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One can notice that quite often difference between so-called "standard students" and "gifted" ones is not because that first are less smart, but they have different "orientation", they consider subject as a collections of rules which should not be broken. The first aim is to overcame this dogmatic point of view on this subject, and only after that possible to judge a person to be talented one or not. This is the first stage of math education, the material needs just to serve it. The technology of overcoming this wrong relation to subject is discoursed in spirit of the I.S.Rubanov paper "Method of Mathematical induction" (see chapter 9, http://www.ams.org/books/mawrld/007/). Giftness problems and staging of math (and scientific) education are discoursed., Comment: 6 pages, In Russian

A series of papers in the ISJAEE Journal on 'dam-free hydroelectric power station' concluded by paper: Zotyev, D. B., Alternative energy vs pseudo-science, ISJAEE. 2013. 8(130). P.131-136, is reviewed and commented. A comparison with the generally accepted energy conservation law in hydrodynamics reveals a disappointingly low scientific level of the reviewed papers (both pro- and contra- the dam-free concept), not excluding the published peer-reviewer reports. In the present version we emphasize that the ISJAEE journal published several papers, which neglect and reject the basic physical concepts, such as the Bernoulli integral, the energy conservation law in hydrodynamics, the wave function of photon and some others, with all these rejected concepts being far beyond the scientific scope of the journal. Some readers will be more concerned about the energy equation in hydrodynamics, in its theoretical form or in the Bernoulli integral form as being more traditional in technical hydromechanics. Some readers will be shocked with the statement that a photon does not possess the wave function. Overall, in this way or in that way, all readers will hardly stay unsurprised., Comment: 15 pages, in Russian. Submitted to ISJAEE

In this survey we motivate studies of the invariants from the title. A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. We introduce integer invariants of almost embeddings: winding number, cyclic and triodic Wu numbers. We prove some relations between the invariants. We demonstrate connection of these relations to homology of the deleted product of a graph. We construct almost embeddings realizing some values of these invariants. This paper is accessible to mathematicians not specialized in the area (and to students). All the necessary definitions are recalled. We present some ideas of algebraic and geometric topology in a language accessible to non-topologists. However elementary, this paper is motivated by frontline of research; there are some conjectures and an open problem., Comment: 27 pages, many figures, in Russian. The paper belongs to math.AT because the invariants are special cases of the degree; to math.GT because the most closely related papers are 1805.10237 [math.GT], 2205.01013 [math.GT], and almost embeddings are studied in 2303.14503 (math.CO math.GT), 2008.02523 (math.GT math.AT), 1703.06305 (math.GT), 1904.02404 (math.AT math.GT), 2206.13486 (math.GT math.CO)

In this paper, we consider the simplest version of a linear neural network (LNN). Assuming that for training (constructing an optimal weight matrix $Q$) we have a set of training pairs, i.e. we know the input data \begin{equation} G=\left\{g^{\left(1\right)},g^{\left(2\right)},\cdots,g^{\left(K\right)}\right\}, \end{equation} as well as the correct answers to these input data \begin{equation} H=\left\{h^{\left(1\right)},h^{\left(2\right)},\cdots,h^{\left(K\right)}\right\}. \end{equation} We will study the possibilities of constructing a weight matrix $Q$ of a neural network that will give correct answers to arbitrary input data based on the connection of the specified problem with a system of linear algebraic equations (SLAE). Consider a class of neural networks in which each neuron has only one output signal and performs linear operations. We will show how such LNEs are reduced to SLAEs. Since the questions $G$ and the correct answers $H$ are known to us, the desired weight matrix $Q$ must satisfy the equations \begin{equation} Qg^{\left(k\right)}=h^{\left(k\right)}, k=1,2,\cdots,K. \end{equation} It is required to restore $Q$. In the general case, the matrix $Q$ is rectangular $Q=Q_{MN}=\left\{q_{mn}\right\}$, $m$ is the row number, and $g^{\left(k\right)}\in\mathbb{R}^N$, $h^{\left(k\right)}\in\mathbb{R}^M$. Let $G_{NK}$ be a matrix composed of columns $g^{\left(1\right)}, g^{\left(2\right)},\cdots,g^{\left(k\right)}$, and $H_{MK}$ be a matrix composed of columns $h^{\left(1\right)},h^{\left(2\right)},\cdots,h^{\left(k\right)}$. Then, with respect to $Q_{MN}$, we obtain a matrix SLAE. \begin{equation} Q_{MN}G_{NK}=H_{MK}. \end{equation} This paper will present methods for regularizing the constructed system., Comment: in Russian language

Practically relevant problems of quadratic optimization often contain multidimensional arrays of variables interconnected by linear constraints, such as equalities and inequalities. The values of each variable depend on its specific meaning and can be binary, integer, discrete, and continuous. These circumstances make it technically difficult to reduce the original problem statement to the QUBO form. The paper identifies and considers three main transformations of the original problem statement, namely, the transition from a multidimensional to a one-dimensional array of variables, the transition in mixed problems to binary variables, and the inclusion of linear constraints in the objective function in the form of quadratic penalties. Convenient formulas for calculations are presented and proven, simplifying the implementation of these transformations. In particular, the formulas for the transition in the problem statement from a multidimensional to a one-dimensional array of variables are based on the use of the Kronecker product of matrices. The considered transformations are illustrated by numerous examples., Comment: 26 pages, 3 figures; in Russian

