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学者姓名：朱玉灿
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Abstract ：
This article studies the stability of woven frames by introducing some special limits. We show that there exist certain relations among the different types of convergence of frames and obtain some new and more general stability results. As an application of these results, we provide a method for constructing woven frames.
Keyword ：
convergence of frames convergence of frames frames frames stability stability weaving frames weaving frames woven frames woven frames
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| GB/T 7714 | Li, Xue-Bin , Zhu, Yu-Can . Stability of Woven Frames [J]. | FRONTIERS IN PHYSICS , 2022 , 10 . |
| MLA | Li, Xue-Bin 等. "Stability of Woven Frames" . | FRONTIERS IN PHYSICS 10 (2022) . |
| APA | Li, Xue-Bin , Zhu, Yu-Can . Stability of Woven Frames . | FRONTIERS IN PHYSICS , 2022 , 10 . |
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针对测度双K-框架的性质问题,提出任给一个测度双K-框架构造紧测度K-框架的方法,并讨论不同空间的测度双K-框架在有界线性算子扰动下的稳定性.
Keyword ：
测度双K-框架 测度双K-框架 测度框架 测度框架 紧测度K-框架 紧测度K-框架
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| GB/T 7714 | 尚蒙娟 , 朱玉灿 . R~n上的测度双K-框架 [J]. | 福州大学学报(自然科学版) , 2021 , 49 (06) : 727-731 . |
| MLA | 尚蒙娟 等. "R~n上的测度双K-框架" . | 福州大学学报(自然科学版) 49 . 06 (2021) : 727-731 . |
| APA | 尚蒙娟 , 朱玉灿 . R~n上的测度双K-框架 . | 福州大学学报(自然科学版) , 2021 , 49 (06) , 727-731 . |
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In this paper we find that a result of an equivalent characterization of tight K-g-frames obtained by Huang and Shi is incorrect, and we give a sufficient condition for a given Bessel sequence to be a tight K-frame. We also characterize the weaving of K-frames in Hilbert spaces. We give several kinds of sufficient conditions such that the type {T(1)f(i)}i is an element of I and {T-2gi}(i is an element of I) are K-woven (resp. woven) on H or its subspace R(K), given that {f(i)}(i is an element of I) and {g(i)}(i is an element of I) are K-frames (resp. frames) on H and T-1,T-2 are surjective operators on H. Finally we discuss that we can plus two different Bessel sequences to a K-woven pair such that the new obtained pair are K-woven on H.
Keyword ：
Frame Frame K-frame K-frame K-woven K-woven Tight Tight Weaving Weaving
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| GB/T 7714 | Xiao, Xiangchun , Yan, Kai , Zhao, Guoping et al. Tight K-frames and weaving of K-frames [J]. | JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS , 2021 , 12 (1) . |
| MLA | Xiao, Xiangchun et al. "Tight K-frames and weaving of K-frames" . | JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 12 . 1 (2021) . |
| APA | Xiao, Xiangchun , Yan, Kai , Zhao, Guoping , Zhu, Yucan . Tight K-frames and weaving of K-frames . | JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS , 2021 , 12 (1) . |
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Abstract ：
该文在Hilbert空间中讨论K-框架和紧K-框架在算子扰动中的稳定性.首先给出K-框架经过有界线性算子T扰动后为K-框架的充要条件,其次讨论了用两个Bessel序列或者两个K-框架构造新的K-框架的方法,最后给出用两个Bessel序列构造紧K-框架的充要条件.这些结果推广和改进了由Christensen和Casazza等得到的著名结果.
