Sentence examples for valid for models from inspiring English sources

The results are valid for models with low fracture density; further work should be performed using models with high fracture density and that the fracture orientation is not in the direction of the injector to the producer.

We fear that similar unfortunate properties, to those discussed in this paper, might be valid for models which can be written in the form begin{aligned} mathbf{z}'(t) =&mathbf{F}_{beta}bigl t,mathbf{z}(t) bigr), quad t in 0,T], mathbf{z}(0) =& mathbf{z}_{0}, end{aligned} where (| mathbf{F}'_{beta} | rightarrowinfty) when (beta rightarrowinfty).

In addition to this, the likelihood ratio test is only valid for models that are hierarchically nested, meaning that the more general model can be converted to the less general one by parameter manipulation.

Since the method is valid for model correction in conjunction with a model reduction method, no test data expansion is necessary so that any contamination of test data quality can be avoided and therefore the accuracy of subsequent model correction can be ensured.

This model is valid for modeling the multiple-antenna transmission systems proposed in [25, 29].

The first proposal (Jones and Larsen 2004) is only valid for modeling data above the diagonal.

Thus, the trilinear model (21) reduces to classical space time spreading using multiple spreading codes and can be written as: Y ̄ 1 = ( C ◇ H ̄ Ω ) S T ∈ ℂ P M r × N. (26) This model is valid for modeling the multiple-antenna transmission systems proposed in [25, 29].

Physics-based energy functions are expected to be globally valid for modeling interactions between proteins, including the non-native states.

Non-real numbers are not valid arguments for models and can cause non-convergence to a valid solution in simulators.

While the presented test corresponds to Vuong's test for strictly nonnested models, it is also valid for nested models when we adopt penalized likelihood scores (see File S1, for further details).

For simplicity, we applied residuals obtained with the IGRF and CHAOS-5 geomagnetic field models, but our conclusions are valid for all models with comparable resolution.