We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore the...We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire geometric object and the noncommutative differential calculus on regular lattice. In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations, the Euler-Lagrange cohomological concepts and content in the configuration space are employed.展开更多
A new heterometallic cluster W2Ag2S4(tdt)2(PPh3)2·CH2Cl2(H2tdt=H2CH3C6H3S2)(Ⅱ) has been prepared from the reaction of a well-defined molecular building block W2S4(tdt)22-(I) with Ag complex. The compound has bee...A new heterometallic cluster W2Ag2S4(tdt)2(PPh3)2·CH2Cl2(H2tdt=H2CH3C6H3S2)(Ⅱ) has been prepared from the reaction of a well-defined molecular building block W2S4(tdt)22-(I) with Ag complex. The compound has been characterized by X-ray diffraction study, IR., UV-Vis Spectroscopy and cyclic voltammetry.Crystallographic data for the compound are: space group P21/n,a=17.234(4), b=17.622(4), c=19. 094(4) A,β= 99. 22(2)°,V=5704(2) A3, Z=4,final R=0. 042 and Rw=0. 049 for 5983 independent reflections with I≥3σ(I) The structure analysis reveals that the cluster contains a cubane-like core [W2Ag2S4]4+ . The coordination geometry of each tungsten atom is a square pyramid just as that in the building block. Two types of metal-metal bonds of W-W bond and W-Ag bond exist in the core. The distance between two Ag atoms is out of the range of bonding.展开更多
文摘We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire geometric object and the noncommutative differential calculus on regular lattice. In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations, the Euler-Lagrange cohomological concepts and content in the configuration space are employed.
文摘A new heterometallic cluster W2Ag2S4(tdt)2(PPh3)2·CH2Cl2(H2tdt=H2CH3C6H3S2)(Ⅱ) has been prepared from the reaction of a well-defined molecular building block W2S4(tdt)22-(I) with Ag complex. The compound has been characterized by X-ray diffraction study, IR., UV-Vis Spectroscopy and cyclic voltammetry.Crystallographic data for the compound are: space group P21/n,a=17.234(4), b=17.622(4), c=19. 094(4) A,β= 99. 22(2)°,V=5704(2) A3, Z=4,final R=0. 042 and Rw=0. 049 for 5983 independent reflections with I≥3σ(I) The structure analysis reveals that the cluster contains a cubane-like core [W2Ag2S4]4+ . The coordination geometry of each tungsten atom is a square pyramid just as that in the building block. Two types of metal-metal bonds of W-W bond and W-Ag bond exist in the core. The distance between two Ag atoms is out of the range of bonding.
