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Weyl定理与(R)性质的判定
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作者 赵巨涛 曹小红 董炯 《华南师范大学学报(自然科学版)》 CAS 北大核心 2023年第2期109-115,共7页
利用半Fredholm算子的扰动不变性,研究有界线性算子与上三角算子矩阵的Weyl型定理。首先,给出有界线性算子同时满足Browder定理和(R_(1))性质,或者同时满足Weyl定理和(R)性质的充要条件;然后,讨论上三角算子矩阵同时满足Weyl定理和(R)... 利用半Fredholm算子的扰动不变性,研究有界线性算子与上三角算子矩阵的Weyl型定理。首先,给出有界线性算子同时满足Browder定理和(R_(1))性质,或者同时满足Weyl定理和(R)性质的充要条件;然后,讨论上三角算子矩阵同时满足Weyl定理和(R)性质的条件。 展开更多
关键词 有界线性算子 上三角算子矩阵 (r)性质 WEYL定理
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有界线性算子的(R)性质及亚循环性
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作者 胡添翼 窦艳妮 《中山大学学报(自然科学版)(中英文)》 CAS CSCD 北大核心 2023年第2期172-180,共9页
令H为无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体。σ(T)表示算子T∈B(H)的谱集。称算子T∈B(H)满足(R)性质,若σa(T)\σab(T)=π00(T),其中σa(T),σab(T)分别表示算子T的逼近点谱和Browder本质逼近点谱,π00(T)={λ∈iso... 令H为无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体。σ(T)表示算子T∈B(H)的谱集。称算子T∈B(H)满足(R)性质,若σa(T)\σab(T)=π00(T),其中σa(T),σab(T)分别表示算子T的逼近点谱和Browder本质逼近点谱,π00(T)={λ∈isoσ(T):0<n(T-λI)<+∞}.给出了有界线性算子满足(R)性质的新的判定方法,并讨论了算子的(R)性质和亚循环性之间的关系。 展开更多
关键词 (r)性质 亚循环性
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算子及其函数的(R)性质的判定
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作者 胡添翼 窦艳妮 《河南师范大学学报(自然科学版)》 CAS 北大核心 2023年第2期63-69,共7页
令H为无限维复可分的Hilbert空间,H上有界线性算子的全体为B(H).用σ(T),σ_(ab)(T)和σ_(a)(T)分别表示为算子T∈B(H)的谱集,Browder本质逼近点谱和逼近点谱.称算子T∈B(H)满足(R)性质,若σ_(a)(T)\σ_(ab)(T)=π_(00)(T),其中π_(00)(... 令H为无限维复可分的Hilbert空间,H上有界线性算子的全体为B(H).用σ(T),σ_(ab)(T)和σ_(a)(T)分别表示为算子T∈B(H)的谱集,Browder本质逼近点谱和逼近点谱.称算子T∈B(H)满足(R)性质,若σ_(a)(T)\σ_(ab)(T)=π_(00)(T),其中π_(00)(T)={λ∈isoσ(T)∶0<n(T-λI)<∞}.主要借助新的谱集给出了算子满足(R)性质新的判定,并进一步得出了算子函数满足(R)性质的充分必要条件. 展开更多
关键词 (r)性质 算子函数
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算子函数的a-Weyl定理和(R)性质
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作者 赵玲玲 高凯 +1 位作者 洪明理 王福昌 《华南师范大学学报(自然科学版)》 北大核心 2023年第5期80-87,共8页
文章利用谱集的关系给出判定有界线性算子分别满足a-Weyl定理和(R)性质的新方法,在此基础上,得到算子同时满足a-Weyl定理和(R)性质的充要条件;然后,讨论了算子函数满足a-Weyl定理和(R)性质的充要条件,最终得到算子函数同时满足a-Weyl定... 文章利用谱集的关系给出判定有界线性算子分别满足a-Weyl定理和(R)性质的新方法,在此基础上,得到算子同时满足a-Weyl定理和(R)性质的充要条件;然后,讨论了算子函数满足a-Weyl定理和(R)性质的充要条件,最终得到算子函数同时满足a-Weyl定理和(R)性质的判定方法。 展开更多
关键词 a-Weyl定理 (r)性质 算子函数
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有界线性算子的一致Fredholm指标性质及Weyl型定理
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作者 赵巨涛 曹小红 《河南师范大学学报(自然科学版)》 CAS 北大核心 2022年第5期42-48,共7页
