Sentence examples for triple solutions from inspiring English sources

However, Feng and Ge did not obtain any results of triple solutions on problem (1.2).

In 2005, Chyan and Wong [8] obtained triple solutions of the same BVPs with [7].

It is also proved that the problem might have multiple stationary solutions (unique, dual and triple solutions) depending on the values of the parameters of the model.

Figures 11, 12, 13 present samples of velocity profiles and induced magnetic profiles supporting the existence of triple solutions for β = 0, β = 0.03 and β = 0.1, respectively.

Figure 12 (a) Velocity profiles f ′ and (b) induced magnetic profiles g ′ showing the existence of triple solutions when β = 0.03, S = 0.5 and λ = − 0.222.

To be more specific, our computation shows that for β = 0.03, a unique solution has been found for the range − 0.8365 ≤ λ ≤ − 0.2502 and λ ≥ − 0.336, while triple solutions have been found for the range − 0.335 ≤ λ ≤ − 0.2503.

Then the existence of a tripled solution for (6.1) provides the existence of a unique solution of (6.1) in C ( I, R ).

Now, let be a tripled solution of the initial value problem (6.1); then we have α ≤ F , F ≤ β and γ ≤ F.

The experimental triple-solution multiplicity disappears for fuel concentrations in excess of ∼25% or below ∼7% H2 in N2, and was only found in the pressure range between ∼1.5 and 7 atm, at 9% H2 in N2 and a pressure-weighted strain rate of 300 s−1.

Finally, template was removed by triple solvent extraction in HCl/C2H5OH solution at room temperature for 24 h.

Then, the template was removed by triple solvent extraction in HCl/C2H5OH solution at room temperature for 24 h.