Sentence examples for proved that the initial from inspiring English sources

Generally the obtained results proved that the initial debonding pattern and stiffeners arrangement have a crucial effect on the bending behavior of the structure.

In [20], the authors proved that the initial multidimensional fixed point result, Theorem 9 in [11], can be derived from Theorem 2.1 in [21] either.

It is proved that the initial prototype can not only self-sustain an equilibrium pressure for more than 2 months without power but also withstand the mechanical vibration test and space environment simulation test.

In [5, 6], Gal and Grasselli proved that the initial and boundary value problem generates a strongly continuous semigroup on a suitable phase space which possesses the global attractor A and establish the existence of an exponential attractor E which entails that A has finite fractal dimension.

The obtained results, shown in Figure 4, proved that the initial rate of degradation of Rh6G increases with the concentration of H2O2 in the solution.

Moreover, we proved that, as the initial data satisfy (|u_{0}|^{2}_{H^{1}_{mathbb{R}^{3}}}+|b_{0}|^{2}_{H^{1}_{mathbb{R}^{3}}}+|theta _{0}|^{2}_{H^{1}_{mathbb{R}^{3}}}leqvarepsilon), where ε is a suitably small positive number, then the 3D magnetic Bénard system with mixed partial dissipation, magnetic diffusion and thermal diffusivity admits global smooth solutions.

We prove that the initial phase difference Ψ plays an important role in suppressing or inducing chaos in complex systems.

The function will be a solution to the mixed problem (3.9) after proving that the initial condition is satisfied.

The post-wrinkling behavior is also considered to prove that the initial pattern of wrinkles is not affected.

We prove that the initial boundary value problem of the incompressible two-dimensional Euler equations admits a unique solution and discuss the stability of the solution.

The simulation results prove that, the initial growth stage of a 10 nm single hemispherical silver nucleus always starts under kinetic control, regardless of concentration and electrode potential.