Sentence examples for have a unique representation from inspiring English sources

To have a unique representation, all node values are defined to be odd.

Finally, all itemsets in ({mathcal F}{mathcal S}_{C_{10} subseteq L_{C_{11}},nsubseteq C_{21}}) have a unique representation and are generated completely and distinctly by itemsets in ({mathcal F}{mathcal S}_{{C}_{10} subseteq L_{C_{11}},nsubseteq C_{21} }^*).

The rational spline scheme has a unique representation.

Hence, we deduce that y has a unique representation by (3.1), which implies that x has a unique representation by (3.2).

By considering the part (a), one can say that (y= y_{k})) has a unique representation.

Hence, every (x in b_{0}^{r,s}) has a unique representation, as desired.

This implies that (x=(x_{k})) has a unique representation, as desired in part (b).

Therefore, every (x in b_{p}^{r,s}) has a unique representation.

A base for is a nonempty convex subset of with such that every, has a unique representation, where and.

Then; the sequence is a basis for the space and any has a unique representation of the form.

A BK space (Xsupset phi) is said to have AK if every sequence (x=(x_{k})in X) has a unique representation (x=sum_{k=0}^{infty}x_{k}{e}^{ k)}).