A note on unit and class number of real quadratic fields

Letp be an odd prime withp1 (mod 4) andQ(p) be the real quadratic field. Also let andh denote the fundamental unit and the class number of Q(p), respectively. The main purpose of this paper is to study the explicit expressions of ^h and ^2h , and to discuss the problems related to the conjecture of Ankeny-Artin-Chowla.     

Effect of pressure on the solubilities ofo-,m- andp-xylene in water

The solubilities of o-, m- and p-xylene in water were measured at 25.0°C up to 250, 385, and 50 MPa, respectively. The solubility increased with increasing pressure up to 120 MPa (50 MPa for p-xylene) and then decreased. The reaction volumes, V^o accompanying the dissolution at 0.1 MPa were estimated as –3.6±0.5, –3.4±0.5, and –4.1±0.5 cm³-mol^–1 for o-, m-, and p-xylene, respectively, from the pressure dependences of the solubilities. The limiting partial molar volumes, of p- and o-xylene in water under high pressure were estimated from V^o and the molar volume of the xylene. The partial molar volumes decreased with increasing pressure. The reaction volume for the formation of intra-molecular pairwise hydrophobic interaction between the methyl groups, as proposed by Ben-Naim, is discussed for the V^o of p- and o-xylene at 0.1 MPa.     

Highly regio- and stereocontrolled SN2′ reactions of gem-difluorinated vinyloxiranes with monoalkylcopper reagents

Reaction of gem-difluorinated vinyloxiranes with RCu(X)Li allowed us to introduce the R group regioselectively at the fluorine-attached terminal carbon atom in an S_N2′ manner to afford (E)-allylic alcohols exclusively, while homoallylic alcohols with anti stereochemical relationship were found to be obtained selectively from higher-ordered cuprates derived from CuCl and RMgBr in a ratio of 1:3.     

Inhibitory effects of non-steroidal anti-inflammatory drugs on superoxide generation.

Effects of non-steroidal anti-inflammatory drugs (NSAID: amfenac sodium, diclofenac sodium, indomethacin and ketoprofen) on the generation of superoxide anion (O2-) by isolated rat polymorphonuclear leukocytes (PMN) were studied spectrophotometrically using cytochrome c. The effects of these drugs were also studied on O2- production by the xanthine-xanthine oxidase and reduced nicotinamide adenine dinucleotide phosphate (NADPH)-NADPH oxidase systems. Amfenac sodium, at 0.1 mM, inhibited significantly O2- generation in rat PMN induced by opsonized zymosan. At 0.5 mM, diclofenac sodium and indomethacin inhibited the O2- generation in rat PMN. All of the above drugs slightly inhibited O2- production by the xanthine-xanthine oxidase system. On the other hand, O2- production by the NADPH-NADPH oxidase system was significantly inhibited by the addition of amfenac sodium, ketoprofen or indomethacin. These results suggest that non-steroidal anti-inflammatory drugs do not work as an O2- scavenger and block O2- production by the NADPH-NADPH oxidase system of rat PMN. It is concluded that amfenac sodium and the other drugs are able to inhibit granulocyte O2- production by blocking the activation of NADPH-oxidase.     

Fluorescence spectra,fluorescence quantum yields and fluorescence lifetimes of polymers having trans-1,2-dicarbazolylyclobutane or carbazolyl group

Quantum yields, lifetimes and shapes of fluorescence from polymers containing the trans-1,2-dicarbazolylcyclobutane (DCZB) or carbazolyl structures were studied in N,N-dimethylformamide. No sandwich-type excimer formation was observed for DCZB polymers. The so-called second excimer observed in poly(9-vinylcarbazole) might also be produced in poly(9-ethyl-3-vinylcarbazole).     

A facile synthesis of (−)-prostaglandin E1 via a three-component coupling process

A very short synthesis of chiral prostaglandin E₁ methyl ester is described.