• Proceedings of the Korean Vacuum Society Conference
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• 2010.02a
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• pp.161-161
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• 2010

InAsSb alloy system 은 HgCdTe 를 대체하는 적외선 광소자 및 검출기 등에 응용이 가능한 유망한 물질이지만 정확한 유전함수 및 전이점의 연구는 미흡한 실정이다. 본 연구에서는 타원 편광 분석법을 이용하여 1.5 ~ 6 eV 의 분광 영역에서 As 조성비를 각기 (x = 0, 0.127, 0.337, 0.491, 0.726 및 1.00) 다르게 한 $InAs_xSb_{1-x}$ alloy의 유전함수를 측정하였다. 또한 표면에 자연산화막을 제거하기 위하여 Methanol 과 DI Water 로 표면을 세척 한 후 $NH_4OH$, Br in Methanol, HCl 등으로 적절한 화학적 에칭을 하여 산화막을 제거함으로서 순수한 InAsSb 의 유전함수를 측정할 수 있었다. 측정된 InAsSb 유전함수를 Standard analytic critical point line shape 방법으로 As 조성비에 따른 에너지 전이점을 얻을 수 있었다. 또한 얻어진 에너지 전이점 값을 이용하여 linear augmented Slater-type orbital 방법으로 전자 밴드 구조 계산을 하였고, 이를 바탕으로 $E_0$, $E_1$, $E_2$ 전이점 지역의 여러 전이점 ($E_1$, $E_1+\Delta_1$, $E_0'$, $E_0'+\Delta_0'$, $E_2$, $E_2+\Delta_2$, $E_2'$, $E_2'+\Delta_2$, $E_1'$) 의 특성을 정확히 정의할 수 있었다. 또한 As 조성비가 증가하면서 $E_2$, $E_2+\Delta_2$, $E_2'$, $E_2'+\Delta_2$ 전이점들이 서로 교차 되는 것을 발견하였고, 저온에서만 관측이 가능하였던 InSb 의 두 saddle-point (${\Delta_5}^{cu}-{\Delta_5}^{vu}$, ${\Delta_5}^{cl}-{\Delta_5}^{vu}$)를 상온에서 찾아내었다. 타원 편광 분석법을 이용한 전이점 연구 및 물성 분석은 InAsSb alloy 의 광학적 데이터베이스를 확보하는 성과와 더불어 새로운 디바이스기술 및 광통신 산업에도 유용한 정보가 될 것이다.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1129-1135
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• 2011

In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscala operator is nilpotent. We also prove that every subscalar operator with property (${\delta}$) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.355-361
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• 2006

We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on $S^1$, then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.

• 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.

• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.711-722
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• 2019

Considering stress singularities at point support locations, buckling solutions for plates with arbitrary number of point supports are hard to obtain. Thus, new Hp-Cloud shape functions with Kronecker delta property (HPCK) were developed in the present paper to examine elastic buckling of point-supported thin plates in various shapes. Having the Kronecker delta property, this specific Hp-Cloud shape functions were constructed through selecting particular quantities for influence radii of nodal points as well as proposing appropriate enrichment functions. Since the given quantities for influence radii of nodal points could bring about poor quality of interpolation for plates with sharp corners, the radii were increased and the method of Lagrange multiplier was used for the purpose of applying boundary conditions. To demonstrate the capability of the new Hp-Cloud shape functions in the domain of analyzing plates in different geometry shapes, various test cases were correspondingly investigated and the obtained findings were compared with those available in the related literature. Such results concerning these new Hp-Cloud shape functions revealed a significant consistency with those reported by other researchers.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.23-32
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• 1998

In the present paper the author studies the decomposition property ($\delta$) of the bounded linear operators.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.397-409
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• 2023

Let R be an associative ring with identity and M be a left R-module. In this paper, we define modules that have the property (δ-CE) ((δ-CEE)), these are modules that have a δ-supplement (ample δ-supplements) in every cofinite extension which are generalized version of modules that have the properties (CE) and (CEE) introduced in [6] and so a generalization of Zöschinger's modules with the properties (E) and (EE) given in [23]. We investigate various properties of these modules along with examples. In particular we prove these: (1) a module M has the property (δ-CEE) if and only if every submodule of M has the property (δ-CE); (2) direct summands of a module that has the property (δ-CE) also have the property (δ-CE); (3) each factor module of a module that has the property (δ-CE) also has the property (δ-CE) under a special condition; (4) every module with composition series has the property (δ-CE); (5) over a δ-V -ring a module M has the property (δ-CE) if and only if M is cofinitely injective; (6) a ring R is δ-semiperfect if and only if every left R-module has the property (δ-CE).

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.170-177
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• 1998

In this paper, a unified solution of Hankel norm approximation problem is proposed by $\delta$-operator. To derive the main result, all-pass property is derived from the inner and co-inner property in the $\delta$-domain. The solution of all-pass becomes an optimal Hankel norm approximation problem in .delta.-domain through LLFT(Low Linear Fractional Transformation) inserting feedback term $\phi(\gamma)$, which is a free design parameter, to hold the error bound desired against the variance between the original model and the solution of Hankel norm approximation problem. The proposed solution does not only cover continuous and discrete ones depending on sampling interval but also plays a key role in robust control and model reduction problem. The verification of the proposed solution is exemplified via simulation for the zero-order Hankel norm approximation problem and the model reduction problem applied to a 16th order MIMO system.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.19-34
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• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.61-73
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• 2002

We consider the inverse shadowing property of a dynamical system which is an "inverse" form of the shadowing property of the system. In particular, we show that every Morse-Smale system f on a compact smooth manifold has the inverse shadowing property with respect to the class $\mathcal{T}_h(f)$ of continuous methods generated by homeomorphisms, but the system f does not have the inverse\mathrm{T} shadowing property with respect to the class $\mathcal{T}_c(f)$ of continuous methods.