• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.19-28
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• 1997

Let $H$ and $K$ be separable, complex Hilbert spaces and $L(H, K)$ denote the space of all linear, bounded operators from $H$ to $K$. If $H = K$, we write $L(H)$ in place of $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$ T^*h \right\$\mid$ \leq \left\$\mid$ Th \right\$\mid$$ for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1269-1283
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• 2015

An operator $T{{\in}}{\mathcal{L}}({\mathcal{H}})$ is said to be skew complex symmetric if there exists a conjugation C on ${\mathcal{H}}$ such that $T=-CT^*C$. In this paper, we study properties of skew complex symmetric operators including spectral connections, Fredholmness, and subspace-hypercyclicity between skew complex symmetric operators and their adjoints. Moreover, we consider Weyl type theorems and Browder type theorems for skew complex symmetric operators.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.701-708
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• 2007

In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1.

• Proceedings of the KIEE Conference
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• 1997.07c
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• pp.936-938
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• 1997

Up to date, operator assistance systems -fault diagnosis system, fault restoration system etc.- are developed for power system automation. In this condition, an efficiency test of assistance system must be performed to prove application in real power system. This paper presents an SCADA simulator for an efficiency test of the operator assistance system, which is developed in the SCADA system. The proposed simulator is implemented under Win95 with Pentium-PC.

• Kyungpook Mathematical Journal
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• v.21 no.1
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• pp.135-145
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• 1981

• Korean Journal of Computational Design and Engineering
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• v.20 no.4
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• pp.420-430
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• 2015

Operator Training Simulators (OTSs) provide macroscopic training environment for plant operation. They are equipped with simulation systems for the emulation of remote monitoring and controlling operations. OTSs typically provide 2D block diagram-based graphic user interface (GUI) and connect to process simulation tools. However, process modeling for OTSs is a difficult task. Furthermore, conventional OTSs do not provide real plant field information since they are based on 2D human machine interface (HMI). In order to overcome the limitation of OTSs, we propose a new type of plant training system. This system has the capability required for collaborative training between operators and field workers. In addition, the system provides 3D virtual training environment such that field workers feel like they are in real plant site. For this, we designed system architecture and developed essential functions for the system. For the verification of the proposed system design, we implemented a prototype training system and performed experiments of collaborative training between one operator and two field workers with the prototype system.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1981-1990
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• 2017

Let R be a root system in $\mathbb{R}^d$ with Coxeter-Weyl group W and let k be a nonnegative multiplicity function on R. The generalized volume mean of a function $f{\in}L^1_{loc}(\mathbb{R}^d,m_k)$, with $m_k$ the measure given by $dmk(x):={\omega}_k(x)dx:=\prod_{{\alpha}{\in}R}{\mid}{\langle}{\alpha},x{\rangle}{\mid}^{k({\alpha})}dx$, is defined by: ${\forall}x{\in}\mathbb{R}^d$, ${\forall}r$ > 0, $M^r_B(f)(x):=\frac{1}{m_k[B(0,r)]}\int_{\mathbb{R}^d}f(y)h_k(r,x,y){\omega}_k(y)dy$, where $h_k(r,x,{\cdot})$ is a compactly supported nonnegative explicit measurable function depending on R and k. In this paper, we prove that for almost every $x{\in}\mathbb{R}^d$, $lim_{r{\rightarrow}0}M^r_B(f)(x)= f(x)$.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.673-680
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• 1996

It is proved that $K(c_0,Y)$ is an M-ideal in $L(c_0,Y)$ if Y is a closed subspace of $c_0$. And a new direct proof of the fact that $K(L_1[0,1],\ell_1)$ is not an M-ideal in $L(L_1[0,1],\ell_1)$ is given.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.221-267
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• 2019

In the five first sections of this paper we define and study the hypergeometric transmutation operators $V^W_k$ and $^tV^W_k$ called also the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam's theory on ${\mathbb{R}}^d$. By using these operators we define the hypergeometric translation operator ${\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, and its dual $^t{\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, we express them in terms of the hypergeometric Fourier transform ${\mathcal{H}}^W$, we give their properties and we deduce simple proofs of the Plancherel formula and the Plancherel theorem for the transform ${\mathcal{H}}^W$. We study also the hypergeometric convolution product on W-invariant $L^p_{\mathcal{A}k}$-spaces, and we obtain some interesting results. In the sixth section we consider a some root system of type $BC_d$ (see [17]) of whom the corresponding hypergeometric translation operator is a positive integral operator. By using this positivity we improve the results of the previous sections and we prove others more general results.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.119-124
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• 2001

In the paper we show that some operators defined on L$^1$($\mu$) and on C(K) into Banach space with the RNP have the lifting property.