Sentence examples for exist a sequence of from inspiring English sources

For otherwise, there would exist a sequence of solutions of system (2.4) such that, for all with.

Then by Lemma 2.1, for, there exist a sequence of functions, a sequence of complex number, and such that (3.9).

Then by Lemma 2.1, there exist a sequence of functions, a sequence of complex numbers and such that (3.1).

Assume by contradiction that there exist a sequence of number { μ n } ⊂ [ 0, 1 ] and corresponding solutions { u n } of (2.1) such that ∥ u n ∥ ∞ → + ∞ as  n → + ∞. (2.3).

We assume without loss of generality that, then by Lemma 2.1, for, there exist a sequence of points, a sequence of positive numbers and a sequence of functions of such that (3.7).

If the following three conditions hold: (E1) there exist a sequence of positive scalars α ¯ and positive definite diagonal matrices P such that the following LMI conditions hold: Θ ˜ > 0, (4.3).

Then there exists a sequence of diffeomorphisms fk converging to f in the Sobolev Orlicz space W1,Φ Ω,R2).

It is shown that there exists a sequence of operators {Tn} such that dim(C*(Tn))<∞ and ‖T−Tn‖→0 if and only if C*(T) is exact.

The assumption indicates that there exists a sequence of inclusions of the manifold and its singular structures, called a weak-Lyapunov filtration.

Then there exists a sequence of positive numbers with, for.

Suppose that there exists a sequence of such that (2.5).