• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.325-334
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• 2006

For $f{\in}L^2(B,d{\nu})$, ${\parallel}f{\parallel}_{BMO}=\widetilde{{\mid}f{\mid}^2}(z)-{\mid}{\tilde{f}}(z){\mid}^2$. For f continuous on B, ${\parallel}f{\parallel}_{BO}=sup\{w(f)(z):z{\in}B\}$ where $w(f)(z)=sup\{{\mid}f(z)-f(w){\mid}:{\beta}(z,w){\leq}1\}$. In this paper, we will show that if $f{\in}BMO$, then ${\parallel}f{\parallel}_{BO}{\leq}M{\parallel}f{\parallel}_{BMO}$. We will also show that if $f{\in}BO$, then ${\parallel}f{\parallel}_{BMO}{\leq}M{\parallel}f{\parallel}_{BO}^2$. A homomorphic function $f:B{\rightarrow}{\mathbb{C}}$ is called a Bloch function ($f{\in}{\mathcal{B}}$) if ${\parallel}f{\parallel}_{\mathcal{B}}=sup_{z{\in}B}\;Qf(z)$<${\infty}$. In this paper, we will show that if $f{\in}{\mathcal{B}}$, then ${\parallel}f{\parallel}_{BO}{\leq}{\parallel}f{\parallel}_{\mathcal{B}}$. We will also show that if $f{\in}BMO$ and f is holomorphic, then ${\parallel}f{\parallel}_{\mathcal{B}}^2{\leq}M{\parallel}f{\parallel}_{BMO}$.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.289-295
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• 2012

In this note we prove the space (A, ${\parallel}.{\parallel}$) is a Banach space and ${\parallel}ab{\parallel}{\leq}{\parallel}a{\parallel}{\parallel}b{\parallel}$ for $a,b{\in}A$ where $A:=\{a:=(a_t)_{t{\in}G}:{\sum}_{t{\in}G}{\parallel}a_t{\parallel}_t<{\infty}\}$, $G=\mathbb{N}^*$. Also we show some property in (A, ${\parallel}.{\parallel}$).

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.311-317
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• 1998

For Hilbert spaces H, K, a compact operator T: H $\rightarrow$ K, and column, row, operator Hilbert spaces $H_c,\;K_c,\;H_r,\;K_r,\;H_o, K_o$,we show that ${\parallel}T_{co}{\parallel}_{cb}={\parallel}T_{ro}{\parallel}_{cb}={\parallel}T_{oc}{\parallel}_{cb}={\parallel}T_{or}{\parallel}_{cb}={\parallel}T{\parallel}_4$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.851-860
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• 2007

In this paper, we prove that a function satisfying the following inequality $${\parallel}f(x)+2f(y)+2f(z){\parallel}{\leq}{\parallel}2f(\frac{x}{2}+y+z){\parallel}+{\epsilon}({\parallel}x{\parallel}^r{\cdot}{\parallel}y{\parallel}^r{\cdot}{\parallel}z{\parallel}^r)$$ for all x, y, z ${\in}$ X and for $\epsilon{\geq}0$, is Cauchy additive. Moreover, we will investigate for the stability in Banach spaces.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.623-630
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• 2017

For any nonzero elements x, y in a normed space X, the angular and skew-angular distance is respectively defined by ${\alpha}[x,y]={\parallel}{\frac{x}{{\parallel}x{\parallel}}}-{\frac{y}{{\parallel}y{\parallel}}}{\parallel}$ and ${\beta}[x,y]={\parallel}{\frac{x}{{\parallel}y{\parallel}}}-{\frac{y}{{\parallel}x{\parallel}}}{\parallel}$. Also inequality ${\alpha}{\leq}{\beta}$ characterizes inner product spaces. Operator version of ${\alpha}$ has been studied by $ Pe{\check{c}}ari{\acute{c}}$, $ Raji{\acute{c}}$, and Saito, Tominaga, and Zou et al. In this paper, we study the operator version of ${\beta}$ by using Douglas' lemma. We also prove that the operator version of inequality ${\alpha}{\leq}{\beta}$ holds for commutating normal operators. Some examples are presented to show essentiality of these conditions.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.309-318
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• 2006

Let X and Y be real Banach spaces and ${\varepsilon}\;>\;0$, p > 1. Let f : $X\;{\to}\;Y$ be a bijective mapping with f(0) = 0 satisfying $$|\;{\parallel}f(x)-f(y){\parallel}-{\parallel}{x}-y{\parallel}\;|\;{\leq}{\varepsilon}{\parallel}{x}-y{\parallel}^p$$ for all $x\;{\in}\;X$ and, let $f^{-1}\;:\;Y\;{\to}\;X$ be uniformly continuous. Then there exist a constant ${\delta}\;>\;0$ and N(${\varepsilon},p$) such that lim N(${\varepsilon},p$)=0 and a unique surjective isometry I : X ${\to}$ Y satisfying ${\parallel}f(x)-I(x){\parallel}{\leq}N({\varepsilon,p}){\parallel}x{\parallel}^p$ for all $x\;{\in}\;X\;with\;{\parallel}x{\parallel}{\leq}{\delta}$.

• Proceedings of the KIEE Conference
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• 2001.07e
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• pp.134-140
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• 2001

Parallel processing has the potential to be cost effectively used on computationally intense power system problems. But this technology is not still available is not only parallel computer but also parallel processing scheme. Testing these algorithms to ensure accuracy, and evaluation of their performance is also an issue. Although a significant amount of parallel algorithms of power system problem have been developed in last decade, actual testing on processor architectures lies in the beginning stages. This paper presents the parallel processing algorithm to supply the base being able to treat power flow by newton's method by the distributed memory type parallel computer. This method is to assign and to compute teared blocks of sparse matrix at each parallel processors. The testing to insure accuracy of developed method have been done on serial computer by trying to simulate a parallel environment.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.267-273
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• 2009

A representation for the Drazin inverse of an arbitrary square matrix in terms of the eigenprojection was established by Rothblum [SIAM J. Appl. Math., 31(1976) :646-648]. In this paper perturbation results based on the representation for the Darzin inverse $A^D\;=\;(A-X)^{-1}(I-X)$ are developed. Norm estimates of $\parallel(A+E)^D-A^D\parallel_2/\parallel A^D\parallel_2$ and $\parallel(A+E)^#-A^D\parallel_2/\parallel A^D\parallel_2$ are derived when IIEI12 is small.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.105-110
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• 2013

A logarithmic composition inequality in Besov spaces is derived which generalizes Vishik's inequality: ${\parallel}f{\circ}g{\parallel}_{B^s_{p,1}}{\leq}(1+{\log}({\parallel}{\nabla}g{\parallel}_{L^{\infty}}{\parallel}{\nabla}g^{-1}{\parallel}_{L^{\infty}})){\parallel}f{\parallel}_{B^s_{p,1}}$, where $g$ is a volume-preserving diffeomorphism on ${\mathbb{R}}^n$.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 2002.11a
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• pp.157-163
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• 2002

Consideration for parallel operation in a high power system has been increased due to the advantages of parallel operation like as high productivity, simplicity of design, and redundancy of power. This paper discussed the parallel operation of DC-DC Converter, Which Can be used as a high power system, is studied. Based on the small signal model of DC-DC Converter, the simple and exact power stage model of parallel operation system is derived and the parallel operation system using current balance method for the uniform current distribution among the parallel operation system is discussed. To verify the high performance of the proposed DC-DC converter system for parallel operation, the simulation test of the parallel operation, which has 2 Converter modules, is accomplished.