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Moscow University Computational Mathematics and Cybernetics
Number of Followers: 1 Hybrid journal (It can contain Open Access articles) ISSN (Print) 1934-8428 - ISSN (Online) 0278-6419 Published by Springer-Verlag [2570 journals] |
- Factorization of a Symbol Corresponding to the Sum of a Finite Number of
Singular Integral Operators with Non-Carleman Shifts- Abstract: Abstract An equation containing a finite sum of singular integral operators with non-Carleman shifts is considered. The unique solvability of this equation in the Hölder classes under certain constraints imposed on the coefficients is proved. It is shown that the solution can be written in quadratures.
PubDate: 2018-10-01
- Abstract: Abstract An equation containing a finite sum of singular integral operators with non-Carleman shifts is considered. The unique solvability of this equation in the Hölder classes under certain constraints imposed on the coefficients is proved. It is shown that the solution can be written in quadratures.
- Calculating the Number of Functions with a Given Endomorphism
- Abstract: Abstract An iterative procedure is proposed for calculating the number of k-valued functions of n variables such that each one has an endomorphism different from any constant and permutation. Based on this procedure, formulas are found for the number of three-valued functions of n variables such that each one has nontrivial endomorphisms. For any arbitrary semigroup of endomorphisms, the power is found of the set of all three-valued functions of n variables such that each one has endomorphisms from a specified semigroup.
PubDate: 2018-10-01
- Abstract: Abstract An iterative procedure is proposed for calculating the number of k-valued functions of n variables such that each one has an endomorphism different from any constant and permutation. Based on this procedure, formulas are found for the number of three-valued functions of n variables such that each one has nontrivial endomorphisms. For any arbitrary semigroup of endomorphisms, the power is found of the set of all three-valued functions of n variables such that each one has endomorphisms from a specified semigroup.
- Properties of Open Procedure of Sequential Veto-Voting
- Abstract: Abstract Game-theoretic properties of joint decision making are considered. Procedures based on sequential open voting by veto are investigated. The paper is aimed at the question how to make voters’ behavior intuitively rational when they choose their optimal strategies. The review of the existing results is also presented and the connection between them is established. Further research is discussed as well.
PubDate: 2018-10-01
- Abstract: Abstract Game-theoretic properties of joint decision making are considered. Procedures based on sequential open voting by veto are investigated. The paper is aimed at the question how to make voters’ behavior intuitively rational when they choose their optimal strategies. The review of the existing results is also presented and the connection between them is established. Further research is discussed as well.
- A Procedure for Constructing Optimum Functional Filters for Linear
Stationary Stochastic Systems- Abstract: Abstract Three problems closely related to the classical unbiased optimal filtration problem: an unbiased optimal filtration problem without a control in the system,a biased optimal filtration problem where the bias does not exceed a given value, and the joint problem of stabilization and optimal filtration. It is proposed these problems be reduced to ones of nonlinear optimization. For unbiased filtration with no control, conditions are provided that allow the one for classical unbiasedness to be weakened or excluded for the filter. A new estimate of the bias of the mean filtration error is proposed.
PubDate: 2018-10-01
- Abstract: Abstract Three problems closely related to the classical unbiased optimal filtration problem: an unbiased optimal filtration problem without a control in the system,a biased optimal filtration problem where the bias does not exceed a given value, and the joint problem of stabilization and optimal filtration. It is proposed these problems be reduced to ones of nonlinear optimization. For unbiased filtration with no control, conditions are provided that allow the one for classical unbiasedness to be weakened or excluded for the filter. A new estimate of the bias of the mean filtration error is proposed.
- A Solution to Fuller’s Problem Using Constructions of
Pontryagin’s Maximum Principle- Abstract: Abstract The classical two-dimensional Fuller problem is considered. The boundary value problem of Pontryagin’s maximum principle is considered. Based on the central symmetry of solutions to the boundary value problem, the Pontryagin maximum principle as a necessary condition of optimality, and the hypothesis of the form of the switching line, a solution to the boundary value problem is constructed and its optimality is substantiated. Invariant group analysis is in this case not used. The results are of considerable methodological interest.
PubDate: 2018-10-01
- Abstract: Abstract The classical two-dimensional Fuller problem is considered. The boundary value problem of Pontryagin’s maximum principle is considered. Based on the central symmetry of solutions to the boundary value problem, the Pontryagin maximum principle as a necessary condition of optimality, and the hypothesis of the form of the switching line, a solution to the boundary value problem is constructed and its optimality is substantiated. Invariant group analysis is in this case not used. The results are of considerable methodological interest.
