• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1579-1589
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• 2014

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ${\nabla}$ with skew torsion $T{\in}{\Lambda}^3M$ in the situation where the tangent bundle splits under the holonomy of ${\nabla}$ and the torsion of ${\nabla}$ is of 'split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.617-627
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• 2004

Let (equation omitted) denote the class of bounded linear Hilbert space operators with the property that $\midA^2\mid\geq\midA\mid^2$. In this paper we show that (equation omitted)-operators are finitely ascensive and that, for non-zero operators A and B, A (equation omitted) B is in (equation omitted) if and only if A and B are in (equation omitted). Also, it is shown that if A is an operator such that p(A) is in (equation omitted) for a non-trivial polynomial p, then Weyl's theorem holds for f(A), where f is a function analytic on an open neighborhood of the spectrum of A.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.701-707
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• 1998

An operator $T{\in} {{\mathcal L}(H)}$ is generalized k-quasihyponormal if there exist a constant M>0 such that $T^{\ast k}[M^2(T-z)^{\ast}(T-z)-(T-z)(T-z)^{\ast}]T^k{\geq}0$ for some integer $k{\geq}0$ and all $Z{\in} {\mathbf C}$. In this paper, we show that it T is a generalized k-quasihyponormal operator with the property $0{\not\in}{\sigma}(T)$, then T is subscalar of order 2. As a corollary, we get that such a T has a nontrivial invariant subspace if its spectrum has interior in C.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.571-575
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• 2002

In this paper we show that Weyl's theorem holds for f(T) when an Hilbert space operator T is “algebraically totally-paranormal” and f is any analytic function on an open neighbor-hood of the spectrum of T.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.285-291
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• 2012

Let $M_n$ be the algebra of all complex $n{\times}n$ matrices and ${\phi}:M_n{\rightarrow}M_n$ a surjective map (not necessarily additive or multiplicative) satisfying one of the following equations: $${\det}({\phi}(A){\phi}(B)+{\phi}(X))={\det}(AB+X),\;A,B,X{\in}M_n,\\{\sigma}({\phi}(A){\phi}(B)+{\phi}(X))={\sigma}(AB+X),\;A,B,X{\in}M_n$$. Then it is an automorphism, where ${\sigma}(A)$ is the spectrum of $A{\in}M_n$. We also show that if $\mathfrak{A}$ be a standard operator algebra, $\mathfrak{B}$ is a unital Banach algebra with trivial center and if ${\phi}:\mathfrak{A}{\rightarrow}\mathfrak{B}$ is a multiplicative surjection preserving spectrum, then ${\phi}$ is an algebra isomorphism.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.75-80
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• 2013

Let T be a bounded linear operator on a complex Hilbert space $\mathfrak{H}$. An operator T is called class A operator if ${\mid}T^2{\mid}{\geq}{\mid}T{\mid}^2$ and is called class $A({\kappa})$ operator if $(T^*{\mid}T{\mid}^{2{\kappa}}T)^{\frac{1}{{\kappa}+1}}{\geq}{\mid}T{\mid}^2$ for a positive number ${\kappa}$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class $A({\kappa})$ operators.

• Nuclear Engineering and Technology
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• v.52 no.9
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• pp.1983-1989
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• 2020

The human reliability analysis is a method by which, in general terms, the human impact to the safety and risk of a nuclear power plant operation can be modelled, quantified and analysed. It is an indispensable element of the PSA process within the nuclear industry nowadays. The paper herein presents a sensitivity study of the human reliability analysis performed on a real nuclear power plant-specific probabilistic safety assessment model. The analysis is performed on a pre-selected set of post-initiator operator actions. The purpose of the study is to investigate the impact of these operator actions on the plant risk by altering their corresponding human error probabilities in a wide spectrum. The results direct the fact that the future effort should be focused on maintaining the current human reliability level, i.e. not letting it worsen, rather than improving it.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.885-892
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• 2015

In this paper, we mainly obtain the following assertions: (1) If T is a quasi-*-n-paranormal operator, then T is finite and simply polaroid. (2) If T or $T^*$ is a quasi-*-n-paranormal operator, then Weyl's theorem holds for f(T), where f is an analytic function on ${\sigma}(T)$ and is not constant on each connected component of the open set U containing ${\sigma}(T)$. (3) If E is the Riesz idempotent for a nonzero isolated point ${\lambda}$ of the spectrum of a quasi-*-n-paranormal operator, then E is self-adjoint and $EH=N(T-{\lambda})=N(T-{\lambda})^*$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.389-393
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• 2006

In this paper it is shown that the spectrum ${\sigma}$ is continuous at every p-hyponormal operator when restricted to the set of essentially p-hyponormal operators and moreover ${\sigma}$ is continuous when restricted to the set of compact perturbations of p-hyponormal operators whose spectral pictures have no holes associated with the index zero.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.277-281
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• 2009

A Hilbert space operator T is a 2-isometry if $T^{{\ast}2}T^2\;-\;2T^{\ast}T+I$ = O. We shall study some properties of 2-isometries, in particular spectra of a non-unitary 2-isometry and give an example. Also we prove with alternate argument that the Weyl's theorem holds for 2-isometries.