Sentence examples for function does not need from inspiring English sources

Note that the functional dependency between variables in the covariance function does not need to be a cross product, but can be any function that takes into account the similarity between the input data points and also complies with the properties of a covariance.

Of particular importance are the facts that the underlying scaling function does not need to satisfy any a priori conditions, and that the freedom offered by redundancy can be fully exploited in these constructions.

Remember that such function does not need to be a solution of (3.1) in the sense of Definition 2.2.

The first derivative of such a function does not need to be continuous at and hence, due to the lack of smoothness, does not need to be a solution of (2.1) in the sense of Definition 2.2.

Therefore we fitted parametric regression model methods that allow for the baseline hazards to vary for different categories for an independent variable and the hazard function does not need to be proportional.

The values on the intersection of vertical line and the region of membership function do not need all to be weighted same.

This ensures that the data sampling functions do not need to wait for the slow LCD to finish updating before beginning another iteration of data acquisition.

On the other hand, the human embryo of similar stages and even after organogenesis still uses the placenta for energy and metabolite supply, so the genes associated with such functions do not need to be upregulated at late organogenesis stages.

As the sparsity level is hard to be estimated in image sequences reconstruction, we propose a novel optimization function which does not need the sparsity level known as a prior.

Furthermore, a new stack frame for a function call does not need to be cache-consistent with the main memory.

The Matlab function eigs does not need J, only its product with an arbitrary vector, which can be implemented as above.