Fundamental building-up principle

A principle for the building—up of single coronoids, which is stronger than Principle 6.1, shall presently be referred to as the fundamental building-up principle. It is formulated in the following. 

The corresponding strengthening of the building-Hip principle for benzenoids quoted above (Par. 6.5.1) has been formulated elsewhere as a theorem (Cyvin SJ, Cyvin and Brunvoll 1993e). 

Principle 6.2 states the sufficiency of one-, two— and three-contact additions in the building-up process. It is easy to prove that these three types also are necessary in general. That is for instance proved by examples where all free edges occur in (i) Lj—, (ii) or (iii) mode hexagons exclusivdy (see Fig. 4). It is dear that the last step in the building-up of the a ve systems had to employ a (i) one-contact—, (ii) two-contact— and (iii) three-contact addition. 

Let the above types of systems be termed L —added, P —added and L -added for (i), (ii) and (iii), respectivdy. A precise definition is given bdow. 

Definition 6.5 A single coronoid C is L -added, Pg-added or added when all the free edges of C occur in Lj—mode—, Pg—mode- or mode hexagons, respectivdy, apart from those free 

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Pig. 6.5. Illustration of the fundamental building-up principle applied to isomers (Principle 6.3). The formulas are arranged as in Table 5.3. 

Example. The method of perforating benzenoids shall presently be exemplified by the C46H20 (h = 13, 71 = 6) single coronoid isomers. The application of the fundamental building-up principle would be somewhat laborious in this case it would imply the appropriate additions to (i) 2 C42H18, (ii) 37 C43H19 and (iii) 142 C44H20 coronoid isomers. 

The principle of tu quoque is dangerous because it can lead to a disintegration of the fundamentals of international law, whereas what we need to do is to build up and consohdate a system of international law. If, however, two warring parties consistently disregard a judicial norm, the evolution and development of the law must be reviewed in the context of this desuetude.24 Such a case represents a modification of common law. 

Very few synthetic systems reach similar strengths without polyvalency and so present a current challenge. With the plethora of natural examples, and in order to build to the nanoscale quickly, supramolecular chemists rarely design molecular systems from fundamental principles, but rather they find unique ways to combine simple building blocks, which have often been studied and understood as individual components to build up larger stable and functional architectures (Figure 5). ... 

The measurement principle of the technique is relatively simple, and the direct measurement on actual components is a desirable feature. Selected small areas can be irradiated, to monitor the degradation of a particular weld zone, for example. The technique can be applied to study erosion effects. The instrumentation used to irradiate the surfaces can accommodate only small components. The technological infrastructure required to perform the surface activation is substantial and is not readily accessible in all countries. From fundamental principles, the measurements are meaningful only if the radioactive isotopes are removed from the surface undergoing corrosion damage. If they remain in the corrosion products building up on surfaces, the thickness reduction will not be detected. The sensitivity of the technique is generally relatively low. The technique is not yet widely utilized. 

In investigating the highly different phenomena in nature, scientists have always tried to find some fundamental principles that can explain the variety from a basic unity. Today they have shown not only that all the various kinds of matter are built up from a rather limited number of atoms but also that these atoms are composed of a few basic elements or building blocks. It seems possible to understand the innermost structure of matter and its behavior in terms of a few elementary particles electrons, protons, neutrons, photons, etc., and their interactions. Since these particles obey not the laws of classical physics but the rules of modem quantum theory of wave mechanics established in 1925, there has developed a new field of quantum science which deals with the explanation of nature on this basis. 

Another policy in writing the book has been the attempt to base the deduction of all equations on first principles. What actually constitutes such principles is, to an extent, a matter of individual preference. Any attempt at definition would immediately lead one into the field of the professional philosopher. Such an intrusion the author is, above everything, anxious to avoid. Fie feels, however, that the attempt to build from the ground up has been accomplished in most of the subjects considered. Exceptions are, however, the extension of the Debye-Huckel theory, and the application of the interionic attraction theory to electrolytic conductance. In the latter case the fundamentals lie in the field of statistical mechanics, which cannot be adequately treated short of a book the size of this one, and which, in any case, would not be written by the author. 

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