Sentence examples for mapping and that from inspiring English sources

Suppose that (mathcal{L}:mathcal {A}times mathcal {A}to mathcal {A}) is a bilinear mapping and that ξ and η are mappings satisfying (mathcal{L} x,y)= xxi y)+ yeta(x)) for all (x,y in mathcal {A}).

In fact, having as -inverse-strongly monothat, isplies that is -Lipschitz continuous monotone mapping and that domain of is equal to.

Assume that (dJ=I-T), where T is a compact mapping, and that (p_{0}) is an isolated critical point of J. Then we have operatorname {ind} dJ,p_{0})=sum_{q=0}^{infty} -1)^{q} -1eratorname {rank}C_{q}(J,p_{0}). [10].

Proof Let A : = I − T, we note that A is a continuous accretive mapping and that 〈 j ( y − z ), T z 〉 − 1 r 〈 j ( y − z ), ( 1 + r ) z − x 〉 ≤ 0 is equivalent to 〈 j ( y − z ), A z 〉 + 1 r 〈 j ( y − z ), z − x 〉 ≥ 0. Thus, by a similar argument as in [24], the conclusions of (i - iv) hold.

In summary, the method works best using paired-end reads with a length at least 37 nucleotides and allowing one mismatch in the mapping, and that calls are more sensitive to read length than the number of reads.

It allowed compounds with diverse structures to find the common chemical features by ligand pharmacophore mapping, and that is different from CoMFA and CoMSIA with the common structure constraint.

"It was kind of secret, off the map, and that's why I chose it.

Buruma's plot strays all over the map, and that's part of the problem with this ambitious book.

"That's what we are moving forward to and everybody is on board in terms of that road map and that agenda and is committed to delivering that.

Along with banners and planter boxes came an information kiosk and tourist maps, and that was only in the first year.

For whatever reason, Apple decided to go its own way for maps, and that's awesome.