• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.777-787
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• 2005

In this paper we study (n + 1)-dimensional compact contact CR-submanifolds of (n - 1) contact CR-dimension immersed in an odd-dimensional unit sphere $S^{2m+1}$. Especially we provide necessary conditions in order for such a sub manifold to be the generalized Clifford surface $$S^{2n_1+1}(((2n_1+1)/(n+1))^{\frac{1}{2}})\;{\times}\;S^{2n_2+1}(((2n_2+1)/(n+1)^{\frac{1}{2}})$$ for some portion (n1, n2) of (n - 1)/2 in terms with sectional curvature.

• Honam Mathematical Journal
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• v.6 no.1
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• pp.117-122
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• 1984

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.91-102
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• 2002

Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m ＋ 1 and 2n ＋ 1, respectively, where 1 $\leq$ m $\leq$ n. Let f : M longrightarrow N be a CR mapping. Under a generic assumption we construct a complete system of finite order for the infinitesimal deformations of f. In particular, we prove the space of infinitesimal deformations of f forms a finite dimensional Lie algebra.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.541-549
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• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.27-60
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• 1996

We compute low order terms of automorphisms of a quadric CR manifold defined by $v^a$ =< $A^az$, z > where there is a real vector ${\kappa}{\in}R^m$ such that $det({\kappa}{\cdot}A){\neq}0$.

• Journal of the Korean Society for Heat Treatment
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• v.28 no.2
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• pp.68-74
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• 2015

The low cycle fatigue (LCF) and creep-fatigue (hold time tension fatigue, HTTF) tests were performed on the modified 25Cr-13Ni cast stainless steel, which was selected as a candidate material for exhaust manifold in automotive engine. The exhaust manifold is subjected to an environment in which heating and cooling cycle occur due to the running pattern of automotive engine. Several types of fatigue behaviour such as thermal fatigue, thermal mechanical fatigue and creep-fatigue are belong to the main failure mechanisms. High temperature tensile test was firstly carried out to compare the sample with the traditional cast steel for the component. The low cycle fatigue and HTTF tests were carried out under the strain controlled condition with the total strain amplitude from ${\pm}0.6%$ to ${\pm}0.7%$ at $800^{\circ}C$. The hysteresis loops of HTTF tests showed significant stress relaxation during tension hold time. With the increase of tension hold time, the fatigue life was remarkably deceased which caused from the formation of intercrystalline crack by the creep failure mechanism.

• Journal of Power System Engineering
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• v.14 no.1
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• pp.59-64
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• 2010

Ferritic stainless steel is currently increasingly used for automotive exhaust material. The material for exhaust manifold is used in the temperature range of 500∼$850^{\circ}C$. Therefore, high temperature characteristic is an important one that affects it's life span. It has been investigated the effect of alloying elements of Cr, Mo, Nb, Ti in the ferritic stainless steel for exhaust manifold on the high temperature tensile strength. There was a few difference in the tensile strength at $600^{\circ}C$ with the exception of low Cr steel, but the steels containing higher Cr, Mo or Nb elements showed significantly higher tensile strength at the temperature of $800^{\circ}C$. The precipitates of the specimens after heat treating at the test temperature were electrolytic extracted, and quantitatively analysed using by SEM-EDS and TEM. The alloying elements of Cr and Mo increased the tensile strength as a solid solution strengthener, and on the other hand Nb element enhanced the strength by forming the fine intermetallic compounds such as NbC or $Fe_2Nb$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.183-201
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• 1999

Let M be an 0-minimal structure on the standard structure :=( , +, ,<) of the field of real numbers. We study Cr -G manifolds (0$\leq$r$\leq$w) which are generalizations of Nash manifolds and Nash G manifolds. We prove that if M is polynomially bounded, then every Cr -G (0$\leq$r<$\infty$) manifold is Cr -G imbeddable into some n, and that if M is exponential and G is a compact affine Cw -G group, then each compact $C\infty$ -G imbeddable into some representation of G.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.503-519
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• 2000

It is well-known that an analytic generic CR submainfold M of codimension m in Cn+m is locally transformed by a biholomorphic mapping to a plane Cn$\times$Rm ⊂ Cn$\times$Cm whenever the Levi form L on M vanishes identically. We obtain such a normalizing biholomorphic mapping of M in terms of the defining function of M. Then it is verified without Frobenius theorem that M is locally foliated into complex manifolds of dimension n.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1269-1281
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• 2020

In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric 3-manifold equipped with the canonical affine connection ${\hat{\nabla}}^t$ is a slant helix with pseudo-Hermitian curvature ${\hat{\kappa}}={\mid}q{\mid}\;sin\;{\theta}$ and pseudo-Hermitian torsion ${\hat{\tau}}=q\;cos\;{\theta}$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric 3-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve γ in a quasi-Sasakian 3-manifold M is a slant curve with curvature κ = |(t - α) cos θ + q| sin θ and torsion τ = α + {(t - α) cos θ + q} cos θ. These curves are not helices, in general. Note that if the ambient space M is an α-Sasakian 3-manifold, then γ is a slant helix.