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Universal Polynomials of Several Variables for Classes of Linear Functions Moscow Univ. Comput. Math. Cybern. Pub Date : 2024-02-04 A. A. Voronenko
Abstract It was shown earlier that product \(xy\) for \(k=6l\pm 1\) is a universalfunction in the class of linear functions of two variables, and there exist no universal polynomials for even \(k\) in classes of linear functions of two variables. This work proves that polynomial \(xy+xz+yz\) is universal for classes of linear functions of three variables for arbitrary odd \(k\) and polynomial \(xy+zw\)
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A Hadamard Product of Linear Codes: Algebraic Properties and Algorithms for Calculating It Moscow Univ. Comput. Math. Cybern. Pub Date : 2024-02-04 I. V. Chizhov
Abstract A study is performed of the algebraic properties of the Hadamard product (Schur product, component-wise product) of linear error-correcting codes. The complexity of constructing a product basis using known multiplier bases is discussed. The concept is introduced of quotient, quasi-quotient, and maximal inclusion quasi-quotient obtained from the Hadamard division of one linear code by another
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Intelligent Technologies for the Segmentation and Classification of Microbiological Photographic Images Moscow Univ. Comput. Math. Cybern. Pub Date : 2024-02-04 O. E. Gorokhov, M. A. Kazachuk, I. S. Lazukhin, I. V. Mashechkin, L. L. Pankrat’eva, I. S. Popov
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Verifying Hypotheses of Drug Bioequivalence Moscow Univ. Comput. Math. Cybern. Pub Date : 2024-02-04 M. A. Dranitsyna, T. V. Zakharova, P. V. Panov
Abstract The problem of testing pharmaceuticals on their bioequivalence is considered. Investigations of drug bioequivalence are the basis for reproducing drugs that confirm their efficiency and safety. The main way of verifying drug bioequivalence is to conduct two one-sided Schuirmann tests. Two one-sided tests have been used for many years and proven their validity for proving equivalent bioavailability
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Transitioning between Different Representations of Interval Controlled Systems Moscow Univ. Comput. Math. Cybern. Pub Date : 2024-02-04 E. I. Atamas’
Abstract A description is given of algorithms for converting linear controlled systems with interval parameters from a state-space representation to a representation in the form of transfer functions and vice versa. Results are accompanied by computational examples demonstrating the capabilities and limitations of the proposed approach.
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A Lower Bound for Bilinear Complexity of Matrix Multiplication over a Finite Field Moscow Univ. Comput. Math. Cybern. Pub Date : 2024-02-04 A. A. Nazarov
Abstract An improved lower bound is found for the bilinear complexity of the multiplication of arbitrary matrices over finite fields.
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Queue Length in a System with an Autoregressive Hyperexponential Incoming Flow at a Critical Load Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-12-01
Abstract A study is performed of a single-channel queuing system with two classes of priority requests, a relative priority discipline, a Poisson incoming flow with random intensity, and an infinite number of waiting places. The intensity is selected at the moment the countdown begins until the next request arrives, and the intensity does not change with a predetermined probability. The limit distribution
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A Modified Brachistochrone Problem with State Constraints and Thrust Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-12-01
Abstract The problem of maximizing the horizontal coordinate of a mass point moving in a vertical plane driven by gravity, viscous drag, curve reaction force, and thrust is considered. It is assumed that inequality-type constraints are imposed on the angle of inclination of the trajectory. The system of equations belongs to a certain type that allows us to reduce the optimal control problem with constraints
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Swarm Simulation Modeling Using the Hadamard Product Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-10-20 R. A. Girgidov
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On Rational Algorithms for Recognition of Belonging to Congruence Classes Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-10-20 Kh. D. Ikramov
Abstract The theory of similarity transformations, which is the main part of square matrix theory, deals with numerous classes of special matrices. Accordingly, there are many ways to describe such classes. In most cases, the fact that a matrix belongs to a required class can be checked by a rational calculation, that is, by a finite algorithm that uses arithmetic operations only. Congruence transformations
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Solving the Inverse Magnetoencephalography Problem in the Multidipole Model Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-10-20 T. V. Zakharova, A. I. Sabirov
