Sentence examples for explicitly depend on from inspiring English sources

In a simplified case of using of the effective field hypothesis for analyzing composites with one sort of heterogeneities, one proves that the effective moduli explicitly depend on both the strain and stress concentrator factor for one heterogeneity inside the infinite matrix and does not directly depend on the elastic properties (local or nonlocal) of heterogeneities.

For autonomous differential equations (i.e. ones which do not explicitly depend on time) there is an invariance with respect to time shifts, in the same way that we saw invariance with respect to spatial shifts in Sect.

We immediately note that the angular speed (dot {theta }) can be directly control by u, while the radial one, (dot {r}), does not explicitly depend on the field.

Disregarding generalised body forces, which may be position dependant, the energy functional in Eq. 10 does not explicitly depend on the spatial coordinates, and therefore, the Beltrami identity may be used to obtain the stationary points of the Euler-Lagrange equation.

The fundamental valuation equation will explicitly depend on time.

These are models that explicitly depend on a fixed number of parameters.

Subprime loans were offered on generous terms that, implicitly or explicitly, depended on rising house prices.

As a sequence, waveform optimization for maximizing the SINR explicitly depends on these pre-assigned values.

We shall concentrate our attention on the third term in (39) since it explicitly depends on the initial condition.

We derive an upper bound for the input delay tolerance, which explicitly depends on the agent dynamics.

The key step is the construction of a monotone mapping, which explicitly depends on some of the estimator tuning parameters.