Similarity structural, definitions

Similar operational definitions have to be taken into account for every experimental tool of structural chemistry to define the meaning of the observables that it provides6. In microwave spectroscopy, for example, structural information is obtained from the rotational constants... 

There is some arbitrariness in the definition of the ion pair, and hence the association constant. Often a structural definition of the ion pairs is preferred—for example, by adopting a cutoff distance such as rc = 2a [141, 207] or similar choices [208, 209]. In contrast, Bjerrum (Bj) theory [140] uses an energetic criterion by defining ions as being associated, when their interaction energy is twice the thermal energy kBT. Bjerrum theory yields... 

The underlaying assumption in the evaluation of both information, the Sij and the representation of a group, is that compounds with similar properties have similar structural features thus producing similar spectra. In view of the fact that no strict rule for quantitative definition of similarity between structures exists it is hard to justify the above assumption. However, many valuable results can be obtained using the correlation between the similarity of properties (structures) and similarity of spectra. If the reduced representation of a spectrum i is written in a vector form Ri as... 

Some of the intriguing properties of the golden ratio include (i) its connection with self-similar structures, evidenced by its definition as a continued fraction ... 

For (ET)2ClO4(TCE)0 5 (TCE = trichloroethane), solvent is incorporated into the structure at positions similar to those occupied by the anions, i.e., separating the sheets of ET molecules (59). For this structure definite stacks cannot be identified at all, and, as a consequence, the electronic structure is also very two-dimensional. It is not unlikely that this structure (triclinic with space group PI) is also adopted by (ET)2ReO4(THF)0 5 with the only difference being that the solvent here is THF (tetrahydrofuran) (57). 

Chart 1) have particular preferences for the formation of a 14-helix and a 12-helix, respectively. The crystal structure of oligomers 6 (based on the former monomer) indeed revealed a perfect 14-helix, but although strong indications for the presence of a similar structure in solution were obtained, no definitive solution data have been presented yet.29 For a hexamer (7a) and an octamer (7b) of the cyclopen-tane-derived /1-peptide, the solution structure was determined using NMR. This supported the existence of the 12-helix structure which was also found in the solid state.30 More recently also X-ray data on the packing of these helices in the solid state have become available, which may help to design tertiary structures based on these foldamers.31... 

Before the requirements that remain from Section 7.1.3 are formalized, the additional service properties that standard fail-stop signature schemes should have according to Section 6.1.2 are considered. It turns out that most of these requirements are automatically fulfilled according to the assumed structure of the entities around the algorithms from Definition 7.1 or 7.2, respectively. The only remaining one, the strong requirement of the signer on disputes in the case with special risk bearers, can be fulfilled by similar structural measures. 

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