Abstract In the paper flows of shock waves in multiphase media are described. Gas suspensions are considered as a multiphase medium—liquid drops or solid particles suspended in a gas. In this work, a continual approach in mathematical modeling of the dynamics of multiphase media is applied. The continual approach involves solving the complete hydrodynamic system of equations for each of the mixture

Abstract In [1], Mazhar has proved two theorems on absolute summability of infinite series. In the present paper, these two theorems have been generalized for absolute matrix summability of the series \(\sum a_{n}\lambda_{n}\) by using almost increasing sequence.

Abstract A problem of functions factorization is studied with respect to the fundamental solution of a fractional generalization of the Helmholtz equation. A factorization technique that is applicable for a wide class of functions represented by the Mellin–Barnes type integral is proposed. Factorized representations in integral form and in terms of the H-function are obtained for the fundamental solution

Abstract A one-parameter family of smooth solutions of a two-dimensional differential-difference hyperbolic equation with \(n\) translations with respect to the spatial variable is constructed. The theorem is proved that the obtained solutions are classical if the real part of the symbol of the difference operator of the equation is positive. The class of equations such that the specified condition

Abstract Density functional theory method was used to study the interaction of 3d-transition metal ions with divacancy in graphene. Calculations demonstrate that in all cases, except for that of the structure with the Sc ion, the metal is located in the divacancy center, compensating for the four dangling chemical bonds of carbon atoms. Interaction energies are close to 1000 kJ/mol. The strongest interaction

Abstract In this paper we introduce a reduction theory based on the hyperbolic center of mass, which is different from the reduction introduced by Julia (1917). We show that the zero map via the Julia quadratic is different than the hyperbolic center of mass. Moreover, we discover some interesting formulas for computing the hyperbolic centroid.

Abstract The aim of this research is to construct and analyze the mathematical model of \(n\) parallel circular FIFO-queues, located in a shared memory. The mathematical model is built in the form of random walks on an integer lattice in \(n\)-dimensional space. Operations (with given probabilities) occur at each step of the discrete time.

Abstract In the present paper, we study simple-direct-injective modules and simple-direct-projective modules over a formal matrix ring \(K=\left(\begin{matrix}R&M\\ N&S\end{matrix}\right)\), where \(M\) is an \((R,S)\)-bimodule and \(N\) is a \((S,R)\)-bimodule over rings \(R\) and \(S\). We determine necessary and sufficient conditions for a \(K\)-module to be, respectively, simple-direct-injective

Abstract A mathematical model of unsaturated filtration in swelling soils under conditions of constant volume of the medium as a whole has been developed. On the basis of the developed model, a solution to the problem of capillary rise of moisture in swelling soils was obtained, and the characteristic features of the process were revealed. A series of experiments on the capillary rise of moisture in

Abstract This paper focuses on the development of a new process for solving state-space singular continuous-time fractional linear systems based on Caputo fractional derivative-integral. The main idea of this new approach consists in using Sumudu transform since its interesting properties. State-of-the-art methods are used to compare the obtained results.

Abstract A method is proposed of evaluation of symbol and/or bit error probabilities for coherent diversity receiving of multipositional signal constructions in communication channel with fadings, which are described with the help of classical and generalized models Multiple-Wave with Diffuse Power (MWDP) fading and of additive white Gaussian noise (AWGN). This method uses the hypergeometric functions

Abstract We consider the problem of the realization of \(k\)-meaning logics functions(\(k\geq 3\)) by circuits from unreliable elements in full basis consisting of the Webb function. We assume that elements of the circuit pass to fault states independently of each other, and they are exposed to single-type constant faults of type \(k-1\) at the outputs. We prove that almost any \(k\)-meaning logics

Abstract We consider transformations of random variables on finite sets by algebraic operations. A system of operations is said to be approximation complete if any random variable may be approximated with arbitrary precision by applying the given operations to mutually independent identically distributed random variables whose distributions have no zero components. We establish some necessary conditions

Abstract In this paper, we extend some polynomial inequalities to the polar derivative of a polynomial having all its zeros inside or outside a circle of radius \(k\), \(k>0\) and thereby present some compact generalizations and improvements of certain well-known inequalities concerning the maximum modulus of the polar derivative of a complex polynomial.

