The role of microorganisms in the weathering of rocks. 1 - Microflora of the surface layer of rocks

Microbiological analyses of surface layers of rocks to determine role of microorganisms in weathering of rock

The subalgebra of graded central polynomials of an associative algebra

Let $F$ be a field and let $F \langle X \rangle$ be the free unital associative $F$-algebra on the free generating set $X = \{ x_1, x_2, \dots \}$. A subalgebra (a vector subspace) $V$ in $F \langle X \rangle$ is called a $T$-subalgebra (a $T$-subspace) if $\phi (V) \subseteq V$ for all endomorphisms $\phi$ of $F \langle X \rangle$. For an algebra $G$, its central polynomials form a $T$-subalgebra $C(G)$ in $F \langle X \rangle$. Over a field of characteristic $p > 2$ there are algebras $G$ whose algebras of all central polynomials $C (G)$ are not finitely generated as $T$-subspaces in $F \langle X \rangle$. However, no example of an algebra $G$ such that $C(G)$ is not finitely generated as a $T$-subalgebra is known yet. In the present paper we construct the first example of a $2$-graded unital associative algebra $B$ over a field of characteristic $p>2$ whose algebra $C_2 (B)$ of all $2$-graded central polynomials is not finitely generated as a $T_2$-subalgebra in the free $2$-graded unital associative $F$-algebra $F \langle Y,Z \rangle$. Here $Y = \{ y_1, y_2, \dots \}$ and $Z = \{ z_1, z_2, \dots \}$ are sets of even and odd free generators of $F \langle Y,Z \rangle$, respectively. We hope that our example will help to construct an algebra $G$ whose algebra $C(G)$ of (ordinary) central polynomials is not finitely generated as a $T$-subalgebra in $F \langle X \rangle$.Comment: 8 page

The role of microorganisms in the weathering of rocks. 2 - Focal distribution of microorganisms on the surface of rocks

Microorganism growth in synthetic medium using rock as mineral nutrient source, and rock weathering due to microorganism

The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3

Let $\mathbb Z \langle X \rangle$ be the free unital associative ring freely generated by an infinite countable set $X = \{ x_1,x_2, \dots \}$. Define a left-normed commutator $[x_1,x_2, \dots, x_n]$ by $[a,b] = ab - ba$, $[a,b,c] = [[a,b],c]$. For $n \ge 2$, let $T^{(n)}$ be the two-sided ideal in $\mathbb Z \langle X \rangle$ generated by all commutators $[a_1,a_2, \dots, a_n]$ $( a_i \in \mathbb Z \langle X \rangle )$. Let $T^{(3,2)}$ be the two-sided ideal of the ring $\mathbb Z \langle X \rangle$ generated by all elements $[a_1, a_2, a_3, a_4]$ and $[a_1, a_2] [a_3, a_4, a_5]$ $(a_i \in \mathbb Z \langle X \rangle)$. It has been recently proved in arXiv:1204.2674 that the additive group of $\mathbb Z \langle X \rangle / T^{(4)}$ is a direct sum $A \oplus B$ where $A$ is a free abelian group isomorphic to the additive group of $\mathbb Z \langle X \rangle / T^{(3,2)}$ and $B = T^{(3,2)} /T^{(4)}$ is an elementary abelian $3$-group. A basis of the free abelian summand $A$ was described explicitly in arXiv:1204.2674. The aim of the present article is to find a basis of the elementary abelian $3$-group $B$.Comment: 23 pages; extended introduction, additional reference

EAS spectrum in the primary energy region above 10 to the 15th power eV by the Akeno and Yakutsk array data

The extensive air showers spectrum on scintillation desity Rko in primary energy region E sub approx. 10 to the 15th power - 10 to the 20th power eV on the Yakutsk array data and recent results of the Akeno is given

Order of Selection and Design of Magnetic Clutches for Sealed Machines

A technique for selection and design of magnetic clutches with highly coercive permanent magnets (barium oxide magnets or magnets produced from such alloys of rare-earth elements as samarium-cobalt and neodymium-iron-boron) for sealed machines (pumps, compressors, mixers) is presented. © 2013 Springer Science+Business Media New York

Prevention of destructive tropical and extratropical storms, hurricanes, tornadoes, dangerous thunderstorms, and catastrophic floods

International audienceTropical cyclones and storms, hurricanes, powerful thunderclouds, which generate tornadoes, destructive extratropical cyclones, which result in catastrophic floods, are the powerful cloud systems that contain huge amount of water. According to the hypothesis argued in this paper, an electric field coupled with powerful clouds and electric forces play a cardinal role in supporting this huge mass of water at a high altitude in the troposphere and in the instability of powerful clouds sometimes during rather a long time duration. Based on this hypothesis, a highly effective method of volume electric charge neutralization of powerful clouds is proposed. It results in the decrease in an electric field, a sudden increase in precipitation, and subsequent degradation of powerful clouds. This method, based on the natural phenomenon, ensures the prevention of the intensification of tropical and extratropical cyclones and their transition to the storm and hurricane (typhoon) stages, which makes it possible to avoid catastrophic floods. It also ensures the suppression of severe thunderclouds, which, in turn, eliminates the development of dangerous thunderstorms and the possibility of the emergence and intensification of tornadoes