Sentence examples for exists a minimal from inspiring English sources

As presented below the algorithm Minimize, when called on the output of FindAll, returns, if exists, a minimal hyperpath linking a given target to the source.

By Lemma 2.3, there exists a minimal such that.

(i there exists a minimal such that and ; (ii there exists such that.

If is compact and continuous, then there exists a minimal such that.

(i there exists a minimal such that and ; (ii there exists a maximal such that.

Then there exists a minimal compact subset of such that (3.14).

Then, there exist a minimal weak solution and a maximal weak solution of (2.3) satisfying (2.10).

Despite the pluralism of the Vienna Circle's views, there did exist a minimal consensus which may be put as follows.

By Theorem 2 there exist a minimal, nonempty, T-invariant, weakly compact, and convex subset E. By hypothesis there exists a weakly convergent a.s.p. sequence ((x_{n})) in E, say weakly convergent to (xin E).

From Theorem 2 there exist a minimal nonempty, weakly compact, and convex T-invariant subset E of C and (alpha>0) such that for each a.s.p. sequence ((z_{n} )) in E limsup_{nrightarrowinfty} Vert z_{n} - z Vert geqalpha, quad z in E. Consider an a.s.p. sequence ((x_{n})) in E, which exists by hypothesis.

Hence, if T has two minimal period-two solutions, then there exists a third minimal period-two solution.