We compute the structure of the Lie algebra associated to two examples of branch groups, and show that one has finite width while the other has unbounded width. This answers a question by Sidki. We then draw some general results relating the growth of a branch group, of its Lie algebra, of its graded group ring, and of a natural homogeneous space we call parabolic space. Finally we use this inf...

We give a short, self-contained derivation of the Möbius function for the Bruhat orderings of Coxeter groups and their parabolic quotients.

An adiabatic mode time-dependent parabolic equation for the 3D problems of underwater acoustic propagation problem is derived by the multiple-scale method. The Cauchy problem for this equation is considered.

To certain types of generic distributions (subbundles in a tangent bundle) one can associate canonical Cartan connections. Many of these constructions fall into the class of parabolic geometries. The aim of this article is to show how strong restrictions on the possibles sizes of automorphism groups of such distributions can be deduced from the existence of canonical Cartan connections. This ne...

We show that elementary algebraic techniques lead to surprising results on automorphism groups of Cartan geometries and especially parabolic geometries. The example of three–dimensional CR structures is discussed in detail.

Let G be a reductive linear algebraic group, P a parabolic subgroup of G and Pu its unipotent radical. We consider the adjoint action of P on the Lie algebra pu of Pu. Richardson’s dense orbit theorem says that there is a dense P -orbit in pu. We consider some instances when P acts with a dense orbit on terms p u of the descending central series of pu. In particular, we show (in good characteri...

Energy and exergy analyses were carried out for a pilot parabolic solar dish-Stirling System. The system was set up at a site at Kerman City, located in a sunny desert area of Iran. Variations in energy and exergy efficiency were considered during the daytime hours of the average day of each month in a year. A maximum collector energy efficiency and total energy efficiency of 54% and 12.2%, res...