A note on approximate controllability for semilinear one-dimensional heat equation

The one-dimensional semilinear heat equation is considered. It is shown that if the nonlinear functionF(y) is uniformly bounded then the system is approximately controllable for every given terminal timeT>0 under some ordinary condition onb. The results may be extended to the general one-dimensional semilinear heat equation with one-dimensional control or to a boundary control heat system with semilinear boundary condition.     

Linear dichroism and fluorescence polarization of diphenyl polyenes in stretched polyethylene films

A study of the linear diehroism and fluorescence polarization of diphenylpolyenes (C₆H₅—(CH=CH)_n—C₆H₅) with n = 1,2,3,4,6,8 in stretched polyethylene films shows that the polyenes orient in the anisotropic matrix with their transition dipole (emission and absorption, π → π^*) aligned with the direction of stretch. The maximum dichroic ratio is observed for 1,6-diphenyl-1,3,5-hexatriene (DPH), with n = 3, whereas the values are substantially lower for n < 3 or n > 3. The high orientation of DPH and poor alignment of the higher polyenes may be accounted for in terms of the growing flexibility of the polyene chains with increasing chain length. The results justify the use of DPH as a convenient fluorescence probe for biological and synthetic membranes.     

Constraint Variational Calculations on Excited States

The difficulties of the SCF and MCSCF calculations on excited states have been reviewed. Three constraint variational methods are then developed which can perform the SCF and MCSCF calculations on excited states in the scheme of the generalized Brillouin theorem method. The proper constraints and the ways to incorporate the constraints into the variational calculations on excited states have been studied and the comparison with other approaches have been accessed.     

Conjugated enynes as a new type of substrates for olefin metathesis

[reaction: see text] It has been demonstrated for the first time that conjugated enynes can be employed as a facile substrate in olefin metathesis with the use of a bispyridine-substituted ruthenium benzylidene catalyst. Cross-metathesis of the enynes with alkenes turns out to proceed with preferential formation of (Z)-isomers over (E)-isomers up to >25:1 in moderate to good yields. The intramolecular version of conjugated enynes affords novel butadienyl cycloalkenes, which are a highly useful synthetic building blocks, in acceptable yields.     

On [Fe4S4]2+ -(mu2-SR)-M II bridge formation in the synthesis of an A-cluster analogue of carbon monoxide dehydrogenase/acetylcoenzyme A synthase

The construction of a synthetic analogue of the A-cluster of carbon monoxide dehydrogenase/acetylcoenzyme synthase, the site of acetylcoenzyme A formation, requires as a final step the formation of an unsupported [Fe(4)S(4)]-(mu(2)-SR)-Ni(II) bridge to a preformed cluster. Our previous results (Rao, P. V.; Bhaduri, S.; Jiang, J.; Holm, R. H. Inorg. Chem. 2004, 43, 5833) and the work of others have addressed synthesis of dinuclear complexes relevant to the A-cluster. This investigation concentrates on reactions pertinent to bridge formation by examining systems containing dinuclear and mononuclear Ni(II) complexes and the 3:1 site-differentiated clusters [Fe(4)S(4)(LS(3))L'](2-) (L' = TfO(-) (14), SEt (15)). The system 14/[{Ni(L(O)-S(2)N(2))}M(SCH(2)CH(2)PPh(2))](+) results in cleavage of the dinuclear complex and formation of [{Ni(L(O)-S(2)N(2))}Fe(4)S(4)(LS(3))]- (18), in which the Ni(II) complex binds at the unique cluster site with formation of a Ni(mu(2)-SR)(2)Fe bridge rhomb. Cluster 18 and the related species [{Ni(phma)}Fe(4)S(4)(LS(3))](3)- (19) are obtainable by direct reaction of the corresponding cis-planar Ni(II)-S(2)N(2) complexes with 14. The mononuclear complexes [M(pdmt)(SEt)]- (M = Ni(II), Pd(II)) with 14 in acetonitrile or Me(2)SO solution react by thiolate transfer to give 15 and [M(2)(pdmt)(2)]. However, in dichloromethane the Ni(II) reaction product is interpreted as [{Ni(pdmt)(mu(2)-SEt)}Fe(4)S(4)(LS(3))](2-) (20). Reaction of Et(3)NH(+) and 15 affords the double cubane [{Fe(4)S(4)(LS(3))}(2)(mu(2)-SEt)](3-) (21). Cluster 18 contains two mutually supportive Fe-(mu(2)-SR)-Ni(II) bridges, 19 exhibits one strong and one weaker bridge, 20 has one unsupported bridge (inferred from the (1)H NMR spectrum), and 21 has one unsupported Fe-(mu(2)-SR)-Fe bridge. Bridges in 18, 19, and 21 were established by X-ray structures. This work demonstrates that a bridge of the type found in the enzyme A-clusters is achievable by synthesis and implies that more stable, unsupported single thiolate bridges may require reinforcement by an additional covalent linkage between the Fe(4)S(4) and nickel-containing components. (LS(3) = 1,3,5-tris((4,6-dimethyl-3-mercaptophenyl)thio)-2,4,6-tris(p-tolylthio)benzene(3-); L(O)-S(2)N(2) = N,N'-diethyl-3,7-diazanonane-1,9-dithiolate(2-); pdmt = pyridine-2,6-methanedithiolate(2-); phma = N,N'-1,2-phenylenebis(2-acetylthio)acetamidate(4-); TfO = triflate.).