• Restorative Dentistry and Endodontics
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• v.24 no.4
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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).

• Journal of the Korean Mathematical Society
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• v.41 no.5
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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.

• Journal of radiological science and technology
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• v.30 no.4
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• pp.335-341
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• 2007

General anatomy classifies diaphragm as muscle of boundary between chest and abdomen, while radiology divides it into right and left hemidiaphragm, because it is more advantageous in radiological diagnosis on chest and abdomen. Based on these anatomic characteristics of diaphragm, this study aimed to measure the height and curvature of right and left diaphragm in simple chest radiography. As a result, this study came to the following conclusions : 1. For all subjects who joined this study, it was found that their mean transverse diameter in internal diameter of thorax(ID) amounted to 293.3 mm(min. 221.0 mm, max 335.3 mm). 2. For the right and left height of diaphragm, it was found that 81.4% showed higher right diaphragm ; 16.2% showed equivalent height between right and left diaphragm ; and only 2.4% showed higher left diaphragm. 3. For higher right diaphragm, it was found that the mean height of right diaphragm amounted to 15.2 mm(min. height = 2.0 mm, max. height = 41.7 mm). 4. For higher left diaphragm, it was found that the mean height of left diaphragm amounted to 11.5 mm(min. height = 4.7 mm, max. height = 30.4 mm). 5. The mean curvature of right diaphragm amounted to 22.9 mm(min. curvature = 10.4 mm, max. curvature = 37.3 mm). 6. The mean curvature of left diaphragm amounted to 22.4 mm(min. curvature = 11.3 mm, max. curvature = 42.2 mm). 7. For possible associations between ID and right/left diaphragm curvature, it was noted that ID was in significantly positive correlations with right diaphragm curvature(r= .427, p<.001) and left diaphragm curvature(r= .425, p<.001) on statistical level. 8. For possible associations between right and left diaphragm curvature, it was found that right diaphragm curvature was in significantly positive correlations with left diaphragm curvature(r= .403, p<.001).

• Journal of the Korean Mathematical Society
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• v.53 no.4
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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 ${\mathbb{H}}_{\kappa}^{n+1}$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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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).

• Honam Mathematical Journal
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• v.30 no.4
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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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• v.56 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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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.

• 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.