2016
8
2
2
0
A cultural algorithm for data clustering
2
2
Clustering is a widespread data analysis and data mining technique in many fields of study such as engineering, medicine, biology and the like. The aim of clustering is to collect data points. In this paper, a Cultural Algorithm (CA) is presented to optimize partition with N objects into K clusters. The CA is one of the effective methods for searching into the problem space in order to find a near optimal solution. This algorithm has been tested on different scale datasets and has been compared with other wellknown algorithms in clustering, such as Kmeans, Genetic Algorithm (GA), Simulated Annealing (SA), Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) algorithm. The results illustrate that the proposed algorithm has a good proficiency in obtaining the desired results.
1

99
106


M. R.
Shahriari
Faculty of Management, South Tehran Branch, Islamic Azad University, Tehran, Iran.
Faculty of Management, South Tehran Branch,
Iran
shahriari.mr@gmail.com
Data Clustering
Genetic algorithm
Cultural Algorithm
Particle Swarm Optimization.
Fixed point theorem for nonself mappings and its applications in the modular space
2
2
In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357366.] a fixed point theorem for nonself contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a continuous nonself contraction mapping and $S$ is continuous mapping such that $S(C)$ resides in a compact subset of $X_rho$, where $C$ is a nonempty and complete subset of $X_rho$, also $C$ is not bounded. Our result extends and improves the result announced by Hajji and Hanebally [A. Hajji and E. Hanebaly, Fixed point theorem and its application to perturbed integral equations in modular function spaces, Electron. J. Differ. Equ. 2005 (2005) 111]. As an application, the existence of a solution of a nonlinear integral equation on $C(I, L^varphi) $ is presented, where $C(I, L^varphi)$ denotes the space of all continuous function from $I$ to $L^varphi$, $L^varphi$ is the MusielakOrlicz space and $I=[0,b] subset mathbb{R}$. In addition, the concept of quasi contraction nonself mapping in modular space is introduced. Then the existence of a fixed point of these kinds of mapping without $Delta_2$condition is proved. Finally, a three step iterative sequence for nonself mapping is introduced and the strong convergence of this iterative sequence is studied. Our theorem improves and generalized recent know results in the literature.
1

107
117


R.
Moradi
Department of Mathematics, Faculty of Science, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran.
Department of Mathematics, Faculty of Science,
Iran


A.
Razani
Department of Mathematics, Faculty of Science, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran.
Department of Mathematics, Faculty of Science,
Iran
razani@sci.ikiu.ac.ir
Modular space
Nonself mappings
Quasi contraction
Krasnoseleskii's fixed point theorem
Integral equation.
Stability analysis of the transmission dynamics of an HBV model
2
2
Hepatitis B virus (HBV) infection is a major public health problem in the world today. A mathematical model is formulated to describe the spread of hepatitis B, which can be controlled by vaccination as well as treatment. We study the dynamical behavior of the system with fixed control for both vaccination and treatment. The results shows that the dynamics of the model is completely determined by the basic reproductive number R_0. if R_0<1, the diseasefree equilibrium is globally asymptotically stable by using approach that given by Kamgang and Sallet. Then the authors prove that if R_0>1, the diseasefree equilibrium is unstable and the disease is uniformly persistent. Furthermore, If R_0>1, the unique endemic equilibrium is globally asymptotically stable by using a generalization of the Poincar eBendixson criterion.
1

119
129


R.
Akbari
Department of Mathematical Sciences, Payame Noor University ,P.O.Box 193953697 , Tehran ,Iran.
Department of Mathematical Sciences,
Iran
r9reza@yahoo.com


A.
Vahidian Kamyad
Department of Mathematics Sciences , University of Ferdowsi, Mashhad, Iran.
Department of Mathematics Sciences ,
Iran


A. A.
Heydari
Research Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.
Research Center for Infection Control and
Iran


A.
Heydari
Department of Mathematical Sciences, Payame Noor University, P. O. Box 193953697, Tehran, Iran.
Department of Mathematical Sciences,
Iran
Hepatitis B virus (HBV)
Basic reproduction number ($R_0$)
Gompound matrices
Global stability.
NonNewtonian thermal convection of eyringpowell fluid from an isothermal sphere with biot number effects
2
2
This article investigates the nonlinear, steady boundary layer flow and heat transfer of an incompressible EyringPowell nonNewtonian fluid from an isothermal sphere with Biot number effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a secondorder accurate implicit finitedifference Keller Box technique. The influence of a number of emerging dimensionless parameters, namely the EyringPowell rheological fluid parameter $left( varepsilon right) $, the local nonNewtonian parameter based on length scale $left( delta right) $, Prandtl number (Pr), Biot number $left( gammaright) $ and dimensionless tangential coordinate $left(xi right) $ on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. It is found that the velocity and heat transfer rate (Nusselt number) decrease with increasing $left( varepsilon right) $, whereas temperature and skin friction increase. An increasing $left(deltaright) $ is observed to enhance velocity, local skin friction and heat transfer rate but reduces the temperature. An increase $left( gamma right) $ is seen to increase velocity, temperature, local skin friction and Nusselt number. The study is relevant to chemical materials processing applications.
1

