• Honam Mathematical Journal
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• v.44 no.4
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• pp.594-617
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• 2022

In this study, firstly Smarandache ruled surfaces whose base curves are Smarandache curves derived from Frenet vectors of the curve, and whose direction vectors are unit vectors plotting Smarandache curves, are created. Then, the Gaussian and mean curvatures of the obtained ruled surfaces are calculated separately, and the conditions to be developable or minimal for the surfaces are given. Finally, the examples are given for each surface and the graphs of these surfaces are drawn.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.387-395
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• 2021

In this paper, we give a characterization of a Delaunay surface in ℝ³. Let Σ be a CMC-H surface in ℝ³ with H ≠ 0. If Σ meets a plane with constant contact angle along a circle, then it is rotationally symmetric, i.e., Σ is part of a Delaunay surface.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.299-306
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• 2010

In this article we consider axes of a complete embedded minimal surface in $R^3$ of finite total curvature, and then prove that there is no planar ends at which the Gauss map have the minimum branching order if the minimal surface has a single axis.

• 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.

• The Journal of the Korea Contents Association
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• v.10 no.10
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• pp.451-455
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• 2010

Hydraulics usually deals with flows with free surface. When the surface curvature is small, the assumption of hydrostatic pressure distribution is enough. However, in the case, when the curvature is big, the non-hydrostatic pressure distribution should be taken into account and the Navier-Stokes equations should be employed instead of the depth-averaged shallow water equations. For the simulation of two immiscible fluids with different characteristics (e.g. water and air, water and oil), the level set method is selected for this purpose. The developed model is applied to classical dam break problem and the computational results are compared with the experimental data. The effectiveness of the developed model is confirmed.

• Bulletin of the Korean Chemical Society
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• v.32 no.10
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• pp.3702-3706
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• 2011

The conformation of a neuropeptide, substance P (SP), in isotropic (q = 0.5) acidic bicelles was investigated using two-dimensional NMR techniques. By the nuclear Overhauser effect (NOE) cross peaks between SP and long-chain lipid molecules SP was probed to bind on the flat surface of the disc-like bicelles. Structural analysis of NMR data indicated that the helical conformation of SP extended to the C-terminal region of Leu10 as well as in the mid-region from Pro4 to Phe8. As compared with the conformations of SP bound on the sodium dodecylsulfate (SDS) or the dodecylphosphocholine (DPC) micelles with curved surfaces, the surface curvature of the membrane mimics was found to be one of the major factors inducing the biologically relevant conformation of SP. The negative surface charge of the membrane is also a key factor inducing both the binding of SP on the membrane and its biologically active structure.

• Transactions of Materials Processing
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• v.7 no.2
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• pp.177-185
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• 1998

The kinematically admissible veolcity field is developed for the shapes of dead metal zone and the curving velocity distribution in the eccentric plane dies extrusion. The shape of dead metal zone is defined as the boundary surface with the maximum friction constant between the deformable zone and the rigid zone. The curving phenomenon in the eccentric lane dies is caused by the eccentricity of plane dies. The axial velocity distribution in the plane dies is divided in to the uniform velocity and the deviated velocity. The deviated velocity is linearly changed with the distance from the center of cross-section of the workpiece. The results show that the curvature of products and the shapes of the dead metal one are determined by the minimization of the plastic work and that the curvature of the extruded products increase with the eccentricity.

• Journal of KSNVE
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• v.11 no.1
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• pp.156-166
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• 2001

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.777-787
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• 2005

In this paper we study (n + 1)-dimensional compact contact CR-submanifolds of (n - 1) contact CR-dimension immersed in an odd-dimensional unit sphere $S^{2m+1}$. Especially we provide necessary conditions in order for such a sub manifold to be the generalized Clifford surface $$S^{2n_1+1}(((2n_1+1)/(n+1))^{\frac{1}{2}})\;{\times}\;S^{2n_2+1}(((2n_2+1)/(n+1)^{\frac{1}{2}})$$ for some portion (n1, n2) of (n - 1)/2 in terms with sectional curvature.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.683-695
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• 2019

In the present paper, we study curves in 𝔼³ with density $e^{ax^2+by^2}$, where a, b ∈ ℝ not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanishing weighted curvature and the ruling curves are Smarandache curves of this curve. Then, we give some characterizations about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them.