This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. ...This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.展开更多
A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copre...A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copres∞（U）. A module U is a co-＊∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞（U） and I is a set, N∈Copres∞（U） is equivalent to Ext1R（N,U）→Ext1R（UI,U） is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞（U）, N∈Copres∞（U） is equivalent to the induced sequence 0→Δ（N）→Δ（M）→Δ（L）→0 which is exact if and only if U induces a duality ΔUS：⊥USCopres∞（U）：ΔRU. Moreover, U is a co-＊n-module if and only if U is a co-＊∞-module and Copres∞（U）=Copresn（U）.展开更多
In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen...In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.展开更多
激光粉末床熔融(Laser Powder Bed Fusion,LPBF)技术是定制化多孔纯Mo结构的重要技术。然而,LPBF成形纯Mo试样仍面临表面粗糙度值高及耐蚀性差等问题。电化学抛光(Electrochemical Polishing,ECP)是LPBF成形纯Mo的主要环保型后处理工艺...激光粉末床熔融(Laser Powder Bed Fusion,LPBF)技术是定制化多孔纯Mo结构的重要技术。然而,LPBF成形纯Mo试样仍面临表面粗糙度值高及耐蚀性差等问题。电化学抛光(Electrochemical Polishing,ECP)是LPBF成形纯Mo的主要环保型后处理工艺。研究了不同ECP抛光状态对LPBF成形纯Mo的表面粗糙度及降解特性的影响。结果表明:经电化学抛光处理后,试样表面粗糙度由4.55μm显著降低至1.05μm;相比原始态试样,抛光后试样腐蚀电流密度降低了78.4%。失重率从大到小顺序为:原始态>半抛光>抛光,且随着浸泡时间增加,失重率逐渐增加。溶液pH值波动≤0.5,验证了降解过程未引发局部酸化,符合生物医用材料要求。通过采用ECP处理Mo基材料表面,为合理调控其植入体的降解行为及降解速率的均匀性提供了重要理论依据。展开更多
In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some pr...In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules（in Chinese）. Acta Math. Sinica, 2011, 54（1）: 1–8.).展开更多
In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that thes...In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.展开更多
Compared with Zn^(2+),the current mainly reported charge carrier for zinc hybrid capacitors,small-hydrated-sized and light-weight NH_(4)^(+)is expected as a better one to mediate cathodic interfacial electrochemical b...Compared with Zn^(2+),the current mainly reported charge carrier for zinc hybrid capacitors,small-hydrated-sized and light-weight NH_(4)^(+)is expected as a better one to mediate cathodic interfacial electrochemical behaviors,yet has not been unraveled.Here we propose an NH_(4)^(+)-modulated cationic solvation strategy to optimize cathodic spatial charge distribution and achieve dynamic Zn^(2+)/NH_(4)^(+)co-storage for boosting Zinc hybrid capacitors.Owing to the hierarchical cationic solvated structure in hybrid Zn(CF_(3)SO_(3))_(2)–NH_4CF_(3)SO_(3)electrolyte,high-reactive Zn^(2+)and small-hydrate-sized NH_4(H_(2)O))(4)^(+)induce cathodic interfacial Helmholtz plane reconfiguration,thus effectively enhancing the spatial charge density to activate 20%capacity enhancement.Furthermore,cathodic interfacial adsorbed hydrated NH_(4)^(+)ions afford high-kinetics and ultrastable C···H(NH_(4)^(+))charge storage process due to a much lower desolvation energy barrier compared with heavy and rigid Zn(H_(2)O)_6^(2+)(5.81 vs.14.90 eV).Consequently,physical uptake and multielectron redox of Zn^(2+)/NH_(4)^(+)in carbon cathode enable the zinc capacitor to deliver high capacity(240 mAh g^(-1)at 0.5 A g^(-1)),large-current tolerance(130 mAh g^(-1)at 50 A g^(-1))and ultralong lifespan(400,000cycles).This study gives new insights into the design of cathode–electrolyte interfaces toward advanced zinc-based energy storage.展开更多
In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the con...In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.展开更多
文摘This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.
