• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1459-1468
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• 2018

We show that an umbilic-free minimal surface in ${\mathbb{R}}^3$ belongs to the associate family of the catenoid if and only if the geodesic curvatures of its lines of curvature have a constant ratio. As a corollary, the helicoid is shown to be the unique umbilic-free minimal surface whose lines of curvature have the same geodesic curvature. A similar characterization of the deformation family of minimal surfaces with planar lines of curvature is also given.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.777-790
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• 2010

We study surfaces in the 3-dimensional Euclidean space with two family of planar lines of curvature. As a result, we establish some characterization theorems for such surfaces.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.685-692
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• 2012

Consider a hypersurface $M^n$ in $\mathbb{R}^{n+1}$ with $n$ distinct principal curvatures, parametrized by lines of curvature with vanishing Laplace invariants. (1) If the lines of curvature are planar, then there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations Dupin hypersurfaces with constant M$\ddot{o}$bius curvature. (2) If the principal curvatures are given by a sum of functions of separated variables, there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations, Dupin hypersurfaces with constant M$\ddot{o}$bius curvature.

• 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.

• Transactions of Materials Processing
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• v.6 no.2
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• pp.118-135
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• 1997

In order to analyze the deformation and residual curvature of steel sheets in the strip processing lines, a program for calculating curvature and work hardening of sheet was developed. Strip deformation caused by repeated bending under tension in the process lines was analyzed on the basis of the incremental-plasticity theory with the mixed hardenting model for the purpose of predicting the strip shape and the yield stress change. The developed calculation program was applied to predict curl and gutter of sheets within a 10% difference. The yield stress increment was also predicted with the similar accuracy. Application of the model to tension legvelling process showed that gutter could be controlled by intermesh and elongation. The yield stress increment in the electro-galvanizing line calculated by the developed program was found to be dependent on the yield strength, the applied tension and the diameter of the smallest roll.

• The Journal of the Acoustical Society of Korea
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• v.23 no.3
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• pp.192-196
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• 2004

A decision of the modulus of elasticity is made by using the degree of bending strength of materials for loudspeaker damper and the radius of corrugation lines and the radius of curvature of each corrugation as a geometrical element. And it is compared with experimental measurements. As a result. the elasticity of damper is proportional to the degree of bending strength and inversely proportional to the radius of corrugation lines and inversely proportional to the square of the radius of curvature. We made a small loudspeaker using a modified damper which take the form of inner small curvature and outer large curvature of each corrugation. This loudspeaker have the increased sensitivity in high frequency and also in low frequency region.

• Journal of the Korean Society of Industry Convergence
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• v.20 no.4
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• pp.307-311
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• 2017

Ultra short pulse laser processing with the PI (polyimide) substrate is conducted to increase flexibility and radius of curvatures. A femtosecond laser is used to perform micro machining by minimizing the heat effect in PI substrate. The laser processing according to the parameters, such as fabricated line width, depth, laser power, distance between lines, is carried out to understand the characteristics of fabricated lines. A bending test is carried out to evaluate bending shapes and the radius of curvature after bending and spreading it 1000 times. The results demonstrates that the radius of curvature decreases in deepen lines and increases with the augment of the number of the fabricated lines, and distance between lines.

• Journal of the Korean Society of Clothing and Textiles
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• v.14 no.3 s.35
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• pp.183-195
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• 1990

The author has studied the effect of clothes design to mask the dorsal curvature that is one of the commonest changes in elderly women. Body measurements including the body type and the status of dorsal curvature were perfor-med on 153 women of over 60 years of age, and then a body form to fit to the mean measure-ments was made to evaluate the effects of various designs to it. With 31 pattern designs modified by changing in their slash lines and gathers using darts, the diminishing effect of the rounded back were evaluated by means of sensory test. The results of this study can be summarized as follows: I . Results from the body measurements 1) The mean body type in elderly women was that of obesity. 2) With the advancement of age, the angle to indicate the degree of dorsal curvature as well as the angle to indicate the posture are increased. II . Concerning to the clothes design to diminish the shape of dorsal curvature 1) Among the designs by the position of darts, the basic pattern (Fig. 5-1-(1)) showed the best effect to mask the shape of dorsal curvature. 2) Out of the applied designs of princess lines, that in which the slash line is pointing toward the shoulder point (Fig. 5-2-(1)) seemed to be most effective. 3) What has angled princess line (Fig. 5-3-(1)) had the most diminishing effect among the waist darts and armhole princess lines. 4) Among the V-shaped designs, the slashed at the shoulder point (Fig. 5-4-(1)) had the best effect to lessen the shape of the dorsal cuuature. 5) Wider angle yoke had better effect to the narrow angle one among the designs with straight yoke, and that with downward direction (Fig. 5-5-(1)) showed the best effect. 6) Between straight wide angle yoke and curved yoke, that of curved one with downward direction (Fig. 5-6-(1)) had better effect as far as the masking effect of dorsal curvature is concerned. 7) Gathers around the neck showed better effect to those around the shoulder, and the more amount of gathers (Fig. 5-7-(1)), there was better effect. 8) The design with midline gathers at the level of horizontal slash line of armhole (Fig. 5-8-(1)) showed better effect to that with seperated gathers. 9) In case of design with gathers at the horizontal line of armhole, it showed the better effect with less amount of gathers in midline ones, but with more amount in the side ones. 10) Considering all 7 different designs with better effect in covering the shape of dorsal curvature, it was evident that the design with gathers was far better than the design with application of slash lines.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.5
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• pp.365-371
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• 2015

Hull plate consists of various types of curved plates and there also exists corresponding processing methods. Typically, curved plates can be divided into convex type and saddle type. Large amount of research has been conducted mainly focusing on application of processing method of convex type, saddle type and hybrid type, but research on determination and processing method application of the most difficult S-shaped curved plate that has inflection lines has not been carried out yet. In this paper, as the fundamental research of appropriate processing method application, a calculation method is proposed to calculate inflection lines on curved plates. In order to calculate inflection lines, normal curvature and information of fabricated curved plates should be utilized. We compare the workability of the fabrication for hull plate using inflection line.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.210.2-210.2
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• 2005