• Honam Mathematical Journal
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• v.46 no.2
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• pp.279-290
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• 2024

In this study, tubular surfaces were introduced according to the modified orthogonal frame defined at the points where the torsion is different from zero in the 3-dimensional Euclidean space. First, the relations between the Frenet frame and the modified orthogonal frame with torsion are given. Then, the singularity, Gaussian curvature, mean curvature and basic forms of the tubular surface given according to the modified orthogonal frame with torsion were calculated. In addition, the conditions for the parameter curves of the tubular surface to be geodesic, asymptotic and line of curvature were examined. Finally, tubular surface examples based on both the Frenet frame and the modified orthogonal frame with torsion were given to support the study.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.05a
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• pp.879-880
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• 2010

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.579-593
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• 2007

In this paper, we study some properties of ruled surfaces in a three-dimensional Lorentz-Minkowski space related to their Gaussian curvature, the second Gaussian curvature and the mean curvature. Furthermore, we examine the ruled surfaces in a three-dimensional Lorentz-Minkowski space satisfying the Jacobi condition formed with those curvatures, which are called the II-W and the II-G ruled surfaces and give a classification of such ruled surfaces in a three-dimensional Lorentz-Minkowski space.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.295-298
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• 2000

In this research, a novel sampling strategy for a CMM to inspect freeform surfaces is proposed. Unlike primitive surfaces, it is not easy to determine the number of sampling points and their locations for inspecting freeform surfaces. Since a CMM operates with slower speed in measurement than optical measuring devices, it is important to optimize the number and the locations of sampling points in the inspection process. When a complete inspection of a surface is required, it becomes more critical. Among various factors to cause shape errors of a final product, curvature characteristic is essential due to its effect such as stair-step errors in rapid prototyping and interpolation errors in NC tool paths generation. Shape errors are defined in terms of the average and standard deviation of differences between an original model and a produced part. Proposed algorithms determine the locations of sampling points by analyzing curvature distribution of a given surface. Based on the curvature distribution, a surface area is divided into several sub-areas. In each sub-area, sampling points are located as further as possible. The optimal number of sub-areas. In each sub-area, sampling points are located as further as possible. The optimal number os sub-areas is determined by estimating the average of curvatures. Finally, the proposed method is applied to several surfaces that have shape errors for verification.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.285-289
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• 1999

In this paper, we estimate the total curvature of non-parametric minimal surfaces by using the properties of univalent harmonic mappings defined on ${\Delta}=\{z:{\mid}z:{\mid}>1\}$.

• Korean Journal of Optics and Photonics
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• v.18 no.2
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• pp.130-134
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• 2007

I present a novel curvature profilometer devised fur the profile measurement of aspheric and free-form surfaces on the nanometer scale. A profile is reconstructed from measuring the curvature of a test part of the surface at several locations along a line. For profile measurement of free-farm surfaces, methods based on local part curvature sensing have strong appeal. Unlike full-aperture interferometry they do not require customized null optics. The measurement accuracy of the curvature profilometer was assessed by comparison with a well-calibrated interferometer in NIST. Experimental results prove that the maximum discrepancy turns out to be 37 nm on the 28 mm measurement range for the spherical mirror.

• Journal of the Korea Institute of Military Science and Technology
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• v.15 no.6
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• pp.779-785
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• 2012

In this paper, we have analyzed the curvature effects of the finite FSS(frequency selective surface) using the 3-D method of moment using the BiCGSTab algorithm as an iterative method. To validate the analysis method in this paper, we compared the RCS(radar cross section) of PEC(perfect electric conductor) sphere with theoretical results and it shows well agreements. The tripole slot FSSs which have many application in military were selected for the investigation of curvature effect and RCS as a frequency characteristics were observed with the variation of the curvature rate. Simulation results shows that curvature effect can significant effect the passband frequency and bandwidth of FSS. We suggest that the curvature effect must be considered at the stage of design FSS application like FSS radome.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.59-71
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• 2018

In the present paper, we study and classify factorable surfaces in a 3-dimensional isotropic space with constant isotropic Gaussian (K) and mean curvature (H). We provide a non-existence result relating to such surfaces satisfying ${\frac{H}{K}}=const$. Several examples are also illustrated.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.155-169
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• 2009

In this paper, we mainly discuss factorable surfaces in 3-dimensional Minkowski space and give classification of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1261-1269
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• 2023

For a fixed parametrization of a curve in an orientable two-dimensional Riemannian manifold, we introduce and investigate a new frame and curvature function. Due to the way of defining this new frame as being the time-dependent rotation in the tangent plane of the standard Frenet frame, both these new tools are called flow.