JournalTOCs

Moscow University Computational Mathematics and Cybernetics
Number of Followers: 0

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1934-8428 - ISSN (Online) 0278-6419
Published by Springer-Verlag

[2469 journals]

An Unusual Criterion for Normality of Nonsingular Matrices
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  Abstract: The following proposition is proved: A nonsingular matrix \(A\) is normal if and only if its cosquare is a unitary matrix. An unusual feature of this criterion is that normality, the most important concept in the theory of similarity transformations, is characterized in terms of transformations of an entirely different type, namely, congruence transformations.
  PubDate: 2022-03-01
Inverse Problem for a Model of the Dynamics of a Population with Symmetric
Cell Division
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  Abstract: An inverse problem is considered for the simultaneous determination of two coefficients in a model of cell population evolution. The model is obtained by moving from the Bell–Anderson problem with the distribution of the individuals that make up the population over time, age, and size to the distribution of the individuals according to time and age. Values of the solution of the direct problem with fixed values of age at the boundary points (at the date of birth and in the age limit) are used as additional information for solving the inverse problem.
  PubDate: 2022-03-01
A Minimax Control Model
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  Abstract: A minimax dynamic control model is investigated. Minimax problems arise in game theory and operation research. In problems of this kind, the minimax can be treated as the least guaranteed result of one controlling subject under arbitrary actions of another controlling subject. In dynamic control problems, another controlling subject is frequently Nature, and its behavior is not predictable in advance. A model of the controlled object is studied in combination with perturbing agents, which can be treated as noise or perturbations. Properties of the corresponding least guaranteed result are considered. Theorems of the existence of a minimax are proved, and conditions are obtained that guarantee the least guaranteed result is a continuous and locally Lipschitzian function of the initial state of the given controlled system.
  PubDate: 2022-03-01
Observers for Dynamic Systems with Uncertainty under the Condition of a
Non-Ideal Relay
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  Abstract: The problem of constructing observers for linear scalar systems with uncertainty is considered. A way of constructing an observer was created earlier that ensured an asymptotically accurate estimate of the state vector for ideal switching elements. The properties of such observers when there are typical imperfections in the relay elements (dead zones, hysteresis, and delays) are analyzed theoretically and numerically.
  PubDate: 2022-03-01
Analyzing the Influence of Spatial Dispersion on the Optical
Characteristics of Cylindrical Bimetallic Nanostructures with the Discrete
Sources Method
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  Abstract: The problem of plane electromagnetic wave diffraction on an infinite plasmon nanocylinder with a core-shell structure is considered. The solution is based on the computational scheme of the discrere sources method. This takes into account the presence of nonlocal effect in both core and shell of the cylinder. Conjugation conditions accounting for plasmonic properties of metals are employed as additional boundary conditions on the metal-metal interface. Numerical investigation of the nonlocal effect influence on the optical properties of cylindrical particles with their deformation is carried out.
  PubDate: 2022-03-01
Multiaffinity Testing of Boolean Functions Using Their Zhegalkin
Polynomials
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  Abstract: A polynomial algorithm is proposed for testing the multiaffinity of Boolean functions determined by Zhegalkin polynomials. The multiaffinity of functions is verified more easily using this algorithm than with other well-known algorithms for solving this problem.
  PubDate: 2022-03-01
Difference Approach to Solving Boundary Value Problems for Elliptic
Partial Differential Equations in the Sense of Generalized Functions
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  Abstract: An approach is described for constructing homogeneous difference schemes using difference analogs of partial derivatives of regular generalized functions. Homogeneous difference operator schemes on an irregular three simplicial grid corresponding to the Dirichlet and Robin boundary value problems for an elliptic differential equation are considered as examples.
  PubDate: 2022-03-01
Spectral Peculiarities of Products of Special Matrices
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  Abstract: Certain known facts concerning spectral peculiarities of products of symmetric, skew-symmetric, and Hermitian matrices are extended to paired products of matrices belonging to some special classes.
  PubDate: 2021-10-01
  DOI: 10.3103/S0278641921040026
A Refinement of the Farkas Lemma
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  Abstract: A refinement is presented of the Farkas lemma on inequality corollaries of a system of linear inequalities where the strict fulfillment of one system inequality implies the same of the inequality corollary. Examples are given of the lemma’s use in financial market and linear production models.
