• School Mathematics
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• v.10 no.4
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• pp.573-581
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• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.989-990
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• 2006

This paper presents a design of 3D Graphics Geometry processor. A geometry processor needs to cope with a large amount of computation and consists of transformation processor and lighting processor. To deal with the huge computation, a vector processing structure based on pipeline chaining is proposed. The proposed geometry processor performs 4.3M vertices/sec at 100MHz using 11 floating-point units.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.1_2
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• pp.135-143
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• 2004

3D Graphics accelerator is usually composed of two parts, geometry engine and rasterizer. In this paper, VGE(Vector Geometry Engine) which exploits vertex-level parallelism is proposed. In VGE, Common Floating-Point Unit by adding four-FADD, four-FMUL unit and 128-vector register accelerates geometry calculation. In comparison with SH4, Performance result show that the VGE can achieve performance gain over 4.7 times. To evaluate VGE performance, we make simulator to rebuild Simple-Scalar, general purpose processor simulator. In simulator model, we use Viewperf-benchmark.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.647-659
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• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

• Korean Journal of Optics and Photonics
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• v.5 no.3
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• pp.379-385
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• 1994

The sensitivity vector which depends on geometry of object illumination angles and distances of ESPI was analyzed. And the sensitivities of in-plane and out-of-plane displacements have been investigated. From these results, we have the conclusion that it is useful to use the diverging beam for object illumination. With diverging object illumination, only little errors are occurred when we approximate the sensitivity vector to constant all over the object surface.urface.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1219-1233
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• 2019

Let $E{\rightarrow}M$ be an arbitrary vector bundle of rank k over a Riemannian manifold M equipped with a fiber metric and a compatible connection $D^E$. R. Albuquerque constructed a general class of (two-weights) spherically symmetric metrics on E. In this paper, we give a characterization of locally symmetric spherically symmetric metrics on E in the case when $D^E$ is flat. We study also the Einstein property on E proving, among other results, that if $k{\geq}2$ and the base manifold is Einstein with positive constant scalar curvature, then there is a 1-parameter family of Einstein spherically symmetric metrics on E, which are not Ricci-flat.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.819-835
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• 1998

The main purpose of this paper is to prove that if a real hypersurfaces M of a complex space form satisfies ${\nabla}_{\xi}S$=0 and $S{\xi}=\sigma\xi$ for some constant on $\sigma$ on M, then the structure vector field $\xi$ is principal, where S denotes the Ricci tensors of M.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.765-782
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• 2006

We describe the moduli spaces of stable vector bundles of rank 2 on Enriques surfaces. They all have the structure of the fibrations reflecting those of Enriques surfaces.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.165-171
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• 2021

The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton (Mn, g, f, λ) with constant scalar curvature admitting a non-homothetic conformal vector field V leaving the potential vector field invariant. We show that in such manifolds the potential function f is constant and the scalar curvature of g is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field V, without constant scalar curvature assumption, we show that g has constant curvature and determines the potential function f explicitly.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.389-394
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• 1997

Consider a tetrhedron is composed of six dihedral angles .phi.(i=1,2..., 6), and a vertex of a tetrahedron is also three dihedral angles. It will assume that a vertex A, for an example, is composed of there angles definded such as .alpha..betha. and .gamma. !. then there is a corresponding angle can be given as .phi1.,.phi2.,.phi3.. Here, in order to differentiate between a conventional triangle and dihedral angle, if a dihedral angle degined in this paper is symbolized as .phi..LAMBDA.,the value of cos.theta.of .phi./sab a/, in a trigonometric function rule,can be defined to tecos.phi..LAMBD/sab A/., and it is defined as a tetradedral cosine .phi. or simply called a tecos.phi.. Moreover, in a simillar method, the dihedral angle of tetrahedron .phi..LAMBDA. is given as : value of sin .theta. can defind a tetra-sin.phi..LAMBDA., and value of tan .theta. of .phi..LAMBDA. is a tetra-tan .phi..LAMBDA. By induction it can derive that a tetrahedral geometry on the basis of suggesting a geometric tetrahedron