We use the vorticity formulation to study the long-time behaviour of solutions to the Navier-Stokes equation on R(3). We assume that the initial vorticity is small and decays algebraically at infinity. After introducing self-similar variables, we compute the long-time asymptotics of the rescaled vorticity equation up to second order. Each term in the asymptotics is a self-similar divergence-fre...

Let f : C −→ C be a polynomial function. By definition c ∈ C is a regular value at infinity if there exists a disc D centred at c and a compact set C of C such that the map f : f(D) \ C −→ D is a locally trivial fibration. There are only a finite number of critical (or irregular) values at infinity. For c ∈ C and a sufficiently large real number R, the link at infinity Kc = f (c) ∩ S R is well-...

The distributed SLAM system has a similar estimation performance and requires only one-fifth of the computation time compared with centralized particle filter. However, particle impoverishment is inevitably because of the random particles prediction and resampling applied in generic particle filter, especially in SLAM problem that involves a large number of dimensions. In this paper, particle f...

This paper studies certain inverse problems in the optimal frequency-domain synthesis of robust controllers, in both the 2-norm and the infinity-norm. These inverse problems identify the class of controllers which are optimal for some choice of weights. Their implications for loopshaping are discussed. Keywords—Inverse optimality, loopshaping, H2 control, H∞ control. c.t/ g− + K.s/ u.t/ G0.s/ g...

The origin of jets emitted from black holes is not well understood; however, there are two possible energy sources: the accretion disk or the rotating black hole. Magnetohydrodynamic simulations show a well-defined jet that extracts energy from a black hole. If plasma near the black hole is threaded by large-scale magnetic flux, it will rotate with respect to asymptotic infinity, creating large...