The article discusses the dynamic model of the rocket
motor electromagnetic type, consisting of a source of
electromagnetic waves of radio frequency band and a
conical cavity in which electromagnetic waves are
excited. The processes of excitation of
electromagnetic oscillations in a cavity with
conducting walls, as well as the waves of the YangMills
field are investigated. The multi-dimensional
transient numerical model describing the processes of
electromagnetic oscillations in a cavity with
conducting wall created. Separately, the case of
standing waves in the cavity with conducting walls
considered. It is shown that the oscillations mode in
the conducting resonator different from that in an
ideal resonator, both in steady and unsteady
processes. The mechanism of formation of traction
for the changes in the space-time metric, the
contribution of particle currents, the Yang-Mills and
electromagnetic field proposed. It is shown that the
Yang-Mills field calls the change of the dielectric
constant, which leads to a change in the capacitance
of the resonator. Thus, the parametric resonance
occurs in the system, which leads to a strengthening
of the Yang-Mills amplitude, and to the emergence of
traction. We have developed a dynamic model, which
enables optimal traction on a significant number of
parameters. It was found that the thrust increases in
the Yang-Mills field near the main resonance
frequency. A model describing the excitation and
emission of nonlinear waves of the Yang-Mills field
was proposed. It is shown that nonlinear waves of the
Yang-Mills field more effectively carry the
momentum from the system in comparison with
electromagnetic waves, and it explains the significant
increase by several orders of thrust in the engines of
the electromagnetic type, compared with the photon
rocket
In many applications, we study the time series (or a
random process), which is the sum of the periodic
deterministic function of time and random errors that
distort the periodic signal. It is required to estimate
the length of the period and the periodic component.
It does not assume that the periodic function is
included in any parameter family of functions, such
as finite sums of sines and cosines. It is obvious that
the assumption of occurrence of a periodic function
in parametric family does not meet the
characteristics of the real world, ie, is conditional,
internal mathematical (look for the keys under the
lamp because there is a light, not in the bush, where
lost, because there are dark). For similar reasons, it
is impossible to assume that the distribution function
of the random errors is included in any parameter
family of distributions. In accordance with the new
paradigm of mathematical statistics in this article we
studied the problem of nonparametric estimation
(minimum) length of the period and the periodic
component of the signal. On the basis of natural
variation and scope of indicators is suggested a new
class of nonparametric estimators of the length of the
period and the periodic component in the time
series. Based on the general results of statistics of
objects of non-numeric nature we proved the
consistency of these estimates. From the practical
point of view it is necessary to minimize the
numerical (one parameter - ability length of period
of time) one or more of the 66 functionals, described
in the article
The general scheme of modern statistical science is
just like this. Mathematical Statistics is a part of
mathematics that studies the statistical structure (it
itself does not give recipes analysis of statistical
data, however, it is developing methods that are
useful for use in theoretical statistics). Theoretical
Statistics - the science dedicated to the models and
methods of analysis of concrete statistical data.
Applied Statistics (in the narrow sense) is devoted to
the statistical techniques of data collection and
processing (it includes the methodology of statistical
methods, the organization of sample surveys, the
development of statistical techniques, the creation
and use of statistical software). Applications of
statistical methods in concrete fields (in economics
and management - Econometrics, in biology -
Biometrics, in chemistry - Chemometrics, in
technical research - Technometric, in geology,
demography, sociology, medicine, history, etc.).
Often positions 2 and 3 together are called Applied
Statistics. Sometimes position 1 is called Theoretical
Statistics. These terminological differences are
related to the fact that the above-described
development of the considered scientific and applied
field not once, not completely and not always
adequately reflected in the minds of experts.
Meanwhile, there are still textbooks of appropriate
level of representation of the mid-twentieth century.