基金The National Natural Science Foundation of China (No.10971024)Specialized Research Fund for the Doctoral Program of Higher Education (No.200802860024)
文摘A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copres∞（U）. A module U is a co-＊∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞（U） and I is a set, N∈Copres∞（U） is equivalent to Ext1R（N,U）→Ext1R（UI,U） is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞（U）, N∈Copres∞（U） is equivalent to the induced sequence 0→Δ（N）→Δ（M）→Δ（L）→0 which is exact if and only if U induces a duality ΔUS：⊥USCopres∞（U）：ΔRU. Moreover, U is a co-＊n-module if and only if U is a co-＊∞-module and Copres∞（U）=Copresn（U）.
文摘In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.
文摘激光粉末床熔融(Laser Powder Bed Fusion,LPBF)技术是定制化多孔纯Mo结构的重要技术。然而,LPBF成形纯Mo试样仍面临表面粗糙度值高及耐蚀性差等问题。电化学抛光(Electrochemical Polishing,ECP)是LPBF成形纯Mo的主要环保型后处理工艺。研究了不同ECP抛光状态对LPBF成形纯Mo的表面粗糙度及降解特性的影响。结果表明:经电化学抛光处理后,试样表面粗糙度由4.55μm显著降低至1.05μm;相比原始态试样,抛光后试样腐蚀电流密度降低了78.4%。失重率从大到小顺序为:原始态>半抛光>抛光,且随着浸泡时间增加,失重率逐渐增加。溶液pH值波动≤0.5,验证了降解过程未引发局部酸化,符合生物医用材料要求。通过采用ECP处理Mo基材料表面,为合理调控其植入体的降解行为及降解速率的均匀性提供了重要理论依据。
基金The NSF(11271148,11561057)of Chinathe NSF(20151BAB201007)of Jiangxi Provincethe Science and Technology Project(GJJ151061)of Jiangxi Education Department
文摘In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules（in Chinese）. Acta Math. Sinica, 2011, 54（1）: 1–8.).
文摘In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.
基金financially supported by the National Natural Science Foundation of China(Nos.22272118,22172111 and 22309134)the Science and Technology Commission of Shanghai Municipality,China(Nos.22ZR1464100,20ZR1460300 and 19DZ2271500)+3 种基金China Postdoctoral Science Foundation(2022M712402)Shanghai Rising-Star Program(23YF1449200)Zhejiang Provincial Science and Technology Project(2022C01182)the Fundamental Research Funds for the Central Universities(22120210529 and 2023-3-YB-07)。
文摘Compared with Zn^(2+),the current mainly reported charge carrier for zinc hybrid capacitors,small-hydrated-sized and light-weight NH_(4)^(+)is expected as a better one to mediate cathodic interfacial electrochemical behaviors,yet has not been unraveled.Here we propose an NH_(4)^(+)-modulated cationic solvation strategy to optimize cathodic spatial charge distribution and achieve dynamic Zn^(2+)/NH_(4)^(+)co-storage for boosting Zinc hybrid capacitors.Owing to the hierarchical cationic solvated structure in hybrid Zn(CF_(3)SO_(3))_(2)–NH_4CF_(3)SO_(3)electrolyte,high-reactive Zn^(2+)and small-hydrate-sized NH_4(H_(2)O))(4)^(+)induce cathodic interfacial Helmholtz plane reconfiguration,thus effectively enhancing the spatial charge density to activate 20%capacity enhancement.Furthermore,cathodic interfacial adsorbed hydrated NH_(4)^(+)ions afford high-kinetics and ultrastable C···H(NH_(4)^(+))charge storage process due to a much lower desolvation energy barrier compared with heavy and rigid Zn(H_(2)O)_6^(2+)(5.81 vs.14.90 eV).Consequently,physical uptake and multielectron redox of Zn^(2+)/NH_(4)^(+)in carbon cathode enable the zinc capacitor to deliver high capacity(240 mAh g^(-1)at 0.5 A g^(-1)),large-current tolerance(130 mAh g^(-1)at 50 A g^(-1))and ultralong lifespan(400,000cycles).This study gives new insights into the design of cathode–electrolyte interfaces toward advanced zinc-based energy storage.
基金Supported by the National Natural Science Foundation of China (61175055)the Innovation Term of Higher Education of Hubei Province,China (T201109)+1 种基金the Natural Science Foundation of Hubei Province (2012FFB01101)the Natural Science Foundation of Education Committee of Hubei Province (D20131903)
文摘In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.