131
146


S.
Abdul Gaffar
Department of Mathematics, Jawaharlal Nehru Techological University Anantapur, Anantapuramu515002, India.
Department of Mathematics, Jawaharlal Nehru
Iran
abdulsgaffar0905@gmail.com


V.
Ramachandra Prasad
Department of Mathematics, Madanapalle Institute of Technology and Sciences, Madanapalle517325, India.
Department of Mathematics, Madanapalle Institute
Iran


E.
Keshava Reddy
Department of Mathematics, Jawaharlal Nehru Techological University Anantapur, Anantapuramu515002, India.
Department of Mathematics, Jawaharlal Nehru
Iran
NonNewtonian EyringPowell fluid model
Isothermal sphere
Finite difference numerical method
Boundary layers
Biot number
Chaotic convection in couple stress liquid saturated porous layer
2
2
In this paper, we have investigated the chaotic behavior of thermal convection in couple stress liquid saturated porous layer subject to gravity, heated from below and cooled from above, based on theory of dynamical system. A low dimensional Lorenz like model is obtained by using Galerkintruncation approximation. We found that there is proportional relation between scaled couple stress parameter and rescaled Rayleigh number. We analyzed that increase in level of couple stress parameter increases the level of chaos.
1

147
156


Vinod
K. Gupta
Department of Mathematics, DIT University, Dehradun, India$248009$.
Department of Mathematics, DIT
Iran
vinodguptabhu@gmail.com


A. K.
Singh
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India.
Department of Mathematics, Institute
Iran


B. S.
Bhadauria
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India.
Department of Mathematics, Institute
Iran


I.
Hasim
School of Mathematical Sciences, Faculty of Science,Universiti Kebangsaan Malaysia (UKM).
School of Mathematical Sciences, Faculty
Iran


J. M.
Jawdat
Department of Applied Mathematics, University of Tabuk, Saudi Arabia.
Department of Applied Mathematics, Unive
Iran
Chaotic behavior
Couple stress liquid
Porous media
Lorenz equations
Theory of blockpulse functions in numerical solution of Fredholm integral equations of the second kind
2
2
Recently, the blockpulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a main part. By providing a new method based on BPFs for solving FIEs of the second kind, the least squares and nonleast squares solutions are defined for this problem. First, the convergence of the nonleast squares solution is proved by the Nystr$ddot{o}$m method. Then, considering the fact that the set of all invertible matrices is an open set, the convergence of the least squares solution is investigated. The convergence of Nystr$ddot{o}$m method has the main role in proving the basic results. Because the presented convergence trend is independent of the orthogonality of the basis functions, the given method can be applied for any arbitrary method.
1

157
163


A.
Abdollahi
Department of Mathematics, Maragheh Branch, Islamic Azad University, Maragheh, Iran.
Department of Mathematics, Maragheh Branch,
Iran
a.abdollahi@iaumaragheh.ac.ir


E.
Babolian
Department of Mathematics, College of Basic Sciences, Tehran Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, College of Basic
Iran
Blockpulse functions
Fredholm integral equation
Least squares approximation
New characterization of some linear groups
2
2
There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$subgroups for each prime $p$, etc. In this paper, we investigate the possibility of characterizing the projective special linear groups $L_{n}(2)$ by simple conditions when $2^{n}1$ is a prime number. Our result states that: $Gcong L_{n}(2)$ if and only if $G=L_{n}(2)$ and $G$ has one conjugacy class length $frac{L_{n}(2)% }{2^{n}1}$, where $2^{n}1=p$ is a prime number. Furthermore, we will show that Thompson's conjecture holds for the simple groups $L_{n}(2)$, where $2^{n}1$ prime is a prime number. By Thompson's conjecture if $L$ is a finite nonAbelian simple group, $G$ is a finite group with a trivial center, and the set of the conjugacy classes size of $L$ is equal to $G$, then $Lcong G$.
1

165
170


A.
Khalili Asboei
Young Researchers Club and Elite, Buinzahra Branch, Islamic Azad University, Buinzahra, Iran.
Young Researchers Club and Elite, Buinzahra
Iran
khaliliasbo@yahoo.com


R.
Mohammadyari
Young Researchers Club and Elite, Buinzahra Branch, Islamic Azad University, Buinzahra, Iran.
Young Researchers Club and Elite, Buinzahra
Iran


M.
RahimiEsbo
Young Researchers Club and Elite, Buinzahra Branch, Islamic Azad University, Buinzahra, Iran.
Young Researchers Club and Elite, Buinzahra
Iran
Projective special linear groups
conjugacy class size
Thompson's conjecture