Abstract This article is devoted to the study of irregular singular points of the linear partial differential equations with holomorphic coefficients. In this paper we consider two important cases of differential equations. In the first case we consider partial differential equation with a special condition on the main symbol of the differential operator, in the second case considered Laplace equation

Abstract We consider the simplest class of countably connected domains with the unique limit point boundary component. We find the domains in this class where the limit component is simultaneously perfect in the Grötzsch sense, i.e. corresponds to a point boundary component under any conformal mapping, and regular in the sense of the Dirichlet problem. We call the regular point the Wiener point in

Abstract In this paper, we focus on combining the theories of interval-valued fuzzy soft sets over ternary semigroups, and establishing a new framework for interval-valued fuzzy soft ternary semigroups. The aim of this manuscript is to apply interval-valued fuzzy soft set for dealing with several kinds of theories in ternary semigroups. First, we present the concepts of interval-valued fuzzy soft sets

Abstract Modern supercomputers are so large and complex that some of their hardware components inevitably go out of order from time to time. Therefore, supercomputer systems require constant and careful health monitoring, and such control is set up in everyday practice of any large HPC center. But a lot of attention should be also paid to the quality of supercomputer usage, describing how fully and

Abstract In this paper we study a subdirect irreducibility of algebras with one operator and the main near-unanimity operation defined by the specific way. It is shown that congruence lattices of algebras of given class are atomic. In given class, the full description of atoms in congruence lattices of algebras, of subdirectly irreducible algebras, and of algebras with atomistic congruence lattices

Abstract Strong single expansion and collapse of the central bubble in a streamer of an odd number of cavitation bubbles in acetone is numerically studied. The conditions considered are close to those in the well-known experiments on neutron emission during acoustic cavitation of deuterated acetone. Initially, all the bubbles are spherical, with the same radius of 5 \(\mu\)m, equidistant from the neighboring

Abstract The article is about the research of a optimum number of processor cores for launching the Parallel Cluster Multiple Labeling Technique in the course of conducting simulation experiments during multi-agent modeling of the spread of mass epidemics on modern supercomputer systems installed in the JSCC RAS. This technique may be used in any field as a tool for differentiating large lattice clusters

Abstract We construct a three-component system of PDEs describing dynamics of van der Walls gas in one-dimensional nozzle. The group of conservation laws for this system is described. We also compute the Lie algebras of point symmetries and present group classification. Examples of exact invariant solutions are given.

Abstract Widespread application of supercomputer technologies in various spheres of life, as well as the need of high-performance calculations allows us to speak about the relevance of the problem of increasing the performance of computer codes on supercomputers of modern architectures. Vectorization of program code is a low-level optimization that can, with a relatively local and compact application

Abstract The lifecycle of a supercomputer job includes queue waiting time, allocation of computational resources, job initialization, job execution on allocated resources, result saving and resources freeing. The paper focuses on scheduling optimization of supercomputer jobs with a long initialization time, which reduces useful load of the supercomputer. Grouping jobs could increase the useful load

Abstract We consider the constrained optimal control problems governed by a parabolic initial-boundary value problem with time-fractional derivative and mixed boundary conditions. Control is carried out on the right side of the equation and on the right side of Neumann boundary condition. Finite element method with the quadratures is used for the approximation of the problem with respect to the spatial

Abstract The paper presents a finite-difference analogue of the differential problem formulated in terms of the theory of ‘‘Mean Field Games’’ for solving the planning problem of convey to a given state. Here optimization problem is formulated as coupled pair of parabolic partial differential equations of the Kolmogorov (Fokker–Planck) and Hamilton–Jacobi–Bellman type. The proposed Euler–Lagrange finite-difference

Abstract The implementation of a set of measures aimed to regular monitoring and analyzing the activity of users of the National Research Computer Network of Russia in the inter-network interaction, evaluation of the level of its involvement in joint research projects, the intensity of using the technological infrastructure of Russian and the world’s national research and education networks are discussed

Abstract The paper is devoted to machine learning methods and algorithms for the supercomputer jobs execution prediction. The supercomputers statistics shows that the actual runtime of the most of the jobs substantially diverges from the time requested by the user. This reduces the efficiency of scheduling jobs, since an inaccurate job execution time estimation leads to a suboptimal jobs schedule.

