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The paper deals with various generalized solutions to one-dimensional pressureless gas dynamics. Along with the entropy solutions other solutions are considered that include the combination of concentration and decay processes. This research is motivated by multidimensional case where the concentration mechanism seems to be not enough for the construction of rigorous theory. Thus the present paper describes in one-dimensional setting a possible behavior that could appear in multidimensional case.

The paper is devoted to the new approach to systems of quasilinear conservation laws which leads to the alternative view of weak solution and to the possibility of developing a new type calculation algorithms for such systems on the basis of neural networks technology. The approach under consideration is the further development of variational point of view to systems of conservation laws that was earlier described by the author. In this paper the multi-dimensional setting is considered but main results are shown in one- and two-dimensional cases.

The paper describes the approaches and methods to create a semantic library within the ‘‘Mathematics’’ subject domain. The theoretical background of the research involves the approach based on ontologies used when creating semantic libraries. The paper suggests a step-by-step description of the general ontology within the subject domain. The results obtained are well-grounded and contribute to distinct data integration.

Since the second half of the twentieth century, wide studies of Sobolev-type equations are undertaken. These equations contain items that are derivatives with respect to time of the second order derivatives of the unknown function with respect to space variables. They can describe nonstationary processes in semiconductors, in plasm, phenomena in hydrodinamics and other ones. Notice that wide studies of qualitative properties of solutions of Sobolev-type equations exist. Namely, results about existence and uniqueness of solutions, their asymptotics and blow-up are known. But there are few results about exact solutions of Sobolev-type equations. There are books and papers about exact solutions of partial equations, but they are devoted mainly to classical equations, where the first or second order derivative with respect to time or the derivative with respect to time of the first order derivative of the unknown function with respect to the space variable is equal to a stationary expression. Therefore it is interesting to study exact solutions of Sobolev-type equations. In the present paper, a third order nonlinear partial equation containing a $$p$$ -Laplacian is studied. Six classes of its exact solutions are built. They are expressed in terms of elementary functions, quadratures and special functions (solutions of some ordinary differential equations).

This paper describes a modification of the algorithm classification, which forms the basis of the AlgoWiki Open encyclopedia of parallel algorithmic features. The previously existing version of this page, implemented on the basis of wiki technologies, did not fully implement the functionality needed for the hierarchical structure of the domain descriptions in the form of chains of concepts ‘‘problem-method-algorithm-implementation’’. The approach described in this paper implements the work with an algorithm classification page based on a client-server architecture and prepares a functional basis for the further development of the AlgoWiki project.

In this paper, we consider the trajectories of real and model asteroids that lead to collisions with Earth. They highlight the close approaches to Earth that precede impact. The presence of such approaches allows us to detect a dangerous object in advance, clarify its orbit, and use the effect of a gravitational maneuver to economically prevent an asteroid from hitting Earth. In the paper we consider various families of collision trajectories: possible trajectories of real dangerous asteroids, as well as model trajectories that are not linked to a specific object. It is shown that in the first case, the approaches preceding the collision are noticeably greater.

The paper is devoted to the study of the metric properties of regular and semiregular polyhedra in Euclidean spaces. In the first part, we prove that every regular polytope of dimension greater or equal than 4, and different from 120-cell in $$\mathbb {E}^4 $$ is such that the set of its vertices is a Clifford–Wolf homogeneous finite metric space. The second part of the paper is devoted to the study of special properties of Archimedean solids. In particular, for each Archimedean solid, its description is given as the convex hull of the orbit of a suitable point of a regular tetrahedron, cube or dodecahedron under the action of the corresponding isometry group.

