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If used for establishing ranking of importance of variables it should be applied with caution, running several times the model (we suggest at least 100 times) with different order of the set of 10 12 variables (as recommended by the authors of the HP module; [18]).
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Some social franchises have established ranking systems to track the progress of franchisees and to incentivize strong performance.
Allometric relationships established ranked performance: small-sized individuals have higher mass-specific metabolic rates (photosynthesis, nutrient uptake and respiration) and sink more slowly than do individuals in the larger size-classes.
Furthermore, there are many problems on establishing rank formulas for generalized inverses of matrix products and their applications.
Especially, a comprehensive result on establishing rank formulas of (D - CA^{ i,ldots,j }B) was given in [26].
With a strong history of cue-sports, an established ranking tournament and the emergence of Aditya Mehta as a ranking-event finalist, could India - with a population of 1.25 billion - live up to its billing as 'the new China' and become a real hot-bed for snooker?
This can result in an earnest, single-minded ambition to join the established ranks.
The improv contests take various messy forms, but they most resemble the spontaneous dissing that can be heard in clusters around schoolyards and bus stops, wherever kids try to establish rank by matching wits.
To establish rank(G k ) ≤ 1, we use the complementarity slackness condition Tr G k Z k )=0 and prove rank(Z k )=M−1.
Now, to establish rank(X k )=1, we use the complementary slackness condition Tr(X k Z k )=0 and prove rank(Z k )=M−1.
Even among the older, more established ranks of the Republican Party, there are voices of support.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com