研究了单个线性关系是可闭线性关系的充分必要条件;并对L0=(A B C D),其中A,B,C,D是相应Hilbert空间上的线性关系,利用C相对A的有界性与B相对D的有界性及A,D的可闭性,推出了L_(0)也是可闭线性关系;同时,对于有界线性算子S=(S_(1) S_(2) ...研究了单个线性关系是可闭线性关系的充分必要条件;并对L0=(A B C D),其中A,B,C,D是相应Hilbert空间上的线性关系,利用C相对A的有界性与B相对D的有界性及A,D的可闭性,推出了L_(0)也是可闭线性关系;同时,对于有界线性算子S=(S_(1) S_(2) S_(3) S_(4)),得到当满足一定条件时L_(0)-μS的Frobenius-Schur分解公式,并得到了当L_(0)可闭时L_(0)的表达式,最后研究了L_(0)的S-本质谱。展开更多
The dominant oxidation state for lanthanide ions is+3 due to the loss of 5d and 6s electrons from their shared configuration of[Xe]4f^(0-14)5d^(0-16)s(2).There are however several exceptions because of the completely ...The dominant oxidation state for lanthanide ions is+3 due to the loss of 5d and 6s electrons from their shared configuration of[Xe]4f^(0-14)5d^(0-16)s(2).There are however several exceptions because of the completely empty(Ce(Ⅳ)),half-filled(Eu(Ⅱ)),or fully filled(Yb(Ⅱ))4f subshell.As such,stable complexes are formed primarily with Ln(Ⅲ)ions[1].展开更多
文摘研究了单个线性关系是可闭线性关系的充分必要条件;并对L0=(A B C D),其中A,B,C,D是相应Hilbert空间上的线性关系,利用C相对A的有界性与B相对D的有界性及A,D的可闭性,推出了L_(0)也是可闭线性关系;同时,对于有界线性算子S=(S_(1) S_(2) S_(3) S_(4)),得到当满足一定条件时L_(0)-μS的Frobenius-Schur分解公式,并得到了当L_(0)可闭时L_(0)的表达式,最后研究了L_(0)的S-本质谱。
基金supported by the National Natural Science Foundation of China(22101116,92261203,21971106)Shenzhen Fundamental Research Program(JCYJ20220530115001002 and JCYJ20220818100417037).
文摘The dominant oxidation state for lanthanide ions is+3 due to the loss of 5d and 6s electrons from their shared configuration of[Xe]4f^(0-14)5d^(0-16)s(2).There are however several exceptions because of the completely empty(Ce(Ⅳ)),half-filled(Eu(Ⅱ)),or fully filled(Yb(Ⅱ))4f subshell.As such,stable complexes are formed primarily with Ln(Ⅲ)ions[1].
