An Erratum to this paper has been published: https://doi.org/10.1134/S1063454121010143

Abstract In this paper, we consider generalizations of the optimal choice problem. There is a sequence of n identically distributed random variables on the interval [0, 1]. Sequentially obtaining the observed values of these quantities, it is necessary at some point to stop at one of them, taking it as the starting point for counting the upper or lower record values. In the optimal choice problem and

Abstract C. Jacobi found that in the general N-body problem (including N = 3), the negativity of the total energy of the system was necessary for the Lagrangian stability of any solution. For the restricted three-body problem, this statement is trivial, since a zero-mass body makes zero contribution to the system energy. If we consider only the equations describing the motion of a zero-mass point,

Abstract In this paper, the study of the structural arrangement of generalized normal forms (GNFs) is continued. A planar system that is real-analytic at the origin of coordinates is considered. Its unperturbed part forms a first degree quasi-homogeneous polynomial (\(\alpha x_{1}^{2}\) + x2, x1x2) with weight (1, 2), in which parameter α ∈ (–1/2, 0) ∪ (0, 1/2]. For the given values of α, this polynomial

Abstract In this paper, a second-order discrete-time automatic control system is studied. This study is a continuation of the research presented in the author’s papers “On the Aizerman problem: coefficient conditions for the existence of a four-period cycle in a second-order discrete-time system” and “On the Aizerman problem: coefficient conditions for the existence of three- and six-period cycles

Abstract The Monte Carlo method to solve the Cauchy problem for large systems of linear differential equations is proposed in this paper. Firstly, a quick overview of previously obtained results from applying the approach towards the Fredholm-type integral equations is made. In the main part of the paper, the method is applied towards a linear ODE system that is transformed into an equivalent system

Abstract A dynamically symmetric satellite in a circular orbit of small inclination is considered. The problem of the Lorentzian stabilization of the satellite in the orbital coordinate system in the indirect equilibrium position is solved under the conditions of the perturbing effect of the gravitational torque. To solve this problem, which is characterized by incomplete control, a method of averaging

Abstract Recently, W. Lao and M. Mayer (2008) developed U-max-statistics, where instead of averaging the values of the kernel over various subsets, the maximum of the kernel is considered. Such statistics often appear in stochastic geometry. This is the second part of the work devoted to the study of the generalized perimeter of a random inscribed polygon and the limit behavior of U-max-statistics

Abstract In the paper, the generalization of the Hardy theorem for power series of several variables inverse to the power series with positive coefficients is considered. It is proved that if the sequence of coefficients {as} = \({{a}_{{{{s}_{1}},{{s}_{2}}, \ldots ,{{s}_{n}}}}}\) of a power series satisfies the condition similar to the condition of the logarithmical convexity of the coefficients and

Abstract Various record achievements are recorded in a number of areas of human activity. In this case, some discretization of the obtained observation results repeatedly occurs with varying accuracy (up to a second, up to a meter, and up to a thousand individuals). Using exponential and geometric distributions as an example, we show how such a transition from continuous to discrete probability distributions

Abstract The results of the numerical studies of the influence of the reinforcement orientation of rigid layers and relative thickness of a soft isotropic viscoelastic polymer layer on the values of natural frequencies and loss factors of the coupled vibrations of symmetric and asymmetric unsupported three-layer rectangular composite plates are discussed. It is shown that in a symmetric three-layer

Abstract We consider the linear Kalman–Bucy filter problem for a system in which a signal and a noise are independent vector stationary autoregressive processes with orders higher than 1. Recurrent equations for the filtration and its error are derived. The optimal definition of the initial data is proposed. We describe an example in which the algorithm leads to a stationary mode at infinity, as well

Abstract A problem of the optimal scheduling is considered for a project that consists of a certain set of works to be performed under given constraints on the time of starting and finishing the works. The deviation of the starting time of the works that needs to be minimized is taken as the optimality criterion for scheduling. Such problems arise in project management when it is required, due to technological

Abstract In this paper we study in detail the so-called Chow-weight homology of Voevodsky motivic complexes and relate it to motivic homology. We generalize earlier results and prove that the vanishing of higher motivic homology groups of a motif M implies similar vanishing for its Chow-weight homology along with effectivity properties of the higher terms of its weight complex t(M) and of higher Deligne

Abstract This study is a continuation of the article “Formulation and solution of a generalized Chebyshev problem: First Part,” in which a generalized Chebyshev problem was formulated and two theories of motion for nonholonomic systems with higher order constraints were presented for its solution. These theories were used to study the motion of the Earth’s satellite when fixing the magnitude of its