Abstract The article discusses the approach to the analysis of business processes, called process mining, and the directions of its application. In particular, a description of the process discovery algorithm is provided, with the help of which the process model is reconstructed from the event log in the form of a workflow graph. The implementation and improvement of the algorithm are proposed, which

Abstract Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation. Solutions obtained are multivalued and we provide a method of finding caustics, as well as wave front displacement. The method can be applied to any model of thermodynamic

Abstract A mathematical model and numerical method for simulation of the continuous casting process in a variable in time domain are presented. The variable geometry of the slab is caused by the change in time of the width of the mould. The mathematical model of the process is a Stefan problem with prescribed convection and non-linear Robin boundary condition. Considered differential equation is approximated

Abstract The paper concerns global solvability of initial value problem for one class of hyperbolic quasilinear second order equations with two independent variables, which have a rather wide range of applications. Besides existence and uniqueness of maximal solutions of this problem it is proved that a maximal solution possess the completeness property that is an analog of the corresponding property

Abstract In this note we apply noncommutative versions of Lyapunov convexity theorem to obtaning new results in comparison theory of states and functional on von Neumann algebras and \(JBW^{\ast}\) triples. We show that in many cases the sets of projections or tripotents on which functionals attain constant single numerical value are determining for them. We discuss connection of our results with quantum

Abstract We introduce the Friedrichs model at the finite temperature which is one- and zero-particle restriction of the spin-boson model in the rotating wave approximation and obtain the population of the excited state for this model. We also consider the oscillator interacting with bosonic thermal bath in the rotating wave approximation and obtain dynamics of the mean excitation number for this oscillator

Abstract Symmetric coherent states are of interest in quantum cryptography, since for such states there is an upper bound for unambiguous state discrimination (USD) probability, which is used to resist USD attack. But it is not completely clear what an eavesdropper can do for shorter channel length, when USD attack in not available. We consider the task of generalized discrimination between symmetric

Abstract We study the relationship between random processes with values in Euclidian space \(\mathbb{R}^{d}\) and operator valued functions \(\mathbb{R}_{+}\to B(H)\), where \(H=L_{2}(\mathbb{R}^{d})\) and \(B(H)\) is the Banach space of bounded linear operators in the space \(H\). A random process with values in the space \(\mathbb{R}^{d}\) can be presented by the pseudomeasures on the algebra \(

Abstract Symmetries and the corresponding fields of differential invariants of the inviscid flows on a curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.

Abstract This work considers an open two-level quantum system evolving under coherent and incoherent piecewise constant controls constrained in their magnitude and variations. The control goal is to steer an initial pure density matrix into a given target density matrix in a minimal time. A machine learning algorithm was developed, which combines the approach of \(k\) nearest neighbors and training

Abstract A contact structure on a three-dimensional manifold is a two-dimensional distribution on this manifold which satisfies the condition of complete non-integrability. If the distribution fails to satisfy this condition at points of some submanifold, we have a contact structure with singularities. The singularities of contact structures were studied by J. Martinet, B. Jakubczyk and M. Zhitomirskii

Abstract We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed under concatenations and tensor products. We obtain asymptotically tight universal continuity bounds for the output entropy of two types of quantum channels:

Abstract State of a \(d\)-dimensional quantum system can only be inferred by performing an informationally complete measurement with \(m\geqslant d^{2}\) outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here we show that a single informationally incomplete measuring apparatus is still able to provide all the information about the quantum system if applied

Abstract In this paper we classify the symbols of the linear differential operators of order \(k\), which act from the module \(C^{\infty}(\xi)\) to the module \(C^{\infty}(\xi^{t})\), where \(\xi\colon E(\xi)\to M\) is vector bundle over the smooth manifold \(M\), bundle \(\xi^{t}\) is either \(\xi^{*}\) with fiber \(E^{*}:=\textrm{Hom}(E,\mathbb{C})\) or \(\xi^{\flat}\) with fiber \(E^{\flat}:=\textrm{Hom}(E

Abstract We consider singular rank one perturbations of the semigroup of shifts on the half-axis changing the domain of its generator. Only one example using the projection on the exponential vector is considered.

Abstract Under consideration is a new version of the Discriminant Analysis that was created on the basis of the approaches of quantum computing. Unlike the Classical Discriminant Analysis, there are no a priori assumptions about the probabilistic distributions of empirical data as well as binding to geometric data representations, which are not always consistent with real observations.

Abstract We discuss a model of genome as a program with functional architecture and consider the approach to Darwinian evolution as a learning problem for functional programming. In particular we introduce a model of learning for some class of functional programs.