We study a class of nonlinear integral equations with a noncompact Hammerstein– Nemytskii operator on the entire line. Some special cases of such equations have specific applications in various fields of natural science. The combination of a method for constructing invariant cone segments for the corresponding nonlinear monotone operator with methods of the theory of functions of a real variable allows one to prove a constructive theorem on the existence of bounded positive solutions of equations of the class under consideration. The asymptotic behavior of the solution at $$ \pm \infty $$ is studied as well. In particular, we prove that the solution constructed in the paper is an integrable function on the negative half-line and that the difference between the limit at $$+\infty $$ and the solution is integrable on the positive half-line. In one special case, we show that our solution generates a one-parameter family of bounded positive solutions. At the end of the paper, we give specific applied examples of nonlinearities to illustrate the results.

We consider a nonlinear integro-differential equation with zero operator in the differential part whose integral operator contains several rapidly varying kernels. This paper continues the research carried out earlier for equations with only one rapidly varying kernel. We prove that the conditions for the solvability of the corresponding iteration problems, as in the linear case, are not differential (as in problems with nonzero operator in the differential part) but rather integro-differential equations, and the structure of these equations is substantially influenced by the nonlinearity. In the nonlinear case, so-called resonances can arise, significantly complicating the development of the corresponding algorithm of the regularization method. The paper deals with the nonresonant case.

This paper continues the study of P. S. Alexandroff’s problem: When can a Hausdorff space $$X$$ be one-to-one continuously mapped onto a compact Hausdorff space? For a cardinal number $$\tau$$ , the classes of $$a_\tau$$ -spaces and strict $$a_\tau$$ -spaces are defined. A compact space $$X$$ is called an $$a_\tau$$ -space if, for any $$C\in[X]^{\le\tau}$$ , there exists a one-to-one continuous mapping of $$X\setminus C$$ onto a compact space. A compact space $$X$$ is called a strict $$a_\tau$$ -space if, for any $$C\in[X]^{\le\tau}$$ , there exits a one-to-one continuous mapping of $$X\setminus C$$ onto a compact space $$Y$$ , and this mapping can be continuously extended to the whole space $$X$$ . In this paper, we study properties of the classes of $$a_\tau$$ - and strict $$a_\tau$$ -spaces by using Raukhvarger’s method of special continuous paritions.

Supercomputer job management systems (JMS) are complex software which have a number of parameters and settings. Various simulating methods have been used in order to explore impact of such parameters on the JMS efficiency metrics. At the same time evaluating accuracy (adequacy) of the applied JMS models is one of the key points. The paper contains the results of adequacy measure experiments for various JMS models, including simulating with a virtual supercomputing nodes and with the Alea job scheduling simulator. JMS SUPPZ functioning at the Joint Supercomputer Center of the Russian Academy of Sciences (JSCC RAS) was used for the experiments. Source data for such simulating was created upon the statistics of supercomputer MVS–10P OP installed at JSCC RAS. The normalized Euclidean distance between the job residence (turnaround) time vectors, obtained from the job streams of the real supercomputer and JMS model, was used as a measure of adequacy. The experiments results have confirmed intuitive ideas about the studied simulating methods accuracy, that allows using the normalized Euclidean distance between the jobs turnaround times vectors as a measure of various JMS models adequacy.

The paper is devoted to the current state and development plans of the monitoring and control system of the National Research Computer Network of Russia (NIKS). Some aspects of industry standards, best practice-based procedures and methodologies for network management, including FCAPS, eTOM, ITIL are briefly discussed. An overview of collaborative National Research and Education Networks (NRENs) experience in network monitoring and management is given, key functions of Network Operations Centers and examples of commercial and free program solutions used in real practice are provided. A general architecture and individual components of the monitoring and control system of NIKS taking into account the planned modernization are presented.

The paper systematizes and generalizes well-established practices of operation and development of service platforms for the research and education sphere from leading National Research and Education Networks and network consortia. The current state and planned directions of enhancement of the service platform of the new generation National Research Computer Network of Russia are presented, including the scaling and improving of already operated information technology services and specialized services for the target audience, and the implementation of new, potentially demanded services, taking into account the accumulated world experience and domestic features.

