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This statement is not entirely valid because perturbation is not variation such that it may be corrected by applying the variational principle to eq. (2), for example.
It is possible that there is a pattern of decadal variation such that the Arctic will stop warming so quickly, and so Arctic sea-ice decline could appear to stall, while the increase in global temperatures will resume a rapid increase.
Then there exists a sequence of maps convergent pointwise on I to a map f : I → K of bounded variation such that.
( H 0 ) A is an increasing function of bounded variation such that G ( s ) ≥ 0 for s ∈ [ 0, 1 ] and 0 ≤ C < 1, where is defined by (2.9).
Theorem 1.3 Let G : [ a, b ] → R be a function of bounded variation such that G ( a ) ≤ G ( x ) ≤ G ( b ), G ( b ) > G ( a ), (2).
Using the Riesz representation theorem, there exists a 2 × 2 matrix function η , θ ∈ [ − 1, 0 ] → R 2 × 2 whose elements are of bounded variation, such that L μ ϕ = ∫ − 1 0 d η , ϕ ∈ C ( [ − 1, 0 ], R 2 ).
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Note that Rscale showed clear seasonal variations, such that smaller values occurred in winter/spring and larger values occurred in summer/autumn.
This is due to vast linguistic variations such that the lexical category of a Chinese word might not be completely consistent across different contexts.
ICD-9 CM codes for surgical complications had some variations such that unknown biases may have arisen in the estimation of prevalence rates.
The tests were adjusted to high task difficulty by selection of small pitch variations such that the tests were sensitive to impairments [ 10, 15].
Yet another 425 bp transcript (GenBank accession no. EF050083 and EF051516) demonstrated variations such that the point nucleotide changes were either shared between the spermatozoa/gonads or spermatozoa/somatic tissues (Additional file 11).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com