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D. N. Azarov, Ye. I. Churakova
On the residuality a finite p-groups of some split extensions Split extensions of 2-generated free Abelian group by infinite cyclic group are considered. For such groups the necessary and sufficient conditions to be residually a finite p-group and to be residually a nilpotent group are obtained.
A. S. Belov
On new coefficient conditions for uniform convergence of trigonometrical series The new sufficient conditions on coefficients of trigonometrical series for uniform convergence (boundedness) its partial sums are offered.
Yu. V. Gruzdeva, S. V. Puhov
The optimal principle in the convex vector optimization problem The necessary conditions for the Pareto minimum point in the convex vector optimization problem are obtained.
S. R. Kogalovskii
Results on universal axiomatizable classes of algebras in the new elucidation From simple topological considerations are removed transparent characterizations of universal axiomatizable classes of algebras, as well as the known modifications of the theorem G. Birkhoff, giving characterization of varieties, and characterizations of quasivarieties of algebras. There are found characterizations of the classes of algebras, defined by infinitary universal sentences.
D. I. Moldavanskii
On the conjugacy separability of generalized direct products of groups The sufficient condition for generalized direct product of two groups to be conjugacy separable is obtained.
S. V. Puhov
The Fan Ky - Glicksberg - Hoffman theorem for the convex mappings with values in
ordered vector spaces We obtain the generalization of the Fan Ky - Glicksberg - Hoffman theorem about systems inequalities involving convex functions for the convex mappings from vector spaces into partially ordered vector spaces.
S. I. Khashin
Comparative efficiency of discrete wavelets of small order The method of comparison of efficiency of different variants of discrete wavelet-transformations is offered. Haar, Dobeshi D4 and D6 wavelets are compared. Efficiency of Discrete Fourier Transformation of length from 4 to 16 is compared also.
N. I. Yatskin
Defect-metric on the set of classes of similarity of square matrices We constuct some special Z-valued pseudometric (the defect-pseudometric) on the algebra of (n x n)-matrices over some field P. The defect-pseudodistance \delta(A, B) between two matrices A and B may be interpreted as a measure of their nonsimilarity. Being similarity-invariant the pseudometric \delta descends to the quotient set and generates a true metric (the defect-metric) on similarity classes. Assuming that P is algebraically closed we present an evaluation algorithm for the defect-distance. |
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