One of the common problems in multiuser supercomputer systems is inaccurate user walltime request for a job. Usually, this time is significantly overestimated by the user. Scheduling algorithms implemented in modern supercomputer job management systems (JMS) are quite complicated and have a lot of settings. In this regard, the influence of the job walltime overestimate on the scheduling efficiency is not obvious. The job walltime prediction simulation can obtain the such influence estimation. The article contains simulation results when the predicting accuracy achieves 100 $$\%$$ . JMS referred to as SUPPZ is applied at the Joint Supercomputer Center of the RAS (JSCC RAS). SUPPZ was used for our simulations. Actual statistics of MVS–10P OP supercomputer installed at JSCC RAS was used for simulation as the source data. In this paper we used the SUPPZ simulation with virtual supercomputing nodes due to its highest accuracy. The simulation results showed a noticeable improvement of such metrics as average queue job wait time, average queue length and average slowdown.

In the present paper we study $$G_2$$ -periodic $$p$$ -adic quasi Gibbs measures for $$p$$ -adic Potts model on a Cayley tree of order two. In the case $$q=3$$ , we prove the occurrence of a phase transition and construct ART quasi Gibbs measures for $$p$$ -adic Potts model on a Cayley tree of order $$k\geq3$$ .

In this paper I consider a property of sets in the real line such that every non-empty union of finitely many sets with the property does not contain a set with a positive Lebesgue measure. Selectors of the real numbers $$\mathbb R$$ related to any proper dense subgroup of the additive group $$(\mathbb R, +)$$ as well as cosets of any proper dense subgroup of $$(\mathbb R, +)$$ possess this property.

The aim of this paper is to give some sufficient conditions for the boundedness of commutators of $$p$$ -adic Hardy-Cesaro operators with symbols in weighted central BMO type spaces on the Herz spaces, Morrey spaces and Morrey-Herz spaces with both the Muckenhoupt and power weights.

In this paper, we study the approximate control problem from the exterior of a nonlocal equation of Sobolev–Galpern type, specifically the Barenblatt–Zheltov–Kochina equation, involving the fractional Laplace operator of order $$s\in(0,1)$$ . We prove that the system under consideration is approximate controllable at any time $$T>0$$ .

The paper investigates the features of reflection and refraction of acoustic waves incident at a right angle on a system of layers of multifractional gas suspensions. Formulas for calculating the reflection and refraction coefficients are obtained. The dependences of the reflection coefficients on the dimensionless frequency for different mass content of particles and layer thickness are plotted.

At scattered places of his notebooks, Ramanujan recorded over 30 values of singular moduli $$\alpha_n$$ . All those results were proved by Berndt et. al by using Weber–Ramanujan’s class invariants. In this paper, we initiate to derive the explicit evaluations formula for $$\alpha_{9n}$$ and $$\alpha_{n/9}$$ by involving the class invariant. For this purpose, we establish several new $$P-Q$$ mixed modular equations involving theta-functions. We apply these modular equations further, deriving a new formula for the explicit evaluation of the Ramanujan–Selberg continued fraction.

In this paper, we introduce a new class of algebras satisfying certain conditions which has been named power algebras and we prove some fixed point theorems for a new class of contractions. We give new conditions for the existence and uniqueness of fixed points for this new class of mappings which are not a contraction in the usual algebra. Also, we introduce a new iterative algorithm for fixed-point problems in a Banach algebra. This results improve and extend the corresponding conclusions of the Ishikawa algorithm under weaker conditions and lead to stronger results. In conclusion, we give an application to nonlinear integral equations.

The paper considers the problem of designing an aerofoil with a Fowler flap. The proposed approach is based on the use of artificial neural networks for rapid evaluation of aerodynamic characteristics. The linear method of principal component analysis (PCA) is used to reduce the dimensionality of design parameter space and to generate ‘‘random’’ airfiols. The simulated annealing method is used to find the optimal shape of the airfoil and flap.