Keyword ：
Bessel序列 Bessel序列 K-框架 K-框架 稳定性 稳定性 紧K-框架 紧K-框架
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| GB/T 7714 | 杜丹丹 , 朱玉灿 . K-框架和紧K-框架的算子扰动的稳定性 [J]. | 数学物理学报:A辑 , 2021 , 41 (1) : 29-38 . |
| MLA | 杜丹丹 et al. "K-框架和紧K-框架的算子扰动的稳定性" . | 数学物理学报:A辑 41 . 1 (2021) : 29-38 . |
| APA | 杜丹丹 , 朱玉灿 . K-框架和紧K-框架的算子扰动的稳定性 . | 数学物理学报:A辑 , 2021 , 41 (1) , 29-38 . |
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Abstract ：
公共基础课是高校的一类大课,其信息化程度对本科生的基础素质培养具有深远的影响.公共基础课通常采用教考分离的模式,课程考核主要通过统一命题、统一考试和流水阅卷实现.基于公共基础课的特点、试卷管理和教学评估的需求,结合信息技术和高考阅卷经验,自主研发了一套适合公共基础课的网上评卷系统,并首次在数学类公共基础课体系中实施.经过两年多的成功实践,有效地克服了手工评卷的种种弊端,突破了时空限制,降低了管理复杂度,方便了广大教师,促进了科教融合和本科生的能力培养,确保了评卷质量和水平.
Keyword ：
公共基础课 公共基础课 手工评卷 手工评卷 科教融合 科教融合 网上评卷 网上评卷
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| GB/T 7714 | 刘文丽 , 吕书龙 , 周勇 et al. 基于网上评卷系统的教学信息化实践 ——以数学类公共基础课为例 [J]. | 中国轻工教育 , 2020 , (1) : 19-24 . |
| MLA | 刘文丽 et al. "基于网上评卷系统的教学信息化实践 ——以数学类公共基础课为例" . | 中国轻工教育 1 (2020) : 19-24 . |
| APA | 刘文丽 , 吕书龙 , 周勇 , 薛美玉 , 朱玉灿 . 基于网上评卷系统的教学信息化实践 ——以数学类公共基础课为例 . | 中国轻工教育 , 2020 , (1) , 19-24 . |
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Abstract ：
众所周知,自然K-对偶Bessel序列指的是所有K-对偶Bessel序列中分析算子的范数最小的那个K-对偶Bessel序列,但是通过该定义无法直接知道自然K-对偶Bessel序列的具体形式.本文先给出两种特殊情况下,K-框架的自然K-对偶Bessel序列的具体形式和最佳K-框架界.特别地,有限维Hilbert空间中的K-框架的最佳K-框架界可以用特征值来表示.最后,通过本文所得到的自然K-对偶Bessel序列的具体形式来刻画出所有的K-对偶Bessel序列.
Keyword ：
K-对偶Bessel序列 K-对偶Bessel序列 K-框架 K-框架 最佳K-框架界 最佳K-框架界 自然K-对偶Bessel序列 自然K-对偶Bessel序列
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| GB/T 7714 | 傅元康 , 朱玉灿 . K-框架的自然K-对偶Bessel序列 [J]. | 中国科学（数学） , 2020 , 50 (2) : 287-300 . |
| MLA | 傅元康 et al. "K-框架的自然K-对偶Bessel序列" . | 中国科学（数学） 50 . 2 (2020) : 287-300 . |
| APA | 傅元康 , 朱玉灿 . K-框架的自然K-对偶Bessel序列 . | 中国科学（数学） , 2020 , 50 (2) , 287-300 . |
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利用线性无关的Bessel序列定义一个迭代算子,并用该算子迭代表示一个K-框架.得出一个算子迭代表示的K-框架所应该具备的条件,讨论K-Riesz基有关算子迭代表示的问题,并在具有有界算子迭代表示的前提下,给出K-框架成为K-Riesz基的等价条件.
Keyword ：
Bessel序列 Bessel序列 Hilbert空间 Hilbert空间 K-框架 K-框架 框架 框架 算子迭代 算子迭代
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| GB/T 7714 | 林焕程 , 朱玉灿 . K-框架的算子迭代表示 [J]. | 福州大学学报（自然科学版） , 2020 , 48 (2) : 140-145 . |
| MLA | 林焕程 et al. "K-框架的算子迭代表示" . | 福州大学学报（自然科学版） 48 . 2 (2020) : 140-145 . |
| APA | 林焕程 , 朱玉灿 . K-框架的算子迭代表示 . | 福州大学学报（自然科学版） , 2020 , 48 (2) , 140-145 . |
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Let X be a Banach space and A, B, C, D be bounded linear operators on X. In this paper we show that the Drazin (resp. generalized Drazin) spectrum of AC coincides with the Drazin (resp. generalized Drazin) spectrum of BD under certain assumptions. Moreover, several interesting Banach space properties, such as SVEP and polaroidness, are considered.
