Abstract This paper presents a new class of robust zero-order algorithms for the solution real-time optimization problems with acceleration. In particular, we propose family extremum seeking (ES) dynamics that can be universally modeled as singularly perturbed hybrid dynamical systems restarting mechanisms. From this dynamics, synthesize four fast convex, strongly constrained, and unconstrained...

We develop the perturbation theory for bosons interacting via a weak two-body potential $V$, attractive and repulsive parts of which cancel each other. find that leading nonpairwise contribution to energy emerges in third order $V$ represents an effective three-body interaction, sign most cases (although not general) is anticorrelated with long-range tail $V$. apply our few particular interacti...

For any fixed positive integer k , let α denote the smallest ∈ (0,1) such that random graph sequence { G ( n, n -α )} does not satisfy zero-one law for set ε of all existential first-order sentences are quantifier depth at most . This article finds upper and lower bounds on showing as → ∞, we have = - 2 t )) -1 some function ) Θ -2 ). We also establish precise value when 4.