Evaluation Of Sums Involving Products Of Gaussian $Q$-Binomial Coefficients With Applications To Fibonomial Sums,
2017
TÜBİTAK
Evaluation Of Sums Involving Products Of Gaussian $Q$-Binomial Coefficients With Applications To Fibonomial Sums, Emrah Kiliç, Helmut Prodinger
Turkish Journal of Mathematics
Sums of products of two Gaussian $q$-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.
Numerical Method For Solving Linear Stochasticito-Volterra Integral Equations Driven By Fractional Brownian Motion Using Hat Functions, Bentol Hoda Hashemi, Morteza Khodabin, Khosrow Maleknejad
Turkish Journal of Mathematics
In this paper, we present a numerical method to approximate the solution of linear stochastic Ito-Volterra integral equations driven by fractional Brownian motion with Hurst parameter $ H \in (0,1)$ based on a stochastic operational matrix of integration for generalized hat basis functions. We obtain a linear system of algebraic equations with a lower triangular coefficients matrix from the linear stochastic integral equation, and by solving it we get an approximation solution with accuracy of order $ \emph{O}(h^2)$. This numerical method shows that results are more accurate than the block pulse functions method where the rate of convergence is $ …
A Two-Obstacle Problem With Variable Exponent And Measure Data,
2017
TÜBİTAK
A Two-Obstacle Problem With Variable Exponent And Measure Data, Hongtao Li, Xiaojuan Chai
Turkish Journal of Mathematics
We consider a two-obstacle problem with measure data. For measures that do not charge sets of zero $p(\cdot)$-capacity, we obtain the existence and uniqueness of the solution. On the other hand, for the measure concentrated on a set with zero $p(\cdot)$-capacity, we prove a nonexistence result in the sense that when one looks for solutions via approximation, one cannot find a reasonable solution; see Theorem 2.3 and Remark 2.1 below.
Simultaneous Strong Proximinality In Banach Spaces,
2017
TÜBİTAK
Simultaneous Strong Proximinality In Banach Spaces, Sahil Gupta, Tulsi Dass Narang
Turkish Journal of Mathematics
Several researchers have discussed the problem of strong proximinality in Banach spaces. In this paper, we generalize the notion of strong proximinality and define simultaneous strong proximinality. It is proved that if $W$ is a simultaneously approximatively compact subset of a Banach space $X$ then $W$ is simultaneously strongly proximinal and the converse holds if the set of all best simultaneous approximations to every bounded subset $S$ of $X$ from $W$ is compact. We show that simultaneously strongly Chebyshev sets are precisely the sets that are simultaneously strongly proximinal and simultaneously Chebyshev. It is also proved that if $F$ and …
Asymptotic For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term,
2017
TÜBİTAK
Asymptotic For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term, Ramzi May
Turkish Journal of Mathematics
In this short note, we recover by a different method the new result due to Attouch, Chbani, Peyrouqet, and Redont concerning the weak convergence as $t\rightarrow+\infty$ of solutions $x(t)$ to the second-order differential equation $x^{\prime\prime}(t)+\frac{K}{t}x^{\prime}(t)+\nabla\Phi(x(t))=0,$ where $K>3$ and $\Phi$\ is a smooth convex function defined on a Hilbert space $\mathcal{H}.$ Moreover, we improve their result on the rate of convergence of $\Phi(x(t))-\min\Phi.$
Choosing The Relaxation Parameter In Sequential Block-Iterativemethods For Linear Systems,
2017
TÜBİTAK
Choosing The Relaxation Parameter In Sequential Block-Iterativemethods For Linear Systems, Touraj Nikazad, Shsghayegh Heidarzade
Turkish Journal of Mathematics
In this paper we introduce two strategies for picking relaxation parameters to control the semiconvergence behavior of a sequential block-iterative method. A convergence analysis is presented. We also demonstrate the performance of our strategies by examples taken from tomographic imaging.
$Cc$-Normal Topological Spaces,
2017
TÜBİTAK
$Cc$-Normal Topological Spaces, Lutfi Kalantan, Manal Alhomieyed
Turkish Journal of Mathematics
A topological space $X$ is called \it $CC$-normal \rm if there exist a normal space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f_{ _A}:A\longrightarrow f(A)$ is a homeomorphism for each countably compact subspace $A\subseteq X$. We will investigate this property and produce some examples to illustrate the relation between $CC$-normality and other weaker kinds of normality.
