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
From a modern point of view we have discussed Kolmogorov’s researches in the axiomatic approach to probability theory, the goodness-of-fit test of the empirical distribution with theoretical, properties of the median estimates as a distribution center, the effect of "swelling" of the correlation coefficient, the theory of averages, the statistical theory of crystallization of metals, the least squares method, the properties of sums of a random number of random variables, statistical control, unbiased estimates, axiomatic conclusion of logarithmic normal distribution in crushing, the methods of detecting differences in the weather-type experiments
The movements of electric locomotives create the interferences affecting the wired link. The creation of sufficiently technical effective and at the same time cost-effective means of protection from wireline interferences generated traction networks assumes as a preparatory phase to develop mathematical models of interference caused by electric locomotives. We have developed a probabilistic-statistical model of interferences caused by electric locomotives. The asymptotic distribution of the total interference is the distribution of the length of the two-dimensional random vector whose coordinates - independent normally distributed random variables with mean 0 and variance 1. Limit theorem is proved for the expectation of the total amplitude of the interferences. Monte-Carlo method is used to study the rate of convergence of the expectation of the total amplitude of the interferences to the limiting value. We used an algorithm of mixing developed by MacLaren-Marsaglia (M-algorithm). Five sets of amplitudes are analyzed, selected in accordance with the recommendations of experts in the field of traction AC networks. The most rapid convergence to the limit takes place in the case of equal amplitudes. It was found that the maximum possible average value of the amplitude of the random noise by 7.4% less than the previously used value, which promises a significant economic impact
The statistics of objects of non-numerical nature (statistics of non-numerical objects, non-numerical data statistics, non-numeric statistics) is the area of mathematical statistics, devoted to the analysis methods of non-numeric data. Basis of applying the results of mathematical statistics are probabilistic-statistical models of real phenomena and processes, the most important (and often only) which are models for obtaining data. The simplest example of a model for obtaining data is the model of the sample as a set of independent identically distributed random variables. In this article we have considered the basic probabilistic models for obtaining non-numeric data. Namely, the models of dichotomous data, results of paired comparisons, binary relations, ranks, the objects of general nature. We have discussed the various options of probabilistic models and their practical use. For example, the basic probabilistic model of dichotomous data - Bernoulli vector (Lucian) i.e. final sequence of independent Bernoulli trials, for which the probabilities of success may be different. The mathematical tools of solutions of various statistical problems associated with the Bernoulli vectors are useful for the analysis of random tolerances; random sets with independent elements; in processing the results of independent pairwise comparisons; statistical methods for analyzing the accuracy and stability of technological processes; in the analysis and synthesis of statistical quality control plans (for dichotomous characteristics); the processing of marketing and sociological questionnaires (with closed questions like "yes" - "no"); the processing of socio-psychological and medical data, in particular, the responses to psychological tests such as MMPI (used in particular in the problems of human resource management), and analysis of topographic maps (used for the analysis and prediction of the affected areas for technological disasters, distributing corrosion, propagation environmentally harmful pollutants, various diseases (including myocardial infarction), in other situations), etc.
We should have trained staff to implement
innovative strategies. Therefore, it is natural, that a
lot of attention is paid to the staffing of the
management processes of innovative activity at the
enterprises of the rocket and space industry (RCP).
Training and human resources management in
accordance with current legislation should be based
on professional standards. The content of
professional standards should reflect the results of
forecasting scientific and technical progress in the
field, for example, in the RCP. It is necessary to
forecast trends in the use of information and
communication technologies in solving management
problems in the socio-economic sphere in order to
reflect these developments in professional standards.
The approach to solving this problem is the subject
of this article. What should the professional standard
be like in the RCP? The main problem lies in the
fact that although the standard is to be enacted in the
near future, its actual impact on the industry will
start in 5 - 10 years and will continue for at least
another 10 years, ie, until the 2030s. Professional
standards should come from "Education through
Science" concept, ie, knowledge, skills,
competences, provided by a professional standard,
should be based on modern scientific achievements.
For example, mathematical methods of research
should be based on a new paradigm in the area of
knowledge and statistical data analysis methods
must meet high statistical techniques. For the
development of professional standards in the field of
the RCP it is necessary to predict the characteristics
of the qualification (level of knowledge, skills and
experience) required the employee to carry out
professional activities in the RCP in 2020 - 2030.
