu _\alpha }( \omega )}}{{s + \omega }}{\rm{d}}\omega }$. Afterwards, the limited frequency band diffusive representation and the unit impulse response are derived for a series of nabla fractional order transfer functions. Finally, an …
Existence Of Solutions For An Infinite System Of Tempered Fractional Order Boundary Value Problems In The Spaces Of Tempered Sequences, Khuddush Mahammad, Rajendra Prasad Kapula, Leela Doddi
Existence Of Solutions For An Infinite System Of Tempered Fractional Order Boundary Value Problems In The Spaces Of Tempered Sequences, Khuddush Mahammad, Rajendra Prasad Kapula, Leela Doddi
Turkish Journal of Mathematics
This paper deals with infinite system of nonlinear two-point tempered fractional order boundary value problems $$ \begin{aligned} {}^\mathtt{RL}_{~0}\mathbb{D}^{δ_2,\ell}_\mathtt{z}\Big[\mathtt{p}_\mathtt{j}(\mathtt{z})&{}^\mathtt{RL}_{~0}\mathbb{D}^{δ_1,\ell}_\mathtt{z} \vartheta_\mathtt{j}(\mathtt{z})\Big]=λ_\mathtt{j}\varphi\big(\mathtt{z},\vartheta(\mathtt{z})\big),\, \mathtt{z}\in[0,\mathtt{T}], δ_1,δ_2\in(1,2),\\ &\hskip0.25cm\vartheta_\mathtt{j}(0)=\lim_{\mathtt{z}\to0}\left[{}^\mathtt{RL}_{~0}\mathbb{D}^{δ_1,\ell}_\mathtt{z}(e^{\ell\mathtt{z}}\vartheta_\mathtt{j}(\mathtt{z}))\right]=0,\\ &e^{\ell\mathtt{T}}\vartheta_\mathtt{j}(\mathtt{T})=\lim_{\mathtt{z}\to\mathtt{T}}\left[{}^\mathtt{RL}_{~0}\mathbb{D}^{δ_1,\ell}_\mathtt{z}(e^{\ell\mathtt{z}}\vartheta_\mathtt{j}(\mathtt{z}))\right]=0, \end{aligned} $$ where $\mathtt{j}\in\{1,2,3,\cdot\cdot\cdot\},\,\ell\ge 0,$ ${}^\mathtt{RL}_{~0}\mathbb{D}^{\star,\ell}_\mathtt{z}$ denotes the Riemann--Liouville tempered fractional derivative of order $\star\in\{δ_1,δ_2\}$, $\vartheta(\mathtt{z})=\left(\vartheta_\mathtt{j}(\mathtt{z})\right)_{\mathtt{j}=1}^{\infty},$ $\varphi_\mathtt{j}:[0,\mathtt{T}]\to[0,\mathtt{T}]$ are continuous and we derive sufficient conditions for the existence of solutions to the system via the Hausdorff measure of noncompactness and Meir-Keeler fixed point theorem in tempered sequence spaces.
Solving Nonlinear Integro-Differential Equations Using Numerical Method, Nedjem Eddine Ramdani, Sandra Pinelas
Solving Nonlinear Integro-Differential Equations Using Numerical Method, Nedjem Eddine Ramdani, Sandra Pinelas
Turkish Journal of Mathematics
The aim of this paper is to establish conditions for the existence and uniqueness of the solution of a nonlinear integro-differential equation. Moreover, it is to propose a quadrature method in order to find an approximate solution and establish the convergence of the method. We conclude by providing the algorithm and some numerical simulation to confirm our theoretical results.
The Complex Error Functions And Various Extensive Results Together With Implications Pertaining To Certain Special Functions, Hüseyi̇n Irmak, Praveen Agarwal, Ravi P. Agarwal
The Complex Error Functions And Various Extensive Results Together With Implications Pertaining To Certain Special Functions, Hüseyi̇n Irmak, Praveen Agarwal, Ravi P. Agarwal
Turkish Journal of Mathematics
The error functions play very important roles in science and technology. In this investigation, the error functions in the complex plane will be introduced, then comprehensive results together with several nonlinear implications in relation to the related complex functions will be indicated, and some possible special results of them will be next presented. Furthermore, various interesting or important suggestions will be also made for the scientific researchers who are interested in this topic.
