The Stone-Weierstrass theorem can be applied to conclude that is surjective.
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.
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)).
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,) ).
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.
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).
To conclude a long discussion, QC methods have been applied to a number of RNAP and DNAP mechanisms.
Now, the same reasoning as that used for the susceptible endemic equilibrium component is applied to (3.18) to conclude that, since there is a nonzero vaccinated population for at most two endemic equilibrium points with, then (3.19).
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.
