Splitting fields and general differential Galois theory

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions..Comment: 33 pages, this version coincides with the published on

Graphene oxide-polyamine preprogrammable nanoreactors with sensing capability for corrosion protection of materials.

Corrosion is one of the major issues for sustainable manufacturing globally. The annual global cost of corrosion is US$2.5 trillion (approximately 3.4% of the world's GDP). The traditional ways of corrosion protection (such as barriers or inhibiting) are either not very effective (in the case of barrier protection) or excessively expensive (inhibiting). Here, we demonstrate a concept of nanoreactors, which are able to controllably release or adsorb protons or hydroxides directly on corrosion sites, hence, selectively regulating the corrosion reactions. A single nanoreactor comprises a nanocompartment wrapped around by a pH-sensing membrane represented, respectively, by a halloysite nanotube and a graphene oxide/polyamine envelope. A nanoreactor response is determined by the change of a signaling pH on a given corrosion site. The nanoreactors are self-assembled and suitable for mass-line production. The concept creates sustainable technology for developing smart anticorrosion coatings, which are nontoxic, selective, and inexpensive