2016
8
4
0
0
Extensions of Regular Rings
2
2
Let $R$ be an associative ring with identity. An element $x in R$ is called $mathbb{Z}G$regular (resp. strongly $mathbb{Z}G$regular) if there exist $g in G$, $n in mathbb{Z}$ and $r in R$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). A ring $R$ is called $mathbb{Z}G$regular (resp. strongly $mathbb{Z}G$regular) if every element of $R$ is $mathbb{Z}G$regular (resp. strongly $mathbb{Z}G$regular). In this paper, we characterize $mathbb{Z}G$regular (resp. strongly $mathbb{Z}G$regular) rings. Furthermore, this paper includes a brief discussion of $mathbb{Z}G$regularity in group rings.
1

331
337


SH. A.
Safari Sabet
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, Central
Iran


M.
Farmani
Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University, Roudehen, Iran
Young Researchers and Elite Club, Roudehen
Iran
mino.farmani@gmail.com
Group ring
$pi$Regular
$mathbb{Z}G$Regular
Strongly $mathbb{Z}G$regular
Computational technique of linear partial differential equations by reduced differential transform method
2
2
This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calculated in the form of a series with easily computable components. There test modeling problems from mathematical mechanic, physic, electronic and so on, and are discussed to illustrate the effectiveness and the performance of the our method.
1

339
346


H.
Rouhparvar
Department of Mathematics, College of Technical and Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran
Department of Mathematics, College of Technical
Iran
rouhparvar59@gmail.com
Reduced differential transform method
Taylor series
Parabolic equations
Hyperbolic equations
Effect of slip and variable thermal boundary conditions on hydromagnetic mixed convection flow and heat transfer from a nonlinearly stretching surface
2
2
The effect of partial slip and temperature dependent fluid properties on the MHD mixed convection flow from a heated, nonlinearly stretching surface in the presence of radiation and nonuniform internal heat generation/absorption is investigated. The velocity of the stretching surface was assumed to vary according to powerlaw form. Thermal transport is analyzed for two types of nonisothermal boundary conditions, variable wall temperature (VWT) and variable surface heat flux (VHF) of the powerlaw form. The analysis accounts for both temperature dependent viscosity and temperature dependent thermal conductivity. The governing differential equations are transformed by introducing proper nonsimilarity variables and are solved numerically. The physical significance of the slip parameter, magnetic parameter, radiation parameter, viscositytemperature parameter, thermal conductivity parameter and buoyancy force parameter on the flow and the thermal fields are shown through graphs and discussed in detail. The values of wall shear stress and the local Nusselt number are tabulated.
1

347
363


M.
Abd ElAziz
King Khaled University, Faculty of Science, Mathematics Department, Abha 9004, Saudi Arabia.Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt P. O. Box 11795.
King Khaled University, Faculty of Science,
Iran
$m_{}$abdelaziz999@yahoo.com
Slip flow
Mixed convection
Heat source
Stretching surface
Magnetic field
Radiation
A new attitude coupled with the basic thinking to ordering for ranking fuzzy numbers
2
2
Ranking fuzzy numbers is generalization of the concepts of order, and class, and so have fundamental applications. Moreover, deriving the final efficiency and powerful ranking are helpful to decision makers when solving fuzzy problems. Selecting a good ranking method can apply to choosing a desired criterion in a fuzzy environment. There are numerous methods proposed for the ranking of fuzzy numbers, some of them seem to be good in a particular context but not in general. In this paper, a new attitude coupled with the basic thinking of ordering for ranking of fuzzy numbers is proposed. The properties of the proposed method are discussed in detail. The ranking results show that the proposed method can overcome certain shortcomings that exist in the previous ranking methods.The method also has very easy and simple calculations compared to other methods. Finally, numerical examples are presented to illustrate the advantage of our proposed method, and compare them with other common ranking methods. The future prospect of this paper is a new attitude to fuzzy distance, which will be referred to in the end.
1

365
375


F.
Abbasi
Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.
Department of Mathematics, Ayatollah Amoli
Iran
k.9121946081@gmail.com


