Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem

This article presents a branch-and-bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm economizes the required computations by conducting the branch-and-bound search in ^p, rather than in ⁿ, where p is the number of ratios in the objective function of problem (P) and n is the number of decision variables in problem (P). To implement the algorithm, the main computations involve solving a sequence of convex programming problems for which standard algorithms are available.     

Effects of buffer gases on the infrared multiphoton dissociation of C2H4DCl: A chemical clock to explore highly excited molecules

Observations are reported of the effect of the buffer gases He, Ne, and CF₄, in the pressure range of 0–30 torr, on the branching ratio [HCl]/[DCl] of the unimolecular decomposition The ratio R = k_H/k_D has been measured in high-pressure thermal decomposition (670–1100 K) and was shown to give a unique measure of the internal energy of the decomposing molecules and hence, with RRKM theory and pressure fall-off data, a time scale for their decomposition. Applying the thermal data to the photolysis leads to the conclusion that excitation and decomposition are produced by the laser spike (high intensity, 70 ns FWHM) and also at a slower rate by the larger, less intense tail (1.6 μs). Added buffer gases quench the latter, leaving the former which, from measurements of R, is shown to correspond to excitations of 115 ± 15 kcal/mol and lifetimes of ～30 ps. No bond breaking is seen despite the high energies, in accord with theoretical expectations. The results require an enhanced rate of photon absorption by the highly excited molecules, which are about hundredfold greater than that observed for 300 K molecules. Data are also reported for C₂H₂F₂ and the secondary multiphoton photolysis of the ethylenes produced. Effects of beam geometry and wavelength are explored.     

Kinetic studies of the reactions CH2I2 + HI⇄CH3I + I2 and 2 CH3I⇄CH4 + CH2I2 the heat of formation of the iodomethyl radical

The rate of the reaction CH₂I₂ + HI ? CH₃I + I₂ has been followed spectrophotometrically from 201.0 to 311.2°. The rate constant for the reaction fits the equation, log (k₁/M^?1 sec^?1) = 11.45 ± 0.18 - (15.11 ± 0.44)/θ. This value, combined with the assumption that E₂ = 0 ± 1 kcal/mole, leads to ΔH (CH₂I, g) = 55.0 ± 1.6 kcal/mole and DH (H? CH₂I) = 103.8 ± 1.6 kcal/mole. The kinetics of the disproportionation, 2 CH₃I ? CH₄ + CH₂I₂ were studied at 331° and are compatible with the above values.     

VLPR study of the reaction Br + CH3CHO

The reaction \documentclass{article}\pagestyle{empty}\begin{document}${\rm Br} + {\rm CH}_3 {\rm CHO}\buildrel1\over\rightarrow{\rm HBr} + {\rm CH}_3 {\rm CO}$\end{document} has been studied by VLPR at 300 K. We find k₁ = 2.1 × 10¹² cm³/mol s in excellent agreement with independent measurements from photolysis studies. Combining this value with known thermodynamic data gives k_-1 = 1 × 10¹⁰ cm³/mol s. Observations of mass 42 expected from ketene suggest a rapid secondary reaction: in which step 2 is shown to be rate limiting under VLPR conditions and k₂ is estimated at 10^12.6 cm³/mol s from recent theoretical models for radical recombination. It is also shown that 0 ? E₁ ? 1.4 kcal/mol using theoretical models for calculation of A₁ and is probably closer to the lower limit. Reaction ?1 is negligible under conditions used.     

Fractional iteration and a generalised abel's equation in two variables

Aequationes mathematicae -