This study has demonstrated, for the first time, a microfluidic autonomous analyser for the direct determination of nitrate, incorporating a modified version of the chromotropic method resulting in a direct, quick, inexpensive and simple procedure to measure nitrate in situ.

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Lyapunov functions are an important tool to determine the basin of attraction of equilibria. In particular, the connected component of a sublevel set, which contains the equilibrium, is a forward invariant subset of the basin of attraction.One method to compute a Lyapunov function for a general nonlinear autonomous differential equation constructs a Lyapunov function, which is continuous and piecewise affine (CPA) on each simplex of a fixed triangulation. In this paper we propose an algorithm to determine the largest connected sublevel set of such a CPA Lyapunov function and prove that it determines the largest subset of the basin of attraction that can be obtained by this Lyapunov function.

No abstract