Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Articles 4861 - 4890 of 10319

Full-Text Articles in Physical Sciences and Mathematics

Multilayer Authorization Model And Analysis Of Authorization Methods, Alper Uğur, İbrahi̇m Soğukpinar Jan 2016

Multilayer Authorization Model And Analysis Of Authorization Methods, Alper Uğur, İbrahi̇m Soğukpinar

Turkish Journal of Electrical Engineering and Computer Sciences

There are various methods proposed in the literature to provide authorization control in workflows and information systems. Authorization implementations have deficiencies based on procedural scope. Basic login mechanisms grant system-wide access; the provided margins are broad. Access control lists provide limited definition on access restrictions; the authorization is bounded by these definitions. Role based authorizations do not cover regulations in institutions where the regulations describe specific operations and their operational procedures in institutional workflows. The proposed multilayer authorization model depicts the attributes of authorization mechanisms and analyzes the methods according to their authorization capabilities and contributions to the reliability of …


Design And Implementation Of A Genetic Algorithm Ip Core On An Fpga For Path Planning Of Mobile Robots, Adem Tuncer, Mehmet Yildirim Jan 2016

Design And Implementation Of A Genetic Algorithm Ip Core On An Fpga For Path Planning Of Mobile Robots, Adem Tuncer, Mehmet Yildirim

Turkish Journal of Electrical Engineering and Computer Sciences

This paper presents a hardware realization of a genetic algorithm (GA) for the path planning problem of mobile robots on a field programmable gate array (FPGA). A customized GA intellectual property (IP) core was designed and implemented on an FPGA. A Xilinx xupv5-lx110t FPGA device was used as the hardware platform. The proposed GA IP core was applied to a Pioneer 3-DX mobile robot to confirm its path planning performance. For localization tasks, a camera mounted on the ceiling of the laboratory was utilized to receive images and allow the robot to determine its own location and the obstacles in …


Video Temporal Error Concealment Using Improved Directional Boundary Matching Algorithm, Seyed Mojtaba Marvasti-Zadeh, Hossein Ghanei-Yakhdan Jan 2016

Video Temporal Error Concealment Using Improved Directional Boundary Matching Algorithm, Seyed Mojtaba Marvasti-Zadeh, Hossein Ghanei-Yakhdan

Turkish Journal of Electrical Engineering and Computer Sciences

Nowadays some systems such as multimedia systems try to present a high quality of digital videos every day. Because of the possible errors in communication channels, compressed video data would be damaged in the sending process. Error concealment is a useful technique for concealing the effects of sending errors at the decoder. In this paper, an improved directional boundary matching algorithm is presented, in which by using adjacent macroblocks (MBs) of the damaged MB a direction is identified for each boundary. Then every boundary of candidate MBs is compared to an identified direction. Finally, the candidate motion vector (MV) that …


Dynamic Characteristics Of An Isolated Self-Excited Synchronous Reluctance Generator Driven By A Wind Turbine, Mosaad Mohiedden Ali, Said Mahmoud Allam, Talaat Hamdan Abdel-Moneim Jan 2016

Dynamic Characteristics Of An Isolated Self-Excited Synchronous Reluctance Generator Driven By A Wind Turbine, Mosaad Mohiedden Ali, Said Mahmoud Allam, Talaat Hamdan Abdel-Moneim

Turkish Journal of Electrical Engineering and Computer Sciences

This paper studies the dynamic characteristics of an isolated three-phase self-excited synchronous reluctance generator (SESRG) driven by a variable-speed wind turbine under different operating conditions. Self-excitation is achieved via capacitors connected across the generator terminals. A detailed mathematical modeling of the proposed self-excited wind generation system is presented. The proposed analysis is based on the dynamic qd-axis model of the SESRG. Magnetic saturation is taken into account and is assumed to be confined to the direct axis and is accounted for as a variable direct-axis magnetizing reactance. Effect of wind-speed variation, excitation-capacitance variation, and loading-conditions variation on the generated output …


A Distributed Map Animation Framework For Spatiotemporal Datasets, Ahmet Sayar Jan 2016

