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Regular version of the site
Of all publications in the section: 8
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Article
Chistyakov V. Siberian Advances in Mathematics. 2006. Vol. 16. No. 3. P. 15-41.
Added: Jan 19, 2010
Article
Veretennikov A., Veretennikova E. Siberian Advances in Mathematics. 2016. Vol. 26. No. 4. P. 294-305.

It is shown that Bernstein polynomials for a multivariate function converge to this function along with partial derivatives provided that the latter derivatives exist and are continuous. This result may be useful in some issues of stochastic calculus.

Added: Oct 16, 2016
Article
Grines V., Gurevich E., Zhuzhoma E. V. et al. Siberian Advances in Mathematics. 2019. Vol. 29. No. 2. P. 116-127.

We study relations between the structure of the set of equilibrium points of a gradient-like flows

and the topology of the support manifold of dimension 4 and higher. We introduce a class

of manifolds that admit a generalized Heegaard splitting. We consider gradient-like 

flows such that the non-wandering set consists of exactly μ node and ν

saddle equilibrium points of indices equal to either 1 or n − 1. We show that, for such a 

flow, there exists a generalized Heegaard splitting of the support manifold of genius

g =( ν − μ+2)/2. We also suggest an algorithm for constructing gradient-like flows on closed manifolds of dimension 3

and higher with prescribed numbers of node and saddle equilibrium points of prescribed indices.

Added: May 29, 2019
Article
Popova S. Siberian Advances in Mathematics. 2017. Vol. 27. No. 1. P. 26-75.

We study the limit probabilities of first-order properties for random graphs with vertices in a Boolean cube. We find sufficient conditions for a sequence of random graphs to obey the zero-one law for first-order formulas of bounded quantifier depth. We also find conditions implying a weakened version of the zero-one law.

Added: Oct 5, 2019
Article
Ульянов В.В., Липатьев А. Математические труды. 2016. Т. 19. № 2. С. 109-118.
Added: Mar 10, 2017
Article
Гринес В. З., Жужома Е. В., Медведев В. С. и др. Математические труды. 2018. Т. 21. № 2. С. 163-180.

In this paper, we study the relationship between the structure of the set of equilibrium states of a gradient-like flow and the topology of a carrier manifold of dimension 4 and higher. We introduce a class of manifolds admitting a generalized Heegaard decomposition. It is established that if a non-wandering set of a gradient-like flow consists of exactly $ \ mu $ nodal and $ \ nu $ saddle equilibrium states of the Morse indices $ 1 $ and $ (n-1) $, then its carrying manifold admits a generalized Heegaard decomposition of genus $ g = \ frac {\ nu- \ mu 2} {2} $. An algorithm is given for constructing gradient-like flows on closed manifolds of dimension $ n \ geq 3 $ with respect to a given number of nodal equilibrium states and given numbers of saddle equilibrium states for various Morse indices.

Added: May 27, 2018
Article
Веретенников А. Ю., Веретенникова Е. В. Математические труды. 2015. Т. 18. № 2. С. 22-38.
Added: Oct 27, 2015