Sentence examples for be applied to conclude from inspiring English sources
The Stone-Weierstrass theorem can be applied to conclude that is surjective.
If (|sigma '| ge 2), then induction can be applied to conclude that (n sigma ') subseteq mathrm{ns(dom}({p}))) = mathrm{ns}({p}) = mathrm{ns}(p)); hence, (n sigma ) = {gamma } cup n sigma ') subseteq {gamma } cup mathrm{ns}(p)).
Then, induction can be applied to conclude that there exist two transitions (t"_1) and (t"_2) such that ({mathrm{dec}} overline{q}_1)[t"_1rangle {mathrm{dec}} overline{q}'_1)), ({mathrm{dec}} overline{q}_2)[t"_2rangle {mathrm{dec}} overline{q}'_2)), with (overline{p}'_i equiv overline{q}'_i) for (i = 1, 2).
Then, induction can be applied to conclude that (q_1 {{{,mathop {longrightarrow }limits ^{sigma _1}}}} q'_1) and (q_2 {{{,mathop {longrightarrow }limits ^{sigma _2}}}} q_2'); hence, by rule (S-Com), also (q_1 q_2 {{{,mathop {longrightarrow }limits ^{sigma }}}} q_1' q_2') is derivable, and by rule (Cong), (p_1 p_2 {{{,mathop {longrightarrow }limits ^{sigma }}}} q_1' q_2'), as required.
By a careful calculation (there are 21 nontrivial cases) it can be checked that condition (3.2) (i.e., condition (3.3)) is satisfied for all X, S ∈ X 2. Hence, Theorem 2 can be applied to conclude that f has a coupled fixed point (which is ( 0, 0,) ).
For example, latent variables were applied to conclude the natural and social effects on grassland productivity in Mongolia and Inner Mongolia, China (Chen et al. 2015).
Energy consumption indexes from modeling of sample society and Reference Buildings were applied to conclude the boundaries for grades A G of the label.
It goes on to other information management tasks and considers how the concepts and methods developed for retrieval may be applied to these, concluding by arguing that such ways of dealing with information may also have wider relevance to AI.
So Theorem 2 can be applied to F in this example to conclude that F has a (unique) coupled fixed point ( 0, 0 ), while Theorem 1 cannot be applied since (1.6) is not satisfied.
If this cut-off is to be applied to our data, we can conclude that while kallikrein gene expression is absent or low in breast cancer, medium-to-high levels of expression are found in the normal breast.
