V. Gubarev | Searcharxiv

arXiv2026

Inner post-Lie algebras and inner post-groups

In this paper, using extension theory and cohomological approach we introduce the notion of the obstruction class for an inner post-Lie algebra being induced by a Rota-Baxter operator, and show that an inner post-Lie algebra is induced by a Rota-Baxter operator if and only if the obstruction class is trivial. Similarly, we introduce the notion of the obstruction class for an inner post-group being induced by a Rota-Baxter operator, and prove a parallel result. Finally, we give some applications of inner post-Lie algebras and inner post-groups.

math.RA↗

arXiv2022

Free special Gelfand-Dorfman algebra

A Gelfand-Dorfman algebra is called special if it can be embedded into a differential Poisson algebra. We find a new basis of the free Novikov algebra. With its help, we construct the monomial basis of the free special Gelfand-Dorfman algebra.

math.RA↗

arXiv2022

Dynamics of H atoms surface recombination in low-temperature plasma

The dynamics of H atom recombination on materials of interest for a EUV lithographer was studied under a longterm low-pressure H2 plasma exposure. The similarity of the experimental plasma with the typical EUV-induced plasma over the multi-layer mirrors (MLMs) surface of the EUV lithographic machine is demonstrated by means of 2D PIC MC simulation. The measurement of the temporal dynamics of the H atom surface loss probability is chosen for testing the surface modification during the treatment. Time-resolved actinometry of H atoms with Kr as the actinometer gas was used to detect the dynamics of the H-atom loss probability on the surface of Al, Ru, RVS and SiO2. It is demonstrated that significant changes of the materials surface occur only at the very beginning of the treatment and ist due to the surface heating and cleaning effects. After that no changes of the H recombination rate are found, indicating that the surface stays absolutely stable. A special test of the sensitivity of the used method to the state of surface was carried out. Dynamics of the H recombination rate changes with the small O2 addition clearly demonstrated modification of the Al surface due to oxidation with the next removal of the oxygen by the H2 plasma treatment. The rate of oxide removal is shown to be determined by plasma parameters such as the ion energy and flux to the surface.

physics.plasm-ph↗