Abstract The author considers ways of localizing the inverse problem of magnetoencephalography (MEG). Localization is important in real clinical practice. Different parts of the brain (including ones that are irreparable) can be damaged during neurosurgical interventions. Since the location of functional areas in the human brain depends on the individual, the doctor must be able to localize these areas
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Applying the Separation of Probability Distribution Mixtures to Problems of Financial Analysis Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-10-20 A. O. Lagno, I. S. Kuz’min
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Identifying a Workplace from a Monitor Snapshot Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-10-20 V. O. Piskovskii, D. A. Seminikhin, A. A. Grusho, M. I. Zabezhailo
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Near-Polynomial Recursive Sequences with Algorithmically Unsolvable Problems Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-10-20 S. S. Marchenkov
Abstract The author considers recursive sequences over a set of integers with generating functions that are arbitrary superpositions of polynomial functions and functions that are close to polynomial, i.e., near-polynomial recursive sequences. A series of functions in the form \(b\cdot j_{i}(x)\) is distinguished. Along with polynomial functions, each of these functions allows us to define near-polynomial
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The Implicit Function Theorem in the Neighborhood of an Abnormal Point Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-10-20 A. V. Arutyunov, K. I. Salikhova
Abstract The authors study the existence of the implicit function defined by equation \(G(x,\sigma)=0\) in the neighborhood of abnormal point \((x_{0},\sigma_{0})\). It is proved that if some \(\lambda\)-truncation of mapping \(F(x)=G(x,\sigma_{0})\) is regular in a certain direction, the sought implicit function exists.
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Continuity of the Optimum Period of Performance as a Function of the Initial State of a Linear Controlled Object Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-11 M. S. Nikol’skii
Abstract A study is performed of the continuity of the optimum period of performance as a function of the initial state for a linear controlled object. The author generalizes parts of Theorem 21 and the proposition of Theorem 22 from Foundations of Optimal Control Theory by E. B. Lee and L. Markus on the continuity of the optimum period of performance as a function of the initial state of a controlled
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The Approximate Bilinear Complexity of the Multiplication of Matrices of Sizes $$2\times n$$ and $$n\times 4$$ Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-11 A. A. Nazarov, A. V. Smirnov
Abstract Approximate bilinear algorithms are constructed for problems of multiplying matrices of sizes \(2\times 3\) and \(3\times 4\) (complexity 18), \(2\times 4\) and \(4\times 4\) (complexity 24), and \(2\times 5\) and \(5\times 4\) (complexity 30), and are used to obtain approximate bilinear algorithms for the problem of multiplying \(2\times n\) and \(n\times 4\) matrices of complexity \(6n\)
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Elliptic Differential Operators with Noninteger Order Degeneration Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-11 D. P. Emel’yanov
Abstract A study is performed of the Dirichlet boundary value problem for an elliptic-type equation with irregular degeneracy in a rectangle with noninteger order of degeneracy and analytic coefficients. Spectral selection of singularities is used to construct a formal solution of the problem as a series where the character of the nonanalytical dependence of the solution on the variable \(y\) in the
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Constructing a Controllability Set for One Second-Order System with a Phase Constraint Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-11 M. N. Goncharova, S. P. Samsonov
Abstract The authors investigate the problem of performance with a phase constraint. The object’s behavior is described by a system of second-order differential equations. The coefficient matrix for phase variables has zero eigenvalues. The phase constraint is linear. An admissible control is a piecewise continuous function that takes values from a given compact set. Controllability sets to the origin
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The Existence of Universal Polynomials for the Class of Linear Functions in Even-Valued Logics Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-11 A. A. Voronenko
Abstract It was shown earlier that product \(xy\) is a universal function for the class of linear functions of two variables for \(k=6l\pm 1\). In this work, it is shown that there are no universal polynomials for classes of linear functions of two variables for even \(k\).