  PubDate: 2021-10-01
  DOI: 10.3103/S0278641921040051
Studying the Accuracy of Forecasting Electric Power Generation by Solar
Panels of the Zarya Service Module on the International Space Station
Using a Mathematical Model
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  Abstract: An investigation is performed of the accuracy of forecasting the generation of electricity by solar panels of the Zarya service module on the International Space Station by comparing actual data obtained in processing telemetric information to data obtained using a mathematical model proposed earlier by the author. Twelve time intervals of 3–7 days from December 2019 to November 2020 are selected for analysis. Specified parameters of the mathematical model and true values of the discrepancy between the actual volumes of electricity generation and modeling results are obtained for each interval. An estimate of the random component of the power of solar panels is obtained, due in particular to the reflection of solar radiation by the Earth’s surface and atmosphere.
  PubDate: 2021-10-01
  DOI: 10.3103/S0278641921040063
User Behavior Authentication Based on Computer Mouse Dynamics
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  Abstract: The aim of this work was to investigate existing algorithms for dynamic user authentication and develop our own, based on an analysis of computer mouse handling characterized by high-quality performance and a supporting dynamic mode. Existing ways of constructing and preliminarily processing the feature space are considered, along with means of dynamic authentication based on the use of classical techniques of machine learning and neural networks. Modifications with better efficiency are proposed for the ones most promising. A cross-platform application for dynamic user authentication based on an analysis of computer mouse handling is designed and implemented using the proposed technique, which shows the best performance (ROC AUC = 0.82). This system and its individual modules can serve as a basis for building advanced information security systems. Experimental studies are conducted that confirm the validity of the obtained results and the correctness of the system’s operation.
  PubDate: 2021-10-01
  DOI: 10.3103/S027864192104004X
The Problem of Target Control for a Quadrotor When Moving in a Horizontal
Plane Avoiding Obstacles
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  Abstract: A solution is sought for the problem of control in a mathematical model of the quadrotor. The main aim is moving an autonomous air vehicle from a given initial position to a target location in a finite time under the condition that the quadrotor must keep a safe distance from obstacles at every intermediate moment in time. The position of obstacles is known beforehand and they are immobile. Allowable values of the control parameters are subject to pointwise constraints. The control must be constructed in a feedback form, based on information about the current state of the object. This allows a control algorithm to be obtained that is resistant to small errors in the current state of the system and external actions. A nonlinear mathematical model of the quadrotor motion in space is presented. Movement in a given horizontal plane is considered in detail. The problem is solved using piecewise linearization and ellipsoidal calculus. An interior estimate is made of the solvability tube containing all positions from which the control problem is solvable. Formulas allowing calculations for feedback control strategy are written. Theoretical results are supplemented by a computational example.
  PubDate: 2021-10-01
  DOI: 10.3103/S0278641921040075
Effective Application of the Fourier Technique for Constructing a Solution
to a Mixed Problem for a Telegraph Equation
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  Abstract: An algorithm is presented for constructing and calculating a rapidly converging series that is a (generalized or classical) solution to a mixed problem for a telegraph equation considered in a half-strip. The case of an essentially non-self-adjoint operator with respect to the spatial variable is considered. The constructed series is a generalized d’Alembert formula. The proposed approach supersedes traditional variable separation for solving mixed problems, which usually results in slowly converging series.
  PubDate: 2021-10-01
  DOI: 10.3103/S0278641921040038
Rate of Convergence of a Risk Estimator to the Normal Law in a Multiple
Hypothesis Testing Problem Using the FDR Threshold
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  Abstract: Problems of the multiple testing of hypotheses on the significance of observations hold an important place in applied statistics and are used in a wide variety of areas such as genetics, biology, astronomy, and computer graphics. These problems arise especially ehen processing multidimensional data in order to identify significant features and remove insignificant (noise) features. Modern studies devoted to this topic classify different means of filtering based on sparse representation of experimental data. A popular approach to constructing statistical estimates of patterns in experimental data includes the multiple testing of hypotheses on the significance of observations. In this work, we consider the Benjamini–Hochberg algorithm for multiple hypothesis testing when selecting the FDR threshold for sparse data. A theorem is proved by estimating the rate of convergence of the risk estimator to the normal distribution.
