• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1297-1310
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• 2008

Main purpose of this paper is to combine the optimal form of Fan's best approximation theorem and Nash's equilibrium existence theorem into a single existence theorem simultaneously. For this, we first prove a general best proximity pair theorem which includes a number of known best proximity theorems. Next, we will introduce a new equilibrium concept for a generalized Nash game with normal form, and as applications, we will prove new existence theorems of Nash equilibrium pairs for generalized Nash games with normal form.

• Journal of the Korean Society of Hazard Mitigation
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• v.1 no.3 s.3
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• pp.73-82
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• 2001

This study examines the applicability of the Nash model and the Diskin model, which are linear and nonlinear runoff models, respectively, by applying optimization techniques to the parameter calibration of the two models. Nonlinear programming which is one of traditional optimization techniques and Genetic Algorithm which has been actively applied recently are used in this study. The Nash and Diskin models which use the calibrated parameter with a flood events are applied to a different flood event in Soyang Dam basin. The results obtained from the parameter calibration show slight discrepancy depending upon the flood events. It has been found in the comparion between the observed hydrograph and the hydrographs obtained from the parameter calibration that the Diskin model can better simulate the observed hydrograph than the Nash model can, especially, for the peak flow. This can be analyzed that the Diskin model which is a nonlinear runoff model is better off in simulating the nonlinear characteristic of the rainfall-runoff process.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.883-899
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• 2003

In this paper, we will introduce the general concepts of generalized multiobjective game, generalized weight Nash equilibria and generalized Pareto equilibria. Next using the fixed point theorems due to Idzik [5] and Kim-Tan [6] , we shall prove the existence theorems of generalized weight Nash equilibria under general hypotheses. And as applications of generalized weight Nash equilibria, we shall prove the existence of generalized Pareto equilibria in non-compact generalized multiobjective game.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.425-430
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• 2012

In this paper, we will prove a social equilibrium existence theorem of a generalized Nash game with affine constraint correspondences which is comparable with Nash's equilibrium existence theorem in several aspects.

• Journal of Korea Water Resources Association
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• v.36 no.3 s.134
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• pp.399-411
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• 2003

An approach determining a confidence interval of Nash's observed mean instantaneous unit hydrograph is developed. In the approach, both two parameters are treated as correlated gaussian random variables based on the theory of Box-Cox transformation and the regional similarity relation, so that linear statistical parameter estimation is possible. A parametric bootstrap method is adopted to give the confidence interval of the mean observed hydrograph. The proposed methodology is also applicable to estimate the parameters of Nash's model for un-gauged basins. An application to a watershed has shown that the proposed approach is adequate to assess the uncertainty of the Nash's hydrograph and to evaluate parameters for un-gauged basins.

• Journal of Korea Water Resources Association
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• v.43 no.6
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• pp.559-569
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• 2010

This study proposes an empirical method for estimating the concentration time and storage coefficient of a basin using the Nash unit hydrograph. This method is based on the analytically derived concentration time and storage coefficient of the Nash model. More fundamentally, this method recursively searches convergent number of linear reservoirs and storage coefficient of linear reservoir representing the basin given. This method is to overcome the problem of HEC-HMS to use an optimization technique to estimate the basin concentration time and storage coefficient. The proposed method was applied to the Bangrim station of the Pyungchang river basin, also found to estimate physically reasonable values.

• Proceedings of the Korean Information Science Society Conference
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• 2005.11b
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• pp.784-786
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• 2005

본 논문에서 대상으로 하는 네트워크 구조는 서비스 센터, 터미널(사용자), 그리고 연결 케이블로 이뤄져 있고 서비스 센터의 구성을 위한 의사 결정자와 서비스 일터와 사용자의 터미널을 연결하는 의사 결정자들이 존재하고 각자의 목적함수를 최적화 하기위해 비타협적으로 의사 결정과정에서 창설한다고 가정한다. 이러한 문제는 Nash 게임으로 정식화될 수 있다. 본 논문에서는 연결비용, 평균 메시지 지연, 네트워크 신뢰도를 고려하여, Nash 게임으로 정식화되는 광대역 통신 네트워크의 네트워크 토폴로지 설계 문제들을 풀기 위해 Nash 유전 알고리즘을 이용한다. 수치 실험을 통해 본 논문에서 이용한 Nash 유전 알고리즘이 효율적이여 효과적인 방법이라는 것을 살펴본다.

• 한국방재학회:학술대회논문집
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• 2009.02b
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• pp.112.2-112.2
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• 2009

• Journal of Korea Water Resources Association
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• v.33 no.1
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• pp.123-132
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• 2000

In the study the instantaneous unit hydrographs (IUHs) based on the linear Nash (1957) and the nonlinear Diskin (1964) models are derived and compared for the Soyang river basin. Total 14 rainfall runoff events are used for the study and the model parameters are estimated by minimizing the sum of square error considering runoff hydrograph ordinates as relative weights. The representative IUHs for both models are decided to show an average shape of derived IUHs. In the application of the representative IUHs of Nash and Diskin, Diskin model shows better performances in reproducing the observed outflows, especially the peak flow. In the comparison of two Diskin models little difference could be found between the IUHs with the same or different number of two characteristic reservoirs.rvoirs.

• Journal of Korea Water Resources Association
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• v.43 no.4
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• pp.399-408
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• 2010

The sensitivity of Nash model parameters is analyzed about characteristic velocities considering geomorphological dispersion in the present study. And changing shape of IUH compared and analyzed as variation of characteristic velocities through numerical experiment. Application watersheds are selected 4 subwatersheds which are located at main stream of Bocheong basin. The mean and variance of hillslope and stream path length are estimated in each watershed with GIS. And Nash model parameters are estimated with moments of path lengths and characteristic velocities. The changing trend about IUH which is derived Nash model parameters are compared as variation of characteristic velocities. The Major results of this study are summarized as follows. The Nash model parameters sensitively present changes about hillslope characteristic velocity. And the effect of the peak discharge and shape of recession in IUH dominate with hillslope's characteristic velocity, the effect of the peak time and shape of ascension in IUH dominate with channel's characteristic velocity.