• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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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.

• Honam Mathematical Journal
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• v.44 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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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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• v.19 no.5
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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.

• Journal of Korea Game Society
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• v.2 no.2
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• pp.28-36
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• 2002

In general, triangular meshes have been used for modeling geometric objects such as virtual game characters. The dense meshes give us considerable advantages in representing complex, highly detailed objects, while they are more expensive for storing, transmitting and rendering the objects. Therefore, several researches have been performed for producing a high quality approximation in place of detailed objects, that is, a simplification of triangular meshes. In this paper, we propose a new measure with respect to edges and vertices, which is called an approximate mean curvature and is used as criteria to simplify an original mesh. An edge mean curvature is computed by considering its neighboring edges, and a vertex mean curvature is defined as an average of its incident edges' mean curvatures. And we apply the proposed measure to simplify the models such as a bunny, dragon and teeth. As a result, we can see that the mean curvatures can be used as good criteria for providing much better approximation of models.

• Communications for Statistical Applications and Methods
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• v.16 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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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.

• Honam Mathematical Journal
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• v.38 no.3
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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.