This paper introduces a novel methodology for modeling stationary shock waves in porous materials, which employs the recently developed moving window technique. The core of this method is the iterative adjustment of the reference frame to the boundary conditions that regulate the entry and exit of Lagrangian particles from a fixed computational domain, which are used to model the flow of a compressible medium. A Godunov-type smoothed particle hydrodynamics (SPH) method with reconstruction of values at the contact is employed for the purposes of modeling. Kernel gradient correction for this method is proposed to enhance the precision of the approximation. The shock Hugoniot of porous copper is calculated, and the structure of the compacting wave and elastic precursor in porous copper at shock amplitude near the yield strength of solid copper is studied., Comment: Accepted in "VANT" (in Russian)

In countries with a growing number of elderly and a shrinking workforce, one of which is Russia, it becomes impossible to maintain a solidary pension system and a need to switch to a more stable funded system appears. This paper analyzes various scenarios of Russia's transition to such a system. This is the first study on the Russian economy in which an Overlapping Generations Model is used to simulate the pension transition. It is demonstrated that in the long term, the transition to a funded system slightly reduces the welfare of pensioners, and during the transition, the situation of pensioners deteriorates strongly. However, it is also important to emphasize that the transition imposes a heavy burden on all generations living during the reform, they are forced to consume less and greatly change their savings, while also often starting to work more. Such conclusions are made concerning average population cohorts, and the results may not be the same for different groups of individuals within these cohorts. In different scenarios, the pension system transition can cause both economic growth and economic recession, as well as a corresponding increase or decrease in wages and consumption., Comment: Comments: 23 pages, in Russian

In this paper, we study a two-dimensional Lorentzian problem on the anti-de Sitter plane. Using methods of geometric control theory and differential geometry, it was possible to construct an orthonormal frame, calculate extremal trajectories, describe the reachable set, construct an optimal synthesis, and describe the Lorentzian distance., Comment: In Russian

Multiple magnetic and kinetic solar wind plasma parameters are used to detect coronal mass ejections (CMEs) as they travel through the heliosphere. There are various interplanetary CME (ICME) catalogues, but due to differences between their ICME identification criteria they can significantly vary. In this paper we analyze Richardson and Cane and CCMC CME Scoreboard ICME catalogues and the SRI RAS solar wind types catalogue, and propose an algorithm of merging them. A unified catalogue is constructed for 2010 to 2022. The resulting catalogue is completed with data from the OMNI database. Analysis of the unified catalogue demonstrated high accuracy when merging events present in multiple catalogues and a tendency of events defined in all three initial catalogues to demonstrate greater duration, speed and geoeffectiveness. The catalog is presented on the SINP MSU Space Weather Exchange website: https://swx.sinp.msu.ru/tools/icme_list.php, Comment: 22 pages, in Russian language, 4 figures

In 1957, Nemytskii proved the following fact: if in a locally compact or in an Abelian connected group there is a neighborhood of the identity in which some identity holds, then it holds in the entire group. The following question was also posed there: Let G be a connected topological group. In some neighborhood of the identity of the group G the identity $x^3=1$ holds. Is it true that then the identity $x^3=1$ holds in the entire group $G$? The same question is posed for the identity $gx^2 = x^2g$, where $g$ is a fixed element of the group. Platonov formulated the following generalized formulation of the Mytselsky problem: for a topological connected group, is it true that if the identity holds in a neighborhood of the identity, then the identity holds everywhere? In this paper, a negative answer to Platonov's question is given, the following theorem is proven: if $n > 1010$ is odd, then there exists a connected topological group in which the identity $x^n=1$ holds in some neighborhood of unity, but not in the entire group., Comment: in russian

The search for equilibrium in a two-stage traffic flow model reduces to the solution of a special nonsmooth convex optimization problem with two groups of different variables. For numerical solution of this problem, the paper proposes to use the accelerated block-coordinate Nesterov-Stich method with a special choice of block probabilities at each iteration. Theoretical estimates of the complexity of this approach can markedly improve the estimates of previously used approaches. However, in the general case they do not guarantee faster convergence. Numerical experiments with the proposed algorithms are carried out in the paper., Comment: in Russian language

This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second Lyapunov method guarantees asymptotic stability for the above described class of nonlinear systems. It is well known that the search for a Lyapunov function is the "cornerstone" of mathematical stability theory. Methods for selecting or finding the Lyapunov function to analyze the stability of closed linear stationary systems, as well as for nonlinear objects with explicit linear dynamic and nonlinear static parts, have been well studied (see works by Lurie, Yakubovich, Popov, and many others). However, universal approaches to the search for the Lyapunov function for a more general class of nonlinear systems have not yet been identified. There is a large variety of methods for finding the Lyapunov function for nonlinear systems, but they all operate within the constraints imposed on the structure of the control object. In this paper we propose another approach, which allows to give specialists in the field of automatic control theory a new tool/mechanism of Lyapunov function search for stability analysis of smooth continuous dynamic nonlinear systems with measurable state vector. The essence of proposed approach consists in representation of some function through sum of nonlinear terms, which are elements of object's state vector, multiplied by unknown coefficients, raised to positive degrees. Then the unknown coefficients are selected using genetic algorithm, which should provide the function with all necessary conditions for Lyapunov function (in the framework of the second Lyapunov method)., Comment: in Russian language

