Sentence examples for given any sequence from inspiring English sources

Given any sequence, the notation means and.

Given any sequence the notation means and For any matrix entry.

Given any sequence, the notation means that and For any matrix entry.

if given any sequence ({ x_{n} } ) in X, the conditions (x_{n}rightarrow x) and (varphi ( x_{n} ) rightarrow r) imply (varphi ( x ) leq r).

Given any sequence ((z^{n}) subset B), from the positive invariance of B we see that (S t z^{n} = (u^{n}(t),u^{n}_{t}(t),eta_{n}^{t})) is uniformly bounded in (mathcal{H}).

Kirk and Saliga [24], p.2769, say that for a Hausdorff space ((X,tau)) a mapping (psi: X rightarrow mathbb {R}) is τ-lower semicontinuous from above if given any sequence ((x_{n})_{n inmathbb{N}}) in X, the conditions: ((psi(x_{n}))_{n inmathbb{N}}) decreases to α and (lim_{n rightarrowinfty}x_{n}= x), yield (psi(x) leqalpha).

F is said to be lower semicontinuous at, if we give any sequence converging to and any, there exists a sequence that converges to. is said to be continuous at if it is both upper semicontinuous and lower semicontinuous at.

Other bands in the reduced residual protein fraction (indicated by dots in Fig.  2A, lane 2) did not react with the antibodies and did not give any sequences on Edman degradation (carried out as described by Shewry et al., 2009 b ).

Given any finite sequence (or vector ), where, its (periodic) extension is the sequence defined by.

Given any unbounded sequence, Zeller [10] constructed a regular matrix with convergence domain.

Given any convergent sequence ({{x}_{j}}subset{mathcal{C}}), such that ({x}_{j}rightarrow{x}_{0}) as (jrightarrowinfty).