Imperfect staircase

Furthermore, one should observe the termination of each row in the right-hand direction. This termination results in the staircase boundary. It is determined by the formulas situated at the extreme—right of each row, namely the formulas which pertain to the extremal polyhexes, as should be dear from the definition of these systems (Par. 3.3.4). When perfect extremal p-tuple coronoids are involved, then the corresponding staircase boundary reflects a part of the staircase boundary for benzenoids. It is specifically the part which corresponds to the benzenoids associated with the tuple coronoids in question. Thus, for instance, the staircase boundary for single coronoids has the same shape as the one for benzenoids when starting from C32H14 ovalene (cf. Table 5, where the start of this staircase boundary for benzenoids is indicated by thin lines). A staircase boundary of this kind, determined by perfect extremal coronoids or extremal benzenoids, shall be referred to as a perfect staircase (boundary). If imperfect extremal coronoids are involved we shall call it an imperfect staircase. 

Figure 5 HREEL spectra recorded after small O2 doses at E = 0.39 eV on flat Ag(l 0 0) (bottom spectrum), Ag(41 0) (middle) and Ag(2 1 0) (top) at T = 105 K. O2 is dosed at normal incidence for Ag(l 0 0) and close to the normal to the step heights for the stepped surfaces. The losses in the 30-40 meV region are due to adatom surface vibrations, those at 80-84 meV to the internal stretch mode of the O2 admolecules. It is evident that only molecular adsorption takes place on flat Ag(l 00), while adatoms and admolecules coexist on Ag(41 0) and the final adsorption state is purely dissociative for Ag(2 1 0). The residual intensity at 84meV in the upper spectrum is most probably due to imperfections of the (21 0) staircase leading to larger terraces. We remind that the oxygen dose is expressed in ML of surface atoms, which are therefore referred to the corresponding face density.

Fractals are self-similar objects, e.g., Koch curve, Menger sponge, or Devil s staircase. The self-similarity of fractal objects is exact at every spatial scale of their construction (e.g., Avnir, 1989). Mathematically constructed fractal porous media, e.g., the Devil s staircase, can approximate the structures of metallic catalysts, which are considered to be disordered compact aggregates composed of imperfect crystallites with broken faces, steps, and kinks (Mougin et al., 1996). 

In the above diagrams the staircase boundaries are indicated by heavy lines. For the portions where they are imperfect they are augmented by stippled lines to the shapes which conform with perfect boundaries. Hence it should be understood that the parenthesized formulas actually do not exist for the coronoids in question. The heavy formulas pertain to perfect extremal coronoids. 

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