• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.109-121
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• 2015

In this paper, we investigate horizontal lightlike hypersurfaces of Robertson-Walker spacetimes. Some results involving the unique existence of the screen distribution and the symmetry of the induced Ricci curvature tensor of horizontal lightlike hypersurfaces are presented. We also obtain some properties concerning the symmetry and the parallelism of the second fundamental forms of such lightlike hypersurfaces.

• 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 Korean Ophthalmic Optics Society
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• v.9 no.2
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• pp.211-221
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• 2004

The purpose of this study is to evaluate the distribution and change of curvature of the anterior corneal surface with age in emmetropia. 504 subjects who have emmetroia with good naked vision of at least 0.6-1.0 (spherical equivalent: +0.75D- -0.75D) participated in this study. The 504 subjects into 8 groups with 10 year interval from 3-year to 83-year, and their corneal curvatures were analyzed using manual keratometry. The results are as follows. In individual analysis: First, regression analysis of corneal curvature radius with age has given an equation: Y = -0.003x + 7.796 (r = -0.26). The average corneal curvature radii was measured to be $7.68{\pm}0.25mm$ at 38.3-year and range was 6.98-8.54 mm. Second, frequency of corneal curvature radius were obtained in 36% between 7.61 and 7.80 mm, 78% between 7.41 and 8.00 mm, 96% between 7.21 and 8.20 mm, 100% between 6.98 and 8.54 mm. Third, as for the comparison of corneal curvature radius with respect to sex, The mean value of male (n = 304, mean: 37.6-year $7.72{\pm}0.24mm$, Range: 7.09-8.54 mm) is larger than that of female (n = 200, mean: 39.3-year $7.62{\pm}0.24mm$, Range: 6.98-8.42 mm) by 0.1mm (p<0.01). In groups analysis: First, regression analysis of corneal curvature radius with age has given an equation: $Y=-0.0066x^2+0.0227x+7.7282$ (r = -0.90). Second, vertical and horizontal curvature radius decreased with age (p < 0.01). Especially the decrease of horizontal curvature radius were more pronounced than the decrease of vertical (horizontal:10-70 age group: 0.38 mm decrease, vertical:10-70 age group: 0.20 mm decrease). Third, difference between steep and flat meridian (astigmatism) progressively decreased with age. (low age group:0.18 mm difference, high age group: 0.08 mm difference). Fourth, the corneal curvature radius of male was larger than female's in total groups(p < 0.01). Consequently, the change of corneal curvature radius with age progressively decreased in all conditions (mean, vertical, horizontal, male, and female) and this change was more outstanding in horizontal rather than in vertical.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.335-342
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• 2011

In this paper, we prove that minimal hypersurfaces when n $\geq$ 3 and nonzero constant mean curvature hypersurfaces when n $\geq$ 2 foliated by spheres in parallel horizontal hyperplanes in $\mathbb{H}^n{\times}\mathbb{R}$ must be rotationally symmetric.

• International Journal of Highway Engineering
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• v.14 no.1
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• pp.1-8
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• 2012

The horizontal alignment of road is deeply related with the stability of the road and traffic capacity. It is necessary to analyze horizontal alignment of road accurately for efficient maintenance of the road and relevance judgment about the standard. Recently the study on horizontal alignment of road using Lidar data and GPS was concluded, but they were many problem analyzing horizontal alignment radius of curvature in wide area. In this study, the tool which the radius of curvature can evaluate the suitability about "Rules about the Road Structure & Facilities Standards" by using center lines of the road of the digital map tries to implement on GIS. The interface was designed and implemented which can automatically estimate the Road Centerline Horizontal Alignment by using $ESRI^{(R)}$ $ArcObject^{TM}$.

• The Journal of Engineering Geology
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• v.25 no.2
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• pp.273-280
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• 2015

Delays in horizontal well drilling when encountering heterogeneous sediments can have negative effects on the construction process at a riverbank filtration site. Grain size analysis, including calculation of the coefficient of uniformity and the coefficient of curvature, was conducted on soil samples collected at each drilling depth during the process of drilling horizontal wells. These results were then used to develop a linear equation for estimating drilling velocity using the coefficient of uniformity and the coefficient of curvature as inputs. Testing of the linear equation in other horizontal wells indicates that the equation is most appropriate for coarse-sand-sized and well-sorted sediment. Because this study was conducted in a region with small- to medium-sized streams, more data are needed from larger rivers to modify the general equation. Our results will provide better estimates of drilling velocity, in turn enabling more detailed design and more effective construction management at riverbank filtration sites.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.265-275
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• 2001

In the previous paper we studied n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space CP(sup)(n+p)/2, and especially determined such submanifolds under curvature conditions related to vertical direction; In the present article we determine such submanifolds under curvature conditions related to horizontal directions.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.575-592
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• 2021

In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle T^*M over an anti-paraKähler manifold (M, 𝜑, g) as a new natural metric with respect to g non-rigid on T^*M. Firstly, we investigate the Levi-Civita connection of this metric. Secondly, we study the curvature tensor and also we characterize the scalar curvature.

• Computers and Concrete
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• v.11 no.6
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• pp.515-529
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• 2013

The moment-curvature relation for simple bending is a well-studied subject and the classical moment-curvature diagram is commonly found in literature. The influence of axial forces has generally been considered as compression onto symmetrically reinforced cross-sections, thus strain at the reference fiber never has been an issue. However, when dealing with integral structures, which are usually statically indeterminate in different degrees, these concepts are not sufficient. Their horizontal elements are often completely restrained, which, under imposed deformations, leads to moderate compressive or tensile axial forces. The authors propose to analyze conventional beam cross-sections with moment-curvature diagrams considering asymmetrically reinforced cross-sections under combined influence of bending and moderate axial force. In addition a new diagram is introduced that expands the common moment-curvature relation onto the strain variation at the reference fiber. A parametric study presented in this article reveals the significant influence of selected cross-section parameters.

• Journal of Korean Ophthalmic Optics Society
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• v.1 no.2
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• pp.71-76
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• 1996

As the results of measurement of the radius of corneal curvature with keratometer, for the right eye of 91 male adults, horizontal radius is 7.16 mm to 8.49 mm and vertical radius is 7.03 mm to 8.34 mm, and for the left eye of male adults, horizontal radius is 7.10 mm to 8.48 mm and vertical radius is 7.01 mm to 8.24 mm. In case of 61 female adults, horizontal radius is 7.16 mm to 8.45 mm, vertical radius 7.11 mm to 8.18 mm for the right eye, and horizontal radius 7.15 mm 108.43 mm and vertical radius 7.01 mm to 8.26 mm for the left eye. The mean value of radius of corneal curvature is 7.74 mm for male and 7.69 mm for female. Also the mean value of horizontal radius is 7.79 mm and vertical radius is 7.64 mm. Overall mean value of the radius of corneal curvature is 7.71 mm that is corresponded to Gullstrand's eye. The horizontal radius is 0.15 mm bigger than vertical radius.