Nickel(Ⅱ)complexes with pyrazole-based ligands are widely employed in catalysis of ethylene oligomerization and subsequent Friedel-Crafts alkylation of toluene.We have prepared ten new nickel(Ⅱ)dibromide complexes w...Nickel(Ⅱ)complexes with pyrazole-based ligands are widely employed in catalysis of ethylene oligomerization and subsequent Friedel-Crafts alkylation of toluene.We have prepared ten new nickel(Ⅱ)dibromide complexes with various substituted bis(azolyl)methanes.They have been characterized using^(1)H NMR,IR,high resolution mass spectrometry and elemental analysis.The structures of three complexes have been unambiguously established using X-ray diffraction.It was found that these complexes in the presence of Et2AlCl or Et_(3)Al_(2)Cl_(3)are active both in ethylene oligomerization and Friedel-Crafts alkylation processes(activity up to 3720 kgoligomer·mol[Ni]^(−1)·h^(−1)).The use of Et_(3)Al_(2)Cl_(3)results in a higher share of alkylated products(up to 60%).Moreover,catalytic systems activated with Et_(3)Al_(2)Cl_(3)produced small amounts of odd carbon number olefins(up to 0.8%).The Friedel-Crafts alkylation was used as a trap for previously undetected short-chain odd carbon number olefins(C_(3)and C_(5)).展开更多
We determine all square-free odd positive integers n such that the 2-Selmer groups Sn and (S)n of the elliptic curve En: y2 = x(x - n)(x - 2n) and its dual curve (E)n: y2 =x3 + 6nx2 + n2x have the smallest size: Sn = ...We determine all square-free odd positive integers n such that the 2-Selmer groups Sn and (S)n of the elliptic curve En: y2 = x(x - n)(x - 2n) and its dual curve (E)n: y2 =x3 + 6nx2 + n2x have the smallest size: Sn = {1}, (S)n = {1, 2, n, 2n}. It is well known that for such integer n, the rank of group En(Q) of the rational points on En is zero so that n is a non-congruent number. In this way we obtain many new series of elliptic curves En with rank zero and such series of integers n are non-congruent numbers.展开更多
基金This work was financially supported by the Russian Science Foundation-Russia(Project No.22-23-00578)NMR measurement was performed according to the Development Program of the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University"The future of the planet and global environmental change"'X-Ray analysis was supported by the RUDN University Strategic Academic Leadership Program.Elemental and GC analyses were performed with the financial support from the Ministry of Science and Higher Education of the Russian Federation using the equipment of the Centre for molecularcomposition studies of INEOS RAS.
文摘Nickel(Ⅱ)complexes with pyrazole-based ligands are widely employed in catalysis of ethylene oligomerization and subsequent Friedel-Crafts alkylation of toluene.We have prepared ten new nickel(Ⅱ)dibromide complexes with various substituted bis(azolyl)methanes.They have been characterized using^(1)H NMR,IR,high resolution mass spectrometry and elemental analysis.The structures of three complexes have been unambiguously established using X-ray diffraction.It was found that these complexes in the presence of Et2AlCl or Et_(3)Al_(2)Cl_(3)are active both in ethylene oligomerization and Friedel-Crafts alkylation processes(activity up to 3720 kgoligomer·mol[Ni]^(−1)·h^(−1)).The use of Et_(3)Al_(2)Cl_(3)results in a higher share of alkylated products(up to 60%).Moreover,catalytic systems activated with Et_(3)Al_(2)Cl_(3)produced small amounts of odd carbon number olefins(up to 0.8%).The Friedel-Crafts alkylation was used as a trap for previously undetected short-chain odd carbon number olefins(C_(3)and C_(5)).
基金This work was supported by the National Scientific Research Project 973 of China(Grant No.2004 CB 3180004)the National Natural Science Foundation of China(Grant No.60433050).
文摘We determine all square-free odd positive integers n such that the 2-Selmer groups Sn and (S)n of the elliptic curve En: y2 = x(x - n)(x - 2n) and its dual curve (E)n: y2 =x3 + 6nx2 + n2x have the smallest size: Sn = {1}, (S)n = {1, 2, n, 2n}. It is well known that for such integer n, the rank of group En(Q) of the rational points on En is zero so that n is a non-congruent number. In this way we obtain many new series of elliptic curves En with rank zero and such series of integers n are non-congruent numbers.
