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Year 2007

D. N. Azarov On the residual finiteness of a free product of two groups with amalgamated subgroups of finite index

The necessary and sufficient condition for free product of two polycyclic groups with amalgamated subgroups of finite index to be residually finite group is obtained.

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A. S. Belov One method of proof of nonnegativity for all partial sums of trigonometrical series

Basic theorems of new method of proof of nonnegativity for all partial sums of trigonometrical series with monotone coefficients are stated.

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S. V. Kolesnikov On the sets of divergence for Fourier series of bounded functions

This article includes descriptional-metrical conditions on a subset E of [0,2\pi) sufficient to be the set of all points of divergence for Fourier series of a bounded function.
The metrical condition is formulated in terms of \alpha-capacity.

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A. E. Kruchinin, S. I. Khashin The image segmentation by the allocation of continuous borders

The algorithm building borders on the image in the form of continuous lines that allows to construct some segmentation of the initial image at once is offered.

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E. D. Loginova On the residual finiteness of a commuted HNN-extension of group

By analogy with construction of free product with commuting subgroups the construction of commuted HNN-extension is offered and a criterion of residual finiteness of resulting group is given.

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D. I. Moldavanskii On the conjugacy separability in the class of finite p-groups of certain one-relator groups

It is known that group Gk = <a, b; a-1ba = bk>, where k is not equal to 0, is residually a finite p-group if and only if p divides the integer k-1. We prove here that if k is not equal to 1 or -1 then for any prime p group Gk is not conjugacy separable in the class of finite p-groups.

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S. I. Khashin The alternative form of Butcher equations

The alternative form of Butcher equations for a finding of Runge-Kutta methods is offered. This form allows to pass to consideration of each such method as some algebraic object. Such approach should allow reduce essentially the sizes of system of the equations and presumes to find new, more effective Runge-Kutta methods.

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