• 충청수학회지
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• 제28권3호
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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.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.459-468
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• 2011

Let T ${\in}$ L(X), S ${\in}$ L(Y), A ${\in}$ L(X, Y) and B ${\in}$ L(Y, X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares the same local spectral properties SVEP, Bishop's property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and and subscalarity. Moreover, the operators ${\lambda}I$ - T and ${\lambda}I$ - S have many basic operator properties in common.

• 공업화학
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• 제23권2호
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• pp.138-142
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• 2012

블루 안료 15 : 6이라 불리는 ${\epsilon}$ 결정상의 동프탈로시아닌(${\epsilon}$-CuPc)는 LCD 패널에서 청색화소를 제공하는 중요한 소재로써, 본 연구에서는 ${\epsilon}$-CuPc 시료를 ${\epsilon}$-CuPc 나노 입자를 seed로 이용하는 방법으로 여러 조건에서 합성하여 적합한 용매 및 온도조건 등을 규명하였고, 이를 미리 합성한 ${\alpha}$ 및 ${\beta}$ 결정상의 CuPc 시료들과 비교함으로써 ${\epsilon}$-CuPc 시료의 결정상, 결정 순도, 합성 수율 및 미세구조를 상호 비교 분석하였다. 시료들의 화학 구조 및 결정 구조는 푸레어 변환 적외선(FT-IR) 분광기 및 X선 회절 분석기(XRD)를 이용하여 각각 비교 분석하였다. 또한, 입자의 형상 및 크기는 주사 전자현미경(FE-SEM)으로 비교 분석하였고, 열적 특성은 열중량분석기(TGA)를 이용하여 비교 분석하였다.

• 호남수학학술지
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• 제31권2호
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• pp.137-145
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• 2009

Let T ${\in}$ $\mathcal{L}$(X), S ${\in}$ $\mathcal{L}$(Y ), A ${\in}$ $\mathcal{L}$(X, Y ) and B ${\in}$ $\mathcal{L}$(Y,X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares that same local spectral properties SVEP, property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and decomposability. From these common local spectral properties, we give some results related with Aluthge transforms and subscalar operators.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.487-496
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• 2021

In this paper we show that if A ∈ L(X) and B ∈ L(Y), X and Y complex Banach spaces, then A ⊕ B ∈ L(X ⊕ Y) is subscalar if and only if both A and B are subscalar. We also prove that if A, Q ∈ L(X) satisfies AQ = QA and Q^p = 0 for some nonnegative integer p, then A has property (C) (resp. property (𝛽)) if and only if so does A + Q (resp. property (𝛽)). Finally, we show that A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA and BA ∈ L(X) is subscalar with property (𝛿) then both Lat(BA) and Lat(AC) are non-trivial.

• 충청수학회지
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• 제25권4호
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• pp.655-668
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• 2012

An operator $T\;{\varepsilon}\;B(\mathcal{H})$ is said to be $k$-quasi-paranormal operator if $||T^{k+1}x||^2\;{\leq}\;||T^{k+2}x||\;||T^kx||$ for every $x\;{\epsilon}\;\mathcal{H}$, $k$ is a natural number. This class of operators contains the class of paranormal operators and the class of quasi - class A operators. In this paper, using the operator matrix representation of $k$-quasi-paranormal operators which is related to the paranormal operators, we show that every algebraically $k$-quasi-paranormal operator has Bishop's property ($\beta$), which is an extension of the result proved for paranormal operators in [32]. Also we prove that (i) generalized Weyl's theorem holds for $f(T)$ for every $f\;{\epsilon}\;H({\sigma}(T))$; (ii) generalized a - Browder's theorem holds for $f(S)$ for every $S\;{\prec}\;T$ and $f\;{\epsilon}\;H({\sigma}(S))$; (iii) the spectral mapping theorem holds for the B - Weyl spectrum of T.

• 한국주조공학회지
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• 제9권1호
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• pp.58-66
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• 1989

The effect of heat treating temperature and ${\alpha}$ phase In the ${\beta}$ phase matrix were investigated for ${\beta}-CuZnAl$ shape memory alloys by tension test, fatigue test, and shape memory effect test. After heat treatment at $677^{\circ}C$, $750^{\circ}C$, $800^{\circ}C$ and $850^{\circ}C$ for 10 min. respectively, static fracture stress(${\sigma}_f$), fatigue fracture stress(${\tau}_{max}$) at $10^6$ cycle, and elongation(${\epsilon}_f$) was $24.2kg/mm^2$, $17.21kg/mm^2$ and 11.8%, respectively. As heat treating temperature decreased, fracture surfaces of the specimens were changed from the intergranular to the transgranular fracture mode. Especially, the a phase precipitated in the ${\beta}$ phase matrix had an effect on crack propagation and the fracture surface was characterized by dimple-like pattern when crack propagated in transgranular cracking mode. Precipitation of the ${\alpha}$ phase in the ${\beta}$ phase matrix lowered the transformation temperature by $10^{\circ}C$, and about 2.5 vol.% ${\alpha}$ phase did not affect the shape memory effect examined by the bending test.

• 대한금속재료학회지
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• 제50권4호
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• pp.316-323
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• 2012

The aim of this study is to investigate the effect of post heat treatment on bonding properties of roll cladded Ti/MS/Ti materials. First grade Ti sheets and SPCC mild steel sheets were prepared and then Ti/MS/Ti clad materials were fabricated by a cold rolling and post heat treatment process. Microstructure and point analysis of the Ti/MS interfaces were performed using the SEM and EDX Analyser. Diffusion bonding was observed at the interfaces of Ti/MS. The thickness of the diffusion layer increased with post heat treatment temperature and the diffusion layer was verified as having $({\epsilon}+{\zeta})+({\zeta}+{\beta}-Ti)$ intermetallic compounds at $700^{\circ}C$ and an $({\zeta}+{\beta}-Ti)$ intermetallic compound at $800^{\circ}C$, respectively. The micro Knoop hardness of mild steel decreased with post heat treatment temperature; however, those of Ti decreased at a range of $500{\sim}600^{\circ}C$ and showed a uniform value until $800^{\circ}C$ and then increased rapidly up to $900^{\circ}C$. The micro Knoop hardness value of the diffusion layer increased up to $700^{\circ}C$ and then saturated with post heat treatment. A T-type peel test was used to estimate the bonding forces of Ti/Mild steel interfaces. The bonding forces decreased up to $800^{\circ}C$ and then increased slightly with post heat treatment. The optimized temperature ranges for post heat treatment were $500{\sim}600^{\circ}C$ to obtain the proper formability for an additional plastic deformation process.