Sentence examples for more complicated expression from inspiring English sources

In this case, we have to establish a more complicated expression of operator T and to find the proper lower and upper bounds of Green's functions (Lemma 2.2 and Lemma 2.4).

I-DirI is in the same orientation as the Pol I rRNA transcript [ 64], and has a more complicated expression mechanism.

For example, I can show (see Methods) that for binding sites evolving in the absence of selection, A similar, albeit more complicated expression is available for the variance (see Methods).

In C. ocellatus, we detected a far more complicated expression profile of cadherins with significant upregulation of CDH1 (epithelial cadherin), 2, 4, 11, 15, 22, and 24 and downregulation of CDH5 and 13.

Second, for all parameter ranges, there is very close fit between our simple expressions for protein noise and the more complicated expression of Thattai and Van Oudenaarden, with the exception of very weak repressors in Figure 1 d) where their expression fits the data slightly better.

Subsequent work has shown that the relationship loses its validity at higher pressures, but more complicated expressions that more accurately match experimental results can be derived.

Transformation into real states is possible but comes at the cost of more complicated expressions for the convolutions.

Nevertheless, for more complicated expressions of S, such as (12) and (13) (SSPA and TWTA models), the derivation of analytical expressions for the parameters K and σ d 2 is intractable.

However, there are many cases in the real world where we need more complicated expressions based on universal and existential quantifiers, as well as logical implications in action models to precisely describe the underlying mechanisms of the actions.

The main result is that theorems in LPF using weak equality can be straightforwardly translated into ones that are true in FoPC; translation in the other direction results, in general, in more complicated expressions but in many cases these can be readily simplified.

More accurate (but slightly more complicated) expressions are derived in the Methods.