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2017

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Articles 961 - 990 of 1334

Full-Text Articles in Mathematics

Characterization Of Substantially And Quasi-Substantially Efficient Solutions In Multiobjective Optimization Problems, Latif Pourkarimi, Masoud Karimi Jan 2017

Characterization Of Substantially And Quasi-Substantially Efficient Solutions In Multiobjective Optimization Problems, Latif Pourkarimi, Masoud Karimi

Turkish Journal of Mathematics

In this paper, we study the notion of substantial efficiency for a given multiobjective optimization problem. We provide two characterizations for substantially efficient solutions: the first one is based on a scalar problem and the second one is in terms of a stability concept. Moreover, this paper introduces the notion of quasi-substantial efficiency. Similar to those of substantial efficiency, two characterizations for quasi-substantially efficient solutions are obtained.

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Computation Of Conditional Expectation Based On The Multidimensional J-Process Using Malliavin Calculus Related To Pricing American Options, Mohamed Kharrat Jan 2017

Computation Of Conditional Expectation Based On The Multidimensional J-Process Using Malliavin Calculus Related To Pricing American Options, Mohamed Kharrat

Turkish Journal of Mathematics

In this work, we extend the uni-dimensional results, already found by Jerbi and Kharrat, for the multidimensional case: we compute the Malliavin weights related to the conditional expectation $\mathbb{E}(P_{t}(X_{t}) (X_{s}))$ for $0 \leq s \leq t$, where the only state variable follows a multidimensional J-process.

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Approximation Of Analytic Functions Of Severalvariables By Linear K-Positive Operators, Tüli̇n Coşkun Jan 2017

Approximation Of Analytic Functions Of Severalvariables By Linear K-Positive Operators, Tüli̇n Coşkun

Turkish Journal of Mathematics

We investigate the approximation of analytic functions of several variables in polydiscs by the sequences of linear k-positive operators in the Gadjiev sense.

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Regularity Of Solutions Of The Anisotropic Hyperbolic Heat Equation With Nonregular Heat Sources And Homogeneous Boundary Conditions, Juan Antonio López Molina, Macarena Trujillo Jan 2017

Regularity Of Solutions Of The Anisotropic Hyperbolic Heat Equation With Nonregular Heat Sources And Homogeneous Boundary Conditions, Juan Antonio López Molina, Macarena Trujillo

Turkish Journal of Mathematics

We study regularity properties for the solution of homogeneous boundary value problems for the anisotropic hyperbolic heat equation in the case of infinitely differentiable coefficients but irregular distributions as internal heat sources.

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Factorization With Respect To A Divisor-Closed Multiplicative Submonoid Of A Ring, Ashkan Nikseresht, Abdulrasool Azizi Jan 2017

Factorization With Respect To A Divisor-Closed Multiplicative Submonoid Of A Ring, Ashkan Nikseresht, Abdulrasool Azizi

Turkish Journal of Mathematics

In this paper, we consider factorizations of elements of a divisor-closed multiplicative submonoid of a ring and also factorizations of elements of a module as a product of elements coming from a divisor-closed multiplicative submonoid of the ring and another element of the module. In particular, we study uniqueness and some other properties of such factorizations and investigate the behavior of these factorizations under direct sum and product of rings and modules.

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Ranges And Kernels Of Derivations, Mohamed Ech Chad Jan 2017

Ranges And Kernels Of Derivations, Mohamed Ech Chad

Turkish Journal of Mathematics

In this paper we establish some properties concerning the class of operators $A\in {\cal L(H)}$ that satisfy $\overline{ { \cal R }(\delta_{A})}\cap\{A\}'=\{0\}$, where $\overline{ { \cal R }(\delta_{A})}$ is the norm closure of the range of the inner derivation $\delta_{A},$ defined on ${\cal L(H)}$ by $\delta_{A}(X)=AX-XA$. Here ${\cal H}$ stands for a Hilbert space; as a consequence, we show that the set $\{ A \in { \cal L(H)}\;\;/\;\;\overline{ { \cal R }(\delta_{A})}\cap\{A\}'=\{0\} \}$ is norm-dense. We also describe some classes of operators $A,\;B$ for which we have $\overline{ { \cal R }(\delta_{A,B})}\cap\ker(\delta_{A^{\ast},B^{\ast}})=\{0\}$ ($\ker(\delta_{A^{\ast},B^{\ast}})$ is the kernel of the generalized derivation …

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A Note On The Generalized Matsumoto Relation, Eli̇f Dalyan, Eli̇f Medetoğullari, Mehmetci̇k Pamuk Jan 2017

A Note On The Generalized Matsumoto Relation, Eli̇f Dalyan, Eli̇f Medetoğullari, Mehmetci̇k Pamuk

Turkish Journal of Mathematics

~We give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists.

