• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.12
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• pp.1825-1833
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• 1990

This paper proposes an efficient algorithm that constructs 3-dimensional solid object from 3 orthogonal views. This algorithm inputs vertex and edge information of 3 orthogonal views and generates 2 dimensional surfaces, 3 dimensional vertices, edges and surfaces and then compares 2 dimensional projections of 3 dimensional surfaces with surfaces from othorgonal views. This algorithm is useful for CAD system, 3 dimensional scene analysis system and object modeling for real-time animation and has been implemented in C language on IRIS workstation. The effectiveness of this algorithm is shown by examples of aircrafts' models.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.191-198
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• 2012

Minimal surfaces with given boundaries are the solutions of Plateau's problem. In studying the calculus of variations for the minimal surfaces, the functional ${\varepsilon}$, corresponding to the energy of surfaces, is introduced in [Ki09]. In this paper we derive a formula for the second derivative of ${\varepsilon}$, which is necessary for further theories of the calculus of variations.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.269-274
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• 2011

We investigate the divisor class group of surfaces over finite fields. For some surfaces the divisor class group depends on the characteristic of the field. We calculate the determinant of a matrix which will provide an information about the divisor class group of the surfaces.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.41-61
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• 2008

We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.199.1-199.1
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• 2014

In nonlinear optics, the properties of nonlinear optical responses such as polarization and nonlinear analysis of the nonlinear surfaces were investigated using the jellium model by optical second harmonic generation. The nonlinear response of the Al metal surfaces were calculated using TDLDA. Band structure, lattice constant and bulk modulus of the Al metal were investigated. Effective potential and electron density were compared by changing different.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.1
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• pp.120-129
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• 1990

In this paper, 3-dimensional object segmentation and classification are proposed. Planar object is segmented surface using jump boundary and internal boundary. Curved object is segmented surfaces by maximin clustering method. Segmented surfaces are classified by depth trends and angle measurement of normal vectors. Classified surfaces are merged according to adjacent surfaces and compared to Guassian curvature and mean curvature method. The proposed methods have been successfully applied to the synthetic range images and shows good classification.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.547-557
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• 2018

We establish some characterizations of isoparametric surfaces in the three-dimensional Euclidean space, which are associated with the Laplacian operator defined by the so-called II-metric on surfaces with non-degenerate second fundamental form and the elliptic linear Weingarten metric on surfaces in the three-dimensional Euclidean space. We also study a Ricci soliton associated with the elliptic linear Weingarten metric.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.353-359
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• 2011

In this paper, we characterize a semi-Riemannian manifolds satisfies the axiom of indefinite surfaces. We obtain the following result: If a semi-Riemannian manifold satisfies the axiom of indefinite surfaces, then it is a real space form.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.461-477
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• 2016

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.515-520
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• 2019

We give new evidence that "complicated" Heegaard surfaces behave like incompressible surfaces. More precisely, suppose that a closed connected orientable 3-manifold M contains a closed connected incompressible surface F which separates M into two (connected) components $M_1$ and $M_2$. Let S be a Heegaard surface of M. Our result is that if the Hempel distance of S is at least four, then S is isotoped so that $S{\cap}M_i$ is incompressible for each i = 1, 2.