The results are formally proven and supported by simulations.
The approach is both formally proven and experimentally validated on a lab apparatus.
The convergence properties of the overall solution proposed have been formally proven.
This was first pointed out by Villeneuve (2003) and formally proven by Olivella and Vera-Hernandez (2010).
We then demonstrated a theoretical framework whereby such experimentally discovered relations can, in many cases, be formally proven.
Ultimate boundedness of the observation errors is formally proven and an arbitrarily small ultimate bound is then achieved.
The computational problem defined in the NP-StructurePredictor system has been formally proven to be NP-complete; it constitutes a chemical substituent core combinatorial problem (CSCCP) [20].
The chaotic properties of a single-neuron have been formally proven using the theory of Lyapunov analysis and by examining its Jacobian matrix.
It is formally proven that the inclusion of an additional inlet stream, free of the limiting substrate, enables global controllability and thereby provides the solution to the controllability problems pointed out by Szederkényi et al. [30], fact that have not been reported previously.
Since the adversary knows U, but not T, he will only learn that two inputs from x 1,x 2,x 4,x 5 sum up to 7, and two inputs from x 1,x 2,x 3,x 4,x 5 sum up to 4. The effects of this new security measure are formally proven in Theorem 1 of the next subsection and are independent of the output function.
The existence of human NK cells displaying regulatory properties has been already hypothesized but not formally proven [5].
