• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.579-590
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• 2020

The flatness property of a unilateral weighted shifts is important to study the gaps between subnormality and hyponormality. In this paper, we first summerize the results on the flatness for some special kinds of a weighted shifts. And then, we consider the flatness property for a local-cubically hyponormal weighted shifts, which was introduced in [2]. Let α : ${\sqrt{\frac{2}{3}}}$, ${\sqrt{\frac{2}{3}}}$, $\{{\sqrt{\frac{n+1}{n+2}}}\}^{\infty}_{n=2}$ and let W_α be the associated weighted shift. We prove that W_α is a local-cubically hyponormal weighted shift W_α of order ${\theta}={\frac{\pi}{4}}$ by numerical calculation.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.589-598
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• 2004

We consider bilateral operator weighted shift T on $L^2$(K) with weight sequence ${[A_{n}]_{n=-{\infty}}}^{\infty}$ of positive invertible diagonal operators on K. We give a characterization for T to be hypercyclic, and show that the conditions are far simplified in case T is invertible.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.907-916
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• 1995

The unilateral weighted shift operator $W_r$ with the weighted sequence ${r^n}^\infty_{n=0}$ is unicellular if $0 < r < 1$. In general, A + B is not unicellular even if A and B are unicellular. We will prove that $W_r + W^2_r$ is unicellular if $0 < r < 1$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.943-957
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• 2016

We introduce a 2-variable weighted shift, denoted by $S_2$(a, b, c, d), which arises naturally from analytic function space theory. We investigate when it is subnormal, and compute the Berger measure of it when it is subnormal. And we apply the results to investigate the relationship among 2-variable subnormal, hyponormal and 2-hyponormal weighted shifts.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.721-727
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• 2008

Let $W_{\alpha}$ be a weighted shift with positive weight sequence ${\alpha}=\{\alpha_i\}_{i=0}^{\infty}$. The semi-cubical hyponormality of $W_{\alpha}$ is introduced and some flatness properties of $W_{\alpha}$ are discussed in this note. In particular, it is proved that if ${\alpha}_n={\alpha}_{n+1}$ for some $n{\geq}1$, ${{\alpha}_{n+k}}={\alpha}_n$ for all $k{\geq}1$.

• East Asian mathematical journal
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• v.31 no.5
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• pp.635-652
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• 2015

It is shown that for a general Haar shift operator, and a weight in the $A_2$ weight class, we establish the weighted norm estimate which linearly depends on $A_2$-characteristic $[w]_{A_2}$. Although the result is now well known, we introduce the new method, which is called the iterated Bellman function method, to provide the estimate.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.185-189
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• 2013

In this note we study a class of invertible weighted bilateral shifts on Hilbert space introduced by Haskell Rosenthal recently. We show that every Rosenthal shift is unitarily equivalent to its inverse, not quasisimilar to its adjoint, and has a nontrivial hyperinvariant subspace.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.899-910
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• 2016

It is known that a semi-cubically hyponormal weighted shift need not satisfy the flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe all semi-cubically hyponormal weighted shifts $W_{\alpha}$ with first two weights equal. Let ${\alpha}$ : 1, 1, ${\sqrt{x}}$(${\sqrt{u}}$, ${\sqrt{v}}$, ${\sqrt{w}}$)^ be a backward 3-step extension of a recursively generated weight sequence with 1 < x < u < v < w and let $W_{\alpha}$ be the associated weighted shift. In this paper we characterize completely the semi-cubical hyponormal $W_{\alpha}$ satisfying the additional assumption of the positive determinant coefficient property, which result is parallel to results for quadratic hyponormality.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.3
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• pp.1377-1389
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• 2016

This paper presents a target model update scheme for the mean-shift tracking with background weighted histogram. In the scheme, the target candidate histogram is corrected by considering the back-projection weight of each pixel in the kernel after the best target candidate in the current frame image is chosen. In each frame, the target model is updated by the weighted average of the current target model and the corrected target candidate. We compared our target model update scheme with the previous ones by applying several test sequences. The experimental results showed that the object tracking accuracy was greatly improved by using the proposed scheme.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.73-83
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• 2019

In this article, we introduce a new kind of subnormal weighted shifts, which is a generalized form of Bergman shift, and discuss the k-hyponormality of its backward extensions.