This paper offers a description of an approach to modeling a synthesized element featuring a complex geometry. Owing to the region under examination being pre-parametrized with parameters of a parallelepiped and a synthesis of three-dimensional elements with a cubic approximation of unknown variables in all three directions of the region under examination and two-dimensional elements with cubic approximation of unknown variables in a thin layer on its edges, one is enabled to obtain high-precision curved aligned finite elements. The synthesized element obtained substantially expands the range of tasks which now may be solved. Specifically, it enables one to calculate the stress—strain state of coated structures, including those with local fibration while also allowing for specific surface properties which differ from the properties of the primary array to be taken into consideration, including the presence of distributed surface features resultant, for instance, from ion implantation, surface treatment and defects. Different cases have been studied to provide illustration for the method, in particular, a calculation of the stress-strain state of a three-layer plate.

The paper is devoted to the study of conditional bounds for the expectation of the maximum of independent identically distributed standardized random variables for which the values of the skewness and kurtosis coefficients are known. With the aid of Holder’s inequality, an upper bound (in the form of a lower bound for a certain expression with parameters) is obtained and a criterion for the reachability of this estimate is formulated. A lower bound for the upper boundary of the expectation of the maximum is also found. A simpler and rougher upper bound is given in explicit form.

An ideal triangulation of a compact $ 3 $ -manifold with nonempty boundary is known to be minimal if and only if the triangulation contains the minimum number of edges among all ideal triangulations of the manifold. Therefore, every ideal one-edge triangulation (i.e., an ideal singular triangulation with exactly one edge) is minimal. Vesnin, Turaev, and Fominykh showed that an ideal two-edge triangulation is minimal if no $ 3 $ – $ 2 $ Pachner move can be applied. In this paper we show that each of the so-called poor ideal three-edge triangulations is minimal. We exploit this property to construct minimal ideal triangulations for an infinite family of hyperbolic $ 3 $ -manifolds with totally geodesic boundary.

In the present paper, we propose a new method of derivation of number-theoretic identities which is applied to the proof of the multidimensional analogue of one of the Ramanujan identities. This method allows us to obtain new infinite series representations for the number $$\pi$$ , of the values of the Riemann zeta function, and of the $$L$$ -Dirichlet series at integer points.

Two examples illustrating properties of discrete measures are given. In the first part of the paper, it is proved that, for any probability measure $$\mu$$ with $$\operatorname{supp}{\mu}=[-1,1]$$ whose logarithmic potential is continuous on $$[-1,1]$$ , there exists a (discrete) measure $$\sigma=\sigma(\mu)$$ with $$\operatorname{supp}{\sigma}=[-1,1]$$ such that the corresponding orthogonal polynomials $$P_n(x;\sigma)=x^n+\dotsb$$ satisfy the condition $$(1/n)\chi(P_n(\,\cdot\,;\sigma))\xrightarrow{*}\mu$$ , $$n\to\infty$$ , where $$\chi(\,\cdot\,)$$ is the measure counting the zeros of a polynomial. The proof of the existence of such a measure $$\sigma$$ is based on properties of weighted Leja points. In the second part, an example of a compact set and a sequence of discrete measures supported on it with a special property is given. Namely, the sequence of measures converges in the $$*$$ -weak topology to the equilibrium measure on the compact set, but the corresponding sequence of logarithmic potentials converges in capacity to the equilibrium potential in no neighborhood of this compact set.

An algebra is called a binary Leibniz algebra if each of its two-generated subalgebras is a Leibniz algebra. In the present paper, we give a description of binary Leibniz algebras in terms of identities. As a consequence, we show that the variety of binary Leibniz algebras is not Schreier and that the freedom theorem fails to hold for this variety.

The paper deals with the problem of recovering solutions of a generalized Cauchy–Riemann system in a multidimensional spatial domain from their values on a piece of the boundary of this domain, i.e., an approximate solution of this problem based on the Carleman–Yarmukhamedov matrix method is constructed.

In this paper, a modified Rayleigh–Plesset equation is derived, which takes into account the radial oscillations of a gas bubble covered with a viscoelastic shell and located in a viscoelastic liquid. For the case of small oscillations of the inclusion with a small amplitude, a comparison is made of the dependence of the damping parameter on the disturbance frequency according to the rheological model of Kelvin–Voigt and Maxwell.