When Zero-Divisor Graphs Are Divisor Graphs,
2017
TÜBİTAK
When Zero-Divisor Graphs Are Divisor Graphs, Emad Abu Osba, Osama Alkam
Turkish Journal of Mathematics
Let $R$ be a finite commutative principal ideal ring with unity. In this article, we prove that the zero-divisor graph $\Gamma(R)$ is a divisor graph if and only if $R$ is a local ring or it is a product of two local rings with at least one of them having diameter less than $2$. We also prove that $\Gamma(R)$ is a divisor graph if and only if $\Gamma(R[x])$ is a divisor graph if and only if $\Gamma(R[[x]])$ is a divisor graph.
A Goal Programming Approach For Solving The Random Interval Linear Programming Problem,
2017
TÜBİTAK
A Goal Programming Approach For Solving The Random Interval Linear Programming Problem, Ziba Arjmandzadeh, Mohammadreza Safi
Turkish Journal of Mathematics
This paper presents a goal programming model for solving linear programming problems involving random interval coefficients. In this model, a random interval with known characters is considered as the aspiration level (target) of the objective function. The original problem involving random interval parameters is transformed into a biobjective equivalent problem using the proposed model. Defining an auxiliary variable, an approach for solving the biobjective problem is presented. Two numerical examples are carried out to show the efficiency of the proposed model.
Convergence Analysis Of Parabolic Basis Functions For Solving Systems Of Linear And Nonlinear Fredholm Integral Equations,
2017
TÜBİTAK
Convergence Analysis Of Parabolic Basis Functions For Solving Systems Of Linear And Nonlinear Fredholm Integral Equations, Yousef Jafarzadeh, Bagher Keramati
Turkish Journal of Mathematics
In this paper, a computational method based on a hybrid of parabolic and block-pulse functions is proposed to solve a system of linear and special nonlinear Fredholm integral equations of the second kind. The convergence and error bound are analyzed. Numerical examples are given to illustrate the efficiency of the method.
Arithmetic Properties Of $\Ell$-Regular Overpartition Pairs,
2017
TÜBİTAK
Arithmetic Properties Of $\Ell$-Regular Overpartition Pairs, Megadahalli Siddanaika Mahadeva Naika, Chandrappa Shivashankar
Turkish Journal of Mathematics
In this paper, we investigate the arithmetic properties of $\ell$-regular overpartition pairs. Let $\overline{B}_{\ell}(n)$ denote the number of $\ell$-regular overpartition pairs of $n$. We will prove the number of Ramanujan-like congruences and infinite families of congruences modulo 3, 8, 16, 36, 48, 96 for $\overline{B}_3(n)$ and modulo 3, 16, 64, 96 for $\overline{B}_4(n)$. For example, we find that for all nonnegative integers $\alpha$ and $n$, $\overline{B}_{3}(3^{\alpha}(3n+2))\equiv 0\pmod{3}$, $\overline{B}_{3}(3^{\alpha}(6n+4))\equiv 0\pmod{3}$, and $\overline{B}_{4}(8n+7)\equiv 0\pmod{64}$.
Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient,
2017
TÜBİTAK
Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient, Nuretti̇n Irmak
Turkish Journal of Mathematics
In this paper, we solve completely the Diophantine equation \begin{gather} F_{n_{1}}F_{n_{2}}\ldots F_{n_{k}}\pm 1={m\brack t}_{F} \end{gather} for $t=1$ and $t=2$ where $2$ < $n_{1}$ < $n_{2}$ < $\ldots$ < $n_{k}$ positive integers and ${m\brack t}_{F}$ is the Fibonomial coefficient.
Penalty-Free Method For Nonsmooth Constrained Optimization Via Radial Basis Functions,
2017
TÜBİTAK
Penalty-Free Method For Nonsmooth Constrained Optimization Via Radial Basis Functions, Fardin Rahmanpour, Mohammad Mehdi Hosseini, Farid Mohammad Maalek Ghaini
Turkish Journal of Mathematics
We consider a general class of nonlinear constrained optimization problems, where derivatives of the objective function and constraints are unavailable. This property of problems can often impede the performance of optimization algorithms. Most algorithms usually determine a quasi-Newton direction and then use line search techniques. We propose a smoothing algorithm without the need to use a penalty function. A new algorithm is developed to modify the trust region and to handle the constraints based on radial basis functions (RBFs). The value of the objective function is reduced according to the relation of the predicted reduction of constraint violation achieved by …
Generalized $\Ast$-Lie Ideal Of $\Ast$-Prime Ring,
2017
TÜBİTAK
Generalized $\Ast$-Lie Ideal Of $\Ast$-Prime Ring, Seli̇n Türkmen, Neşet Aydin
Turkish Journal of Mathematics
Let $R$ be a $\ast$-prime ring with characteristic not $2,$ $\sigma, \tau:R\rightarrow R$ be two automorphisms, $U$ be a nonzero $\ast$-$\left( \sigma,\tau\right) $-Lie ideal of $R$ such that $\tau~$commutes with $\ast$, and $a,b$ be in $R.$ $\left( i\right) $ If $a\in S_{\ast}\left( R\right) $ and $\left[ U,a\right] =0$, then $a\in Z\left( R\right) $ or $U\subset Z\left( R\right) .$ $\left( ii\right) $ If $a\in S_{\ast}\left( R\right) $ and $\left[ U,a\right] _{\sigma,\tau}\subset$ $C_{\sigma,\tau}$, then $a\in Z\left( R\right) ~$or$~U\subset Z\left( R\right) .$ $\left( iii\right) $ If $U\not \subset Z\left( R\right) $ and $U\not \subset C_{\sigma,\tau}$, then there exists a nonzero $\ast$-ideal $M$ of …
Graph-Directed Fractal Interpolation Functions,
2017
TÜBİTAK
Graph-Directed Fractal Interpolation Functions, Ali̇ Deni̇z, Yunus Özdemi̇r
Turkish Journal of Mathematics
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system, which is called a fractal interpolation function. We generalize the notion of the fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates a corresponding data set in $\mathbb{R}^2$ such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system.
