• Communications of the Korean Mathematical Society
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• v.23 no.3
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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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• v.5 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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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.

• Proceedings of the KIEE Conference
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• 2001.11b
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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

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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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 $\mathbb{E}^4_1$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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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.

• Journal of Korean Orthopaedic Sports Medicine
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• v.9 no.1
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• pp.28-34
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• 2010

Purpose: The aim of this study was to evaluate short-term clinical results and second-look arthroscopic findings after double-bundle anterior cruciate ligament (DB ACL) reconstruction. Materials and Methods: Forty-nine patients, who were followed up for at least 24 months after DB ACL reconstruction, were included. Clinical results, such as, Lysholm knee and Tegner activity scores, and manual laxity and instrumented anterior laxity test results were evaluated. In fifteen patients (15 knees), second-look arthroscopy with staple removal was performed. At second-look arthroscopy, the authors assessed about reconstructed ACL rupture, subjective graft tension and extent of synovial coverage. Results: Lysholm knee scores significantly improved from 67.4 preoperatively to 96.1 at last follow-up (p<0.01). Tegner activity scale improved from 2.0 to 6.1. The Lachman test, at last follow-up, showed normal laxity in 39 (of 49) patients, and the pivot-shift test showed normal laxity in 36 (of 49) patients. Mean side-to-side differences improved significantly from 10.8 mm to 3.3 mm (p<0.01). Second-look arthroscopic findings showed that all patients had a normal or a near normal anteromedial bundle. However, 8 patients (53.3%) were found to have partial or complete posterolateral bundle rupture. Conclusion: Even though double-bundle ACL reconstruction was clinically effective means of restoring knee rotational and anteroposterior stabilities, there were some ruptured posterolateral bundles observed in cases under arthroscopy after double-bundle ACL reconstruction.

• Transactions of Materials Processing
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• v.18 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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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.