In the article, we have considered the economic-mathematical model of selection of projects targeted programs on the example of the Russian Federation. The article also defines criteria of their distribution. We have proposed the parallel algorithm with the guaranteed estimates of the allocation of graph
This article explores the multicriteria problems arise
in the organization of routes in large-scale transport
management system. As a mathematical tool for constructing
a model, we were using the prefractal
graphs. Prefractal graphs naturally reflect structure of
the device of communications of transport system,
reflecting its important features – locality and
differentiation. Locality is provided with creation of
internal routes (city, raionwide, etc.). Differentiation
is understood as division of routes on intra regional,
interregional and international. The objective is
reduced to a covering of prefractal graphs by the
simple paths which are crossed on edges and nodes.
On the set of feasible solutions, vector criterion
function with certain criteria is based. In concepts of
transport system, the given criteria have concrete
substantial interpretation, the transport routes allowing
to design considering features of system.
In this article, we construct polynomial algorithms for
finding optimal according to certain criteria decision.
By the criteria which aren't optimizing the allocated
routes their estimates of the lower and upper bounds
are given. On all given algorithms the estimates of
computing complexity confirming advantage of use
of methods of prefractal and fractal graphs before
classical methods of the theory of graphs are
constructed and proved
In accordance with the new paradigm of mathematical statistics the statistics of objects of nonnumerical nature (statistics of nonnumerical objects, non-numerical data statistics, non-numeric statistics) is one of the four main areas of mathematical statistics. Statistics of objects of nonnumerical nature consists of a central core - statistics in spaces of arbitrary nature - and statistical theories of analysis of specific types of non-numeric data. To identify possibilities of application of statistics of objects of nonnumerical nature it is useful to explore the multiformity of objects of non-numeric nature. This is the subject of this article. We have considered the results of measurements at scales other than absolute; binary relations; dichotomous (binary) data; sets. We have also analyzed the objects of non-numerical nature as statistical data, and their importance in the formation of statistical or mathematical model of a real phenomenon, as a result of data analysis
Multilevel bionic algorithm for detection and identification of software and hardware impacts on telecommunication networks is considered in the article. The results of applying of the software implementation of the algorithm are discussed
The special states of a hydrogen atom, arising from the interaction of a proton with a scalar massless field studied on the basis of Kaluza-Klein theory. It is shown that some states of the atoms have parameters of the neutron.
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
An analysis of the experimental data obtained by the
authors, as well as reference books, allowed to
hypothesize about the essential role of gravitational
convection in electromembrane systems with
ampholytes even in underlimiting current regimes. The
article is devoted to the development of the
mathematical model of ion transport in a flow
elecrtomembrane system during electrodialysis of
ampholyte-containing solutions with taking into
account a possible appearance of gravitational
convection, in particular, due to nonisothermal
protonation–deprotonation reactions of ampholytes.
The article presents the boundary value problem that is
the new mathematical model for diffusion, convection
and electromigration of four components of the
solution (ions of sodium, dihydrogen phosphate and
hydrogen, as well as molecules of orthophosphoric
acid) in a half of an electrodialysis desalination
channel, adjacent to an anion-exchange membrane. The membrane is considered as ideally selective and
homogeneous. The system of partial differential
equations, that is the base of the model, also includes
equations of Navier-Stokes, material balance,
convective heat conduction and the electroneutrality
condition. The system of equations is supplemented by
a number of natural and original boundary conditions.
A distinctive feature of this study is the absence of
assumptions about the equilibrium of chemical
reactions in a diffusion layer. The results of the study
can be used for the development of environmentally
rational and resource saving membrane technologies
for a processing of products of agro-industrial complex
We continue the series of articles about the history of statistics. We discuss the development of nonparametric and applied statistics in our country in 1930 - 1980 years. We have presented the studies of the great statisticians of the twentieth century, such as N.V. Smirnov, L.N. Bolshev, V.V. Nalimov. American statistics show Russian debate about applied statistics. We have briefly listed the
process of creation of the All-Union Statistical Association (1990) and its further developments
The article is devoted to the nonparametric point and
interval estimation of the characteristics of the
probabilistic distribution (the expectation, median,
variance, standard deviation, variation coefficient) of
the sample results. Sample values are regarded as the
implementation of independent and identically
distributed random variables with an arbitrary
distribution function having the desired number of
moments. Nonparametric analysis procedures are
compared with the parametric procedures, based on
the assumption that the sample values have a normal
distribution. Point estimators are constructed in the
obvious way - using sample analogs of the
theoretical characteristics. Interval estimators are
based on asymptotic normality of sample moments
and functions from them. Nonparametric asymptotic
confidence intervals are obtained through the use of
special output technology of the asymptotic relations
of Applied Statistics. In the first step this technology
uses the multidimensional central limit theorem,
applied to the sums of vectors whose coordinates are
the degrees of initial random variables. The second
step is the conversion limit multivariate normal
vector to obtain the interest of researcher vector. At
the same considerations we have used linearization
and discarded infinitesimal quantities. The third step
- a rigorous justification of the results on the
asymptotic standard for mathematical and statistical
reasoning level. It is usually necessary to use the
necessary and sufficient conditions for the
inheritance of convergence. This article contains 10
numerical examples. Initial data - information about
an operating time of 50 cutting tools to the limit
state. Using the methods developed on the
assumption of normal distribution, it can lead to
noticeably distorted conclusions in a situation where
the normality hypothesis failed. Practical
recommendations are: for the analysis of real data we
should use nonparametric confidence limits
In the article we have considered A. N. Kolmogorov and N. V. Smirnov papers dedicated to one-sided and two-sided goodness-of-fit and homogeneity tests. It has been shown that the term "Kolmogorov - Smirnov test" used incorrectly. We have also given the recommendations on use of the terms "Kolmogorov test", "Smirnov test", "test of Kolmogorov-Smirnov type" and discussed omega-square test (Cramer-von Mises–Smirnov test). Typical errors in the application of these criterions have been considered, in particular to test for normality of the distribution of measurement results