• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.61-74
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• 2011

In this paper, we introduce a new iteration method based on the hybrid method in mathematical programming and the descent-like method for finding a common element of the solution set for a variational inequality and the set of common fixed points of a nonexpansive semigroup in Hilbert spaces. We obtain a strong convergence for the sequence generated by our method in Hilbert spaces. The result in this paper modifies and improves some well-known results in the literature for a more general problem.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1181-1203
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• 2018

In this paper, we are mainly devoted to find out the general meromorphic solution of some specific type of differential equation. We have also answered an open question posed by Banerjee-Chakraborty [4] by extending their results in a large extent. We have provided an example showing that the conclusion of the results of Zhang-Yang [16] is not general true. Some examples have been exhibited to show that certain claims are true in our main result. Finally some questions have been posed for the future research in this direction.

• The Pure and Applied Mathematics
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• v.21 no.3
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• pp.195-206
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• 2014

In this paper, we consider, under a hybrid iterative scheme with errors, a weak convergence theorem to a common element of the set of a finite family of asymptotically k-strictly pseudo-contractive mappings and a solution set of an equilibrium problem for a given bifunction, which is the approximation version of the corresponding results of Kumam et al.

• Journal of Intelligence and Information Systems
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• v.19 no.2
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• pp.125-140
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• 2013

We call a data set in which the number of records belonging to a certain class far outnumbers the number of records belonging to the other class, 'imbalanced data set'. Most of the classification techniques perform poorly on imbalanced data sets. When we evaluate the performance of a certain classification technique, we need to measure not only 'accuracy' but also 'sensitivity' and 'specificity'. In a customer churn prediction problem, 'retention' records account for the majority class, and 'churn' records account for the minority class. Sensitivity measures the proportion of actual retentions which are correctly identified as such. Specificity measures the proportion of churns which are correctly identified as such. The poor performance of the classification techniques on imbalanced data sets is due to the low value of specificity. Many previous researches on imbalanced data sets employed 'oversampling' technique where members of the minority class are sampled more than those of the majority class in order to make a relatively balanced data set. When a classification model is constructed using this oversampled balanced data set, specificity can be improved but sensitivity will be decreased. In this research, we developed a hybrid model of support vector machine (SVM), artificial neural network (ANN) and decision tree, that improves specificity while maintaining sensitivity. We named this hybrid model 'hybrid SVM model.' The process of construction and prediction of our hybrid SVM model is as follows. By oversampling from the original imbalanced data set, a balanced data set is prepared. SVM_I model and ANN_I model are constructed using the imbalanced data set, and SVM_B model is constructed using the balanced data set. SVM_I model is superior in sensitivity and SVM_B model is superior in specificity. For a record on which both SVM_I model and SVM_B model make the same prediction, that prediction becomes the final solution. If they make different prediction, the final solution is determined by the discrimination rules obtained by ANN and decision tree. For a record on which SVM_I model and SVM_B model make different predictions, a decision tree model is constructed using ANN_I output value as input and actual retention or churn as target. We obtained the following two discrimination rules: 'IF ANN_I output value <0.285, THEN Final Solution = Retention' and 'IF ANN_I output value ${\geq}0.285$, THEN Final Solution = Churn.' The threshold 0.285 is the value optimized for the data used in this research. The result we present in this research is the structure or framework of our hybrid SVM model, not a specific threshold value such as 0.285. Therefore, the threshold value in the above discrimination rules can be changed to any value depending on the data. In order to evaluate the performance of our hybrid SVM model, we used the 'churn data set' in UCI Machine Learning Repository, that consists of 85% retention customers and 15% churn customers. Accuracy of the hybrid SVM model is 91.08% that is better than that of SVM_I model or SVM_B model. The points worth noticing here are its sensitivity, 95.02%, and specificity, 69.24%. The sensitivity of SVM_I model is 94.65%, and the specificity of SVM_B model is 67.00%. Therefore the hybrid SVM model developed in this research improves the specificity of SVM_B model while maintaining the sensitivity of SVM_I model.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.3
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• pp.203-217
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• 1994

In this paper we develop an exponentialization procedure for the modelling of open FMS networks with general processing time at each station and limited buffer size. By imposing a reasonable assumption on the solution set, the nonlinear equation system for the exponentialization procedure is formulated as a variational inequality problem and the solution existence is examined. The efficient algorithm for the nonlinear equation system is developed using linearized Jacobi approximation method.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1161-1178
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• 2018

In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.3
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• pp.101-111
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• 1993

The purpose of this paper is to show the graphic representation of a linear programming problem by a projection method. First, we develop a projection method which conserves the optimality in the projected space, and next we introduce an algorithm to visualize the feasible solution set and the solution process by the projection method. Finally, we give an example to represent a 4-dimensional linear programming problem graphically.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1225-1233
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• 2011

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133 (2007), 151-161].

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.495-524
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• 2016

In this paper, we propose an iterative algorithm for finding a common solution of a system of generalized equilibrium problems, a split equilibrium problem and a hierarchical fixed point problem over the common fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently.

• Proceedings of the Safety Management and Science Conference
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• 2002.05a
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• pp.237-241
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• 2002

This paper deals with the problem of determining the buyer's economic lot sizing policy for exponentially deteriorating products under trade credit. It is also assumed that the ordering cost consists of a fixed set-up cost and a freight cost, where the freight cost has a quantity discount offered due to the economies of scale. We formulate the mathematical model and the solution algorithm is developed based on the properties of an optimal solution.