The thermal decomposition of fluorinated esters. II. The effect of γ-substitution

The gas-phase kinetics of thermal decomposition of ethyl difluoroacetate, pentafluoropropionate, and hepatfluorobutyrate have been studied. The normal ester decomposition route to ethylene plus carboxylic acid is taken in each case, but the fluorinated acids decompose rapidly at the temperatures used. The primary decompositions are homogeneous and unimolecular, and the three Arrhenius equations are The postulate of a slightly electron-rich γ carbon in six-center ester transition states is supported by the higher rates and lowered activation energies observed when increasingly electron-withdrawing fluorinated groups are linked to this center. The stabilization is reflected in a ρ constant of +0.30. The results are compared with previous work on α substitution in fluorinated esters.     

Martingales,the smoothing index and ergodic theory

A classical theorem of Meyer Jerison which shows that the convergence in the pointwise ergodic theorem is equivalent to the convergence of an associated martingale is expanded to a conditional setting. An equiconvergence theorem of the type established for martingales by N.F.G. Martin and E. Boylan is established in the ergodic case for an ergodic, non-invertible, measure-preserving transformation.     

Response functions for crystals and surfaces,with applications to surface scattering

A general solution of the equations of forced motion of a harmonic crystal or other vibrating system with arbitrary time-dependent forces acting on the atoms is given. The solution is given in terms of dynamical “response functions”, for which expressions in terms of the normal mode frequencies and eigenvectors (polarization vectors) are given. Numerical calculations of the response functions are described for (111) and (100) surfaces of face-centered cubic crystals interacting with Lennard-Jones 6–12 potentials, and the qualitative features of the surface and bulk response functions are discussed. The use of these functions in problems of atomic scattering from surfaces is outline, and conveneint parameterized forms for this application are given.     

Cross section of the reaction 6Li(p, γ)7Be

The cross section of the reaction ⁶Li(p, γ)⁷Be has been measured using Ge(Li) γ-ray spectrometers for proton bombarding energies E_p from 200 keV to 1200 keV. At E_p = 800 keV, the total (p, γ) integrated cross section is found to be 3.1 ± 0.4 μb. The cross section adopted from consideration of this and previous measurements is in good agreement with that predicted from the known thermal neutron cross section for ⁶Li(n, γ)⁷Li on the assumption that properties of mirror direct capture reactions can be well described by optical potentials that use the same parmeter values for the two reactions.     

Monotone norms and tensor products

Various refinements of orthant monotonicity for norms are studied. A partial order is induced in the tensor product of two partially ordered vector spaces. The induced norm in the tensor product is shown to be orthant monotone in certain cases.     

Balance equation formulation and memory effects in retarded high field semiconductor transport

The role of the finite, non-zero collision duration in high electric fields is examined for its effect on transient and overshoot response of carrier velocity and energy. A quantum kinetic equation approach is used to develop modifications of the balance equations obtained in a drifted Maxwellian approach for treating high-field transport. These result in corrections which require convolution integrals to be evaluated on the short-time scale.