Uniform complexity

A big advantage of the solid-solid technique is the possibility of obtaining complexes that are not obtainable from solution. It must, however, be shown that uniform complexes rather than microcrystalline mixtures occur. Apart from X-ray powder diffraction (which does not properly account for very small crystallites), proof is obtained by solid-state spectroscopy (IR, UV, luminescence) or, in the case of stable radicals, by magnetic susceptibility measurements. The 1 1 and 2 1 complexes 68-72 were prepared by stoichiometric milling and relevant physical properties are collected in Table 3 [20]. 

An alternative to uniform complex scaling (used in the studies mentioned so far) is exterior complex scaling [45,46], where the scaling of the coordinates starts at some finite distance from the origin. This approach has been used extensively on electron scattering problems in the absence of resonances, for example, in Refs. [47-50], for a review see Ref. [51], as well as to obtain resonance parameters in connection with electronic autoionization [52,53]. 

J Bengtsson, E. Lindroth, S. Selsta, Solution of the time-dependent Schrodinger equation using uniform complex scaling, Phys. Rev. A 78 (3) (2008) 032502. 

Alternatively, non-uniform complexity is used quite often, i.e, polynomial-size sequences of probabilistic circuits. (For details about non-uniform complexity, see [Sch685].) The argument for using non-uniform complexity is that allowing attackers to be non-uniform yields a stronger notion of security [GoMi84]. 

What are the computational abilities of the attacker Usually, as mentioned in Section 2.3, only one distinction is made Attackers are either restricted to feasible computations, then they may use arbitrary polynomial-time interactive Turing machines or computationally unrestricted, then they may use arbitrary probabilistic interactive functions. (For more distinctions, see, e.g., the footnote about non-uniform complexity in Section 4.3.)... 

Uniform complexity. Most definitions are non-uniform, i.e., they use circuit complexity. A uniform definition was given in [Gold93], and this (mainly Remark 18) was adapted here. 

Gold91 Oded Goldreich A Uniform-Complexity Treatment of Encryption and Zero-Knowledge ... 

Figure 4 Complex scaling in three different forms the original Uniform complex scaling of Balslev and Combes. The Exterior complex scaling proposed by Simon and the Smooth exterior complex scaling studied by Helffer are all discussed in the text.

Complete and uniform complex equipment priming in the automobile... 

The ecology of marine lichens is rather unknown. Below the spray belt the more specialized lichens such as Lichina and Verrucaria occur (e.g., sixteen species in Europe Zschacke, 1925). Here in the litoral zone (middle and lower hygrohalinic belt) the lichens still are not frequently inundated. The width of this belt depends on the exposure of the coastal sites (Fig. 20). At sheltered coasts the belt is very small and the lichens concentrate at the medium-high water level. This shows a dependence upon the direct influence of seawater, which may be due primarily to the competition with other, less water-resistant species. The species here which are normally considered as a uniform complex behave very differently (Grummann, 1937). Lichina confinis avoids action of waves but tolerates intense insolation (as observed on the Baltic seacoast), while the very thin thalli of Verrucaria maura are extremely scotophilous and, being closely fixed to the rocks, they tolerate stronger washing by the waves but not permanent inundation. 

Cationic detergents able to condense plasmid DNA into small uniform complexes (42). 

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