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The Hahn-Banach Theorem For $A$-Linear Operators, Bahri̇ Turan, Fatma Bi̇li̇ci̇ Jan 2017

The Hahn-Banach Theorem For $A$-Linear Operators, Bahri̇ Turan, Fatma Bi̇li̇ci̇

Turkish Journal of Mathematics

In this short paper we present a generalization of the Hahn--Banach extensiontheorem for $A$-linear operators. Some theoretical applications andresults are given.

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On The Rate Of $L_P$-Convergence Of Balakrishnan—Rubin-Type Hypersingular Integrals Associated To The Gauss-Weierstrass Semigroup, Meli̇h Eryi̇ği̇t, Seli̇m Çobanoğlu Jan 2017

On The Rate Of $L_P$-Convergence Of Balakrishnan—Rubin-Type Hypersingular Integrals Associated To The Gauss-Weierstrass Semigroup, Meli̇h Eryi̇ği̇t, Seli̇m Çobanoğlu

Turkish Journal of Mathematics

We introduce a family of Balakrishnan—Rubin-type hypersingular integrals depending ona parameter $\varepsilon$ and generated by the Gauss—Weierstrass semigroup. Then the connection between the order of $L_p$—smoothness of a $L_p$—function $\varphi$and the rate of $L_p$-convergence of these families to $\varphi$, as $\varepsilon$ tends to 0, is obtained.

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Generalized Drazin Invertibility Of The Product And Sum Of Two Elements In A Banach Algebra And Its Applications, Honglin Zou, Dijana Mosic, Jianlong Chen Jan 2017

Generalized Drazin Invertibility Of The Product And Sum Of Two Elements In A Banach Algebra And Its Applications, Honglin Zou, Dijana Mosic, Jianlong Chen

Turkish Journal of Mathematics

Let $a,b$ be two commutative generalized Drazin invertible elements in a Banach algebra; the expressions for the generalized Drazin inverse of the product $ab$ and the sum $a+b$ were studied in some current literature on this subject. In this paper, we generalize these results under the weaker conditions $a^{2}b=aba$ and $b^{2}a=bab$. As an application of our results, we obtain some new representations for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, extending some recent works.

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Asymptotic Stability Of Solutions For A Certain Non-Autonomous Second-Order Stochastic Delay Differential Equation, Ahmed Mohamed Abou-El-Ela, Abdel-Rahiem Sadek, Ayman Mohammed Mahmoud, Eman Sayed Farghaly Jan 2017

Asymptotic Stability Of Solutions For A Certain Non-Autonomous Second-Order Stochastic Delay Differential Equation, Ahmed Mohamed Abou-El-Ela, Abdel-Rahiem Sadek, Ayman Mohammed Mahmoud, Eman Sayed Farghaly

Turkish Journal of Mathematics

In this paper, sufficient criteria that guarantee the existence of stochastic asymptotic stability of the zero solution of the nonautonomous second-order stochastic delay differential equation \eqref{3e1} were established with the aid of a suitable Lyapunov functional. Two examples are given in the last section to illustrate our main result.

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$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren Jan 2017

$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren

Turkish Journal of Mathematics

Let $\mathcal{V,W}$ be two classes of modules. In this paper, we introduce and study $\mathcal{VW}$-Gorenstein complexes as a common generalization of $\mathcal{W}$-complexes, Gorenstein projective (resp., Gorenstein injective) complexes, and $G_C$-projective (resp., $G_C$-injective) complexes. It is shown that under certain hypotheses a complex $X$ is $\mathcal{VW}$-Gorenstein if and only if each $X^n$ is a $\mathcal{VW}$-Gorenstein module. This result unifies the corresponding results of the aforementioned complexes. As an application, the stability of $\mathcal{VW}$-Gorenstein complexes is explored.

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Application Of A Generalised Function Method To The Infinitely Deep Square Well Problem, Basri̇ Ünal Jan 2017

Application Of A Generalised Function Method To The Infinitely Deep Square Well Problem, Basri̇ Ünal

Turkish Journal of Mathematics

The Schrödinger equation for the eigenvalues of the infinitely deep square well potential is solved within the class of generalised functions. It is found that the ground state consists of a step function like eigenfunction with the eigenvalue zero.

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The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç Jan 2017

The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç

Turkish Journal of Mathematics

The intention of this article is to investigate the most important inequalities of $m$-convex functions without using their derivatives. The article also provides a brief survey of general properties of $m$-convex functions.

