Sentence examples for exists the first from inspiring English sources

There exists the first simplex in that sequence, call it σ j 1, such that for all j > j 1 the last barycentric coordinate of all vertices of σ j in S 2 are less than k 1 / m.

In this case, given a sequence where one gene exists, the first step would be to search for a homologous of it and run our program using in a useful way some information concerning the homologous gene.

Inasmuch as It exists, the First Principle partially coincides with the subject-matter of metaphysics, so that theology is included in ontology: the existence of God is part of existence (Ilāhiyyāt, I, 2, 14, 4 10: the Principle is the Principle of part of being).

Thus, in view of the finiteness of T and the fact that no ((n-2))-face (sigma') of some (sigma^{j}), (jin[J+1]), with (l sigma')=[n-1]) is contained in (partial({S})), we conclude that there exists the first index (Jinmathbb{N}) such that (0in l sigma_{J})).

If there exists the first component (widehat{x}) of an eigenvector of H associated with some eigenvalue (widehat{lambda }) such that (Delta widehat{x})=0) and (3.4) holds, then the root vector system of H is complete in the CPV sense in (Xtimes X) if and only if the collection of the first components of the root vector system of H is a Schauder basis in X.

The first venue I went looking for no longer exists, the second had hugely disappointing stock and the third was a veritable mad house.

Thus there exists the third critical point of (tilde{I}(Y)).

There also exists the second BPP frequency range for ω > ωp.

Outside the crossing region, where only one fiber exists, the second component is aligned with the first.

When there is no societal entitlement, the first or second method must be used; and when it exists, the third must be used.

The 2012 election was "baptism through fire" for the conservative media, he said, especially since some outlets didn't even exist the first time Obama ran.