Melting temperatures of poly(2,6-dimethyl-1,4-phenylene oxide) in methylene chloride solutions: Thermodynamic analysis

Melting temperatures were observed visually for poly-(2,6-dimethyl-1,4-phenylene oxide) in methylene chloride at nine concentrations (polymer weight fractions ranging from 0.0042 to 0.2362). The data were analyzed upon the assumptions that ΔH_u and ΔS_u, the molar heat and entropy of fusion per polymer unit, are constant over the temperature range studied, and that a Flory-Huggins chemical potential expression with a concentration-independent pair interaction parameter, χ₁ = (0.5 + ψ₁) + ψ₁Φ/T, satisfactorily describes the polymer unit activity in the binary solutions. Computation gave ΔH_u = 1404 cal/mole of units (therefore Δh = 11.7 cal/g), ψ₁ = ?0.569₁, and Φ = 342.₄°K. The effect of using various combinations of data points upon the values of these three parameters, as determined by least-squares linear regression treatment of the melting temperature expression, is indicated.     

The synthesis of some pyrrolo[1,5-b:2,3-c′]dipyridazines

A facile method for the preparation of the aromatic pyrrolo[1,5-b:2,3-c']dipyridazine ring system is reported. A number of compounds have been prepared and the biological screening data reported.     

Necessary conditions for normed convergence of critical multitype Bienaymé-Galton-Watson processes without variance

The condition on the offspring distribution in the critical multitype Bienaymé-Galton-Watson process without variance, which was previously shown to be sufficient for the existence of the analogue of the exponential limit law, is now shown also to be necessary. This completely extends previous one-type work of R. S. Slack.     

Convergence of double Fourier series

Summary Let a2π-periodic function f(x, y) be continuous in some neighbourhood of the point (x, y) except possibly along finitely many lines l ₁ , l ₂ , ..., l_k terminating at (x, y). The problem of convergence of the Fourier series of f(x, y) at the point (x, y) is examined in some detail. It is established that under certain restrictions on the variation of f(x, y), and also on the lines l ₁ , l ₂ , ..., l_k, the fourier series converges to a value bounded above by the limit superior, and below by the limit inferior of f(x+u, y+v), u, v →0, this value depending on the manner in which the series is summed. The preparation of this paper was financed, in part, by a Canadian Mathematical Congress Summer Research Grant (1968). Entrata in Redazione il 3 febbraio 1969.