2 research outputs found
The General Solution of Bianchi Type Vacuum Cosmology
The theory of symmetries of systems of coupled, ordinary differential
equations (ODE) is used to develop a concise algorithm in order to obtain the
entire space of solutions to vacuum Bianchi Einstein Field Equations (EFEs).
The symmetries used are the well known automorphisms of the Lie algebra for the
corresponding isometry group of each Bianchi Type, as well as the scaling and
the time re-parametrization symmetry. The application of the method to Type
VII_h results in (a) obtaining the general solution of Type VII_0 with the aid
of the third Painlev\'{e} transcendental (b) obtaining the general solution of
Type with the aid of the sixth Painlev\'{e} transcendental (c) the
recovery of all known solutions (six in total) without a prior assumption of
any extra symmetry (d) The discovery of a new solution (the line element given
in closed form) with a G_3 isometry group acting on T_3, i.e. on time-like
hyper-surfaces, along with the emergence of the line element describing the
flat vacuum Type VII_0 Bianchi Cosmology.Comment: latex2e source file, 27 pages, 2 tables, no fiure
Intramolecular cycloaddition/cycloreversion of (E)-3 beta,17 beta-diacetoxy-5,10-secoandrost-1(10)-en-5-one
Treatment of 3 beta,17 beta-diacetoxy-5,10-secoandrost-1(10)-en-5-one with (BF3Et2O)-Et-. was shown to proceed with cleavage of the macrocycle and formation of a new compound containing a cyclopentenone ring. Based on DFT calculations, an intramolecular Lewis acid promoted [2+2]cycloaddition, followed by a cycloreversion of the intermediate oxetane, is proposed as a possible reaction mechanism