Sentence examples for case provided that from inspiring English sources
We show that for f and g harmonic, TfTg=Th only in the trivial case, provided that h is of class C2 with the invariant laplacian bounded.
Our model thus applies to that case, provided that time 0 refers to the creation of the population (while the mutation occurred earlier).
In this case, provided that γ < 1 (it is normally between 0.6 and 0.8), this model predicts that the individual eventually reaches an asymptotic size (W∞) that depends on the assimilation rate scale φ.
All of the heterogeneous drought probability expressions reduce down to homogeneous case provided that sub-areal probabilities are equal to each other.
The relevant equations for the identification process are (4.10a), in the general case, and (4.10b) in the linear-in-the parameters case, provided that the measured data sequence is scalar (i.e. the first component of the regressor).
Sexual selection models of speciation have demonstrated that this may indeed be the case, provided that there are mechanisms leading to variation in female preferences.
On the other hand, the equilibrium contribution of C increases with π in all cases, provided that joint contribution occurs.
The number of samples required to obtain the mean salinity over a typical length of fairways (250 300 m) within a deviate range of 20% averaged 6 in deep sandy Aridisols and Alfisols, and 13 each in other cases, provided that sampling of Entisols is made based on soil type distributions.
This second part shows that the same approach can be extended to the general case providing that a somewhat more complex, nonlinear algorithm, is acceptable.
The substitution of one test with another will be acceptable in such a case providing that the magnitude of the correlation coefficient between the two is really big (and in the positive direction).
In 1968, Congress had passed a law permitting the Justice Department to place wiretaps on American citizens in certain cases, provided that it first obtained a court warrant in each case.
