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The Green's functions for the indentation of an elastic layer resting on or bonded to a rigid base by a line load are found efficiently and accurately by a combination of contour integration with a series expansion for small arguments.
Our method exhibits the worst results for small arguments, but the errors decrease dramatically with argument increasing.
Numerical result shows that 20 points are capable of producing an accuracy of seven-decimal place for small arguments.
Moreover, the sum of Rayleigh fading used in the derivation of BER is only an approximation valid for small arguments only.
For small arguments of sinh, Equations 3 and 6 result in linear MKT [31]: σ cos θ 0 − cos θ = ζU (7).
For this reason we argue that it is incorrect to fit to either the logarithm or the logit of target cell frequencies (the logit function being approximately equal to the logarithm for small arguments).
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In a subsequent step, the complete elastodynamic fundamental solution along with its spatial derivatives and an asymptotic expansion for small argument, are all derived in closed-form using the Radon transform.
We can obtain (zeta (2n)) through (4) systematically for small argument.
For smaller arguments, the inverse is extended by zero, and for higher arguments, the asymptotic unbiased inverse transform is used, see [25].
which in the limit of small argument for the exponential (k η >> 2 Λ) becomes.
The shift-parameters x0 = k0, L0 account for the potential flattening of the decay at small arguments discussed above.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com