Sentence examples for obviously a sequence from inspiring English sources

Obviously, a sequence of pairwise NQD random variables is a family of very wide scope, which contains sequences of pairwise independent random variables.

Obviously, a sequence of pairwise NQD random variables is a family of very wide scope, which contains a pairwise independent random variable sequence and a negatively orthant dependent (NOD) random variable sequence as special cases.

We say that { x n } is Cauchy if and only if for every ε > 0 there exists a positive integer N = N such that d ( x n, x m ) < ε for all m, n > N. Obviously, a sequence { x n } in a quasi-metric space is Cauchy if and only if it is left-Cauchy and right-Cauchy.

Obviously, a sequence ({ vec{x}_{i} }_{i inmathbf{Z}} subsetmathbf{C}^{n}) satisfies the first-order matrix difference equation (17) if and only if begin{aligned} vec{x}_{i} = mathbf{A}^{-i} vec{x}_{0} end{aligned} (20) for all (i inmathbf{Z}), where we set (mathbf{A}^{-i} = ( mathbf{A}^{-1} )^{i}) for each integer (i geq0).

Obviously, a -mixing sequence is a -mixing sequence.

Obviously, if a sequence of H-valued random vectors is NA, then it is CNA.

Obviously, if a sequence of random vectors in Hilbert space is NA, it is CNA.

If (x_{0}in bigcup _{i=1}^{m}A_{i}) then Picard's sequence ({ f^{n}x_{0} } ) is obviously a Cauchy sequence (the proof is as in [6]) and converges to some (zin bigcup _{i=1}^{m}A_{i}).

Indeed, every sequence of contractions (applications of rule 2, combined as necessary with alphabetic changes of bound variables) of a wff is finite; obviously, if such a sequence cannot be extended, it terminates with a wff in β-normal form.

Only once does the strain show: the invading French turn up on the English coast in a sequence rather obviously lifted from Saving Private Ryan, even down to the carnage in the water.

"But that," he says indignantly, "came after a sequence where some obviously quite thick woman was having a pop at me about taking her kid's sticky toffee pudding away, and we gave them fruit and yoghurt instead.