The article continues the work on the description of integrable nonlinear chains with three independent variables of the following form $u^j_{n+1,x}=u^j_{n,x}+f(u^{j+1}_{n}, u^{j}_n,u^j_{n+1 },u^{j-1}_{n+1})$ by the presence of a hierarchy of reductions integrable in the sense of Darboux, started in (1). The classification algorithm is based on the well-known fact that the characteristic algebras of Darboux integrable systems have a finite dimension. In this paper, we used the characteristic algebra in the direction $x$, whose structure for a given class of models is determined by some polynomial $P(\lambda)$, whose degree does not exceed three for known examples. The article assumes that $P(\lambda)=\lambda^2$, in this case the classification problem is reduced to finding eight unknown functions of one variable. In the paper, a rather narrow class of candidates for integrability is obtained, among which there is a new example of an integrable chain., Comment: in Russian language

It is well known that whenever a class of structures $\mathcal{K}_1$ is interpretable in a class of structures $\mathcal{K}_2$, then the hereditary undecidability of (a fragment of) the theory of $\mathcal{K}_1$ implies the hereditary undecidability of (a suitable fragment of) the theory of $\mathcal{K}_2$. In the present paper, we construct a $\Sigma_1$-interpretation of the class of all finite bipartite graphs in the class of all pairs of equivalence relations on the same finite domain; from this we obtain the hereditary undecidability of the $\Sigma_2$-theory of the second class. Next, we construct a $\Sigma_1$-interpretation of the class of all pairs of equivalence relations on the same finite domain in the class of all pairs consisting of a linear ordering and an equivalence relation on the same finite domain; this gives us the hereditary undecidability of the $\Sigma_2$-theory of the second class. The corresponding results are, in a sense, optimal, since the $\Pi_2$-theories of the classes under consideration are decidable. Keywords: undecidability, elementary theories, prefix fragments, Comment: in Russian language

In this paper we study holomorphically homogeneous model submanifolds CR-type (1, 3) complex space $\mathbb C^4$. One finds moduli space of five-dimensional model surfaces Bloom-Graham type ((2, 1), (3, 1), (4, 1)). It is shown that there exists unique model surface of this type with property of holomorphical homogeneous, which is equivalent to tube surface $\mathcal C$ with affin homogeneous base. One describes and classifies with respect to model surfaces the orbits relative to the group of holomorhical automorphisms of $\mathcal C$, Comment: in Russian language

The paper studies the quantum action for the five-dimensional real $\phi^3$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed., Comment: LaTeX, 20 pages, 5 figures. Firstly appeared in Russian, April 9, 2024, see https://www.pdmi.ras.ru/preprint/2024/24-05.html

This paper presents the experience of developing and utilizing computer simulations for student laboratory assignments in atomic physics, specifically focusing on emission atomic spectra. The fundamental component of each laboratory assignment is a computer simulator of a spectrograph, which displays atomic line spectra on the monitor screen. The simulator operates by converting the wavelength of radiation into an RGB triplet. Calibration of the spectrograph is conducted using the atomic spectrum of mercury. The configuration of setup parameters and experimental conditions is unique to each student conducting the laboratory assignment using the simulator. Individualized parameters, stored in Google Sheets, are transferred to the HTML template of the laboratory assignment via the Google Apps Scripts service. This individualization of simulator parameters serves to encourage students to engage in independent work., Comment: 17 pages, in Russian, 9 figures

The paper discusses an applicability criterion for a cutoff regularization in the coordinate representation in the Euclidean space with a dimension larger than two. It is shown that the set of functions satisfying the criterion is not empty. As an example, an explicit function is presented. It is proved by explicit construction that there are functions satisfying the criterion in a stronger formulation., Comment: LaTeX, 8 pages, 1 figure. Firstly appeared in Russian, March 5, 2024. Compared to the Russian version, some comments and minor corrections have been added. The forgotten imaginary unit in the Fourier transform has also been restored. See https://www.pdmi.ras.ru/preprint/2024/24-04.html

The paper presents various modifications of the Frank-Wolfe algorithm in the equilibrium traffic assignment problem. The Beckman model is used as a model for experiments. In this article, first of all, attention is paid to the choice of the direction of the basic step of the Frank-Wolfe algorithm. Algorithms will be presented: Conjugate Frank-Wolfe (CFW), Bi -conjugate Frank-Wolfe (BFW), Fukushima Frank-Wolfe (FFW). Each modification corresponds to different approaches to the choice of this direction. Some of these modifications are described in previous works of the authors. In this article, following algorithms will be proposed: N-conjugate Frank-Wolfe (NFW), Weighted Fukushima Frank-Wolfe (WFFW). These algorithms are some ideological continuation of the BFW and FFW algorithms. Thus, if the first algorithm used at each iteration the last two directions of the previous iterations to select the next direction conjugate to them, then the proposed algorithm NFW is using more than N previous directions. In the case of Fukushima Frank-Wolfe, the average of several previous directions is taken as the next direction. According to this algorithm, a modification WFFW is proposed, which uses a exponential smoothing from previous directions. Experiments with various modifications were carried out on several datasets representing urban structures and taken from publicly available sources. The relative gap value was taken as the quality metric. The experimental results showed the advantage of algorithms using the previous directions for step selection over the classic Frank-Wolfe algorithm. In addition, an improvement in efficiency was revealed when using more than two conjugate directions. For example, on various datasets, the modification 3FW showed the best convergence. In addition, the proposed modification WFFW often overtook FFW and CFW, although performed worse than NFW., Comment: 14 pages, in Russian language, 8 figures

