Science and Research Branch, Islamic Azad University, Tehran, Iran
International Journal of Industrial Mathematics
2008-5621
2008-563X
8
2
2015
04
01
A cultural algorithm for data clustering
99
106
EN
M. R.
Shahriari
Faculty of Management, South Tehran Branch, Islamic Azad University, Tehran, Iran.
shahriari.mr@gmail.com
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 well-known algorithms in clustering, such as K-means, 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.
Data Clustering,Genetic algorithm,Cultural Algorithm, Particle Swarm Optimization.
http://ijim.srbiau.ac.ir/article_8552.html
http://ijim.srbiau.ac.ir/article_8552_c21ba0c29bb767e4b0ec1555f361ce74.pdf
Science and Research Branch, Islamic Azad University, Tehran, Iran
International Journal of Industrial Mathematics
2008-5621
2008-563X
8
2
2016
04
01
Fixed point theorem for non-self mappings and its applications in the modular space
107
117
EN
R.
Moradi
Department of Mathematics, Faculty of Science, Imam Khomeini International University, Postal code: 34149-16818, Qazvin, Iran.
A.
Razani
Department of Mathematics, Faculty of Science, Imam Khomeini International University, Postal code: 34149-16818, Qazvin, Iran.
razani@sci.ikiu.ac.ir
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) 357-366.] a fixed point theorem for non-self 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 non-self 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) 1-11]. 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 Musielak-Orlicz space and $I=[0,b] subset mathbb{R}$. In addition, the concept of quasi contraction non-self 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 non-self mapping is introduced and the strong convergence of this iterative sequence is studied. Our theorem improves and generalized recent know results in the literature.
Modular space,Non-self mappings,Quasi contraction,Krasnoseleskii's fixed point theorem,Integral
equation.
http://ijim.srbiau.ac.ir/article_8613.html
http://ijim.srbiau.ac.ir/article_8613_d73fddac8faf2edae1304495cece010b.pdf
Science and Research Branch, Islamic Azad University, Tehran, Iran
International Journal of Industrial Mathematics
2008-5621
2008-563X
8
2
2016
04
01
Stability analysis of the transmission dynamics of an HBV model
119
129
EN
R.
Akbari
Department of Mathematical Sciences, Payame Noor University ,P.O.Box 19395-3697 , Tehran ,Iran.
r9reza@yahoo.com
A.
Vahidian Kamyad
Department of Mathematics Sciences , University of Ferdowsi, Mashhad, Iran.
A. A.
Heydari
Research Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.
A.
Heydari
Department of Mathematical Sciences, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran.
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_01, the disease-free 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 e-Bendixson criterion.
Hepatitis B virus (HBV),Basic reproduction number ($R_0$),Gompound matrices,Global stability.
http://ijim.srbiau.ac.ir/article_8628.html
http://ijim.srbiau.ac.ir/article_8628_c612c41cfcb34054ee7a2f04d58e4e0d.pdf
Science and Research Branch, Islamic Azad University, Tehran, Iran
International Journal of Industrial Mathematics
2008-5621
2008-563X
8
2
2016
04
01
Non-Newtonian thermal convection of eyring-powell fluid from an isothermal sphere with biot number effects
131
146
EN
S.
Abdul Gaffar
Department of Mathematics, Jawaharlal Nehru Techological University Anantapur, Anantapuramu-515002, India.
abdulsgaffar0905@gmail.com
V.
Ramachandra Prasad
Department of Mathematics, Madanapalle Institute of Technology and Sciences, Madanapalle-517325, India.
E.
Keshava Reddy
Department of Mathematics, Jawaharlal Nehru Techological University Anantapur, Anantapuramu-515002, India.
This article investigates the nonlinear, steady boundary layer flow and heat transfer of an incompressible Eyring-Powell non-Newtonian fluid from an isothermal sphere with Biot number effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The influence of a number of emerging dimensionless parameters, namely the Eyring-Powell rheological fluid parameter $left( varepsilon right) $, the local non-Newtonian 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.
Non-Newtonian Eyring-Powell fluid model,Isothermal sphere,Finite difference numerical method,Boundary layers,Biot number
http://ijim.srbiau.ac.ir/article_8647.html
http://ijim.srbiau.ac.ir/article_8647_a9a7dc63b48bcc70cddb065246babce7.pdf
Science and Research Branch, Islamic Azad University, Tehran, Iran
International Journal of Industrial Mathematics
2008-5621
2008-563X
8
2
2016
04
01
Chaotic convection in couple stress liquid saturated porous layer
147
156
EN
Vinod
K. Gupta
Department of Mathematics, DIT University, Dehradun, India-$248009$.
vinodguptabhu@gmail.com
A. K.
Singh
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India.
B. S.
Bhadauria
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India.
I.
Hasim
School of Mathematical Sciences, Faculty of Science,Universiti Kebangsaan Malaysia (UKM).
J. M.
Jawdat
Department of Applied Mathematics, University of Tabuk, Saudi Arabia.
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 Galerkin-truncation 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.
Chaotic behavior,Couple stress liquid,Porous media,Lorenz equations
http://ijim.srbiau.ac.ir/article_8684.html
http://ijim.srbiau.ac.ir/article_8684_4a3cecd529207aa4f8aa75057c951b76.pdf
Science and Research Branch, Islamic Azad University, Tehran, Iran
International Journal of Industrial Mathematics
2008-5621
2008-563X
8
2
2016
04
01
Theory of block-pulse functions in numerical solution of Fredholm integral equations of the second kind
157
163
EN
A.
Abdollahi
Department of Mathematics, Maragheh Branch, Islamic Azad University, Maragheh, Iran.
a.abdollahi@iau-maragheh.ac.ir
E.
Babolian
Department of Mathematics, College of Basic Sciences, Tehran Science and Research Branch, Islamic Azad University, Tehran, Iran.
Recently, the block-pulse 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 non-least squares solutions are defined for this problem. First, the convergence of the non-least 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.
Block-pulse functions,Fredholm integral equation,Least squares approximation
http://ijim.srbiau.ac.ir/article_8689.html
http://ijim.srbiau.ac.ir/article_8689_217f70fcdd0a78e06279efb5ed20d6bb.pdf
Science and Research Branch, Islamic Azad University, Tehran, Iran
International Journal of Industrial Mathematics
2008-5621
2008-563X
8
2
2016
04
01
New characterization of some linear groups
165
170
EN
A.
Khalili Asboei
Young Researchers Club and Elite, Buinzahra Branch, Islamic Azad University, Buinzahra, Iran.
khaliliasbo@yahoo.com
R.
Mohammadyari
Young Researchers Club and Elite, Buinzahra Branch, Islamic Azad University, Buinzahra, Iran.
M.
Rahimi-Esbo
Young Researchers Club and Elite, Buinzahra Branch, Islamic Azad University, Buinzahra, Iran.
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 non-Abelian 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 $Lcong G$.
Projective special linear groups,conjugacy class size,Thompson's conjecture
http://ijim.srbiau.ac.ir/article_8690.html
http://ijim.srbiau.ac.ir/article_8690_357e1f256bdcabaf1422bcbefdb8e2e3.pdf