- Selecting the Superpositioning of Models for Railway Freight Forecasting
- Abstract: Abstract The problem of selecting the optimum system of models for forecasting short-term railway traffic volumes is considered. The historical data is the daily volume of railway traffic between pairs of stations for different types of cargo. The given time series are highly volatile, noisy, and nonstationary. A system is proposed that selects the optimum superpositioning of forecasting models with respect to features of the historical data. A model of sliding averages, exponential and kernel-smoothing models, the ARIMA model, Croston’s method, and LSTM neural networks are considered as candidates for inclusion in superpositioning.
PubDate: 2018-10-01
- Abstract: Abstract The problem of selecting the optimum system of models for forecasting short-term railway traffic volumes is considered. The historical data is the daily volume of railway traffic between pairs of stations for different types of cargo. The given time series are highly volatile, noisy, and nonstationary. A system is proposed that selects the optimum superpositioning of forecasting models with respect to features of the historical data. A model of sliding averages, exponential and kernel-smoothing models, the ARIMA model, Croston’s method, and LSTM neural networks are considered as candidates for inclusion in superpositioning.
- Evolution of Replicator Systems: A Mathematical Model
- Abstract: Abstract Variations in elements of a replicator system are considered with the aim of increasing the adaptiveness mean value (mean fitness). To solve this problem, we propose an algorithm such that it is reduced to a linear programming problem at each step. An example of the algorithm’s action is provided.
PubDate: 2018-07-01
- Abstract: Abstract Variations in elements of a replicator system are considered with the aim of increasing the adaptiveness mean value (mean fitness). To solve this problem, we propose an algorithm such that it is reduced to a linear programming problem at each step. An example of the algorithm’s action is provided.
- A Numerical Way of Determining the Boundaries of a System of Bodies in a
Three-Dimensional Medium by Means of Integral Equations- Abstract: Abstract The propagation of acoustic waves in a three-dimensional medium with several local inhomogeneities of different shapes is analyzed. Solving the inverse problem of determining boundaries of local inhomogeneities from measurements of a field in a bounded receivers location domain is reduced to a system of integral equations. An iteration approach to solving the inverse problem is proposed, and the results from numerical experiments are presented.
PubDate: 2018-07-01
- Abstract: Abstract The propagation of acoustic waves in a three-dimensional medium with several local inhomogeneities of different shapes is analyzed. Solving the inverse problem of determining boundaries of local inhomogeneities from measurements of a field in a bounded receivers location domain is reduced to a system of integral equations. An iteration approach to solving the inverse problem is proposed, and the results from numerical experiments are presented.
- Calculating the Isotropic Subspace of a Symmetric Quasi-Definite Matrix
- Abstract: Abstract Solutions to the sesquilinear matrix equation X*DX + AX + X*B + C = 0, where all matrices are of size n × n, are put in correspondence with n-dimensional neutral (or isotropic) subspaces of the associated matrix M of order 2n. A way of constructing such subspaces is proposed for when M is a symmetric quasi-definite matrix of the (n, n) type.
PubDate: 2018-07-01
- Abstract: Abstract Solutions to the sesquilinear matrix equation X*DX + AX + X*B + C = 0, where all matrices are of size n × n, are put in correspondence with n-dimensional neutral (or isotropic) subspaces of the associated matrix M of order 2n. A way of constructing such subspaces is proposed for when M is a symmetric quasi-definite matrix of the (n, n) type.
- Specific Features of Finite Mixtures of Normal Distributions
- Abstract: Abstract Properties of finite mixtures of normal distributions are considered. Their behavioral similarities and differences relative to normal distributions are studied. A practical application of finite mixtures of normal distributions for the simulating the noise of neurophysiological signals is described. It is shown that the Aitken estimate can be used for the source amplitudes in the considered model.
PubDate: 2018-07-01
- Abstract: Abstract Properties of finite mixtures of normal distributions are considered. Their behavioral similarities and differences relative to normal distributions are studied. A practical application of finite mixtures of normal distributions for the simulating the noise of neurophysiological signals is described. It is shown that the Aitken estimate can be used for the source amplitudes in the considered model.
- Modeling a Simultaneous Confidence Band of the Mean Value of Multiple
Responses with a Rectangular Domain for Predictors- Abstract: Abstract The problem is considered of modeling simultaneous confidence intervals for the mean values of multiple responses in a linear multivariate normal regression model with predictor variables defined in intervals. To solve it, a numerical way of calculating the critical value that determines the simultaneous confidence interval of a given level is used. Simultaneous confidence intervals are numerically modelled and analyzed by comparison for regression, the mean value of multiple responses, and individual observation.