Weyl型定理反映了线性算子的局部谱结构,对Weyl型定理的研究是算子谱理论研究的热点问题,近年来备受关注.利用一致Fredholm指标性质,给出了有界线性算子或算子函数同时满足(R)性质和Weyl定理的充要条件.之后有界线性算子或者算子函数的... Weyl型定理反映了线性算子的局部谱结构,对Weyl型定理的研究是算子谱理论研究的热点问题,近年来备受关注.利用一致Fredholm指标性质,给出了有界线性算子或算子函数同时满足(R)性质和Weyl定理的充要条件.之后有界线性算子或者算子函数的(R)性质、Weyl定理及亚循环性三者之间的关系得到了讨论. 展开更多
关键词 (r)性质 BrOWDEr定理 WEYL定理 亚循环性
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有界线性算子及其函数的(R)性质 被引量:2
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作者 赵小鹏 戴磊 曹小红 《云南大学学报(自然科学版)》 CAS CSCD 北大核心 2022年第1期9-15,共7页
设H为无限维复可分的Hilbert空间,B(H)为H上的有界线性算子的全体.T∈B(H)称为满足(R_(1))性质,若σ_(a)(T)σ_(ab)(T)?π_(00)(T),其中σ_(a)(T)和σ_(ab)(T)分别表示算子T的逼近点谱和本质逼近点谱,π_(00)(T)={λ∈isoσ(T):0<dim... 设H为无限维复可分的Hilbert空间,B(H)为H上的有界线性算子的全体.T∈B(H)称为满足(R_(1))性质,若σ_(a)(T)σ_(ab)(T)?π_(00)(T),其中σ_(a)(T)和σ_(ab)(T)分别表示算子T的逼近点谱和本质逼近点谱,π_(00)(T)={λ∈isoσ(T):0<dimN(T-λI)<∞}.若σ_(a)(T)σ_(ab)(T)=π_(00)(T),则称T满足(R)性质.运用新的谱集,给出了有界线性算子及其函数满足(R_(1))性质或者(R)性质的充要条件;同时得到了a-Weyl定理和(R)性质的新的判定方法. 展开更多
关键词 有界线性算子 (r_(1))性质 (r)性质 a-Weyl定理
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有界线性算子及其函数的(R)性质
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作者 赵小鹏 戴磊 曹小红 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2022年第3期294-299,323,共7页
设H为无限维复可分的Hilbert空间,B(H)为H中有界线性算子的全体。若σ_(a)(T)\σ_(ab)(T)■π_(00)(T),则称T∈B(H)满足(R_(1))性质,其中σ^(a)(T)和σ_(ab)(T)分别表示算子T的逼近点谱和Browder本质逼近点谱,π00(T)={λ∈isoσ(T):0&l... 设H为无限维复可分的Hilbert空间,B(H)为H中有界线性算子的全体。若σ_(a)(T)\σ_(ab)(T)■π_(00)(T),则称T∈B(H)满足(R_(1))性质,其中σ^(a)(T)和σ_(ab)(T)分别表示算子T的逼近点谱和Browder本质逼近点谱,π00(T)={λ∈isoσ(T):0<dimN(T-λI)<∞};若σ^(a)(T)\σ_(ab)(T)=π00(T),则称T满足(R)性质。给出了有界线性算子满足(R_(1))性质或(R)性质的充要条件,研究了算子函数满足(R_(1))性质或(R)性质的判定方法,并讨论了完全*-paranormal算子及其函数的(R_(1))性质或(R)性质。 展开更多
关键词 (r_(1))性质 (r)性质
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有界线性算子的a-Browder定理及(R_(1))性质
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作者 车雨红 戴磊 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2022年第6期676-681,共6页
给出了有界线性算子满足a-Browder定理且具有(R_(1))性质的充要条件,研究了算子函数满足a-Browder定理且具有(R_(1))性质的判定方法,应用所得结论,给出了一类重要算子及其函数满足a-Browder定理且具有(R_(1))性质的判别定理。
关键词 a-Browder定理 (r1)性质
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The Property of Bair in r-Space
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作者 宋振明 《Chinese Quarterly Journal of Mathematics》 CSCD 1994年第3期19-20,共2页
In this paper,we study properties of Bair by symmetric difference.
