Sentence examples for need the corresponding from inspiring English sources

We also need the corresponding result for the case (1< r< p

To formulate such theorems, we need the corresponding comparison results for fractional differential inequalities by use of the Banach fixed point theorem and the method of successive approximations.

Once u 0 is constructed, the formulae for the subsequent approximations are derived automatically by rescaling the projection map to the corresponding subintervals (we do not need the corresponding explicit formulae here and, therefore, omit the details).

In the copula formulation we also need the corresponding marginal distribution functions.

These initiatives put human-resource issues at the forefront, but need the corresponding leadership and strategic vision of government and decision-makers.

Apart from the first two studies, the other studies listed above need the corresponding control functions and protection strategies to be implemented in the model.

When needed, the corresponding transient response is obtained by means of the inverse Fourier transform.

Similarly, we need the following lemmas corresponding to the boundary conditions (1.12).

Hence, in the pre-possessing stage, we need find the corresponding V V,E) and map it into the related G V,E).

Since the gauge field propagator and the three-gauge field vertex are given by ansätze the only additional information these structures need are the corresponding definitions.

For this, we need the Laplace transform of the corresponding 'ramp' function.