In Shallit’s problem (SIAM Review, 1994), it was proposed to justify a two-term asymptotics of the minimum of a rational function of $$n$$ variables defined as the sum of a special form whose number of terms is of order $$n^2$$ as $$n\to\infty$$ . Of particular interest is the second term of this asymptotics (“Shallit’s constant”). The solution published in SIAM Review presented an iteration algorithm for calculating this constant, which contained some auxiliary sequences with certain properties of monotonicity. However, a rigorous justification of the properties, necessary to assert the convergence of the iteration process, was replaced by a reference to numerical data. In the present paper, the gaps in the proof are filled on the basis of an analysis of the trajectories of a two-dimensional dynamical system with discrete time corresponding to the minimum points of $$n$$ -sums. In addition, a sharp exponential estimate of the remainder in Shallit’s asymptotic formula is obtained.

In this paper, the properties of the primitives of Legendre polynomials on the interval $$[0;1]$$ are studied. It is proved that the Legendre polynomials form an “almost” orthogonal system. Namely, for a fixed order of the primitive, only finitely many of these polynomials can be nonorthogonal. These properties underly the relationship between the spectral problems for differential operators in $$L_2[0;1]$$ and the spectral properties of generalized Jacobi matrices.

The subject of the present paper is a material connection that describes the sources of incompatibility in growing solids. There are several possibilities to introduce such a connection on the body manifold, which provides formal description of a body as a continuous collection of material particles. Two of them are discussed in detail. The first sets the geometry of Riemannian manifold, while the second sets Weitzenbock geometry. To derive particular connection functions, related with given evolutionary problem for growing solid, one has to use some intermediate configurations, whose choice is also uncertain. The purpose of this study is to find out how the ambiguity affects on the stress-strain state modelling. The main results are the following. It is proven that the geometrical invariants of considered material connections, namely the invariants of torsion and curvature, are independent on particular choice of intermediate configuration. It is shown that Weitzenbock connection contains all metric information that completely defines Riemannian ones, but, except it, provides additional description for contorsion, which characterizes inhomogeneity by specific term in balance of momentum. Thus, the two connections do not contradict each other. To describe the body’s response to deformation it is sufficient to construct more simpler Riemannian connection, while to completely describe balance laws it is advisable to obtain more complete Weitzenbock connection.

We consider an initial-boundary value problem for the heat equation with an inhomogeneous initial condition and boundary conditions. One of the boundary conditions contains a mixed derivative. When solving this problem by the method of separation of variables, a spectral problem arises. A system of eigenfunctions of this spectral problem and a biorthogonally conjugate system, are constructed explicitly. Also we obtain an asymptotic formula for the eigenvalues. In this paper we formulate theorems on the properties of the system of eigenfunctions of the spectral problem and a theorem about representing the solution of the initial initial-boundary value problem in the form of a Fourier series in the system of eigenfunctions. Thus, the existence of a solution is shown if the initial condition belongs to the Holder class. However, it has been shown that the solution is not unique. We show that additional condition guarantees the uniqueness of the solution. The unique solution of this problem is also obtained in the article.

This paper is dedicated to the solution of a coupled problem on creep and viscoplastic flow in a flat heavy layer. The layer is on an inclined surface and subject to heating and cooling. The problem has been solved in the framework of the large elastoplastic strain mathematical model, which generalized for the case of taking into account rheological and thermophysical material properties. The thermophysical and deformation processes are interconnected; a yield limit, a viscosity factor and creep parameters depend on temperature. The patterns of the motion of elastoplastic boundaries are shown, stresses, strains and strain rates in the areas of flow and thermoviscoelastic deformation has been calculated.