A Discussion On The Existence And Uniqueness Analysis For The Coupled Two-Term Fractional Differential Equations, Sachin Kumar Verma, Ramesh Kumar Vats, Avadhesh Kumar, Velusamy Vijayakumar, Anurag Shukla
A Discussion On The Existence And Uniqueness Analysis For The Coupled Two-Term Fractional Differential Equations, Sachin Kumar Verma, Ramesh Kumar Vats, Avadhesh Kumar, Velusamy Vijayakumar, Anurag Shukla
Turkish Journal of Mathematics
This paper mainly concentrates on the study of a new boundary value problem of coupled nonlinear two-term fractional differential system. We make use of the theories on fractional calculus and fixed point approach to derive the existence and uniqueness results of the considered two-term fractional systems. To confirm the application of the stated outcomes, two examples are provided.
Mathematical Analysis Of Local And Global Dynamics Of A New Epidemic Model, Sümeyye Çakan
Mathematical Analysis Of Local And Global Dynamics Of A New Epidemic Model, Sümeyye Çakan
Turkish Journal of Mathematics
In this paper, we construct a new $SEIR$ epidemic model reflecting the spread of infectious diseases. After calculating basic reproduction number $% \mathcal{R}_{0}$ by the next generation matrix method, we examine the stability of the model. The model exhibits threshold behavior according to whether the basic reproduction number $\mathcal{R}_{0}$ is greater than unity or not. By using well-known Routh-Hurwitz criteria, we deal with local asymptotic stability of equilibrium points of the model according to $% \mathcal{R}_{0}.$ Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle's Invariance Principle associated with Lyapunov …
A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya
A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya
Turkish Journal of Mathematics
In this study, a new class of sequential fractional differential problems of pantograph type is introduced. New existence and uniqueness criteria for the existence and uniqueness of solutions are discussed. Some existence results using Darbo's fixed point and measure of noncompactness are also studied. At the end, two illustrative examples are discussed.
On Extended Interpolative Single And Multivalued $F$-Contractions, İsa Yildirim
On Extended Interpolative Single And Multivalued $F$-Contractions, İsa Yildirim
Turkish Journal of Mathematics
The main objective of this paper is to study an extended interpolative single and multivalued Hardy-Rogers type $F$-contractions in complete metric spaces. We prove some fixed point theorems for such mappings. Further, we give an application to integral equations to verify our main results. The results presented in this paper improve the recent works of Karapinar et al. [12] and Mohammadi et al. [16].
$P$-Strong Convergence With Respect To An Orlicz Function, Ni̇lay Şahi̇n Bayram
$P$-Strong Convergence With Respect To An Orlicz Function, Ni̇lay Şahi̇n Bayram
Turkish Journal of Mathematics
The concepts of strong convergence, statistical convergence, and uniform integrability are of some interest in convergence theories. Recently Ünver and Orhan [19] have introduced the concepts of $P$-strong and $P$-statistical convergences with the help of power series methods and established a relationship between them. In the present paper, we introduce the notion of $P$-strong convergence with respect to an Orlicz function and prove that all these three concepts are boundedly equivalent provided that Orlicz function satisfies $\triangle _{2}-$condition. We also get an improvement of this result by using the concept of uniform integrability.
Two Classes Of Permutation Polynomials With Niho Exponents Over Finite Fields With Even Characteristic, Qian Liu
Turkish Journal of Mathematics
In this paper, by transforming the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations, we investigate the permutation behavior of the type $f(x)=x+x^{2^{3m}-2^m+1}+x^{2^{4m}-2^{3m}+2^m}$ over $F_{2^{4m}}$ and $f(x)=x+x^{2^m}+x^{2^{m+1}-1}+ax^{2^{2m}-2^m+1}$ over $F_{2^{2m}}$, respectively.
