Decomposition rule

If we return to our equilateral triangle example and apply the above rules, we obtain the numbers in Table 9-6.1. Using this table in conjunction with the character table (Table 9-7.2) and the decomposition rule ... 

The decomposition rule (eqn (7-4.2)) in conjunction with these results shows that p p , pr1(((... 

The decomposition (2.172) can be evaluated, as the direct product reduction to the group irreducible representations, from case to case, according to the procedure explained in above Section, yet the systematization mles with the aid of the decomposition rules in Table 2.11 help a lot. 

TABLE 2.11 Decomposition Rules for the Direct Product in the Symmetry Groups After (Lancashire, 2002 Putz, 2006)... 

A rule for the correlation of ease of pyrolytic elimination with structure has been suggested by DePuy. The order of ease of decomposition among the commonly used esters is ... 

If the consequences of not waiting until the pressure had dropped were serious and/or omitting to check the pressure was likely, then it would be necessary to break down the operation "charge reactor" to its component steps. This approach to deciding on the level of decomposition is called the PxC rule (where P is the probability of failing to carry out an operation and C the cost of the consequences). The size of the product PxC determines whether or not to describe the operation in more detail (Shepherd, 1985). 

During the final stage of the decomposition approach, the task element probabilities in the event tree are combined together using the rules described in Section 5.3.3 to give the overall task failure probability. At this stage, various corrections for dependencies among task elements may be applied. 

Organic metal salts have frequently failed to produce an appreciable chemical stabilization effect, either during dehydrochlorination induction periods or in later decomposition stages. While this does not rule out the occurrence of Frye and Horst substitution reactions, it does suggest that these reactions may not be responsible for the observed retardation of color developments [126-128]. 

Fig. 2.9 The state transition graph Gc, computed for a Tdim lattice consisting of iV = 4 points (with periodic boundary conditions), and totalistic rule T2 . The vertices labeled ti represent transient configurations those labeled cd represent cyclic states, and give rise to the formal cycle cum decomposition C[ j =[3, lj-f[2,2].

More recently Hand et al. (ref. 9) have studied the decomposition reaction of N-chloro-a-amino acid anions in neutral aqueous solution, where the main reaction products are carbon dioxide, chloride ion and imines (which hydrolyze rapidly to amine and carbonyl products). They found that the reaction rate constant of decarboxylation was independent of pH, so they ruled out a proton assisted decarboxylation mechanism, and the one proposed consists of a concerted decarboxylation. For N-bromoamino acids decomposition in the pH interval 9-11 a similar concerted mechanism was proposed by Antelo et al. (ref. 10), where the formation of a nitrenium ion (ref. 11) can be ruled out because it is not consistent with the experimental results. Antelo et al. have also established that when the decomposition reaction takes place at pH < 9, the disproportionation reaction of the N-Br-amino acid becomes important, and the decomposition goes through the N,N-dibromoamino acid. This reaction is also important for N-chloroamino compounds but at more acidic pH values, because the disproportionation reaction... 

In all of the above cases involving decompositions of vinyl diazonium ions, the observed products are consistent with a vinyl cation formulation, but extensive mechanistic studies of these reactions have not been reported. It is difficult, for instance, to establish to what extent reaction proceeds through the diazonium ion via a backside nucleophilic attack and concerted loss of nitrogen rather than through the free vinyl cation. In the absence of kinetic data, it is also difficult to rule out competing or alternative mechanisms not involving vinyl cations. 

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