In this paper, the unsteady vibrations of an ortotropic rectangular Kirchhoff–Love plate are studied. In general formulation, the plate is under the action of longitudinal and transverse forces, bending and torque moments. It also set a diffusion fluxes density and a diffusion fluxes relaxation. The coupled elastic diffusion orthotropic multicomponent continuum model has been used to formulate the problem. The d’Alembert variational principle has been used to obtain the plate transverse elastic diffusion vibrations equations from the model.

The paper addresses the issue of filling the gaps in the semantic library based on the distributional semantics of the terms of its thesaurus and the ontology relations. The goal of the study is to fully reflect the actual structure of relations between mathematical subject domains. This is done through identifying context-sensitive semantic relations, and with the use of an algorithm that is based on the word2vec feedforward neural networks. The understanding of the query is analyzed after preliminary processing of set of articles and metadata saturation. The proposed procedure helps to improve the work with the full-text index and, as a result, improves the quality of search in the library. Using a full-text index of a digital semantic library as an example, we demonstrate the process of filling gaps by saturating the semantic relations of the ontology of mathematical subject domains.

Trefftz approximation scheme on the structure of subdomains-blocks for the problems of the gradient elasticity is proposed. This scheme based on the analytical representation for the gradient elasticity solutions of Papkovich–Neuber type. Independent in blocks, complete systems of functions are used for approximation, that analytically exact satisfy the initial fourth-order equations. It is shown that the generalized Trefftz scheme allows simultaneously with minimizing the energy functional to stitch together all the necessary quantities on the block boundaries: functions, their derivatives, cohesive moments and surface forces. It is achieved exclusively due to the analytical construction of the used functions. The paper gives a derivation of the Papkovich–Neuber representation for the gradient elasticity and formulates the uniqueness conditions. The analytical representation of the solution has a great advantage over the finite element one, since it opens up the possibility of constructing finite elements on unstructured meshes with independent local shape functions.

For a linear inhomogeneous system of first-order partial differential equations with three independent variables, we prove the existence and uniqueness of a solution of the Darboux problem, which is constructed in terms of the Riemann–Hadamard matrix defined in the paper.

The paper is dedicated to the construction of a computational algorithm for the investigation of solids, taking into account the material and geometric nonlinearity and contact interaction. In the framework of the previously developed algorithm for the investigation of large elastoplastic deformations of solids the solutions of contact problems are derived. The algorithm has been based on the equation of the principle of virtual work in velocity terms. Contact interaction is modeled over the basis of the master-slave approach with penalty method. The closest point projection procedure is used to find the contact area. For the solution of the nonlinear system of equations incremental method is applied. The numerical implementation is based on the finite element method.

This paper is concerned with the observer-based controller for the stabilization of linear systems with multiple delays. We design a state observer for the delay systems and derive a separation property for the observer-based controller of the delay systems.

The main purpose of the paper is to strengthen the results of P. R. Mercer (2003) concerning the comparison of arithmetic, geometric, and harmonic weighted means.

In this paper, we study the third boundary value problem for the convection-diffusion equation with a time fractional derivative and variable coefficients in a multidimensional domain. For an approximate solution in a rectangular parallelepiped of the problem set, in the same area, the third boundary value problem for a differential equation with a small parameter is considered. An a priori estimate is obtained from which it follows the convergence of the solution of the differential problem with a small parameter to the solution of the original problem for small values of the parameter. For a problem with a small parameter, a locally one-dimensional difference scheme by A. A. Samarski is constructed. Using the maximum principle for solving the difference problem, an a priori estimate is obtained in the grid norm $$C$$ , which expresses the stability of the locally one-dimensional difference scheme. The uniform convergence of the locally one-dimensional scheme is proved for $$0

Distributed computing environments execute great amount of various computing jobs that can fail or break for some reason. The analysis of the error messages describing the reasons of failures has become one of the most crucial parts of the existing monitoring systems. This analysis is complicated by the presence of a large number of messages, especially in the case of the retrospective analysis. ClusterLogs framework was developed as a modular and flexible tool for the clustering of error messages of computing jobs in distributed computing infrastructures. The general purpose of this tool is to simplify the error messages analysis by grouping together messages that share similar failure reasons and textual patterns. Proposed clustering method includes a set of sequential data processing stages and provides various clustering options: deterministic similarity-based clustering and unsupervised multiple machine learning methods with preliminary vectorization of error messages using the word embedding technique. The performance tests had revealed the most time consuming stages. In this paper we describe the parallelilzing method for these stages and demonstrate how it has allowed the increased performance of the whole clustering pipeline. The performance tests were executed on the HPC system Polus.