Abstract In the paper we describe the properties of the \(C^{*}\)-algebras on a ring of the complex plane generated by polynomials and rational functions. We show that these algebras are isomorphic to the Toeplitz algebras generated by generalized shift operators.

Abstract Given a quantum channel it is possible to define the non-commutative operator graph whose properties determine a possibility of error-free transmission of information via this channel. The corresponding graph has a straight definition through Kraus operators determining quantum errors. We are discussing the opposite problem of a proper definition of errors that some graph corresponds to. Taking

Abstract In this paper evolution of the enrichment factor for zirconium isotopes separation by the laser assisted retardation of condensation has been found for specific choice of iterative policy of isotopes recovery. It has been evaluated for a set of gas flow temperatures, corresponding to its maximal value, provided all values of other important parameters of the system such as gas flow pressure

Abstract We examine a way of using the parametric continuation method to compute mappings of the unit ball in \(n\)-dimensional real space. The proposed approach yielded sufficient and necessary conditions for the global injectivity of mappings were obtained. It is established that these conditions actually coincide with the known features of the \(n\)-dimensional complex space. The concretization

Abstract We prove new integral inequalities for real-valued test functions defined on subdomains of the Euclidean space. Namely, we obtain several new Hardy-type inequalities that contain the scalar product of gradients of test functions and of the gradient of the distance function from the boundary of an open subset of the Euclidean space. Our method of proof is based on interior and exterior approximations

Abstract We study integrability cases for the multiple Loewner differential equation which generates conformal mappings from the upper half-plane \(\mathbb{H}\) of the complex plane with multiple slits onto \(\mathbb{H}\). The research is reduced to constant, square root and exponential driving functions of the Loewner equation. Moreover, conformal mappings from \(\mathbb{H}\) minus symmetric circular

Abstract Solutions of functional differential equation of pointwise type (FDEPT) are in one-to-one correspondence with the traveling-wave type solutions for the canonically induced infinite-dimensional ordinary differential equation and vice versa. In particular, such infinite-dimensional ordinary differential equations are finite difference analogues of equations of mathematical physics. An important

Abstract This article is devoted to the study of mappings with bounded and finite distortion, as well as the Sobolev classes that have been actively studied recently. We study the homeomorphisms of the Sobolev classes \(W^{1,p}_{\textrm{loc}}\) for the case when \(p=n-1\), where \(n\) is the corresponding dimension of space. For these classes, we prove the estimate of the distortion of the modulus

Abstract The aim of this paper is to study the multiple interpolation problem in the spaces of analytical functions of finite order \(\rho>1\) in the half-plane. The necessary and sufficient conditions for solvability of interpolation problem are obtained. These conditions are obtained in terms of the Nevanlinna product of interpolation nodes. The solution of the interpolation problem is constructed

Abstract In this paper, we study a Cauchy-type problem for one ordinary fractional differential equation with a fractional derivative of Riemann–Liouville in the main part. To achieve this objective, a generalized polynomial projection method based on two pairs of spaces of the required elements and the right parts of its correct statement is proposed and its theoretical and functional justification

Abstract In the spaces \(L_{p}(0,1)\), \(1\leq p<\infty\), we investigate the systems consisting of contractions and shifts of one function. We study Fourier type series expansions with integer coefficients by such systems. The resulting decompositions have the property of image compression, that is, many their coefficients vanish. This study may also be of interest to the specialists in transmission

Abstract In this work, for a class of nonlinear weakly singular integral equations defined in the space of quadratically summable functions in a circle, the rationale for the general projection method is given. Using the obtained general results, the convergence of the well-known Galerkin method is proved.

Abstract The Lebesgue constant corresponding to the classical Fourier operator is approximated by a logarithmic function depending on two parameters. The difference between the Lebesgue constant and this function is studied, various extreme problems are considered, algorithms of successive reduction of values of the obtained best uniform approximations are given.

Abstract For an inhomogeneous three-dimensional equation of mixed parabolic-hyperbolic type in a rectangular parallelepiped, the initial-boundary problem is studied. A criterion for the uniqueness of a solution is established. The solution is constructed as the sum of an orthogonal series. In substantiating the convergence of the series, the problem of small denominators of two natural arguments arose

Abstract We investigate smooth one-parameter families of complex tori over the Riemann sphere. The main problem is to describe such families in terms of projections of their branch-points. Earlier we investigated the problem for the case where, for every torus of the family, there is only one point lying over infinity. Here we consider the general case. We show that the uniformizing functions satisfy