• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.425-434
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• 2010

Here we see that the $p-Ces{\grave{a}}ro$ operators, the generalized $Ces{\grave{a}}ro$ operators of order one, the discrete generalized $Ces{\grave{a}}ro$ operators, and their adjoints are all posinormal operators on ${\ell}^2$, but many of these operators are not dominant, not normaloid, and not spectraloid. The question of dominance for $C_k$, the generalized $Ces{\grave{a}}ro$ operators of order one, remains unsettled when ${\frac{1}{2}}{\leq}k<1$, and that points to some general questions regarding terraced matrices. Sufficient conditions are given for a terraced matrix to be normaloid. Necessary conditions are given for terraced matrices to be dominant, spectraloid, and normaloid. A very brief new proof is given of the well-known result that $C_k$ is hyponormal when $k{\geq}1$.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.481-487
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• 1998

Let (equation omitted) denote the closure of the set (equation omitted) of dominant operators in the norm topology. We show that the Weyl spectrum of an operator T $\in$ (equation omitted) satisfies the spectral mapping theorem for analytic functions, which is an extension of [5, Theorem 1]. Also we show that an operator approximately equivalent to an operator of class (equation omitted) is of class (equation omitted).

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.53-62
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• 2000

In this paper we explore relations between joint Weyl and Browder spectra. Also, we give a spectral characterization of the Taylor-Browder spectrum for special classes of doubly commuting n-tuples of operators and then give a partial answer to Duggal's question.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.387-400
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• 2023

The purpose of the present paper is to obtain some subordination and superordination preserving properties with the sandwich-type theorems for multivalent functions in the open unit disk associated with Srivastava-Attiya operator. Moreover, applications for integral operators are also considered.

• Nuclear Engineering and Technology
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• v.28 no.5
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• pp.467-481
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• 1996

An integrated framework of modeling the human operator cognitive behavior during nuclear power plant accident scenarios is presented. It incorporates both plant and operator models. The basic structure of the operator model is similar to that of existing cognitive models, however, this model differs from those existing ones largely in too aspects. First, using frame and membership function, the pattern matching behavior, which is identified as the dominant cognitive process of operators responding to an accident sequence, is explicitly implemented in this model. Second, the non-task-related human cognitive activities like effect of stress and cognitive biases such as confirmation bias and availability bias, are also considered. A computer code, OPEC is assembled to simulate this framework and is actually applied to an SGTR sequence, and the resultant simulated behaviors of operator are obtained.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.117-123
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• 2009

This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ${\ell}^2$; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that $MM^*=M^*PM$ for some positive operator P on ${\ell}^2$; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint $M^*$ to be posinormal, and it is observed that, unless M is essentially trivial, $M^*$ cannot be hyponormal. A few examples are considered that exhibit special behavior.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.611-620
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• 2008

The purpose of this present paper is to derive some subordination and superordination results involving Carlson-Shaffer operator for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.631-646
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• 2009

In the present investigation, we introduce new classes of p-valent meromorphic functions defined by Liu-Srivastava linear operator and the multiplier transform and study their properties by using certain first order differential subordination and superordination.

• Nuclear Engineering and Technology
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• v.54 no.11
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• pp.4195-4208
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• 2022

In this study, operator habitability was numerically evaluated in the event of a fire at the main control bench board (MCB) in a reference main control room (MCR). It was investigated if evacuation variables including hot gas layer temperature (HGLT), heat flux (HF), and optical density (OD) at 1.8 m from the MCR floor exceed the reference evacuation criteria provided in NUREG/CR-6850. For a fire model validation, the simulation results of the reference MCR were compared with existing experimental results on the same reference MCR. In the simulation, various input parameters were applied to the MCB panel fire scenario: MCR height, peak heat release rate (HRR) of a panel, number of panels where fire propagation occurs, fire propagation time, door open/close conditions, and mechanical ventilation operation. A specialized-average HRR (SAHRR) concept was newly devised to comprehensively investigate how the various input parameters affect the operator's habitability. Peak values of the evacuation variables normalized by evacuation criteria of NUREG/CR-6850 were well-correlated as the power function of the SAHRR for the various input parameters. In addition, the evacuation time map was newly utilized to investigate how the evacuation time for different SAHRR was affected by changing the various input parameters. In the previous studies, it was found that the OD is the most dominant variable to determine the MCR evacuation time. In this study, however, the evacuation time map showed that the HF is the most dominant factor at the condition of without-mechanical ventilation for the MCR with a partially-open false ceiling, but the OD is the most dominant factor for all the other conditions. Therefore, the method using the SAHRR and the evacuation time map was very useful to effectively and comprehensively evaluate the operator habitability for the various input parameters in the event of MCB fires for the reference MCR.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.63-71
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• 2015

Let H be a separable infinite dimensional complex Hilbert space, and let $\mathcal{L}(H)$ denote the algebra of all bounded linear operators on H into itself. Let $A,B{\in}\mathcal{L}(H)$ we define the generalized derivation ${\delta}_{A,B}:\mathcal{L}(H){\mapsto}\mathcal{L}(H)$ by ${\delta}_{A,B}(X)=AX-XB$, we note ${\delta}_{A,A}={\delta}_A$. If the inequality ${\parallel}T-(AX-XA){\parallel}{\geq}{\parallel}T{\parallel}$ holds for all $X{\in}\mathcal{L}(H)$ and for all $T{\in}ker{\delta}_A$, then we say that the range of ${\delta}_A$ is orthogonal to the kernel of ${\delta}_A$ in the sense of Birkhoff. The operator $A{\in}\mathcal{L}(H)$ is said to be finite [22] if ${\parallel}I-(AX-XA){\parallel}{\geq}1(*)$ for all $X{\in}\mathcal{L}(H)$, where I is the identity operator. The well-known inequality (*), due to J. P. Williams [22] is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory [23]). In [16], the author showed that a paranormal operator is finite. In this paper we present some new classes of finite operators containing the class of paranormal operators and we prove that the range of a generalized derivation is orthogonal to its kernel for a large class of operators containing the class of normal operators.