Sentence examples for be solved explicitly in from inspiring English sources

Moreover, it is shown that the resulting implicit equations can be solved explicitly in the case of constant transport properties.

Unlike other implicit or semi-implicit schemes proposed in the literature, our semi-implicit schemes can be solved explicitly in the spectral space.

Most boundary value problems stated for the planar Poisson equation in a rectangle for which series-only representations of solution were known, may thus be solved explicitly in closed-form using the method of images.

Write and for the mean and variance of the distribution function C K. The saddlepoint approximations to the expectations m g,1 t) and m g,0 t) are given by where (7) where and where is the root to the equation, which can be solved explicitly in some cases, or, when not possible, numerically.

For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices.

The elastic problem of the contact between an axisymmetric indenter and a general anisotropic (21 independent elastic constants) half space has not been solved explicitly in closed form.

If there is no boundary condition (in particular,, and (H3; ) is vacuous) and the system can be solved explicitly for in terms of and its derivatives.

It also opens for further simplification into one-variable optimisation problems, which in many cases can be solved explicitly, as shown in the results section.

Since the transcription ODE model is linear with respect to m j (t), it can be solved explicitly as shown in the supplementary information.

While a sigmoidal form for the response function G was considered in all our experiments, our algorithms could easily be adapted to handle different forms for G. Furthermore, the simple linear translation equation can be solved explicitly as shown in the supplementary information.

We propose to penalize the nonlinear collision term by a BGK-type relaxation term, which can be solved explicitly even if discretized implicitly in time.