The article analyzes the post-war development of
the national statistics. We have identified five
"growth points": nonparametrics, robustness,
bootstrap, statistics of interval data, and statistics of
non-numeric data. We have discussed content,
development and the basic ideas of statistics of nonnumeric
data. We have given a number of
unresolved problems of theoretical and applied
statistics
We have given a critical analysis of statistical
models and methods for processing text information
in historical records to establish the times when
there were certain events, ie, to build science-based
chronology. There are three main kinds of sources
of knowledge of ancient history: ancient texts, the
remains of material culture and traditions. The
specific date of the extracted by archaeologists
objects in most cases can not be found. The group of
Academician A.T. Fomenko has developed and
applied new statistical methods for analysis of
historical texts (Chronicle), based on the intensive
use of computer technology. Two major scientific
results were: the majority of historical records that
we know now, are duplicated (in particular,
chronicles, describing the so-called "Ancient Rome"
and "Middle Ages", talking about the same events);
the known historical chronicles tell us about real
events, separated from the present time for not more
than 1000 years. It was found that chronicles
describing the history of "ancient times" and
"Middle Ages" and the chronicle of Chinese history
and the history of various European countries do not
talk about different, but about the same events. We
have the attempt of a new dating of historical events
and restoring the true history of human society
based on new data. From the standpoint of statistical
methods of historical records and images of their
fragments – they are special cases of non-numeric
objects of nature. Therefore, developed by the group
of A.T. Fomenko computer-statistical methods are
the part of non-numerical statistics. We have
considered some methods of statistical analysis of
chronicles applied by the group of A.T. Fomenko:
correlation method of maximums; dynasties method;
the method of attenuation frequency; questionnaire
method codes. New chronology allows us to
understand much of the battle of ideas in modern
science and mass consciousness. It becomes clear
the root cause of cautious attitude of the West
towards Russia
The article presents the problem of spanning trees with
topological criteria and interval scales. We have
introduced relationship preferences and
incomparability to find the complete set of alternatives
in the case of interval scales. The base for
mathematical calculations is interval mathematics
This question is about the speed of wave
propagation in electromagnetic environment.
Electromagnetic environment (field) is the space
that fills the whole Universe, occupied by the
electromagnetic particles-photons. At the heart of
the special relativity theory, the constancy of the
speed of light in vacuum is affirmed. According to
modern concepts, the speed of light in vacuum is the
maximum speed of the particle motion and
propagation of interactions. However, light is the
narrow range of electromagnetic radiation –
(4÷8)·1014 Hz, therefore experimentally measured
speed of light is referred to this frequency range.
The fact that this speed of electromagnetic waves
can theoretically be non permanent – physicists have
pondered for a long time and this question is
periodically excited in the scientific literature. The
author of this article also had an impression that the
speed of light, in which he understands distribution
speed of waves of a wide range of frequencies in the
electromagnetic environment, is not a constant. The
article attempts to prove it. Many photons of
different frequencies move simultaneously in
different directions in a photonic electromagnetic
field in environment. They are involved in the
formation of a wave of compression –
decompression in this field under the influence of
the antenna radiated photons. It is approved that the
speed of photons of different frequencies can change
within a wide range from 1,285·103
m/s (ν = 1024
Hz) to 1,285·1012 m/s (ν = 106 Hz) and, therefore,
the speed of wave propagation in the
electromagnetic environments that are filled by
photons of the same frequency or a narrow
frequency range can change widely from 8,58·102
m/s to 8,58·1011 m/s and be significantly different
from the experimentally discovered speed of light.
