• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.685-692
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• 2003

In this paper, we study some properties of (equation omitted) (defined below). In particular we show that an operator T $\in$(equation omitted) satisfying the translation invariant property is hyponormal and an invertible operator T $\in$ (equation omitted) and its inverse T$^{-1}$ have a common nontrivial invariant closed set. Also we study some cases which have nontrivial invariant subspaces for an operator in (equation omitted).

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1129-1135
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• 2011

In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscala operator is nilpotent. We also prove that every subscalar operator with property (${\delta}$) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.895-903
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• 2009

We define a semi-symmetric metric connection in an almost $\gamma$-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $\gamma$-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1863-1874
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• 2014

In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space $\mathbb{E}^4_1$. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface with pointwise 1-type Gauss map.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.261-278
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• 2002

Let G = O(2) $\times$ O(2) $\times$O(2) and let M$^4$be closed G-invariant minimal hypersurface with constant scalar curvature in S$^{5}$ . If M$^4$has 2 distinct principal curvatures at some point, then S = 4. Moreover, if S > 4, then M$^4$does not have simple principal curvatures everywhere.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1229-1236
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• 2009

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator S$_K$ on a vector-valued Hardy space H$^2$(${\Omega}$, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.289-294
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• 2009

We show that on a Hermitian surface M, if M is weakly *-Einstein and has J-invariant Ricci tensor then M is Einstein, and vice versa. As a consequence, we obtain that a compact *-Einstein Hermitian surface with J-invariant Ricci tensor is $K{\ddot{a}}hler$. In contrast with the 4- dimensional case, we show that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold which is not weakly *-Einstein.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.565-568
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• 1996

In this paper, a solution method is proposed to calculate the optimum solution to discrete optimal H$_{.inf}$ control problem for feedback of linear time-invariant system states and disturbance variable. From the results of this study, condition of existence and uniqueness of its solution is that transfer matrix of controlled variable to input variable is left invertible and has no invariant zeros on the unit circle of the z-domain as well as extra geometric conditions given in this paper. Through a numerical example, the noniterative solution method proposed in this paper is illustrated.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.211-217
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• 2012

In this paper, we give the weighted Lebesgue-Radon-Nikodym theorem with respect to $p$-adic invariant integral on $\mathbb{Z}_p$.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.75-85
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• 2003

Let M be 3 Semi-invariant submanifold of codimension 3 with lift-flat normal connection in a complex projective space. Further, if the mean curvature of M is constant, then we prove that M is a real hypersurface of a complex projective space of codimension 2 in the ambient space.