Authors:Yu. G. Evtushenko; A. A. Tret’yakov Pages: 427 - 429 Abstract: A new proof of the Kuhn–Tucker theorem on necessary conditions for a minimum of a differentiable function of several variables in the case of inequality constraints is given. The proof relies on a simple inequality (common in textbooks) for the projection of a vector onto a convex set. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050039 Issue No:Vol. 96, No. 2 (2017)

Authors:A. V. Arutyunov; A. V. Greshnov Pages: 438 - 441 Abstract: The properties of (q 1, q 2)-quasimetric spaces are examined. Multivalued covering mappings between (q 1, q 2)-quasimetric spaces are investigated. Given two multivalued mappings between (q 1, q 2)-quasimetric spaces such that one of them is covering and the other satisfies the Lipschitz condition, sufficient conditions for these mappings to have a coincidence point are obtained. A theorem on the stability of coincidence points with respect to small perturbations in the considered mappings is proved. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050064 Issue No:Vol. 96, No. 2 (2017)

Authors:S. V. Astashkin; P. A. Terekhin Pages: 442 - 444 Abstract: Boundedness conditions for operators generated by Haar multishifts in symmetric spaces with nontrivial Boyd indices are obtained. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050076 Issue No:Vol. 96, No. 2 (2017)

Authors:N. Yu. Lukoyanov; A. R. Plaksin Pages: 445 - 448 Abstract: A functional Hamilton–Jacobi equation with covariant derivatives which corresponds to neutral-type dynamical systems is obtained. The definition of a minimax solution of this equation is given. Conditions under which such a solution exists and is unique and well defined are found. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050106 Issue No:Vol. 96, No. 2 (2017)

Authors:V. I. Bogachev; E. D. Kosov; S. N. Popova Pages: 449 - 453 Abstract: In this note we give a characterization of Nikolskii–Besov classes of functions of fractional smoothness (see [1–3]) by means of a nonlinear integration by parts formula in the form of a certain nonlinear inequality. This characterization is motivated by the recent papers [4–6] on distributions of polynomials in Gaussian random variables, where it has been shown that the distribution densities of nonconstant polynomials in Gaussian random variables belong to Nikolskii–Besov classes. Our main result is a generalization of the classical description of the class BV of functions of bounded variation in terms of integration by parts. PubDate: 2017-09-01 DOI: 10.1134/s106456241705012x Issue No:Vol. 96, No. 2 (2017)

Authors:G. A. Mikhailov; S. M. Prigarin; S. A. Rozhenko Pages: 461 - 464 Abstract: There are two versions of weighted vector algorithms for the statistical modeling of polarized radiative transfer: a “standard” one, which is convenient for parametric analysis of results, and an “adaptive” one, which ensures finite variances of estimates. The application of the adaptive algorithm is complicated by the necessity of modeling the previously unknown transition density. An optimal version of the elimination algorithm used in this case is presented in this paper. A new combined algorithm with a finite variance and an algorithm with a mixed transition density are constructed. The comparative efficiency of the latter is numerically studied as applied to radiative transfer with a molecular scattering matrix. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050143 Issue No:Vol. 96, No. 2 (2017)

Authors:V. V. Napalkov; A. U. Mullabaeva Pages: 465 - 467 Abstract: It is known that any function in a Hilbert Bargmann–Fock space can be represented as the sum of a solution of a given homogeneous differential equation with constant coefficients and a function being a multiple of the characteristic function of this equation with conjugate coefficients. In the paper, a decomposition of the space of entire functions of one complex variable with the topology of uniform convergence on compact sets for the convolution operator is presented. As a corollary, a solution of the de la Vallée Poussin interpolation problem for the convolution operator with interpolation points at the zeros of the characteristic function with conjugate coefficient is obtained. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050155 Issue No:Vol. 96, No. 2 (2017)

Authors:V. N. Chugunov; Kh. D. Ikramov Pages: 468 - 471 Abstract: Conditions for commuting a Toeplitz matrix and a Hankel matrix were obtained relatively recently (in 2015). The solution to the problem of describing all anti-commuting pairs (T, H), where T is a Toeplitz matrix and H is a Hankel matrix, is sketched below. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050131 Issue No:Vol. 96, No. 2 (2017)

Authors:A. O. Belyakov; A. A. Davydov; V. M. Veliov Pages: 472 - 474 Abstract: The paper obtains existence of a solution and necessary optimality conditions for a problem of optimal (long run averaged) periodic extraction of a renewable resource distributed along a circle. The resource grows according to the logistic law, and is harvested by a single harvester periodically moving around the circle. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050180 Issue No:Vol. 96, No. 2 (2017)

Authors:A. I. Prilepko Pages: 477 - 479 Abstract: Control and observation problems for operator equations of the first kind in reflexive strictly convex Banach spaces are considered. A BUME (Banach uniqueness and existence) method and a method of monotone nonlinear mappings for finding optimal (i.e., norm-minimal) controls are proposed, and an abstract maximum principle is stated. Under the additional assumption of separability and smoothness on (B)-spaces, an optimal control is found by the Galerkin method. As applications, ODE systems and partial differential equations are considered. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050210 Issue No:Vol. 96, No. 2 (2017)

Authors:A. V. Chikitkin; B. V. Rogov Pages: 480 - 485 Abstract: For the numerical solution of nonstationary quasilinear hyperbolic equations, a family of symmetric semidiscrete bicompact schemes based on collocation polynomials is constructed in the one- and multidimensional cases. A dispersion analysis of a semidiscrete bicompact scheme of six-order accuracy in space is performed. It is proved that the dispersion properties of the scheme are preserved on highly nonuniform spatial grids. It is shown that the phase error of the sixth-order bicompact scheme does not exceed 0.2% in the entire range of dimensionless wave numbers. A numerical example is presented that demonstrates the ability of the bicompact scheme to adequately simulate wave propagation on coarse grids at long times. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050192 Issue No:Vol. 96, No. 2 (2017)

