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Any probability density function (PDF) can be approximated with an MTE potential, which can always be marginalized in closed form.
The front for the slowest crack can be approximated with an ellipse of semi-axes a = 3h and b = 0.85h (h stands for the specimen thickness), which agrees well with the conclusion inferred from a propagation velocity lower than 1700 m/s by Sherman and Be'ery16.
The first validation rule is based on the assumption that a generic brushstroke can be approximated with an elliptical shape.
The number of sampling points can be approximated with an upper bound or increased on the fly should a peer be unable to interpolate a polynomial.
The optimal IBO that minimizes the BER can be bounded by the proposed expressions when the relay-destination channel is flat in frequency and it can be approximated with an acceptable error for frequency-selective channels.
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In parallel to the univariate setting, the distribution of λ ~ ∗ 1 can be approximated with a Satterthwaite approximation: λ ~ ∗ 1 ν ∗ / λ ∗ 1 ∼ χ 2 ν ∗ with ν ∗ = b ν est · ∊ ^ d / ∊ ~ n.
The former can be approximated with a variety of techniques including numerical integration and asymptotic formulas.
The change of the mean nanotube length with time could be approximated with a second-order exponential decay function.
For higher energies above this value, the EEDF could be approximated with a Maxwellian fit in the limited interval of energies.
However, DalkS can be approximated with a constant factor.
When N is large enough, the binomial random variables can be approximated with a Gaussian distribution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com