Given two ideals I and J of a commutative ring R,there are two extreme connections between I and J:I+J=R and I∩J={0}.For the former case,graphs whose vertices are defined as the proper ideals of R and that two vertic...Given two ideals I and J of a commutative ring R,there are two extreme connections between I and J:I+J=R and I∩J={0}.For the former case,graphs whose vertices are defined as the proper ideals of R and that two vertices are adjacent if and only if their sum is the whole ring R are known as co-maximal ideal graphs.In this paper,we introduce a new kind of graph structure on R,called co-minimal ideal graph,according to the second case:Its vertices are the nonzero ideals of R and two vertices are adjacent if and only if their intersection is zero.Some important graph parameters(including girth,diameter,clique number and chromatic number)and graph structures(including tree and bipartite graph)of co-minimal ideal graphs over finite commutative rings are studied.In particular,we show that the co-maximal ideal graph and the co-minimal ideal graph over R are isomorphic if and only if the number of maximal ideals of R and the number of minimal ideals of R coincide.展开更多
This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along wit...This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.展开更多
Lead-tin(Pb-Sn)perovskites with an ideal bandgap of 1.34-1.40 eV show great promise in perovskite solar cells(PSCs).Recently,to address the environmental pollution and Sn^(2+)oxidation problems of dimethyl sulfoxide,m...Lead-tin(Pb-Sn)perovskites with an ideal bandgap of 1.34-1.40 eV show great promise in perovskite solar cells(PSCs).Recently,to address the environmental pollution and Sn^(2+)oxidation problems of dimethyl sulfoxide,methylammonium acetate(MAAc)ionic liquid has been developed as an alternative to fabricate ideal bandgap MAPb_(0.7)Sn_(0.3)I_(3)(1.36 eV)film via hot-casting in air.However,the spontaneous crystallization of Pb-Sn perovskite initiated by heat-induced supersaturation is fast and random,setting critical challenges in regulating crystal growth during the film-forming process.Herein,a lattice activation strategy is developed to control the crystallization dynamics of MAPb_(0.7)Sn_(0.3)I_(3)in MAAc to produce films with micrometer-sized grains in air.FA is shown to activate the crystal lattice that facilitates the formation of intermediates and balances the crystal growth of MAPb_(0.7)Sn_(0.3)I_(3),producing films with a grain size of 2.78±0.17μm.Furthermore,4-fluoro-phenethylammonium and phenethylammonium are adopted to passivate the defects in the film and promote the energy level alignment at the top interface,respectively.The optimized PSC device achieved an efficiency of 18.24%with a short-circuit current of 29.84 mA/cm^(2),which are both the highest values in 1.36 eV Pb-Sn PSCs to date.Notably,the unencapsulated devices show excellent storage and air stability under various conditions.展开更多
In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal...In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.展开更多
基金partially supported by the Open Research Fund of Key Laboratory of Nonlinear Analysis&Applications(Central China Normal University),Ministry of Education,P.R.Chinathe Guiding Science and Technology Plan Project of Suqian City in 2023(No.Z2023130)partially supported by NSFC(No.12271234)。
文摘Given two ideals I and J of a commutative ring R,there are two extreme connections between I and J:I+J=R and I∩J={0}.For the former case,graphs whose vertices are defined as the proper ideals of R and that two vertices are adjacent if and only if their sum is the whole ring R are known as co-maximal ideal graphs.In this paper,we introduce a new kind of graph structure on R,called co-minimal ideal graph,according to the second case:Its vertices are the nonzero ideals of R and two vertices are adjacent if and only if their intersection is zero.Some important graph parameters(including girth,diameter,clique number and chromatic number)and graph structures(including tree and bipartite graph)of co-minimal ideal graphs over finite commutative rings are studied.In particular,we show that the co-maximal ideal graph and the co-minimal ideal graph over R are isomorphic if and only if the number of maximal ideals of R and the number of minimal ideals of R coincide.
基金Sponsored by Foreign Expert Program of China(Grant No.DL2023041002L)Yulin City Industry University Research Project(Grant No.CXY-2022-59).
文摘This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.
基金financially supported by the Natural Science Foundation of China(52372226,52202300,62288102,62350013,52303325)National Key Research and Development Program of China(2023YFB3608900)+5 种基金the Postdoctoral Fellowship Program ofthe China postdoctoral Science Foundation(CPSF)(Grant GZC20233506)the China Postdoctoral Science Foundation(Grant2024M764252)the Natural Science Foundation of Chongqing China(2023NSCQ-MSX0097)Guangdong Basic and Applied Basic Research Foundation(2024A1515010918)Shenzhen Science and Technology Program(Grant JCYJ20240813150819026)the Fundamental Research Funds for the Central Universities。
文摘Lead-tin(Pb-Sn)perovskites with an ideal bandgap of 1.34-1.40 eV show great promise in perovskite solar cells(PSCs).Recently,to address the environmental pollution and Sn^(2+)oxidation problems of dimethyl sulfoxide,methylammonium acetate(MAAc)ionic liquid has been developed as an alternative to fabricate ideal bandgap MAPb_(0.7)Sn_(0.3)I_(3)(1.36 eV)film via hot-casting in air.However,the spontaneous crystallization of Pb-Sn perovskite initiated by heat-induced supersaturation is fast and random,setting critical challenges in regulating crystal growth during the film-forming process.Herein,a lattice activation strategy is developed to control the crystallization dynamics of MAPb_(0.7)Sn_(0.3)I_(3)in MAAc to produce films with micrometer-sized grains in air.FA is shown to activate the crystal lattice that facilitates the formation of intermediates and balances the crystal growth of MAPb_(0.7)Sn_(0.3)I_(3),producing films with a grain size of 2.78±0.17μm.Furthermore,4-fluoro-phenethylammonium and phenethylammonium are adopted to passivate the defects in the film and promote the energy level alignment at the top interface,respectively.The optimized PSC device achieved an efficiency of 18.24%with a short-circuit current of 29.84 mA/cm^(2),which are both the highest values in 1.36 eV Pb-Sn PSCs to date.Notably,the unencapsulated devices show excellent storage and air stability under various conditions.
文摘In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.
