Self-intersections of curves on surfaces

Let M be a compact orientable surface with nonempty boundary (x(M)<0) and fundamental group . Let be a geodesic on M (with a fixed hyperbolic structure), and let W be a (cyclically reduced) word in a fixed set of generators of which represents . In this paper, we give an algorithm to count the number of self-intersections of in terms of W, generalizing a result of Birman and Series, where an algorithm was given to decide if was simple. Some applications of the algorithm to surfaces with one boundary and the Markoff spectrum are also given.     

The application of C-N.M.R. spectroscopy to the determination of the stereochemistry of Diels-Alder adducts

Long-range (³J) ¹³C-H coupling is a reliable probe to evaluate the stereochemistry of cycloaddition products. The method is best applied to carbonyl containing adducts but not restricted to them. Several structures have been revised and new ones evaluated.     

Reduction and methyl transfer kinetics of the alpha subunit from acetyl coenzyme a synthase

Stopped-flow was used to evaluate the methylation and reduction kinetics of the isolated alpha subunit of acetyl-Coenzyme A synthase from Moorella thermoacetica. This catalytically active subunit contains a novel Ni-X-Fe4S4 cluster and a putative unidentified n = 2 redox site called D. The D-site must be reduced for a methyl group to transfer from a corrinoid-iron-sulfur protein, a key step in the catalytic synthesis of acetyl-CoA. The Fe4S4 component of this cluster is also redox active, raising the possibility that it is the D-site or a portion thereof. Results presented demonstrate that the D-site reduces far faster than the Fe4S4 component, effectively eliminating this possibility. Rather, this component may alter catalytically important properties of the Ni center. The D-site is reduced through a pathway that probably does not involve the Fe4S4 component of this active-site cluster.     

Partial oscillator strengths for the photoionization of N2O and CO2 (20–60 eV)

The photoelectron branching ratios and the partial oscillator strengths (cross sections) for photoionisation of the valence orbitals of N₂O and CO₂ have been obtained in the energy range 20–60 eV using the magic angle dipole (e, 2e) method. In addition to single electron ionization processes there is a large contribution from multiple electron transitions at higher energies in agreement with recent theoretical predictions. The photoionization efficiency and the dipole oscillator strenght for total photoabsorption have also been measured.     

Can TMS and DSS be used as NMR references for cyclodextrin species in aqueous solution?

Tetramethylsilane (TMS) can be included by -cyclodextrin (-CD), and sodium 2,2-dimethylsilapentane-5-sulphonate (DSS) can form inclusion complexes with - and -CD. The NMR chemical shifts are changed considerably as a result of the strong interaction between CD and the guest compound in the inclusion complexes. A downfield shift of as much as 0.63 ppm shift downfield has been observed for the protons of external TMS in CD aqueous solution. In view of this, the question arises of whether TMS and DSS can be used as internal references. DSS in D₂O is suggested as an external reference for aqueous cyclodextrin solution in NMR measurements.     

Direct titrations of antibiotics with iodate solutions: Part 2. Some selected cephalosporins

A previous method for the determination of penicillins by direct titration with potassium iodate under strongly acidic conditions has been extended to the assay of some selected cephalosporins. Results are presented, including error and precision analyses, for the determination of cephaloridine, cephalothin and cephalexin. The appropriate stoichiometries are 1 mol cephalosporin to 3 mol iodate for cephalothin and cephaloridine; 1 mol to 2 mol iodate for cephalexin. An irreversible aqueous end-point technique has been compared with the chloroform layer method; the latter gives more precise results for the determination of cephaloridine and cephalothin (0.8% and 1.3% r.s.d. respectively). Comparable precision was obtained by either technique for the determination of cephalexin (1.39% r.s.d.).