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D. N. Azarov, E. A. Ivanova
The residual properties of free products of finitely generated nilpotent groups with cyclic amalgamation Free products with one amalgamated cyclic subgroup of a family of finitely generated nilpotent torsion free groups with bounded polycyclic ranks are considered. For such groups the necessary and sufficient conditions to be residually a finite \pi-group (where \pi is a non-empty set of primes) and to be residually a finite nilpotent group are obtained.
A. S. Belov
The investigation of the positiveness in some neighborhood of zero of all partial sums of trigonometrical series The conditions of positiveness in some neighborhood of zero of all partial sums of trigonometrical series with monotone coefficients are investigated. One of the effective ways of proof of positiveness of all partial sums of a cosine-series are presented.
S. V. Kolesnikov
On the classes of functions on compact with connected complement similar to Bair classes Similary to Bair classes the classes of functions on compact with connected complement of complex plane are defined. For the class number zero the class of polinomials is taken. And every following class is defined as the class of functions being the pointwise limits on the compact of unifomly bounded sequences of functions from the precedings classes. Necessary and sufficient conditions of belonging to these classes are found.
E. D. Loginova, D. I. Moldavanskii
On the cyclic subgroup separability of the commuted HNN-extension of a group The sufficient condition for the commuted HNN-extension of some group to be a group with finitely separable cyclic subgroups is obtained.
M. E. Luzina, S. V. Puhov
On the high-order Newton-Chebyshev method for solution of operational equations and systems of equations In this article the explicit formulas for numerical solution of 2x2 nonlinear systems are obtained by the second-order Newton - Chebyshev method. The convergence of the method is investigated by using recurrence relations.
D. I. Moldavanskii
On the intersection of finite index subgroups of certain generalized free products of groups For generalized free product of two groups the criterion to be residually finite is given and the intersection of all normal finite index subgroups is found provided the amalgamated subgroup is contained in the center of one of free factors and any finite index subgroup of amalgamated subgroup is finitely separable in this factor.
S. I. Khashin
The optimal orthonormal basis for computer graphics Efficiency of Fourier basis in computer graphics is defined and calculated. The most effective basis in sense of the given definition and its efficiency is calculated. |
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