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The dynamic behaviour when crossing singular points is compared with a closed form standard transform.
In particular, the possibility to estimate with sufficient accuracy the behavior of natural rubber at any intermediate concentration of S-TBBS-DPG having engineerelevancevance has been proved, calibrating the model by means of simple closed form standard best fitting on few experimental data.
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Closed form formulas to estimate the standard deviation of INL, DNL and the power consumption are derived.
The obtained closed form analytical expressions for stress can be a standard reference tool in this important area of stress-modulated soft tissue growth.
Closed form solutions for the calculation of the mean value, the standard deviation and the minimum and maximum values of the factor of safety, are thus provided.
Under standard prior assumptions, all fully conditional distributions have closed form, and samples from the joint posterior distribution can be obtained via Gibbs sampling.
Since this term is non-local, we introduce a non-standard adjoint state, which allows to obtain a closed form for the topological derivative.
The standard errors of the two-step logistic and two-step Probit models cannot be expressed in closed form and were calculated using bootstrapping methods (using 1000 iterations).
The elastic energy can be expressed in closed form, and with the availability of high speed computing the atomic misfit energy in the glide plane can be calculated by standard numerical integration without any difficulties.
Analytical closed form solutions have been considered.
Closed form SW dispersion equations are introduced.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com