Sentence examples for normalized basic from inspiring English sources

Obviously, is also a normalized basic sequence.

Let be a normalized basic sequence in and let.

For every normalized basic sequence in a Banach space and for every, there exist a subsequence and a normalized basic sequence such that for all, and, (2.5).

A normalized basic sequence generates a spreading model if for some, for all, and, (2.22).

To study the propagation of ion acoustic waves, we write the following normalized basic fluid equations.

An equivalent norm is constructed onTso that ‖s1+s2‖<2 whenever (sn) is a spreading model of a normalized basic sequence inT.

We prove that there exist Banach spaces not containing ℓ1, failing the point of continuity property and satisfying that every semi-normalized basic sequence has a boundedly complete basic subsequence.

Every normalized block basic sequence of the canonical basis of (g(mathcal{M},Delta^{(m)}, v, p)) is 1-dominated by the canonical basis of (l_{p}).

Suppose (y_{k}= sum_{j=p_{k}}^{p_{k+1}-1}a_{j}g_{j}) forms a normalized block basic sequence and satisfies (lim_{jrightarrowinfty}a_{j}=0).

Among several consequences we show that, provided E is order continuous with Fatou property, E contains an order isomorphic copy of ℓp if and only if either E contains a normalized ℓp-basic sequence which converges to zero in measure, or E contains the function t−1/p.

As the Bcd variance can be exaggerated in the data normalized by the basic method, we considered the same ensemble of Bcd profiles but normalized by the alternative artificial normalization method, which minimizes variance in the ensemble (see Methods).