Sentence examples for been shown that analytical from inspiring English sources

It has been shown that analytical and empirical results are coincide with each other.

The simplicity of such models is also appealing from a theoretical perspective, and for a threshold described by an Ornstein Uhlenbeck process it has recently been shown that analytical (and non-perturbative) expressions for the first-passage time distribution can be obtained [20].

It is shown that analytical buckling loads differ from numerical ones for less than 12%, and that force displacement curves are well predicted.

It is shown that analytical solutions can be found in the case of a pit of quadratic profile and for uniform damping properties (without added layer).

It has been shown that the analytical and numerical results are in good agreement with experimental data.

It has been shown that the analytical solution provides an accurate estimate of the critical load and does not involve any computationally expensive procedures.

It has been shown that the analytical formula presented in this paper provides an efficient means for rapid and reliable calculation of the fundamental frequency which can be used for the assessment of the structural stiffness of the shells in the design analysis.

It has been shown that preanalytical and analytical heterogeneity amongst various research groups has led to differing results [ 38, 41, 42].

However, it has been shown that the available analytical methods do not necessarily depict the complete picture of health hazards that are associated with DEE (Bünger et al., 2007; Krahl et al., 2008).

In the previous sections it has been shown that process evolution functions are an analytical time continuous representation of event series.

A simple analytical model that incorporates evolving damage within the composite is proposed, and it is shown that the analytical predictions are consistent with the experimental observations over a wide range of strain rates.