Authors:I. V. Savitskii Pages: 486 - 487 Abstract: Register machines with counters (RC machines) are studied. It is shown that any computable function can be strictly computed on RC machines with a bounded number of counters and programs. The place in the Kleene–Mostowski hierarchy of certain algorithmic problems related to RC machines is determined. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050222 Issue No:Vol. 96, No. 2 (2017)

Authors:Yu. I. Zhuravlev; V. V. Ryazanov Pages: 488 - 490 Abstract: A learning-based classification problem with a large number of classes is considered. The error-correcting-output-codes (ЕСОС) scheme is optimized. An initial binary matrix is formed at random so that the number of its rows is equal to the number of classes and each column corresponds to the union of several classes in two macroclasses. In the ЕСОС approach, a binary classification problem is solved for every object to be recognized and for every union. The object is assigned to the class with the nearest code row. A generalization of the ЕСОС approach is presented in which a discrete optimization problem is solved to find optimal unions, probabilities of correct classification are used in dichotomy problems, and the degree of dichotomy informativeness is taken into account. If the solution algorithms for the dichotomy problems are correct, the recognition algorithm for the original problem is correct as well. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050271 Issue No:Vol. 96, No. 2 (2017)

Authors:A. G. Chechkina Pages: 510 - 513 Abstract: A Steklov-type problem with rapidly alternating Dirichlet and Steklov boundary conditions in a bounded n-dimensional domain in considered. The regions on which the Steklov condition is given have diameter of order ε, and the distance between them is larger than or equal to 2ε. It is proved that, as the small parameter tends to zero, the eigenvalues of this problem degenerate, i.e., tend to infinity. It is also proved that the rate of increase to infinity is larger than or equal to ln ε δ, δ ∈ (0;2 − 2/n) as ε, tends to zero. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050301 Issue No:Vol. 96, No. 2 (2017)

Authors:V. I. Golubev; O. Ya. Voinov; Yu. I. Zhuravlev Pages: 514 - 516 Abstract: Seismic waves propagating in a fractured geological medium are numerically simulated. Their dynamic behavior is described using a linear elastic model with an explicit description of all crack boundaries (a contact discontinuity problem is solved). An algorithm for seismic imaging of the fractured medium is proposed. A distinctive feature of this approach is the use of an initially fractured background model. The forward and adjoint wave fields are numerically computed by applying the grid-characteristic method on hexahedral meshes. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050088 Issue No:Vol. 96, No. 2 (2017)

Authors:S. A. Stepanenko Pages: 522 - 527 Abstract: A structure and implementation principles of a photon computer are proposed. Its functioning is based on effects of the interaction between coherent light wave systems generated by a laser source. The performance of photon computers, consumed energy, and physical sizes are estimated. These estimates show possible advantages of photon computers over electronic ones. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050234 Issue No:Vol. 96, No. 2 (2017)

Authors:E. I. Druzhinin Pages: 528 - 530 Abstract: A new method for calculating space vehicle (SV) attitude controls ensuring their effective implementation by a system of collinear pairs of single-gimbal forced unrestrained gyros (gyrodynes) has been proposed. The novelty of the method consists in a virtual kinematic configuration of the gyro system, i.e., the precession of gyro units in the collinear pairs of gyrodynes is coupled in a nonmechanical manner. In addition, the angular momentum of the system as a state variable for describing the dynamics of the SV permanent rotation was used for the first time at the stage of computing controls performed nonstop by gyrodynes. In the general formulation, when the desired final state of the SV is arbitrary, the SV attitude control problem can be reduced to a sequence of permanent rotations. The performance of the method is demonstrated as applied to the calculation of program gyrodyne controls with a permanent reduction in the SV angular velocity around its center of mass with a nonzero SV angular momentum after its discharge. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050027 Issue No:Vol. 96, No. 2 (2017)

Authors:S. S. Postnov Pages: 531 - 534 Abstract: Two optimal control problems are studied for linear stationary systems of fractional order with lumped variables whose dynamics is described by equations with Hadamard derivative, a minimum-norm control problem and a time-optimal problem with a constraint on the norm of the control. The setting of the problem with nonlocal initial conditions is considered. Admissible controls are sought in the class of functions p-integrable on an interval for some p. The main approach to the study is based on the moment method. The well-posedness and solvability of the moment problem are substantiated. For several special cases, the optimal control problems under consideration are solved analytically. An analogy between the obtained results and known results for systems of integer and fractional order described by equations with Caputo and Riemann–Liouville derivatives is specified. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050118 Issue No:Vol. 96, No. 2 (2017)

Authors:M. M. Khrustalev Pages: 535 - 537 Abstract: Sufficient conditions for an endpoint cost criterion in a controllable stochastic diffusion system to be constant with probability 1 (i.e., for weak invariance condition) and sufficient conditions for absolute invariance, i.e., the independence of an endpoint cost criterion on the realization of the random process and the initial data, are obtained. PubDate: 2017-09-01 DOI: 10.1134/s106456241705009x Issue No:Vol. 96, No. 2 (2017)

Authors:V. I. Berdyshev Pages: 538 - 540 Abstract: Suppose that an object t moves within a given corridor Y in the presence of a groups S of hostile observers S ∉ Y, each having a fixed visibility cone K(S). The problem is solved of searching for object’s trajectory most distant from S assuming that the covering of Y by the cones K(S) has a multiplicity of at most two. PubDate: 2017-09-01 DOI: 10.1134/s1064562417050246 Issue No:Vol. 96, No. 2 (2017)