• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제16권4호
• /
• pp.217-223
• /
• 2012

In this note we examine the effects on subnormality of adding a new weight or changing some weights for a given subnormal weighted shift. We consider a subnormal weighted shift with a positive point mass at the origin by means of continuous functions. Finally, we introduce some methods for evaluating point mass at the origin about moment measures associated with weighted shifts.

• 대한치과교정학회지
• /
• 제13권1호
• /
• pp.31-43
• /
• 1983

The following results were abtained based on the research of the occlusal patterns among 1074 handicapped persons (cerebral palsy: 46, mental subnormality: 619, deafmute: 285, blind: 111, childish autism:8, cleft lip and cleft palate:3, polimyelitis:2) of the age between 6 and 23 in Chollanamdo, Korea, in comparison with a normal group of 1048 children of the age between 6 and 15 selected at random in J primary school in Gwang-ju City. 1. According to Angle's malocclusion classification, all the handicapped groups, except the cerebral palsy and the blind, showed a higher prevalence of malocclusion than that of the normal. Especially the prevalence of Class II, devision 1 malocclusion in the cerebral palsy was the highest, and the prevalence of Class III malocclusion in all the handicapped groups was higher than that of the normal group. Among these groups the highest prevalence of Class III malocclusion was in the Down's syndrome group. 2. On the the abnormal pattern of the anterior region, there was no significant difference $(P\leqq0.05)$ between the normal and the cerebral palsy, the deafmute, and e blind. The open bite $(7.27{\pm}1.04\%)$ and the cross-bite $(32.7{\pm}6.33\%)$ of the Down's syndrome wire higher than that of the normal, and the forward position of the mandible could be recognized in the Down's syndrome group. 3. On the midline position of the dentition, all the handicapped showed the same percentage of deviation, but the degree of mandibular shift to the right $(20.00{\pm}5.39\%)$ or left $(10.91{\pm}4.20\%)$ was higher than that of the normal only in the Down's syndrome group. 4. On the abnormal pattern of the posterior region, the cross-bite of the Down's syndrome was higher than that of the normal by $20.00{\pm}5.39\%$, the cross-bite of the cerebral palsy and the cross-bite and the open bite of the mental subnormality were slightly higher than that of the normal. The other handicapped groups showed no significant difference $(P\leq0.05)$ to the normal.

• East Asian mathematical journal
• /
• 제31권5호
• /
• pp.695-706
• /
• 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).

• Journal of applied mathematics & informatics
• /
• 제38권5_6호
• /
• pp.579-590
• /
• 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.

• 대한수학회보
• /
• 제57권1호
• /
• pp.81-93
• /
• 2020

Let m ∈ ℕ₀, p > 1 and $${\alpha}^{[m,p]}(x)\;:\;{\sqrt{x}},\;\{{\sqrt{\frac{(m+n-1)p-(m+n-2)}{(m+n)p-(m+n-1)}}}\}^{\infty}_{n=1}$$. In this paper, we consider the backward extensions of Bergman-type weighted shift W_α^[m,p](x). We consider its subnormality, k-hyponormality and positive quadratic hyponormality. Our results include all the results on Bergman weighted shift W_α(x) with m ∈ ℕ and $${\alpha}(x)\;:\;{\sqrt{x}},\;{\sqrt{\frac{m}{m+1}},\;{\sqrt{\frac{m}{m+2}},\;{\sqrt{\frac{m+2}{m+3}},{\cdots}$$.

• 대한수학회지
• /
• 제44권4호
• /
• pp.949-970
• /
• 2007

By considering a bridge between Bram-Halmos and Embry characterizations for the subnormality of cyclic operators, we extend the Curto-Fialkow and Embry truncated complex moment problem, and solve the problem finding the finitely atomic representing measure ${\mu}$ such that ${\gamma}_{ij}={\int}\bar{z}^iz^jd{\mu},\;(0{\le}i+j{\le}2n,\;|i-j|{\le}n+s,\;0{\le}s{\le}n);$ the cases of s = n and s = 0 are induced by Bram-Halmos and Embry characterizations, respectively. The former is the Curto-Fialkow truncated complex moment problem and the latter is the Embry truncated complex moment problem.

• Journal of applied mathematics & informatics
• /
• 제40권1_2호
• /
• pp.15-24
• /
• 2022

Let p > 1 and α^[p](x) : $\sqrt{x}$, $\sqrt{\frac{p}{^2p-1}}$, $\sqrt{\frac{2p-1}{3p-2}}$, … , with 0 < x ≤ $\frac{p}{2p-1}$. In [10], the authors considered the subnormality, n-hyponormality and positive quadratic hyponormality of W_α^[p](x). By continuing to study, in this paper, we give a sufficient condition of quadratic hyponormality of W_α^[p](x). Finally, we give an example to characterize the gaps of W_α^[p](x) distinctively.

• 대한수학회논문집
• /
• 제39권2호
• /
• pp.437-460
• /
• 2024

In this paper we present the weighted shift operators having the property of moment infinite divisibility. We first review the monotone theory and conditional positive definiteness. Next, we study the infinite divisibility of sequences. A sequence of real numbers γ is said to be infinitely divisible if for any p > 0, the sequence γ^p = {γ^p_n}^∞_n=0 is positive definite. For sequences α = {α_n}^∞_n=0 of positive real numbers, we consider the weighted shift operators W_α. It is also known that W_α is moment infinitely divisible if and only if the sequences {γ_n}^∞_n=0 and {γ_n+1}^∞_n=0 of W_α are infinitely divisible. Here γ is the moment sequence associated with α. We use conditional positive definiteness to establish a new criterion for moment infinite divisibility of W_α, which only requires infinite divisibility of the sequence {γ_n}^∞_n=0. Finally, we consider some examples and properties of weighted shift operators having the property of (k, 0)-CPD; that is, the moment matrix M_γ(n, k) is CPD for any n ≥ 0.