• 한국작물학회:학술대회논문집
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• 한국작물학회 2002년도 추계 학술대회지
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• pp.48-48
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• 2002

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.243-248
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• 2012

We consider the (possible) finite time blow-up of the smooth solutions of the 3D incompressible Euler equations in a smooth domain or in $R^3$. We derive blow-up criteria in terms of $L^{\infty}$ of the partial component of Hessian of the pressure together with partial component of the vorticity.

• 에너지공학
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• 제10권3호
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• pp.183-187
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• 2001

Impedance imaging for binary mixture is a kind of nonlinear inverse problem, which is usually solved iteratively by the Newton-Raphson method. Then, the ill-posedness of Hessian matrix often requires the use of a regularization method to stabilize the solution. In this study, the Levenberg-Marquredt regularization method is introduced for the binary-mixture system with various resistivity contrasts (1:2∼1:1000). Several mixture distribution are tested and the results show that the Newton-Raphson iteration combined with the Levenberg-Marquardt regularization can reconstruct reasonably good images.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권1호
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• pp.7-14
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• 2003

The main concern of this paper is to develop a new class of quasi-newton methods. These methods are intended for use whenever memory space is a major concern and, hence, they are usually referred to as limited memory methods. The methods developed in this work are sensitive to the choice of the memory parameter ${\eta}$ that defines the amount of past information stored within the Hessian (or its inverse) approximation, at each iteration. The results of the numerical experiments made, compared to different choices of these parameters, indicate that these methods improve the performance of limited memory quasi-Newton methods.

• 호남수학학술지
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• 제27권3호
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• pp.477-485
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• 2005

Let ($M^n$, g) be a compact oriented Riemannian manifold. It has been conjectured that every solution of the equation $z_g=D_gdf-{\Delta}_gfg-fr_g$ is an Einstein metric. In this article, we deal with the 3 dimensional case of the equation. In dimension 3, if the conjecture fails, there should be a stable minimal hypersurface in ($M^3$, g). We study some necessary conditions to guarantee that a stable minimal hypersurface exists in $M^3$.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 하계학술대회 논문집 D
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• pp.2576-2578
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• 2003

RBF 네트워크에서 기저함수의 위치는 네트워크의 성능에 매우 큰 영향을 미친다. 몇몇 응용들에서 교사학습을 이용한 기저함수의 위치 선정이 비교사학습에 비해 우수함을 보인다. 그러나 교사학습에 의한 네트워크는 시그모이드 네트워크와 같은 긴 학습시간을 필요로 한다. 본 논문에서는 오차함수의 gradient와 Hessian을 이용해 교사학습에서 요구하는 학습시간을 단축시키면서 기저함수의 최적위치를 추정하였다.

• 대한수학회지
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• 제56권2호
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• pp.421-437
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• 2019

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

• 호남수학학술지
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• 제43권4호
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• pp.701-715
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• 2021

In this paper, we study almost complex Norden Silver manifolds and Kaehler-Norden Silver manifolds. We define adapted connections of first, second and third type to an almost complex Norden Silver manifold and establish the necessary and sufficient conditions for the integrability of almost complex Norden Silver structure. Moreover, we investigate that a complex Norden Silver map is a harmonic map between Kaehler-Norden Silver manifolds.

• 대한수학회보
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• 제59권2호
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• pp.507-528
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• 2022

We propose a path integral method to construct a time stepwise local volatility for the stock index market under Dupire's model. Our method is focused on the pricing with the Monte Carlo Method (MCM). We solve the problem of randomness of MCM by applying numerical integration. We reconstruct this task as a matrix equation. Our method provides the analytic Jacobian and Hessian required by the nonlinear optimization solver, resulting in stable and fast calculations.

• 한국지구과학회지
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• 제37권5호
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• pp.277-285
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• 2016

We introduce a depth scaling strategy to improve the accuracy of frequency-domain elastic full waveform inversion (FWI) using the new pseudo-Hessian matrix for seismic data without low-frequency components. The depth scaling strategy is based on the fact that the damping factor in the Levenberg-Marquardt method controls the energy concentration in the gradient. In other words, a large damping factor makes the Levenberg-Marquardt method similar to the steepest-descent method, by which shallow structures are mainly recovered. With a small damping factor, the Levenberg-Marquardt method becomes similar to the Gauss-Newton methods by which we can resolve deep structures as well as shallow structures. In our depth scaling strategy, a large damping factor is used in the early stage and then decreases automatically with the trend of error as the iteration goes on. With the depth scaling strategy, we can gradually move the parameter-searching region from shallow to deep parts. This flexible damping factor plays a role in retarding the model parameter update for shallow parts and mainly inverting deeper parts in the later stage of inversion. By doing so, we can improve deep parts in inversion results. The depth scaling strategy is applied to synthetic data without lowfrequency components for a modified version of the SEG/EAGE overthrust model. Numerical examples show that the flexible damping factor yields better results than the constant damping factor when reliable low-frequency components are missing.