四阶p-Laplacian方程多时滞问题周期解的存在性

通过使用Mawhin连续性定理,研究四阶p-Laplacian微分方程多时滞问题(φ_p(x″(t)))″+f(t,x″(t))+(?)β_i(t)g(x(t-γ_i(t)))=p(t)周期解的存在性,并得到了存在周期解的充分性条件     

Synthesis and Crystal Structure of a Novel Tetranuclear Complex [Pb4（HQ）6（NO3）2]

Reaction of 8-hydroxyquinoline （HQ） with Pb（NO3）2 in water resulted in the formation of a tetranuclear complex [Pb4（HQ）6（NO3）2] 1. It has been characterized by IR, elemental analyses and X-ray diffraction. Crystal data for this complex： triclinic system, space group P1, a = 9.7399（6）, b = 11.6535（8）, c = 12.6806（8） A, α = 62.8050（10）, β = 78.4910（10）, γ = 80.5490（10）°, C54H36N8O12Pb4, Mr= 1817.67, Z = 1, V = 1250.04（14）A^3, Dc = 2.415 g/cm^3,μ = 13.503 mm^-1, -12≤h≤8, -14≤k≤13, -15≤1≤15, F（000） = 840, Rint = 0.0217, R= 0.0348 and wR = 0.0927. X-ray crystal structure analysis revealed that in 1 each Pb（ II ） contains a stereo- chemically active lone pair of electrons. The Pb…C interaction, C-H……O weak interaction and π…π stacking interactions are observed in the complex. In the solid state, the complex possesses strong photoluminescent emission at 485 and 528 nm.