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Том 42, № 3 (2018)
- Год: 2018
- Статей: 8
- URL: https://journals.rcsi.science/0278-6419/issue/view/10809
Article
Calculating the Isotropic Subspace of a Symmetric Quasi-Definite Matrix
Аннотация
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.
97-99
A Numerical Way of Determining the Boundaries of a System of Bodies in a Three-Dimensional Medium by Means of Integral Equations
Аннотация
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.
100-104
Equilibrium Integral Equations with Kurtosian Kernels in Spaces of Various Dimensions
Аннотация
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.
105-113
Modeling a Simultaneous Confidence Band of the Mean Value of Multiple Responses with a Rectangular Domain for Predictors
Аннотация
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.
114-118
Discipline-Priority Queuing Systems without Serving Interruptions
Аннотация
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.
119-125
Specific Features of Finite Mixtures of Normal Distributions
Аннотация
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.
126-132
Evolution of Replicator Systems: A Mathematical Model
Аннотация
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.
133-137
On the Complexity and Depth of Embedded in Boolean Cube Circuits That Implement Boolean Functions
Аннотация
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.
138-144