Hierarchical character

The significance of the proposition is the following statement (a) yields immediately that for a Pareto-character rationality is equivalent to harmonicity. Statement (b) demonstrates that the above-mentioned problematic feature of a hierarchical character, namely to require a full ranking of aspects, vanishes exactly on harmonic bundles. Similarly with statement (c), which shows that the selection problem for cardinal aggregation devices, mentioned earlier, vanishes exactly on harmonic bundles. The utilitarian aggregation device is one example covered by (c), but there are others (e.g. some kinds of modified Rawls aggregation devices such as w - / , with mtj > 0). 

The hierarchical character of reaction systems does not end with decomposition of reactions into steps. At the next level, many reactions taken together make up pathways. In bioprocesses, such pathways form long chains, cycles, and branching structures that accomplish biologically identifiable functions. In other processes, a pathway is used to describe the sequence of transformations that are needed to obtain the desired product from the available raw materials. One might even envision, at the next level, pathways combined to describe entire chemical plants or families of processing technologies. 

Fig. 4. Example of international patent classification (stmctured, hierarchical), where numbers ia square brackets identify edition of IPC ia which class was first used. In C07c 45/50, the first four characters iadicate section C (chemistry). Class 07 (organic chemistry), and subclass c (acycHc compounds) the number 45 /00 iadicates the preparation of compounds having carbonyl groups bound only to carbon or hydrogen atoms by any method and 45 /50...

Another important consideration regarding the character of constraints, h,, is their hierarchical articulation at multiple lerels of detail. For example, suppose that one is planning the routine startup procedure for a chemical plant. Safety considerations impose the following constraint on the temporal ordering of operations ... 

In the first chapter of Volume 2 (hereinafter referred to as 21 1) we presented the general framework of MODEL.LA., a modeling language that can capture the hierarchical and distributed character of processing systems. We will employ all aspects of MODEL.LA. in order to develop a complete and consistent description of plants that will satisfy the modeling needs for the synthesis of operating procedures. 

Fig. 13.17 shows an example of the hierarchic (multilevel) character of a molecular architecture ... 

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