PubDate: 2018-07-01
- Abstract: Abstract The problem is considered of modeling simultaneous confidence intervals for the mean values of multiple responses in a linear multivariate normal regression model with predictor variables defined in intervals. To solve it, a numerical way of calculating the critical value that determines the simultaneous confidence interval of a given level is used. Simultaneous confidence intervals are numerically modelled and analyzed by comparison for regression, the mean value of multiple responses, and individual observation.
- Discipline-Priority Queuing Systems without Serving Interruptions
- Abstract: Abstract A one-channel queuing system with r types of requirements, relative priority, and random-intensity Poissonian input flow is studied. The current intensity value is taken at the beginning of the time reckoned for the arrival of the next requirement. Successive values of the flow intensity form a Markov chain of a special kind. A nonstationary distribution of the vector of lengths is found for queues of requirements of different types.
PubDate: 2018-07-01
- Abstract: Abstract A one-channel queuing system with r types of requirements, relative priority, and random-intensity Poissonian input flow is studied. The current intensity value is taken at the beginning of the time reckoned for the arrival of the next requirement. Successive values of the flow intensity form a Markov chain of a special kind. A nonstationary distribution of the vector of lengths is found for queues of requirements of different types.
- On the Complexity and Depth of Embedded in Boolean Cube Circuits That
Implement Boolean Functions- Abstract: Abstract A class of circuits of functional elements over the standard basis of the conjunction, disjunction, and negation elements is considered. For each circuit Σ in this class, its depth D(Σ) and dimension R(Σ) equal to the minimum dimension of the Boolean cube allowing isomorphic embedding Σ are defined. It is established that for n = 1, 2,… and an arbitrary Boolean function f of n variables there exists a circuit Σf for implementing this function such that R(Σf) ⩽ n − log2 log2n + O(1) and D(Σf) ⩽ 2n − 2 log2 log2n + O(1). It is proved that for n = 1, 2,… almost all functions of n variables allow implementation by circuits of the considered type, whose depth and dimension differ from the minimum values of these parameters (for all equivalent circuits) by no more than a constant and asymptotically no more than by a factor of 2, respectively.
PubDate: 2018-07-01
- Abstract: Abstract A class of circuits of functional elements over the standard basis of the conjunction, disjunction, and negation elements is considered. For each circuit Σ in this class, its depth D(Σ) and dimension R(Σ) equal to the minimum dimension of the Boolean cube allowing isomorphic embedding Σ are defined. It is established that for n = 1, 2,… and an arbitrary Boolean function f of n variables there exists a circuit Σf for implementing this function such that R(Σf) ⩽ n − log2 log2n + O(1) and D(Σf) ⩽ 2n − 2 log2 log2n + O(1). It is proved that for n = 1, 2,… almost all functions of n variables allow implementation by circuits of the considered type, whose depth and dimension differ from the minimum values of these parameters (for all equivalent circuits) by no more than a constant and asymptotically no more than by a factor of 2, respectively.
- Equilibrium Integral Equations with Kurtosian Kernels in Spaces of Various
Dimensions- Abstract: Abstract Integral equations emerging in a model of stationary biological communities such that their kernels have variable coefficients of excess (kurtosian kernels)are investigated. The dependence of the first and second spatial moment on the dimension of the environment is considered. A fast-computation algorithm for the multi-dimensional nonlinear convolution is considered. The existence of a radial solution is proved.
PubDate: 2018-07-01
- Abstract: Abstract Integral equations emerging in a model of stationary biological communities such that their kernels have variable coefficients of excess (kurtosian kernels)are investigated. The dependence of the first and second spatial moment on the dimension of the environment is considered. A fast-computation algorithm for the multi-dimensional nonlinear convolution is considered. The existence of a radial solution is proved.
- Numerical Solution of a Semilinear Matrix Equation of the Stein Type in
the Normal Case- Abstract: Abstract It is known that the solution of the semilinear matrix equation X − AX*B = C can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. A technique for solving the original semilinear equation in the normal case is proposed. For equations of the order n = 3000, this allows us to cut the time of computation almost in half, compared toMatlab’s library function dlyap, which solves Stein equations in the Matlab package.
PubDate: 2018-04-01
DOI: 10.3103/S0278641918020036
- Abstract: Abstract It is known that the solution of the semilinear matrix equation X − AX*B = C can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. A technique for solving the original semilinear equation in the normal case is proposed. For equations of the order n = 3000, this allows us to cut the time of computation almost in half, compared toMatlab’s library function dlyap, which solves Stein equations in the Matlab package.
