In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear...In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear transformation algebras L(X),we show that every anti-left multiplier on these algebras is zero.Furthermore,let A be a zero product determined algebra andδbe a linear mapping from A into itself,satisfying that for any a,b in A,ab=0 impliesδ(b)a+bδ(a)=0.We show thatδ(x)=D(x)+δ(1)x,where D is an anti-derivation andδ(1)∈Z(A).展开更多
Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reve...Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.展开更多
Some relationships between the representation of Hom-Jacobi-Jordan algebra and that of Jacobi-Jordan algebra are studied.Moreover,by using the notion ofαk-anti-derivation,a property theorem of multiplicative Hom-Jaco...Some relationships between the representation of Hom-Jacobi-Jordan algebra and that of Jacobi-Jordan algebra are studied.Moreover,by using the notion ofαk-anti-derivation,a property theorem of multiplicative Hom-Jacobi-Jordan algebras is also given.展开更多
基金Supported by the General Program of Shanghai Natural Science Foundation(Grant No.24ZR1415600)the National Natural Science Foundation of China(Grant Nos.1232637412401157)。
文摘In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear transformation algebras L(X),we show that every anti-left multiplier on these algebras is zero.Furthermore,let A be a zero product determined algebra andδbe a linear mapping from A into itself,satisfying that for any a,b in A,ab=0 impliesδ(b)a+bδ(a)=0.We show thatδ(x)=D(x)+δ(1)x,where D is an anti-derivation andδ(1)∈Z(A).
文摘Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.
基金National Natural Science Foundation of China(12071405,11571145)。
文摘Some relationships between the representation of Hom-Jacobi-Jordan algebra and that of Jacobi-Jordan algebra are studied.Moreover,by using the notion ofαk-anti-derivation,a property theorem of multiplicative Hom-Jacobi-Jordan algebras is also given.
