• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.355-367
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• 2010

In this paper, the existence of periodic solutions is obtained for a kind of p-Laplacian systems by the minimax methods in critical point theory. Moreover, the existence of infinite periodic solutions is also obtained.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.723-734
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• 2013

A robust optimization problem, which has a maximum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differentiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.8
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• pp.958-964
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• 1999

The distance in load parameter space to the closest saddle node bifurcation (CSNB) point provides the worst case power margin to voltage instability and the left eigenvector at CSNB identifies the most effective direction to steer the system to maximize voltage stability under contingency. This paper presents an improved direct method for computing CSNB: the order of nonlinear systems equations is reduced to about twice of the size of load flow equations in contrast to about three-times in Dobson's direct method; the initial guess for the direct method is computed efficiently and robustly by combined use of continuation power flow, a pair of multiple load flow solution with Lagrange interpolation. It is also shown that voltage stability may be enhanced significantly with shift of generations in the direction of the left eigenvector at CSNB.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1355-1364
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• 2001

Characteristics of secondary vortices is topologically investigated in the near-wake region of a circular cylinder, where the Taylor's hypothesis does nut hold. The three-dimensional flow fields in the wake-transition regime were measured by a time-resolved PIV for various planes of view. The convection velocities of the Karman and secondary vortices are evaluated from the trajectory of the vortex center. Then, saddle points are determined by applying the critical point theory. It is shown that the inclination angle of the secondary vortices agrees well with the previous experimental data. The flow fields in a moving frame of reference have several critical points and the mushroom-like structure appears in the streamline patterns of the secondary vortices. Since the distributions of fluctuating Reynolds stresses defined by triple decomposition are closely related with the existence of secondary vortices, the physical meaning of them is explained in conjunction with the vortex center and saddle point trajectories.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.491-504
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• 2018

In this article, we consider a fourth order nonlinear difference system. By making use of the critical point theory, we obtain some new existence theorems of at least one periodic solution with minimal period. Our main approach used in this article is the variational technique and the Saddle Point Theorem.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1195-1207
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• 2015

Lagrange multiplier method for solving the contact problem in elasticity is considered. Based on lower semicontinuity of sensitivity functional we prove the convergence of modified dual scheme to corresponding saddle point.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.1
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• pp.107-112
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• 1992

A slight extension of the classical saddle point and the global optimality condition has been discussed relative to some algorithmic implications. It also involves an economic interpretation which shows satisfying, rather than optimizing, decision making behavior under bounded rationality.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.457-470
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• 2008

This paper is concerned with the robust boundary control of the chemotaxis reaction diffusion system. That is, we show that the existence of the saddle point for the robust control problem when the control and the disturbance are given by the boundary condition.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.669-684
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• 2012

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of degenerate Dirichlet problem in the case near resonance.

• Proceedings of the Korean Society of Postharvest Science and Technology of Agricultural Products Conference
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• 2003.10a
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• pp.225.1-225
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• 2003

잣을 이용한 쌀가루즉석죽 제조조건의 최적화와 제조조건에 따른 관능적 특성을 4차원 반응표면분석에 의하여 모니터링 하였다. 죽의 제조에 이용되는 잣은 가루같이 으깬 것을 첨가하는 것이 바람직하였다. 관능적 특성에 의한 잣죽의 점성에 대한 최적조건은 주입액의 양과 잣의 첨가비율이 각각 쌀가루 무게의 15.52배, 16%, 가열조리시간 7.79 분이었으며 이때 $R^2$는 0.9518, 관능평점은 7.45, 임계점은 maximum point였다. 색상에 대한 최적조건은 19.09배, 45%, 2.16분($R^2$=0.7917)이었고 관능평점은 5.44, saddle point였으며, 맛에 대한 최적조건은 12.90배, 22%, 11.40분($R^2$=0.9361), 관능평점은 7.11, maximum point였고, 향에 대한 최적조건은 15.06배, 20%, 4.9분($R^2$=0.8372), 관능평점은 6.16, saddle point였다. 관능적 특성을 모두 만족시켜주는 최적조건은 주입액의 양과 잣의 첨가비율이 각각 쌀가루무게의 16.86배와 15%, 가열조리시간 5.48분이었고 이때 $R^2$는 0.9738, 관능적 평점은 7.69, 임계점은 maximum point였다. 관능적 특성 중 점성은 맛과 전반적기호도에 큰 영향을 주었으며 상관계수는 각각 0.8173($R^2$=0.0001), 0.7878($R^2$=0.0002)이었고 맛은 향과 전반적인 기호도와 밀접한 관계가 있으며 상관계수는 각각 0.5196($R^2$=0.0325)과 0.7004($R^2$=0.0017)이었다.