It is also worth noting that this case cannot be represented in the notation of FPO.
The problem with the system of Groenendijk (2009) and Mascarenhas (2009) is manifested by the fact that this issue cannot be represented by means of an indifference relation.
Note that this description cannot be represented by a Kronecker product, because does not show a block structure, as indicated by the size of the zero matrices.
For a more complex case, where a traditional mesh is augmented with some additional diagonal links, after providing a telling expression for the average distance between its two processors, we prove that this latter expression cannot be represented in a closed-form format, with respect to a fairly general class of "standard operations", namely, the class of the hypergeometric terms.
Once again, it is worth stressing that most of this genetic diversity cannot be represented nor can it be simultaneously analyzed with their homologs from cultured organisms in conventional phylogenetic analyses, because the vast majority of our cliques of distant homologs cannot be confidently aligned with their cultured homologs.
This complex reticulate scenario cannot be represented by a single area cladogram because the hierarchical relationships between areas change over time (Fig. 2).
This disparity of spatial and temporal scales is overcome in the hybrid atomistic-continuum multiscale frameworks where the molecular description models only a small part of the computational domain, since the physics of this part of the system cannot be represented by the continuum model.
However, we show that even though the usual set R of real numbers can be represented as the branch space of a tree with countable height and countable levels, most subsets of R cannot be represented in this way.
The only known vowels that cannot be represented in this scheme are vowels with unexpected roundedness, which would require a dedicated diacritic, such as and (or and ).
Curved roads cannot be represented, although this is unlikely to be important for larger roads.