The paper tests the validity of the critique of the fiscal theory of the price level. A stochastic general equilibrium model with continuous time is constructed. An active fiscal policy and a passive monetary policy have been set. Monetary policy manages the interest rate through the Taylor rule. The stochastic default factor in the special form is introduced. A complete definite system of equations is obtained for the detection of equilibrium. It is asserted that the peculiarities of the approach to modeling are of critical importance for verifying the presence of certain hypotheses and formulating conclusions. The results of this work are in support of the fiscal theory of the price level., Comment: Master Thesis, in Russian. Supervisor: Sergey E. Pekarski

The article is devoted to the problem of synthesis of observers of state variables for linear stationary objects operating under conditions of noise or disturbances in the measurement channel. The paper considers a fully observable linear stationary system with known parameters. It is assumed that the state variables are not measured, and the measured output variable contains a small amplitude (in general, modulo less than one) additive noise or disturbance. It is also assumed that there is no a priori information about the disturbance or noise in the measurement channel (for example, frequency spectrum, covariance, etc.). It is well known that a large number of methods of observer synthesis have been obtained for this type of objects, including the Kalman filter, which has proven itself in practice. Under the condition of complete observability and the presence of some a priori information about the process (which is typical for the case when a disturbance in the measurement channel can be represented as white noise), approaches based on Kalman filtering demonstrate the highest quality of convergence of estimates of state variables to true values. Without taking into account the numerous results obtained using the application of the Kalman filter, an alternative idea of constructing an observer of state variables is considered in this paper. The alternative of the new approach is primarily due to the fact that there is no need to use the usual approaches based on the Luenberger observer. The paper proposes an approach based on the evaluation of unknown parameters (in this case, an unknown vector of initial conditions of the variables of the object state) of a linear regression model., Comment: in Russian language

The paper is devoted to the study of combinatorial determinacy properties of a family of substitution complexes consisting of quadrilaterals glued side-to-side with each other. These properties are useful in constructing algebraic structures with a finite number of defining relations. In particular, this method was used when constructing a finitely presented infinite nisemigroup satisfying the identity x^9 =0. This construction responds to the problem of L. N. Shevrin and M. V. Sapir. In this paper, we investigate the possibility of coloring the entire sequence of complexes into a finite number of colors, in which the property of weak determinism is fulfilled: if the colors of the three vertices of a certain quadrilateral are known, then the color of the fourth side is uniquely determined, except in some cases of a special arrangement of the quadrilateral., Comment: in Russian language

This paper continues a series of papers in which 2-by-2 matrix joint solutions of two scalar evolutionary equations are constructed, which are analogs of the Schrodinger time equations. These equations correspond to the Hamiltonian system $H^{2+2+1}$, being one of the representatives of the hierarchy of degenerations of the isomonodromic Garnier system. The mentioned hierarchy was described by H. Kimura in 1986. In terms of solutions of linear systems of ordinary differential equations of the method of isomnodromic deformations, the compatibility condition of which are the Hamiltonian equations of the system $H^{2+2+1}$, the constructed joint matrix solutions of analogs of the time equations of the Schrodinger equations in this paper will be written out explicitly., Comment: in Russian language

In this paper we propose a generalized condition for a sharp minimum, somewhat similar to the inexact oracle proposed recently by Devolder-Glineur-Nesterov. The proposed approach makes it possible to extend the class of applicability of subgradient methods with the Polyak step-size, to the situation of inexact information about the value of the minimum, as well as the unknown Lipschitz constant of the objective function. Moreover, the use of local analogs of the global characteristics of the objective function makes it possible to apply the results of this type to wider classes of problems. We show the possibility of applying the proposed approach to strongly convex non-smooth problems, also, we make an experimental comparison with the known optimal subgradient method for such a class of problems. Moreover, there were obtained some results connected to the applicability of the proposed technique to some types of problems with convexity relaxations: the recently proposed notion of weak $\beta$-quasi-convexity and ordinary quasi-convexity. Also in the paper, we study a generalization of the described technique to the situation with the assumption that the $\delta$-subgradient of the objective function is available instead of the usual subgradient. For one of the considered methods, conditions are found under which, in practice, it is possible to escape the projection of the considered iterative sequence onto the feasible set of the problem., Comment: in Russian language

