• 한국멀티미디어학회논문지
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• 제20권12호
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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.

• Restorative Dentistry and Endodontics
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• 제24권4호
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• pp.623-627
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• 1999

During canal instrumentation of a curved canal, restoring force of endodontic instrument remove more dentin from the inner wall of the curvature. This effect tends to straighten the canal and thus may significantly shorten the working length. This study was to determine the mean reduction in working length after instrumentation according to the curvature. The curvature of mandibular mesial root was determined before instrumentation. 30 canals were divided into 3 groups each 10 on the basis of degree of curvature. Experimental groups as follows. In group 1, canals having curvature from 15 to 20 degrees: in group 2, canals having curvature from 20 to 30degrees; in group 3, canals having curvature above 30 degrees. Experimental teeth in all groups were accessed, and their actual working length determined by passing a size 15 K-file(IAF) just through the minor apical foramen. The canals were sequentially enlarged to size 35 with ProFile .06 series. The change of working length was calculated by measuring the tip of IAF beyond apical foramen by using stereomicroscope. The change of canal curvature following instrumentation were measured using the Schneider technique. The results were as follows. 1. The greatest changes of curvature and working length were observed in the group 3 canals(P<0.05), next were group 2 canals and group 1 canals(P>0.05). 2. Group 1 canals showed a mean reduction in 1.61 degrees and length of 0.12m respectively(P>0.05). 3. Group 2 canals showed a mean reduction in 3.42 degrees(P<0.05) and length of 0.25mm(P>0.05) respectively. 4. Group 3 canals showed a mean reduction in 7.23 degrees(<0.05) and length of 0.64mm respectively(P<0.05).

• 대한수학회지
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• 제41권5호
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• pp.795-808
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• 2004

In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension. mean curvature, sectional curvature, shape operator, k-Ricci curvature, locally conformal Kaehler space form, totally real submanifold.

• 대한방사선기술학회지:방사선기술과학
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• 제30권4호
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• pp.335-341
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• 2007

Simple chest radiography에서 정상인의 가로막(diaphragm)에 대한 계측치는 다음과 같다. 1. 전체 대상자에 대한 흉곽(internal diameter of thorax: ID)의 평균은 293.3 mm이었으며, 최소 221.0 mm, 최대 335.3 mm이었다. 2. 가로막의 높이는 오른 가로막이 높은 경우가 81.4%, 오른 가로막과 왼 가로막이 동일한 경우가 16.2%, 왼 가로막이 높은 경우가 2.4% 순으로 나타났다. 3. 오른 가로막이 높은 경우 오른 가로막의 평균 높이는 15.2 mm이었으며, 가장 낮은 경우는 2.0 mm, 가장 높은 경우는 41.7 mm이었다. 4. 왼 가로막이 높은 경우 왼 가로막의 평균 높이는 11.5 mm이었으며, 가장 낮은 경우는 4.7 mm, 가장 높은 경우는 30.4 mm이었다. 5. 가로막의 만곡도에서 오른 가로막의 평균 만곡은 22.9 mm이었고, 가장 작은 경우는 10.4 mm, 가장 큰 경우는 37.3 mm이었다. 6. 왼 가로막의 평균 만곡은 22.4 mm이었고, 가장 작은 경우는 11.3 mm, 가장 큰 경우는 42.2 mm이었다. 7. ID와 오른 가로막과 왼 가로막 만곡에 대한 관계에서 ID는 오른 가로막 만곡(r= .427, p<.001)과 왼 가로막 만곡(r= .425, p<.001)에서 모두 통계적으로 유의미한 정적 상관관계를 보였다. 8. 오른 가로막 만곡과 왼 가로막 만곡의 관계는(r= .403, p<.001) 통계적으로 유의미한 정적 상관관계를 보였다.

• 대한수학회지
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• 제53권4호
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• pp.737-767
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• 2016

This paper concerns closed hypersurfaces of dimension $n{\geq}2$ in the hyperbolic space ${\mathbb{H}}_{\kappa}^{n+1}$ of constant sectional curvature evolving in direction of its normal vector, where the speed equals a power ${\beta}{\geq}1$ of the mean curvature. The main result is that if the initial closed, weakly h-convex hypersurface satisfies that the ratio of the biggest and smallest principal curvature at everywhere is close enough to 1, depending only on n and ${\beta}$, then under the flow this is maintained, there exists a unique, smooth solution of the flow which converges to a single point in ${\mathbb{H}}_{\kappa}^{n+1}$ in a maximal finite time, and when rescaling appropriately, the evolving hypersurfaces exponential convergence to a unit geodesic sphere of ${\mathbb{H}}_{\kappa}^{n+1}$.

• 대한수학회보
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• 제42권1호
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• pp.39-44
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• 2005

Let M be a compact hypersurface in hyperbolic space and let A be the area of M and V be the volume of the compact domain bounded by M. In this paper, we find a lower bound for $\frac{A}{V}$ in two cases, M has constant scalar curvature and M has constant mean curvature.

• 대한수학회보
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• 제57권4호
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• pp.1049-1060
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• 2020

We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in [26] and we also remove the condition that the second fundamental form is uniformly bounded when t ∈ (-∞, -1).

• 호남수학학술지
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• 제30권4호
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• pp.637-644
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• 2008

In this paper, we study some properties about the parallel surfaces of ruled surfaces in a Euclidean 3-space. Furthermore, we classify the parallel surfaces of ruled surfaces in a Euclidean 3-space satisfying a linear type and a quadric type with respect to the Gaussian curvature and the mean curvature.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.273-293
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• 2016

In this paper, we obtain that every biharmonic non-degenerate hypersurfaces in semi-Euclidean space $E^5_s$ with constant scalar curvature of diagonal shape operator has zero mean curvature.

• 대한수학회논문집
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• 제37권3호
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• pp.851-864
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• 2022

We define a kind of sectional curvature and 𝛿-invariants for statistical manifolds. For statistical submanifolds the sum of the squared mean curvature and the squared dual mean curvature is bounded below by using the 𝛿-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds.