Active change in the state of self-oscillations in machines and mechanisms in a system with various types of nonlinearities of an arbitrary structure under the action of a impulse or harmonic disturbing force

The method of actively changing the state of self-oscillations in machines and mechanisms in a system with various types of nonlinearities of an arbitrary structure under the action of external periodic perturbations was proposed. The differential equations of the method take into account two types of external force periodic disturbances: impulse and harmonic.

Finitely forcible graphons with an almost arbitrary structure

A basic result from the theory of quasirandom graphs, due to Andrew Thomason, is that if is a graph with vertices and density , and if the number of 4-cycles in is approximately , then resembles a random graph of the same density. In particular, between any two sets and of vertices the number of edges is approximately . (Here, “approximately” means "to within a small fraction of , so the statement is non-trivial only for sets and that are not too small.)