• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.363-368
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• 2018

The aim of this work is to derive a partial differential equation that explains the movement of vortex lines on a vortex trajectory surface in a three dimensional incompressible inviscid flow.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.36-51
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• 2022

We study the translation surfaces in the pseudo-Galilean space with the condition that one of generating curves is planar. We classify these surfaces whose mean and Gaussian curvatures are functions of one variable.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.2
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• pp.187-194
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• 2002

For the fine grinding process development of semiconductor monocrystalline silicon, wheel rotational speed, chuck rotational speed, feed rate and hysteresis force were controlled. Magic mirror system was used for grinding wheel pattern analysis. Curvature of wheel pattern was measured by fitting equation. The modeling of surface wheel pattern was related to wheel and chuck rotational speed. The calculated curvature of the model was well matched with the measured curvature. The statistical analysis indicated wheel and chuck rotational speed were significantly effective on.

• 한국연소학회:학술대회논문집
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• 1998.10a
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• pp.91-101
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• 1998

The effect of secondary flow on both methane/air and propane/air premixed flame was investigated experimentally. By changing the radius of curvature, various flame behavior was observed. In the V-bend nozzles, flame surface is deformed from axisymmetry. As the exit velocity increased, flame lifted off partially. When the radius of curvature of the V-bend increased, the region where premixed flame is entirely on the rim increased. Since the axial velocity field is changed due to the secondary flow effect, comparison of V-bend and straight tube with the same diameter shows larger V-bend nozzle exit velocity for both flash back and flame blowout. The flame characteristics are mapped with a equivalence ratio, a velocity, and a nozzle radius of curvature. To identify physical reasoning on the flame surface deformation, numerical calculations are conducted. OH radical distributions in flames are visualized by PLIF technique.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.81-92
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• 2008

In this paper, the trajectory scroll in 3-dimensional Minkowski space-time $E_1^3$ is given by a firmly connected oriented line moving with Cartan frame along curve. Some theorems and results between curvatures of base curve and distribution parameter of this surface are obtained. Moreover, some theorems and results related to being developable and minimal of this surface are given. And also, some relationships among geodesic curvature, geodesic torsion and the curvatures of base curve of trajectory scroll are found.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1539-1550
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• 2019

We classify minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles and ruled constant mean curvature (cmc) surfaces in ${\mathbb{S}}^3$. First we show that minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric ${\mathbb{S}}^1$-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in ${\mathbb{S}}^3$ up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in ${\mathbb{S}}^3$(cf. Theorem 3).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.2
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• pp.121-136
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• 1989

In this paper, an attempt has been made to analyze the theoretically and verify experimentally the effect of curvature on the radiation characteristics of microstrip array antennas mounted conformally on the concave surface and the convex surface of the cylindrical body. The analysis of single element microstrip antenna is made by using the analysis method of Transmission Line Model. The theory of array antennas is established by application of the method of transformed coordinates, in which the translation and the ratation about each single element arrayed two-demensionally on the nonplanar surface are under consideration, and it is investigated by computation of the synthetic electric field strength in the far zone. In addition, various radiation characteristics, such as return loss, resonant frequency, radiation pattern, half-power, beamwidth, gain, are measrued and compared with the theroetical values according to the variation of curvature, by designing and building 4-element array microstrip antenna operating at 10 GHz, and microstrip feed lines. As predicted in theroy, it is verified that radiation pattern of antennas mounted on the concave and the convex surfaces alike broadens as the radius of curvature decreases. And for the curved surfaces, aggrement between computed values of the total synthetic radiation power pattern by the method of transformed coordinates and measured valuse is good. Besides, it is found that resonant frequency, input impedance and gain are hardly affected by the radius of curvature.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.8
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• pp.597-602
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• 2016

In image guided surgery, a patient registration process is a critical process for the successful operation, which is required to use pre-operative images such as CT and MRI during operation. Though several patient registration methods have been studied, we concentrate on one method that utilizes 3D surface measurement data in this paper. First, a hand-held 3D surface measurement device measures the surface of the patient, and secondly this data is matched with CT or MRI data using optimization algorithms. However, generally used ICP algorithm is very slow without a proper initial location and also suffers from local minimum problem. Usually, this problem is solved by manually providing the proper initial location before performing ICP. But, it has a disadvantage that an experience user has to perform the method and also takes a long time. In this paper, we propose a method that can accurately find the proper initial location automatically. The proposed method finds the proper initial location for ICP by converting 3D data to 2D curvature images and performing image matching. Curvature features are robust to the rotation, translation, and even some deformation. Also, the proposed method is faster than traditional methods because it performs 2D image matching instead of 3D point cloud matching.

• Journal of the Korean Chemical Society
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• v.16 no.6
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• pp.341-348
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• 1972

The significance of the curvature dependency correction of surface tension is studied in calculating the pore volume distribution of porous adsorbent from nitrogen adsorption isotherm. That is, Kelvin radii are calculated with curvature dependent surface tension values calculated by Chang et al, and then with these Kelvin radii, pore volume distributions of three porous adsorbents, silica alumina (steam deactivated), silica gel (Davidson 59), and silica gel (Mallinc-krodt Standard Luminescent), are calculated. The results are compared with those obtained by the previous method in which surface tension is taken as constant and also with the others. obtained by the modelless method proposed by Brunauer et al. The maximum point of the distribution curve shift to the larger pore radius, when the curvature dependency is considered. Furthermore, the relative pressure at which capillary condensation commences is by far the lower than that accepted previously. This effect becomes significant as the pore radius approaches to the micropore range.

• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.605-616
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• 2004

A new practical implementation of a facial verification system using cumulative histogram of surface curvatures for the local and contour line areas is proposed, in this paper. The approach works by finding the nose tip that has a protrusion shape on the face. In feature recognition of 3D face images, one has to take into consideration the orientated frontal posture to normalize after extracting face area from the original image. The feature vectors are extracted by using the cumulative histogram which is calculated from the curvature of surface for the contour line areas: 20, 30 and 40, and nose, mouth and eyes regions, which has depth and surface characteristic information. The L1 measure for comparing two feature vectors were used, because it was simple and robust. In the experimental results, the maximum curvature achieved recognition rate of 96% among the proposed methods.