Sentence examples for for which necessary from inspiring English sources

Near-optimality for one kind of stochastic control problem with controlled diffusion and nonconvex control domain was studied in [14], for which necessary and sufficient conditions of near-optimality were established.

In [13] we have investigated a class of boundary conditions for which necessary and sufficient conditions were obtained such that the associated operator pencil consists of self-adjoint operators, while in [14] we have continued the work of [13] in the direction of [12] to derive eigenvalue asymptotics associated with boundary conditions which lead to self-adjoint operator representations.

Consequently, using terms from these two terminologies that have been linked, these new subsumptive inferences can only be made between subject terms for which necessary and sufficient definitions can be created (e.g. substance-transport terms) and not with the object terms (e.g. the substances that are being transported) used in these definitions.

Further characterization revealed the local region in which necessary conditions for limit-cycle oscillation were met.

The analysis can be extended easily to multidimensional splited advection for which a necessary stability condition is presented.

There are many others, however, for which the necessary treatments are widely available and for which a plan of attack has already been drawn.

We have the capacity for a big bomb now, for which a necessary command-and-control system is also in place.

The stability condition refers to the asymptotic sample stability, for which the necessary and sufficient condition is that the largest Lyapunov exponent be negative.

Finally, the results are employed to cope with the decentralized set-point formation control problem, for which some necessary and/or sufficient conditions are developed.

(1) Quantum correlations exhibit temporary freezing and permanent freezing even at high temperature of the environment, for which the necessary and sufficient conditions are given by three propositions.

We focus on the period 1995 2006, for which data necessary for computing index number formulae is available for the largest number of 18 countries.