Coefficient Bounds For A New Subclass Of Analytic Bi-Close-To-Convex Functions By Making Use Of Faber Polynomial Expansion,
2017
TÜBİTAK
Coefficient Bounds For A New Subclass Of Analytic Bi-Close-To-Convex Functions By Making Use Of Faber Polynomial Expansion, Fethi̇ye Müge Sakar, Hatun Özlem Güney
Turkish Journal of Mathematics
Recently, in the literature, we can see quite a few papers about general coefficient bounds for subclasses of bi-univalent functions. However, we can find just a few papers about general coefficient estimates for subclasses of bi-close-to-convex functions. In the present study, we give and look into a new subclass of analytic and bi-close-to-convex functions in the open unit disk. Making use of the Faber series, we have an upper bound for the general coefficient of functions in this class. We also demonstrate the invisible behavior of the beginning coefficients of a special subclass of bi-close-to-convex functions.
On The Stochastic Decomposition Property Of Single Server Retrialqueuing Systems,
2017
TÜBİTAK
On The Stochastic Decomposition Property Of Single Server Retrialqueuing Systems, Nawel Arrar, Natalia Djellab, Jean-Bernard Baillon
Turkish Journal of Mathematics
The study of retrial queuing systems presents great analytical difficulties. Detailed results are available for some models, whereas for other models the obtained results revealed poor information and are cumbersome (they contain Laplace transforms, integral expressions, etc.). Therefore, in practice, they present limited performance. Often, to overcome this difficulty, we use an approach based on the stochastic decomposition property that can be possessed by the model. It offers the advantages of simplification of solving complex models. This paper deals with the stochastic decomposition property of an M$^{X}$/G/1 retrial queue with impatient customers and exponential retrial times and of an M/G/1 …
Singular Dirac Systems In The Sobolev Space,
2017
TÜBİTAK
Singular Dirac Systems In The Sobolev Space, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper we construct Weyl's theory for the singular left-definite Dirac systems. In particular, we prove that there exists at least one solution of the system of equations that lies in the Sobolev space. Moreover, we describe the behavior of the solution belonging to the Sobolev space around the singular point.
On Golden Semisymmetric Metric $F$-Connections,
2017
TÜBİTAK
On Golden Semisymmetric Metric $F$-Connections, Aydin Gezer, Çağri Karaman
Turkish Journal of Mathematics
In this paper, we construct a golden semisymmetric metric $F$-connection on a locally decomposable golden Riemannian manifold and investigate some properties of its curvature, conharmonic curvature, Weyl projective curvature, and torsion tensors. Moreover, we define the transposed connection of this connection and study its curvature properties.
Cardinal Hermite Interpolant Multiscaling Functions For Solving A Parabolic Inverse Problem,
2017
TÜBİTAK
Cardinal Hermite Interpolant Multiscaling Functions For Solving A Parabolic Inverse Problem, Elmira Ashpazzadeh, Mehrdad Lakestani, Mohsen Razzaghi
Turkish Journal of Mathematics
An effective method based upon cardinal Hermite interpolant multiscaling functions is proposed for the solution of the one-dimensional parabolic partial differential equation with given initial condition and known boundary conditions and subject to overspecification at a point in the spatial domain. The properties of multiscaling functions are first presented. These properties together with a collocation method are then utilized to reduce the parabolic inverse problem to the solution of algebraic equations. The scheme described is efficient. The numerical results obtained using the present algorithms for test problems show that this method can solve the model effectively.
