We consider the problem of approximating functions of one variable within the class of nonlinear approximations with a set of two required parameters. The approximating function is linear in the first parameter; these parameters are assumed to be positive. The individual terms of the approximating function represent a given function that depends nonlinearly on the second parameter. The computational algorithm is based on residual minimization in a Hilbert space. The first key point of the developed approach is related to the actual transition to a standard linear problem of best approximation of functions when the second parameter is given on an extended set of points within the interval of permissible values. The second key point consists in determining the set of linear approximation parameters at each separate iteration of the classical nonnegative least squares (NNLS) method. Numerical results are presented that illustrate the capabilities of this computational algorithm for nonlinear approximation of functions.
Asymptotic behavior of test powers for random-size samples is considered in the problem of testing a simple hypothesis concerning a univariate parameter against a sequence of closely related alternatives. The concept of test power is introduced in this case. Specific tests are asymptotically compared (for normal samples) using the concept of deficiency, which is the additional number of observations required for a competing test to asymptotically achieve the power of the best test. Two examples are considered to illustrate the results obtained. The first example concerns a truncated binomial distribution, and the second example considers a truncated Poisson distribution. These distributions describe random sample sizes.
An initial-boundary value problem for an evolution equation with involution in the spatial variable and a nonlocal boundary condition is studied. The uniqueness of the solution is established, and classes of initial-value functions that ensure its existence and stability are described.
A nonlinear, two-phase mathematical model of production at a mining facility is proposed. In this model, material flows are represented as two phases (ore and the useful substance contained within it), linked through the concentration of the useful substance. The process of material balance calculation is studied, which represents the solution to an optimization problem with nonlinear constraints at nodes with product accumulation. The solution to this problem is proposed to be sought using the interior point method. Known measured values of useful substance concentrations are considered, as well as the results of indirect measurements, ranges of flow values, stockpiles, and unknown concentration values. The results of test calculations for material balance calculations at a small section of a mining facility are presented.
This paper examines three methods for constructing universal functions for a class of literals: by definition, based on a classical construction (the Hamming code), and a modified gradient method. For the constructed universal functions, estimates for the cardinality of their domains are obtained.
A modification of the Lanchester spatially distributed model is considered, which describes a zero-sum game between two military forces in a two-dimensional domain. The model was first developed in 1916 to simulate a combat between two military forces during World War I. The model takes into account directional strikes given by the velocity vector and the initial displacement of troop concentrations using a step function. The system incorporates diffusion terms, nonlinear responses, Gaussian white noise, and a topographic obstacle (an arbitrarily shaped lake) that restricts the troop displacement. The numerical solution is implemented using the finite element method with domain triangulation to allow for irregular domains. The simulation results demonstrate an increase in spatial heterogeneity due to noise and obstacles as well as a significant impact of directional movement and initial displacement on the conflict dynamics. A stability analysis confirms that system is stable, including an analysis for the finite element method. In addition, a sensitivity analysis to parameters is performed and the computational error is estimated. The results are visualized to illustrate the evolution of troop densities over time. The proposed approach has the advantages over existing methods that it better handles irregular domains and the model is scalable.
A certain characterization of the logistic distribution is proposed by the property of identical distribution of two linear forms.
The purpose of equivalence testing is to verify that two parameters are sufficiently close or, alternatively, that the parameter under consideration lies between two predetermined limits. The procedure of two one-sided tests is perhaps the best-known approach to assessing equivalence in the pharmaceutical field. Using a model that accounts for missing data, it is shown analytically that a Type I error can exceed the specified significance level. A refined estimate of this error is also obtained. A way of controlling Type I errors when there are missing data is proposed for a 2× 2 crossover design.
This study presents a modified vector autoregression (VAR) method for forecasting the quality metrics of overlay channels. The modification introduces weighted coefficients for time series quantiles, with two approaches proposed for calculating these weighting coefficients: exponential EVAR) and linear (LVAR). Experimental results have demonstrated that the proposed modification improves prediction accuracy by 2.6 to 25.2 % compared to classical AR and VAR methods, albeit at the expense of higher computational complexity.
The authors describe the implementation of an algorithm for constructing a variable-structure stabilizing controller for a switched interval linear system with slow, unobservable switching. A neural network is proposed as an observer of the closed-loop system’s active modes. Results are presented from modeling the resulting stabilization system.
It was earlier shown that the product xy for k=6l± 1 is a universal function in the class of linear functions of two variables. Subsequently, the existence of universal polynomials was proved in the class of linear functions of any number of variables for arbitrary k . This study proves that the polynomial xy is universal in the class of linear functions over the Galois field GF(p^m) , where p is a prime number and m is a natural number, m⩾ 2 .