A Distributed Map Animation Framework For Spatiotemporal Datasets, Ahmet Sayar

Turkish Journal of Electrical Engineering and Computer Sciences

Maps are an excellent way to present data that have spatial components. However, when the data being presented vary over time, a simple two-dimensional map ignores an important feature of the data. An animated map that shows a series of two-dimensional maps at successive points in time allows one to add a time dimension to the display of data. The current study proposes a distributed service-oriented architecture to create map animations from spatiotemporal datasets. We extend the open standards GIS web services definitions with a topic-based publish-subscribe paradigm, which best suits the animation requirements. The effectiveness of the technique is …


Commutation Angles Adjustment In Srm Drives To Reduce Torque Ripple Below The Motor Base Speed, Ali Shahabi, Amir Rashidi, Milad Afshoon, Seyyed Mortaza Saghaian Nejad Jan 2016

Commutation Angles Adjustment In Srm Drives To Reduce Torque Ripple Below The Motor Base Speed, Ali Shahabi, Amir Rashidi, Milad Afshoon, Seyyed Mortaza Saghaian Nejad

Turkish Journal of Electrical Engineering and Computer Sciences

This paper investigates the problem of high torque ripple in switched reluctance motor (SRM) drives. A method is proposed for below the base speed operation of SRM that determines both the turn-off and the turn-on angles for reducing motor torque ripple. Determination of the turn-off angle is an offline process performed through solving a multiobjective optimization function consisting of two criteria: torque ripple and copper loss. Turn-on angle adjustment, however, is an online process based on the intersection approach of consecutive phase currents, particularly proposed in this paper. Simulation and experimental results are presented to validate the reduction in torque …


Thermal Diffusion In Thin Plates And Coatings: Influence Of Thickness And Substrate Material, Harshan Soumya, Jacob Philip Jan 2016

Thermal Diffusion In Thin Plates And Coatings: Influence Of Thickness And Substrate Material, Harshan Soumya, Jacob Philip

Turkish Journal of Physics

The dependence of thermal diffusivity/conductivity on thickness for a variety of coatings and free-standing thin metallic plates was measured using a traveling photothermal technique. The selected materials have large differences in terms of their thermal conductivity. Measurements were carried out on coatings prepared on substrates with two widely different values for thermal conductivity to bring out the influence of substrate thermal conductivity on the thermal diffusivity/conductivity of the coating. Thermal diffusivity/conductivity increases exponentially with coating thickness with the value saturating at a definite thickness. The variation follows an empirical relation, which can predict thermal diffusivity of a coating at any …


Calculation Of Thermophysical Properties Of Magnesium Antimonide ($\Alpha $-Mg$_{3}$Sb$_{2})$, Seçki̇n Dündar Günay Jan 2016

Calculation Of Thermophysical Properties Of Magnesium Antimonide ($\Alpha $-Mg$_{3}$Sb$_{2})$, Seçki̇n Dündar Günay

Turkish Journal of Physics

Magnesium antimonide ($\alpha $-Mg$_{3}$Sb$_{2})$ is investigated by molecular dynamics simulation to find thermophysical properties. Lattice parameters and heat capacities are calculated from room temperature to the melting point. Nearest neighbor distances of ions are measured from the radial distribution function and compared with experimental values. Bulk properties like elastic constants and bulk and shear moduli are found and tabulated with first-principle and experimental data.


Magnetic Effect On The Phase Properties Of Neodymium-Activated Yttrium Disilicate Nanomaterials, Murat Erdem, Ci̇hat Boyraz Jan 2016

Magnetic Effect On The Phase Properties Of Neodymium-Activated Yttrium Disilicate Nanomaterials, Murat Erdem, Ci̇hat Boyraz

Turkish Journal of Physics

Under varying temperature conditions, undoped Y$_{2}$Si$_{2}$O$_{7}$ and neodymium-doped Y$_{2}$Si$_{2}$O$_{7}$ nanopowders were synthesized by the sol-gel method. The phase transitions from $\alpha $ to $\delta $ were observed in neodymium nanopowders by XRD measurements. TEM images showed ball-shaped structure forms for synthesized samples. The elemental compositions of all samples were established and quite close stoichiometry to all compound formulas was found using an attached component for TEM. To reveal the Nd dopant effect in different-phased Y$_{2}$Si$_{2}$O$_{7}$ nanopowders, diffuse reflectance measurements were conducted. To establish the magnetic properties of undoped Y$_{2}$Si$_{2}$O$_{7}$ and neodymium-doped Y$_{2}$Si$_{2}$O$_{7}$ nanopowders, an extensive study was carried out including …


