Sentence examples for equivalence system from inspiring English sources
The order-one periodic solution (Gamma') of system (1) is stable if int_{0}^{T} biggl(frac{partial P}{partial x}+ frac{partial Q}{partial y} biggr),dt< 0. Based on the Bendixson-Dulac theorem (see, e.g., [43]), we can find that system (1) is the topological equivalence system of the following system (12).
In what follows, (17) is called the Nash certainty equivalence (NCE) equation system (see (Huang 2010 Huang et al. 2007 2012 Huang et al. 2006)).
The equivalent system is obtained on the basis of the equivalence of the averaged system energy.
For the coupled BFSDE (14) and (15), we are going to decouple it and try to derive the Nash certainty equivalence (NCE) system satisfied by the decentralized control policy.
Numerical and simulation results are presented in this section to demonstrate the asymptotic equivalence between systems with stochastic and deterministic energy sources.
Going one step further, it will even become necessary to clear contradictory information with an expert who is sufficiently authorized to do this, before equivalence between systems is established.
Now we are ready to present the second main result of this paper in the following theorem, which states the asymptotic equivalence between systems with stochastic and deterministic energy sources in terms of MSE performance.
end{gathered} end{aligned} (19) From these notations we obtain equivalence of the system of equations (18) to the system of equations (17).
This in particular establishes equivalence of the system dynamics (effectively the same Ehrenfest equations for system observables) as well as equivalence of the outputs.
Other scaffold-capturing organization schemes include the molecular equivalence number classification system [38], the related chemotype approach [39] and hierarchical scaffold clustering (HierS) [40].
We now establish the equivalence between the system of extended regularized nonconvex variational inequalities (3.1) and a system of nonconvex variational inclusions.
