Identifiability a priori

Because the olefin geometry in compound 9 will most certainly have a bearing on the stereochemical outcome of the hydroboration step, a reliable process for the construction of the trans trisubsti-tuted olefin in 9 must be identified. A priori, the powerful and predictable Wittig reaction28 could be used to construct E u, [3-unsaturated ester 10 from aldehyde 11. Reduction of the ethoxycarbonyl grouping in 10, followed by benzylation of the resulting primary alcohol, would then complete the synthesis of 9. Aldehyde 11 is a known substance that can be prepared from 2-furylacetonitrile (12). 

Reactive trajectories can be identified a priori, without any numerical simulation, if the moving separatrices are used instead of the standard dividing surfaces. In relative coordinates, the portion of the barrier ensemble that is forward reactive can immediately be identified from Fig. 3 those trajectories are reactive whose initial velocity is so large that it lies above both the stable and unstable manifolds. Because the initial conditions in the ensemble (49) lie at Ax(0) = —xj, this reactivity criterion reads explicitly... 

The knowledge of thermochemistry is also important in early parts of mechanism development. For example, by examining the heats of reaction of competing elementary processes, unlikely reaction paths can be identified a priori and eliminated from further consideration. To illustrate this, consider the following simple unimolecular decomposition processes for CH3CI ... 

A limited number of sub-groups identified a priori with an apparent biological/clinical reason for the difference of interest. 

The examples of C6o dissolution in benzene derivatives considered in the present work evidence the clear dependence of C6o solubility on the electron density distribution in the benzene ring. We have identified a priori the electron density with the distribution of ortho-, meta-, para-isomers which form in the reactions of electrophilic substitution of the benzene derivative considered. This identification is evaluated but in some cases, such as in a series of homologs for alkyl derivatives of benzene, the total agreement between the C6o solubility and the amount of ort/io-isomers is observed (Table 2 and Fig. 7). 

Genes of interest must be identified a priori and novel genes are not identified, A positive association does not prove causation but represent close inkage between the gene of interest and a nearby disease-causing locus... 

The a priori identification of specific risk hypotheses leads to the ability to take some of the methodology normally applied to hypothesis testing of efficacy results and apply it to safety assessment. The most important difference between these two analysis domains is that in the case of efficacy, outcomes of interest are identified a priori with great specificity, and clear statistical hypotheses are laid out in advance with complete analysis and decision rules documented in the clinical protocol. In practice, only a few efficacy variables are identified as primary, and only a few others as second-ary. Sensitivity, statistical power, and sample size are all carefully analyzed in advance to assure the trial will have a high probability of detecting differences of interest in these few critical variables. 

In designing a forced convection cooled furnace component, the most critical factor is the expected peak heat load or heat flux that it is expected to withstand under emergency conditions, as visualized for a slag spall in Figure 4. Peak heat flux is often difficult to estimate and is scenario dependent. Not all emergency scenarios can be identified a priori. If previous operational data for similar furnaces are available (for at least one entire smelting campaign). 

In conclusion for current discussion of multiple comparisons (discussions wiU resume in Chap. 5), it is not appropriate statistical practice to conduct many tests, find one statistically significant result, and present this lone result as a noteworthy finding. It is particularly not appropriate to present this result in the spirit that this is something that was anticipated before the study was conducted (i.e., that this was identified a priori as a comparison of interest). If a situation occurs in which one of many tests is significant, and it is believed that the result is biologically plausible and worthy of further investigation, a subsequent trial needs to be conducted, and this comparison needs to be identified in the study protocol as the primary comparison of interest. 

Let us remark in this context that the H numbers 01, thus the A -th column of matrix A does not generally determine the species Q uniquely consider isomery, possibly stereoisomery. Certain columns of A can be linear combinations of other columns, or even be equal and a vector space generated by the columns makes no sense physically. The chemical species have to be identified a priori. 

For the three types of fibers, three categories of carbon bonds (noted cl to c3) can be identified a priori by XPS ... 

Equations (18) and (19) represent the dependence of the equilibrium melting temperature on chain length for a pure polymer system which adheres to the crystallite model of Figure 14. Here dg represents the interfacial free energy associated with the basal plane of the equilibrium crystallite. Tjn g is the equilibrium melting temperature of a crystallite of size Ce which is comprised of chains of x units. It should not be identified a priori with the melting temperature of a molecular crystal formed by chains of the same size. Equation (18) can be rewritten in more compact form as... 

---