Determination Of The Effective Atomic Numbers Of Fe$_{X}$Cu$_{1-X} $Binary Ferroalloys Using A Nondestructive Technique: Rayleigh-To-Compton Scattering Ratio, Mehmet Büyükyildiz Jan 2016

Determination Of The Effective Atomic Numbers Of Fe$_{X}$Cu$_{1-X} $Binary Ferroalloys Using A Nondestructive Technique: Rayleigh-To-Compton Scattering Ratio, Mehmet Büyükyildiz

Turkish Journal of Physics

The aim of the present study is to determine effective atomic numbers ($Z_{eff})$ of Fe$_{x}$Cu$_{1-x} $ binary ferroalloys using scattering of 59.54 keV gamma photons at 130$^{\circ}$ ($x=4.36{{\unicode{x212B}}}^{-1})$ scattering angle. For this purpose, the Rayleigh ($R)$ and Compton ($C)$ scattering intensities for the given alloys were measured using a monoenergetic beam of 59.54 keV gamma rays and the Rayleigh-to-Compton scattering ratio $R/C $was determined. Then the $Z_{eff}$ values of these alloys were determined by interpolating the $R/C$ of the material using the $R/C$ data of adjacent elements in between the $R/C$ of the alloys. For comparison, $Z_{eff}$s of alloys were …


Effect Of Glow Discharge Plasma On Step Index Polymer Optical Fiber Parameters, Mohamed Medhat, El-Sayed El-Zaiat, Mohamed Sauday, Mona Omar, Hassanein Shaaban Jan 2016

Effect Of Glow Discharge Plasma On Step Index Polymer Optical Fiber Parameters, Mohamed Medhat, El-Sayed El-Zaiat, Mohamed Sauday, Mona Omar, Hassanein Shaaban

Turkish Journal of Physics

DC glow discharge plasma of power 40 W was applied to step index polymer optical fibers for different exposure times. Nitrogen, oxygen, and hydrogen gases were used to obtain the glow discharge. The fiber core material was poly methyl methacrylate and the cladding was fluorinated polymer. The effect of plasma on the optical parameters, such as core index profile, cladding index, and the numerical aperture, was studied by multiple beam interference fringes and Fourier transformation of infrared spectroscopy spectra. It was found that the plasma treatment affected the optical parameters of both the cladding and the core regions of optical …


Structural And Optical Properties Of Gallium Sulfide Thin Film, Hüseyi̇n Ertap, Tarik Baydar, Mustafa Yüksek, Mevlüt Karabulut Jan 2016

Structural And Optical Properties Of Gallium Sulfide Thin Film, Hüseyi̇n Ertap, Tarik Baydar, Mustafa Yüksek, Mevlüt Karabulut

Turkish Journal of Physics

Structural, morphological, and optical properties of gallium sulfide film grown by chemical bath deposition have been investigated by XRD, SEM, AFM, and optical absorption techniques. The XRD spectrum indicated that the gallium sulfide film grew in crystalline form and the phase was identified as GaS. Gallium sulfide film had an island-like structure with a random distribution on a glass substrate. The particle size of the crystallites and surface roughness of the film were found to be 28-48 nm and 11.84 nm, respectively. The direct and indirect band gaps of gallium sulfide thin film were calculated from the absorption spectra as …


Isospin Mixing And Fermi Transitions For Some Deformed Nuclei, Serdar Ünlü, Hasan Ali̇ Aygör, Necla Çakmak, Cevad Selam Jan 2016

Isospin Mixing And Fermi Transitions For Some Deformed Nuclei, Serdar Ünlü, Hasan Ali̇ Aygör, Necla Çakmak, Cevad Selam

Turkish Journal of Physics

We have tried to give a self-consistent explanation of isospin mixing and Fermi beta decays for 54 $\le $ Z $\le $ 68 deformed nuclei. The effect of isospin impurity in nuclear ground states on Fermi beta transitions has been investigated considering the restoration of symmetry violations stemming from the mean field approximation. The isobar analogue excitations in neighbor odd-odd nuclei have been obtained by following the proton-neutron quasiparticle random phase approximation (pnQRPA) procedure. The dependence of isospin admixture probability on the deformation parameter has been determined for various isotopes of Z = 54-68 nuclei. Then the variations of isobar …


