The predictions of f from the stand-level model were compared with those from the Maestra model using criteria such as the relative average error (average bias, e%, Equation 8), the relative mean absolute error (MAE%, Equation 9), and the mean square error (MSE, Equation 10) (Janssen and Heuberger [1995]; Vanclay and Skovsgaard [1997]).
The reaction progress variable approach, which is established for isenthalpic flames, is extended to the present nonisenthalpic flames by including mean and mean square mixture fraction equations.
{c}_2={a}_3+{a}_4times left SP{H}_{init}-SP{H}_{fin}right) (10) Tableft SP{H}_{init}-SP{H}_{fin}rightting variants of Equation 7 to the Ribbonwood dataset Model fitted Mean residual Standard deviation Range of residuals Error mean square 10 EquaTable7: individual trees −0.019 7.44 −22.5 to 44.4 3.
Table 4 Model fit statistics from fitting variants of Equation 7 to the Kaingaroa dataset Model fitted Mean residual (mm) Standard deviation Range of residuals (mm) Error mean square 1. Equation 7: individual trees −0.050 8.49 −31.0 to 24.6 24.6
A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed.
The estimation of the contribution of each factor to the total variance using the estimated mean square values and the equations for expected mean square was used to interpret the ANOVA table.
error of the estimate Equation 5 0.881 0.776 0.774 2.7629 Table 4 ANOVA table Model Sum of squares df Mean square F Sig. Equation 5 Regression 25506.452 6 4251.075 556.872 0.000 Residual 7374.302 966 7.634 Total 32880.754 972 Table 5 Multiple regression coefficients Model Unstandardized coefficients Standardized coefficients t Sig.
Besides, the methods introduced to deal with the exponential stability of random impulsive integrodifferential equations in [18] and study the exponential stability in mean square of random impulsive differential equations in [19], can not be applied to deal with our problem since the neutral item arises.
We measured the displacement of wild type cells during 15 minutes (see Fig. 6A), and fitted the observed mean square displacement to this equation, yielding a speed of S = 10.4+/−2.1 µm/min and a persistence time of P = 3.4+/−0.5 min (mean and 95% confidence; Fig. 6E,F).
The overall root mean square error of the reach equations across the males and females ranged from 4 to 17 mm for the NRA and 12 39 mm for the MRE.