Abstract The issues of studying shock-wave processes in structural materials are relevant; however, it is difficult, expensive, and sometimes even impossible to perform field studies. Therefore, all research on this topic is reduced to various options for modeling the processes rapidly loading materials under laboratory conditions. In the paper, we consider the following areas of the mathematical modeling

Abstract Generalized Honda formal groups are a class of formal groups, which includes all formal groups over the ring of integers of local fields weakly ramified over \({{\mathbb{Q}}_{p}}\). This class is the next in the chain multiplicative formal group–Lubin-Tate formal groups–Honda formal groups. The Lubin-Tate formal groups are defined by distinguished endomorphisms [π]F. Honda formal groups have

Abstract The variation in the irregularity degree of a finite unramified local field extensions of a local field is investigated with respect to a polynomial formal group and in the multiplicative case. The necessary and sufficient conditions for the existence of the psth primitive roots of the psth power of 1 and (endomorphism \({{[{{p}^{s}}]}_{{{{F}_{m}}}}}\)) in the Lth unramified extension of the

Abstract Recently, W. Lao and M. Mayer (2008) developed U-max-statistics, where instead of averaging the values of the kernel over various subsets, the maximum of the kernel is considered. Such statistics often appear in stochastic geometry. Their limit distributions are related to the distributions of extreme values. In this paper, we begin to consider the limit theorems for the generalized perimeter

Abstract The necessary and sufficient conditions are found for convergences of series of weighted probabilities of large deviations for combinatorial sums \(\sum\nolimits_i {{{X}_{{ni{{\pi }_{n}}(i)}}}} \), where ||Xnij|| is an n-order matrix of independent random variables and (πn(1), πn(2), …, πn(n)) is a random permutation with the uniform distribution on the set of permutations of numbers 1, 2

Abstract In a restricted circular three-body problem, the concept of the minimum velocity surface \(\mathscr{S}\) is introduced, which is a modification of the zero-velocity surface (Hill surface). The existence of the Hill surface requires the occurrence of the Jacobi integral. The minimum velocity surface, apart from the Jacobi integral, requires conservation of the sector velocity of a zero-mass

Abstract The paper contributes to the theory of the elimination of wild ramification for two-dimensional fields and continues the research related to the classification of fields introduced in the work of Masato Kurihara. We consider two-dimensional mixed-characteristic local fields with the characteristic of the finite residue field not equal to 2. The structure of fields that are weakly unramified

Abstract In this paper, we investigate the existence of a solution of the Cauchy problem (initial-value problem) with the initial point located on the boundary of the domain of definition of a first-order differential equation. This formulation of the problem differs from the one accepted in classical theory, where the initial point is always an internal point of the domain. Our aim is to find the

Abstract A theorem on the strong law of large numbers for linear functions of concomitants (induced order statistics) for sequences of independent identically distributed two-dimensional random vectors is proved in this paper. The result complements previous work by S.S. Yang (1981) and N. Gribkova and R. Zitikis (2017, 2019). The proof is based on the conditional independence property of the concomitants

Abstract An efficient numerical tool for studying shock waves in viscous carbon dioxide flows is proposed. The developed theoretical model is based on the kinetic theory formalism and is free of common limitations such as constant specific heat ratio, approximate analytical expressions for thermodynamic functions and transport coefficients. The thermal conductivity, viscosity and bulk viscosity coefficients

Abstract We study transverse vibrations of an inhomogeneous circular thin plate in this work. Using the perturbation method, asymptotic formulas are obtained for free-vibration frequencies of a plate whose thickness and Young’s modulus linearly depend on radius. The effect of the boundary conditions on frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For lower

Abstract We study the asymptotic behavior at zero of distributions and densities of a sum of several independent positive random variables under certain assumptions on the decay rate of their distributions at zero. We consider cases where the distributions (densities) of summable random variables are regularly or slowly varying at zero or can decrease at zero at an arbitrary rate.

Abstract The author previously obtained a strong law of large numbers for combinatorial sums \(\sum\nolimits_i {{{X}_{{ni{{\pi }_{n}}(i)}}}} \), where \(\left\| {{{X}_{{nij}}}} \right\|\) is an n-order matrix of random variables with finite fourth moments and (πn(1), πn(2), …, πn(n)) is a random permutation uniformly distributed on the set of all permutations of numbers 1, 2, …, n, independent from

Abstract It is known that if each pre-orbit of a non-injective endomorphism is dense, the endomorphism is transitive (i.e., a dense orbit exists). However, it is still unknown whether the pre-orbits of an Anosov map are dense, and the conditions necessary for all pre-orbits to be dense are also unknown. Using the properties of integral lattices, we construct our proof by considering the pre-orbits

