• 제어로봇시스템학회논문지
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• 제8권11호
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• pp.970-975
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• 2002

We suggests an effective method to construct time-varying C-obstacles in the 3-dimensional configuration space (C-space) using free arc. The concept of free arc was defined mathematically and the procedure to find free arc in the case off-dimensional C-space was derived in [1]. We showed that time-varying C-obstacles can be constructed efficiently using this concept, and presented simulation results for two SCARA robot manipulators to verify the efficacy of the proposed approach. In this paper, extensions of this approach to the 3-dimensional C-space is introduced since nearly all industrial manipulators are reasonably treated ill the too or three dimensional C-space f3r collision avoidance problem The free arc concept is summarized briefly and the method to find lice arc in the 3-dimensional f-space is explained. To show that this approach enables us to solve a practical collision avoidance problem simulation results f3r two PUMA robot manipulators are presented.

• 대한수학회지
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• 제32권3호
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• pp.471-482
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• 1995

A complex n-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a comples space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form consists of a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. The induced almost contact metric structure of a real hypersurface M of $M_n(c)$ is denoted by $(\phi, \zeta, \eta, g)$.

• 대한수학회논문집
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• 제35권3호
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• pp.967-977
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• 2020

In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms 𝓜³₁(H) except the case constant curvature -1. Next, we find that for a slant curve in a 3-dimensional Sasakian Lorentzian manifold, its ratio of "geodesic curvature" and "geodesic torsion -1" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with 𝜅² - 𝜏² = -1 + 𝜀₁(H + 1)𝜂(B)² in the Lorentzian Sasakian space forms x1D4DC³₁(H) except the case constant curvature -1. As example, we classify proper biharmonic Frenet curves in 3-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix.

• 대한수학회보
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• 제39권4호
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• pp.681-685
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• 2002

It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $C_1$, $C_2$, …, $C_{r}$ such that (equation omitted)d)

• 대한수학회지
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• 제34권2호
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• pp.321-336
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• 1997

Let S be the Ricci curvature of an n-dimensional compact minimal totally real submanifold M of a quaternion projective space $HP^n (c)$ of quaternion sectional curvature c. We proved that if $S \leq \frac{16}{3(n -2)}c$, then either $S \equiv \frac{4}{n - 1}c$ (i.e. M is totally geodesic or $S \equiv \frac{16}{3(n - 2)}c$. All compact minimal totally real submanifolds of $HP^n (c)$ satisfy in $S \equiv \frac{16}{3(n - 2)}c$ are determined.

• 대한수학회논문집
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• 제17권3호
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• pp.519-529
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• 2002

In this paper. We Study (n + 1)-dimensional Contact CR-submanifolds of (n - 1) contact CR-dimension immersed in a Sasakian space form M$\^$2m+1/(c) (2m=n+p, p>0), and especially determine such submanifolds under additional condition concerning with shape operator.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.781-791
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• 2016

Let $d_*(1,w)^2 ={\mathbb{R}}^2$ with the octagonal norm of weight w. It is the two dimensional real predual of Lorentz sequence space. In this paper we classify the smooth points of the unit ball of the space of symmetric bilinear forms on $d_*(1,w)^2$. We also show that the unit sphere of the space of symmetric bilinear forms on $d_*(1,w)^2$ is the disjoint union of the sets of smooth points, extreme points and the set A as follows: $$S_{{\mathcal{L}}_s(^2d_*(1,w)^2)}=smB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}extB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}A$$, where the set A consists of $ax_1x_2+by_1y_2+c(x_1y_2+x_2y_1)$ with (a = b = 0, $c={\pm}{\frac{1}{1+w^2}}$), ($a{\neq}b$, $ab{\geq}0$, c = 0), (a = b, 0 < ac, 0 < ${\mid}c{\mid}$ < ${\mid}a{\mid}$), ($a{\neq}{\mid}c{\mid}$, a = -b, 0 < ac, 0 < ${\mid}c{\mid}$), ($a={\frac{1-w}{1+w}}$, b = 0, $c={\frac{1}{1+w}}$), ($a={\frac{1+w+w(w^2-3)c}{1+w^2}}$, $b={\frac{w-1+(1-3w^2)c}{w(1+w^2)}}$, ${\frac{1}{2+2w}}$ < c < ${\frac{1}{(1+w)^2(1-w)}}$, $c{\neq}{\frac{1}{1+2w-w^2}}$), ($a={\frac{1+w(1+w)c}{1+w}}$, $b={\frac{-1+(1+w)c}{w(1+w)}}$, 0 < c < $\frac{1}{2+2w}$) or ($a={\frac{1=w(1+w)c}{1+w}}$, $b={\frac{1-(1+w)c}{1+w}}$, $\frac{1}{1+w}$ < c < $\frac{1}{(1+w)^2(1-w)}$).