An advantage of the discontinuous Galerkin method is the ability to describe complex contact surfaces by using unstructured computational grids. However, the use of the discontinuous Galerkin method requires significant computational resources, including at the preprocessing stage. The grid-characteristic method on structured regular computational grids saves computational resources, but problems arise when taking into account complex inhomogeneities, including surface topography. Therefore, it is of interest to combine the grid-characteristic method on structured computational grids with the discontinuous Galerkin method, to which this paper is devoted. The work describes in detail the Galerkin method and the description of the contact boundary between the subdomains of the integration domain in which the grid-characteristic method and the discontinuous Galerkin method are used. The corresponding calculation algorithm is discussed. Examples are given on the calculation of the propagation of seismic waves from the hypocenter of an earthquake to the Earth’s surface, taking into account the surface topography.

For evolution problems, the approximate solution on the upper time level is often obtained from a number of simpler problems. Standard splitting schemes use an additive splitting of the problem operator into operators more convenient for computational implementation and time implicit-explicit approximations. In the present paper, we consider a new class of splitting schemes associated with an additive representation of the solution itself rather than of the problem operator. We suggest a new general solution splitting procedure based on an additive representation of the identity operator via restriction and extension operators for auxiliary spaces. Unconditionally stable splitting schemes for the approximate solution of the Cauchy problem for a second-order evolution equation in a finite-dimensional Hilbert space are constructed and studied.

In this paper, we study a nonlinear integral equation that arises in a model of spatial logistic dynamics. The solvability of this equation is investigated by introducing special spaces of functions that are integrable up to a constant. Sufficient conditions for the biological characteristics and the parameters of the third spatial moment closure are established that guarantee the existence of the solution of the equation described above in some ball centered at zero. In addition, it is shown that this solution is unique in the considered ball and not zero. This means that, under appropriate conditions, the equilibrium state of the population of a certain species exists and does not coincide with the state of extinction.

In this paper, we consider mixed-integer global optimization problems and propose a parallel algorithm for solving problems of this class based on information-statistical approach for solving continuous global optimization problems. Within this algorithm, we suggest using a local tuning scheme based on the assumption that the multiextremality of the discussed problem is weak. We also compare the sequential version of the algorithm with other similar methods. The effectiveness of parallelizing the algorithm has been confirmed by solving a series of mixed-integer global optimization problems on the Lobachevskii supercomputer.

Dark states of atomic ensembles do not interact with light (can neither emit nor absorb a single photon due to destructive interference). Being free of decoherence, they can be widely used in quantum computing (particularly as a mechanism for creating quantum memory). To date, the structure of dark states of two-level atoms has been sufficiently well studied; meanwhile, this problem remains open for three-level atomic ensembles. For ensembles of two-level atoms (in a chosen range), it was established that the dimension of the dark subspace is equal to the Catalan numbers. It is difficult to generalize this statement to the case of three-level, and even more so, multi-level atomic ensembles and has not been done so far. This paper proposes a supercomputer algorithm for numerical confirmation of a similar statement for ensembles of a limited number (not exceeding several tens) of three-level atoms.

The problem of weighted finite-rank series approximation of a time-series aimed at estimating the signal in the “signal plus noise” model, where the inverse covariance noise matrix is (2p + 1) diagonal, is considered in this paper. The problem of searching for weights that improve the estimation accuracy is solved. An efficient numerical method for the search for weights is constructed and theoretically validated. A numerical simulation is performed for several noise models to study the improvement of accuracy of the signal estimation method.