Underlying Assumptions

Only one of the steps is rate-limiting (the rate-determining step, rds), which generally requires that the rate constant of this reaction step be at least 100 times smaller than those of all other prior steps. 

The same step is also rate limiting in the reverse direction (a condition arising from reversibility of the reaction). 

Intermediates, if adsorbed on the surface of the electrode substrate, are at low coverages (note, however, that when coverages of intermediates do approach saturation, potential-dependent rates can still arise if an electrochemical desorption type of step is involved then = 118 mV dec at 298 K for P taken as 0.5). 

The kinetics of all the other steps do not deviate significantly from either steady-state or quasi-equilibrium conditions (see later discussion). 

The nature of the mechanistic scheme does not change with potential. 

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The "feedback loop in the analytical approach is maintained by a quality assurance program (Figure 15.1), whose objective is to control systematic and random sources of error.The underlying assumption of a quality assurance program is that results obtained when an analytical system is in statistical control are free of bias and are characterized by well-defined confidence intervals. When used properly, a quality assurance program identifies the practices necessary to bring a system into statistical control, allows us to determine if the system remains in statistical control, and suggests a course of corrective action when the system has fallen out of statistical control. 

Clinical Pharmacokinetics. Clinical pharmacokinetics attempts to define the relationship between dmg concentration and therapeutic response. The underlying assumption is that response is proportional to dmg concentration at the site of action. This concentration is dependent on many... 

The basic underlying assumption for the mathematical derivation of chi square is that a random sample was selected from a normal distribution with variance G. When the population is not normal but skewed, square probabihties could be substantially in error. 

The underlying assumption driving marine natural products chemistry research is that secondary metabolites produced by marine plants, animals, and microorganisms will be substantially different from those found in traditional terrestrial sources simply because marine life forms are very different from terrestrial life forms and the habitats which they occupy present very different physiological and ecological challenges. The expectation is that marine organisms will utilize completely unique biosynthetic pathways or exploit unique variations on well established pathways. The marine natural products chemistry research conducted to date has provided many examples that support these expectations. 

Several discrete forms of the conservation of momentum equation, (9.3), can be derived, depending on the type of mesh and underlying assumptions. As an example, assume the equation will be solved on staggered spatial and temporal meshes, in two dimensions, in rectangular geometry, and with the velocities located at the nodes. Assume one quarter of the mass from each adjacent element is associated with the staggered element as shown in Fig. 9.11. 

Often in stress analysis we may be required to make simplified assumptions, and as a result, uneertainties or loss of aeeuraey are introdueed (Bury, 1975). The aeeuraey of ealeulation deereases as the eomplexity inereases from the simple ease, but ultimately the eomponent part will still break at its weakest seetion. Theoretieal failure formulae are devised under assumptions of ideal material homogeneity and isotropie behaviour. Homogeneous means that the materials properties are uniform throughout isotropie means that the material properties are independent of orientation or direetion. Only in the simplest of eases ean they furnish us with the eomplete solution of the stress distribution problem. In the majority of eases, engineers have to use approximate solutions and any of the real situations that arise are so eomplieated that they eannot be fully represented by a single mathematieal model (Gordon, 1991). 

While HiickeTs 4n + 2 rule applies only to monocyclic systems, HMO flieory is applicable to many other systems. HMO calculations of fused-ring systems are carried out in much the same way as for monocyclic species and provide energy levels and atomic coefficients for the systems. The incorporation of heteroatoms is also possible. Because of the underlying assumption of orthogonality of the a and n systems of electrons, HMO dieory is restricted to planar molecules. 

In order to cope with a complex environment, people make extensive use of rules or assumptions. This rule based mode of operation is normally very efficient. However, errors will arise when the underlying assumptions required by the rules are not fulfilled. Chapter 2 discusses the causes of these rule based errors in detail. 

The TSE model of causation that accidents are primarily due to individually controllable unsafe acts is unlikely to be modified over time. This is because very little evidence on the background and conditions which led up to an accident will be collected. The data collection strategy is therefore likely to remain static, since the data collected wiU, by definition, not contradict the underlying assumptions. 

