Einstein metrics in projective geometry

It is well known that pseudo–Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first Bernstein–Gelfand–Gelfand (BGG) equation. The general theory of such equations singles out a subclass of so-called normal solutions. We prove that non-degenerate normal solutions are equivalent to pseudo–Riemannian Einstein metrics in the projective class and observe that this connects to natural projective extensions of the Einstein condition.     

Preparation and utilization of perillyl acetate

Perillyl acetate is a fragrance compound that was prepared by the reaction of β-pinenoxide with acetic anhydride and using acetic acid as an acid catalyst. Several selected catalysts were tested (homogenous: phosphoric acid, boric acid, acetic acid, and citric acid; heterogeneous: zeolite USY, SSA, and montmorillonite K-10) and the reaction conditions optimized for this reaction. The yield 78.7 % of perillyl acetate was obtained. Mayol (4-isopropylcyclohexylmethanol), a valuable fragrance compound, was further obtained by a two-step synthesis from perillyl acetate. Firstly, perillyl acetate was saponified to perillyl alcohol. The yield of alcohol was 94.4 %. The last step of the entire preparation was the hydrogenation of perillyl alcohol to Mayol. The yield of the desired product of this reaction was 94.6 %.     

Enzymatic activity and catalytic hydrogen evolution in reduced and oxidized urease at mercury surfaces

It was originally shown [10] that urease retains its enzymatic activity when adsorbed at bare mercury and solid amalgam surfaces. However the opinion later prevailed that, when adsorbed at bare metal electrodes, proteins are irreversibly denatured. Here we confirm that urease is enzymatically active at a bare solid amalgam surface as found by Santhanam et al., and we show that this enzyme is equally active at a thiol-modified amalgam surface. We also show that it is the reduced form of urease, which is enzymatically active at Hg surfaces. Oxidation of the protein, resulting in formation of disulfide bonds, strongly decreases the enzyme activity. Using constant current chronopotentiometric stripping (CPS) we show that the exposure of surface-attached urease to negative potentials results in the protein unfolding. The extent of the unfolding depends upon the amount of time for which the protein is exposed to negative potentials, and at very short times this unfolding can be avoided. At thiol-modified Hg surfaces the protein is less vulnerable to the effects of the electric field. We conclude that the loss of enzymatic activity, resulting from a 10 min exposure of the protein to −0.58 V, is not due to reduction of the disulfide bonds as suggested by Santhanam et al. This loss is probably a result of protein reorientation, due to reduction of the Hg-S bonds (formed by accessible cysteines), followed by prolonged electric field effect on the surface-attached protein.