• 대한수학회보
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• 제49권2호
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• pp.285-293
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• 2012

In this paper, we investigate the hypersurface M in a unit sphere with constant k-th mean curvature and two distinct principal curvatures, and characterize such a hypersurface.

• 호남수학학술지
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• 제44권1호
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• pp.36-51
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• 2022

We study the translation surfaces in the pseudo-Galilean space with the condition that one of generating curves is planar. We classify these surfaces whose mean and Gaussian curvatures are functions of one variable.

• 대한수학회지
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• 제45권1호
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• pp.41-61
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• 2008

We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

• Journal of Mechanical Science and Technology
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• 제19권5호
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• pp.1065-1071
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• 2005

In this study, residual stress distribution in multi-stacked film by MEMS (Micro-Electro Mechanical System) process is predicted using Finite Element method (FEM). We evelop a finite element program for residual stress analysis (RESA) in multi-stacked film. The RESA predicts the distribution of residual stress field in multi-stacked film. Curvatures of multi­stacked film and single layers which consist of the multi-stacked film are used as the input to the RESA. To measure those curvatures is easier than to measure a distribution of residual stress. To verify the RESA, mean stresses and stress gradients of single and multi layers are measured. The mean stresses are calculated from curvatures of deposited wafer by using Stoney's equation. The stress gradients are calculated from the vertical deflection at the end of cantilever beam. To measure the mean stress of each layer in multi-stacked film, we measure the curvature of wafer with the left film after etching layer by layer in multi-stacked film.

• 한국게임학회 논문지
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• 제2권2호
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• pp.28-36
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• 2002

일반적으로 삼각형 메쉬는 가상 게임 캐릭터와 같은 기하학적 객체를 모델링하기 위해 사용되고 있다. 아주 조밀한 메쉬는 복잡한 객체를 세부적으로 표현하는 장점은 있지만 객체를 저장, 전송 및 렌더링하는데 많은 비용을 요구한다. 그러므로 세밀한 객체를 질 좋게 근사시킬 수 있는 기법, 즉 삼각형 메쉬의 단순화가 연구되어왔다. 본 논문에서는 주어진 메쉬를 단순화하기 위해 사용될 수 있는 정점과 에지에 관한 근사 평균 곡률이라는 새로운 측정치를 제시한다. 에지 평균 곡률은 이웃한 에지를 고려하게 계산되고 정점 평균 곡률은 부속된 에지의 평균 곡률의 평균으로 정의된다. 그리고 제안된 측정치를 토끼, 용 및 치아와 같은 모델에 적용한다. 결과로, 제안된 평균 곡률이 주어진 모델에 더 좋은 근사를 제공하기 위한 좋은 기준치로 사용될 수 있음을 알았다.

• Communications for Statistical Applications and Methods
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• 제16권1호
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• pp.163-168
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• 2009

Given the specific mean shift outlier model, the standard approaches to obtaining test statistics for outliers are discussed. Accuracy of outlier tests is investigated using subset curvatures. These subset curvatures appear to be reliable indicators of the adequacy of the linearization based test. Also, we consider obtaining graphical summaries of uncertainty in estimating parameters through confidence curves. The results are applied to the problem of assessing the accuracy of outlier tests.

• 대한수학회보
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• 제56권1호
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• pp.229-243
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• 2019

We use the so-called pseudoinversion of degenerate metrics technique on foliated compact null hypersurface, $M^{n+1}$, in Lorentzian manifold ${\overline{M}}^{n+2}$, to derive an integral formula involving the r-th order mean curvatures of its foliations, ${\mathcal{F}}^n$. We apply our formula to minimal foliations, showing that, under certain geometric conditions, they are isomorphic to n-dimensional spheres. We also use the formula to deduce expressions for total mean curvatures of such foliations.

• 대한수학회보
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• 제55권2호
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• pp.331-340
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• 2018

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

• 대한수학회논문집
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• 제35권4호
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• pp.1221-1244
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• 2020

In this paper we consider L_K-conjecture introduced in [5, 6] for hypersurface Mⁿ in space form Rⁿ⁺¹(c) with three principal curvatures. When c = 0, -1, we show that every L₁-biharmonic hypersurface with three principal curvatures and H₁ is constant, has H₂ = 0 and at least one of the multiplicities of principal curvatures is one, where H₁ and H₂ are first and second mean curvature of M and we show that there is not L₂-biharmonic hypersurface with three disjoint principal curvatures and, H₁ and H₂ is constant. For c = 1, by considering having three principal curvatures, we classify L₁-biharmonic hypersurfaces with multiplicities greater than one, H₁ is constant and H₂ = 0, proper L₁-biharmonic hypersurfaces which H₁ is constant, and L₂-biharmonic hypersurfaces which H₁ and H₂ is constant.

• 호남수학학술지
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• 제38권3호
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• pp.593-611
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• 2016

This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.