Condensed conditional probabilities

Thus, the square matrix P(Xa IX b) contains only the intrafragment communications, which miss the probability propagations originating from AO of the remaining constituent atoms Xz t Xab-The atomic output reduction of P(XabIXab) [9] gives the associated condensed conditional probabilities of the associated molecular information system,... 

PWRs indicate that most of the containments have relatively low conditional probabilities of early failure, although a large variability exists in the contributions of the different failure mod< "or both large dry and ice condenser containments. 

We could prepare a-alkoxy-y-phenylselenenyl aldehydes as "stable" equivalents of a-alkoxy-P,y-unsaturated aldehydes but their reaction with boron enolates did not lead to the expected condensation products, probably due to inadequate work up conditions. 

The information system in the (condensed) orbital resolution involves the AO events / in its input a = xi] and output b = / . It represents the effective promotion of these basis functions in the molecule via the probability/information scattering described by the conditional probabilities of AO outputs given AO inputs, with the input (row) and output (column) indices, respectively. In the one-electron approach [46-48], these AO-communication connections P(XjlXi) = P(j i) result from the appropriately generalized superposition principle of quantum mechanics [51],... 

The 1,2-dithiafulvalenes of the type 150, which are obtained (if at all) only in extremely small yields by the reaction of the sodium salt of fluorene with 108 or 111, can be prepared in useful yields from fluorene and trithione by a pyrolytic reaction. Trithiones with substituents in position 4, however, do not condense with fluorene under these conditions, probably because of steric factors. Attempts to condense indene with 5-aryltrithiones have also met with failure.46... 

It has been established that random interchange reactions occur with polyesters and polyamides at the higli temperatures at which these thermoplastics are normally polymerized and subsequently extruded or molded. Other condensation polymers probably undergo similar shufflings of repeating units under the proper conditions. This implies that the equilibrium constant for condensation reactions like that in reaction (a) of Fig. 5-2 is independent of the sizes of the molecules which are reacting. 

These resins are quite similar to urea-formaldehyde condensates and, probably for that reason, find similar applications. Melamine reacts with formaldehyde under slightly alkaline conditions to form mixtures of various methylolmelamines ... 

The general mechanism is believed to involve iminium ions as the active electrophiles, rather than the amine simply acting as a base for the aldol condensation. Kinetic evidence in support of this mechanism has been developed in the case of condensation of aromatic aldehydes with nitromethane." Knoevenagel condensation conditions frequently involve both an amine and a weak acid. The reactive electrophile is probably the protonated form of the imine, since this is a more reactive electrophile than the corresponding carbonyl compound. 

Chain length distribution in linear condensation polymers joint and conditional probabilities... 

The reason for this relative lack of reactivity of 2-methylthiazoIium is probably due to the too-weak nucleophilic character of its carbon-2. For example, any /S-alkoxyalcene (29) derivatives resulting from the condensation of o-ester could never have been isolated, whereas they constitute the essential intermediate step in trimethine syntheses for rings of acidic character (64). However, even if a negative 5-substituent such as ethoxy-carbonyl increases the yield (61) by promoting independently the possible formation of the methylene base, it may be stressed that the presence of this base is not the essential condition of the reaction, since the isolated anhydrobase itself is not reactive toward the o-ester (Scheme 41). 

Formaldehyde may react with the active hydrogens on both the urea and amine groups and therefore the polymer is probably highly branched. The amount of formaldehyde (2—4 mol per 1 mol urea), the amount and kind of polyamine (10—15%), and resin concentration are variable and hundreds of patents have been issued throughout the world. Generally, the urea, formaldehyde, polyamine, and water react at 80—100°C. The reaction may be carried out in two steps with an initial methylolation at alkaline pH, followed by condensation to the desired degree at acidic pH, or the entire reaction may be carried out under acidic conditions (63). The product is generally a symp with 25—35% soHds and is stable for up to three months. 

Many variants of this procedure exist. Thus, Kano and coworkers have carried out the condensation of /3-keto sulfoxides with diaminomaleonitrile (Scheme 36) (78S372). This reaction probably yields an intermediate dihydropyrazine which is oxidized under the reaction conditions, and it seems likely that the condensation of the carbonyl group and the amine is the first step. 

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