Reduction of Chandrasekhar's planetary problem in the case of a specularly reflecting boundary to the standard problem

The reduction of Chandrasekhar's planetary problem to the standard problem has been made by several authors (cf. Chandrasekhar⁽¹⁾; Sobolev;⁽²⁾Van de Hulst;⁽³⁾Coulsonet al.; ⁽⁴⁾Ueno; ⁽⁵⁾Kagiwada and Kalaba;⁽⁶⁾. However, the diffuse reflection and transmission problem in a finite anisotropically scattering atmosphere bounded by a specular reflector has not been reduced to the standard problem. In the present paper, starting with an integral equation governing the source function for Chandrasekhar's planetary problem in the case of a specular reflector, we show how to express the required scattering and transmission functions in terms of the Chandrasekhar's scattering and transmission functions. So far as we know, the reduction formulae are new. They will be useful for the numerical study of Chandrasekhar's planetary problem in the case of a specular reflector with the aid of high-speed digital computer.     

Activation of nitroso group with thiols. A new transformation of primary amines to organic sulfides or thiols

Aliphatic primary amines reacted with 2-mercaptobenzothiazole in the presence of t-butylnitrite at room temperature to give condensation products, 2-(alkylthio)benzothiazole.     

Extraction of alkali metal picrates by crown ethers having uncharged coordinating flexible side-chains

Crown ethers were synthesized which have a flexible, neutral side-chain capable of providing the crown ether-bound metal with an additional binding site from the axial direction. Liquid—liquid extraction of alkali metal picrates with these crown ethers was studied; the extraction is compared with that of the normal crown ethers as well as those crown ethers with a proton-dissociable side-chain. The neutral side-chain may assist or suppress the ease of metal extraction depending on the site of the ligating atom on the chain. An anionic ligating side-chain interacts favorably with the lighter metals, resulting in a net decrease in the metal extraction selectivity.     

On the matrix Riccati equation of transport processes

By keeping count of the number of interactions, we obtain some novel perturbation expansions for the Riccati equation. Similar results were obtained in radiative transfer theory by Mingle.     

Behaviors of sodium glycochenodeoxycholate and sodium glycoursodeoxycholate in binary mixed micelles of bile salt and nonionic surfactant

The behavior of sodium glycochenodeoxycholate (NaGCDC) and sodium glycoursodeoxycholate (NaGUDC) in binary mixed micelles consisting of bile salt and octaoxyethylene glycol mono n-decyl ether (C₁₀E₈) has been studied on the basis of micellar compositions, polarities of the interior of intramicelles, mean aggregation numbers and ¹H NMR measurements. Micellar compositions for both NaGCDC---C₁₀E₈ and NaGUDC---C₁₀E₈ systems showed a tendency to change from C₁₀E₈-rich micelles to bile-salt-rich micelles with an increase on the mole fraction of bile salts from the results of both theoretical calculations using the critical micelle concentration and the micellar polarity. The microenvironment of intramicelles for the NaGCDC---C₁₀E₈ system was found to be more hydrophobic than that for the NaGUDC---C₁₀E₈ system. Mean aggregation numbers of mixed micelles for both systems decreased abruptly with an increase in the mole fraction of bile salts in the range of low mole fraction, but those for NaGCDC were larger than those for NaGUDC. Furthermore, from the results of ¹H NMR measurements, the motions of the methyl group protons in the 18 position of the molecular structure of NaGCDC were slightly restricted with an increase in the mole fraction of NaGCDC. In contrast, the methyl group protons in the 18 and 19 positions of the molecular structure of NaGUDC became freer with an increase in the mole fraction of NaGUDC.