The Fermat--Steiner problem is to find all points of the metric space Y such that the sum of the distances from each of them to points from some fixed finite subset A = {A_1, ..., A_n} of the space Y is minimal. This problem is considered in the case when Y=H(X) is the space of non-empty compact subsets of a finite-dimensional normed space X endowed with the Hausdorff metric, i.e. H(X) is a hyperspace over X. The set A is called boundary, all A_i are called boundary sets, and the compact sets that realize the minimum of the sum of distances to A_i are called Steiner compacts. In this paper, we study the question of stability in the Fermat--Steiner problem when passing from a boundary consisting of finite compact sets to a boundary consisting of their convex hulls. By stability here we mean that the minimum of the sum of distances does not change when passing to convex hulls of boundary compact sets. The paper continued the study of geometric objects, namely, hook sets that arise in the Fermat--Steiner problem. The results obtained revealed some geometry of the relationship between Steiner compacts and boundary sets. On its basis, a sufficient condition for the instability of the boundary in H(X) was derived., Comment: in Russian language

The paper studies the quantum action for the four-dimensional real $\phi^4$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The absence of non-local singular contributions and the correctness of the renormalization $\mathcal{R}$-operation on the example of separate three-loop diagrams are also discussed. The explicit form of the first three coefficients for the renormalization constants and for the $\beta$-function is presented. Consistency with previously known results is shown., Comment: LaTeX, 71 pages, 8 figures. Firstly appeared in Russian, February 6, 2024, see https://www.pdmi.ras.ru/preprint/2024/pr2024.html

This paper presents the experimental results on research of growth processes of GaAs layers on silicon substrates by molecular beam epitaxy. The formation of buffer Si layer in a single growth process has been found to significantly improve the crystalline quality of the GaAs layers formed on its surface, as well as to prevent the formation of anti-phase domains both on offcutted towards the [110] direction and on singular Si(100) substrates. It has been demonstrated that the use of cyclic thermal annealing at temperatures 350-660{\deg}C in the flow of arsenic atoms makes it possible to reduce the number of threading dislocations and increase the smoothness of the GaAs layers surface. At the same time, the article considers possible mechanisms that lead to an improvement in the quality of the surface layers of GaAs. It is shown that the thus obtained GaAs layers of submicron thickness on the singular Si(100) substrates have a mean square value of surface roughness 1.9 nm. The principal possibility of using thin GaAs layers on silicon as templates for forming on them light-emitting semiconductor heterostructures with active area based on self-organizing InAs quantum dots and InGaAs quantum well is presented. They are shown to exhibit photoluminescence at 1.2 um at room temperature., Comment: 18 pages, in Russian language, 6 figures

For fixed $k$, we consider the subgraph $YF_k=(V_k,E_k)$ of the famous Young--Fibonacci graph formed by the words with at most $k$ 2-s. The jump graph is a graded graph is defined as follows: each level is identified with $V_k$, and an edge between two vertices $(v_1,i)$ and $(v_{2},i+1)$, $v_1,v_2\in V_k$, of neighbouring levels us drawn iff $v_2$ is a descendant of $v_1$ in $YF_k$. The goal of this paper is to describe all central measures on the path space of $YF_k$., Comment: 24 pages, in Russian

In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple subgradient method with switching along productive and non-productive steps, for which, on a class of problems with Lipschitz functions, it would be possible to guarantee convergence with the rate of geometric progression to the set of exact solutions or its vicinity. It is important that to implement the proposed method there is no need to know the sharp minimum parameter, which is usually difficult to estimate in practice. To overcome this problem, the authors propose to use a step djustment procedure similar to that previously proposed by B.~T.~Polyak., Comment: in Russian language

Some variations of $\pi$-regular and nil clean rings were recently introduced in \cite{5,8,7}, respectively. In this paper, we examine the structure and relationships between these classes of rings. Specifically, we prove that $(m, n)$-regularly nil clean rings are left-right symmetric and also show that the inclusions ($D$-regularly nil clean) $\subseteq$ (regularly nil clean) $\subseteq$ ($(m,n)$-regularly nil clean) hold, as well as we answer Questions 1, 2 and 3 posed in \cite{8}. Moreover, some other analogous questions concerning the symmetric properties of certain classes of rings are treated as well by proving that centrally Utumi rings are always strongly $\pi$-regular., Comment: 13 pages to appear in Russian Mathematics

The deployment of the Baikal-GVD deep underwater neutrino telescope is continuing in Lake Baikal. By April 2022, ten clusters of the telescope were put into operation, with 2880 optical modules in total. One of the relevant tasks in this context is to study the possibilities of increasing the efficiency of the detector based on the experience of its operation and the results obtained at other neutrino telescopes in recent years. In this paper, a variant of optimizing the configuration of the telescope is considered, based on the installation of additional strings of optical modules between the clusters (external strings). An experimental version of the external string was installed in Lake Baikal in April 2022. This paper presents a first estimate of the impact of adding external strings on the neutrino detection efficiency, as well as the technical implementation of the detection and data acquisition systems of the external string and first results of its in-situ tests., Comment: 12 pages, in Russian language, 7 figures, 1 Table

This paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the function value at the considered point by the averaged function value over a ball (in $l_1$-norm or $l_2$-norm) of small radius with the center in this point, the original problem is reduced to a smooth problem (whose Lipschitz constant of the gradient is inversely proportional to the radius of the ball). An important property of the smoothing used is the possibility to calculate an unbiased estimation of the gradient of a smoothed function based only on realizations of the original function. The obtained smooth stochastic optimization problem is proposed to be solved in a distributed federated learning architecture (the problem is solved in parallel: nodes make local steps, e.g. stochastic gradient descent, then they communicate - all with all, then all this is repeated). The goal of this paper is to build on the current advances in gradient-free non-smooth optimization and in feild of federated learning, gradient-free methods for solving non-smooth stochastic optimization problems in federated learning architecture., Comment: In Russian language. Redesigned version for publication in the journal Computational Mathematics and Mathematical Physics

In 2010s Fleiner introduced a notion of stable flows in directed networks and showed that such a flow always exists and can be found by use of a reduction to the stable allocation problem due to Baiou and Balinski. Recently Cseh and Matuschke devised a direct strongly polynomial algorithm. In this paper we give an alternative algorithm to find a stable flow in a network with several sources and sinks. It is based on an idea of preflows (appeared in 1970s in a faster algorithm for the classical max-flow problem), and runs in $O(nm)$ time for a network with $n$ vertices and $m$ edges. The results are further generalized to a larger class of objects, so-called stable quasi-flows with bounded excesses in non-terminal vertices. (The paper is written in Russian.), Comment: 19 pages, in Russian language. Compared with the previous version, the reference to a grant is removed

A graph $\Gamma$ is called locally finite if, for each vertex $v$ of $\Gamma$, the set $\Gamma(v)$ of all neighbors of $v$ in $\Gamma$ is finite. For any locally finite graph $\Gamma$ with vertex set $V(\Gamma)$ and for any field $F$, let $F^{V(\Gamma)}$ be the vector space over $F$ of all functions $V(\Gamma) \to F$ (with natural componentwise operations) and let $A^{({\rm alg})}_{\Gamma,F}$ be the linear operator $F^{V(\Gamma)} \to F^{V(\Gamma)}$ defined by $(A^{({\rm alg})}_{\Gamma,F}(f))(v) = \sum_{u \in \Gamma(v)}f(u)$ for all $f \in F^{V(\Gamma)}$, $v \in V(\Gamma)$. In the case of finite graph $\Gamma$ the mapping $A^{({\rm alg})}_{\Gamma,F}$ is the well known operator defined by the adjacency matrix of $\Gamma$ (over $F$), and the theory of eigenvalues and eigenfunctions of such operator is a well-developed (at least in the case $F = \mathbb{C}$) part of the theory of finite graphs. In this paper we develope a theory of eigenvalues and eigenfunctions of $A^{({\rm alg})}_{\Gamma,F}$ for arbitrary infinite locally finite graphs $\Gamma$ (although a few results may be of interest for finite graphs) and fields $F$ with a special emphasis on the case when $\Gamma$ is connected with uniformly bounded vertex degrees and $F = \mathbb{C}$. By the author opinion, previous attempts in this direction were not quite satisfactory since were limited by consideration of rather special eigenfunctions and corresponding eigenvalues., Comment: 52 pages, in Russian; a few minor corrections; published version

This is the third part of a cycle of papers devoted to the construction of a finitely presented infinite nil-semigroup satisfying the identity $x^9 = 0$. This construction answers the problem of L. N. Shevrin and M. V. Sapir, posed, for example, in the Sverdlovsk notebook. A semigroup is realized as a set of path encodings on a family of special uniformly elliptic complexes. In the first paper of the cycle Finitely defined nil semigroup: complexes with uniform ellipticity, a sequence of complexes was constructed with a set of geometric properties. In the second work of the series Deterministic Coloring of a Family of Complexes a finite letter encoding was introduced on the vertices and edges of the constructed complexes. The deterministic property of such a coloring was proved, which makes it possible to introduce a finite set of defining relations on the set of words-codings of paths on complexes. In this paper, we describe an algorithm for reducing an arbitrary semigroup word to canonical form. It is also proved that a word containing a subword with period 9 can be reduced to zero using defining relations. Word encodings corresponding to sufficiently long paths are not reduced to zero and do not change their length, that is, the introduced semigroup is infinite., Comment: in Russian. The work was carried out with the help of the Russian Science Foundation, Grant 22-11-00177. The first author is the winner of the Young Mathematics of Russia competition

The paper presents a review of the state-of-the-art of subgradient and accelerated methods of convex optimization, including in the presence of disturbances and access to various information about the objective function (function value, gradient, stochastic gradient, higher derivatives). For nonconvex problems, the Polak-Lojasiewicz condition is considered and a review of the main results is given. The behavior of numerical methods in the presence of sharp minima is considered. The purpose of this survey is to show the influence of the works of B.T. Polyak (1935 -- 2023) on gradient optimization methods and their neighborhoods on the modern development of numerical optimization methods., Comment: in Russian language

