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The lattice of normal divisors of the Jonquere group over a field of characteristic zero is described.

We construct a cumulant representation of solutions of the Cauchy problem for the BBGKY hierarchy of equations and for the dual hierarchy of equations. We define the notion of dual nonequilibrium cluster expansion. We investigate the convergence of the constructed cluster expansions in the corresponding functional spaces.

Polynomial regression models with errors in variables are considered. A goodness-of-fit test is constructed, which is based on an adjusted least-squares estimator and modifies the test introduced by Zhu et al. for a linear structural model with normal distributions. In the present paper, the distributions of errors are not necessarily normal. The proposed test is based on residuals, and it is asymptotically chi-squared under null hypothesis. We discuss the power of the test and the choice of an exponent in the exponential weight function involved in test statistics.

For a two-dimensional continued fraction another generalization of the Worpitzky theorem is proved and the limit sets are proposed for Worpitzky-like theorems in the case where the element sets of the twodimensional continued fraction are replaced by their boundaries.

We prove an infinite-dimensional version of Sard’s theorem for Fréchet manifolds. Let M (respectively, N) be a bounded Fréchet manifold with compatible metric d M (respectively, d N ) modeled on Fréchet spaces E (respectively, F) with standard metrics. Let f : M → N be an MC k -Lipschitz–Fredholm map with k > max{Ind f, 0}: Then the set of regular values of f is residual in N.

We propose an asymptotic method for the integration of one type of systems of linear differential equations with a small parameter in the coefficients of a part of derivatives.