Sentence examples for dual sequence from inspiring English sources

where the dual sequence is defined by a similar relationship as with the initial data.

Indeed, the sequence of norms in, defined by, is a Cauchy sequence, but the dual sequence is not.

The idea of dual sequence spaces was introduced by Köthe and Toeplitz [36] whose main results concerned α-duals; the α-dual of sequence space X being defined as X α = { a = { a k } : ∑ k | a k x k | < ∞  for all  x = { x k } ∈ X }.

The idea of dual sequence spaces was introduced by Köthe and Toeplitz [4] whose main results concerned α-duals; the α-dual of X ⊂ s being defined as X α = { a = ( a k ) ∈ s : ∑ k | a k x k | < ∞  for all  x = ( x k ) ∈ X }.

More precisely, when each g i is convex for i = 1 and 2, the dual sequence {λ(t)} converges to an optimal dual solution of (5); if further the primal sequence {θ1 t) T θ2 t) T T } is bounded, the sequence converges to an optimal primal solution of (5).

The idea of dual sequence spaces was introduced by Köthe and Toeplitz [34] whose main results concerned α-duals; the α-dual of a sequence space X being defined as X α = { a = ( a k ) : ∑ k | a k x k | < ∞  for all  x = ( x k ) ∈ X }.

Isolate 01/51 was dual sequenced, also on the Roche 454 platform.

The procedure to estimate θ using data from dual sequencing applications is as follows.

In this situation, we strongly suggest using dual sequencing applications to avoid this kind of errors.

SS and CIW conceived using dual sequencing applications to correct sequencing errors and helped to draft the manuscript.

We then propose dual sequencing applications to improve the pooled-line method for analyzing pooled samples of diploids.