On A Class Of Generalized Humbert-Hermite Polynomials Via Generalized Fibonacci Polynomials, Mahmood Ahmad Pathan, Wassem Ahmad Khan
On A Class Of Generalized Humbert-Hermite Polynomials Via Generalized Fibonacci Polynomials, Mahmood Ahmad Pathan, Wassem Ahmad Khan
Turkish Journal of Mathematics
A unified presentation of a class of Humbert's polynomials in two variables which generalizes the well known class of Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinney, Horadam-Pethe, Djordjevi${\acute{c}}$, Gould, Milovanovi${\acute{c}}$ and Djordjevi${\acute{c}}$, Pathan and Khan polynomials and many not so called 'named' polynomials has inspired the present paper. We define here generalized Humbert-Hermite polynomials of two variables. Several expansions of Humbert-Hermite polynomials, Hermite-Gegenbaurer (or ultraspherical) polynomials
Construction Of Minimal Linear Codes With Few Weights From Weakly Regular Plateaued Functions, Ahmet Sinak
Construction Of Minimal Linear Codes With Few Weights From Weakly Regular Plateaued Functions, Ahmet Sinak
Turkish Journal of Mathematics
The construction of (minimal) linear codes from functions over finite fields has been greatly studied in the literature, since determining the parameters of codes based on functions is rather easy due to the nice structures of functions. In this paper, we derive $3$-weight and $4$-weight linear codes from weakly regular plateaued functions in the recent construction method of linear codes over the odd characteristic finite fields. The Hamming weights and weight distributions for codes are, respectively, determined by using the Walsh transform values and Walsh distributions of the employed functions. We also derive projective $3$-weight punctured codes with good parameters …
Multiplicative Conformable Fractional Dirac System, Sertaç Göktaş, Hi̇kmet Kemaloğlu, Emrah Yilmaz
Multiplicative Conformable Fractional Dirac System, Sertaç Göktaş, Hi̇kmet Kemaloğlu, Emrah Yilmaz
Turkish Journal of Mathematics
In multiplicative fractional calculus, the well-known Dirac system in fractional calculus is redefined. The aim of this study is to analyze some spectral properties such as self-adjointness of the operator, structure of all eigenvalues, orthogonality of distinct eigenfunctions, etc. for this system. Moreover, Green's function in multiplicative case is reconstructed for this system.
Some Properties Of The Matrix Wiener Transform With Related Topics On Hilbert Space, Hyun Soo Chung
Some Properties Of The Matrix Wiener Transform With Related Topics On Hilbert Space, Hyun Soo Chung
Turkish Journal of Mathematics
Main purpose of this paper is to obtain fundamental relationships for the integrals and the matrix Wiener transforms on Hilbert space. Using some technics and properties of matrices of real numbers, we state some algebraic structure of matrices. We then establish evaluation formulas with examples. Furthermore, we define the matrix Wiener transform, and investigate some properties of the matrix Wiener transform. Finally, we establish relationships for the matrix Wiener transform.
Application Of Gegenbauer Polynomials For Biunivalent Functions Defined By Subordination, Fethi̇ye Müge Sakar, Saqib Hussain, Ibrar Ahmad
Application Of Gegenbauer Polynomials For Biunivalent Functions Defined By Subordination, Fethi̇ye Müge Sakar, Saqib Hussain, Ibrar Ahmad
Turkish Journal of Mathematics
We present and investigate a new subclass of biunivalent functions by applying Gegenbouer polynomials in this paper. Also, we find nonsharp estimates on the first two coefficients $\left \vert b_{0}\right \vert $ and $% \left \vert b_{1}\right \vert $ for functions belonging to this subclass. Furthermore, the Fekete-Szegö inequality $\left \vert b_{1}-\eta b_{0}^{2}\right \vert $ for this subclass is obtained. We also point out some consequences of results.
Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie
Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie
Turkish Journal of Mathematics
This paper focuses on the oscillation criteria for the third-order neutral differential equations with unbounded neutral coefficients and distributed deviating arguments. Using comparison principles, new sufficient conditions improve some known existing results substantially due to less constraints on the considered equation. At last, two examples are established to illustrate the given theorems.
On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya
On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya
Turkish Journal of Mathematics
By making use of the both Mittag-Leffler and Wright function, we establish a new subfamily of the class $S_{\vartheta }$ of $\vartheta $-spirallike functions. The main object of the paper is to provide sufficient conditions for a function to be in this newly established class and to discuss subordination outcomes.
Boundedness For Variable Fractional Integral Operators And Their Commutators On Herz-Hardy Spaces With Variable Exponent, Yinping Xin
Turkish Journal of Mathematics
Let $E\subset\mathbb{R}^n$ be a bounded open set. In this paper, we establish the boundedness of variable fractional integral operators and their commutators on variable Herz-Hardy spaces $H\dot{K}^{\alpha(\cdot),q(\cdot)}_{p(\cdot)}(E)$ with three variable exponents by using the atomic decomposition.