• Korean Journal of Mathematics
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• v.6 no.2
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• pp.259-279
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• 1998

For the forward-backward semimartingale, we can define the backward semimartingale flow which is generated by the backward canonical stochastic differential equation. Therefore, we define the backward self-similar stochastic processes, and we study the backward self-similar stochastic flows through the canonical stochastic differential equations.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2005.11a
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• pp.289-291
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• 2005

In this paper, we introduce the backward solution of nonlinear wave equation for denoising. The PDE method is approved about 4 PSNR value compare with any convolution method. In neuro images, denoising process using proposed PDE is good about 0.2% increased Voxel Region.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.11
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• pp.984-990
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• 2002

We propose a new type of nonlinear fixed interval smoother to which an existing nonlinear smoother is modified. The nonlinear smoother is derived from two-filter formulas. For the backward filter. the propagation and the update equation of error states are derived. In particular, the modified update equation of the backward filter uses the estimated error terms from the forward filter. Data fusion algorithm, which combines the forward filter result and the backward filter result, is altered into the compatible form with the new type of the backward filter. The proposed algorithm is more efficient than the existing one because propagation in backward filter is very simple from the implementation point of view. We apply the proposed nonlinear smoothing algorithm to off-line navigation system and show the proposed algorithm estimates position, and altitude fairly well through the computer simulation.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.427-435
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• 2007

The existence theorem and continuous dependence property in $"L^2"$ sense for solutions of backward stochastic differential equation (shortly BSDE) with Lipschitz coefficients were respectively established by Pardoux-Peng and Peng in [1,2], Mao and Cao generalized the Pardoux-Peng's existence and uniqueness theorem to BSDE with non-Lipschitz coefficients in [3,4]. The present paper generalizes the Peng's continuous dependence property in $"L^2"$ sense to BSDE with Mao and Cao's conditions. Furthermore, this paper investigates the continuous dependence property in "almost surely" sense for BSDE with Mao and Cao's conditions, based on the comparison with the classical mathematical expectation.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.483-504
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• 2015

This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in (y, z) non-uniformly with respect to t. By establishing some results on deterministic backward differential equations with general time intervals, and by virtue of Girsanov's theorem and convolution technique, we prove a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of [8] and [6] to the general time interval case.

• Journal of Ocean Engineering and Technology
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• v.7 no.2
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• pp.150-161
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• 1993

원초변수를 이용한 Navier-Stokes 방정식의 수치계산기법을 개발하고, 이를 응용하여 backward facing step의 층류 유동을 계산하였다. 직교좌표계에서의 비압축성 Navier-Stokes방정식을 풀기위해 시간과 공간항을 2차 정도의 유한 차분을 사용하여 이산화하였고 비교차격자계를 사용하여 양해법으로 수치 계산하였다. 운동량방정식과 연속방정식으로 부터 유도된 압력방정식(pressure-poisson equation)을 이용하여 무발산 조건을 만족시켰ㄲ다. Backward facing step의 층류 유동을 100.$\leq$R$_e$$\leq$1000 범위에 대해서 수치 계산하였으며 실험결과와 잘 일치하는 결과를 구할 수 있었다. 특히 step뒤에서 생기는 박리구간의 길이는 다른 계산결과들보다 실험치에 가까운 값을 얻을 수 있었으며, Re가 600보다 클때는 위쪽 벽에 또 다른 박리 유동이 발생되는 현상이 예측되었다.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.177.4-177
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• 2001

In this paper, we propose a new type of nonlinear fixed interval smoothing filter which is modified from the existing nonlinear smoothing filter. A nonlinear smoothing filter is derived from two-filter formulas. For the backward filter, the propagation and update equation of error states are derived. Particularly the modified update equation of the backward filter use the estimated error terms from the forward filter. Smoothing algorithm is altered into the compatible form with the new type of the backward fitter. An advantage of the proposed algorithm is more efficient than the existing one because propagation in backward filter is very simple from the implementation point of view. We apply the proposed nonlinear smoothing ...

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1143-1155
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• 2011

In this paper, we shall establish a new theorem on the existence and uniqueness of the solution to a backward doubly stochastic differential equations under a weaker condition than the Lipschitz coefficient. We also show a comparison theorem for this kind of equations.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.313-329
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• 2020

In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.1
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• pp.1-10
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• 1994

The flow and heat transfer characteristics behind a backward facing step located in a vertical channel has been studied. In this study, the numerical prediction has been performed by solving the Navier-Stokes equation and energy equation simultaneously with the SIMPLE algorithm embedied in TEACH code. Local heat flux was measured by using Schlieren Interferometer. The flow visualization was performed using the cylindrical lens and the laser beam that is scattered by the supplied glycerine particles. The velocity and temperature distributions, recirculation region, reattachment length, and local heat flux are obtained under the various parameters to investigate the buoyancy effect on the flow and heat transfer characteristics behind the step.