Sentence examples for derived sections from inspiring English sources

Another corollary of Proposition 8.4 is extended functoriality for the categories of derived sections.

The full subcategory in ({text {Sec}}(M(I),rho ^*mathcal {C})) spanned by derived sections is denoted by ({text {Sec}}_{rho }(M(I),rho ^*mathcal {C})).

As it turns out, if restrict our attention to homotopy special derived sections, then we do not even need to consider the simplicial expansion (Delta I).

In order to apply Proposition 8.4, it is useful to obtain a version of the isomorphisms (7.7) and (7.8) valid for derived sections.

We can also combine this construction with Example 8.12 to apply it to derived sections over the category (I times [1]^o).

For any two derived sections (A,B in {text {DSec}}(I,mathcal {C})), we have a natural spectral sequence converging to ({text {Hom}}^cdot (A,B)) whose (E_1 -term is givE_1 -termis{aligiven E_1^{n,m} = prod _{i in overline{I}_n}{text {Hom}}^m(overline{L}_i(A),overline{M}_i(by).

Both the experimentally and numerically derived section capacities were compared with the strength predictions determined from the current European code, the American specification and the Australian/New Zealand standard, allowing the applicability of each codified method to be assessed.

end{aligned} (9.15 Any object (E in {text {Ho}}(mathcal {C})) defines a constant derived section (E_X in {mathcal {D}} X,mathcal {C})).

This section, derived from section 21a of the Bankruptcy Act [section 44(a) of former title 11], requires the debtor to appear at the meeting of creditors and submit to examination under oath.

This section is derived from section 44b of the Bankruptcy Act [section 72(b) of former title 11] without substantial change.

The stepwise optimization algorithm is derived in Section 5. Section 6 lists evaluation results and Section 7 concludes our study.