Analytic theory of polynomials

TL;DR: In this paper, it was shown that the Hausdorff geometry of the equilibrium points and the charged particles is controlled by the weighted standard deviation of the latter, which is defined as a preorder on sequences of vectors in Euclidean space induced by the Choquet ordering for atomic probability measures.

TL;DR: This work proves that if the complexity of root detection is sub-linear (in a refined sense), relative to the straight-line program encoding, then NEXP⊆P/poly is NP-hard with respect to $BPP-reductions.

TL;DR: In this article, the equations of motion for two models of circular cosmic string loops with windings in a simply connected internal space were numerically solved and bounds on the physical parameters that ensure dynamical stability of the windings were derived.

TL;DR: The act of a person juggling can be viewed as a Markov process if we assume that the juggler throws to random heights and compute the steady state probabilities in terms of the Stirling numbers of the second kind as discussed by the authors.