Significance tables

As discussed in preceding sections, FI and have nuclear spin 5, which may have drastic consequences on the vibrational spectra of the corresponding trimeric species. In fact, the nuclear spin functions can only have A, (quartet state) and E (doublet) symmetries. Since the total wave function must be antisymmetric, Ai rovibronic states are therefore not allowed. Thus, for 7 = 0, only resonance states of A2 and E symmetries exist, with calculated states of Ai symmetry being purely mathematical states. Similarly, only -symmetric pseudobound states are allowed for 7 = 0. Indeed, even when vibronic coupling is taken into account, only A and E vibronic states have physical significance. Table XVII-XIX summarize the symmetry properties of the wave functions for H3 and its isotopomers. 

The most effective Lewis-acid catalysts for the Diels-Alder reaction are hard cations. Not surprisingly, they coordinate to hard nuclei on the reacting system, typically oxygen atoms. Consequently, hard solvents are likely to affect these interactions significantly. Table 1.4 shows a selection of some solvents ranked according to their softness. Note that water is one of the hardest... 

Grading of the product (i.e., size distribution) depends on the discharge opening, which is difficult to measure and adjust owing to wear of the plates in a jaw crusher. Size of feed and wear of plates do not affect grading significantly. Table 20-10 relates sizes of product to crusher settings. 

Assign possible structures to all abundant fragment ions from the tabulated ions listed in the structurally significant tables of Part III. Two or more ions together may define the type of compound. For example, the presence of the following ions suggest specific compounds ... 

We have also considered the effect of increasing the number of optimally located samples on the final estimate. In this case, we start with the optimal minimum set and increase by one (optimally located) the number of samples. Figure 1 shows the results for different values of M = 6,12,20. As expected, the quality of the estimate is better when the number of optimally located samples is increased. However, after a few optimally located samples, the quality of the estimate does not improve significantly. Table 1 shows the corresponding optimal samples for different values of M and for different numbers of optimally located samples. In each case, after the minimum optimal set is determined, the next optimal samples are located around the times corresponding to the values for this optimal minimum set. The quality of the estimate is also directly affected by the variance of the measurements. 

As the time of irradiation is increased, the effect of functionality on the grafting yields becomes much more significant (Table XI) such that after 16 hours there is an order of magnitude difference between TMPTA and TFMA. 

The numerical difference between discrete compound interest and continuous compound interest is small, but when large sums of money are involved, the difference may be significant. Table 9-23 is an abbreviated continuous interest table, assuming that time zero is when start-up occurs. A summary of the equations for discrete compound and continuous compound interest is found in Table 9-24. 

Effect of Oxygen Concentration. The effect of oxygen concentration on the conversion to anthraquinone and anthracene was also determined. As the oxygen partial pressure was increased, the ratio of anthraquinone to anthracene formed increased significantly (Table V). Thus, the data indicate that higher oxygen concentrations favor anthraquinone formation. 

Two para-substituents, phenyl and cyano depress and retard the rate of cyclization significantly (Table 11.2)." p-Phenyl and p-cyano are both radical stabilizing substituents. These conjugative substituents reduce the spin density on the carbon ortho to the nitrene nitrogen. The reduced spin density at carbons ortho to the nitrogen lowers the rate at which the 1,3-biradical cychzes. The effect with p-cyano and p-biphenyl singlet phenylnitrene is quite dramatic. The lifetimes of these singlet nitrenes at ambient temperature are 8 and 15 ns, respectively, and the activation barriers to cychzation are 7.2 and 6.8 kcal/mol, respectively. 

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