• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.557-569
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• 2009

We present a new regularity criterion for suitable weak solutions of the steady-state Navier-Stokes equations near boundary in dimension five. We show that suitable weak solutions are regular up to the boundary if the scaled $L^{\frac{5}{2}}$-norm of the solution is small near the boundary. Our result is also valid in the interior.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1221-1234
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• 2009

In this paper, we construct fully discrete discontinuous Galerkin approximations to the solution of linear Sobolev equations. We apply a symmetric interior penalty method which has an interior penalty term to compensate the continuity on the edges of interelements. The optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^{\infty}(L^2)$ norm is proved.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.679-683
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• 2010

본 연구에서는 공간적 변수인 조도계수를 기지의 수위값을 이용하여 최적값을 결정하는 방법에 대해서 검토하고자 한다. 최적화 기법에 의한 조도계수는 기지의 수위값과 수치모의에 의한 결과 값의 전체 오차를 최소화하는 값으로 결정된다. 본 연구에서는 3가지 최적화 기법을 이용하였으며 가상 수로에 대해서 적용하였다. 수위계산은 표준축차법에 의해 수행하였으며 사용된 최적화 기법은 quasi-Newton 방법이다. 1차원 모형은 Matlab을 이용하여 표준축자법으로 구성하였으며 BFGS 기법, L-BFGS 기법, Steepest Gradient Descent 기법 등도 Matlab으로 구성하였다. 표준축차법은 조도계수가 입력되면 기지의 수위값과의 2-norm을 계산하도록 구성하였다. 계산 결과에 의하면 세가 기법 모두 20 23회 정도의 반복계산을 수행하고 값이 수렴되었는데, L-BFGS의 경우에는 정확하게 음수의 조도계수로 수렴하였으며, BFGS기법과 Steepest Gradient 기법의 경우에는 양의 값으로 정확하게 수렴하였다.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1195-1219
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• 2017

In this paper, the limit behavior of solution for the $Schr{\ddot{o}}dinger$ equation with random dispersion and time-dependent nonlinear loss/gain: $idu+{\frac{1}{{\varepsilon}}}m({\frac{t}{{\varepsilon}^2}}){\partial}_{xx}udt+{\mid}u{\mid}^{2{\sigma}}udt+i{\varepsilon}a(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic $Schr{\ddot{o}}dinger$ equation with white noise dispersion and time-dependent loss/gain: $idu+{\Delta}u{\circ}d{\beta}+{\mid}u{\mid}^{2{\sigma}}udt+ia(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as ${\varepsilon}{\rightarrow}0$ in one-dimensional $L^2$ subcritical and critical cases.

• Honam Mathematical Journal
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• v.6 no.1
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• pp.1-12
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• 1984

Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.417-430
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• 2013

Let X be a Banach space and ${\psi}$ a continuous convex function on ${\Delta}_{K+1}$ satisfying certain conditions. Let $(X{\bigoplus}X{\bigoplus}{\cdots}{\bigoplus}X)_{\psi}$ be the ${\psi}$-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-$l^N_1$-ness of Banach spaces using ${\psi}$-direct sums.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.753-760
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• 2013

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do-main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of $L^2$ norms of the initial velocity and the gradient of the initial velocity and $L^{p,2}$, $p{\geq}4$ norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.1
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• pp.41-48
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• 2022

This paper presents the unified Bayesian Tikhonov regularization method as a solution to total variation regularization. The integrated method presents a formula for obtaining the regularization parameter by transforming the total variation term into a weighted Tikhonov regularization term. It repeats until the reconstructed image converges to obtain a regularization parameter and a new weighting factor based on it. The experimental results show the effectiveness of the proposed method for the image restoration problem.

• Journal of Korea Multimedia Society
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• v.12 no.11
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• pp.1692-1700
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• 2009

This paper proposes the direction distribution of surface normal vectors as a feature descriptor of three-dimensional models. Proposed the feature descriptor handles rotation invariance using a principal component analysis(PCA) method, and performs mesh simplification to make it robust and nonsensitive against noise addition. Our method picks samples for the distribution of normal vectors to be proportional to the area of each polygon, applies weight to the normal vectors, and applies interpolation to enhance discrimination so that the information on the surface with less area may be less reflected on composing a feature descriptor. This research measures similarity between models with a L1-norm in the probability density histogram where the distances of feature descriptors are normalized. Experimental results have shown that the proposed method has improved the retrieval performance described in an average normalized modified retrieval rank(ANMRR) by about 17.2% and the retrieval performance described in a quantitative discrimination scale by 9.6%~17.5% as compared to the existing method.