Mn-Doped Zns Quantum Dots As A Room-Temperature Phosphorescent Probe For Analysis Of Glutamic Acid In Foodstuffs, Hayri̇ye Eda Şatana Kara, Burak Demi̇rhan, Buket Er Demi̇rhan Jan 2016

Mn-Doped Zns Quantum Dots As A Room-Temperature Phosphorescent Probe For Analysis Of Glutamic Acid In Foodstuffs, Hayri̇ye Eda Şatana Kara, Burak Demi̇rhan, Buket Er Demi̇rhan

Turkish Journal of Chemistry

L-cysteine-capped Mn-doped ZnS quantum dots (QDs) were used for the determination of glutamic acid in foodstuffs. This method is based on measurement of the quenching of the phosphorescence intensity of the QDs after interacting with glutamic acid. A linear response was observed from 50 to 500 ng mL$^{-1}$ glutamic acid with a limit of detection of 6.79 ng mL$^{-1}$. Room temperature phosphorescence (RTP) intensity of the QDs was quenched rapidly upon the addition of the quencher and the reaction reached equilibrium within 2 min. The quenching mechanism of phosphorescence of Mn-doped ZnS QDs by glutamic acid is dynamic and the …


The Relation Between Rough Wijsman Convergence And Asymptotic Cones, Öznur Ölmez, Sali̇h Aytar Jan 2016

The Relation Between Rough Wijsman Convergence And Asymptotic Cones, Öznur Ölmez, Sali̇h Aytar

Turkish Journal of Mathematics

In this paper, we explore the effect of the asymptotic cone of the limit set of a sequence that is rough Wijsman convergent.


Derivation-Homomorphisms, Lingyue Li, Xiaowei Xu Jan 2016

Derivation-Homomorphisms, Lingyue Li, Xiaowei Xu

Turkish Journal of Mathematics

In this paper, we introduce notions of $(n,m)$-derivation-homomorphisms and Boolean $n$-derivations. Using Boolean $n$-derivations and $m$-homomorphisms, we describe structures of $(n, m)$-derivation-homomorphisms.


Explicit Estimates On A Mixed Neumann-Robin-Cauchy Problem, Luisa Consiglieri Jan 2016

Explicit Estimates On A Mixed Neumann-Robin-Cauchy Problem, Luisa Consiglieri

Turkish Journal of Mathematics

We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We investigate explicit estimates for solutions of the parabolic equations with nonhomogeneous boundary conditions and distributional right-hand sides. The parabolic equation is of divergence form with discontinuous coefficients. We consider a nonlinear condition on a part of the boundary such that the power laws (and the Robin boundary condition) appear as particular cases.


On The Nphss-Kpik Iteration Method For Low-Rank Complex Sylvester Equations Arising From Time-Periodic Fractional Diffusion Equations, Min-Li Zeng, Guo-Feng Zhang Jan 2016

On The Nphss-Kpik Iteration Method For Low-Rank Complex Sylvester Equations Arising From Time-Periodic Fractional Diffusion Equations, Min-Li Zeng, Guo-Feng Zhang

Turkish Journal of Mathematics

Based on the Hermitian and skew-Hermitian (HS) splitting for non-Hermitian matrices, a nonalternating preconditioned Hermitian and skew-Hermitian splitting-Krylov plus inverted Krylov subspace (NPHSS-KPIK) iteration method for solving a class of large and low-rank complex Sylvester equations arising from the two-dimensional time-periodic fractional diffusion problem is established. The local convergence condition is proposed and the optimal parameter is given. Numerical experiments are used to show the efficiency of the NPHSS-KPIK iteration method for solving the Sylvester equations arising from the time-periodic fractional diffusion equations.