T.
Allahviranloo
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science and Research
Iran


S.
Abbasbandy
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science and Research
Iran
Ranking fuzzy numbers
Transmission average (TA)
Fuzzy par
Ambiguity rank
Fuzzy partial order
Ashwini Index of a Graph
2
2
Motivated by the terminal Wiener index, we define the Ashwini index $mathcal{A}$ of trees as begin{eqnarray*} % nonumber to remove numbering (before each equation)
mathcal{A}(T) &=& sumlimits_{1leq i<jleq n} d_{_{T}}(v_{i}, v_{j}) [deg_{_{T}}(N(u_{i})) \
&+& deg_{_{T}}(N(v_{j}))],
end{eqnarray*}
where $d_{T}(v_{i}, v_{j})$ is the distance between the vertices $v_{i}, v_{j} in V(T)$, is equal to the length of the shortest path starting at $v_{i}$ and ending at $v_{j}$ and $deg_{T}(N(v))$ is the cardinality of $deg_{T}(u)$, where $uvin E(T)$. In this paper, trees with minimum and maximum $mathcal{A}$ are characterized and the expressions for the Ashwini index are obtained for detour saturated trees $T_{3}(n)$, $T_{4}(n)$ as well as a class of Dendrimers $D_{h}$.
1

377
384


Sunilkumar
M. Hosamani
Department of Mathematics, Rani Channamma University, Belagavi, India.
Department of Mathematics, Rani Channamma
Iran
sunilkumar.rcu@gmail.com
Wiener index
terminal Wiener index, Ashwini index
A new evaluation model for selecting a qualified manager by using fuzzy Topsis approach
2
2
Considering the contemporary business settings, managers’ role is more than essential to the viability and further development of an organization. Managers should possess such skills in order to effectively cope with the competition. Multiple attributes decision making (MADM) is an approach employed to solve problems involving selection from among a finite number of alternatives. The aim of this study is to develop a methodology to evaluate managers based on integrating fuzzy AHP and fuzzy TOPSIS approaches. In this paper, I have taken into consideration some important criteria which affect the process of managers selection. I have calculated the weights for each criterion based on Intervalvalued fuzzy AHP and then inputted these weights to the fuzzy TOPSIS method to rank managers. The entire methodology is illustrated with the help of a numerical example and finally the rank of each managers is determined according to its results. The proposed method enables decision analysts to better understand the complete evaluation process and provide a more accurate, effective, and systematic decision support tool. Also, the proposed method provides a useful
way for handling fuzzy TOPSIS based on fuzzy numbers.
1

385
394


S. M.
Hosseini
Department of Manegment, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran.
Department of Manegment, Firoozkooh Branch,
Iran
seimehhos@yahoo.com
Fuzzy number
Fuzzy TOPSIS
Multiple criteria decisionmaking
The Solution of Fully Fuzzy Quadratic Equations Based on Restricted Variation
2
2
Firstly, in this paper, we apply the Fuzzy Restricted Variation Method to achieve an analytical and approximate unsymmetrical fuzzy solution for Fully Fuzzy Quadratic Equation. In this application, after finding the real root of 1cut of $tilde{A}tilde{X}^{2}+tilde{B}tilde{X}+tilde{C}=tilde{D}$, initial guess is always chosen with possible unknown parameters that leads to highly accurate solution. This technique is applying to solve mentioned equation in four cases via the sign of coefficients and variable that there is not zero in support of them and we solve the problems to find positive or negative solution. This method has been shown to solve effectively, easily and accurately a large class of nonlinear quadratic equations with approximations converging rapidly to accurate solution. In this paper we present the solutions in four cases with formulas, that can be used to write the algorithm for this technique. Finally to illustrate easy application and rich behavior of this method, several examples are given.
1