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Periodic Solutions to the Navier–Stokes Equation for a Viscous Incompressible Fluid and Gas in Space $${\mathbb{R}}^{n}$$ Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-08 A. V. Baev
Abstract Initial value problems are considered for equations of motion of a viscous incompressible fluid and gas in Lagrangian variables. It is shown that the incompressible fluid motion is not related to pressure. In the absence of external forces, the pressure is constant and allows the fluid to make free motion. This motion is purely turbulent and is described by quasi-linear equations of parabolic
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Numerical Implementation of an Algorithm for Searching for a Superstabilizer for Switched Interval Systems Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-08 Yu. M. Mosolova
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Estimation of Digamma Distribution Parameters for Random Sample Size Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-08 A. A. Kudryavtsev, O. V. Shestakov
Abstract In this paper asymptotic theorems are proved for estimates of the characteristic index, the scale parameter, and the shape and scale parameters for the remaining fixed parameters of the digamma distribution with a random sample size. Particular cases of limit distributions are given in the case when the sample size has a mixed Poisson distribution.
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On Normal and Binormal Matrices Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-08 Kh. D. Ikramov
Abstract The problem discussed is how to obtain a normal matrix from a binormal one and, conversely, a binormal matrix from a normal one via the right multiplication on a suitable unitary matrix. Let \(N\) be a normal matrix badly conditioned with respect to inversion, that is, having a large condition number \(\textrm{cond}_{2}N\). We show that, among the binormal matrices \(B\) that can be obtained
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A Priority System with Working Vacations of a Server Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-08 A. K. Bergovin
Abstract A one-channel queuing system is studied for the recurrent input flow, relative priority, and working vacations of a server. The distribution functions of intervals between the arrivals of requests, service times for requests of each priority and durations of server working vacations are characterized by arbitrary absolutely continuous distributions. A joint distribution of the number of requests
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Genetic Algorithm for Guide Tree Optimization Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-08 M. V. Shegay, N. N. Popova
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Optimizing Storage Parameters for Consumers in the Electricity Market Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-09-08 A. A. Vasin, O. M. Grigoryeva, I. Yu. Seregina
Abstract Problems of optimizing consumption and storage are formulated and analyzed for a small consumer whose actions do not affect the market prices of electricity. Possibilities associated with new technological and economic instruments (renewable energy sources and storage devices) are considered in the proposed models.
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Depth of a Conditional Full Diagnostic Test for Contact Circuits Implementing a Parity Counter Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-02-07 A. A. Voronenko
Abstract The author considers the classical problem of testing contact circuits implementing a parity counter of \(n\) variables. The lower bound of the test depth is raised from \(2^{n-1}\) to \(2^{n-1}+n\) for conditional full diagnostic tests.
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On the Coincidence of Complexity Classes BPC and TC $${}^{0}$$ Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-02-07 I. V. Savitskii
Abstract It is shown that the class of dictionary functions defined on the basis of bounded prefix concatenation coincides with the familiar complexity class \(\textrm{TC}^{0}\).
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Inverse Problem for a Mathematical Model of Sorption Dynamics with a Variable Kinetic Coefficient Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-02-07 A. V. Denisov, Dongqin Zhu
Abstract The authors consider an inverse problem for a nonlinear mathematical model of sorption dynamics with an unknown variable kinetic coefficient. The theorem of existence of a solution to the inverse problem is proved, and an iteration procedure for solving it is substantiated. Examples are presented of using the proposed procedure to numerically solve the inverse problem.
