A note on “small representations of finite distributive lattices as congruence lattices”

G. Grätzer, H. Lakser, and E. T. Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a small lattice L, that is, a lattice L with O(n ² ) elements. G. Grätzer, I. Rival, and N. Zaguia proved that, for any <2, O(n ² ) can not be improved to O(n ). In this note we show that the theorem about small representation can be improved further to get a more delicate result.     

Chemistry of 1-Alkoxy-1-glycosyl Radicals: The Manno- and Rhamnopyranosyl Series. Inversion of alpha- to beta-Pyranosides and the Fragmentation of Anomeric Radicals

The formation and stereoselective quenching of 1-mannopyranosyl radicals by a tributyltin hydride-mediated intramolecular 1,5-hydrogen abstraction sequence is described. A competing process is 1,4-hydrogen atom abstraction leading principally to glucopyran-2-ulosides. Fragmentation of the anomeric radical resulting in the formation of ring opened products is a problem in certain series. The chemistry is dictated to a considerable extent by the nature of the protecting groups employed with the 4,6-benzylidene series and, for rhamnose, the Ley 3,4-dispiroketal, being particularly susceptible to the 1,4-hydrogen atom abstraction but less to the fragmentation. Photochemical conditions are described, in which these side reactions are practically eliminated, and applied to the inversion of an alpha- to a beta-mannoside in a disaccharide.     

High sensitivity flow-based analysis system using a semiconductor laser and thin long flow-through cell for the determination of total phosphorus in water

A highly sensitive detection system using a semiconductor laser (SCL) and a thin long flow-through cell (TLFCT) to match flow-based analysis, such as flow injection analysis (FIA), has been developed. The SCL was a GaAlAs semiconductor laser emitting at 780 nm (5 mW), and the TLFTC, which has a 100 mm thin long light path, was made of a poly(tetrafluoroethylene) (PTFE) rod. The sensitivity was essentially improved about 10-fold in comparison to usual FIA-spectrophotometry using a 10 mm conventional flow cell. When this detection system was applied to the determination of total phosphorus (P) in water by molybdenum-blue spectrophotometry, the relative standard deviation, detection limit and linear range were 1.0% (n = 10 at 20 mug P 1(-1)), 0.6 (3 sigma) and 1.0-50 mug P 1(-1), respectively, and the results for the samples were fairly consistent with those by the official method. It may also be possible to apply the present detection system to other flow-based analytical methods such as the liquid chromatography family.     

One-step preparation of highly concentrated well-stable gold colloids by direct mix of polyelectrolyte and HAuCl4 aqueous solutions at room temperature

Highly concentrated, well-stable gold colloids can be prepared directly from an amine-bearing polyelectrolyte-HAuCl4 aqueous solution at room temperature. It is found that increasing molar ratio of polyelectrolyte to gold leads to increasing particle size. UV-vis spectra, transmission electron microscopy (TEM), and X-ray photoelectron spectra (XPS) were used to characterize the products thus formed.