In the development of materials for structural purposes, the main focus is on the advantageous combination of mechanical and volume-mass properties. Due to the development of production, solid plates are increasingly being replaced by modern composite materials with improved properties, one of the varieties of which is layered composites with a honeycomb core. The most widespread are three-layer plates with solid face layers and a hexagonal honeycomb core. However, with the development of new technologies, including 3D printing, honeycombs with new geometries are gaining popularity, the mechanical properties of which make it possible to obtain layered composites with improved features. In this paper, three-layer plates with solid face layers and a tetrachiral honeycomb core are investigated. The influence of discretization (number of unit cells), relative density and thickness of the honeycomb core on the stress state of three-layer composites subjected to static bending under various boundary conditions is studied. Mathematical modeling is carried out within the framework of the theory of elasticity by the finite element method via three-dimensional modeling in the Comsol Multiphysics system, as well as using algorithms developed by the author for analyzing the stress state of multilayer plates with tetrachiral honeycombs by solving a plane problem of the theory of elasticity. As a result, good agreement is shown between the numerical results obtained using algorithms for solving a plane problem and via three-dimensional finite element modeling in the Comsol Multiphysics system, while the numerical results are qualitatively consistent with laboratory test data., Comment: in Russian language

Our previous paper shows that the (vertex) spanning tree degree enumerator polynomial of a connected graph $G$ is a real stable polynomial (id est is non-zero if all variables have positive imaginary parts) if and only if $G$ is distance-hereditary. In this note we generalize the result on weighted graphs. This generalization allows us to define the class of weighted distance-hereditary graphs., Comment: in Russian

The paper investigates the behavior of 0 degree domain boundaries arising in uniaxial magnetic films with flexomagnetoelectric effect in a magnetic field. It is shown that at certain orientations of the magnetic field, it is possible to significantly enhance (or weaken) the degree of manifestation of the flexomagnetoelectric effect in the studied films. In addition, by varying the magnitude and directions of the magnetic field, it is possible to significantly lower (up to zero) the value of the critical electric field of the origin of this inhomogeneity. It is also established that a 0 degree domain boundary of non-Anelian type, in which induced bound charges do not create a resultant field (field shielding), when a magnetic field directed perpendicular to the plane of rotation of magnetic moments is applied, a flexomagnetoelectric effect occurs, which increases with increasing magnitude of the magnetic field., Comment: 9 pages, in Russian language, 12 figures

Decision forest (decision tree ensemble) is one of the most popular machine learning algorithms. To use large models on big data, like document scoring with learning-to-rank models, we need to evaluate these models efficiently. In this paper, we explore MatrixNet, the ancestor of the popular CatBoost library. Both libraries use the SSE instruction set for scoring on CPU. This paper investigates the opportunities given by the AVX instruction set to evaluate models more efficiently. We achieved 35% speedup on the binarization stage (nodes conditions comparison), and 20% speedup on the trees apply stage on the ranking model., Comment: in Russian language

In the monograph "Strong artificial intelligence. On the Approaches to Superintelligence" contains an overview of general artificial intelligence (AGI). As an anthropomorphic research area, it includes Brain Principles Programming (BPP) -- the formalization of universal mechanisms (principles) of the brain work with information, which are implemented at all levels of the organization of nervous tissue. This monograph contains a formalization of these principles in terms of category theory. However, this formalization is not enough to develop algorithms for working with information. In this paper, for the description and modeling of BPP, it is proposed to apply mathematical models and algorithms developed earlier, which modeling cognitive functions and base on well-known physiological, psychological and other natural science theories. The paper uses mathematical models and algorithms of the following theories: P.K.Anokhin Theory of Functional Brain Systems, Eleanor Rosch prototypical categorization theory, Bob Rehder theory of causal models and "natural" classification. As a result, a formalization of BPP is obtained and computer experiments demonstrating the operation of algorithms are presented., Comment: 28 pages, in Russian, 4 figures

Let $Z$ and $W$ are distributions of points on the complex plane $\mathbb C$. The following problem goes back to the studies of F. Carlson, T. Carleman, L. Schwartz, A. F. Leont'ev, B. Ya. Levin, J.-P. Kahane and others. For which $Z$ and $W$ for an entire function $g\neq 0$ of exponential type vanishing on $W$, there is an entire function $f\neq 0$ of exponential type vanishing on $Z$ such that $|f|\leq |g|$ on the imaginary axis? The classical Malliavin-Rubel theorem of the early 1960s completely solves this problem for "positive" $Z$ and $W$ lying only on the positive semiaxis. A number of generalizations of this criterion were established by us in the late 1980s for "complex" $Z\subset\mathbb C$ and $W\subset\mathbb C$ separated by angles from the imaginary axis, with some advances in the 2020s. In this paper, tougher problems are solved in a more general subharmonic framework for distributions of masses on $\mathbb C$. All the previously mentioned results can be obtained from the main results of the paper in a much stronger form even in the initial formulation for distributions of points $Z$ and $W$ and entire functions $f$ and $g$ of exponential type. Some of the results of the article are closely related to the famous Beurling-Malliavin theorems on the radius of completeness and the multiplier., Comment: 49 pages, in Russian

In the paper we consider a stochastic model which called Markov Q-processes that forms a continuous-time Markov population system. Markov Q-processes are defined as stochastic Markov branching processes with trajectories continuing in the remote future. Estimation of the structural parameter of the Markov Q-process is the main goal of this paper. To estimate this parameter, an unbiased estimator of the Lotka-Nagaev type is proposed. An asymptotic expansion of the variance of this estimator is found., Comment: in Russian language

