Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Nonisothermal kinetic analysis of the chemiluminescence from tetramethyl-1,2-dioxetane

A computerized method is given for the evaluation of Arrhenius parameters which describe the chemiluminescent decomposition of tetramethyl-1,2-dioxetane. The parameters were determined in several solvents by linear regression methods and the equation ln ln \documentclass{article}\pagestyle{empty}\begin{document}$ [(\sum\nolimits_0^\infty I - \sum\nolimits_0^t I)/(\sum\nolimits_0^\infty I - \sum\nolimits_0^t I - \sum\nolimits_0^{t + \Delta t} I)] = \ln\, (A_1 \Delta t) - E_1 /RT$\end{document}, where I refers to photons counted by increments of Δt, and E₁ and A are the first-order Arrhenius parameters. The average of E₁ and log A₁ (s^?1) from this method from six runs in CCl₄ with initial concentrations of 4.9 × 10^?5-8.45 × 10^?4M were 27.21 ± 0.88 kcal/mol (113.7 ± 3.7 kJ/mol) and 13.88 ± 0.50, respectively. Simulated curves of chemiluminescence versus time were obtained with the use of a computer program and an auxiliary plotter.     

Holographic vibration study of a rotating propeller blade

Holographic interferometry has often been used to determine the natural frequencies and the associated mode patterns of vibrating objects with rigidly fixed or stationary boundaries. This paper describes a new pulse-laser holographic technique whereby the vibration-mode patterns of a rotating propeller blade were determined. This technique consists of rotating the holographic plate on the same axis as the rotating object and using spherically symmetric wavefronts for object and reference beams.