• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.859-881
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• 2010

The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.

• Journal of Mechanical Science and Technology
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• v.16 no.4
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• pp.564-571
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• 2002

Three-dimensional numerical analysis of the turbulent premixed flame propagation in a constant volume combustion chamber is performed using the KIVA-3V code (Amsden et. al. 1997) by the flame surface density (FSD) model. A simple near-wall boundary condition is eaployed to describe the interaction between turbulent premixed flame and the wall. A mean stretch factor is introduced to include the stretch and curvature effects of turbulence. The results from the FSD model are compared with the experimental results of schlieren photos and pressure measurements. It is found that the burned mass rate and flame propagation by the FSD model are in reasonable agreement with the experimental results. The FSD combustion model proved to be effective for description of turbulent premixed flames.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.5 s.170
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• pp.55-62
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• 2005

This paper presents mainly a procedure to get the mathematical form of the manufactured aspherical lens. Generally Schulz formula describes the aspherical lens profile. Therefore, the base curvature, conic constant. and high-order polynomial coefficient should be set to get the approximated design equation. To find the best-approximated aspherical form, lens profile is measured by a commercial stylus profiler, which has a sub-micrometer measurement resolution. The optimization tool is based on the minimization of the root mean square of error sum to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the lens refractive power measurement shows the experimental consistency with the curvature distribution of the best-approximated aspherical surface equation

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1337-1346
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• 2015

We examine the relationship of the shape operator of a surface of Euclidean 3-space with its Gauss map of pointwise 1-type. Surfaces with constant mean curvature and right circular cones with respect to some properties of the shape operator are characterized when their Gauss map is of pointwise 1-type.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.555-561
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• 2017

We show that a closed curve invariant under inversions with respect to two intersecting circles intersecting at angle of an irrational multiple of $2{\pi}$ is a circle. This generalizes the well known fact that a closed curve symmetric about two lines intersecting at angle of an irrational multiple of $2{\pi}$ is a circle. We use the result to give a different proof of that a compact embedded cmc surface in ${\mathbb{R}}^3$ is a sphere. Finally we show that a closed embedded cmc surface which is invariant under the spherical reflections about two spheres, which intersect at an angle that is an irrational multiple of $2{\pi}$, is a sphere.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.17 no.4
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• pp.426-434
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• 1988

Series expansion is applied to solve the laminar boundary layer equations for the problem of natural convection from vertical cylinder with uniform surface heat flux. The series in terms of transverse curvature parameter ${\xi}$ is extended to five terms and is well converged by applying the Shanks transform twice. In case of natural convection from a vertical cylinder heated with uniform surface heat flux, it is possible to consider the vertical cylinder as vertical plate under the condition of D/L${\geq}$A/$(Gr_L^*)^{1/5}$, where A is in the range of 5.7~55.2. Also, mean Nusselt number ${\overline{Nu_L}}$ can be represented as $C_1(Ra_L^*)^{1/5}$, where $C_1$ is a constant which depends on Pr and is in the range of 0.5~0.8.

• The KIPS Transactions:PartB
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• v.11B no.3
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• pp.297-302
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• 2004

In this paper, the 3-D shape description for the objects with the cone ridge and valley surfaces, and the corresponding threshold value selection for surface classification are considered. The existing method based on the mean and Gaussian curvatures(H and K) of differential geometries cannot properly describe cone primitives, which are some of the most common objects in the real world. Also the existing method for surface classification based on the sign values of H and K has Problems in practical applications. For this, cone surface shapes are classified cone ridges and cone valleys are derived from surfaces using the fact that H values are constant case of cylinder surfaces and variable for cone surfaces, respectively. Also threshold value selection for surface classification from a statistical point of view is proposed. The effectiveness of the proposed methods are verified through experiments.