• Korean Journal of Mathematics
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• v.8 no.2
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• pp.121-126
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• 2000

B.Djafari Rouhani and W.A.Kirk [3] proved the following theorem: Let Xbe a reflexive Banach space and $(x_n)_{n{\geq}0}$ be a nonexpansive (resp., firmly nonexpansive )sequence in X. Then the set of weak ${\omega}$-limit points of the sequence $(\frac{x_n}{n})_{n{\geq}1}$(resp., $(x_{n+1}-x_n)_{n{\geq}0$) always lies on a convex subset of a sphere centered at the origin of radius $d={\lim}_{n{\rightarrow}{\infty}}\frac{{\parallel}x_n{\parallel}}{n}$. In this paper we show that the above theorem for nonexpansive(resp., firmly nonexpansive) sequences holds in a general Banach space(resp., a strictly convex dual $X^*$).

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.5
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• pp.368-373
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• 2004

Surface visualization can be useful, particularly for internet-based education and simulation system. Since the mesh data size directly affects the downloading and operational performance, the problem that should be solved for efficient surface visualization is to reduce the total number of polygons, constituting the surface geometry as much as Possible. In this paper, an efficient polygon reduction algorithm based on Stokes＇ theorem, and topology preservation to delete several adjacent vertices simultaneously for past polygon reduction is proposed. The algorithm is irrespective of the shape of polygon, and the number of the polygon. It can also reduce the number of polygons to the minimum number at one time. The performance and the usefulness for medical imaging application was demonstrated using synthesized geometrical objects including plane. cube. cylinder. and sphere. as well as a real human data.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.89-95
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• 2002

In this paper, we obtain an integral formula relating the measure of great spheres $S^{n-2}$ and arc length of a curve on the unit sphere $S^{n-1$ As an application of the formula, we develop a geometric inequality for a spherical curve and prone generalized version of Fenchel＇s theorem in $S^n$.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.661-679
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• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1273-1283
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• 2018

Let ($M,{\mathcal{F}}$) be a closed, oriented Riemannian manifold of a foliation ${\mathcal{F}}$ with a nonisometric transversal conformal field. Then ($M,{\mathcal{F}}$) is transversally isometric to the sphere under some transversal concircular curvature conditions.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.395-402
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• 1999

We introduce the notion of strongly k-disk homogeneous apace and establish a characterization theorem. More specifically, we prove that any analytic Riemannian manifold (M,g) of dimension n which is strongly k-disk homogeneous with 2$\leq$k$\leq$n-1 is a space of constant curvature. Its K hler analog is obtained. The total mean curvature homogeneity of geodesic sphere in k-disk is also considered.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.403-416
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• 2021

It is known that the rank 2 stably free syzygy module P⁽²⁾ is not free. This algebraic fact was proved analytically, but this remarkable fact still lacks of a simple algebraic proof. The main purpose of this paper is to give a partially algebraic proof by making use of a theorem whose proof is quite topological, and the further properties of the module will be discussed.

• Journal for History of Mathematics
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• v.36 no.2
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• pp.21-34
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• 2023

Spherical trigonometry refers to the geometry related to spherical triangles. It has been an important tool for studying astronomy since ancient times. In trigonometry, concepts such as trigonometric functions naturally emerge from the relationship between arcs and chords of a circle. In this paper, we briefly examine the origin of spherical trigonometry. To introduce the basics of spherical trigonometry, we present fundamental and important theorems such as Menelaus's theorem, the law of sines and the law of cosines on a sphere, along with their proofs. Furthermore, we discuss the educational value and potential applications of spherical trigonometry.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.1
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• pp.81-92
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• 1992

This paper deals with the procedure for developing a computer program which can predict the pressure fluctuation on the ship hull by solving the boundary value problem on the hull subject to the influence of the unsteady propeller and cavity motions. The program is applied to the solution of flow around a sphere under the influence of point sources simulating the propeller cavity, and then is compared with the analytic solution based on Butler's sphere theorem. The effect of free surface condition, either pressure-free or rigid-wall, upon the pressure distribution is studied. The computer code is also applied to a RO-RO ship, leading to the conclusion that the package may be useful for the analysis of excitation forces on the ship hull induced by the propeller in the design process.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.51-54
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• 1983

Let M be a n-dimensional compact Riemannian manifold with sectional curvature bounded below by one. Then Li and Zhong[3], and Li and Treibergs [4] proved that if the first eigenvalue of the Laplacian .lambda.$_{1}$ is less than some universal constant and if n.leq.4, then M is diffeomorphic to the n-sphere S$^{n}$ . The purpose of this paper is to prove this pinching theorem for all n with some extra condition.