In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed...In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.展开更多
Three s-triazine derivatives have been synthesized and their structures been de-termined. These are Compound I: 2,4-dimethyl-6-(p-N,N-dimethylaminostyryl)-s-triazine (abbre-viated to NMe-1), Compound II: 2,4-dimethyl-...Three s-triazine derivatives have been synthesized and their structures been de-termined. These are Compound I: 2,4-dimethyl-6-(p-N,N-dimethylaminostyryl)-s-triazine (abbre-viated to NMe-1), Compound II: 2,4-dimethyl-6-(p-N,N-diethylaminostyryl)-s-triazine (to NEt-1), and Compound III: 2-methyl-4,6-bis(p-N,N-dimethylaminostyryl)-s-triazine (NMe-2). NMe-1 and NEt-1 molecules belong to the D-π-A type with a one-dimensional charge-transfer character. NMe-1 crystallizes to centrosymmetric P1 space group, while NEt-1 to non-centrosymmetric polar Cc space group with all of the molecular charge-transfer axes taking the same orientation. Under the irradiation of 1064 nm fundamental laser, NEt-1 powder crystals radiate a 2-order harmonic light with an intensity 46.8 times that of urea. The Λ typed NMe-2 molecule, which has a two-dimensional charge-transfer character, crystallizes to polar P21 space group. Its powder crystals exhibit a 2-order harmonic intensity 46.2 times that of urea. The quantum chemical cal-culations and tensor analyses have been carried out to reveal the dependence of the macro 2-order nonlinear optical (NLO) efficiency on the micro 2-order NLO coefficients (β) and on the crystalline packing styles.展开更多
基金Research supported by National Science Foundation of China(No.10071081)special financial support of Chinese Academy of Sciences
文摘In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.
基金the National Natural Science Foundation of China(Grant Nos.20472044&20172034) the PhD.Programs Foundation of the Ministry of Education of China.
文摘Three s-triazine derivatives have been synthesized and their structures been de-termined. These are Compound I: 2,4-dimethyl-6-(p-N,N-dimethylaminostyryl)-s-triazine (abbre-viated to NMe-1), Compound II: 2,4-dimethyl-6-(p-N,N-diethylaminostyryl)-s-triazine (to NEt-1), and Compound III: 2-methyl-4,6-bis(p-N,N-dimethylaminostyryl)-s-triazine (NMe-2). NMe-1 and NEt-1 molecules belong to the D-π-A type with a one-dimensional charge-transfer character. NMe-1 crystallizes to centrosymmetric P1 space group, while NEt-1 to non-centrosymmetric polar Cc space group with all of the molecular charge-transfer axes taking the same orientation. Under the irradiation of 1064 nm fundamental laser, NEt-1 powder crystals radiate a 2-order harmonic light with an intensity 46.8 times that of urea. The Λ typed NMe-2 molecule, which has a two-dimensional charge-transfer character, crystallizes to polar P21 space group. Its powder crystals exhibit a 2-order harmonic intensity 46.2 times that of urea. The quantum chemical cal-culations and tensor analyses have been carried out to reveal the dependence of the macro 2-order nonlinear optical (NLO) efficiency on the micro 2-order NLO coefficients (β) and on the crystalline packing styles.
