INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS
Year:2016 | Volume:8 | Issue:2|Papers Count:7

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.

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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 vac-cination 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 disease-free equilibrium is globally asymptot-ically stable by using approach that given by Kamgang and Sallet. Then the authors prove that if R0>1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, If R0>1, the unique endemic equilibrium is globally asymptotically stable by using a generalization of the Poincar e-Bendixson criterion.

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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.

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 Nystrom 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 Nystrom 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.

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