Sentence examples for and the corresponding initial from inspiring English sources

First, each edge metric and the corresponding initial state metric are added together.

Under diffusion control, both processes are irreversible and the corresponding initial two-electron transfer is the rate-determining step.

For the purpose, the COD and the VSS were measured for the undiluted sample and the corresponding initial COD and the initial X in each RU were calculated based on the dilution factor.

It is shown that the magnitudes of interference and the corresponding initial stresses have important and apparent affections to the results determined by the lock-in infrared thermography technique.

External loadings are decomposed into Prony series, and the initial conditions are transferred from the system into the reconstructed loadings, which are combinations of the initial loadings and the corresponding initial conditions in the Laplace domain.

The impact energy and the corresponding initial velocity at 2.1, 5.2 and 8.1 m/s for both reinforced nanocomposites are conducted and found to have the linear relationship with both impact results.

In this paper we add two initial conditions to the differential equation and consider the corresponding initial value problem.

If such an ℓ does not exists, we formally set ℓ = ∞ and we call the corresponding initial condition and the corresponding geodesic trapping.

For example, in both cases R i_cie ∗ and R i_cde ∗ are not uniquely determined and depend on the corresponding initial values.

We define the efficacy function E f (t) by (11) E f t = 1 − I ∗ t + I c ∗ t I 0 + I c 0, where I ∗ (t) and I c ∗ (t) denote the optimal solutions associated with the optimal control of the corresponding variable and I 0) and I c (0) denote the corresponding initial condition.

Such properties as isomorphism, coerciveness with respect to the spectral parameter, completeness and Abel bases property of a system of root functions of some boundary value problems with transmission conditions and its applications to the corresponding initial boundary value problems for parabolic equations have been investigated in [16 19].