The local mathematical model of stress-strain state of granular composite material, based on a generalized Fourier's method, is developed. The numerical realization of model has allowed to receive character of distribution of local stress in the field of their concentration. The comparison of results with the solution on a finite element method is carried out.

About one-dimensional perturbation of the selfadjoint operators with simple spectrum.} One of major tasks of perturbation theory is to study spectrum of the perturbed operator and to describe spectral projectors of it. A classic result which gives the solution of this task in finite-dimensional case for operators with a simple spectrum is the Lowner theorem. In the paper the infinite-dimensional analogue of this statement for operators with a simple discrete spectrum is obtained.

The purpose of this paper is to construct dependencies for the best in mean square value of an estimation $\bar{m}_\gamma(u,v)$ Wiener fields $w(u,v)$ on its realizations on sites of two monotonously not decreasing curves $w(x,y),\,(x,y)\in\gamma_1\bigcup{\gamma_2}$,$(u,v)\notin\gamma$ and its error $d_\gamma (u,v)$. The given dependencies are received in work for various variants of an arrangement of a point $(u,v)$ concerning curves $\gamma_1$ and $\gamma_2$.

We study meromorphic functions $f(z)$ in $\mathbb{C}^* = \mathbb{C}\backslash\{0\} $, for which the family $\{f(\lambda z)\}_{\lambda\in\mathbb{C}^*}$ is normal. Such functions (with additional restriction, namely, presence of a pole or removable singularity in zero) were studied by A.~Ostrovsky. We have generalized some him theorems and also have proved new properties of normal functions in $\mathbb{C}^*$.

In the paper the means and families of operators generated by generalized Bochner-Riesz kernels are studied. It is proved that under condition of convergence of means or families of operators generated by generalized Bochner-Riesz kernels the rate of approximation of functions by these methods is equivalent to $K$-functional or their realization in the case $0 < p < 1$.