• 대한수학회지
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• 제47권5호
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• pp.925-934
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• 2010

A crystallization of a closed connected PL manifold M is a special edge-colored graph representing M via a contracted triangulation. The regular genus of M is the minimum genus of a closed connected surface into which a crystallization of M regularly embeds. We disprove a conjecture on the regular genus of $\mathbb{S}\;{\times}\;\mathbb{S}^n$, $n\;{\geq}\;3$, stated in [J. Korean Math. Soc. 41 (2004), no. 3, p. 420].

• 대한수학회보
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• 제48권2호
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• pp.335-342
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• 2011

In this paper, we prove that minimal hypersurfaces when n $\geq$ 3 and nonzero constant mean curvature hypersurfaces when n $\geq$ 2 foliated by spheres in parallel horizontal hyperplanes in $\mathbb{H}^n{\times}\mathbb{R}$ must be rotationally symmetric.

• 호남수학학술지
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• 제4권1호
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• pp.75-84
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• 1982

Let M be a complete and orientable hypersurface of an odd-dimensional sphere $S^{2n+1}$ with quasi-integrable $(f,\;g,\;u,\;{\nu},\;{\lambda})$ -structure. The purpose of the present paper is to prove the following two theorems. (I) If the scalar curvature of M is constant and the function $\lambda$ is not locally constant, then M is a great sphere $S^{2n}$(1) or a product of two spheres with the same dimension $S^{n}(1/\sqrt{2}){\times}S^{n}(1/\sqrt{2})$. (II) Suppose that the sectional curvature of the section $\gamma(u,\;{\nu})$ spanned by u and $\nu$ is constant on M and M is compact. If the second fundamental tensor H of M is positive semi-definite and satisfies trace $$^{t}HH{\leq_-}{2n}$$, then M is a great sphere $S^{2n}$ (1) or a product of two spheres $S^{n}{\times}S^{n}$ or $S^{p}{\times}S^{2n-p}$, p being odd.

• Macromolecular Research
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• 제10권4호
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• pp.236-239
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• 2002

Centrifugation is a method to create functionally graded materials (FGM) with a thermosetting matrix. In this study the movement of short carbon fibers in an epoxy resin during the centrifugation process was modeled to determine the fiber distribution in the final product. For this purpose a form factor K was introduced to modify a set of equations that was previously shown to be valid for the motion of spheres. It was shown that the results of the simulation were in good agreement with the experimental data, when an empirical K factor of four was chosen.

• 대한수학회보
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• 제42권3호
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• pp.521-525
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• 2005

We give a necessary and sufficient condition of a rationally elliptic space X such that the Dold-Lashof classifying space Baut1X for fibrations with the fiber X is rank one. It is only when X has the rational homotopy type of a sphere or the total space of a spherical fibration over a product of spheres.

• 대한수학회보
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• 제50권1호
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• pp.135-142
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• 2013

In the present paper, we discuss the rigidity phenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in $S^4$.

• 대한수학회보
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• 제25권2호
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• pp.171-174
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• 1988

Let M be an n-dimensional compact connected and oriented Riemannian manifold isometrically immersed in an (n+2)-dimensional Euclidean space $R^{n+2}$. Moore [5] proved that if M is of positive curvature, then M is a homotopy sphere. This result is generalized by Baldin and Mercuri [2], Baik and Shin [1] to the case of non-negative curvature, which is stated as follows: If M of non-negative curvature, then M is either a homotopy sphere or diffeomorphic to a product of two spheres. In particular, if there is a point at which the curvature operator is positive, then M is homeomorphic to a sphere.e.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.515-540
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• 2013

Let $G=O(2){\times}O(2){\times}O(2)$. Then a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$ is a product of spheres, i.e., the square norm of its second fundamental form, S = 4.

• 대한수학회보
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• 제49권2호
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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.

• 한국정밀공학회지
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• 제13권6호
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• pp.90-101
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• 1996

Determination of assembly sequence of components is a key issue in assembly operation. Although a number of articles dealing with assembly sequence determination have appeared, an efficient and general methodology for complex products has yet to appear. The objective of this paper is to present the problems and models used to generate assembly sequence from design data. An essential idea of this research is to acquire a finite number of voxels from any complex geometric entity, such as 3D planar polygons, hollow spheres, cylinders. cones, tori, etc. In order to find a feasible assembly sequence, the following four steps are needed: (1) The components composing of an assembly product are identified and then the geometric entities of each component are extracted. (2) The geometric entities extracted in the first step are translated into a number of voxels. (3) All the mating or coupling relations between components are found by considering relations between voxels. (4) The components to be disassembled are determined using CCGs (Component Coupling Graph).