Sentence examples for compact note from inspiring English sources

Note (S_{alpha} phi R_{alpha} in M C,C)) is compact (note ϕ is compact and the map (x mapsto q_{1}(p_{1}^{-1}(x))) is upper semicontinuous with nonempty compact values [2]).

Also, it isobvious from (e) that ⋂ y ∈ M F ( y ) ⊆ N and so ⋂ y ∈ M F ( y ) is compact (note that F ( y ) is closed for each y ∈ Y and M is compact).

Let (j_{alpha} C_{alpha} hookrightarrow W ) be the inclusion and note (psi_{alpha} phi j_{alpha} in M(C_{alpha}, C_{alpha})) is compact (note ϕ is compact and the map (x mapsto q_{alpha}(p_{alpha}^{-1}(x))) is upper semicontinuous with nonempty compact values [2]).

Hence by Lemma 1.3there exists x ¯ ∈ K such that x ¯ ∈ ⋂ x ∈ K F ( x ). and it is easy to see that the solution set of IVEP is equal to the set ⋂ x ∈ K F ( x ) and hence x ¯ is a solution of IVEP and further it is compact (note ⋂ x ∈ K F ( x ) ⊆ ⋂ x ∈ M F ( x ) ⊆ N ) and hence the proof is complete.

Towelroot is reported to have worked on the Sony Xperia Z1 Compact, Samsung Galaxy Note 3, Google Nexus 5, Google Nexus 7 (2013), and the LG G2 Android phones.[3].

The fact that measurable cardinals are weakly compact was noted in Tarski [1962].

Moreover, considering the operator (J: Xto X^) given by langle Ju, vrangle= -int_{Omega} u v,dx quad text{for } u,v in X, it can be seen that J is compact, by noting that the embedding (i: L^{p}(Omega)hookrightarrow L^{p'}(Omega)) is continuous and (J=-I^circ icirc I).

In general, à priori the existence such a kind of measure μ is not known, since there is not much information on topological properties, such as compactness, of the set of all p-adic measures defined even on compact spaces.b Note that certain properties of the set of p-adic measures has been studied in [32, 33], but those properties are not enough to prove the existence of the limiting measure.

Moreover, with the compact model, we note a decrease of the DER from 4.32% to 2.17% (always with FDW) which corresponds to a relative decrease of about 50%.

The new version also now allows paying users to make the icons smaller and hide the labels to make the widget more compact, the company notes.

If compact lipiodolization was noted and no viable HCC was identified, than radiologic evaluation and tumor marker measurement were done within 3 months to assess HCC recurrence.