• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.217-225
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• 2006

We consider the nonrelativistic limit for the radial solutions to the self-dual equations in the self-dual Abelian Chern-Simons model. We achieve the limit by fixing the common maximum value of solutions.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.997-1012
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• 2007

We consider the nonrelativistic limit in the self-dual Abelian Chern-Simons model, and give a rigorous proof of the limit for the radial solutions to the self-dual equations with the nontopological boundary condition when there is only one-vortex point. By keeping the shooting constant of radial solutions to be fixed, we establish the convergence of radial solutions in the nonrelativistic limit.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1111-1117
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• 2011

Using the moving plane method, we establish the radial symmetry of topological one-vortex solutions of a semilinear elliptic system arising from the self-dual Maxwell-Chern-Simons O(3) model.

• Journal of Korean Society for Quality Management
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• v.40 no.4
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• pp.481-496
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• 2012

Purpose: This paper aims at improving inefficiency of an existing posterior preference articulation method proposed for dual response surface optimization. The method generates a set of non-dominated solutions and then allows a decision maker (DM) to select the best solution among them through an interval selection strategy. Methods: This paper proposes an iterative posterior preference articulation method, which repeatedly generates the predetermined number of non-dominated solutions in an interval which becomes gradually narrower over rounds. Results: The existing method generates a good number of non-dominated solutions not used in the DM's selection process, while the proposed method generates the minimal number of non-dominated solutions necessitated in the selection process. Conclusion: The proposed method enables a satisfactory compromise solution to be achieved with minimal cognitive burden of the DM as well as with light computation load in generating non-dominated solutions.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.24-29
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• 1996

If the LP problem doesn't have the optimal soultion uniquely, the solution fo the primal-dual barrier method converges to the interior point of the optimal face. Therefore, when the optimal vertex solution or the optimal basis is required, we have to perform the additional procedure to recover the optimal basis from the final solution of the interior point method. In this paper the exisiting methods for recovering the optimal basis or identifying the optimal solutions are analyzed and the new methods are suggested. This paper treats the two optimal basis recovery methods. One uses the purification scheme and the simplex method, the other uses the optimal face solutions. In the method using the purification procedure and the simplex method, the basic feasible solution is obtained from the given interior solution and then simplex method is performed for recovering the optimal basis. In the method using the optimal face solutions, the optimal basis in the primal-dual barrier method is constructed by intergrating the optimal solution identification technique and the optimal basis extracting method from the primal-optimal soltion and the dual-optimal solution.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.765-777
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• 2016

In this paper, we prove the existence of nontopological solutions to the self-dual equations arising from the Chern-Simons gauged O(3) sigma models. The property of solutions depends on a parameter ${\tau}{\in}[-1,1]$ appearing in the nonlinear term. The case ${\tau}=1$ lies on the borderline for the existence of solutions in the previous results [4, 5, 7]. We prove the existence of solutions in this case when there are only vortex points. Moreover, if $-1{\leq}{\tau}$<1, we establish solutions which are perturbed from the solutions of singular Liouville equations.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.9
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• pp.2981-2990
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• 1996

Dual solutions for steady natural convection of air between two horizontal concentric cylinders are numerically investigated in the range of $D_i$/TEX>/L(=diameter of inner cylinder/gap width)$\leq$10. It is found that, when the Rayleigh number based on the gap width exceeds a certain critical value, a new flow pattern forming two counter-rotating eddies in the half of the annulus can be realized, which is different from the crescent-shaped flow commonly observed. In the new flow pattern, the fluid near the top of the hot inner cylinder moves downward. This solution is found for D$_{i}$/L.geq.0.3, but not for$D_i$/TEX>/L$\leq$0.2. As $D_i$/TEX>/L increase, the critical Rayleigh number is decreased, and tends to a finite limit.t.

• Computers and Concrete
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• v.17 no.1
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• pp.53-66
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• 2016

Currently, most of the investigations on chloride diffusion were based on the experiments and simulations concerning single cation type chlorides. Chloride diffusion associated with dual or multi cation types was rarely studied. In this paper, several groups of diffusion experiments are conducted using chloride solutions containing single, dual and multi cation types. A multi-ionic model is also proposed to simulate the chloride diffusion behavior in the experimental tests. The MATLAB software is used to numerically solve the nonlinear PDEs in the multi-ionic model. The experimental and simulated results show that the chloride diffusion behavior associated with different cation types is significantly different. When the single cation type chlorides are adopted, it is found that the bound rates of chloride ions combined with divalent cations are greater than those combined with monovalent cations. When the dual/multi cation type chlorides are adopted, the chloride bound rates increase with the $Ca^{2+}/Mg^{2+}$ percentage in the source solutions. This evidence indicates that the divalent cations would markedly enhance the chloride binding capacity and reduce the chloride diffusivity. Moreover, on the basis of the analysis, it is also found that the complicated cation types in source solutions are beneficial to reducing the chloride diffusivity.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.185-195
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• 2019

In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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• pp.124-131
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• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.