• 대한수학회보
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• 제56권4호
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• pp.841-852
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• 2019

We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler n-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$-norm (for p > n/2) have bounded diameter and finite fundamental group.

• 전자공학회논문지SC
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• 제45권4호
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• pp.68-78
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• 2008

연속적인 경로 사이를 부드러운 곡선으로 잇기 위해서 기존의 로봇 제어기들은 일반적으로 연속적인 경로를 시간 축에서 합성하는 방법을 사용해 왔다. 하지만 이런 방법은 다음과 같은 두 가지 단점을 내재하고 있다. 천이 경로의 형태가 연접하게 생성될 수 없다는 점과 천이하는 동안 속력을 제어할 수 없다는 점이 그것이다. 이러한 문제점들을 극복하기 위해서 본 논문은 매끄럽지 않게 연결된 두 경로들을 부드럽게 잇기 위해 곡률이 제한된 새로운 천이 궤적 생성 방법을 제시하고자 한다. 실험 결과는 기존의 방법들보다 천이 궤적이 더 부드럽게 생성되는 것을 보여주며, 또한 보장된 곡률의 제한 수준은 $0.02{\sim}1$임을 보여준다.

• 대한수학회보
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• 제41권2호
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• pp.213-220
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• 2004

In this paper, we generalize the Bishop-Gromov volume comparison theorem by considering an integral bound for the part of the radial Ricci curvature which lies below a given smooth function. We also establish a compactness theorem from this result.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.235-246
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• 2005

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original(in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.

• 대한수학회보
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• 제50권3호
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• pp.833-837
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• 2013

In this note we establish a generalized Myers theorem under line integral curvature bound for Finsler manifolds.

• 대한수학회보
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• 제46권1호
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• pp.61-66
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• 2009

We provide a generalized Myers theorem under integral curvature bound and use this result to obtain a closure theorem in general relativity.

• 호남수학학술지
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• 제30권4호
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• pp.677-683
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• 2008

On a compact n-dimensional manifold M, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of volume 1, should be Einstein. The purpose of the present paper is to prove that a 3-dimensional manifold (M,g) is isometric to a standard sphere if ker $s^*_g{{\neq}}0$ and there is a lower Ricci curvature bound. We also study the structure of a compact oriented stable minimal surface in M.

• 대한수학회보
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• 제42권1호
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• pp.39-44
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• 2005

Let M be a compact hypersurface in hyperbolic space and let A be the area of M and V be the volume of the compact domain bounded by M. In this paper, we find a lower bound for $\frac{A}{V}$ in two cases, M has constant scalar curvature and M has constant mean curvature.

• 충청수학회지
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• 제34권4호
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• pp.369-378
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• 2021

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L²-norm of the traceless second fundamental form. If M is weakly stable, then λ₁(M) is bounded above by n² + O(n^2+s) for arbitrary s > 0.

• 소성∙가공
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• 제7권2호
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• pp.177-185
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• 1998

The kinematically admissible veolcity field is developed for the shapes of dead metal zone and the curving velocity distribution in the eccentric plane dies extrusion. The shape of dead metal zone is defined as the boundary surface with the maximum friction constant between the deformable zone and the rigid zone. The curving phenomenon in the eccentric lane dies is caused by the eccentricity of plane dies. The axial velocity distribution in the plane dies is divided in to the uniform velocity and the deviated velocity. The deviated velocity is linearly changed with the distance from the center of cross-section of the workpiece. The results show that the curvature of products and the shapes of the dead metal one are determined by the minimization of the plastic work and that the curvature of the extruded products increase with the eccentricity.