• 한국지능시스템학회논문지
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• 제22권6호
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• pp.700-705
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• 2012

본 논문은 미리 설계된 타카기-수게노 퍼지 모델 기반 아날로그 제어기를 상태 정합의 의미에서 등가인 샘플치 제어기로 효율적으로 변환하기 위해, 관측기 기반 출력 궤환 퍼지 제어기에 대한 지능형 디지털 재설계 기법을 제안한다. 아날로그 제어 시스템과 샘플치 제어 시스템 사이의 점근적 연관성을 위해 델타 연산자를 사용한다. 지능형 디지털 재설계 문제는 정합될 선형 연산자 간의 놈의 거리를 최소화하는 문제로 생각한다. 제어기 설계 조건은 선형행렬부등식의 형태로 유도되며, 디지털 재설계시 관측기와 제어기에 대한 분리 설계 조건이 만족함을 보인다.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.553-563
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• 2006

Let A be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of A is the set ${\sigma}_{B{\omega}}(A)$ of all ${\lambda}{\in}\mathbb{C}$ such that $A-{\lambda}I$ is not a B-Fredholm operator of index 0. Let E(A) be the set of all isolated eigenvalues of A. Recently in [6] Berkani showed that if A is a hyponormal operator, then A satisfies generalized Weyl's theorem ${\sigma}_{B{\omega}}(A)={\sigma}(A)$\E(A), and the B-Weyl spectrum ${\sigma}_{B{\omega}}(A)$ of A satisfies the spectral mapping theorem. In [51], H. Weyl proved that weyl's theorem holds for hermitian operators. Weyl's theorem has been extended from hermitian operators to hyponormal and Toeplitz operators [12], and to several classes of operators including semi-normal operators ([9], [10]). Recently W. Y. Lee [35] showed that Weyl's theorem holds for algebraically hyponormal operators. R. Curto and Y. M. Han [14] have extended Lee's results to algebraically paranormal operators. In [19] the authors showed that Weyl's theorem holds for algebraically p-hyponormal operators. As Berkani has shown in [5], if the generalized Weyl's theorem holds for A, then so does Weyl's theorem. In this paper all the above results are generalized by proving that generalizedWeyl's theorem holds for the case where A is an algebraically ($p,\;k$)-quasihyponormal or an algebarically paranormal operator which includes all the above mentioned operators.

• 대한수학회지
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• 제58권6호
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• pp.1385-1405
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• 2021

Let A be a positive bounded linear operator acting on a complex Hilbert space (𝓗, ⟨·,·⟩). Let ω_A(T) and ║T║_A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space (𝓗, ⟨·,·⟩_A), respectively, where ⟨x, y⟩_A := ⟨Ax, y⟩ for all x, y ∈ 𝓗. In this paper, we show with different techniques from that used by Kittaneh in [24] that $$\frac{1}{4}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A{\leq}{\omega}^2_A(T){\leq}\frac{1}{2}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A.$$ Here T^#_A denotes a distinguished A-adjoint operator of T. Moreover, a considerable improvement of the above inequalities is proved. This allows us to compute the 𝔸-numerical radius of the operator matrix $\(\array{I&T\\0&-I}\)$ where 𝔸 = diag(A, A). In addition, several A-numerical radius inequalities for semi-Hilbert space operators are also established.

• 대한수학회지
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• 제23권2호
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• pp.167-173
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• 1986

• 대한수학회논문집
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• 제8권1호
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• pp.1-14
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• 1993

• East Asian mathematical journal
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• 제12권2호
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• pp.167-174
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• 1996

• 대한수학회지
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• 제22권1호
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• pp.35-42
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• 1985

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.277-281
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• 2007

There are many papers on linear operators that preserve commuting pairs of matrices over fields or semirings. From these research works, we have a motivation to the research on the linear operators that preserve commuting pairs of matrices over nonnegative integers. We characterize the surjective linear operators that preserve commuting pairs of matrices over nonnegative integers.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.547-557
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• 2018

We establish some characterizations of isoparametric surfaces in the three-dimensional Euclidean space, which are associated with the Laplacian operator defined by the so-called II-metric on surfaces with non-degenerate second fundamental form and the elliptic linear Weingarten metric on surfaces in the three-dimensional Euclidean space. We also study a Ricci soliton associated with the elliptic linear Weingarten metric.

• Korean Journal of Mathematics
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• 제9권2호
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• pp.115-121
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• 2001

In this paper, we establish the conditions that a mild C-existence family yields a solution to the abstract Cauchy problem. And we show the relation between mild C-existence family and C-regularized semigroup if the family of linear operators is exponentially bounded and C is a bounded injective linear operator.