• 대한수학회보
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• 제39권4호
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• pp.527-534
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• 2002

The weighted shifts have been made a central role in the study of κ-hyponormality for hyponormal and subnormal operators in discrete notion. In this note we discuss the κ-hyponormality of weighted translation semigroups with a symbol function in continuous notion.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.413-421
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• 2005

In this paper, we have a further discussion about quadratically hyponormal weighted shifts with weight sequence ${\alpha}:1,1,{\sqrt{a}},\left({\sqrt{b}},{\sqrt{c}},{\sqrt{d}}\right)^{\wedge}$ on the basis of sufficient conditions for positively quadratically hyponormal weighted shifts. We set examples of quadratically hyponormal weighted shifts with weight sequence of the above form, and also establish a general method for setting examples.

• 대한수학회보
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• 제47권1호
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• pp.179-186
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• 2010

This paper concerns the propagation phenomenon of weighted shifts. We here establish the existence of positive real numbers b and c (1 < b < c) such that the recursive weighted shift $W_{1,(1,\sqrt{b}\sqrt{c})$^ is quadratically but not cubically hyponormal.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.315-324
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• 2019

In this note we introduce a local-cubically hyponormal weighted shift of order ${\theta}$ with $0{\leq}{\theta}{\leq}{\frac{\pi}{2}}$, which is a new notion between cubic hyponormality and quadratic hyponormality of operators. We discuss the property of flatness for local-cubically hyponormal weighted shifts.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.199-203
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• 2015

In this paper we give an example which is a weakly subnormal weighted shift but not 2-hyponormal. Also, we show that every partially normal extension of an isometry T needs not be 2-hyponormal even though p.n.e.(T) is weakly subnormal.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.133-148
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• 2019

This paper is devoted to studying the sharing value problem for the derivative of a meromorphic function with its shift and q-difference. The results in the paper improve and generalize the recent result due to Qi, Li and Yang.

• 대한수학회논문집
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• 제34권2호
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• pp.477-486
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• 2019

Let ${\alpha}:1,(1,{\sqrt{x}},{\sqrt{y}})^{\wedge}$ be a weight sequence with Stampfli's subnormal completion and let $W_{\alpha}$ be its associated weighted shift. In this paper we discuss some properties of the region ${\mathcal{U}}:=\{(x,y):W_{\alpha}$ is semi-cubically hyponormal} and describe the shape of the boundary of ${\mathcal{U}}$. In particular, we improve the results of [19, Theorem 4.2].

• East Asian mathematical journal
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• 제31권5호
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• pp.695-706
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• 2015

Let ${\mathcal{H}}$ be an infinite dimensional complex Hilbert space, and let $B({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. Recall that an operator $T{\in}B({\mathcal{H})$ has property B(n) if ${\mid}T^n{\mid}{\geq}{\mid}T{\mid}^n$, $n{\geq}2$, which generalizes the class A-operator. We characterize the property B(n) of weighted shifts $S_{\lambda}$ over (${\eta},\;{\kappa}$)-type directed trees which appeared in the study of subnormality of weighted shifts over directed trees recently. In addition, we discuss the property B(n) of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with nonzero weights are being distinct with respect to $n{\geq}2$. And we give some properties of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with property B(2).

• 대한전기학회논문지:전력기술부문A
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• 제49권10호
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• pp.486-493
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• 2000

This paper presents an application to a multimachine power system of power system stabilizer using revised pole shift adaptive algorithm. Controller parameters are determined by using adaptive control theory in order to maintain optimal operation of generator under the various operating conditions. To determine the optimal parameters of controller and overcome the problem of pole placement algorithm, this paper presents pole shift algorithm revised pole shift factor. Also, the difference between the speed deviation with weighted factor and voltage deviation is used as the input signal of adaptive controller, which provides good damping characteristics. The results tested on a multimachine power system verify that the proposed controller has better dynamic and transient performance than conventional controller.

• 대한수학회지
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• 제55권1호
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• pp.225-251
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• 2018

The m-isometry of a single operator in Agler and Stankus [3] was naturally generalized to the m-isometric tuple of several commuting operators by Gleason and Richter [22]. Some examples of m-isometric tuples including the recently much studied Arveson-Drury d-shift were given in [22]. We provide more examples of m-isometric tuples of operators by using sums of operators or products of operators or functions of operators. A class of m-isometric tuples of unilateral weighted shifts parametrized by polynomials are also constructed. The examples in Gleason and Richter [22] are then obtained by choosing some specific polynomials. This work extends partially results obtained in several recent papers on the m-isometry of a single operator.