395
400


L.
Gerami Moazam
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science and Research
Iran
lgerami.moazam@yahoo.com
Fuzzy number
Fully fuzzy quadratic equation
Fuzzy parametric form
Restricted variations
Unsymmetrical fuzzy solution
Unsteady MHD CouetteHartmann flow through a porous medium bounded by porous plates with Hall current, ionslip and Coriolis effects
2
2
Effects of Hall current, ionslip and Coriolis force on unsteady MHD CouetteHartmann flow of a viscous incompressible electrically conducting fluid through a porous medium bounded by porous plates in the presence of a uniform transverse magnetic field which is either fixed relative to the fluid or to the moving porous plate is investigated using Laplace transform technique. The expressions for the fluid velocity and shear stress at the moving porous plate are also derived. In order to analyze the physical significance and characteristic features of the problem, the graphs for velocity distribution and shear stress distribution at the moving porous plate are generated for different values of nondimensional parameters. It is observed that the fluid velocity when magnetic field is fixed relative to the moving porous plate is always more than the fluid velocity when magnetic field is fixed relative to the fluid while the shear stress at the moving porous plate when magnetic field is fixed relative to the moving porous plate is always less than the shear stress at the moving porous plate when magnetic field is fixed relative to the fluid.
1

401
414


J. K.
Singh
Department of Mathematics, V. S. K. University, Bellary583105, INDIA.
Department of Mathematics, V. S. K. University,
Iran
s.jitendrak@yahoomail.com


S.
Ghousia Begum
Department of Mathematics, V. S. K. University, Bellary583105, INDIA.
Department of Mathematics, V. S. K. University,
Iran


N.
Joshi
Department of Mathematics, V. S. K. University, Bellary583105, INDIA.
Department of Mathematics, V. S. K. University,
Iran
Magnetic field
Hall current
Ionslip
Coriolis force
Permeability and suction/injection
Modified homotopy perturbation method for solving nonlinear oscillator's equations
2
2
In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy of the Solution equation is very important because the analysis component of the system like vibration amplitude control, synchronization dynamics are dependent to the exact solution of oscillation equation.
1

415
421


A. R.
Vahidi
Department of Mathematics, College of Science,YadegareImam Khomeini (RAH) ShahreRey Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, College of Science,Yade
Iran
alrevahidi@yahoo.com


Z.
Azimzadeh
Department of Mathematics, College of Science,YadegareImam Khomeini (RAH) ShahreRey Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, College of Science,Yade
Iran


M.
Shahrestani
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science and Research
Iran
Homotopy perturbation method (HPM)
Differential equations
Nonlinear oscillator's equation
Laplace transformation
Approximation solution of twodimensional linear stochastic VolterraFredholm integral equation via twodimensional Blockpulse functions
2
2
In this paper, a numerical efficient method based on twodimensional blockpulse functions (BPFs) is proposed to approximate a solution of the twodimensional linear stochastic VolterraFredholm integral equation. Finally the accuracy of this method will be shown by an example.
1

423
430


M.
Fallahpour
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj
Iran


M.
Khodabin
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj
Iran
mkhodabin@kiau.ac.ir


K.
Maleknejad
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj
Iran
Blockpulse function
Twodimensional equation
Stochastic integral equation
Volterrafredholm integral
operational matrix
Brownian motion process
Ito integral
Another Method for Defuzzification Based on Regular Weighted Point
2
2
A new method for the defuzzification of fuzzy numbers is developed in this paper. It is wellknown, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert estimation problems, prediction problems, etc. Accordingly, the necessity to develop a method for the defuzzification of fuzzy numbers, allowing us to save their informative properties has arisen. The purpose of this paper is to develop such a method. The method allows us to find aggregative intervals for fuzzy numbers. These intervals are called the Regular weighted intervals. We start with the definition of regular weighted points for fuzzy numbers. The regular weighted interval for fuzzy number is defined as the set of regular weighted points of all unimodal numbers, that belong to this number. Some propositions and examples about regular weighted point and regular weighted intervals properties are offered.
1

431
435


Rasoul
Saneifard
Department of Engineering Technology, Texas Southern University, Houston, Texas, USA.
Department of Engineering Technology,
Iran


Rahim
Saneifard
Department of Applied Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.
Department of Applied Mathematics, Urmia
Iran
srsaneeifard@yahoo.com
ranking
Fuzzy number
LR type
Defuzzification
Regular weighted point