• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.681-685
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• 2002

It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $C_1$, $C_2$, …, $C_{r}$ such that (equation omitted)d)

• Journal of Integrative Natural Science
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• v.5 no.1
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• pp.42-45
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• 2012

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on Riemannian warped product manifold $M=({\alpha},\;{\infty}){\times}_fN$ with prescribed scalar curvature functions.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.2
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• pp.55-63
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• 1998

Recently the modified mild-slope equation has been developed by several researchers using different approaches, which, compared to the Berkhoff's mild-slope equation, includes additional terms proportional to the square of bottom slope and to the bottom curvature. By examining this equation, it is shown that both terms are equally important in intermediate-depth water, but in shallow water the influence of the bottom curvature term diminishes while that of the bottom slope square term remains significant. In order to examine the importance of these terms in more detail, the modified mild-slope equation and the Berkhoff's mild-slope equation are tested for the problems of wave reflection from a plane slope, a non-plane slope, and periodic ripples. It is shown that, when only the bottom slope is concerned, the mild-slope equation can give accurate results up to a slope of 1 in 1 rather than 1 in 3, which, until now, has been known as the limiting bottom slope for its proper application. It is also shown that the bottom curvature term plays an important role in modeling wave propagation over a bottom topography with relatively mild variation, but, where the bottom slope is not small, the bottom slope square term should also be included for more accurate results.

• Korean Journal of Optics and Photonics
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• v.16 no.5
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• pp.423-427
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• 2005

In this paper, we propose easily tooling method for Seidel third order aberration, which are not well utilized in actual design process due to the complication of mathematical operation and the difficulty of understanding Seidel third order aberration theory, even though most insightful and systematic means in pre-designing for the initial data of optimization. First, using paraxial ray tracing and Seidel third order aberration theory, spherical aberration coefficient is derived for a two-mirror system with a finite object distance. The coefficient, which is expressed as a higher-order nonlinear equation, consists of design parameters(object distance, two curvatures, and inter-mirror distance) and effective focal length(EFL). Then, the expressed analytical equation is solved by using a computer with numerical analysis method. From the obtained numerical solutions satisfying the nearly zero coefficient condition($<10^{-6}$), linear fitting process offers a linear relationship called the curvature linear equation between two mirrors. Consequently, this linear equation has two worthy meanings: the equation gives a possibility to obtain initial design data for optimization easily. And the equation shows linear relationship to a two-mirror system with a finite object distance under the condition of corrected third order spherical aberration.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.6
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• pp.27-38
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• 1996

A two-dimensional FEM program, which considers bending effects in the membrane fromulation, was developed under plane strain assumption for analyzing forming processes of an arbitrarily shaped draw-die of automotive panels. For the evaluation of bending effects with membrane elements, the bending equivalent forces and stiffnesses are calculated from the bending moment computed using the changes in curvature of the formed shape of two membrane ones. The curves depicted with 3 nodes are described by a circle, a quadratic equation, and a cubic equation, respectively, and in the simulation of the stretch/draw sections of an automotive inner panel, three different description results are compared each other. Also, the bending results are compared with membrane results and measurements in order to verify the validity of the developed program.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2002.09a
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• pp.322-329
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• 2002

The purpose of this study is to develop a reasonable design for transverse confinement reinforcement considering ductility and required transverse confinement reinforcement of RC bridge columns. In order to develop relationships between the curvature ductility and the displacement ductility, the analysis for total 21,600 columns using the computer program NARCC have been carried out for parametric studies. Based on the results from the parametric studies, a correlation equation between the curvature ductility and the displacement ductility was developed. In addition, an equation for calculating the required transverse confinement reinforcement based on ductility demand was developed for seismic design of RC bridge columns. The equations proposed by this study will provide more reasonable and more effective design guidelines for performance-based seismic design of RC bridge columns.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.10b
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• pp.123-124
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• 2002

A press shoe is an element of a machine for squeezing water from wood pulp in the field of manufacturing paper. This is used to compress the pulp enveloped by felt sheet with a large roller. The squeezing force is made by hydraulic pressure. The press shoe has a mechanism similar to a partial hydrostatic bearing. The pressure profile between press shoe and roller affects their squeezing ability, and partial peak pressure can tear the wet pulp. The curvature of the surface of press shoe varies to reduce the peak pressure and increase the mean pressure simultaneously. Therefore, the prediction of pressure distribution considering partially changed curvature of hydrostatic bearing is very important for designing the press shoe. In this study, the difference formulation of Reynolds' equation for partial hydrostatic bearing is by direct numerical method and a computer program to calculate the pressure distribution is developed. We investigate the effect of partially changed curvature of bearing surface on the pressure distribution. Other design parameter for hydrostatic bearing such as depth of pocket and relative velocity are also studied.

• KSTLE International Journal
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• v.3 no.2
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• pp.90-94
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• 2002

A press shoe is an element of a machine for squeezing water from wood pulp in the field of manufacturing paper. This is used to compress the pulp enveloped by felt sheet with a large roller. The squeezing farce is made by hydraulic pressure. The press shoe has a mechanism similar to a partial hydrostatic bearing. The pressure profile between press shoe and roller affects their squeezing ability, and partial peak pressure can tear the wet pulp. The curvature of the surface of press shoe varies to reduce the peak pressure and increase the mean pressure simultaneously, Therefore, the prediction of pressure distribution considering partially changed curvature of hydrostatic bearing is very important far designing the press shoe. In this study, the difference formulation of Reynolds equation far partial hydrostatic bearing is derived by direct numerical method and a computer program to calculate the pressure distribution is developed. We investigate the effect of partially changed curvature of bearing surface on the pressure distribution. Other design parameter far hydrostatic bearing such as depth of pocket and relative velocity are also studied.

• Proceedings of the Optical Society of Korea Conference
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• 2005.07a
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• pp.32-33
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• 2005

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.1676-1682
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• 2008

The vertical curve of railway is installed in changing point where the gradient is more than a certain degree to ensure safe operation of train and comfort of passengers. As a result of CAD work with 3D coordination by using the existing equation, it was found that the simple equation about vertical curve installation suggested in the surveying engineering or railway regulations did not reflect theoretical curvature of circular curve in a case of steep grade and large vertical radius. In this study, for derive precision equation and transition curve about vertical curve, gradient parameters, equation of circles and transition curve equation were used, and it was verified by CAD that the derived equation is exactly satisfied with parameters of geometrical circular and transition curve. This equation could be used to provide more smoothing operation of train and comfort of passengers on vertical curves, especially in case that railway requires precision vertical alignment of track such as super high-speed railway, LRT or Maglev system.