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Том 40, № 2 (2016)
- Год: 2016
- Статей: 7
- URL: https://journals.rcsi.science/0278-6419/issue/view/10797
Article
A finite rational algorithm that verifies the diagonalizability of a square matrix by congruence
Аннотация
Let A be a square matrix of order n whose entries are rational or rational Gaussian numbers. A method is described that verifies the possibility of diagonalizing A by means of congruence and uses a finite number of arithmetic (and, in the complex case, conjugation) operations.
53-56
On stationarity conditions in an optimal control problem with a simple contact with the phase boundary
Аннотация
A certain class of optimal control problems with a one-dimensional phase constraint is considered. When a trajectory contacts the phase boundary on an interval, we employ a special procedure (two-stage variation) to obtain optimality conditions in the Gamkrelidze form and then in the Dubovitskii–Milyutin form, including the sign definiteness property measure density and its jumps at junction points.
57-64
Confidence prediction of the mean values of multiple observations
Аннотация
The confidence prediction of the mean value ofmultiple responses in a linear multivariate normal regression model is considered. In order to solve it, confidence intervals of the mean value of multiple responses and its predicted value are obtained. They are numerically modeled and analyzed in comparison with known analogues for regression and individual response.
65-70
Combining endogenous and exogenous variables in a special case of non-parametric time series forecasting model
Аннотация
We address a problem of increasing quality of forecasting time series by taking into account the information about exogenous time series. We aim to improve a non-parametric forecasting algorithm that minimizes the convolution of a histogram of time series with the loss function. We propose to adjust the histogram, using mixtures of conditional histograms as a less sparse alternative to multidimensional histogram and in some cases demonstrate the decrease of loss compared to the basic forecasting algorithm. To the extent of our knowledge, such approach to combining endogenous and exogenous time series is original and has not been proposed yet. The suggested method is illustrated with the data from the Russian Railways.
71-78
On the outcome of false images of linear k-valued functions for composite numbers k when the number of variables increases
Аннотация
The problem of constructing discrete functions such that parts of their value sets determine (generate) arbitrary linear functions is considered. A case in which k is a prime number was considered earlier by the author. It is proved that the existence of such partial functions wshen the number of independent variables is no less then two implies they exists for any arbitrary greater number of independent variables. Upper estimates linear with respect to the number of independent variables are proved for the size of the domain of universal functions. The existence of two-variable universal functions is proved for sufficiently large k.
79-82
On the existence of provably secure cloud computing systems
Аннотация
We study a formal model of cloud computing systems with auxiliary cryptoservers. Assuming an existence of a secure threshold somewhat homomorphic public key cryptosystem we show how to build a cloud computing system secure in this model.
83-88
Contribution from the accuracy of phoneme recognition to the quality of automatic recognition of Russian speech
Аннотация
The dependence of the quality of automatic recognition of Russian speech on the accuracy of feature descriptions and their distribution model is considered. A list of eight phonemes is given whose accuracy of recognition makes the greatest contribution to the quality of speech recognition.
89-95