Keyword ：
Drazin invertibility Drazin invertibility Generalized Drazin invertibility Generalized Drazin invertibility Operator product Operator product Spectral equation Spectral equation
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| GB/T 7714 | Yan, Kai , Zeng, Qingping , Zhu, Yucan . On Drazin Spectral Equation for the Operator Products [J]. | COMPLEX ANALYSIS AND OPERATOR THEORY , 2020 , 14 (1) . |
| MLA | Yan, Kai et al. "On Drazin Spectral Equation for the Operator Products" . | COMPLEX ANALYSIS AND OPERATOR THEORY 14 . 1 (2020) . |
| APA | Yan, Kai , Zeng, Qingping , Zhu, Yucan . On Drazin Spectral Equation for the Operator Products . | COMPLEX ANALYSIS AND OPERATOR THEORY , 2020 , 14 (1) . |
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Abstract ：
Let R be any associative ring with unit 1 and suppose that ac is Drazin (respectively, generalized Drazin, pseudo-Drazin) invertible if and only if 1-bd is Drazin (respectively, generalized Drazin, pseudo-Drazin) invertible. In other words, we give an affirmative answer to the conjecture of D. Mosic. Moreover, some applications to Banach algebra elements and Banach space operators are also given.
Keyword ：
Drazin inverse Drazin inverse generalized Drazin inverse generalized Drazin inverse Jacobson's lemma Jacobson's lemma pseudo-Drazin inverse pseudo-Drazin inverse ring ring
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| GB/T 7714 | Yan, Kai , Zeng, Qingping , Zhu, Yucan . Generalized Jacobson's lemma for Drazin inverses and its applications [J]. | LINEAR & MULTILINEAR ALGEBRA , 2020 , 68 (1) : 81-93 . |
| MLA | Yan, Kai et al. "Generalized Jacobson's lemma for Drazin inverses and its applications" . | LINEAR & MULTILINEAR ALGEBRA 68 . 1 (2020) : 81-93 . |
| APA | Yan, Kai , Zeng, Qingping , Zhu, Yucan . Generalized Jacobson's lemma for Drazin inverses and its applications . | LINEAR & MULTILINEAR ALGEBRA , 2020 , 68 (1) , 81-93 . |
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Abstract ：
In this paper, we mainly discuss the constructions of some new K-g-frames which differ from the existing methods. Meanwhile, we use the relation between a positive operator and the frame operator of a K-g-frame to yield a new K-g-frame. We also obtain a necessary and sufficient condition to generate a new K-g-frame. In addition, we correct some recent results which were obtained by Huang and Leng. In the end, we give an equivalent characterization to construct some new tight K-g-frames by two given g-Bessel sequences. Our results generalize and improve some remarkable results.
Keyword ：
G-Bessel sequence G-Bessel sequence K-g-frame K-g-frame Positive operator Positive operator Tight K-g-frame Tight K-g-frame
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| GB/T 7714 | Du, Dandan , Zhu, Yu-Can . Constructions of K-g-Frames and Tight K-g-Frames in Hilbert Spaces [J]. | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY , 2020 , 43 (6) : 4107-4122 . |
| MLA | Du, Dandan et al. "Constructions of K-g-Frames and Tight K-g-Frames in Hilbert Spaces" . | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 43 . 6 (2020) : 4107-4122 . |
| APA | Du, Dandan , Zhu, Yu-Can . Constructions of K-g-Frames and Tight K-g-Frames in Hilbert Spaces . | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY , 2020 , 43 (6) , 4107-4122 . |
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