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Improving Constants in Esseen–Rozovskii Type Inequalities for Identically Distributed Random terms Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-02-07 A. V. Maksimova, I. G. Shevtsova
Abstract Constants in Esseen–Rozovskii type inequalities proposed by Gabdullin, Makarenko, and Shevtsova (2018) are improved for one of the most important special cases: independent identically distributed random summands. The considered inequalities are used to estimate the uniform distance between the distribution function of the standardized sum of independent identically distributed random summands
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General Algorithm for Analytical Calculations of Jacobi Matrix Elements in Sparse Nonlinear Programming Problems Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-02-07 D. V. Zlobin
Abstract The author deals with sparse non-linear programming problems of high dimension. When solving such problems numerically by gradient means, we must calculate the Jacobi constraint matrix, which contains a significant number of elements that are identically equal to zero. Reducing the number of calculations by eliminating operations for calculating obviously zero elements results in a considerable
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Operation of Bound Prefix Concatenation and Finite Superposition Bases Moscow Univ. Comput. Math. Cybern. Pub Date : 2023-02-07 S. S. Marchenkov
Abstract The BPC class of dictionary functions is defined on the basis of operations of superposition and bound prefix concatenation. A finite superposition basis is constructed in the BPC class.
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A New Way of Constructing a Generalized Solution to a Mixed Problem for a Telegraph Equation Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-10-30 I. S. Lomov
Abstract A new way of constructing a rapidly converging series is presented. The series is a generalized 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. To construct the solution, we apply the axiomatic model of A.P. Khromov based on the active participation of divergent
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Digamma Distribution as a Limit for the Integral Balance Index Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-10-30 A. A. Kudryavtsev, O. V. Shestakov
Abstract The paper considers the Bayesian balance model, within which the weak convergence of the normalized integral balance index to the digamma distribution is proved. As an auxiliary result, a generalization of Renyi’s theorem for structural distributions with a scale parameter is proved.
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Mathematical Model of Building a Neural Network for Diagnosing Circulatory Disorders Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-10-30 A. Ya. Bunicheva, E. V. Kochetov, S. I. Mukhin
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Numerical Modeling of Ocean Dynamics Using the NEMO Model with Data Assimilation Using a Generalized Kalman Filter Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-10-30 K. P. Belyaev, A. A. Kuleshov, I. N. Smirnov
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Rate of Convergence of the Risk Estimate Distribution to the Normal Law Using FDR Multiple Hypothesis Testing with Inverting Linear Homogeneous Operators Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-10-30 S. I. Palionnaya
Abstract To solve problems of economical representation of large data arrays, multiple hypothesis testing is widely used to identify major features and remove noise. The problem of multiple hypothesis testing is solved by means of FDR, controlled by the Benjamini–Hochberg multiple hypothesis testing algorithm. The observed data are often a modification of the original signal. A case where the original
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Modifying the Shooting Model for Solving Equilibrium Problems Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-10-30 Han Dongyu, B. A. Budak
Abstract Equilibrium programming is a broad area of mathematics that studies mathematical models of numerous phenomena in natural sciences and economics. A typical situation is when exact values of functional \(\Phi(v,w)\) are not available when finding the numerical solution to the equilibrium programming problem and only their approximations \(\Phi^{\delta}(v,w)\) are known. It is known that numerical
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Implicit Expressibility in Multiple-Valued Logic Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-10-30 S. S. Marchenkov
Abstract Generalizations of A.V. Kuznetsov’s implicit expressibility are considered for when additional logical connectives are introduced into the language of implicit expressibility. It is established that only three new implicit expressibility form as a result. Implicit extensions generated by all four implicit expressibilities are investigated, and it is shown they all differ on sets \(P_{2}\)
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Stabilizing Riesz Means in Time for the Solution of the Cauchy Problem for the Iterated Heat Equation Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-07-18 P. V. Denisov
Abstract A sufficient condition is obtained for the stabilization of Riesz-type means of order \(\beta\geqslant p-1\) in time for solution \(u(x,t)\) of the Cauchy problem for the iterated heat equation.
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Order Statistics Close to a Minimum Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-07-18 V. I. Pagurova
Abstract A study is performed of the asymptotic distribution of order statistics \(X_{k}^{(n)}\) when size \(n\) of a sample and rank \(k\) grow indefinitely, but \(k/n\to 0\). A similar problem in terms of quantile functions was studied by Teugels for the order statistic \(X_{n-k+1}^{(n)}\) of rank \(n-k+1\).
