Factorization problem with intersection

We propose a generalization of the factorization method to the case when $\mathcal{G}$ is a finite dimensional Lie algebra such that $\mathcal{G}=\mathcal{G}_0\oplus M \oplus N$ (direct sum of vector spaces), where $\mathcal{G}_0$ is a subalgebra in $\mathcal{G}$, $M, N$ are $\mathcal{G}_0$-modules, and $\mathcal{G}_0 +M$, $\mathcal{G}_0 +N$ are subalgebras in $\mathcal{G}$. In particular, we consider the case when $\mathcal{G}$ is a $\Z$-graded Lie algebra. Using this generalization, we construct some top-like systems related to the algebra $so(3,1)$. According to the general scheme, these systems can be reduced to linear systems with variable coefficients. For the top-like systems first integrals and infinitesimal symmetries are found

ANALYSIS OF THE CHEMICAL COMPOSITION OF CHAROITE ROCKS

The unique charoite mineralization, established on the Murun alkaline massif in the northwestern part of the Aldan shield on the border of the Irkutsk region and Yakutia, is still of great interest to some of researchers (geologists, crystallographers, geochemists, etc.). The outcrops of charoite-bearing rocks at the “Sirenevyi Kamen” deposit are noted both in the indigenous outcrops and in eluvial clatters [Bondarenko, 2009].The unique charoite mineralization, established on the Murun alkaline massif in the northwestern part of the Aldan shield on the border of the Irkutsk region and Yakutia, is still of great interest to some of researchers (geologists, crystallographers, geochemists, etc.). The outcrops of charoite-bearing rocks at the “Sirenevyi Kamen” deposit are noted both in the indigenous outcrops and in eluvial clatters [Bondarenko, 2009]