• 충청수학회지
• /
• 제28권3호
• /
• pp.419-429
• /
• 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
• /
• 제21권3호
• /
• pp.325-330
• /
• 2013

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

• 대한수학회지
• /
• 제38권2호
• /
• pp.337-348
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권1호
• /
• pp.93-101
• /
• 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].

• 호남수학학술지
• /
• 제20권1호
• /
• pp.111-115
• /
• 1998

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

• 대한수학회논문집
• /
• 제19권2호
• /
• pp.293-305
• /
• 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.

• 대한수학회논문집
• /
• 제13권3호
• /
• pp.525-538
• /
• 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.

• 한국산림과학회지
• /
• 제87권2호
• /
• pp.260-269
• /
• 1998

본 연구는 전통적인 민간요법으로 많이 이용되고 있는 옻나무의 옻칠액의 주성분인 urushiol의 암세포증식억제 효과를 검정하기 위하여 L1210(mouse 혈액암세포), PC-9(인체폐암세포), A427(인체폐암세포), KATO III(인체위암세포)에 대한 urushiol의 세포독성을 검정하였다. Urushiol은 column chromatography에서 hexane과 acetone을 혼합하여 step-wise법으로 용출한 분획을 암세포주 L1210, PC-9, A427, KATO III에 투여했다. 그 결과 암세포 증식억제효과는 hexane : acetone(9 : 1) 분획이 가장 높았고, 그외 50%억제농도($IC_{50}$)는 A427 에서 $0.018{\mu}g/m{\ell}$로 가장 우수하였다. 이들 암세포에 대한 urushiol의 hexane: acetone(9 : 1)분획의 50%억제농도($IC_{50}$)를 시판용 tetraplatin 비교한 결과 urushiol이 tetraplatin에 대하여 L1210에서 3.4배, PC-9 에서 3.9배, A427에서 105.5배의 낮은 농도에서도 동일한 억제효과를 나타냈고, KATO III에서는 다소 높았다.

• Kyungpook Mathematical Journal
• /
• 제48권1호
• /
• pp.15-24
• /
• 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 $A(x,\xi)={\mid}\xi{\mid}^{p-2}\xi$.

• 한국분말야금학회:학술대회논문집
• /
• 한국분말야금학회 2006년도 Extended Abstracts of 2006 POWDER METALLURGY World Congress Part2
• /
• pp.877-878
• /
• 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.