L. N. Kuskovskiy About one form of Hypercomplex functions, monogenic on several functions in Cⁿ

The notion of hypercomplex function, which is monogenic in several functions, are introduced in a polydisc the n-dimensional complex space Cⁿ. The integral representations, Taylor series expansions for this function are obtained. We found a solution to the overdetermined system, which is a generalization of the overdetermined Cauchy – Riemann system from the theory of functions of several complex variables.

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E. K. Loginov, D. E. Loginov, A. S. Sherudillo The choice of the Higgs mass renormalization in the standard model

We investigate the effective Higgs potential of the standard model in one- and two-loops approximation. We find the numerical values for the Higgs quartic coupling and the Higgs mass renormalized at the different pole masses. We discuss the renormalization procedure and the boundary conditions leading to the particularly interesting features of the standard model parameters.

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D. I. Moldavanskii, K. S. Pelevina On the finitely separability of subgroups of generalized free products

It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroup satisfies the maximum condition for subgroups and contains a finite index subgroup that is normal in each free factor.

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E. V. Sokolov On the application of D. I. Moldavanskii’s method to the study of the approximability of HNN-extensions by root classes of groups

This is an expanded version of a paper read by the author at the International scientific conference dedicated to the 75th anniversary of Professor D. I. Moldavanskii (Ivanovo, 2015). The article provides an overview of the root classes and the approximability by them of free constructions of groups, a brief survey of the known results on the approximability (relatively to the relationship of elements equality) of non ascending HNN-extensions, and a description of some new results on the approximability by root classes of HNN-extensions with central associated subgroups including those obtained using D. I. Moldavanskii's method of the descent and the ascent of compatible subgroups.

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B. Ya. Solon The function pm-degrees

The article is considered the function degrees of enumerability on the very strong enumeration reducibility, the so called pm-reducibility introduced by Yu. L. Ershov.

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S. I. Khashin Optimization of the Fourier basis in the computer graphics

In computer graphics, it is widely used two-dimensional discrete cosine-Fourier transform in the square 8x8. It can be regarded as a transition to a new orthonormal basis in the space of dimension 64. The article is a new orthonormal basis, the most effective in the sense described in.

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