The crystal structure of 1-(1-t-butyl-5-methyl-4-pyrazolylcarbonyl)-3,5-dimeth- yl-1H-yl-pyrazole ([C14H20N4O]2, Mr = 520.68) has been determined by single-crystal X-ray diffraction analysis. The crystal belongs to tr...The crystal structure of 1-(1-t-butyl-5-methyl-4-pyrazolylcarbonyl)-3,5-dimeth- yl-1H-yl-pyrazole ([C14H20N4O]2, Mr = 520.68) has been determined by single-crystal X-ray diffraction analysis. The crystal belongs to triclinic, space group P with a = 11.049(4), b = 11.313(4), c = 13.964(5) , ?= 69.085(6), b = 75.962(6), = 62.245(6), V = 1436.7(9) 3, Z = 2, Dc = 1.204 g/cm3, m = 0.079 mm-1, F(000) = 560, R = 0.0790 and wR = 0.1416 for 4729 unique reflections with 2635 observed ones (I > 2(I)). The results indicate that the pyrazole rings display aromaticity. The four pyrazole moieties are approximately coplanar in each case. The dihedral angles between planes 1 and 2, 3 and 4 are 40.99 and 10.77? respectively.展开更多
Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible c...Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.展开更多
基金the Natural Science Foundation of Shandong Province (No. Y2003B01) and NNSFC (No. 20172031)
文摘The crystal structure of 1-(1-t-butyl-5-methyl-4-pyrazolylcarbonyl)-3,5-dimeth- yl-1H-yl-pyrazole ([C14H20N4O]2, Mr = 520.68) has been determined by single-crystal X-ray diffraction analysis. The crystal belongs to triclinic, space group P with a = 11.049(4), b = 11.313(4), c = 13.964(5) , ?= 69.085(6), b = 75.962(6), = 62.245(6), V = 1436.7(9) 3, Z = 2, Dc = 1.204 g/cm3, m = 0.079 mm-1, F(000) = 560, R = 0.0790 and wR = 0.1416 for 4729 unique reflections with 2635 observed ones (I > 2(I)). The results indicate that the pyrazole rings display aromaticity. The four pyrazole moieties are approximately coplanar in each case. The dihedral angles between planes 1 and 2, 3 and 4 are 40.99 and 10.77? respectively.
基金the National Natural Science Foundation of China (Grant No. 10671009)
文摘Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.
