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Том 42, № 4 (2018)
- Год: 2018
- Статей: 6
- URL: https://journals.rcsi.science/0278-6419/issue/view/10811
Article
Factorization of a Symbol Corresponding to the Sum of a Finite Number of Singular Integral Operators with Non-Carleman Shifts
Аннотация
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.
145-151
A Solution to Fuller’s Problem Using Constructions of Pontryagin’s Maximum Principle
Аннотация
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.
152-162
A Procedure for Constructing Optimum Functional Filters for Linear Stationary Stochastic Systems
Аннотация
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.
163-170
Calculating the Number of Functions with a Given Endomorphism
Аннотация
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.
171-176
Properties of Open Procedure of Sequential Veto-Voting
Аннотация
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.
177-185
Selecting the Superpositioning of Models for Railway Freight Forecasting
Аннотация
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.
186-193