Relationships accidental

The N+ relationship, as discussed above, is a systematization of experimental facts. The equation of Scheme 7-4 has been applied to nearly 800 rate constants of over 30 electrophiles with about 80 anionic, neutral, and even cationic nucleophiles covering a range of measured rate constants between 10-8 and 109s 1 (Ritchie, 1978). Only about a dozen rate constants deviated from the predicted values by more than a factor of 10, and about fifty by factors in the range 5-10. It is therefore, very likely that this correlation is not purely accidental. Other workers have shown it to be valid for other systems, e.g., for ferrocenyl-stabilized cations (Bunton et al., 1980), for coordinated cyclic 7r-hydrocarbons (Alovosus and Sweigart, 1985), and for selectivities of diarylcarbenes towards alkenes (Mayr, 1990 Mayr et al., 1990). On the other hand, McClelland et al. (1986) found that the N+ relationship is not applicable to additions of less stable triphenylmethyl cations. 

The first equation is the well-known Singular Value Decomposition. In the context of PCR the eigenvectors U form the basis for the column vectors of Y. The second equation in (5.72) attempts to also represent the column vector q of qualities in the same space U. If both representations are good then PCR works well, resulting in accurate predictions. A potential drawback of PCR is the fact that U is defined solely by Y. Even if there is good reasoning for a relationship between q and U, as indicated in the derivation of equation (5.60), it is somehow accidental. ... 

Apart from deliberate or accidental introduction of tiny seed crystals to the system, and productive interactions between existing crystals and quasi-crystalline embryos or clusters in solution, the most influential mode of new crystal generation in an industrial crystalliser is contact secondary nucleation between the existing crystals themselves, between crystals and the walls or other internal parts of the crystalliser, or between crystals and the mechanical agitator. Secondary nucleation rates (in m-3 s 1) are most commonly correlated by empirical relationships such as ... 

Among the endocrine organs, the testes are unique because they are suspended in a tissue pouch outside of the body cavity. The testes can be felt and these organs are vulnerable to physical insults, either deliberate or accidental. The effects of castration were described by Aristotle over three hundred years B.C. Removal of the testes or castration as a form of punishment or tribute dates to antiquity. Domestic animals and some cases humans were castrated to make them more docile. Castrata were valued as harem keepers. In addition, seasonal changes in behavior and the dramatic anatomical and behavioral events associated with puberty were components of the natural world (Bronson and Heideman, 1994). Thus, an awareness of a relationship between the testes and human behavior predates written history. 

If we now plot the percent yield vs. the solvent number, we will get the response surface shown in Figure 2.11. There seems to be a trend toward higher yield with increasing solvent number, but such a trend must be meaningless it is difficult to imagine how an arbitrarily assigned number could possibly influence the yield of a chemical reaction. If a relationship does appear to exist between yield and solvent number, it must be entirely accidental - the variation in response is probably caused by some other property of the solvents. 

Family members often develop habits and ways of coping (called enabling ) that accidentally help the addict continue their substance abuse. Group counseling sessions with a licensed counselor or therapist can help family members build healthy relationships and relearn old behaviors. This is particularly important for adolescents in drug treatment, who should be able to rely on the support of family. 

Determine dose-response relationships for 2,3,7,8-TCDD following chronic exposure in rodent models and, accidental or occupational exposure in humans... 

The principles in (1) - (5) thus show that the underlying picture about the relationship between substance, form and body can be made precise. But it is really the underlying picture that is of interest. The picture is of a metaphysical principle, namely form, which is connected to two fundamental aspects of the world substance and motion. The presence of form confers both substantiality and the capacity for motion on a physical body. And its abstraction from body leaves something of a metaphysical shadow, a genus in die category of quantity, which can only have only accidental being. 

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