Sentence examples for exactly obtained in from inspiring English sources

Remark 2.1 Actually, Corollary 2.1 and Corollary 2.2 have been exactly obtained in [11] and [12] in the special case δ = 1.

For the crack subjected to point or uniform temperature loadings, the thermo-elastic field variables are explicitly and exactly obtained in terms of elementary functions, in a complete manner.

where λ is the variational parameter, ψ z) is the wave function of the donor electron which is exactly obtained from the Schrödinger equation in the z-direction without the impurity, and ϕ is the wave function in the (x and y) plane, and it is given by the following: ϕ ρ, λ = 1 λ 2 π 1 2 E x p − ρ / λ. (10).

A near field solution, of the second order, is exactly obtained by a regular perturbation expansion in terms of the amplitude of the source oscillation.

Two design specifications based on H2 norm are formulated in BMIs, and PID parameters can be exactly obtained by solving the BMI problems via branch and bound algorithms.

If (q=0) the results are exactly those obtained in  [11].

The response almost exactly replicated that obtained in the original CBT-E trial.

In this paper, a method is proposed to design the load signal which has to be applied in order to exactly obtain a certain damage content.

09N1-I149V crystals were obtained in exactly the same condition as 09N1 (Li et al., 2010).

The remainder of the results are obtained in exactly the same manner as in the case where z ( n ) does not obey boundary condition (3.28) with s being replaced by s − 1, see (3.36) and the subsequent calculations.

It is evident from Table 3 that the substrate concentration at biofilm liquid interface (S s), found in case 3, i.e., in pseudo analytical solution by Rittmann and McCarty (2001) exactly tallies with that obtained in the proposed biofilm model.