Note on Long Paths in Eulerian Digraphs

Long paths and cycles in Eulerian digraphs have received a lot of attention recently. In this short note, we show how to use methods from [Knierim, Larcher, Martinsson, Noever, JCTB 148:125--148] to find paths of length $d/(\log d+1)$ in Eulerian digraphs with average degree $d$, improving the recent result of $\Omega(d^{1/2+1/40})$. Our result is optimal up to at most a logarithmic factor.

Physical processes in the channel of propagation of CO2 laser pulses during the generation of electric and magnetic fields

The mechanisms of generation of electric and magnetic fields during the propagation of microsecond pulses of a CO2 laser in the atmosphere over long paths are considered. The range of radiated waves selected for research is substantiated. The power of the source required for the realization of the pre-breakdown and breakdown modes of interaction of radiation with the medium is estimated. The dependence of the observed signals on the conditions of radiation propagation is investigated. Comparison of theoretical estimates and results of outdoorexperiments is carried out.