  PubDate: 2021-07-01
  DOI: 10.3103/S0278641921030043
Infinitely Generated Classes of 01-Functions of Three-Valued Logic
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  Abstract: Infinitely generated closed classes \(\Pi_{1}{-}\Pi_{4}\) of 01-functions of three-valued logic are investigated. The property of maximality is proved for classes \(\Pi_{3}\) and \(\Pi_{4}\) . Each proper extension of classes leads to finitely generated closed classes. It is proved that there is no base in class \(\Pi_{1}\) . All of the simplest two- and three-variable functions obtainable by superposition from an arbitrary function not belonging to class \(\Pi_{1}\) are found.
  PubDate: 2021-07-01
  DOI: 10.3103/S027864192103002X
Determining the Parameters of a Mathematical Model of Spacecraft Solar
Batteries from Telemetry Data
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  Abstract: The problem of approximating measurements of the current intensity generated by the solar batteries of the Zarya Functional Cargo Block of the International Space Station is considered using a mathematical model that contains a set of refinable parameters whose values are found by means of least squares. An algorithm is proposed for finding values of the refinable parameters by processing the telemetry data of the power supply system of the Zarya block. A method for forecasting the total power generation by solar batteries is also proposed. Results are presented from applying the proposed methods and algorithms to analyzing the April 14–20, 2020, flight of the Zarya block and estimating the error of the proposed forecasting techniques. The results of the study can be used in the development and operation of spacecraft.
  PubDate: 2021-07-01
  DOI: 10.3103/S0278641921030055
Testing of Read-Once Functions in Extended Elementary Bases
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  Abstract: is shown that if weakly repetitive functions are added to an elementary base, the Shannon function for the length of each test with respect to a read-once alternative remains linear.
  PubDate: 2021-07-01
  DOI: 10.3103/S0278641921030018
Existence of Hypersingular Integrals with a Power Singularity of Arbitrary
Integer Order
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  Abstract: The existence of a hypersingular integral on an interval with a singularity of arbitrary integer order is considered. It is shown that the equivalence of ways of introducing a hypersingular integral in the sense of a Hadamard finite part and on the basis of a formal introduction in the integrand of the derivative with respect to the parameter of the singular Cauchy integral, understood in the sense of its principal value. Sufficient conditions are formulated for the existence of such integrals.
  PubDate: 2021-07-01
  DOI: 10.3103/S0278641921030067
Ways of Synthesizing Binary Programs Admitting Recursive Call of
Procedures
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  Abstract: A model of binary programs implementing the functions of the algebra of logic (Boolean functions) is considered. The programs consist of one or several modules containing instructions of three types: computational and redirecting instructions and instructions for summoning the procedures. In contrast to earleir models of binary programs, a model is introduced that admits the recursive summoning of procedures; i.e., the procedures can directly summon themselves while executing a binary program, or through other procedures. The functioning of this model of programs is described, as is its relationship to other discrete control systems (e.g., circuits made of functional elements or binary decision diagrams). Ways are presented for obtaining lower and upper estimates of the Shannon function for the complexity of using Boolean functions in the class of binary programs. The proposed technique allows the asymptotics of the Shannon function to be established under certain structural and parametric limitations imposed on the model of binary programs.
  PubDate: 2021-07-01
  DOI: 10.3103/S0278641921030079
Problem of Minimizing the Scatter Range of Trajectories of a Controlled
Object
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  Abstract: A minimax control problem for a quasilinear controlled object is conidered. The dynamics of the controlled object includes two types of controls, one of which models the variable impact of perturbations acting on the controlled object. The second control is used to compensate for disturbing factors and is a constant vector selected from a given compact set. The quality of the pair of controls is determined using a continuous function defined on the phase space. The maximum of this function is taken over the reachability set of the considered controlled object, which characterizes the scatter range of trajectories of the control system at a given time. This maximum depends on a constant control from a given compact set. The resulting marginal function must be minimized over the set of constant controls. The properties of this marginal function are studied, and the existence of its minimum on the set of constant controls is substantiated. In addition, sufficient conditions are found under which the marginal function under study has the Lipschitz property.
  PubDate: 2021-07-01
  DOI: 10.3103/S0278641921030031