Fast computation of incomplete elliptic integral of first kind by half argument transformation

We developed a new method to calculate the incomplete elliptic integral of the first kind, F(j|m){F(\varphi|m)} , by using the half argument formulas of Jacobian elliptic functions. The method reduces the magnitude of j{\varphi} by repeated usage of the formulas while fixing m. The method is sufficiently precise in the sense that the maximum relative error is 3–5 machine epsilons at most. Thanks to the simplicity of the half argument formulas, the new procedure is significantly faster than the existing procedures. For example, it runs 20–60% faster than Bulirsch’ function, el1, and 1.9–2.2 times faster than the method using Carlson’s function, R _F .     

Novel photodegradation of the antifungal antibiotic pyrrolnitrin in anhydrous and aqueous aprotic solvents

The UV irradiation of pyrrolnitrin (1a), which is an antibiotic clinically useful against dermatophytosis and possesses a unique 2-(pyrrol-3-yl)nitrobenzene moiety in the molecule, in an anhydrous aprotic solvent resulted in the exclusive formation of transient 7,4'-dichlorospiro[1,3-dihydrobenzo(c)isoxazole-3,3'-pyrrolin-2'-one] (2a) via the intramolecular oxidation of the juxtaposed pyrrole ring by the triplet-excited nitro group. The irradiation in an aqueous aprotic solvent, however, allowed the concurrent occurrence of intramolecular cyclization by the singlet-excited nitro group in 1a and the hydroxylation at the 2-position of the pyrrole ring by water to afford 3,7-dichloro-8-hydroxy-8,8a-dihydropyrrolo[2,3-b]indol-2-one (3a), accompanied by the formation of 2a. Elongation of the irradiation time in these photoreactions caused a rapid consumption of the products, 2a and 3a, to give undetermined polar polymeric products. The present results indicate that the photodegradation of 1a is significantly influenced by the presence of water in the reaction media and by the nature of its excited state. Thus, the loss of the antifungal activities by the photosensitive antibiotic 1a was chemically proved.     

Stereocontrolled synthesis of 8,11-dideoxytetrodotoxin,unnatural analogue of puffer fish toxin

[structure: see text] 8,11-Dideoxytetrodotoxin, an unnatural tetrodotoxin analogue, was synthesized in a highly stereoselective manner from a common intermediate in our synthetic studies on tetrodotoxin. The synthesis features neighboring group participation of trichloroacetamide for stereoselective hydroxylation, protection of ortho ester, and guanidine installation with Boc-protected isothiourea.     

Effects of ionic dissociation of membrane polymer on pervaporation performance

Pervaporation of a water/alcohol mixture through a membrane which has ion-exchange capacity has been investigated. Theoretical equations are introduced which relate the degree of ionic dissociation of the polymer to quantities of water and alcohol dissolved in the polymer. From these equations, an equation for selective dissolution R is derived which does not contain an explicit term for ionic dissociation. Dissociation affects selective dissolution only by changing the degree of swelling of the polymer. Reformulating R asymptotically obtains a reciprocal relationship between permselectivity and permeability for a water-selective membrane. Experiments to check the validity of the relationship have been carried out using chitosan membranes neutralized by several acids. The effect of degree of neutralization also has been investigated. Results can be well understood on the supposition that ionic dissociation depends upon the water/alcohol composition, the kind of acid, and the degree of neutralization. Experimental results indicate that the reciprocal relationship is maintained over an appropriate range of feed compositions which confirm the validity of the theoretical equations for the swelling equilibrium of an ionic membrane. © 1994 John Wiley & Sons, Inc.     

A novel synthesis of (E)-3,7-dimethyl-2-octene-1,8-diol secreted by the african monarch using the ring-opening reaction of α-methyl-β-propiolactone

The regioselective ring-opening reaction of α-methyl-β-propiolactone with 3,3-ethylene-dioxybutylmagnesium bromide in the presence of copper(I) catalyst afforded 2-methyl-6-oxoheptanoic acid, which was easily converted into (E)-3,7-dimethyl-2-2-octene-1,8-diol in good yield.     

Infrared intensities of the fundamental vibrations of liquid H2O

Infrared absorption intensities of the fundamental vibrations of liquid H₂O have been obtained by measuring transmissions at two sample thicknesses (about 9 and 0.9 μ). The effect of multiple internal reflections on the observed absorptions is examined in terms of thin-film optics. It is shown that this simple method yields precise absorption intensities, without corrections for the effects of multiple internal reflections. The resulting intensities are 89.9 × 10³ cm/mmol and 5.91 × 10³ cm/mmol for the stretching and bending vibrations, respectively. The latter value was estimated after eliminating the absorption of intermolecular vibrations from the 1400–2400 cm^-1 region by means of computer simulation.     

Refractive index behavior of SiO2-P2O5 glass in optical fiber application

The refractive index of SiO₂-P₂O₅ glass prepared by a modified chemical vapor deposition method is measured using an interference microscope. It is found that the refractive index in bulk form increases linearly at 9.5×10^-4 (mol.%)^-1 as the P₂O₅ concentration increases. It is also found that quenching at extremely high speed reduces the refractive index over 2 mol.% P₂O₅. The wavelength dispersion of the refractive index dn/dλ is constant up to 5 mol.% P₂O₅ producing a refractive index difference of 5×10^-3 compared with fused silica. Consequently, this glass materials is thought to be suitable for wide band-width optical fiber applications.     

Complete asymmetric induction in heteroconjugate addition on an acyclic system a new synthetic approach directed toward ansamacrolide maytansine

Acyclic asymmetric induction was achieved in >99 % $\text{threo}$ formation via coordinated intermediate ($\text{3}$) in the heteroconjugate addition ($\text{2}$ to $\text{4}$); the heteroatom in the adduct being used for elongation of the carbon chain toward maytansine $\text{1}$).     

PTX phase equilibrium study of new solid solution systems,Cd1−xMxS (M = Mg,Ca, Sr)

Pressure, temperature, and composition phase equilibrium diagrams of new solid solution systems of the Cd_1?xM_xS (M = Mg, Ca, Sr) type were investigated using the quenching method. The stable region for the rock-salt-type phase is widely extended toward the high-temperature/low-pressure region by substituting 10–20 mole% of Cd with Ca or Sr. Temperature and composition phase diagrams for each solid solution system were obtained at 2 GPa. The rock-salt-type phase stability is discussed in view of these phase relations.