• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.419-429
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• 2015

In this paper, we study properties SVEP, Bishop's property (${\beta}$), property (${\delta}$), decomposability, property $({\beta})_{\epsilon}$, subscalarity, Kato spectrum, generalized Kato decomposition, finite ascent for bounded linear operators in Banach spaces.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.325-330
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• 2013

In this paper, we prove Trotter-Kato theorem in the weak topology if $X^*$ is a uniformly convex Banach space.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.337-348
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• 2001

The unitary Lie-Trotter-Kato product formula gives in a simplest way a meaning to the Feynman path integral for the Schroding-er equation. In this note we want to survey some of recent results on the norm convergence of the selfadjoint Lie-Trotter Kato product formula for the Schrodinger operator -1/2Δ + V(x) and for the sum of two selfadjoint operators A and B. As one of the applications, a remark is mentioned about an approximation therewith to the fundamental solution for the imaginary-time Schrodinger equation.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.93-101
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• 2008

In this article we shall characterize the Heinz-Kato-Furuta inequality in several ways, and the best bound for sharpening of the inequality is obtained by the method in [7].

• Honam Mathematical Journal
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• v.20 no.1
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• pp.111-115
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• 1998

In this note, we give an economical Kato's decomposition for a regular operator on a Banach space.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.293-305
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• 2004

Trotter-Kato type approximations of the convoluted solution operator families for the Volterra integral equations (V $E_n$): v(t)=$A_{n} \int_0^t v(t-s) d\mu_n(s) + f_n(t), t \geq 0$ and the convergence of the solutions to the equations (V $E_n$) are studied.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.525-538
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• 1998

Recently, a stability theorem for the Feynman integral as a bounded linear operator on$ L_2$($R^{d}$ /) with respect to measures whose positive and negative variations are in the generalized Kato class was proved. We study a stability theorem for the Feynman integral with respect to measures whose positive variations are in the class of $\sigma$-finite smooth measures and negative variations are in the generalized Kato class. This extends the recent result in the sense that the class of $\sigma$-finite smooth measures properly contains the generalized Kato class.

• Journal of Korean Society of Forest Science
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• v.87 no.2
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• pp.260-269
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• 1998

This study was conducted to screen the biological activity of urushiol in the sap of lac tree(Rhus verniciflua STOKES) which has been used in traditional folk remedies. Cytotoxic activity of urushiol was screened with L1210(mouse luekemia cell), PC-9(human lung adenocarcinoma cell), A427(human lung adenocarcinoma cell) and KATO III (human stomach adenocarcinoma cell) The stepwise hexane : acetone eluent fractions of the urushiol were obtained by the silica gel adsorption column chromatography and added to the culture media containing L1210, PC-9. A427, and KATO III, respectively. A hexane : acetone(90 : 10, v/v) eluent fraction of them showed the lowest 50% inhibition concentration($IC_{50}$) of $0.018{\mu}g/m{\ell}$ for the cell line of A427. Much lower level of $IC_{50}$ of the hexane : acetone(90 : 10, v/v) eluent fraction of the urushiol showed the equal inhibition effect with tetraplatin(i.e., anti-cancer drug of platinum complexes) on the cancer cell lines as follows ; 3.4 times lower for L1210, 3.9 times lower for PC-9, and 105.5 times lower for A427. However, $IC_{50}$ of the hexane : acetone(90 : 10 v/v) eluent fraction for KATO III was exceptionally 3.9 times higher than that of tetraplatin.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.15-24
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• 2008

Let $N{\geq}1$ and p > 1. Let ${\Omega}$ be a domain of $\mathbb{R}^N$. In this article we shall establish Kato's inequalities for quasilinear degenerate elliptic operators of the form $A_pu$ = divA(x,$\nabla$u) for $u{\in}K_p({\Omega})$, ), where $K_p({\Omega})$ is an admissible class and $A(x,\xi)\;:\;{\Omega}{\times}\mathbb{R}^N{\rightarrow}\mathbb{R}^N$ is a mapping satisfying some structural conditions. If p = 2 for example, then we have $K_2({\Omega})\;= \;\{u\;{\in}\;L_{loc}^1({\Omega})\;:\;\partial_ju,\;\partial_{j,k}^2u\;{\in}\;L_{loc}^1({\Omega})\;for\;j,k\;=\;1,2,{\cdots},N\}$. Then we shall prove that $A_p{\mid}u{\mid}\;\geq$ (sgn u) $A_pu$ and $A_pu^+\;\geq\;(sgn^+u)^{p-1}\;A_pu$ in D'(${\Omega}$) with $u\;\in\;K_p({\Omega})$. These inequalities are called Kato's inequalities provided that p = 2. The class of operators $A_p$ contains the so-called p-harmonic operators $L_p\;=\;div(\mid{{\nabla}u{\mid}^{p-2}{\nabla}u)$ for $A(x,\xi)={\mid}\xi{\mid}^{p-2}\xi$.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09b
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• pp.877-878
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• 2006

The sintered parts are mainly used for automobile industry, and a part of air conditioners. In automobile industry, the application range of sintered parts is very broad and use for a driving and a lubricating system. And air conditioner uses them for compressor. Grinding of compressor and pump parts is very difficult these days, because these parts use High hardness materials and require high precision grinding. Tool life has to be extended to decrease production cost. We analyzed processing mechanism and developed new grinding wheels for Double Disk Grinding. And, we introduce new truing technology that improved tool-life and precision.