• 대한수학회논문집
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• 제23권3호
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• pp.421-426
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• 2008

Let $M^n$ be a complete immersed super stable minimal submanifold in $\mathbb{R}^{n+p}$ with fiat normal bundle. We prove that if M has finite total $L^2$ norm of its second fundamental form, then M is an affine n-plane. We also prove that any complete immersed super stable minimal submanifold with flat normal bundle has only one end.

• Korean Journal of Mathematics
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• 제5권1호
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• pp.75-82
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• 1997

We show that the normal bundle of a Lagrangian submanifold in a K$\ddot{a}$hler manifold has a symplectic structure and provide the equivalent conditions for the normal bundle of such to be K$\ddot{a}$hler.

• 대한수학회보
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• 제48권1호
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• pp.105-114
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• 2011

In this paper, we classify (C, $\cal{L}$) such that a smooth curve C of genus g has a nonspecial very ample line bundle $\cal{L}$ of deg $\cal{L}$ = 2g-2-a failing to be normally generated, in terms of the number a.

• 충청수학회지
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• 제21권3호
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• pp.371-376
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• 2008

Let $P(M,G,{\pi})=:P$ be a principal fibre bundle with structure Lie group G over a base manifold M. In this paper we get the following facts: 1. The tangent bundle TG of the structure Lie group G in $P(M,G,{\pi})=:P$ is a Lie group. 2. The Lie algebra ${\mathcal{g}}=T_eG$ is a normal subgroup of the Lie group TG. 3. $TP(TM,TG,{\pi}_*)=:TP$ is a principal fibre bundle with structure Lie group TG and projection ${\pi}_*$ over base manifold TM, where ${\pi}_*$ is the differential map of the projection ${\pi}$ of P onto M. 4. for a Lie group $H,\;TH=H{\circ}T_eH=T_eH{\circ}H=TH$ and $H{\cap}T_eH=\{e\}$, but H is not a normal subgroup of the group TH in general.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 추계학술대회 논문집 전력기술부문
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• pp.406-410
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• 2001

For 4-conductor bundle transmission line spacer damper are equipped so as to keep the spacing between sub conductors. For 4-conductor bundle the subspan spacing of a spacer damper is determined and applied in order that the bundle may get restored to a normal state when 4-conductor bundle is rolled by rigid body vibration due to wind. But 4 conductors of 345kV 4-conductor bundle transmission line were twisted by the angle of $315^{\circ}$ for the first time korea. In this paper, we will analyze the reason of the power line twisting of 4-conductor bundle which occurred for the first time in korea and offer the preventive countermeasures for this

• 대한수학회보
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• 제52권1호
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• pp.301-312
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• 2015

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb{E}^4_1$.

• 대한수학회보
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• 제52권6호
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• pp.2035-2045
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• 2015

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen meridian surfaces and meridian surfaces with parallel normal bundle.

• 대한정형외과스포츠의학회지
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• 제9권1호
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• pp.28-34
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• 2010

목적: 본 연구는 이중 다발 전방십자인대 재건술 후의 단기 임상결과와 이차적 관절경 소견을 알아보았다. 대상 및 방법: 이중 다발 전방십자인대 재건술 후에 최소 24개월 이상 추시가 가능하였던 49 예(환자)를 대상으로 하였다. 임상적 결과로 Lysholm 슬관절 점수, Tegner 활동 점수, 도수 및 기계적 전방 안정성 검사를 시행하였다. 15 예에서 스테플 제거와 함께 이차적 관절경 수술을 시행하여, 재건된 전방십자인대의 파열 유무와 이식건의 주관적인 긴장 정도 및 활액막 형성 정도를 검사하였다. 결과: Lysholm 슬관절 및 Tegner 활동 점수는 각각 술전 67.4, 2.0에서 최종 추시에 96.1, 6.1로 호전되었다 (p<0.01). Lachman 및 pivot-shift 검사에서 39예, 36예가 정상범위로 호전되었다. 스트레스 방사선 검사의 양측 차이 정도는 10.8 mm 에서 3.3 mm로 의미있게 호전되었다 (p<0.01). 이차적 관절경 소견상 모든 환자에서 전내측 다발이 정상 및 정상에 가까운 소견이 관찰되었으나, 8예 (53.3%) 에서 후외측 다발의 부분 및 완전 파열이 관찰되었다. 결론: 이중 다발 전방십자인대 재건술이 임상적으로 슬관절의 회전 및 전, 후방 안정성을 복원하는 효과적인 수술법이라도, 이차적 관절경 수술을 시행한 증례의 몇 예에서 후 외측 다발의 파열이 관찰되었다.

• 소성∙가공
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• 제18권4호
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• pp.342-346
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• 2009

Forming characteristics for the bundle extrusion of Cu-Ti bimetal wires are investigated, which can identify the process conditions for weak mechanical bonding at the contact surface during the direct extrusion of a Cu-Ti bimetal wire bundle. Bonding mechanism between Cu and Ti is assumed as a cold pressure welding. Then, the plastic deformation at the contact zone causes mechanical bonding and a new bonding criterion for pressure welding is developed as a function of the principal stretch ratio and normal pressure at the contact surface by analyzing micro local extrusion at the contact zone. The averaged deformation behavior of Cu-Ti bimetal wire is adopted as a constitutive behavior at a material point in the finite element analysis of Cu-Ti wire bundle extrusion. Various process conditions for bundle extrusions are examined. The deformation histories at the three points, near the surface, in the middle and near the center, in the cross section of a bundle are traced and the proposed new bonding criterion is applied to predict whether the mechanical bonding at the Cu-Ti contact surface happens. Finally, a process map for the direct extrusion of Cu-Ti bimetal wire bundle is proposed.

• 대한수학회보
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• 제39권2호
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• pp.289-297
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• 2002

It was shown by L. Polterovich ([3]) that if L is a totally real submanifold of a symplectic manifold $(M,\omega)$ and L is parallelizable then L is normal. So we try to find an answer to the question of whether there is a compatible almost complex structure J on the symplectic vector bundle $TM$\mid$_{L}$ such that $TL{\cap}JTL=0$ assuming L is normal and parallelizable. Although we could not reach an answer, we observed that the claim holds at the vector space level. And related to the question, we showed that for a symplectic vector bundle $(M,\omega)$ of rank 2n and $E=E_1{\bigoplus}E_2$, where $E=E_1,E_2$are Lagrangian subbundles of E, there is an almost complex structure J on E compatible with ${\omega}$ and $JE_1=E_2$. And finally we provide a necessary and sufficient condition for a given embedding into a symplectic manifold to be normal.