Lusian - dichotomous data model as a finite sequence of independent Bernoulli trials with, generally speaking, different probabilities of success. The tasks of statistical hypothesis testing, classification, averaging lusians are discussed. In accordance with the requirements of practice the problems are considered primarily in the asymptotic behavior of increasing dimension, in which the number of unknown parameters increases in proportion to the size of data. The method of testing hypotheses on set of small samples and the theory of unbiased statistical estimates were proved to be useful
In the article the graph model of management of control of knowledge of pupils in indistinct conditions is offered. The model allows to define the optimum quantity and optimum placement of control actions for a studying course for each discipline
(each its fragment), and also to carry out an assessment of structure of knowledge
In this work it is investigated the propagation of unsteady-state waves in a vicoelastic semi space for the arbitary heterogeneous functions at the different boarded conditions with the help of Laplas
transformation and exponentional Truriers conversion. The received solution has been analyzed in a private case when medium properties are describing by Rzhanitsin’s core
We have proposed the general scheme for studying the stability of the conclusions obtained by mathematical methods and models regarding tolerance deviations of the original data and background models. The concrete problems of stability are discussed: towards a change of data, its size and distributions, to allowable transformations measurement scales, to the temporal characteristics (time of start of the project, the planning horizon). Reducing the uncertainty can be conducted by changing the type of data, i.e. with the aid of the transition to non-numerical data.
The models of concrete management processes of industrial organizations are considered on the examples of stability characteristics of investment projects to change the discount factors and in models of inventory management to change in the coefficients of the model and batch size production
We analyze the probabilistic-statistical methods in the researches of Boris Vladimirovich Gnedenko – the academician of Ukrainian Academy of Science, which are very important for the XXI century. We have also discussed the limit theorems of probability theory, mathematical statistics, reliability theory, statistical methods of quality control and queuing theory. We give some information about the main stages of scientific career of B.V. Gnedenko, his views on the history of mathematics and teaching
The work presents the calculation on the basis of magnetic circuits of magnetic field induction in the "water" gaps of the device for activation of water with alternating magnetic field of industrial frequency. We have executed the calculations of magnetic inductance of the coil of the device taking into account the thickness of layers of winding current-carrying wires. This allowed experimentally determining - with reasonable accuracy - the value of the relative permeability of the steel used, housing, necessary for the specified calculation of the device in general
We have studied the asymptotic behavior of a broad class of nonparametric statistics, which includes statistics of omega-square type and Kolmogorov-Smirnov type. Limit theorems have been proved. We have also developed the method of approximation with step functions. With the help of this method we have obtained a number of necessary and sufficient conditions
The drawbacks of the existing ontology languages and problems of their practical application are discussed in this paper. The requirements for the process of ontologies creating are laid down. A simplified method of constructing the ontological domain model on the basis of the original language SXML is proposed
We discuss the question of the essence of formation and propagation of waves in the electromagnetic environment. We have questioned the reliability of its description by J. Maxwell in the form of alternating electric and magnetic fields. The article justifies the formation of an electromagnetic wave in the form of a wave compression-decompression surrounding electromagnetic photon field flux of photons of different frequencies emitted by different sources or antenna
The equation of parabolic type, describing the evolution of the gravitational field on the scale of the solar system, galaxy and cluster galaxies is derived from the Einstein equation. Space-time metric compatible with the post-Newtonian approximation and the metric of the expanding universe, and allowing hyper-fast travel in Einstein's theory of gravitation is considered. It is shown that the speed of hyper-fast travel depends on the implementation, including the parameters of ground state of the expanding universe. A criterion for the maximum speed of motion of material bodies has been proposed