• International Journal of Contents
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• v.12 no.2
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• pp.42-48
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• 2016

We present efficient algorithms for computing centroid directions for each of the three types of monotonicity in a polyhedron: strong, weak, and directional monotonicity, which can be used for optimizing directions in many 3D manufacturing processes. Strongly- and directionally-monotone directions are the poles of great circles separating a set of spherical polygons on the unit sphere, the centroids of which are shown to be obtained by applying the previous result for determining the maximum intersection of the set of their dual spherical polygons. Especially in this paper, we focus on developing an efficient method for approximating the weakly-monotone centroid, which is the pole of one of the great circles intersecting a set of spherical polygons on the unit sphere. The original problem is approximately reduced into computing the intersection of great bands for avoiding complicated computational complexity of non-convex objects on the unit sphere, which can be realized with practical linear-time operations.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.215-222
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• 2015

We show that homology group on a contact CR-warped product submanifold in odd dimensional sphere is zero under certain conditions in terms of warping function and the dimension of the submanifold.

• Advances in biomechanics and applications
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• v.1 no.2
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• pp.85-93
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• 2014

In this paper, two procedures of enumerating the axial rotation are proposed using the unit sphere of the spherical rotation coordinate system specifying 3D rotation. If the trajectory of the movement is known, the integration of the axial component of the angular velocity plus the geometric effect equal to the enclosed area subtended by the geodesic path on the surface of the unit sphere. If the postures of the initial and final positions are known, the axial rotation is determined by the angular difference from the parallel transport along the geodesic path. The path dependency of the axial rotation of the three dimensional rigid body motion is due to the geometric effect corresponding to the closed loop discontinuity. Firstly, the closed loop discontinuity is examined for the infinitesimal region. The general closed loop discontinuity can be evaluated by the summation of those discontinuities of the infinitesimal regions forming the whole loop. This general loop discontinuity is equal to the surface area enclosed by the closed loop on the surface of the unit sphere. Using this quantification of the closed loop discontinuity of the axial rotation, the geometric effect is determined in enumerating the axial rotation. As an example, the axial rotation of the arm by the Codman's movement is evaluated, which other methods of enumerating the axial rotations failed.

• Kyungpook Mathematical Journal
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• v.12 no.2
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• pp.219-224
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• 1972

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.583-591
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• 1995

Unless otherwise stated, we always assume that X is a Banach space, and $1 < p, q < \infty with \frac{p}{1}+\frac{q}{1} = 1$. We use S(X) and B(X) to denote the unit sphere and the unit ball in X respectively.

• Journal of Korean Academy of Dental Administration
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• v.11 no.1
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• pp.38-46
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• 2023

Composite resins, commonly used in clinical practice, have been developed to improve aesthetics to obtain smooth surfaces. Although the restored composite resin has a smooth surface, it gradually becomes rough over time. Therefore, this study measured glossiness to evaluate the surface of various composite resins and attempted to evaluate the maintenance of glossiness of composite resins by observing surfaces that change to roughness. Specimens were produced using resin used in clinical practice: Gradia direct anterior (GA), Tetric N-Ceram (TN), Ceram.X Sphere TEC one (CX), Filtek Z350XT (FT), Estelite sigma quick (ES). After creating a smooth surface with slide glass, five locations were randomly selected to measure surface gloss, and the average was the representative value of the specimen. Roughness was applied to the specimen under water pouring at the same speed and pressure using SiC paper #2400, 1200, and 400. The gloss unit of different SiC papers was measured. To evaluate the gloss unit and gloss retention between composite resins, one-way analysis of variance and Tukey multiple comparisons test were used. As a result of the study, there was a difference in gloss unit of specimens produced under the same conditions. Although the degree differed depending on the composite resin, there was also a difference in gloss retention. Based on the findings, composite resins show differences in gloss due to their different characteristics. Ceram.X Sphere TEC one (CX) showing the lowest gloss retention and Estelite sigma quick (ES) showing the highest.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.285-293
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• 2012

In this paper, we investigate the hypersurface M in a unit sphere with constant k-th mean curvature and two distinct principal curvatures, and characterize such a hypersurface.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.963-974
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• 2018

We discuss two kinds of almost contact metric structures on a one-parameter family of totally umbilical hyperspheres in the nearly $K{\ddot{a}}hler$ unit 6-sphere $S^6$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.321-329
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• 2009

In this paper, we have considered linear Weingarten hypersurfaces in a sphere and obtained some rigidity theorems. The purpose of this paper is to give some extension of the results due to Cheng-Yau [3] and Li [7].

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.69-90
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• 2021

In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels h and sphere kernels Ω by assuming h ∈ △γ(ℝ+) and Ω ∈ ����β(Sn-1) for some γ > 1 and β > 1. Here Ω ∈ ����β(Sn-1) denotes the variant of Grafakos-Stefanov type size conditions on the unit sphere. Our results essentially improve and extend the previous weighted results for the rough singular integrals and the corresponding maximal truncated operators.