- Limit Theorems for Risk Estimate in Models with Non-Gaussian Noise
- Abstract: Abstract The problem of constructing an estimate of a signal function from noisy observations, assuming that this function is uniformly Lipschitz regular, is considered. The thresholding of empirical wavelet coefficients is used to reduce the noise. As a rule, it is assumed that the noise distribution is Gaussian and the optimal parameters of thresholding are known for various classes of signal functions. In this paper a model of additive noise whose distribution belongs to a fairly wide class, is considered. The mean-square risk estimate of thresholding is analyzed. It is shown that under certain conditions, this estimate is strongly consistent and asymptotically normal.
PubDate: 2018-04-01
DOI: 10.3103/S027864191802005X
- Abstract: Abstract The problem of constructing an estimate of a signal function from noisy observations, assuming that this function is uniformly Lipschitz regular, is considered. The thresholding of empirical wavelet coefficients is used to reduce the noise. As a rule, it is assumed that the noise distribution is Gaussian and the optimal parameters of thresholding are known for various classes of signal functions. In this paper a model of additive noise whose distribution belongs to a fairly wide class, is considered. The mean-square risk estimate of thresholding is analyzed. It is shown that under certain conditions, this estimate is strongly consistent and asymptotically normal.
- Optimal Positioning of Service Stations
- Abstract: Abstract An effective new algorithm is presented for positioning service stations for calls which come from a subset of the line. The coordinate of a call is a random quantity which has a distribution density with compact support. The asymptotic second order optimality of this algorithm is found. A necessary optimality condition of positioning stations for a family of optimality criteria is also found.
PubDate: 2018-04-01
DOI: 10.3103/S0278641918020085
- Abstract: Abstract An effective new algorithm is presented for positioning service stations for calls which come from a subset of the line. The coordinate of a call is a random quantity which has a distribution density with compact support. The asymptotic second order optimality of this algorithm is found. A necessary optimality condition of positioning stations for a family of optimality criteria is also found.
- A Coordinate-Wise Estimate of the Reachability Set of a Controlled System
- Abstract: Abstract The problem of a coordinate-wise estimate of the reachability set for nonlinear controlled systems is considered. Estimates of this kind are useful because they allow us at least in rough form to assess the dynamic possibilities of a controlled system.
PubDate: 2018-04-01
DOI: 10.3103/S0278641918020048
- Abstract: Abstract The problem of a coordinate-wise estimate of the reachability set for nonlinear controlled systems is considered. Estimates of this kind are useful because they allow us at least in rough form to assess the dynamic possibilities of a controlled system.
- A New Algorithm for Generating Tetrahedral Grids
- Abstract: Abstract A new algorithm is presented for generating tetrahedral grids for bound domains of complicated structure and form that consist of the union of several subdomains. The grids obtained using the algorithm have regularity, in that there is no tetrahedron whose vertices lie at different sides of the subdomain boundaries. The algorithm has high fast-action: the time needed to generate a grid consisting of 105−106 tetrahedrons is approximately 20–40 seconds of the work of a standard personal computer. All steps of the algorithm are described in detail, and examples of generated grids are given.
PubDate: 2018-04-01
DOI: 10.3103/S0278641918020097
- Abstract: Abstract A new algorithm is presented for generating tetrahedral grids for bound domains of complicated structure and form that consist of the union of several subdomains. The grids obtained using the algorithm have regularity, in that there is no tetrahedron whose vertices lie at different sides of the subdomain boundaries. The algorithm has high fast-action: the time needed to generate a grid consisting of 105−106 tetrahedrons is approximately 20–40 seconds of the work of a standard personal computer. All steps of the algorithm are described in detail, and examples of generated grids are given.
- Algorithm for Constructing a Guaranteeing Program Package in a Control
Problem with Incomplete Information- Abstract: Abstract A package control problem is considered for a target set at a moment of time. The dynamic system under control is described by linear differential equations, the control area is a convex compact, and the target set is convex and closed. A version of the subsequent approximations method in extended space is proposed for constructing elements of a guaranteeing program package in the case of regular clusters.
PubDate: 2018-04-01
DOI: 10.3103/S0278641918020061
- Abstract: Abstract A package control problem is considered for a target set at a moment of time. The dynamic system under control is described by linear differential equations, the control area is a convex compact, and the target set is convex and closed. A version of the subsequent approximations method in extended space is proposed for constructing elements of a guaranteeing program package in the case of regular clusters.