Arrival of new immigrants which represent different cultures and nationalities increase not only the population, but also the diversity in the host society. If the goal of migration policy implies only the control of open space per inhabitant, the rate of net migration growth is enough for successful migration policy. However, main problems to be considered are heterogeneity of the population, heterogeneity of migrants, demand on the labor market and, most important, possible polarization among local population and migrants. To achieve an optimal resettlement of immigrants we propose to take into account the rate of society polarization. The reasons for polarization might be infinite. For example, two groups might be funs of two different football teams. A polarization of society may emerge due to different social, cultural, ethnic and other measurable characteristics of the population. For the formal statement of the problem we consider the settlements with initial distribution of population and initial distribution of polarization in these settlements. Then we consider migrants with the distribution of polarization among them. Main assumption is that after allocation of migrants in the settlements the final polarization can be changed, thus, this effect should be taken into account.

The equilibrium state of the DW is determined by the minimum total energy (exchange, anisotropy, magnetostatic, and Zeeman energies). The structure Neel domain walls is described a narrow central region (core) with a width being less than 100 nm and two lateral regions symmetrically located relative to the core, with a width on the order of the hundreds microns. The calculations were carried out using a supercomputer with the CUDA architecture using the CUDA C programming language.

We consider the renewal process Rt = 1 ζj < t , where ζi are mutually independent random variables, n=0 j=0 and P{ζi s} = F(s) for i ∈ N (i.e. the distribution function of ζ0 can be not F(s)). For t ∈ (ti,ti+1), where def i def def ζj, we denote xt = t − ti = t − tRt (backward renewal time). The backward renewal process Xt = (xt) is It is well known, that the backward renewal processes and a knowledge about its convergence rate to the sta- tionary distribution are very important in the queueing theory. Asymptotic estimates of the convergence rate of the distribution of the backward renewal process are well known. Namely, if the condition (i) {Eζk < ∞, k > 1} or (ii) {E exp(aζ) < ∞, a > 0} is satisfied, then (correspondingly) for all κ < k − 1 or α < a the following inequality is true for A ∈ σ(X) and all t > 0: (i′) |P{Xt ∈ A}−P(A)| < K(κ)t−κ or (ii′) |P{Xt ∈ A}−P(A)| < K(α)e−αt, where P is the stationary distribution of Xt, and K(·) are some (unknown) constants. Our goal is to find strong bounds for this constants.