Modern information and communication
technologies are creating a fundamentally new
situation in the organization of the economy. We
have an ability to manage the work of organizational
units, scattered throughout the world, from a single
center. The requirement of presence in the
workplace is mainly a relic of the past. We have a
lot of advantages in a remote work
The aim of work is to get prognostic equations, taking into account the natural growth of pine forest stands
of Krasnoyarsk forest-steppe along with influence
of forestry arrangements and elemental factors. Dependences of weight average diameter and mean square deviation from age and plantation density were received in the article.
In this work, we develop a model describing the
propagation and branching of a streamer in a conducting
medium in external electric field. To describe the
contribution of the conductivity currents, we modified
the standard electrostatic equation taking into account
the vortex component of the electric field. As a result of
this generalization, the streamer model is formulated in
the form of nonlinear equations of parabolic type. In the
framework of the proposed model, the problem of the
propagation of a streamer in the form of a traveling wave
is considered, which leads to the emergence of SaffmanTaylor
streamers. For streamers of this type, the
branching problem is formulated, which has a unique
solution. The dependence of the branch point on the
parameters of the problem-the speed of the streamer, the
diffusion coefficient of the electrons and the strength of
the external electric field, is found. The branching
mechanism of the streamer head by dividing it into two
parts has been well studied and several alternative
models have been formulated for its description. The
novelty of the problem in question is that the streamer
splits into two three-dimensional channels that are
symmetric with respect to the given plane. Numerical
experiments also revealed the mechanism of branching
of the streamer in the cathode region, connected with the
separation of the main channel into several lateral
branches. It is noted, that in nature both branching
mechanisms are realized, whereas in theory the
instability of the surface of the streamer head is
investigated
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
In the article, a text is considered as a system, which includes both verbal and nonverbal subsystems of different levels of hierarchy. System generalization of the classical Shannon measure of information in text and a quantitative measure of the level of systematic text, called the "coefficient of emergence of Shannon", which is based on it, is proposed. This article shows mathematical relationship between the obtained coefficients of emergence of Hartley in 2002 and Shannon's proposed rate of emergence. It is shown that every object of cognition can be associated with a text reflecting its composition and structure. The process of learning from this perspective is seen as a process of constructing a text object models of learning and research process of these models. The definition of procedures for encryption and decryption, as well as quantitative measures of their effectiveness based on quantitative measures systematic texts is given. From this standpoint, the relationship of encryption and decryption with zipping and unzipping is shown. We propose a computer program for the numerical measurement of systemic and specific texts of the simulated systems and present some numerical examples in this article
In the USSR higher attestation Commission from
1975 to the collapse of the USSR was subordinated
not to the Ministry of education and science, but to
the Council of Ministers of the USSR directly.
However, since then there is a steady trend of gradual
reduction of the status of the Commission. Today
it is not just included in the Ministry of education,
it is just one of the units of one of its structures:
the Rosobrnadzor. Reduced status of the HAC inevitably
leads to a decline in the status and in the adequacy
of scientific degrees assigned as well as scientific
ranks. This process of devaluation of traditional
academic degrees and titles assigned to the HAC,
has reached the point when a few years ago there
were abolished salary increments for them. Now,
instead of that, every university and research institutes
have developed their local, i.e. non-comparable
with each other scientometric methods of evaluation
of the results of scientific and teaching activities.
Despite the diversity of these techniques, there is a
common thing among all of them, which is the disproportionate
role of the h-index. The value of the
Hirsch index starts to play an important role in the
protection, when considering competitive cases for
positions, as well as in determining the monthly
rewards for the results of scientific and teaching
activities. By itself, this index is well founded, theoretically.
However, in connection with the practice
of its application in our conditions, in the collective
consciousness of the scientific community there was
a kind of mania, which the authors call the "Hirschmania".
This mania is characterized by elevated
unhealthy interest to the value of the Hirsch index,
as well as incorrect manipulation of its value, i.e.
inadequate artificial exaggeration of this value, as
well as a number of negative consequences of that
interest. In this study we have made an attempt to construct a quantitative measure for assessing the
extent of improper manipulation of the value of the
Hirsch index, and offered a science-based modification
of the h-index, insensitive (resistant) to the manipulation.
The article presents a technique for all
the numerical calculations, which is simple enough
for any author to use