Multiplicity of examples

In contrast to the multiplicity of examples of diastereotopic face discriminations in combination with other enzyme specificity discussed later, there are relatively few alcohol dehydrogenase catalyzed reductions that involve diastereotopic face selectivity alone. However, whenever a carbonyl group is present in a single chiral stereoisomer, diastereotopically face-selective reductions are possible. The reductions of the L-homocysteine derivative (47) (48), and of the (-)-oxocineole (15,4/ )-(49) (50), are two... 

Whereas there is a multiplicity of examples for the above-mentioned reactions of acetylene with nucleophiles to give heterovinyl compounds, it is comparatively rare to find industrially relevant additions of C-H-acidic compounds to acetylenes. 

This labeled graph is easily entered into a computer by storing each pair of labels of nodes together with the multipUcity of the bond in between, including 0 if there is no bond. By pairs we mean unordered pairs or sets of two different nodes. To be exact, for unordered pairs i, we always have i, = , i. In contrast, ordered pairs are denoted as (i, j) and in this case we have (i, j) ( , i) if i j. The pairs of nodes and the bond multiplicities of example (1.4) are as follows ... 

Once the atoms arc defined, the bonds between them arc specified in a bond block. Each line of this block specifies which two atoms are bonded, the multiplicity of the bond (the bond type entry) and the stereo configuration of the bond (there arc also three additional fields that arc unused in Molfiles and usually set to 0). The indices of the atoms reflect the order of their appearance in the atom block. In the example analyzed, V relates to the first carbon atom (see also Figure 2-24). "2" to the second one, 3" to oxygen atom, etc. Then the two first lines of the bond block of the analyzed file (Figure 2-29) describe the single bond between the two carbon atoms C1-C2 and the double bond C2=0-5, respectively. 

The correction term in Eq. (9) shows that the basic assumption of additivity of the fragmental constants obviously does not hold true here. Correction has to be appHed, e.g., for structural features such as resonance interactions, condensation in aromatics or even hydrogen atoms bound to electronegative groups. Astonishingly, the correction applied for each feature is always a multiple of the constant Cu, which is therefore often called the magic constant . For example, the correction for a resonance interaction is +2 Cj, or per triple bond it is -1 A detailed treatment of the Ef system approach is given by Mannhold and Rekker [5]. 

Mciny of the theories used in molecular modelling involve multiple integrals. Examples include tire two-electron integrals formd in Hartree-Fock theory, and the integral over the piriitii >ns and momenta used to define the partition function, Q. In fact, most of the multiple integrals that have to be evaluated are double integrals. 

The purpose of these comparisons is simply to point out how complete the parallel is between the Rouse molecular model and the mechanical models we discussed earlier. While the summations in the stress relaxation and creep expressions were included to give better agreement with experiment, the summations in the Rouse theory arise naturally from a consideration of different modes of vibration. It should be noted that all of these modes are overtones of the same fundamental and do not arise from considering different relaxation processes. As we have noted before, different types of encumbrance have different effects on the displacement of the molecules. The mechanical models correct for this in a way the simple Rouse model does not. Allowing for more than one value of f, along the lines of Example 3.7, is one of the ways the Rouse theory has been modified to generate two sets of Tp values. The results of this development are comparable to summing multiple effects in the mechanical models. In all cases the more elaborate expressions describe experimental results better. 

Multiplication of symmetry species is carried out using the usual mles so that, for example. 

S remains a good quantum number and, for states with A > 0, there are 25+1 components corresponding to the number of values that I can take. The multiplicity of the state is the value of 25 + 1 and is indicated, as in atoms, by a pre-superscript as, for example, in n. 

It was not their reactivity but their chemical inertness that was the true surprise when diazirines were discovered in 1960. Thus they are in marked contrast to the known linear diazo compounds which are characterized by the multiplicity of their reactions. For example, cycloadditions were never observed with the diazirines. Especially surprising is the inertness of diazirines towards electrophiles. Strong oxidants used in their synthesis like dichromate, bromine, chlorine or hypochlorite are without action on diazirines. Diazirine formation may even proceed by oxidative dealkylation of a diaziridine nitrogen in (186) without destruction of the diazirine ring (75ZOR2221). The diazirine ring is inert towards ozone simple diazirines are decomposed only by more than 80% sulfuric acid (B-67MI50800). 

In general, replacement prefixes should not be added to heterocyclic parent names, because of the resulting multiplicity of possible synonyms. For example, structure (27) should not be named 2,3,4,6-tetraazaindole or 3,4,6-triazaindazole without very good... 

The fusion name l//-triazolo[4,5-d]pyrimidine for (140) is preferred by practitioners in the field and appears in CA indexes. On the other hand, the nonspecialist, who may well be uncertain about his command of fusion nomenclature, might more easily grasp the replacement name l//-l,2,3,4,6-pentaazaindene. (This is an appropriate place to emphasize that, by lUPAC rules, replacement names are to be based only on a completely carbocyclic parent. Notwithstanding the attractive simplicity of 8-azapurine for the example at hand, it has no sanction see, however. Section 1.02.3.2. The purpose of this avoidance is to forestall a multiplicity of names for systems containing several hetero atoms.)... 

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