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Том 41, № 2 (2017)
- Год: 2017
- Статей: 8
- URL: https://journals.rcsi.science/0278-6419/issue/view/10802
Article
Simulating the heart’s electric activity: Numericalmethods for inverse problems
Аннотация
For a two-dimensional modified FitzHugh–Nagumo mathematical model, the inverse problem is considered to find a coefficient of the system of partial differential equations, depending on spatial variables. Additional dynamic measuring of the potential is done throughout the inner boundary of the domain. A numerical way of solving the specified inverse problem is proposed and the results from numerical experiments are presented.
51-57
Parallel assimilation of observed data in the hydrodynamic model of the ocean circulation
Аннотация
The parallel use of the Kalman ensemble filter technique for assimilating data from observations in theHYCOMmodel of theWorldOcean is described. Data from satellite observations of the sea’s surface temperature and the sea’s surface height are assimilated both separately and conjointly. Numerical experiments on correcting model calculations using data from observations are performed. The results from the corrections are compared to model calculations without assimilation. The effectiveness of the employed parallelization algorithm is confirmed.
58-63
Optimal modes in a multidimensional model of economic growth
Аннотация
An n-dimensional problem of optimal economic growth in a multifactor model with the Cobb–Douglas production function and an integral-type functional with discounting is investigated. The model is studied by assuming that all amortization coefficients are equal. A constructive description of an optimal solution for a sufficiently large planning horizon and a sufficiently small discount coefficient is obtained. The extremal solution is described in analytical form. The studied problem with other production functions has a biological interpretation in an optimal growth model of agricultural plants with n vegetative organs during a specific finite time interval.
64-69
Stabilized hard thresholding for an unknown noise level
Аннотация
The effect wa ys of estimating noise variance on the statistical characteristics of the stabilized hard thresholding of signal wavelet coefficients is studied. An unbiased estimator of the mean-square risk is analyzed. It is shown that under certain conditions, the estimator distribution tends to a normal law with variance that depends on the type of noise variance estimate.
70-75
Boundaries of the precision of restoring information lost after rounding the results from observations
Аннотация
Lower and upper estimates are obtained for deviations of the limit of a selectedmean from estimated mathematical expectations when rounded data are processed. Different cases of error distribution are considered: normal, Simpson (triangle), and Laplace (double exponential)distributions.
76-80
Complexity of the satisfiability problem for multilinear forms over a finite field
Аннотация
Multilinear forms over finite fields are considered. Multilinear forms over a field are products in which each factor is the sum of variables or elements of this field. Each multilinear form defines a function over this field. A multilinear form is called satisfiable if it represents a nonzero function. We show the N P-completeness of the satisfiability recognition problem for multilinear forms over each finite field of q elements for q ≥ 3. A theorem is proved that distinguishes cases of polynomiality and NP-completeness of the satisfiability recognition problem for multilinear fields for each possible q ≥ 3.
81-88
Some asymptotically optimal one-sided embeddings of trees of similar formulas into rectangular lattices
Аннотация
We consider the problem of optimally placing trees of formulas in rectangular lattices. We construct and study two types of these trees and corresponding ways of placing (embedding) them into such lattices. The first is based on perfect binary trees, while the second is based on special binary trees. For the second type of tree embeddings, we prove asymptotic optimality among the trees of all formulas similar to the initial formula of no greater depth.
89-96
Constructing a speech audio–video corpus by aligning long segments of speech and text
Аннотация
A new algorithm for aligning text with speech audio signals having lengths of up to several hours is proposed. The algorithm allows its quality to be effectively evaluated. The requirements on the acoustic model are not very demanding. The algorithm can be used to design an audio–video course for learning the Russian language.
97-103