Approximation Of $B$-Continuous And $B$-Differentiable Functions By Gbs Operators Of $Q$-Bernstein-Schurer-Stancu Type, Manjari Sidharth, Nurhayat İspi̇r, Purshottam Narain Agrawal Jan 2016

Approximation Of $B$-Continuous And $B$-Differentiable Functions By Gbs Operators Of $Q$-Bernstein-Schurer-Stancu Type, Manjari Sidharth, Nurhayat İspi̇r, Purshottam Narain Agrawal

Turkish Journal of Mathematics

B&acaron;rbosu and Muraru (2015) introduced the bivariate generalization of the $q$-Bernstein-Schurer-Stancu operators and constructed a GBS operator of $q$-Bernstein-Schurer-Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In the last section we estimate the degree of approximation by means of Lipschitz class function and the rate of convergence with the help of mixed modulus of smoothness for the GBS operator of $q$-Bernstein-Schurer-Stancu type. Furthermore, we show comparisons by some illustrative graphics …


Uniqueness Of Entire Graphs In Riemannian Warped Products, Junhong Dong, Ximin Liu Jan 2016

Uniqueness Of Entire Graphs In Riemannian Warped Products, Junhong Dong, Ximin Liu

Turkish Journal of Mathematics

In this paper, by applying the generalized Omori-Yau maximum principle for complete spacelike hypersurfaces in warped product spaces, we obtain the sign relationship between the derivative of warping function and support function. Afterwards, by using this result and imposing suitable restrictions on the higher order mean curvatures, we establish uniqueness results for the entire graph in a Riemannian warped product space, which has a strictly monotone warping function. Furthermore, applications to such a space are given.


Erratum To "The Geometry Of Hemi-Slant Submanifolds Of A Locally Product Riemannian Manifold", Hakan Mete Taştan, Fatma Özdemi̇r Jan 2016

Erratum To "The Geometry Of Hemi-Slant Submanifolds Of A Locally Product Riemannian Manifold", Hakan Mete Taştan, Fatma Özdemi̇r

Turkish Journal of Mathematics

No abstract provided.


Relay Coordination Analysis And Protection Solutions For Smart Grid Distribution Systems, Mehmet Tan Turan, Erdi̇n Gökalp Jan 2016

Relay Coordination Analysis And Protection Solutions For Smart Grid Distribution Systems, Mehmet Tan Turan, Erdi̇n Gökalp

Turkish Journal of Electrical Engineering and Computer Sciences

Growing complexity of conventional power grids and their management, increasing power demand and energy quality expectations considering grid reliability, and efficiency and security concerns have triggered the evolution of smart grids. This is an expected result of implementing new technologies in existing grids, including renewable sources such as wind turbines and photovoltaic modules. With implementation of such new elements to the system, the protection concept should be considered by system regulators. In order to analyze protection problems, simulation-based analysis should be carried out before high-cost experimental studies. In this study, a simulation-based evaluation for a smart grid-based distribution system is …


Highly Non-Concurrent Longest Paths In Lattices, Yasir Bashir, Faisal Nadeem, Ayesha Shabbir Jan 2016

Highly Non-Concurrent Longest Paths In Lattices, Yasir Bashir, Faisal Nadeem, Ayesha Shabbir

Turkish Journal of Mathematics

In this paper we consider graphs in which any pair of vertices is missed by some longest path. We are proving the existence of such graphs in the infinite triangular, square and hexagonal lattices in the plane. Moreover, we extend our investigation to lattices on several surfaces such as the torus, the M\"obius strip and the Klein bottle.


Abundance Of $E$-Order-Preserving Transformation Semigroups, Lei Sun, Xuefeng Han Jan 2016

Abundance Of $E$-Order-Preserving Transformation Semigroups, Lei Sun, Xuefeng Han

Turkish Journal of Mathematics

Let ${\cal T}_X$ be the full transformation semigroup on a finite totally ordered set $X=\{1<2<\ldots


Homothetic Motions With Dual Octonions In Dual $8-$Space, Hesna Kabadayi Jan 2016

Homothetic Motions With Dual Octonions In Dual $8-$Space, Hesna Kabadayi

Turkish Journal of Mathematics

In this study, for dual octonions in dual $8-$space $D^{8}$ over the domain of coefficients $D,$ we give a matrix that is similar to a Hamilton operator. By means of this matrix a new motion is defined and this motion is proven to be homothetic. For this one parameter dual homothetic motion, we prove some theorems about dual velocities, dual pole points, and dual pole curves. Furthermore, after defining dual accelerations, we show that the motion defined by the regular order $m$ dual curve, at every $t$-instant, has only one acceleration center of order $\left( m-1\right) .$


