In this paper,we show that for a connected compact Lie group to be acceptable,it is necessary and sufficient that its derived subgroup is isomorphic to a direct product of the groups SU(n),Sp(n),SO(2n+1),G2,SO(4).We s...In this paper,we show that for a connected compact Lie group to be acceptable,it is necessary and sufficient that its derived subgroup is isomorphic to a direct product of the groups SU(n),Sp(n),SO(2n+1),G2,SO(4).We show that there are invariant functions on SO4(ℂ)2 which are not generated by 1-argument invariants,though the group SO4(ℂ)is acceptable.展开更多
The ABAB-type 1,4,15,18-tetrapentyloxy-8,11,22,25-tetrachlorophthalocyaninato magnesium compound Mg(trans-TPTCPc)(1)was successfully isolated from the mixed cyclic tetramerization of 4,7-bis(pentyloxy)-1,3-diiminoisoi...The ABAB-type 1,4,15,18-tetrapentyloxy-8,11,22,25-tetrachlorophthalocyaninato magnesium compound Mg(trans-TPTCPc)(1)was successfully isolated from the mixed cyclic tetramerization of 4,7-bis(pentyloxy)-1,3-diiminoisoindoline as precursor A,actually the 1,3-diiminoisoindoline form of 3,6-bis(pentyloxy)-1,2-benzenedinitrile,and 4,5-dichlorophthalonitrile as precursor B in refluxing pentanol in the presence of magnesium pentoxide in a relatively good yield of 6.2%.Its molecular structure was clearly revealed on the basis of single crystal X-ray diffraction analysis,representing the first structurally characterized ABAB-type phthalocyanine compound,simultaneously bearing electron-donating pentyloxy groups and electron-accepting chloro substituents.Nevertheless,with 1 as the starting material,the corresponding sandwich-type bis(phthalocyaninato)lutetium double-decker complex Lu^(Ⅲ)(trans-TPTCPc)_(2)(2)was also prepared and structurally characterized,showing a high hyperpolarizability of 1240×10^(-30) esu as determined by harmonic light scattering(HLS),indicating the great potential of these kinds of phthalocyanine compounds in the field of second-order NLO materials.展开更多
基金research is partially supported by the NSFC Grant 11971036.
文摘In this paper,we show that for a connected compact Lie group to be acceptable,it is necessary and sufficient that its derived subgroup is isomorphic to a direct product of the groups SU(n),Sp(n),SO(2n+1),G2,SO(4).We show that there are invariant functions on SO4(ℂ)2 which are not generated by 1-argument invariants,though the group SO4(ℂ)is acceptable.
基金the National Key Basic Research Program of China(Grant No.2013CB933402)the National Natural Science Foundation of China(Grant No.21290174,21301017,and 21401009)the Beijing Municipal Commission of Education is gratefully acknowledged.
文摘The ABAB-type 1,4,15,18-tetrapentyloxy-8,11,22,25-tetrachlorophthalocyaninato magnesium compound Mg(trans-TPTCPc)(1)was successfully isolated from the mixed cyclic tetramerization of 4,7-bis(pentyloxy)-1,3-diiminoisoindoline as precursor A,actually the 1,3-diiminoisoindoline form of 3,6-bis(pentyloxy)-1,2-benzenedinitrile,and 4,5-dichlorophthalonitrile as precursor B in refluxing pentanol in the presence of magnesium pentoxide in a relatively good yield of 6.2%.Its molecular structure was clearly revealed on the basis of single crystal X-ray diffraction analysis,representing the first structurally characterized ABAB-type phthalocyanine compound,simultaneously bearing electron-donating pentyloxy groups and electron-accepting chloro substituents.Nevertheless,with 1 as the starting material,the corresponding sandwich-type bis(phthalocyaninato)lutetium double-decker complex Lu^(Ⅲ)(trans-TPTCPc)_(2)(2)was also prepared and structurally characterized,showing a high hyperpolarizability of 1240×10^(-30) esu as determined by harmonic light scattering(HLS),indicating the great potential of these kinds of phthalocyanine compounds in the field of second-order NLO materials.
