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The iterative sequences in Theorem 3.5 starting with a simple function is helpful for calculating.
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But being able to calculate the derivative of simple functions is both more advanced and more widely used.
Nevertheless, the use of simple functions is recommended to keep up with the stated goals.
Each ℛ-simple function is of course η-integrable - recall that η comes from a functional of ( L 1 ∗ - and then the density of this set in L p gives that the inequality involving ϕ 0 that was proved using Ky Fan's lemma can be rewritten as ∥ T 0 ( f ) ∥ ≤ ( ∫ | f | p d η ) 1 / p, f ∈ L p , since for such functions, ∫ | f | p d η = 〈 | f | p, ϕ 0 〉.
In practice, once the derivatives of a few simple functions are known, the derivatives of other functions are more easily computed using rules for obtaining derivatives of more complicated functions from simpler ones.
To investigate the relationship between imputation reliability for a SNP and the factors that may influence its value, a few simple functions were used.
Instead of considering all the higher-order terms, a simple aggregation function is used.
The exact bit error rate of this scheme is derived, and a simple threshold function is proposed.
Since the simple distribution function is defined on the circle, for simplicity, it is termed as circular function hereafter.
Since the simple distribution function is defined on the spherical surface, for simplicity, it is termed as sphere function hereafter.
A simple bias function is introduced and bias correcting formulas are proposed for both complete and censored data.
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