• 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.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.777-798
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• 2018

In this paper, we study a new iterative method for solving mixed equilibrium problem and a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. Moreover, we prove a strong convergence theorem for finding common fixed points which also are solutions of a mixed equilibrium problem.

• Clean Technology
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• v.17 no.2
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• pp.150-155
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• 2011

The removal process of heavy metal ion in aqueous solution by the functionalized silica bead was simulated using the finite difference method. Equilibrium model and non-equilibrium model were proposed and the effects of dimensionless groups and various parameters were investigated. Freundlich isotherm was used in equilibrium model and 1st order adsorption rate expression was assumed in non-equilibrium model. The comparison results by the predictions of equilibrium and non-equilibrium models showed good agreement. The predictions of equilibrium model were compared with experimental results reported in literature and showed the marginal agreement.

• Applied Chemistry for Engineering
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• v.8 no.3
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• pp.403-409
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• 1997

The equilibrium constants of five deoxyribonucleosides (dDyd, dUrd, dGuo, dThd, dAdo) were estimated by the plate theory and the moment method under isocratic conditions of the Reversed-Phase High Performance Liquid Chromatography (RP-HPLC). The mobile phase in this system was composed of water and organic modifiers(acetonitrile and methanol) The plate theory of linear adsorption isotherm was treated on the basis of continuous flow of eluent through the plates of the column. The moment method was utilized to find the equilibrium constant from the first absolute moment of experimental data. The equilibrium constants of five deoxyribonucleosides in the two methods were very close, and also the equilibrium constants calculated by capacity factor were similar to those by both the plate theory and the moment method. The equilibrium constant was expressed as a semi-log function of the quantity of organic modifier. Excellent agreements between the calculated elusion profile by the plate theory and the experimental data were observed.

• Structural Engineering and Mechanics
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• v.41 no.3
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• pp.339-348
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• 2012

The slope stability analysis is usually done using the methods of calculation to rupture. The problem lies in determining the critical failure surface and the corresponding factor of safety (FOS). To evaluate the slope stability by a method of limit equilibrium, there are linear and nonlinear methods. The linear methods are direct methods of calculation of FOS but nonlinear methods require an iterative process. The nonlinear simplified Bishop method's is popular because it can quickly calculate FOS for different slopes. This paper concerns the use of inverse analysis by genetic algorithm (GA) to find out the factor of safety for the slopes using the Bishop simplified method. The analysis is formulated to solve the nonlinear equilibrium equation and find the critical failure surface and the corresponding safety factor. The results obtained by this approach compared with those available in literature illustrate the effectiveness of this inverse method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.935-938
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• 2004

This paper describes the quantitative analysis on the improvement of equilibrium sensory using virtual bicycle system. We have used a virtual bicycle system that combines virtual reality technology with a bicycle. In this experiment, 10 subjects were tested to investigate the influencing factors on equilibrium sensory. Straight road and curved road driving at several factors including cycling time, number of times of path deviation, and center of pressure(COP) were extracted and evaluated to quantify the extent of control. Also, To improve the effect of balance training, we investigated the usefulness of virtual feedback information by weight shift. The result showed that the system could be effective for equilibrium sensory rehabilitation training device. The analysis method might also have wider applicability to the rehabilitation field.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.749-759
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• 2012

A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely, ${\nabla}({\parallel}x{\parallel}^2_M)$. This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.89-114
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• 2016

In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.203-212
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• 1995

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone($5^{\circ}$) geometry. The effective gamma($\bar{r}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30Km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about $3\sim5$ percent. The skin friction coefficient and heat transfer coefficient were also calculated.