Mass spectrometry in structural and stereochemical problems-CCXXIX: Electron-impact-induced fragmentation of boric acid esters

The mass spectral decompositions of cyclic and acyclic borates have been examined. Straight chain trialkyl borates fragment by C? O cleavage reactions accompanied by transfer of one or two hydrogen atoms, whereas tri-(sec-alkyl) borates primarily undergo α-cleavage reactions. Both types of cleavage are observed in the fragmentation of cyclic borates. B? O bonds are not broken in the formation of most major fragment ions. The fragmentations of borates are compared with those of phenylboronates with special emphasis on the rearrangements leading to hydrocarbon ions in the spectra of the latter.     

Integral formulae on hypersurfaces in Riemannian manifolds

The coefficients of the complete set of n fundamental forms of a hypersuface V_n−1 imbedded in an n-dimensional Riemannian space V_n, as recently introduced[(5)], are used to construct certain tensor fields over V_n−1 which display some remarkable features. In particular, the divergences of these tensor fields can be expressed very simply in terms of polynomials involving the curvature tensor of V_n, the coefficients of the n fundamental forms, and the r^th curvatures of V_n−1. As the result of an application of the generalized divergence theorem of Gauss to these relations a set of integral formulae on V_n−1 is obtained. The integrands of these integral formulae can be expressed very simply in terms of the n fundamental forms of V_n−1. By successive specialization it is indicated how known integral theorems([2], [3], [6], [7], [8]) can be derived as particular cases, which is possible partly as a result of the fact that the polynomial referred to above vanishes identically whenever V_n is a space of constant curvature. This research was supported by the National Research Council of Canada. Entrata in Redazione il 21 agosto 1970.     

The reduction of certain boundary value problems to variational problems by means of transversality conditions

It is shown by means of the classical theory of the transversality conditions of the calculus of variations that certain boundary value problems are equivalent to necessary conditions for the attainment of extreme values of a fundamental integral of a variational problem with variable boundaries. Systems of second order ordinary, as well as partial, differential equations are considered. The method is illustrated for both cases by means of examples, from which well-known theorems of exceptional practical importance emerge effortlessly.     

Formation of long-lived fluorofullerene trianions in collisions with Na

The first experimental observation of long-lived triply charged fluorofullerene anions in the gas phase obtained from C60F48 is reported. The existence of a Coloumb barrier trapping the third electron in the trianion is supposed to be responsible for detection of the species which is estimated to have negative third electron affinity.