However, numerical investigations for these latter two equilibria indicate that, under the parameter regions we are studying (Fig. 4), the non-trivial values for such points are outside the biologically meaningful parameters (i.e., xi*>1, results not shown) imposed by the logistic-like constraint (with carrying capacity C0 = 1), and thus are not analyzed.
All the above expressions are uncomputable exactly, except for a few trivial values of p and q.
Officials may not offer or accept gifts that have more than 'symbolic or trivial value'".
This approach however does not work for i≤L as Xa(i) will be full rank for any choice of X ( i ), and therefore, h with 2L degrees of freedom can always be chosen by least squares (LS) to yield the trivial (zero) value for M X ̂ ( i ).
In particular, considering renewable energies lead to at least two non-trivial problems: exact values for such an exogenous parameter are not always available, moreover the exact value of its next day production is rather tricky to be predicted with enough accuracy.
Determining proper values for these parameters is a non trivial task.
Finally, trivial redundancy was eliminated by discarding sequences with identical values for size, GC1, GC2, and GC3 (or a difference of GC3 <2%).
This way, they search for biclusters with the maximum possible values for MSR below δ, rejecting thus trivial solutions in which there are no expression changes across the samples.
Since the data are in different formats (e.g. numeric values for gene expression, strings for protein sequences), integrating them is non-trivial.
The polynomials contain trivial zeros for even values of p at z = − 1 and at z = 1.
