Billiard Representation for Multidimensional Quantum Cosmology near the Singularity

The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the asymptotical regime is solved and a third-quantized model is suggested.Comment: 6 pages, LaTe

Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology

We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E_{10}-approach to M-theory. We focus on the solutions with non zero electric field determined by geometric configurations (n_m, g_3), n\leq 10. We show that these solutions are associated with rank $g$ regular subalgebras of E_{10}, the Dynkin diagrams of which are the (line) incidence diagrams of the geometric configurations. Our analysis provides as a byproduct an interesting class of rank-10 Coxeter subgroups of the Weyl group of E_{10}.Comment: 48 pages, 27 figures, 5 tables, references added, typos correcte

Induction time in multi-fuels system. Effect of small additives of ozone and hydrogen peroxide on hydrogen-air detonation

Determination of induction time in multi-fuels combustible systems are discussed: using of global kinetic schema of elementary reactions and using of approximate equation for average reaction of induction time. Both types of data for induction time are used for prediction of detonation cell size and critical initiation energy for hydrogen-air mixtures with addition of ozone and hydrogen peroxide. The cell size was calculated with the help of Computer Program “SAFETY”. Calculated results are compared with experimental data. It is shown that small additives of ozone and hydrogen peroxide to hydrogen-air mixtures result in a shortening of the induction-zone length over the entire range of the initial H$_2$ concentrations. The comparative increase in the detonatability of the mixture in the presence of O$_3$ or H$_2$O$_2$ displays a substantially nonmonotonic nature