On vectorial addition chains

We prove the equivalence between the problem of computing a multinominal x₁^n₁·x₂^n₂···x_k^n_k, posed by R. E. Bellman (Amer. Math. Monthly70 1963, 765), and the problem of computing simultaneously the monomials x^n₁,…, x^n_k, posed by D. E. Knuth (“Seminumerical Algorithms”, Sect. 4.6.3, Addison-Wesley, Reading, Mass 1969.     

Surface tension for octafluorocyclobutane,n-butane and their mixtures from 233 K to 254 K,and vapour pressure,excess Gibbs function and excess volume for the mixture at 233 K

The surface tensions of octafluorocyclobutane (234 to 267 K), n-butane (238 to 273 K) and of their mixtures (232 to 254 K) have been measured by differential capillary rise; there is a slight minimum in the isotherms near x(c-C₄F₈) ≈ 0.8 but no maximum. The total vapour pressure and density of the liquid mixture were measured at the triple point temperature of c-C₄F₈, 233 K. The mixture displays marked positive azeotropy. The excess Gibbs function and excess volume are both large and positive but the deviation from ideality is insufficient for liquid—liquid immiscibility whose absence was confirmed by visual observation at temperatures down to the solid—liquid phase boundary. All the foregoing are consistent with theoretical expectations based upon the dominant effect of an interaction energy between the unlike components which is smaller than that predicted by the Berthelot geometric mean rule. No inferences can be drawn as to the role of chain flexibility.     

II. Anorganische Substanzen

The alkaline hydrolysis of these vinyl phosphates gives dimethylphosphoric acid and the corresponding N-methylated acetoacetamide which is titrated with sodium nitrite. The polarovoltry (constant current potentiometry) is well appropriate for end point detection. Free acetoacetamides are determined in the same way in non-hydrolized samples and taken into account.     

Ornstein-Zernike and analyticity properties for classical lattice spin systems

The leading Ornstein-Zernike behavior of the truncated two-point function G(x) is obtained from information on the poles of the Fourier transform G~(p). Analyticity of G~(p) as a function of the complex variables p and the inverse temperature β is studied in detail for |β| sufficiently small.