Single generator problem

Using the Stone-\v{C}ech compactification of integers, we introduce a free extension of an almost periodic flow. Together with some properties of outer functions, we see that, in a certain class of ergodic Hardy spaces , , the corresponding subspaces are all singly generated. This shows the existence of maximal weak- Dirichlet algebras, different from of the disc, for which the single generator problem is settled.

     

Isolation and Stereostructures of Dolastatin G and Nordolastatin G, Cytotoxic 35-Membered Cyclodepsipeptides from the Japanese Sea Hare Dolabella auricularia

A bioassay-directed fractionation of the cytotoxic constituents of the Japanese sea hare Dolabella auricularia resulted in the isolation of two 35-membered depsipeptides dolastatin G (1) and nordolastatin G (2), which showed cytotoxicity against HeLa S(3) cells with IC(50) values of 1.0 and 5.3 &mgr;g/mL, respectively. The gross structures of these substances were established by spectroscopic analysis including 2D NMR techniques. The absolute stereostructure of 1 was determined by chiral HPLC analysis of amino acid components obtained from acid hydrolysis of 1 and by the enantioselective syntheses of two degradation products arising from polyketide portions. Nordolastatin G (2) is a congener that has the same absolute stereochemistry as that of 1.     

Colorimetric assay for lysozyme using Micrococcus luteus labeled with a blue dye, Remazol brilliant blue R, as a substrate.

Micrococcus luteus (M. lysodeikticus) labeled with Remazol brilliant blue R (blue ML) was prepared as a novel substrate for the colorimetric assay of lysozyme. The treatment of the labeled substrate with lysozyme resulted in the release of soluble blue products which can be easily measured spectrophotometrically at 600 nm. The blue color was most efficiently released at pH 7 and ionic strength of 0.2 on incubation with hen lysozyme at 40 degrees C. A new colorimetric method for the assay of lysozyme using this substrate was developed. The assay system gave a linear dose-response curve, and as little as 0.1 microgram of human lysozyme (1 microgram/ml, 100 microliters) can be detected. The present method is more convenient and reproducible than the conventional lysozyme assay with bacterial cells. Application of the system to the determination of lysozyme in human serum is described.     

Aminyl radical cyclization by means of anodic oxidation. Stereoselective synthesis of cis-1-methyl-2,5-disubstituted pyrrolidines

Neutral aminyl radicals generated by anodic oxidation of lithium alkenylamides 2 undergo a stereoselective cyclization to give $\text{cis}$-1-methyl-2,5-disubstituted pyrrolidines 4. Their $\text{cis}$ stereochemistry was confirmed by a comparison with $\text{trans}$-1,2-dimethyl-5-phenylpyrrolidine, the structure of which was established by X-ray crystallographic analysis of its quarternary ammonium bromide 6.