Abstract An electrodynamic space tether system operating in stretched cluster mode in a circular equatorial near-Earth orbit under conditions of nonuniformity of the Earth’s magnetic field is considered in this work. The dynamic equations of motion are analyzed to find equilibrium modes of motion. A possible motion mode of tethered cluster is found, which is close to vertical equilibrium position in

Abstract The diffeomorphism of a plane into itself with three hyperbolic points is studied this paper. It is assumed that the heteroclinic points lie at the intersections of the unstable manifold of the first point and the stable manifold of the second point, of the unstable manifold of the second point and the stable manifold of the third point, of the unstable manifold of the third point and the

Abstract Random sequences with random or stochastic indices controlled by a doubly stochastic Poisson process are considered in this paper. A Poisson stochastic index process (PSI-process) is a random process with the continuous time ψ(t) obtained by subordinating a sequence of random variables (ξj), j = 0, 1, …, by a doubly stochastic Poisson process Π1(tλ) via the substitution ψ(t) = \({{\xi }_{{{{\Pi

Abstract Numerical modeling of nonequilibrium state-to-state carbon dioxide kinetics is a challenging time-consuming computational task that involves solving a huge system of stiff differential equations and requires optimized methods to solve it. In the present study, we propose and analyse optimizations for the Extended Backward Differential Formula (EBDF) scheme. Using adaptive timesteps instead

Abstract This paper is the sixth in a series of papers devoted to two-dimensional homogeneous cubic systems. It considers a case where a homogeneous vectorial polynomial in the right-hand part of the system does not have a common multiplier. A set of such systems is divided into classes of linear equivalence; in each of them, the simplest system is a third-order normal form which is separated on the

Abstract In this paper, a set of optimal subspaces is specified for L2 approximation of three classes of functions in the Sobolev spaces \(W_{2}^{{(r)}}\) defined on a segment and subject to certain boundary conditions. A subspace X of a dimension not exceeding n is called optimal for a function class A if the best approximation of A by X is equal to the Kolmogorov n-width of A. These boundary conditions

Abstract A mathematical model of damped vibrations of three-layer plates formed by two rigid anisotropic layers and a soft middle isotropic viscoelastic polymer layer is proposed in this paper. The model is based on the Hamilton’s variational principle, the refined theory of first-order plates, the model of complex modules, and the principle of elastic-viscoelastic correspondence in the linear theory

Abstract This paper considers the application of the stochastic mesh method in solving the multidimensional optimal stopping problem for a diffusion process with nonlinear payoff functions. A special discretization scheme of the diffusion process is presented to solve the problem in the case of geometric average Asian option payoff functions. This discretization scheme makes it possible to eliminate

Abstract The problem of approximation by entire functions of exponential type defined on a countable set E of continua Gn, E = \(\bigcup\nolimits_{n \in \mathbb{Z}} {{{G}_{n}}} \) is considered in this paper. It is assumed that all Gn are pairwise disjoint and are situated near the real axis. It is also assumed that all Gn are commensurable in a sense and have uniformly smooth boundaries. A function

erratum

Abstract— In the paper, the elementary net closure problem is considered. An elementary net (net without a diagonal) σ = (σij)i ≠ j of additive subgroups σij of field k is called “closed” if elementary net group E(σ) does not contain new elementary transvections. Elementary net σ = (σij) is called “supplemented” if table (with a diagonal) σ = (σij), 1 ≤ i, j ≤ n, is a (full) net for some additive subgroups

Abstract Homological properties of quotient divisible Abelian groups are studied. These groups form an important class of groups, which has been extensively studied in recent years. The first part of the paper is devoted to conditions for the triviality of extension groups in which one of the arguments is a quotient divisible group. Under certain additional assumptions, groups of homomorphisms from

Abstract The initial-value problem (the Cauchy problem) for an ordinary differential equation of the first order is considered. It is assumed that the right-hand side of the equation is a continuous function defined on a set consisting of a connected open set (a domain) of the two-dimensional Euclidean space, as well as on part of its boundary. It is known that, for any point of the domain, the Peano

Abstract Finite quasi-groups without sub-quasi-groups are considered. It is shown that polynomially complete quasi-groups with this property are quasi-primal. The case in which the automorphism groups act transitively on these quasi-groups is considered. Quasi-groups of prime-power order defined on an arithmetic vector space over a finite field are also studied. Necessary conditions for a multiplication

Abstract The notion of a supercharacter theory was proposed by P. Diaconis and I.M. Isaacs in 2008. A supercharacter theory for a given finite group is a pair of the system of certain complex characters and the partition of group into classes that have properties similar to the system of irreducible characters and the partition into conjugacy classes. In the present paper, we consider the group obtained

