By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,th...By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,the relationship between hypercyclic property(or supercyclic property)and property(ω)is discussed.展开更多
In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators w...In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results展开更多
This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman pro...This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman property） under which an into-isometric mapping from the unit sphere of e（Γ） to the unit sphere of a normed space E can be linearly isometric extended.展开更多
The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of...The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of A which can not be presented as iterated Ore extensions.展开更多
Fuzzy Petri net(FPN) has been extensively applied in industrial fields for knowledge-based systems or systems with uncertainty.Although the applications of FPN are known to be successful,the theoretical research of FP...Fuzzy Petri net(FPN) has been extensively applied in industrial fields for knowledge-based systems or systems with uncertainty.Although the applications of FPN are known to be successful,the theoretical research of FPN is still at an initial stage.To pave a way for further study,this work explores related dynamic properties of FPN including reachability,boundedness,safeness,liveness and fairness.The whole methodology is divided into two phases.In the first phase,a comparison between elementary net system(EN_system) and FPN is established to prove that the FPN is an extensive formalism of Petri nets using a backwards-compatible extension method.Next,current research results of dynamic properties are utilized to analyze FPN model.The results illustrate that FPN model is bounded,safe,weak live and fair,and can support theoretical evidences for designing related decomposition algorithm.展开更多
Fibre bundle tensile curves can be used to characterise fibre processing properties and end-use performance directly and to predict single-fibre properties in theory. In this paper, the tensile behaviour of polyester ...Fibre bundle tensile curves can be used to characterise fibre processing properties and end-use performance directly and to predict single-fibre properties in theory. In this paper, the tensile behaviour of polyester fibre-bundles has been analysed in characteristic values and diagramming. The characteristic distributions which include the symmetry distribution on right part, SRBS′ (e), on left part, SLBS′(e) and the curve on base-line modification, MBS′ (e),based on the modulus distribution, BS′ (e), as well as the frequency density function of broken fibres, B′ (e), have been derived from the tail of bundle tensile curves. The theoretical and measured results show that the most important curves are MBS′ ( e ) and B′ ( e ) and can be used to estimate the breaking-extension distribution of single fibres. Especially for MBS′(e), the modulus distribution can accurately characterize single-fibre tensile properties and is no limitation as the calculation of B′(e) because the bundle specific stress Y(e) of no fibre breaking at extension e should be found at first.展开更多
An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(...An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.111501419)the Doctoral Fund of Shaanxi province of China(Grant No.2017BSHEDZZ108)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2021JM-519)。
文摘By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,the relationship between hypercyclic property(or supercyclic property)and property(ω)is discussed.
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11171066）, the Natural Science Foundation of Fujian Province （Grant No. 2011J05002）, and the Specialized Research Fund for the Doctoral Program of Higher Education （Grant Nos. 2010350311001 and 20113503120003）.
文摘In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results
基金supported by the National Natural Science Foundation of China(10871101)the Research Fund for the Doctoral Program of Higher Education (20060055010)
文摘This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman property） under which an into-isometric mapping from the unit sphere of e（Γ） to the unit sphere of a normed space E can be linearly isometric extended.
文摘The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of A which can not be presented as iterated Ore extensions.
基金Project(R.J13000.7828.4F721)supported by Soft Computing Research Group(SCRP),Research Management Centre(RMC),UTM and Ministry of Higher Education Malaysia(MOHE)for Financial Support Through the Fundamental Research Grant Scheme(FRGS),MalaysiaProject(61462029)supported by the National Natural Science Foundation of China
文摘Fuzzy Petri net(FPN) has been extensively applied in industrial fields for knowledge-based systems or systems with uncertainty.Although the applications of FPN are known to be successful,the theoretical research of FPN is still at an initial stage.To pave a way for further study,this work explores related dynamic properties of FPN including reachability,boundedness,safeness,liveness and fairness.The whole methodology is divided into two phases.In the first phase,a comparison between elementary net system(EN_system) and FPN is established to prove that the FPN is an extensive formalism of Petri nets using a backwards-compatible extension method.Next,current research results of dynamic properties are utilized to analyze FPN model.The results illustrate that FPN model is bounded,safe,weak live and fair,and can support theoretical evidences for designing related decomposition algorithm.
文摘Fibre bundle tensile curves can be used to characterise fibre processing properties and end-use performance directly and to predict single-fibre properties in theory. In this paper, the tensile behaviour of polyester fibre-bundles has been analysed in characteristic values and diagramming. The characteristic distributions which include the symmetry distribution on right part, SRBS′ (e), on left part, SLBS′(e) and the curve on base-line modification, MBS′ (e),based on the modulus distribution, BS′ (e), as well as the frequency density function of broken fibres, B′ (e), have been derived from the tail of bundle tensile curves. The theoretical and measured results show that the most important curves are MBS′ ( e ) and B′ ( e ) and can be used to estimate the breaking-extension distribution of single fibres. Especially for MBS′(e), the modulus distribution can accurately characterize single-fibre tensile properties and is no limitation as the calculation of B′(e) because the bundle specific stress Y(e) of no fibre breaking at extension e should be found at first.
基金Supported by the Natural Science Foundation of the Department of Education of Henan Province（12B110025, 102300410012）
文摘An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.
