Sentence examples for under a small condition from inspiring English sources

Under a small condition on the initial value, we prove the global existence and optimal decay estimate of solutions.

In the supercritical case, they obtained local results in H s, s > ( N − α ) / 2 + 1 and extended to be global under a small condition ∥ θ 0 ∥ H s ≤ c ν, for s > N / 2 + 1, where c is a small fixed constant.

A small number of training samples are created by random approach with FEA codes for building the Gaussian process regression (GPR) surrogate model, and the highly nonlinear and implicit performance function is approximated by GPR with an explicit formulation under a small sample condition.

Furthermore, a quasi-ISS/ISDS reduced-order observer for the whole system is designed under a small-gain condition, where the observers for the subsystems are used.

For clusters that are active only under a small subset of conditions, there is less ground for a co-regulation assumption.

Methods that incorporate such information are needed when a gene may belong to multiple pathways or when a pathway is activated under a small set of experimental conditions.

More complex demographics such as a phylogenetic tree structure have been studied but generally under a small set of selective conditions [ 10- 12].

Here, mRNA expression profiles are collected in a database of a range of different cell lines exposed to substances with known mechanisms under a small number of defined conditions.

(Yang et al. 2006) developed the efficient TS method with a mixed objective function for the one dimensional cutting stock problem under a small amount of various cutting conditions.

Consequently, the trend seen in Table 10 suggests additive regulation, that is, when genes are periodically expressed under more conditions, more of the inferred combinations consist of supersets of combinations specific to genes periodically expressed under a smaller set of conditions (see Additional file 3 for all hierarchies).

Under the Dolph-type condition and a small periodic damping term condition, the existence and the uniqueness of a periodic solution have been proved by a constructive method.