In the present paper we study some elementary functions in the ring of periodical functions. A generalization of Cole-Hopf transformation is found. The last allows us to transform nonlinear Burger's equation in the ring to a linear parabolic equation in the ring. 2000 Mathematics Subject Classification: 35Q53. [ Full-text available (PDF) ] Top of the page.

In this paper we construct a monomorphism of the group $H \wr W_n$ to the group $W_{m+1}$, where $H$ is an arbitrary finite group, $W_n = (...((H \wr H) \wr H)... ) \wr H$ ($n$ times), $k=|H|$, $m = (k^n - 1) / (k - 1)$. Based on this monomorphism we construct a monomorphism of any wreath power to group $W_n$ for sufficiently great $n$. 2000 Mathematics Subject Classification: 20E22.   [ Full-text available (PDF) ]   Top of the page.

In this work $N$-dimensional (vector) polynomial sequences are defined and studied ($N\in\mathbb{N}$). A notion of an operator of a $N$-dimensional polynomial sequence is introduced and properties of this operator are studied. A spectral representation for a vector polynomial sequence is obtained. A.N.~Kolmogorov's isomorphism between the space of values of a one-dimensional polynomial sequence and a space $L^2(F)$ is established, where $F$ is a spectral function of the sequence. Under some restrictions, an analogous result is true for vector polynomial sequences as well. 2000 Mathematics Subject Classification: 42C05, 33C45, 60G12.   [ Full-text available (PDF) ]   Top of the page.

The description of the process of interaction between two flows in a gas of hard spheres is obtained. Each of the flows is a screw with acceleration and packing, besides their densities depend on time. Corresponding bimodal distribution minimizes the uniform-integral norm of the difference between the sides of the Boltzmann equation. 2000 Mathematics Subject Classification: 76P05, 45K05, 82C40, 35Q55.   [ Full-text available (PDF) ]   Top of the page.

In the work the problem of suffosion particles redistribution during the liquid infiltration into the soil is considered. A kinematic model is accepted, in which the volumetric flow rate of the liquid, which flows into the soil, is a known function, and the moving suffosion particles velocity depends on the liquid velocity linearly. 2000 Mathematics Subject Classification: 76S05.   [ Full-text available (PDF) ]   Top of the page.

Using methods of the probabilistic number theory, we find the distributions of values on the square-free numbers of some arithmetical functions. The behavior of these functions is closely related to that of the Euler and Carmichael functions. 2000 Mathematics Subject Classification: 11A25.   [ Full-text available (PDF) ]   Top of the page.

The results of numerical calculations of sedimentation of aggregating particles suspension on the basis of a three-phase model are presented. The model takes into account fluid capture and locking in the aggregates. The results of experimental investigations of the erythrocyte sedimentation rate in normalcy and after addition of allergens are given. On the basis of theoretical calculations and experimental data some indexes useful for medical diagnostics are obtained. 2000 Mathematics Subject Classification: 76T20, 83C55.   [ Full-text available (PDF) ]   Top of the page.

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