Interplanetary space in different parts of the
Universe can be represented by different spectra of
photons and therefore they will have different speed
of propagation of electromagnetic waves
The article discusses a model of rocket motor of
electromagnetic type, consisting of a source of
electromagnetic radio frequency oscillations and the
conical cavity, in which electromagnetic waves are
excited. We have created a multi-dimensional
transient numerical model describing the process of
establishing electromagnetic oscillations in the
resonator, taking into account the finite conductivity
of the walls. Separately, the standing waves in the
cavity with conducting walls have been simulated. It
is shown that the oscillations mode in the conducting
resonator different from that in an ideal resonator,
both in a case of steady and unsteady waves. We have
built a dynamic model taking into account the thermal
conductivity and electrical conductivity of the walls,
waves and particles emission and vacuum
polarization. We have also developed a dynamic
model enables to optimize a thrust force on a
considerable number of parameters without the
involvement of the hypotheses about the physics of
the phenomenon. We run the optimization of the
operating parameters of the device, namely by the
excitation frequency, the frequency of the modulating
signal, the magnitude of heat losses of
electromagnetic energy by thermal radiation in the IR
spectrum, the parameters of forced heat transfer and
the temperature dependence of the resistance of the
material of the cavity walls. It is found that the pulse
modulation greatly improves the efficiency of
conversion of electromagnetic energy into thrust. The
mechanism of formation of traction, adjusting the
metrics of space-time, the current contribution of
elementary particles, the Yang-Mills and
electromagnetic fields is proposed. It is shown that
the contribution of the elementary particles in the
thrust force is proportional to the electrical
conductivity of the system multiplied by Abraham
force
When developing management solutions with the
aim of joint consideration and comparison of
various factors, partial removal of uncertainty is
widely used ratings. In the theory of decisionmaking
in almost the same sense, we use the terms
"composite index" or "integrated indicator". The
article is devoted to the mathematical theory of
ratings as tools for studying socio-economic
systems. We considered, primarily, linear ratings
which is a linear function from a single (private)
indicators (factors, criteria), constructed using the
coefficients of importance (weightiness,
importance). The study discusses the factors
affecting the magnitude of the ratings. Three groups
of causes affect the value of a line ranking: the ways
of measurement of individual indicators, the choice
of the set of indicators; the values of the coefficients
of importance. We considered binary ratings when
the rating takes two values. To compare the
proposed rankings we use a new indicator of the
quality of diagnostics and prognostic power.
Significantly, in many managerial situations,
significant differences between objects are identified
using any rating. According to the fundamental
results of stability theory, the same source data
should be processed in several ways. Matching
findings, obtained using multiple methods, likely
reflect the properties of reality. The difference is the
result of a subjective selection method. When using
the results of the comparison of objects according to
several indicators (criteria ratings), including in
dynamics, very useful is the selection of the Pareto
set. We discuss the examples of the application of
the decision theory, expert evaluations and rankings
when developing complex technical systems
The purpose of mathematical statistics is
development of methods for the data analysis
intended to solve applied problems. Over time,
approaches to the development of data analysis
methods have changed. A hundred years ago, it was
assumed, that the distributions of the data have a
certain type, for example, they are normal
distributions, and on that assumption they developed
a statistical theory. The next stage, in the first place
in theoretical studies there are limit theorems. By
"small sample" we mean a sample, which can not be
applied to conclusions based on the limit theorems.
In each statistical problem there is a need to divide
the final sample sizes into two classes - those for
which you can apply the limit theorems, and those
for which you can not do it because of the risk of
incorrect conclusions. To solve this problem we
often used the Monte Carlo method. More complex
problems arise when studying the effect on the
properties of statistical procedures for data analysis
of various deviations from the original assumptions.
To study such impact, we often used the Monte
Carlo method as well. The basic (and not solved in a
general way) problem of the study of the stability of
the findings in the presence of deviations from the
parametric families of distributions is the problem of
choosing some distributions for using in modeling.
We consider some examples of application of the
Monte Carlo method, relating to the activities of our
research team. We have also formulated basic
unsolved problems
In the statistical hypothesis testing, critical values
often point to a priori fixed (nominal) significance
levels. As such, typically researcher uses the values
of three numbers 0.01, 0.05, 0.1, to which may be
added a few levels: 0.001, 0.005, 0.02, and others.
However, for the statistics with discrete distribution
functions, which, in particular, include all
nonparametric statistical tests, the real significance
levels may be different from the nominal, differ at
times. Under the real significance level we refer to
the highest possible significance level of discrete
statistics, not exceeding a given nominal
significance level (ie, the transition to the next
highest possible value corresponding discrete
statistical significance level is greater than a
predetermined nominal). In the article, we have
discussed the difference between nominal and real
significance levels on the example of nonparametric
tests for the homogeneity of two independent
samples. We have also studied two-sample
Wilcoxon test, the criterion of van der Waerden,
Smirnov two-sample two-sided test, sign test, runs
test (Wolfowitz) and calculated the real significance
levels of the criteria for nominal significance level
of 0.05. The study of the power of these statistical
tests is accomplished by means of Monte Carlo
method. The main conclusion: the use of nominal
significance levels instead of real significance levels
for discrete statistics is inadmissible for small
sample sizes