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It is shown that a valid projection property for any basis of the space, and in fact any element, means that they are basis-free.
A Markov-population model can provide a valid projection of the future workforce, provided that the error present in the projection is small and quantifiable, i.e. the inflow and outflow parameters are known with certainty.
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On the other hand, generic models addressing broad clinical questions that can be adapted from one patient to another, can often make valid projections about specific outcomes, such as life expectancy, quality-adjusted life expectancy, and cost-effectiveness issues, and represent a useful approach to clinical decision making.
The Centers for Disease Control and Prevention notes that it "is difficult to make valid projections of heat-related illness and death under varying climate change scenarios" and that "heat related deaths are preventable, as evidenced by the decline of all-cause mortality during heat events over the past 35 years".
However, if a longitudinal covariate, such as age or quadratic mean diameter, is used then valid future height projections can be obtained directly using the generalized h-d model.
In the comparison of methods, direct measurements of widths of resorption zones or subsidence were not used due to difficulties in assigning valid measuring points from projection radiographs on sectional images and also due to the purpose of the study to assess the possible added value of tomosynthesis to conventional hip prosthesis radiography, not its replacement.
10For Croatia, these projections are valid under the (counterfactual) assumption of no EU accession.
end{aligned} (We note that the projection formula is valid not only for quaternion algebras but for the symbol algebras of any degree (n) provided that (n) is prime to (mathrm{char} K) and (K) contains a primitive (n th root of unity).
This result suggests that the Ret CFP allele is a valid tool for visualizing central projection deficits of RA mechanoreceptors at E13.5.
Theorem 2.4 is still valid if we replace the metric projections with the generalized projections as follows: Theorem 2.5.
For food security and environmental health risk from climate change taking the mean of the wide range of results (as AR5) of the crop model projections is not valid- worst-case scenarios must be used.
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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