Sentence examples for useful in the subsequent from inspiring English sources

In this section, we present some lemmas which will be useful in the subsequent sections.

To this end, we first establish a partial relationship between the solution components and, which will be very useful in the subsequent analysis.

An important challenge concerning social design feedback will be to increase the proportion of useful comments or to effectively filter out comments that are not useful in the subsequent development process.

It follows from [[27], Theorem 2.36(i ], [[27], Theorem 2.39(i ], and [[27], Theorem 2.4(i)] that we have the following lemma, which is useful in the subsequent discussion.

The following statements offer an alternative definition for bisimulation, which is easily shown to be equivalent to the one presented in Definition 2.5 and is useful in the subsequent development: Definition 2.6: A finite partition Φ: S → P of the state space S of transition system T = (S, →, Y, h) naturally induces a quotient transition system T/~ = (P, →~, Y, h~) of T provided that.

This loss of power did, however, prove useful in the subsequent investigation, serving as a marker of exactly what circuit in the DC-10's labyrinthine electrical system had failed.

In each sample, we eliminated contigs shorter than 150 bp [ 20] in the two k-mer assemblies with the shortest median contig length, but kept all the contigs in the assembly with the longest median contig length in order to retain any information useful for bridging in the subsequent assembly steps.

To determine whether a single ultrasound scan at or beyond 40 weeks of gestation to detect a single deepest pool of amniotic fluid <2 cm and amniotic fluid index (AFI) <5 cm is clinically useful in the prediction of subsequent adverse pregnancy outcome.

In Section 2, we present some preliminaries which are useful for the subsequent analysis.

We first introduce new algorithms to calculate several transient measures of interest that are useful in the traffic characterization and subsequent performance evaluation of network resources.

In Section 2, we sketch the original Bregman method and the linearized Bregman method which are useful for the subsequent analysis.