In this paper one first shows that the slow flow of a mechanical system with unstable mode coupled to Nonlinear Energy Sink (NES) can be reduced, in neighborhood fold point its critical manifold, normal form dynamic saddle-node bifurcation. This allows us then obtain scaling law for dynamics and improve accuracy theoretical prediction mitigation limit NES previously obtained as part zeroth-orde...

We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for velocity average of solutions kinetic equations. This requires only elementary techniques in Fourier analysis and shows new range assumptions that are sufficient be $L^2([0,T],H^{1/2}_x).$ result not an interesting connection between lemmas local smoothing property dispersive equations, but ...

An appropriate but challenging goal for evolutionary computation (EC) is to evolve systems of biological complexity. However, specifying complex structures requires many genes, and searching for a solution in such a highdimensional space can be intractable. In this paper, we propose a method for finding high-dimensional solutions incrementally, by starting with an initial population of very sma...