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Dynamics Of A Predator-Prey System With A Mate-Finding Allee Effect On Prey, Ruiwen Wu, Xiuxaing Liu Jan 2017

Dynamics Of A Predator-Prey System With A Mate-Finding Allee Effect On Prey, Ruiwen Wu, Xiuxaing Liu

Turkish Journal of Mathematics

We consider a predator--prey system with nonmonotonic functional response and a hyperbolic type of mate-finding Allee effect on prey. A detailed mathematical analysis of the system, including the stability and a series of bifurcations (a saddle-node, a Hopf, and a Bogdanov--Takens bifurcation), has been given. The mathematical results show that the system is highly sensitive to the parameters and initial status. It exhibits a stable limit cycle, or different types of heteroclinic curves, or a homoclinic loop when parameters take suitable values.

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Generalized Trial Equation Method And Its Applications Toduffing And Poisson-Boltzmann Equations, Ali̇ Özyapici Jan 2017

Generalized Trial Equation Method And Its Applications Toduffing And Poisson-Boltzmann Equations, Ali̇ Özyapici

Turkish Journal of Mathematics

The trial equation method, which was proposed by Cheng-Shi Liu, is a very powerful method for solving nonlinear differential equations. After the original trial method, some modified versions of the trial equation method were introduced and applied to some famous nonlinear differential equations. Although each modified trial equation method provides a different perspective, they have some weaknesses according to the given differential equations. This is the main reason for introducing modified trial equation methods. This study aims to define a general representation of trial methods for solving nonlinear differential equations. The generalized trial equation method consists of the simple trial …

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Stability Of Nonmonotone Critical Traveling Waves Forspatially Discrete Reaction-Diffusion Equations With Time Delay, Ge Tian, Guobao Zhang, Zhao-Xing Yang Jan 2017

Stability Of Nonmonotone Critical Traveling Waves Forspatially Discrete Reaction-Diffusion Equations With Time Delay, Ge Tian, Guobao Zhang, Zhao-Xing Yang

Turkish Journal of Mathematics

This paper is concerned with the existence and stability of critical traveling waves (waves with minimal speed $c=c_*$) for a nonmonotone spatially discrete reaction-diffusion equation with time delay. We first show the existence of critical traveling waves by a limiting argument. Then, using the technical weighted energy method with some new variations, we prove that the critical traveling waves $\phi(x+c_{*}t)$ (monotone or nonmonotone) are time-asymptotically stable when the initial perturbations are small in a certain weighted Sobolev norm.

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Evaluation Of Sums Involving Products Of Gaussian $Q$-Binomial Coefficients With Applications To Fibonomial Sums, Emrah Kiliç, Helmut Prodinger Jan 2017

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.

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Numerical Method For Solving Linear Stochasticito-Volterra Integral Equations Driven By Fractional Brownian Motion Using Hat Functions, Bentol Hoda Hashemi, Morteza Khodabin, Khosrow Maleknejad Jan 2017

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 $ …

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A Two-Obstacle Problem With Variable Exponent And Measure Data, Hongtao Li, Xiaojuan Chai Jan 2017

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.

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Simultaneous Strong Proximinality In Banach Spaces, Sahil Gupta, Tulsi Dass Narang Jan 2017

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 …

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Asymptotic For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term, Ramzi May Jan 2017

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 $\Phi(x(t))-\min\Phi.$

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Choosing The Relaxation Parameter In Sequential Block-Iterativemethods For Linear Systems, Touraj Nikazad, Shsghayegh Heidarzade Jan 2017

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.

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$Cc$-Normal Topological Spaces, Lutfi Kalantan, Manal Alhomieyed Jan 2017

$Cc$-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.

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When Zero-Divisor Graphs Are Divisor Graphs, Emad Abu Osba, Osama Alkam Jan 2017

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.

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A Goal Programming Approach For Solving The Random Interval Linear Programming Problem, Ziba Arjmandzadeh, Mohammadreza Safi Jan 2017

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.

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Convergence Analysis Of Parabolic Basis Functions For Solving Systems Of Linear And Nonlinear Fredholm Integral Equations, Yousef Jafarzadeh, Bagher Keramati Jan 2017

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.

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Arithmetic Properties Of $\Ell$-Regular Overpartition Pairs, Megadahalli Siddanaika Mahadeva Naika, Chandrappa Shivashankar Jan 2017

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 $\overline{B}_{4}(8n+7)\equiv 0\pmod{64}$.

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Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient, Nuretti̇n Irmak Jan 2017

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.

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Penalty-Free Method For Nonsmooth Constrained Optimization Via Radial Basis Functions, Fardin Rahmanpour, Mohammad Mehdi Hosseini, Farid Mohammad Maalek Ghaini Jan 2017

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 …

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