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Diagonalizable Matrices as a Result of Rank-One Perturbations of Nilpotent Matrices Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-07-18 Kh. D. Ikramov, V. N. Chugunov
Abstract It is known that every normal matrix with a simple spectrum can be obtained by a rank-one perturbation of some nilpotent matrix \(N\). In this assertion, a normal matrix can actually be replaced by an arbitrary diagonalizable matrix. We determine the possible values of the index of nilpotency of the matrix \(N\).
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Main Probabilistic Characteristics of the Digamma Distribution and the Method of Estimating Its Parameters Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-07-18 A. A. Kudryavtsev, Yu. N. Nedolivko, O. V. Shestakov
Abstract The paper considers a new digamma distribution generalizing the distributions from the gamma and beta classes. The presentation of the digamma distribution as a fractional-scale mixture of gamma distributions is proved. Explicit forms of the moments and density of the considered distribution are given. A method for statistical estimation of unknown parameters based on logarithmic cumulants
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Measuring the Preservation and Ergodicity of 1-Lipschitz Functions on the Ring of 3-Adic Integers in Terms of Coordinate Functions Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-07-18 A. Lopez Perez
Abstract Necessary and sufficient conditions are given under which \(1\)-Lipschitz function \(f(x)\) preserves the Haar measure on the ring of \(3\)-adic integers \({\mathbb{Z}}_{3}\); moreover, necessary and sufficient conditions are given under which \(f(x)\) is ergodic on \({\mathbb{Z}}_{3}\).
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Robustness of Normality Criteria with Respect to Rounding Observations Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-07-18 V. G. Ushakov, N. G. Ushakov
Abstract In some areas of statistical analysis (e.g., biology, medicine),data is often available in a roughly rounded form and relatively large samples. Statistical procedures vary in their sensitivities of data rounding. Different criteria of normality control the probability of Type I errors in rounding data. It is found that criteria based on a sample’s moments are robust when it comes to rounding
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Machine Learning and Optimization Algorithms in Applied Problems of Wireless Cellular Communications Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-07-18 E. A. Bobrov
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Analyzing the Influence of Spatial Dispersion on the Optical Characteristics of Cylindrical Bimetallic Nanostructures with the Discrete Sources Method Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-05-06 A. S. Penzar, Yu. A. Eremin
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Observers for Dynamic Systems with Uncertainty under the Condition of a Non-Ideal Relay Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-05-06 A. O. Vysotskii
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A Minimax Control Model Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-05-06 M. S. Nikol’skii
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
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Inverse Problem for a Model of the Dynamics of a Population with Symmetric Cell Division Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-05-06 A. Yu. Shcheglov
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
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An Unusual Criterion for Normality of Nonsingular Matrices Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-05-06 Kh. D. Ikramov
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.
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Multiaffinity Testing of Boolean Functions Using Their Zhegalkin Polynomials Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-05-06 S. N. Selezneva
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.
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Difference Approach to Solving Boundary Value Problems for Elliptic Partial Differential Equations in the Sense of Generalized Functions Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-05-06 M. N. Sablin
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.
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The Problem of Target Control for a Quadrotor When Moving in a Horizontal Plane Avoiding Obstacles Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-01-04 Kaplunova, E. P., Tochilin, P. A.
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
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Spectral Peculiarities of Products of Special Matrices Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-01-04 Kh. D. Ikramov
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.
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A Refinement of the Farkas Lemma Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-01-04 V. V. Morozov
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.
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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 Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-01-04 Vas. V. Sazonov
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
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User Behavior Authentication Based on Computer Mouse Dynamics Moscow Univ. Comput. Math. Cybern. Pub Date : 2022-01-04 A. V. Berezniker, M. A. Kazachuk, I. V. Mashechkin, M. I. Petrovskiy, I. S. Popov
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