• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.260-267
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• 2002

For an elastically suspended rigid body with the planes of symmetry in a three dimensional space, a novel analysis fur the vibration modes is presented. From the decompositions of the stiffness and inertia matrices, the conditions for the existence of pure translation and pure couple modes are analyzed for an elastically suspended rigid body with the planes of symmetry. From this analysis, it can be showed that how the structure of stiffness and inertia must be related in order to produce the pure translation and pure couple modes when an elastically suspended rigid body has one, two, or three planes of symmetry.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.110-117
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• 2000

Vibration modes obtained from a modal analysis can be better explained from a screw theoretical standpoint. A vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as the twisting motion on a screw in a three dimensional space. This paper, presents the method to diagonalize a spatial stiffness matrix by use of a parallel axis congruence transformation. It also describes that the stiffness matrix diagonalized by a congruence transformation, can have the planes of symmetry depending on the location of the center of elasticity. For a plane of symmetry, any vibration mode can be expressed by the axis of vibration. Analytical solutions for the axis of vibration has been derived.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.1001-1017
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• 2021

In this paper, we first apply parabolic inequalities and a maximum principle to give a new proof for symmetry and monotonicity of solutions to fractional elliptic equations with gradient term by the method of moving planes. Under the condition of suitable initial value, by maximum principles for the fractional parabolic equations, we obtain symmetry and monotonicity of positive solutions for each finite time to nonlinear fractional parabolic equations in a bounded domain and the whole space. More generally, if bounded domain is a ball, then we show that the solution is radially symmetric and monotone decreasing about the origin for each finite time. We firmly believe that parabolic inequalities and a maximum principle introduced here can be conveniently applied to study a variety of nonlocal elliptic and parabolic problems with more general operators and more general nonlinearities.

• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.445-459
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• 2024

In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive-negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive-negative mixed powers in the whole space. We also give two special cases.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.283-291
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• 2004

In this paper we show the radial symmetry of topological one-vortex solutions in the Maxwell-Chern-Simons-Higgs Model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.190-197
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• 2002

A new design methodology is presented for the multi-degree-of-freedom vibration absorber for an elastically suspended rigid body with planes of symmetry in general motion. Unlike the common single degree-of-freedom vibration absorber, the presented methodology makes use of both linear and rotational properties of the absorber. It is suggested that an absorber is designed separately for the in-plane and out-of-plane vibration modes and thereby combined the two cases for a six-degree-of-freedom absorber. The nine possible design methods are suggested for the six-degree-of-freedom absorber when an elastically suspended rigid body has one, two, or three planes of symmetry.

• The korean journal of orthodontics
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• v.50 no.4
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• pp.258-267
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• 2020

Objective: This study aimed to analyze the correlation of horizontal and sagittal planes used in two-dimensional diagnosis with lip canting by using three-dimensional (3D) analysis. Methods: Fifty-two patients (25 men, 27 women; average age: 24 years) undergoing treatment for dentofacial deformity were enrolled. Computed tomography images were acquired, and digital imaging and communication in medicine files were reconstructed into a 3D virtual model wherein horizontal and sagittal craniofacial planes were measured. Subsequently, the correlations of lip canting with these horizontal and sagittal planes were investigated. Results: The mandibular symmetry plane, the occlusal plane, Camper's plane, the mandibular plane, Broadbent's plane, and the nasal axis plane were correlated with the amount of lip canting (Pearson's correlation coefficients: 0.761, 0.648, 0.556, 0.526, 0.438, and 0.406, respectively). Planes associated with the lower part of the face showed the strongest correlations; the strength of the correlations decreased in the midfacial and cranial regions. None of the planes showed statistically significant differences between patients with clinical lip canting (> 3°) and those without prominent lip canting. Conclusions: The findings of this study suggest that lip canting is strongly correlated with the mandibular symmetry plane, which includes menton deviation. This finding may have clinical implications with regard to the treatment of patients requiring correction of lip canting. Further studies are necessary for evaluating changes in lip canting after orthognathic surgery.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1719-1724
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• 2017

In this note, companion to the paper [10], we describe an alternative method for finding Laurent polynomials mirror-dual to complete intersections in Grassmannians of planes, in the sense discussed in [10]. This calculation follows a general method for finding torus charts on Hori-Vafa mirrors to complete intersections in toric varieties, detailed in [5] generalising the method of [8].

• Journal of the Society of Naval Architects of Korea
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• v.47 no.6
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• pp.843-849
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• 2010

This paper presents definition of symmetry of a ship section where three symmetries are proposed: material, geometric, and load symmetries. Precise terminologies of centroid, moment plane, and neutral axis plane are also defined. It is suggested that force vector equilibrium as well as force equilibrium are necessary condition to determine new position of neutral axis due to translational and rotational mobility. It is also stated that new reference datum of ENMP(elastic neutral moment plane), PNMP(fully plastic moment plane), ENAP(elastic neutral axis plane), and INAP(inelastic neutral moment plane) are required to define asymmetric section properties such as second moment of area, elastic section modulus, yield moment, fully plastic moment, and ultimate moment. Since collision-induced damage and flooding-induced biaxial bending moment produce typical asymmetry of section, the section properties are calculated for a typical VLCC. Geometry asymmetry is determined from ABS and DNV rules and two moment planes of 0/30 degs are assumed for load asymmetry. It is proved that the property reduction ratios directly calculated from second moment of area are usually larger than area reduction ratio. Reduction ratio of ultimate moment capacity shows almost linearly proportional to area reduction ratio. Mobility of elastic and inelastic neutral axis planes is visually provided.

• Journal of KSNVE
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• v.9 no.5
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• pp.984-990
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• 1999

This paper presents the geometrical methodology to decouple the vibration modes of an elastically supported single rigid body in three-dimensional space. It is shown that the vibration modes can be decoupled by placing the center of elasticity at suitable locations and thereby yielding the plane(s) of symmetry for the given stiffness matrix. The developed methodology has been applied to the actuator supported by the 4-wire suspensions in optical discs, which has one plane of symmetry. For this numerical example, the axes of vibrations have been computed and illustrated with the natural frequencies. The forced response at the objective lens is represented and its geometrical interpretation has been explained as the mutual moment between the axis of vibration and the applied wrench times the line coordinates of the axis of vibration.