Evaluation in practice

A solution to Equation (8.12) together with its boundary conditions gives a r, z) at every point in the reactor. An analytical solution is possible for the special case of a first-order reaction, but the resulting infinite series is cumbersome to evaluate. In practice, numerical methods are necessary. 

The theoretical and practical problem is analysed, and from the observations facts are gathered to deduce a hypothesis. Subsequently a provisional design is generated from the observed facts and from the analysed practical problems. This provisional design is evaluated in practice and the results are analysed to confirm or reject the hypothesis and develop or refine it. Finally, the enhanced design is re-applied in practice to derive the answers posed by the research questions. The result of the research is a newly developed method informed by cause-effect knowledge, see Figure 7. 

Archibald (1947) showed that measurement of c and dc/dr at the cell boundaries permit Molecular weight determination at any stage in the equilibrium process. However, when measurements are made early enough, before the molecular species have time to redistribute in the cell, the weight-average Molecular weight and second virial coefficient can be evaluated. In practice, measurements can be made... 

CRM is used, the provided uncertainty of the certibed analyte D including the uncertainty contribution of homogeneity, characterization, and stability D could be used as assigned standard deviation for probciency evaluation. In practice, this is seldom done. The common approach is to debne a bt-for-purpose criterion as... 

This is a complex relationship that usually will be difficult to evaluate in practice. In many situations, however, the contributing factors are independent, thus simplifying the picture. Below, some simple examples of combined expressions are shown. The rules are presented in the form of combining SDs or coefficients of variation (CVs) given independent input components. ... 

The Kohn-Sham and Es functionals yield the same numerical values for any pair of pa and pB Es[pA, Pb] = Eks[pa + Pb]) provided pA and pB are both N-representable. This follows from the fact that if two functions satisfy the conditions Eqs. 5-7 their sum does it too. Therefore, if both pa and pB are IV-representable their sum is too. These two functionals differ, however, in the way the kinetic energy is evaluated in practical simulations. If the one-electron orthogonal functions... 

Besides evaluation in practice, the transfer subproject will also deal with major extensions. For instance, the integration rule definition formalism will be extended and repair actions to restore consistency of damaged links will be incorporated into the framework. The transfer is intended to be bidirectional, i.e. our partner s knowledge will influence our research as well. 

X - 0.15 is a good boundary between unreactive clays (X < 0.15) and high reactivity clays (X > 0.15). Intact shale data using dielectric permittivity and magnetic resonance confirm the validity of the Reactivity Coefficient concept. Dielectric data permit rapid shale reactivity evaluation in practical cases. Along with other simple tests, it can be carried out on the drill rig using drilling chips. 

The aforementioned methods can be applied to evaluate the reliability of engineering systems subjected to stochastic input with a given mathematical model. On the other hand, if a parametric model of the underlying system is available and the probability density function of these parameters is obtained by Bayesian methods, the uncertain parameter vector can be augmented to include the model parameters and the uncertain input components. Then, robust reliability analysis can proceed for stochastic excitation with an uncertain mathematical model. This allows for more realistic reliability evaluation in practice so that the modeling error and other types of uncertainty of the mathematical model can be taken into account. 

HEP is evaluated in practice using relevant human reliahiUty analysis (HRA) method with appropriate treating of hiunan and organisational factors that also influence dependencies between abnormal events. The human reliahiUty assessment should be context oriented (Hollnagel 2005). 

Theoretically, if three scattering curves at different contrasts are recorded, the data for each measured scattering vector hi yield a set of three linear equations from which the values of the basic functions related to h, can be evaluated. In practice, however, one has to determine the average density before this procedure can be carried out. Each experimental curve is extrapolated to zero angle using a Guinier plot. Since iih(0) = ii(0) = 0 [1], it follows that... 

First, we must pose the question of whether an odd or an even order shall be evaluated. In practice, mostly even orders are used because the peaks of the derivatives... 

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