Validation motivation

The first column obtained with the Romberg method coincides with the one obtained with the CavaUeri-Simpson method. The other columns can be different with respect to the ones that we can obtain using the close Newton-Cotes formulae. In particular, the formulae with many T are different from the high-order Newton-Cotes and this provides a valid motive for the extrapolation with more elements. 

For clutter suppression, the test statistic used by the noncoherent detector has been proposed as an interesting output signal [1], This was motivated by the fact that, provided that transient and noise models are valid, the test statistic reflects the likelihood that a transient is present. 

This serves to motivate the validity of the maximum principle with regard to equation (58) supplied by the homogeneous boundary conditions (55). By utilizing this fact it is plain to show that the estimate holds ... 

In our own validation sets, experimental heats of formation are preferentially taken from recognized standard compilations [38-40]. If there are enough experimental data for a given element, we normally only use reference values that are accurate to 2 kcal/mol. If there is a lack of reliable data, we may accept experimental heats of formation with a quoted experimental error of up to 5 kcal/mol. This choice is motivated by the target accuracy of the established semiempirical methods. If experimental data are missing for a small molecule of interest, we consider it legitimate [18] to employ computed heats of formation from high-level ab initio methods as substitutes. 

There has been an accelerated interest in polymer electrolyte fuel cells within the last few years, which has led to improvements in both cost and performance. Development has reached the point where motive power applications appear achievable at an acceptable cost for commercial markets. Noticeable accomplishments in the technology, which have been published, have been made at Ballard Power Systems. PEFC operation at ambient pressure has been validated for over 25,000 hours with a six-cell stack without forced air flow, humidification, or active cooling (17). Complete fuel cell systems have been demonstrated for a number of transportation applications including public transit buses and passenger automobiles. Recent development has focused on cost reduction and high volume manufacture for the catalyst, membranes, and bipolar plates. 

The relevant calculations are commonly handled poorly, because the equilibrium equations involved are difficult to solve manually (but not with computers). The few calculations that are actually reported in the biochemical literature use simplified methods of limited and frequently unknown validity. Large excesses of magnesium ion are frequently used in experiments, perhaps in an attempt to avoid such calculations. The relevant theory is well worked out and there are excellent reviews. The limitation appears to involve diffusion to the (mathematically) inexpert user, which is one of the motivations of building expert systems. 

Finally - and equally important - Jens contribution to the formal treatment of GOS based on the polarization propagator method and Bethe sum rules has been shown to provide a correct quantum description of the excitation spectra and momentum transfer in the study of the stopping cross section within the Bethe-Bloch theory. Of particular interest is the correct description of the mean excitation energy within the polarization propagator for atomic and molecular compounds. This motivated the study of the GOS in the RPA approximation and in the presence of a static electromagnetic field to ensure the validity of the sum rules. 

Evaluation of data on subjective reports on reasons for smoking indicates that women smoke for stress reduction and men for stimulation (Best and Hakstian 1978 Frith 1971 Spielberger 1986 Ikard and Tomkins 1973), implying that there may be gender differences regarding the motivation for smoking. However, the validity of self-reports is questionable and empirical evidence based on physiological measures does not support these observations. 

These two facts motivated a critical check of the validity of Eq. 4.11 in a wide Q-range [9,105,154,155]. For this purpose the information obtainable from fully atomistic MD simulations was essential. The advantage of MD simulations is that, once they are validated by comparison with results on the real system, magnitudes that cannot be accessed by experiments can be calculated, as for example the time dependence of the non-Gaussian parameter. The first system chosen for this goal was the archetypal polymer PL The analysis of the MD simulations results [105] on the self-motion of the main chain hydrogens was performed in a similar way to that followed with experimental data. This led to a confirmation of Eq. 4.11 beyond the uncertainties for Q<1.3 A (see Fig. 4.15). However, clear deviations from the Q-dependence of the Gaussian behaviour... 

The initial benchmark results obtained with the full CCSD-R12 method [34] testified that the various simplified CCSD-R12 methods reported earlier were highly accurate approximations to the full CCSD-R12 method unless the basis set was too small. The assumptions about the relative importance of diagrammatic terms made in these simplified methods were proven to be valid. However, these neglected terms do not increase the computational cost scaling of CCSD-R12 and there appears no need to eliminate them from full CCSD-R12, once they are implemented. In other words, it is important to distinguish whether a certain approximation is motivated by a compromise between accuracy and the computational cost or by that between accuracy and the development cost. The latter has become increasingly unjustifiable with the advent of computerized derivation and implementation. 

Recall that considering a simpler reduced model (4.3.1) instead of (4.3.5) is motivated by the smallness of the parameter e and the appropriate results for a nowhere vanishing N x) = 0(1) are expected to be valid for the nonreduced problem, unless very large voltages are applied, causing punch through. ... 

The argument so far has been highly abstract and general, because it is intended to be valid fora number of selection mechanisms. It applies to the biological theory of natural selection, where it first arose, but also to the theory of economic competition, the theory of unconscious motivation and the theory of computer chess programs. Before I consider the first two in more deuil, I shall digress for a moment and say a few words about the relation between biology and the social sciences. 

An experimenf is just a test or series of tests. Experiments are performed in all scientific disciplines and are an important part of the way we learn about how systems and processes work. The validity of the conclusions that are drawn from an experiment depends to a large extent on how the experiment was conducted. Therefore, the design of experiments plays a major role in the eventual solution of the problem that initially motivated the experiment and, as... 

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