Sentence examples for be smooth functions of from inspiring English sources

The polynomial chaos (PC) expansion modes are shown to be smooth functions of the spatial variable x, although each solution realization is discontinuous in the spatial variable x.

This suggests that in the limit of N → ∞, at any instant in time, V and h will be smooth functions of the continuous variable I app.

As one would expect due to the smoothness of the generating tensors the MT phase tensor, as well as the (quasi-) electric phase tensors appeared to be smooth functions of period.

It can happen that even when the Aij are smooth functions of t or constant, the solution X may have a singularity or even infinitely many singularities.

The gradation of orthotropic material properties are smooth functions of spatial coordinates, which are integrated into the element stiffness matrix using the so-called "generalized isoparametric formulation".

where,, are smooth functions of and at least of the third order in variables, (3.17).

where,,, are smooth functions of and at least of order three in variables.

One can see that all tensor elements are smooth functions of period.

An alternative is to consider the system parameters are smooth functions of spatial coordinates, which define a partial differential equation while they make the network structure preserved.

Now, for the case b > 0 small, we first remark that similar dominated convergence arguments as above show that both I ( N ) and I ′ ( N ) are smooth functions of b.

In that case, all but one of the terms in Equation (14) in the vicinity of x are smooth functions of x, because they correspond to energy measurements which are insensitive to the exact location of the pattern, whenever it remains entirely within the patch.