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The proof, assuming the completeness of, is similar to the above.
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In [8], we assume the completeness of B. Exactly speaking, in [8], we obtained a theorem connected with Geraghty's fixed point theorem [12].
The ((CLRg))-property has two main advantages: (1) usually, it is not necessary to assume the completeness of the G-metric space; and (2) usually, the common limit gu is a point of coincidence of f and g, that is, (fu=gu).
Completeness levels between 1996 and 2006 were determined by assuming that the completeness of death registration follows a logistic trend over time; that completeness in any age group did not decrease over the period; and that the trend in completeness is smooth (i.e. fluctuations in the data are not due to fluctuations in completeness).
We assumed that the completeness and misclassification of diagnostic coding in our datasets were similar to those in other administrative databases.
In this theorem, we consider only a completeness hypothesis without assuming the continuity of the nonself-mapping.
In this theorem, we consider only a completeness hypothesis without assuming the continuity of the non-self mapping and the approximate compactness of the subspace.
In this theorem, we consider only a completeness hypothesis without assuming the continuity of the non-self-mapping and the approximatively compactness of subspace.
Assuming completeness of the eigenfunctions, the rate of decay of end effects is then given by the real part of the eigenvalue with smallest positive real part.
A sensitivity analysis was conducted on the specified prior variance, τ2, by using high, medium, and low τ2 values that assumed 95% of the completeness proportions were within the following ranges: 2.2%–95%, 7.3%–85%, and 12.9%75%%, respectively.
Most of our results assume the existence of a good candidate for a fixed point instead of completeness.
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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