• 대한수학회보
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• 제55권5호
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• pp.1351-1370
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• 2018

In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.

• 대한수학회보
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• 제53권3호
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• pp.821-831
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• 2016

A case study is added to our recent work on Quillen phenomenon. Pointwise positivity of polynomials on generalized lemniscates of the complex plane is related to sums of hermitian squares of rational functions, and via operator quantization, to essential subnormality.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.11-36
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• 2023

In this presentation, the particles at the matter surface (metal, crystal, nano) will be considered as the control target outside the physical domain. As is well known that control problems of quantum particles at surface had been investigated in various aspects in last couple of years, but the realization of control would become rather difficult than theoretical results. Especially, whether surface control would be valid? what kind of particles at what kind of matter surfaces can be controlled? so many questions still left as the mystery in the current research literature and papers. It means that the direct control sometime does not easy. On the other hands, control outside the physical domain is quite a interest consideration in mathematics, physics and chemistry. The main plan is to take the quantum systems operator (such as Laplacian ∆) in the form of fractional operator (∆^s , 0 < s < 1), then to consider the control outside of physical domain. Fortunately, there are many published articles in the field of applied mathematics can be referred for the achievement of control outside of domain. The external quantum control would be a fresh concept to do the physical control, first in the theoretic, second in the computational, final in the experimental issues.

• 대한수학회보
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• 제23권2호
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• pp.123-132
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• 1986

Let X be a real Banach space with norm vertical bar . vertical bar and let I denote the identity operator. Then an operator A.contnd.X*X with domain D(A) and range R(A) is said to be accretive if vertical bar x$_{1}$-x$_{2}$ vertical bar.leq.vertical bar x$_{1}$-x$_{2}$+r(y$_{1}$-y$_{2}$) vertical bar for all y$_{i}$.mem.Ax$_{i}$, i=1, 2, and r>0. An accretive operator A.contnd.X*X is m-accretive if R(I+rA)=X for all r>0.r>0.

• 호남수학학술지
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• 제31권4호
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• pp.633-637
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• 2009

We prove using the Szeg$\H{o}$ kernel and the Garabedian kernel that a Toeplitz operator on the boundary of $C^{\infty}$ smoothly bounded domain associated to a smooth symbol vanishes only when the symbol vanishes identically. This gives a generalization of previous results on the unit disk to more general domains in the plane.

• 한국음향학회지
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• 제19권4호
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• pp.3-15
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• 2000

본 논문은 웨이블렛 영역에서 신호성분을 보존하면서 첨부된 잡음성분을 제거할 수 있는 새로운 잡음제거 필터를 제시한다. 적응적 웨이블렛 수축(AWS) 필터라 불리는 제안된 필터는 웨이블렛 제거기와 적응적 수축기의 두 개 연산기로 구성되어 있으며 각각의 연산기는 웨이블렛 계수의 국부적 통계성을 이용하여 적응적으로 추정되는 threshold에 의존하여 선택되는데 웨이블렛 제거기는 threshold보다 작은 웨이블렛 계수들을 0으로 대신하여 웨이블렛 영역에서 잡음을 제거하게 된다. 또한 적응적 수축기는 threshold보다 큰 계수들을 적응적으로 수축하여 신호성분을 보존하면서 잡음성분을 줄이게 된다. 실험 결과, 제안된 필터는 기존의 방법들보다 잡음을 제거하면서 신호성분을 보존하는데 더욱 효과적임을 보여준다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.31-37
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• 2002

In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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• pp.13-19
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• 2016

In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.362-367
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• 1996

In this paper, the eigenstructure of a class of linear time varying systems, termed as linear quasi-time invariant(LQTI) systems, is investigated. A system composed of dynamic devices such as linear time varying capacitors and resistors can be an example of the class. To effectively describe and analyze the LQTI systems, a generalized differential operator G is introduced. Then the dynamic systems described by the operator G are studied in terms of eigenvalue, frequency characteristics, stability and an extended convolution. Some basic attributes of the operator G are compared with those of the differential operator D. Also the corresponding generalized Laplace transform pair is defined and relevant properties are derived for frequency domain analysis of the systems under consideration. As an application example, a LQTI circuit is examined by using the concept of eigenstructure of LQTI system. The LQTI filter processes the sinusoidal signals modulated by some functions.

• 대한수학회보
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• 제41권4호
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• pp.723-730
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• 2004

The definition of a D-admissible fuzzy subset for an operator domain D on a group G is modified to obtain new kinds of (${\in},\;{\in}\;{\vee}q$)-fuzzy subgroups such as an (${\in},\;{\in}\;{\vee}q$)-fuzzy normal subgroup, an (<${\in},\;{\in}\;{\vee}q$)-fuzzy characteristic subgroup, an (<${\in},\;{\in}\;{\vee}q$)-fuzzy fully invariant subgroup which are invariant under D. As results, some of the fundamental properties of such (${\in},\;{\in}\;{\vee}q$)-fuzzy subgroups are obtained.