Then (as proved in [3]), Theorem 1.1 holds (once again, the LS condition amounts to proper ellipticity plus complementing condition and proper ellipticity is equivalent to ellipticity if and ) and it is straightforward to check that the proof of Theorem 1.2 carries over to this case if If so, Corollary 2.1 is also valid, with a similar proof and an obvious modification of the function spaces.
The magnitude of its impact on growth, respectively biomass accumulation or carbon sequestration, depends on complementing conditions like former nutrient deficiencies, moisture and stand age.
By Schur complement, condition (3.2) is equivalent to P A + A T P + ε N T N + ε − 1 P D 1 D 1 T P < − μ 1 P. (3.7).
By Schur complement, condition (3.3) is equivalent to P + α 2 P ( ε 2 I − α 2 P ) − 1 P + ε 2 I < μ 2 P. Substituting the above inequality into (3.9) gives V ( t k + ) < μ 2 x T ( t k ) P x ( t k ) = μ 2 V ( t k ).
This is done by introducing the auxiliary variables Q (5) and Q (6) to relax the equality constraints on the conditional covariance matrices R 2 | R ( 5 ) = R 2 ( 5 ) − R 2 R ( 5 ) R R ( 5 ), ‡ R 2 R ( 5 ), H and R 1 | R ( 6 ) = R 1 ( 6 ) − R 1 R ( 6 ) R R ( 6 ), ‡ R 1 R ( 6 ), H, respectively, before applying the (generalized) Schur complement condition.
The monitoring of bubble formation using AE technology can complement other condition monitoring methods, all of which are aimed at reducing energy losses and improving life cycle costs.
The potential for NIR to be used by conservators as a non-invasive tool for the assessment of textiles, complementing current condition audit practices in use at heritage institutions is also discussed.
To describe tissue flow, Equations 1– 5, which characterize local tissue properties, have to be complemented by the condition of force balance.
This global information is complemented by phase conditioned Abel transformed emission images.
In that case, Eq. (69) needs to be complemented by additional conditions regarding the processes X k and βk,l.