Notes On Cotorsion Dimension Of Hopf--Galois Extensions, Xiaoyan Zhou, Min Wei Jan 2016

Notes On Cotorsion Dimension Of Hopf--Galois Extensions, Xiaoyan Zhou, Min Wei

Turkish Journal of Mathematics

Let $H$ be a finite dimensional Hopf algebra over a field $k$ and $A/B$ be a right $H$-Galois extension. In this note the relationship of cotorsion dimensions between $A$ and $B$ will be studied. We prove that $\mbox{r.cot.D}(A)\leq\mbox{r.cot.D}(B)+\mbox{l.D}(H)$. Moreover, we give some sufficient conditions for which $\mbox{r.cot.D}(A)=\mbox{r.cot.D}(B)$. As applications, we obtain some results about cotorsion dimension of the smash product.


Parameterized Littlewood--Paley Operators And Their Commutators On Herz Spaces With Variable Exponents, Lijuan Wang, Shuangping Tao Jan 2016

Parameterized Littlewood--Paley Operators And Their Commutators On Herz Spaces With Variable Exponents, Lijuan Wang, Shuangping Tao

Turkish Journal of Mathematics

The aim of this paper is to deal with Littlewood--Paley operators with real parameters, including the parameterized Lusin area integrals and the parameterized Littlewood--Paley $g_{\lambda}^{\ast}$-functions, and their commutators on Herz spaces with two variable exponents $p(\cdot),~q(\cdot)$. By using the properties of the Lebesgue spaces with variable exponents, the boundedness of the parameterized Littlewood--Paley operators and their commutators generated respectively by BMO function and Lipschitz function is obtained on those Herz spaces.


Gorenstein Homological Dimensions Of Modules Over Triangular Matrix Rings, Rongmin Zhu, Zhongkui Liu, Zhanping Wang Jan 2016

Gorenstein Homological Dimensions Of Modules Over Triangular Matrix Rings, Rongmin Zhu, Zhongkui Liu, Zhanping Wang

Turkish Journal of Mathematics

Let $A$ and $B$ be rings, $U$ a $(B, A)$-bimodule, and $T=\left(\begin{smallmatrix} A & 0 \\ U & B \\\end{smallmatrix}\right)$ the triangular matrix ring. In this paper, we characterize the Gorenstein homological dimensions of modules over $T$, and discuss when a left $T$-module is a strongly Gorenstein projective or strongly Gorenstein injective module.


Quenching Behavior Of A Semilinear Reaction-Diffusion System With Singularboundary Condition, Burhan Selçuk Jan 2016

Quenching Behavior Of A Semilinear Reaction-Diffusion System With Singularboundary Condition, Burhan Selçuk

Turkish Journal of Mathematics

In this paper, we study the quenching behavior of the solution of a semilinear reaction-diffusion system with singular boundary condition. We first get a local exisence result. Then we prove that the solution quenches only on the right boundary in finite time and the time derivative blows up at the quenching time under certain conditions. Finally, we get lower bounds and upper bounds for quenching time.


Zero-Divisor Graph Of Matrix Rings And Hurwitz Rings, Ci̇hat Abdi̇oğlu Jan 2016

Zero-Divisor Graph Of Matrix Rings And Hurwitz Rings, Ci̇hat Abdi̇oğlu

Turkish Journal of Mathematics

Let $R$ be ring a with identity $1\neq 0$, $S_n(R)$ be a subring of the ring $T_n(R)$ of $n\times n$ upper triangular matrices over $R$, and $H_n(R)$ be the ring defined in the next section using $HR$, the ring of the Hurwitz series over $R$. In this paper, we introduce the zero-divisor graph $\overset{\rightarrow}{\Gamma}(S_n(R))$ and its underlying undirected graph $\Gamma(S_n(R))$ of $S_n(R)$. We give some basic graph theory properties of $\overset{\rightarrow}{\Gamma}(S_n(R))$. Moreover, we obtain some results of the zero-divisor directed graph of $\overset{\rightarrow}{\Gamma}(H_n(R))$.