This study extends the definitions of the generalized Student distributions to a wider range of distribution parameters and presents multiplication theorems that allow the generalized Student and Lomax distributions to be represented as scaled mixtures of the same distributions but with larger parameters. A similar result has been obtained for beta distributions. Analogs of multiplication theorems for the classical Student and Lomax distributions have been obtained as corollaries. Specifically, it has been shown that the Student distribution can be represented as a scaled mixture of the Student distribution with a larger number of degrees of freedom. Also, a representation of strictly stable distributions concentrated on the positive semiaxis has been obtained as scaled mixtures of a special distribution that is not stable. This alternative representation complements the multiplication theorem for these strictly stable laws.
This work considers a means of stabilized hard thresholding for inverting linear homogeneous operators using wavelet decomposition. The unbiased mean squared risk estimate for this procedure is analyzed using a data model with additive Gaussian noise. Assuming there is a long-range dependence among noise coefficients, conditions are given that ensure strong consistency and asymptotic normality of the unbiased risk estimator.
The problem of finding Hausdorff approximation by finite sets of the solution to and the value of a multicriteria bimatrix game in mixed strategies is considered using a representation based on linear scalarization. For 2× 2 matrices, explicit formulas are found for constructing nodes of a δ -net on the product of simplexes of scalarization parameters. The convergence in the Hausdorff metric of the set uniting the equilibrium values obtained for this net to the solution of the original game as δ→ 0 is proven. The possibility of appearance of degenerate bimatrix games under scalarization is taken into account. Examples are given for two-criteria 2× 2× 2 games.
Automated assessment of the spatial structure (SS) of a group of autonomous agents allows engineers to reduce the costs of developing group control systems and eliminate the human factor in the analysis of group behavior. It is proposed that the repeatability characteristic of SS based on autocorrelation be used to construct a metric for SS regularity of a group of agents. The authors consider different ways calculating autocorrelation based on the matrix of pairwise distances between agents and its application to different types of SS.
The inverse Sturm–Liouville problem is to find the coefficient (potential) in the stationary Schrödinger equation on a segment for the collection of eigenvalues. This paper considers a numerical solution of the inverse problem for a finite set of first eigenvalues of two Sturm–Liouville problems. The remaining eigenvalues are specified by classical asymptotics. The method for solving the inverse spectral problem is based on the one-to-one correspondence between the inverse spectral problem and the nonstationary inverse problem for the telegraph equation with a variable coefficient (potential). The reduction to the nonstationary problem is performed analytically using the inverse Laplace transform given by Mellin formula. An explicit formula is obtained for the reaction function in the inverse scattering problem. The inverse scattering problem for the telegraph equation is to find the unknown coefficient using the reaction function. This problem is solved numerically using the method of inversion of difference schemes. This paper solves a series of inverse Sturm–Liouville problems. In conclusion, it is noted that the number of given eigenvalues corresponds to the number of harmonics in the expansion of the sought potential.
In this paper, it is shown that an arbitrary scale mixture of normal laws can be a stationary distribution of the stochastic random difference equation (first order autoregressive scheme). An example is presented of what the (random) diffusion coefficient should look like in order for a specific mixture to be a stationary distribution.
In accordance with the technical requirements, distributed computing systems functioning is determined by where a network service is placed and on what equipment it runs. Network users are provided with a set of information services with a given level of quality and reliability: (1) access to information ‘‘at any time, in any place,’’ i.e., to any participant in the management process, provided they have access rights when the need arises and regardless of their location; (2) information interaction between automated systems; (3) timely monitoring and analysis of data from various types of sources; (4) transition from a centralized ‘‘data loading with cleaning–analysis–distribution’’ scheme to a ‘‘distributed data placement and preprocessing, and (if necessary) subsequent loading, analysis and distribution’’ scheme. The key condition for providing the above services with required probabilistic and temporal parameters is predicting the periods of executing network services on various equipment and virtualization platforms. This work analyzes ways of predicting the temporal performance of network services. Our approaches are based on data from their operation in the current infrastructure, and also allow for the current and predicted state of hardware and software resources. Among the considered solutions are machine learning models that include random forest,multilayer perceptrons, and convolutional neural networks.
All fifty-five implicatively implicit extensions of one-place function systems of three-valued logic are defined using Boolean algebra. It is established that these extensions are defined by systems of one-place functions containing from one to three functions.
