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A simulation example shows that the statistical properties also in this case are much better than predicted by average variance analysis if Δ< 0. For this simple example, it is hence possible to monitor the quality of the estimate by studying the sign of Δ. Traditional variance analysis only considers the average effects and hence misses this two mode (good or bad) situation.

The results from our methods for this simple example are illustrated in Figures 1(f), 1(g), and 1(h).

For this simple example five biodiesel plants were assumed to be operating in the region, with rapeseed as the main oilseed feedstock.

For this simple example, we can also apply Theorem 5.2 to conclude that there exists such that since for any and each we have such that (5.9).

For this simple example, by products (except for press cake) were not considered; however, they are provided here to show the balances for each plant concept.

For comparison, a total of 1,872 tests would be required for this simple example if the initial filtering against the minimum and maximum distance thresholds was not carried out.

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Although pure platinum is not the catalyst of choice for the oxidation of methanol, this simple example shows that our nanoparticles, produced without further purification by cathodic corrosion and prior to any optimization, show a superior catalytic activity over a state-of-the-art commercial Pt catalyst.

This simple example proposed for illustration demonstrates how the analysis of exergy transfer results allows one not only to characterize the global exergy efficiency of the system but also analyze in depth the time and space distribution of exergy flows, exergy variation and irreversibility.

Assuming perfect correlation, the individual data points for potential surrogate and unobserved true endpoints lie on straight lines for groups E and C. In this simple example the unobserved true endpoint is proportional to the potential surrogate endpoint, so the intercept for both lines is zero.

Hence for the simple example above, the stationary planar front is stable due to w ˆ ( k ) ≤ w ˆ ( 0 ).

From the numerical experiments for the simple example we can see that our proposed method has good convergence properties.

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