Abstract This paper presents a brief survey for the theory of stability of weakly hyperbolic invariant sets. It has been proved in several papers that I published along with Pliss and Sell that a weakly hyperbolic invariant set is stable even if the Lipschitz condition fails to hold. However, the uniqueness of leaves of a weakly hyperbolic invariant set of a perturbed system remains an open question

Abstract This paper contains an explanation of Ramanujan-type formulas with cubic radicals of cubic irrationalities in the situation when these radicals are contained in a pure cubic extension. We give a complete description of formulas of such type, answering the Zippel’s question. It turns out that Ramanujan-type formulas are in some sense unique in this situation. In particular, there must be no

Abstract A computational approach to detecting Andronov–Hopf bifurcations in polynomial systems of ordinary differential equations depending on parameters is proposed. It relies on algorithms of computational commutative algebra based on the Groebner bases theory. The approach is applied to the investigation of two models related to the double phosphorylation of mitogen-activated protein kinases, a

Abstract The present communication is devoted to the construction of monotone difference schemes of the second order of local approximation on non-uniform grids in space for 2D quasi-linear parabolic convection-diffusion equation. With the help of difference maximum principle, two-sided estimates of the difference solution are established and an important a priori estimate in a uniform norm C is proved

Abstract In this paper, we consider weak, directional and strong matrix majorizations. Namely, for square matrices A and B of the same size we say that A is weakly majorized by B if there is a row stochastic matrix X such that A = XB. Further, A is strongly majorized by B if there is a doubly stochastic matrix X such that A = XB. Finally, A is directionally majorized by B if Ax is majorized by Bx for

Abstract A two-dimensional periodic system of differential equations with two hyperbolic periodic solutions is considered. It is assumed that heteroclinic solutions lie at the intersection of stable and unstable manifolds of fixed points; more precisely, the existence of a heteroclinic contour is assumed. I study the case in which stable and unstable manifolds intersect nontransversally at the points

Abstract The main fields of application of formal groups are algebraic geometry and class field theory. The later uses both the classical Hilbert symbol (the norm-residue symbol) and its generalization. One of the most important problems is finding explicit formulas for various modifications of this symbol related to formal groups. There are two approaches to constructing formal groups (i.e., power

Abstract In this paper, an automatic control discrete-time system of the second order is studied. The nonlinearity of this system satisfies the generalized Routh–Hurwitz condition. Systems of this type are widely used in solving modern applied problems of the theory of automatic control. This work is a continuation of the results of research presented in the paper “On the Problem of Aizerman: Coefficient

Abstract In this paper, various extensions of local fields are considered. For arbitrary finite extension K of the field of p-adic numbers, the maximum Abelian extension KAb/K and the corresponding Galois group can be described using the well-known Lubin–Tate theory. It is represented as a direct product of groups obtained using the maximum unramified extension of K and a fully ramified extension obtained

Abstract The problem of stability of the zero solution of a system with a “center”-type critical point at the origin of coordinates is considered. For the first time, such a problem for autonomous systems was investigated by A.M. Lyapunov. We continued Lyapunov’s investigations for systems with a periodic dependence on time. In this paper, systems with a quasi-periodic time dependence are considered

Abstract In this paper, we consider the problem of constructing c-optimal designs for polynomial regression without an intercept. The special case of c = f '(z) (i.e., the vector of derivatives of the regression functions at some point z is selected as vector c) is considered. The analytical results available in the literature are briefly reviewed. An effective numerical method for finding f '(z)-optimal

Abstract A matrix whose component are binomial coefficients and determinant was calculated earlier by L. Carlitz is investigated. It is shown that Carlitz matrix is the result of binomal specialization for dual Jacobi–Trudi determinant presentation of certain Schur function. It leads to another way to calculate Carlitz determinant based upon symmetric function theory. The eigenvalues of Carlitz matrix

Abstract Let Zi (i ≥ 1) be a sequence of independent and identically distributed random variables with standard exponential distribution H and let Z(n) (n ≥ 1) be the corresponding sequence of exponential records associated with Zi (i ≥ 1). Let us call the sequence Z(n) (n ≥ 1) the first “record derivative” of the sequence Zi (i ≥ 1). ν1 = Z(1). It is known that ν2 = Z(2) – Z(1), independent variables

Abstract Assume that n independent uniformly distributed random points are set on the unit circle. Construct the convex random polygon with vertices in these points. What are the average area and the average perimeter of this polygon? Brown computed the average area several years ago. We compute the average perimeter and obtain quite similar expressions. We also discuss the rate of the convergence