For each of the 36 bus sections tliat had not already failed, the Weibull distribution was used to detennine tlie probability of failure before tlie next outage. Under assumption (a), tliis probability is P(T < 3301T > 209) i.e., tlie conditional probability of failure before 330 days, given tliat tlie bus section lias survived 209 days. Under assumption (b), tlie corresponding probability is P(T < 330 T > 230). For part (b), tlie estimates of the Weibull distribution parameters used in part (a) were modified to take into consideration tlie absence of failures for 3 additional weeks. 

Deciphering the code. The language of computational chemistry is littered with acronyms, what do these abbreviations stand for in terms of underlying assumptions and approximations ... 

We recall that the MFT assumes that does not induce any correlation between separated sites if all of the sites are mutually uncorrelated at i = 0, MFT assumes that they remain uncorrelated at all later times t > 0. A virtue of this approach is that it permits an easy derivation of the limiting value density, pt->oo- Because the underlying assumption is generally not valid, however, we should hardly be surprised to learn that the limiting densities obtained for most of the interesting (i.e, nonlinear) rules differ significantly from those obtained by Monte Carlo simulations of those same rules. 

Decision-making may be undertaken by an individual under assumptions of certainty, risk, or uncertainty (partial or complete ignorance) on the states of Nature. 

As mentioned, the data obtained by this method are expressed as cumulative size distribution curves. Since the computations assume Stokes law for spherical particles, the plotted curves give the distribution of spherical particles which would behave like the actual sample with respect to this experiment. For this reason, the sizes on the distribution curves should be labelled Stokes Equivalent Diameter . Because of the underlying assumptions and the above interpretation of the results, it is clear that the repeatability of this method has more meaning than accuracy of comparison with results of other methods... 

Vibrational broadening in [162] was taken into account under the conventional assumption that contributions of vibrational dephasing and rotational relaxation to contour width are additive as in Eq. (3.49). This approximation provides the largest error at low densities, when the contour is significantly asymmetric and the perturbation theory does not work. In the frame of impact theory these relaxation processes may be separated more correctly under assumption of their statistical independence. Inclusion of dephasing causes appearance of a factor... 

These five processes have been defined independently of the ligand partition. They are visualized as properties of the skeleton symmetry only. In the coset and double coset formulations of stereoisomerization this idea is expressed in a precise mathematical form. The underlying assumption is that the presence of different ligands does not distort the skeleton geometry. It is certainly possible to find chemical situations where this is reasonably correct. 

Table 4.12. Accepted and Target Impurity Concentrations (Target Concentrations for Impurities, Under Assumption of the Regression Line in Fig. 4.7 (B a = 0.92, b = -0.743, m = 1) If the LOQ of the Method were 0.03%, the Target Concentration in the Last Line (0.011) Would he Inaccessible to Measurement ...

The main challenge to overcome is obtaining the necessary numbers to input to such models. There is a natural distrust of rubbish in, rubbish out, and the teams used to working with hard data may be reluctant to express their underlying assumptions about goals, trade-offs, and business... 

An underlying assumption in these interpretations is that U addition by fluids is the only cause of U/Th fractionation (see Fig. 8b,c) and if the same were true of U/Pa ratios then U addition should likewise produce U-Pa arrays which record a similar time to the U-Th arrays. So far the only arc where this may be true is Tonga, where Turner et al. (1997) showed that the combined Tonga and Kermadec lava array scatters around a 50 kyr U-Th isochron (Fig. 9a). Subsequently, Bourdon et al. (1999) showed that the... 

Integrating equations (2.37) and (2.39) under assumption that in case of direct reaction of surface complex formation (Me C ) the reaction of interaction of oxygen with surface metal atoms is the limiting stage rather than formation of physadsorbed oxygen (i.e. assuming that [02( )J = const and it does not change in time) we arrive to the respective expression for kinetics of direct and inverse reactions ... 

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