A Dynamical Zeta Function for Pseudo Riemannian Foliations

We investigate a generalization of geodesic random walks to pseudo Riemannian foliations. The main application we have in mind is to consider the logarithm of the associated zeta function as grand canonical partition function in a theory unifying aspects of general relativity, quantum mechanics and dynamical systems. Partially supported by DFG, SFB 478.     

Balaton Symposium 2009

JPC – Journal of Planar Chromatography – Modern TLC -     

Tandem olefin metathesis/hydrogenation at ambient temperature: activation of ruthenium carbene complexes by addition of hydrides

Sodium hydride activates ruthenium carbene complexes to catalyze hydrogenation reactions subsequent to ring closing olefin metathesis. Under these conditions, hydrogenation of cyclopentenols proceeds smoothly at ambient temperature and under 1 atm of hydrogen in toluene. An alternative protocol was developed that involves the formation of hydrogen in situ by reaction of excess sodium hydride with protic functional groups and water.     

Equilibrium, 1H and 13C NMR spectroscopy,and X-ray diffraction studies on the complexes Bi(DOTA)- and Bi(DO3A-Bu)

Several Bi(III) complexes are used in medicine as drugs. Bi(DO3A-Bu) has recently been proposed as a nonionic contrast agent in X-ray imaging (H(3)DO3A-Bu = 10-[2,3-dihydroxy-(1-hydroxymethyl)propyl]-1,4,7,10-tetraazacyclododecane-1,4,7,-triacetic acid). The solution equilibria and NMR structure and dynamics of Bi(DO3A-Bu) and of the similar Bi(DOTA)(-) have been investigated (H(4)DOTA = 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid). The stability constants were determined with the study of the competition equilibria between Br(-) ions and the ligands DOTA or DO3A-Bu for the Bi(III) by spectrophotometry. The stability constants, obtained for Bi(DOTA)(-) and Bi(DO3A-Bu), are very high, log K = 30.3 and 26.8, respectively. Potentiometric titrations indicated the dissociation of one of the protons among the three alcoholic OH groups in Bi(DO3A-Bu). The dissociation constant is log K = 7.53 (0.09) indicating that at physiological pH about 50% of the species possess -1 charge. It was shown by (1)H and (13)C NMR spectroscopy that the OH group attached to the middle carbon atom of the "butriol" side chain is coordinated to the Bi(III) and starts to deprotonate at pH > 5.5. The crystal structure of NaBi(DOTA).H(2)O shows an octacoordinated arrangement of the donor atoms around the Bi(III), with no water in the inner sphere. The crystals belong to the centrosymmetric space group C2/c. The temperature dependent (1)H and (13)C NMR spectra indicate that both Bi(DOTA)(-) and Bi(DO3A-Bu)(-) complexes are fluxional. For Bi(DOTA), the Delta(deltadeltadeltadelta) right harpoon over left harpoon Lambda(lambdalambdalambdalambda) fluxionality was identified, and on the basis of the activation parameters, a synchronous motion was suggested for the fluxional motion resulting in the change of ring conformation and of the helicity of the complex. The transition state is supposed to be more symmetrical than the initial state. The deprotonated Bi(DO3A-Bu) has a highly asymmetric NMR structure in solution, and its fluxional motion is slower than that of Bi(DOTA)(-).