• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.59-71
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• 2018

In the present paper, we study and classify factorable surfaces in a 3-dimensional isotropic space with constant isotropic Gaussian (K) and mean curvature (H). We provide a non-existence result relating to such surfaces satisfying ${\frac{H}{K}}=const$. Several examples are also illustrated.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.155-169
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• 2009

In this paper, we mainly discuss factorable surfaces in 3-dimensional Minkowski space and give classification of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.8
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• pp.1173-1182
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• 1998

A throughflow analysis program for axial flow turbines is constructed, which can handle not only the two-dimensional multi-streamline (streamline curvature) method but also the one-dimensional mean line method. Calculations are performed for single stage and multi-stage axial flowturbines. For a wide operating range, the performance and flow field calculated by the present streamline curvature method are close enough to the test data. It is also revealed for the single stage turbine that the present analysis leads to far better correspondence with the experiment than other researchers" throughflow analyses. A special focus is put on the comparison of the results between the streamline curvature analysis and the mean line analysis. It is found that the mean line analysis can not predict the performance for highly off-designed conditions as accurately as the streamline curvature method, which shows the importance of considering the spanwise variation of loss and flow.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.159-162
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• 2008

This paper presents a modified mean curvature diffusion filter to smooth speckle noise in images. Mean curvature diffusion filter has already shown good results in reducing noise in images while preserving fine details. In the mean curvature diffusion, the rate of smoothing is controlled by the local value of the diffusion coefficient chosen to be a function of the local image gradient magnitude. In this paper, the diffusion coefficient is modified to be controlled adaptively by local image surface slope and heterogeneity. The local surface slope contributes to preserving details (e.g.edges) in image and the local surface heterogeneity helps the smoothing filter consider the amount of noise in both edge and non-edge area. The proposed filter's performance is demonstrated by quantitative experiments using speckle noised aerial image and TerraSAR-X satellite image.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.215-236
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• 1994

The purpose of the present paper is to study generic submanifolds of a Sasakian space form with nonvanishing parallel mean curvature vector field such that the shape operator in the direction of the mean curvature vector field commutes with the structure tensor field induced on the submanifold. In .cint. 1 we state general formulas on generic submanifolds of a Sasakian manifold, especially those of a Sasakian space form. .cint.2 is devoted to the study a generic submanifold of a Sasakian manifold, which is not tangent to the structure vector. In .cint.3 we investigate generic submanifolds, not tangent to the structure vector, of a Sasakian space form with nonvanishing parallel mean curvature vactor field. In .cint.4 we discuss generic submanifolds tangent to the structure vector of a Sasakian space form and compute the restricted Laplacian for the shape operator in the direction of the mean curvature vector field. As a applications of these, in the last .cint.5 we prove our main results.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.461-477
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• 2016

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.37-42
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• 2003

We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.

• Journal of Korean Ophthalmic Optics Society
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• v.11 no.3
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• pp.181-185
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• 2006

The measurement of the radius of corneal curvature with keratometer was followed in 184 university students who wearing RGP contact lens and consisted of female(167), male(17) and keratoconus patients(3). Overall mean value in the radius of corneal curvature is 7.77mm, and right and left eyes is appeared the same mean value. Overall mean value in horizontal and vertical is 7.88mm and 7.65mm. Horizontal means is larger than vertical means by 0.22mm of the all female and male students. Male's mean value in the radius of corneal curvature(7.84mm) is larger than female's by 0.08mm, and right and left eyes is also the same mean value. Keratoconus patients' mean value in the radius of corneal curvature(6.86mm) is smaller than others students by 0.91mm.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.135-146
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• 2001

Let M(sup)n be a space-ike submanifold in a de Sitter space M(sub)p(sup)n+p (c) with constant scalar curvature. We firstly extend Cheng-Yau's Technique to higher codimensional cases. Then we study the rigidity problem for M(sup)n with parallel normalized mean curvature vector field.

• Journal of Korea Multimedia Society
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• v.20 no.12
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• pp.1951-1959
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• 2017

Due to the fact that 3D printing is applied to many areas of life, 3D printing models are often used illegally without any permission from the original providers. This paper presents a novel watermarking algorithm for the copyright protection and ownership identification for 3D printing based on the radius curvature of 3D triangle. 3D triangles are extracted and classified into groups based on radius curvature by the clustering algorithm, and then the mean radius curvature of each group will be computed for watermark embedding. The watermark data is embedded to the groups of 3D triangle by changing the mean radius curvature of each group. In each group, we select a 3D triangle which has the nearest radius curvature with the changed mean radius curvature. Finally, we change the vertices of the selected facet according to the changed radius curvature has been embedded watermark. In experiments, the distance error between the original 3D printing model and the watermarked 3D printing model is approximate zero, and the Bit Error Rate is also very low. From experimental results, we verify that the proposed algorithm is invisible and robustness with geometric attacks rotation, scaling and translation.