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Comparison between empirical correlations is given in Table 8.
The power spectrum of correlations is given by ( widehat{rho }_{ f,g } ( lambda ) := int _0^infty rho _{f, g} ( t ) e^{ i lambda t } dt ).
The second best result among the empirical correlations is given by the correlation of Al-Khafaji et al. (1987) which also uses the functional form of f(μ od, R s).
Unlike the results in Sections 3 and 4 where an identity correlation matrix is considered, in this case, the positive definite matrix Ced that expresses the correlations is given by [36] C ed = 1 p 0 … 0 p 1 p ⋮ 0 p 1 ⋱ 0 ⋮ ⋱ ⋱ p 0 … 0 p 1 (90).
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Since we expected weight reduction to correlate with HRQoL improvements, significances of the correlations are given for one-tailed tests.
Engineering correlations are given in terms of dimensionless numbers.
Practical correlations are given for pressure drop, diffusion and the overall performance of the reactor.
The values of the dihedral angle correlation coefficients are below the diagonal, and the P values for the correlations are given above the diagonal for the β-sheet motif (a).
Some empirical correlations are given to quantify the changes in their uniaxial compressive strength and deformation moduli in terms of their contents of calcium carbonate.
Then the semi-empirical correlations were given to predict the expansion ratio and penetration length, the results showed good agreement between the predictions and experiments.
Empirical correlations are given for interphase mass transfer, specific interfacial area and bubble gas holdup which all take the influence of reactor geometry into account.
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