关键词 symmetric difference property of Bair
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Microscopic Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO:Cr^3+
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作者 MADong-Ping LIUYan-Yun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第3期373-380,共8页
By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d<SUP>3</SUP... By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d<SUP>3</SUP> electronic configuration, the values of all the parameters in the expressions of thermal shift (TS) and thermal broadening (TB) due to EPI for the ground level, R level and R line of MgO:Cr<SUP>3+</SUP> have microscopically been evaluated; and then, TS and TB of R line and various contributions to them have uniformly been calculated. The results are in very good agreement with the experimental data. It is found that all the three terms of TS due to EPI are red shifts; the Raman term is the largest one, and the optical-branch term and neighbor-level term are important for TS; the contribution to TS from thermal expansion is blue shift, which is also important. The R-line TS of MgO:Cr<SUP>3+</SUP> comes from the first-order term of EPI. The elastic Raman scattering of acoustic phonons plays a dominant role in R-line TB of MgO:Cr<SUP>3+</SUP>. For both TS and TB, it is very important to take into account all the admixtures of basic wavefunctions within d<SUP>3</SUP> electronic configuration. 展开更多
关键词 crystal fields optical properties thermal shift and broadening electron-phonon interaction thermal expansion
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Influences of Reactive Compatibilizer R-Styrene-Maleic Anhydride Copolymer on PA6/PP Blends
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作者 黄伯芬 李枭 +3 位作者 梁翰轩 Jeffrey X Shi 王俊杰 李知远 《Journal of Donghua University(English Edition)》 EI CAS 2011年第4期367-370,共4页
The effect of R-styrene-maleic anhydride copolymer (R- SMA) compatibilzation on Nylon 6 ( PA6 )/polypropylene ( PP ) blends has been investigated experimentally through Molan test, microscopic morphology, and ch... The effect of R-styrene-maleic anhydride copolymer (R- SMA) compatibilzation on Nylon 6 ( PA6 )/polypropylene ( PP ) blends has been investigated experimentally through Molan test, microscopic morphology, and chemical structure. Results show that the moderate R-SMA addition can promote reaction between anhydride in R-SMA and amino in PA6, and lead to a new PA6-g- R-SMA copolymer in the blends. Such PA6-g-R-SMA eopolymer in the blends can effectively reduce the interfaeial tension and PP particle size, and improve the compatibility of two immiscible phases in the blends. The crystallinity of PA6 in PA6/PP blends has greatly decreased by PP blends. The blends have the best comprehensive mechanical and thermal properties when the mass ratio of PA6/PP/ R-SMA is 90:10:2 to 90:10:4. The impact strength of the PA6/PP blends with the eompatibilizer is increased by more than 150 %. 展开更多
关键词 Nylon 6/polypropylene blends r-styrene-maleic anhydride copolymer r-SMA COMPATIBILIZATION morphology CrYSTALLINITY properties
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有界线性算子的拓扑一致降标与(R)性质 被引量:2
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作者 赵小鹏 戴磊 曹小红 《山东大学学报(理学版)》 CAS CSCD 北大核心 2021年第12期59-66,共8页
设H为无限维复可分的Hilbert空间,B(H)为H上的有界线性算子的全体,T∈B(H)称为满足(R)性质,若σ_(a)\σ_(ab)(T)=π∞(T),其中σ_(a)(T)和σ_(ab)(T)分别表示算子T的逼近点谱和Browder本质逼近点谱,π∞(T)={λ∈isoσ(T):0<dimN(T-... 设H为无限维复可分的Hilbert空间,B(H)为H上的有界线性算子的全体,T∈B(H)称为满足(R)性质,若σ_(a)\σ_(ab)(T)=π∞(T),其中σ_(a)(T)和σ_(ab)(T)分别表示算子T的逼近点谱和Browder本质逼近点谱,π∞(T)={λ∈isoσ(T):0<dimN(T-λΙ)<∞|.利用拓扑一致降标性质,首先给出了有界线性算子满足(R)性质的充要条件;之后通过拓扑一致降标性质,得到了算子函数满足(R)性质的判定方法;最后,上三角算子矩阵的(R)性质得到了研究。 展开更多
关键词 拓扑一致降标 (r)性质
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R-mode Instability of Neutron Star with Non-Newtonian Gravity 被引量:3
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作者 燕晶 文得华 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第1期47-52,共6页
The Chandrasekhar-Friedmann-Schutz (CFS) instabilities of r-modes for canonical neutron stars (1.4 Me) with rigid crusts are investigated by using an equation of state of asymmetric nuclear matter with super-soft ... The Chandrasekhar-Friedmann-Schutz (CFS) instabilities of r-modes for canonical neutron stars (1.4 Me) with rigid crusts are investigated by using an equation of state of asymmetric nuclear matter with super-soft symmetry energy, where the non-Newtonian gravity proposed in the grand unification theories is also considered. Constrained by the observations of the masses and the spin frequencies for neutron stars, the boundary of the r-mode instability window for a canonical neutron star is obtained, and the results show that the observed neutron stars are all outside the instability window, which is consistent with the theoretical expectation. In addition, an upper limit of the non-Newtonian gravity parameters is also given. 展开更多
关键词 neutron star r-mode non-Newtonian gravity
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