Further Enumerations

2 Further Enumerations. - Another, somewhat separate area of chemical enumeration concerns the counting of resonance structures for the purpose of gauging the extent of resonance . Often these structures may have much the flavor of different isomeric structures, though the enumeration is usually taken to 

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In given work the possibilities enumerated above of varieties of thermal analysis used to reseai ch of solid solutions of hydrated diphosphates with diverse composition. So, for example, the results of differential-thermal analysis Zn Co j P O -SH O showed, that it steady in the time of heating on air to 333 K. A further rise of temperature in interval 333 - 725 K is accompanied with the masses loss, which takes place in two basic stages, registered on crooked TG by two clear degrees, attendant to removal 4,0 and 1,0 mole H O. On crooked DTA these stages dehydration registers by two endothermic effects. In interval 603 - 725 K on crooked DTA is observed an exothermal effect. 

Further progress in asymptotic tree enumeration was made by Otter, who in [OttR48] considered the problem of rooted and unrooted trees with maximum degree m. Having enumerated unrooted trees by the method already described, he proceeded to derive asymptotic estimates, and after ten pages of analysis arrived at a number of results, of which the following is typical ... 

The guidelines enumerated above are by no means complete, but they do provide a starting point for the beginning student. Further details are available in publications by Edwards et al. (5) and King (7). 

We can extend these constructions a little further to show that every recursively enumerable set can be obtained as the value language of a monadic program scheme (subject to addition of the final x, of course). 

For the past 50 years the determination of the sanitary quality of water has been based on the enumeration of indicator micro-organisms (e.g. coliform bacteria). The adequacy of coliform enumeration methods for this purpose has been questioned [21]. The current trend of year-round disinfection of waste water effluents and the increasing discharge of both toxic substances and heat from industrial outfalls cast further doubt on the accuracy of biological indicator systems [22]. 

The subject has been very thoroughly reviewed [1-3], but certain fundamental aspects can profitably be reconsidered in the light of some recent developments [4-6]. Certainly the most startling of these is the discovery that under conventional conditions the polymerisation of styrene by perchloric and other acids, and by the syncatalytic system stannic chloride-water, is not an ionic process. These polymerisations have been named pseudocationic . This finding is in direct contradiction to the beliefs held previously about this and related reactions. Hence a new survey of the whole field has become necessary which must start with an enumeration of those systems for which the nature of the polymerisation reaction has been established with reasonable certainty. From these boreholes one can then try to assess the nature of the intervening territory and to decide where further detailed exploration would be most profitable. 

The enumeration of the components of the individual products has been limited to the main constituents and the odor determining compounds further information is available in the literature, e.g., [214, 225-230a]. Physical data for extracts or concentrates consisting largely of nonvolatile material are not given because the composition of these products varies widely according to the isolation and manufacturing procedure used. 

Sequential docking, where pre-enumerated compounds are docked into the receptor binding site, scored, ranked, and selected for further experimental testing the conformational... 

The tetracarboxylatodimolybdenum dimers that result from the reaction of molybdenum hexacarbonyl with a wide variety of carboxylic acids are the initial source of quadruply bound molybdenum units for many further chemical investigations. The initial isolation of Mo2(02CC6H5)4 (2), Mo2(02CCH3)4 (14), and the higher alkyl carboxylate analogues (235) by Wilkinson et al. established a reactivity pattern that has been successfully exploited to prepare many related molybdenum dimers. In addition to those carboxylates enumerated above, a series of substituted aromatic carboxylate derivatives has been prepared by refluxing the appropriate acid with molybdenum hexacarbonyl in diglyme (155). 

To avoid the enumeration of all candidate subproblems we employ the fathoming tests discussed in section 5.3.1.3. These tests allow us to eliminate from further consideration not only nodes of the binary tree but also branches of the tree which correspond to their children nodes. The success of the branch and bound algorithm is based on the percentage of eliminated nodes and the effort required to solve the candidate subproblems. 

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