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Of all publications in the section: 21
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Article
Tretyachenko Y. Russian Mathematics. 2010. Vol. 54. No. 5. P. 35-46.

In this paper we consider sequences of functions that are defined on a subset of the real line and take on values in a uniform Hausdorff space. For such sequences we obtain a sufficient condition for the existence of pointwise convergent subsequences. We prove that this generalization of the Helly theorem includes many results of the recent research. In addition, we prove that the sufficient condition is also necessary for uniformly convergent sequences of functions. We also obtain a representation for regular functions whose values belong to the uniform space.

Article
Sidorov S. V., Shevchenko V. N. Russian Mathematics. 2006. Vol. 50. No. 4. P. 56-63.
Article
Smirnova N., Tarashnina S. Russian Mathematics. 2016. Vol. 60. No. 6. P. 63-74.

We understand a solution of a cooperative TU-game as the α-prenucleoli set, α ∈ R, which is a generalization of the notion of the [0, 1]-prenucleolus. We show that the set of all α-nucleoli takes into account the constructive power with the weight α and the blocking power with the weight (1 − α) for all possible values of the parameter α. The further generalization of the solution by introducing two independent parameters makes no sense. We prove that the set of all α-prenucleoli satisfies properties of duality and independence with respect to the excess arrangement. For the considered solution we extend the covariance propertywith respect to strategically equivalent transformations.

Article
Amosov G. G., Dnestryan A. I. Russian Mathematics. 2013. Vol. 57. No. 3. P. 51-55.

We consider the problem of reconstructing a state (i.e., a positive unit-trace operator) fromincomplete information on its optical tomogram. For the case, when a (pure) state is determined by a function representing a linear combination of N ground and excited states of a quantum oscillator, we propose a technique for reconstructing this state from N values of its tomogram. For N = 3 we find an exact solution to the problem under consideration

Article
Sidorov S. V. Russian Mathematics. 2011. No. 3. P. 86-94.

For matrices with integer elements which have the same integer spectrum and whose Jordan form contains no blocks of the same order for one and the same eigenvalue, we propose a quasipolynomial-time algorithm for recognizing their similarity over the ring of integers. In the case when the algebraic multiplicity of all eigenvalues is equal to 1, we estimate the number of similarity classes.

Article
Maksimov V. P., Chadov A. L. Russian Mathematics. 2010. Vol. 54. No. 10. P. 71-74.
Article
E. I. Yakovlev, Chekmaryov D. T. Russian Mathematics. 2018. Vol. 62. No. 9. P. 72-85.

We discuss numerical schemes of finite element method for solving the continuum mechanics problems. Previously a method of acceleration of calculations was developed which uses the simplicial mesh inscribed in the original cubic cell partition of a three-dimensional body. In this paper we show that the obstacle to the construction of this design may be described in terms of homology groups modulo 2. The main goal of the paper is to develop a method of removing this obstacle. The reaching of the goal is based on efficient algorithms for computing bases of the homology groups which are dual with respect to the intersection form.

Article
Чистяков Д. С. Известия высших учебных заведений. Математика. 2016. № 11. С. 42-52.
Article
Яковлев Е. И., Гончар Т. А. Известия высших учебных заведений. Математика. 2018. № 2. С. 77-95.

We investigate a principal G-bundle with G-invariant Riemannian metric on its total space. We derive formulas describing the Levi-Civita connection and curvatures in two-dimensional directions. We obtain estimates of the influence of properties of sectional curvatures to topological invariants of the bundle.

Article
Яковлев Е. И. Известия высших учебных заведений. Математика. 2013. № 6. С. 60-69.

We investigate dynamics of gyroscopic systems of a relativistic type with multivalued action functionals. We suppose that configuration Lorentzian manifolds have the structure of the twisted product. Earlier solvability of the two-point boundary value problem for such systems was proved only in the situation when the Lorentzian distance from the initial point to the final point was limited. In this work we obtain a new theorem of the existence. According to this theorem the specified distance to achievable points may be arbitrary large. The result is applied to the dynamics of a charged test particle in the external space-time of the Reissner–Nordstr¨om black hole.

Article
Чистяков Д. С. Известия высших учебных заведений. Математика. 2018. С. 1-7.
Article
Жужома Е. В., Арансон С. Х., Медведев Т. В. Известия высших учебных заведений. Математика. 1996. № 4 (407). С. 7-17.
Article
Третьяченко Ю. В. Известия высших учебных заведений. Математика. 2010. № 5. С. 41-54.

In this paper we consider sequences of functions that are defined on a subset of the real line with values in a uniform Hausdorff space. For such sequences we obtain a sufficient condition for the existence of pointwise convergent subsequences. We prove that this generalization of the Helly theorem includes many results of the recent research. In addition, we prove that the sufficient condition is also necessary for uniformly convergent sequences of functions. We also obtain a representation for regular functions whose values belong to the uniform space.

Article
Максимов В. П., Чадов А. Л. Известия высших учебных заведений. Математика. 2012. № 9. С. 72-76.

We consider control problems for linear systems of functional-differential equations with both continuous and discrete time variables. The goal of controlling the systemunder consideration is prescribed by a finite set of linear functionals. The number of these functionals is independent of the dimension of the system. We describe the subset of controls generated by a subsystem with the discrete time variable that solve the stated problems.

Article
Элияшев Ю. В. Известия высших учебных заведений. Математика. 2009. № 10. С. 33-39.
Article
Чистяков Д. С. Известия высших учебных заведений. Математика. 2014. № 2. С. 61-68.
Article
Максимов В. П., Чадов А. Л. Известия высших учебных заведений. Математика. 2010. № 10. С. 82-86.

We consider linear boundary-value problems for systems of functional differential equations when the number of boundary conditions is greater than the dimension of the system. We allow the boundary conditions to be fulfilled approximately. We propose an approach based on theorems whose conditions allow the verification by special reliable computing procedures.

Article
Шевченко В. Н., Сидоров С. В. Известия высших учебных заведений. Математика. 2006. № 4. С. 57-64.
As a solution concept of cooperative TU-game we propose the set of $\alpha$-prenucleoli, $\alpha\in R$, that is a generalization of the $[0,1]$-prenucleolus. In the paper we show that in a cooperative game the set of $\alpha$-prenucleoli takes into account the constructive power with weight $\alpha$ and the blocking power with weight $(1-\alpha)$ for all possible values of parameter $\alpha$. Having introduced two independent parameters we obtain the same result --- the set of vectors which coincides with the set of $\alpha$-prenucleoli. Moreover, the set of $\alpha$-prenucleoli satisfies duality and independence from excess arrangement. Finally, the covariance property has been expanded. Some examples are given to illustrate the results.