• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.321-327
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• 1999

Graves and Nomizu investigated an indefinite version of the Cartan's result. Specifically they obtained the conditions for all non-degenerate planes to have the same sectional curvature in the in-definite Riemannian manifold. In this paper we are to study the cosym-plective version of the results of Graves and Nomizu and characterize an indefinite cosymplectic spce form.

• The korean journal of orthodontics
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• v.21 no.2 s.34
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• pp.367-397
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• 1991

This study was aimed to investigate the occlusal plane inclination in relation to the skeletal and dental assessment measurements in order to provide a reference in orthodontic treatment planning as the occlusal plane should be reconstructed orthodontically or gnathologically. The sample consisted of 73 normal occlusions and 113 malocclusions of adults. The computerized statistical analysis of 38 occlusal plane's and 29 skeletal and dental measurements were carried out with SPSS. The conclusions were as follows; 1 In normal occlusion, COP-NaPog was average $83.63^{\circ}$ (2.44) and occlusal plane inclination had a strong negative correlation with SNB and FH-NaPog. 2. In normal occlusion, ArANS plane was nearly parallel to the occlusal plane. 3. In malocclusion, the larger the mandibular plane angle and the shorter the ramus height was, the more downward the occlusal plane had a tendency to tip anteriorly. 4. Occlusal plane was more horizontal in deep bite group, while it was steeper in openbite group. 5. The curve of Spee was severe in deep bite group but in openbite group mandibular occlusal plane showed average reverse curvature, where it was found that the configuration of the occlusal plane contributed to the excess or deficiency of anterior overbite.

• Journal of Industrial Technology
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• v.37 no.1
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• pp.27-31
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• 2017

In this paper, we have extended the research on the infrared sensor which has been limited to the plane. The reflection mechanism of the light on the curved surface is analyzed according to the curvature change and the emitted angle of photodiode and verified through experiments. The difference in the curvature causes a difference in the measurement distance, and also changes the intensity of the light coming into the phototransistor, thereby causing a difference in the output voltage. However, the difference in the output voltage due to the curvature change can be solved by adjusting the emitted angle of the photodiode to minimize the spot area formed on the curved surface regardless of the curvature. Therefore, it is possible to measure the distance by using the infrared sensor regardless of the curvature by aligning the photodiode to the center of the curved surface and adjusting the angle of the photodiode.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.4
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• pp.132-137
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• 2007

A point-wise car-like robot moving in the plane changes its direction with a constraint on turning curvature. In this paper, we consider the problem of computing a shortest path of bounded curvature between a prescribed initial configuration (position and orientation) and a polygonal goal, and propose a new geometric proof showing that the shortest path is either of type CC or CS (or their substring), where C specifies a non-degenerate circular arc and S specifies a non-degenerate straight line segment. Based on the geometric property of the shortest path, the shortest path from a configuration to a polygonal goal can be computed in linear time.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.901-909
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• 2014

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we study some properties of U and T for strictly convex plane curves. As a result, we establish a characterization for parabolas.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1089-1099
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• 2012

We construct three kinds of complete embedded singly-periodic minimal surfaces in $\mathbb{H}^2{\times}\mathbb{R}$. The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill $\mathbb{H}^2{\times}\mathbb{R}$ by finite Scherk's towers.

• International Journal of Ocean System Engineering
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• v.2 no.2
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• pp.63-70
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• 2012

This paper presents a new curvature based kinematic displacement theory and a numerical method to calculate the planar displacement of structures from a geometrical viewpoint. The theory provides an opportunity to satisfy the kinematic equilibrium of a planar structure using a progressive numerical approach, in which the cross sections are assumed to remain plane, and the deflection curve was evaluated geometrically using the curvature values despite being solved using differential equations. The deflection curve is parameterized with the arc-length, and was taken as an assembly of the chains of circular arcs. Fast and accurate solutions of most complex deflections can be obtained with few inputs.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.511-517
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• 2024

Let (M, p) denote a noncompact manifold M together with arbitrary basepoint p. In [7], Kondo-Tanaka show that (M, p) can be compared with a rotationally symmetric plane M_m in such a way that if M_m satisfies certain conditions, then M is proved to be topologically finite. We substitute Kondo-Tanaka's condition of finite total curvature of M_m with a weaker condition and show that the same conclusion can be drawn. We also use our results to show that when M_m satisfies certain conditions, then M is homeomorphic to ℝⁿ.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.211-235
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• 2007

In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grass-mannians $G_2(\mathbb{C}^{m+2})$ from the equation of Gauss and derive a new formula for the Ricci tensor of M in $G_2(\mathbb{C}^{m+2})$. Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in $G_2(\mathbb{C}^{m+2})$.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.10 s.103
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• pp.1186-1194
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• 2005

In this paper, we have systematically formulated the equations concerned to the in-plane and out-of-plane motions and deformations of a thick circular beam by using the kinetic and strain energies in order to analyse natural frequencies of a thick ring. The effects of variation of radius of curvature across the cross-section and also the effects of bending shear, extension and twist are considered. The equations of motion for natural vibration analysis of a ring are obtained utilizing the cyclic symmetry of vibration modes of the ring. The frequencies calculated using thick ring model and thin ring model are compared and discussed with the ones obtained from finite element analysis using the method of cyclic symmetry with 20-node hexahedral solid elements for rings with the different ratio of radial thickness to mean radius.