In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

We classify invariant and ergodic probability measures on arithmetic homogeneous quotients of semisimple S-algebraic groups invariant under a maximal split torus in at least one simple local factor, and show that the algebraic support of such a measure splits into the product of four homogeneous spaces: a torus, a homogeneous space on which the measure is (up to finite index) the Haar measure, ...

The problem of construction the fundamental solutions for a piecewise-homogeneous transversely isotropic space is reduced to matrix Riemann in slowly increasing distributions. We propose method solution this problem. As result, explicit form, we obtain expressions components vector and simple representations stress tensor displacements plane joint elastic half spaces subjected action concentrat...