Computational model of the deformation of graded wedge with complicated structure

As a computational model of deformation of wedge-shaped gradient coatings lying on a non-deformable base, we propose a solution of the contact problem for a wedge non-uniform in thickness rigidly fixed on the lower face. A closed analytic solution of the contact problem is obtained for the case of elastic moduli (Young’s modulus, Poisson’s ratio, shear modulus), which is a continuous differentiable function with respect to the angular coordinate. The influence of the gradient of the wedge on the distribution of contact stresses under the stamp is illustrated. The problem is posed in connection with the need to predict the phenomenon of delamination of modern coatings of a complex structure from a nondeformable substrate.

Weak linear representation of M-estimaton in GLMs with dependent errors

In this paper, we consider the generalized linear models (GLMs) [Formula: see text] where [Formula: see text] is a continuous differentiable function, [Formula: see text] are dependent errors. We obtain the M-estimator [Formula: see text] of [Formula: see text] from the following equation: [Formula: see text] where [Formula: see text] is assumed to be a convex function. We also show the linear representation and asymptotic normality of the estimator, which extend the correspondingly results of Wu et al. (M-estimation of linear models with dependent errors, Ann. Statist. 2007) to GLMs.

On the Sum of Differentiable Functions

Ryll-Nardzewski has proposed the following problem (New Scottish Book, no. 119). If fn(x) are continuous, differentiable* functions in a closed finite interval, do there always exist constants cn (no cn = 0) (depending on the ), such that converges and is also a continuous differentiable function?