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In the homogenized beam model, the generalized 1D stresses are the axial and the flexural stress field resultants.

Shanley nonlinear spring model was used in conjunction with the concept of 'superbeam' element to model the generalized plastic hinge.

In the Love Kirchhoff model, the generalized stresses are the in-plane (membrane) and the out-of-plane (flexural) stress field resultants.

Under large periodic modulations in the variable coefficients of the LF model, the generalized Akhmediev breathers develop into the breather multiple births (BMBs) from which we obtain the Peregrine combs (PCs).

Here we will discuss four different modified models: the Hubbert model, the generalized Weng model, the H C Z model and the Weibull model, showing different types of bell-shaped transformation.

The results of five models listed in Tables 3, 4 and 5 reveal that for most of provinces in China, the four models (the Hubbert model, the generalized Weng model, the Weibull model, and the H C Z model) with smaller errors are much plausible to the present status of China, compared to GM (1, 1).

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In this study, Model 1 shall denote the (Bayesian) ordinary logistic regression model, Model 2 the generalized linear mixed model with spatially unstructured random effects, Model 3 the generalized linear mixed model with spatially structured random effects, and finally, Model 4 the generalized linear mixed model with both the spatially structured and unstructured random effects.

We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method.

The parameters in the Weibull model, generalized Weng model, and H C Z model can be calculated in a similar way.

The model generalizes the most popular model MEC and the recent model MFC.

The model generalizes the Gurson model to account for both void growth and coalescence with explicit dependence on void shape and distribution effects.

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