Various technologies, including computer vision models, are employed for the automatic monitoring of manual assembly processes in production. These models detect and classify events such as the presence of components in an assembly area or the connection of components. A major challenge with detection and classification algorithms is their susceptibility to variations in environmental conditions and unpredictable behavior when processing objects that are not included in the training dataset. As it is impractical to add all possible subjects in the training sample, an alternative solution is necessary. This study proposes a model that simultaneously performs classification and anomaly detection, employing metric learning to generate vector representations of images in a multidimensional space, followed by classification using cross-entropy. For experimentation, a dataset of over 327,000 images was prepared. Experiments were conducted with various computer vision model architectures, and the outcomes of each approach were compared., Comment: 19 pages, in Russian

The influence of growth regimes of the silicon capping layer on the optical properties of heterostructures with submonolayer InAs quantum dots embedded in a silicon matrix has been studied. The photoluminescence signal at 1650 nm from submonolayer quantum dots at low temperatures up to 120 K was obtained. It was established that the use of a two-stage method of silicon overgrowing InAs nanoislands makes it possible to increase the photoluminescence intensity by improving the crystalline quality of heterostructures. Analysis of the temperature dependence allowed us to calculate an activation energy for electrons confined in the quantum dots potential well at the level of the thermal energy at room temperature., Comment: 22 pages, in Russian language, 4 figures

The author proposed an elementary derivation of the formula of Yu.V. Nesterenko expansion in continued fraction of a number 2*$\zeta(3)$., Comment: in Russian language

Author-made translation of the book published in Russian in 1982. Chapter 1. Channeling of High-Energy Particles in Crystals. Chapter 2. A Channeled Fast Particle as a 2D (1D) Relativistic Atom. Chapter 3. The Foundations of the Theory of $\gamma$-quanta Emission in Crystals under Channeling Conditions. Chapter 4. The Influence of $\gamma$-quanta Refraction and Diffraction on Angular and Spectral Characteristics of Radiation Produced by Particles in Crystals. Chapter 5. Classical Theory of Radiation Formation by Particles in a Medium. Chapter 6. Scattering and Radiation in Crystals Exposed to Variable Fields. Chapter 7. Interference of Independently Generated Beams of $\gamma$-quanta. Chapter 8. Theory of Measurement of Nuclear Reaction Times Using Shadow Effect. Yield of Reactions Induced by High-energy Particles in Crystals. Chapter 9. Spin Rotation and Radiative Self-Polarization of Particles Moving in Bent Crystals. Chapter 10. The Influence of Radiative Transitions on Channeling of Charged Particles in Crystals., Comment: Author-made translation of the book published in Russian in 1982, 232 pages, 10 chapters

In this study, we investigate the contribution of millisecond pulsars (MSPs) to the gamma-ray excess observed in the Galactic Center by analyzing data from high-resolution direct N-body simulations of six globular clusters (GCs) that experience close encounters with the nuclear star cluster. Using the {\phi}-GPU code, we tracked the orbits of individual neutron stars (NSs) formed during the simulations, assuming a fraction of these NSs evolve into MSPs. Our model includes state-of-the-art single stellar evolution code including prescription for neutron star formation. We estimated the gamma-ray flux from these MSPs, considering known values for their gamma-ray emission. Our results show that MSPs originating from the six modeled GCs contribute a small but non-negligible fraction of the observed gamma-ray flux. This finding suggests that the actual gamma-ray flux from MSPs could be much higher when considering the entire population of GCs, potentially significantly contributing to the gamma-ray excess. This study highlights the importance of considering MSPs in the Galactic Center, originating from nearby globular clusters, as a potential source of the observed gamma-ray excess. Future work will involve more sophisticated simulations incorporating binary stellar evolution and comparing the fraction of MSPs in observed GCs to refine our models and improve the accuracy of our estimates., Comment: in Russian language

The effect of violation of $T$-invariance, provided that $P$-parity is preserved, is given by the total cross section of the interaction of a vector-polarized particle with a tensor-polarized target. A formalism for calculating this effect developed previously and based on the spin-dependent Glauber theory of elastic $pd$ scattering is used here to calculate the effect under discussion in the range of collision energies corresponding to the invariant mass of the $pN$ system $\sqrt{s_{pN}}=5$--$30$ GeV. The spin-dependent amplitudes of elastic $pN$ scattering required for this calculation are taken from existing phenomenological models for $pN$ scattering in the energy region considered., Comment: 8 pages, 1 figure;in Russian, presented at Scientific session of Nuclear Physics section of Physics Division of RAS, submitted to PEPAN

The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a certain linear differential equation of the first order, which previously did not appear in the literature and which is satisfied by any Darboux rotation field of a smooth surface. We show that, for some surfaces, this additional equation is functionally independent of the three standard equations that the Darboux rotation field satisfies (and by which it is determined). As a consequence of this additional equation, we prove the maximum principle for the components of the Darboux rotation field for disk-homeomorphic surfaces with strictly positive Gaussian curvature., Comment: 11 pages, in Russian