• 한국터널지하공간학회 논문집
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• 제6권1호
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• pp.71-83
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• 2004

본 연구의 목적은 막장전방에 연약대가 존재할 때 터널 3차원 내공변위를 여러 가지 방법으로 해석하여 변위의 발생경향을 밝히고 지질변화를 예측하는 해석기법을 제시하는 것이다. 안정된 지하 암반에 터널을 굴착하게 되면, 터널 막장면을 포함한 무지보 굴착면 주위에 3차원적인 하중전이 현상이 나타나는데 막장 전방의 지반 상태가 변화하거나 연약대가존재하면 특정한 변위 경향을 보이는 것이 3차원 계측 및 수치해석결과 확인되었다. 그러므로, 시공중인 터널 내에서 3차원 절대 내공 변위를 측정하여 본 연구에서 제시된 계측해석 기법 (L/C비, $C/C_o$ 등)을 적용하면 터널 막장 전방의 지층변화나 연약대의 존재를 사전에 예측할 수 있을 것으로 판단된다.

• 대한수학회보
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• 제50권4호
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• pp.1109-1126
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• 2013

Let $\mathbb{M}^3_q(c)$ denote the 3-dimensional space form of index $q=0,1$, and constant curvature $c{\neq}0$. A curve ${\alpha}$ immersed in $\mathbb{M}^3_q(c)$ is said to be a Bertrand curve if there exists another curve ${\beta}$ and a one-to-one correspondence between ${\alpha}$ and ${\beta}$ such that both curves have common principal normal geodesics at corresponding points. We obtain characterizations for both the cases of non-null curves and null curves. For non-null curves our theorem formally agrees with the classical one: non-null Bertrand curves in $\mathbb{M}^3_q(c)$ correspond with curves for which there exist two constants ${\lambda}{\neq}0$ and ${\mu}$ such that ${\lambda}{\kappa}+{\mu}{\tau}=1$, where ${\kappa}$ and ${\tau}$ stand for the curvature and torsion of the curve. As a consequence, non-null helices in $\mathbb{M}^3_q(c)$ are the only twisted curves in $\mathbb{M}^3_q(c)$ having infinite non-null Bertrand conjugate curves. In the case of null curves in the 3-dimensional Lorentzian space forms, we show that a null curve is a Bertrand curve if and only if it has non-zero constant second Frenet curvature. In the particular case where null curves are parametrized by the pseudo-arc length parameter, null helices are the only null Bertrand curves.

• 호남수학학술지
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• 제46권2호
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• pp.237-248
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• 2024

In this manuscript, the hypersurfaces of non-flat Riemannian 4-space forms are considered. A hypersurface of a 4-dimensional Riemannian space form defined by an isometric immersion 𝐱 : M³ → 𝕄⁴(c) is said to be biconservative if it satisfies the equation (∆²𝐱 )^⊤ = 0, where ∆ is the Laplace operator on M³ and ⊤ stands for the tangent component of vectors. We study an extended version of biconservativity condition on the hypersurfaces of the Riemannian standard 4-space forms. The C-biconservativity condition is obtained by substituting the Cheng-Yau operator C instead of ∆. We prove that C-biconservative hypersurfaces of Riemannian 4-space forms (with some additional conditions) have constant scalar curvature.