• 대한수학회논문집
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• 제15권4호
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

• 대한수학회논문집
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• 제30권3호
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• pp.253-267
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• 2015

Given a complex submanifoldM of the projective space $\mathbb{P}$(T), the hyperplane system R on M characterizes the projective embedding of M into $\mathbb{P}$(T) in the following sense: for any two nondegenerate complex submanifolds $M{\subset}\mathbb{P}$(T) and $M^{\prime}{\subset}\mathbb{P}$(T'), there is a projective linear transformation that sends an open subset of M onto an open subset of M' if and only if (M,R) is locally equivalent to (M', R'). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.

• 대한수학회보
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• 제50권4호
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.

• 대한수학회논문집
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• 제35권2호
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• pp.639-651
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• 2020

Consider a gradient Einstein-type metric in the setting of K-contact manifolds and (κ, µ)-contact manifolds. First, it is proved that, if a complete K-contact manifold admits a gradient Einstein-type metric, then M is compact, Einstein, Sasakian and isometric to the unit sphere 𝕊²ⁿ⁺¹. Next, it is proved that, if a non-Sasakian (κ, µ)-contact manifolds admits a gradient Einstein-type metric, then it is flat in dimension 3, and for higher dimension, M is locally isometric to the product of a Euclidean space 𝔼ⁿ⁺¹ and a sphere 𝕊ⁿ(4) of constant curvature +4.

• 대한수학회보
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• 제44권4호
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• pp.731-742
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• 2007

Let X be a Banach space, $A:D(A){\subset}X{\rightarrow}X$ the generator of a compact $C_0-semigroup\;S(t):X{\rightarrow}X,\;t{\geq}0$, D a locally closed subset in X, and $f:(a,b){\times}C([-q,0];X){\rightarrow}X$ a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order that D be a viable domain of the semi linear differential equation of retarded type $$u#(t)=Au(t)+f(t,u_t),\;t{\in}[t_0,\;t_0+T],{u_t}_0={\phi}{\in}C([-q,0];X)$$ is the tangency condition $$\limits_{h{\downarrow}0}^{lim\;inf\;h^{-1}d(S(h)v(0)+hf(t,v);D)=0}$$ for almost every $t{\in}(a,b)$ and every $v{\in}C([-q,0];X)\;with\;v(0){\in}D$.

• 한국가스학회지
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• 제24권1호
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• pp.33-40
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• 2020

해양플랜트용 HVAC(Heating Ventilation and Air-Conditioning) 시스템의 컨덴싱 유닛(condensing unit)의 경우, DX(Direct Expansion) 코일보다는 온도 안정성이 뛰어난 칠러 시스템(chiller system)을 주로 사용하고 있다. 칠러시스템의 구성품 중 대형 냉매압축기와 전자식 팽창밸브 등은 대부분 수입되고 있다. 이에 칠러 시스템의 크기는 국내에서 제작되는 열교환기(증발기, 응축기)에 의해 좌우된다. 현재 갈수록 심화되고 있는 사용공간의 제한으로 인해 선주사 및 조선소에서는 장비 크기를 컴팩트하게 해줄 것을 메이커에 지속적으로 요구하고 있다. 이에 본 논문에서는 해양플랜트에서 만액식(flooded) 칠러 시스템의 증발기로 주로 사용되고 있는 쉘-튜브형 열교환기를 컴팩트한 플레이트-쉘 열교환기로 대체하기 위한 주요개발과정을 소개하고, 이와 함께 개발된 플레이트-쉘 열교환기를 실제 증발기로 적용한 만액식 칠러 시스템을 제작하여 그 성능을 실험적으로 평가하였으며 그 결과를 제공하고자 한다.