Microwave‐improved polymerization of ϵ‐caprolactone initiated by carboxylic acids

The ring‐opening polymerization of ε‐caprolactone (ε‐CL), initiated by carboxylic acids such as benzoic acid and chlorinated acetic acids under microwave irradiation, was investigated; with this method, no metal catalyst was necessary. The product was characterized as poly(ε‐caprolactone) (PCL) by ¹H NMR spectroscopy, Fourier transform infrared spectroscopy, ultraviolet spectroscopy, and gel permeation chromatography. The polymerization was significantly improved under microwave irradiation. The weight‐average molecular weight (M_w) of PCL reached 44,800 g/mol, with a polydispersity index [weight‐average molecular weight/number‐average molecular weight (M_w/M_n)] of 1.6, when a mixture of ε‐CL and benzoic acid (25/1 molar ratio) was irradiated at 680 W for 240 min, whereas PCL with M_w = 12,100 and M_w/M_n = 4.2 was obtained from the same mixture by a conventional heating method at 210 °C for 240 min. A degradation of the resultant PCL was observed during microwave polymerization with chlorinated acetic acids as initiators, and this induced a decrease in M_w of PCL. However, the degradation was hindered by benzoic acid at low concentrations. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 13–21, 2003     

A study of the atmospheric lead pollution in Seville, Spain. Influence of meteorology and traffic, and relationship with other traffic-generated pollutants

A study of the atmospheric pollution by suspended particulate lead in the city of Seville, Spain, was carried out during the period between March 1983 and February 1984. The results obtained from seven sampling stations allowed us to study the site to site variations; there are two locations with average annual concentrations higher than 2 micrograms X m-3. In one station, the meteorological and traffic effects and relationship with other traffic-related pollutants, were investigated. The regression analyses performed on the average monthly data have shown an inverse correlation with wind speed and temperature and a direct correlation with carbon monoxide and smoke concentrations, but no significant correlation was found with the lead deposition levels.     

Homogeneous renewal equation

Let F be a non-arithmetic distribution on the line , and W be the class of bounded functions w without discontinuity of the second kind such that

.In this paper, we show that the solution of the homogeneous renewal equation w = w F in the class W is a constant-function.     

Elastoplastic torsion theory for whisker crystals

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 127–134, March–April, 1991.     

A generalization of the H-theorem to steady non-equilibrium states. Part 1: A basic decomposition and the linear case

A generalized relative entropy functional is associated to the evolution of gas in a container with (generally) non-uniform boundary data. A decomposition for its rate in ‘bulk’ and in ‘boundary’ terms is given; for the linear case both have a definite sign. The relation with the strong L₁ stability is pointed out.     

Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains

We investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.