There is a 2D mathematical model of ion transport
binary salt with the main conjugate effects of
concentration polarization in the overlimiting current
mode: the bulk charge and the dissociation/
recombination of water, gravity and electroconvection
and Joule heating the solution in the form of a
boundary value problem for systems of differential
equations with partial derivatives in the article. This
system is presented in a form convenient for numerical
solution. We describe the necessary boundary
conditions. This article presents a theoretical study of
the interaction of forced, gravitational and
electroconvection, the dissociation / recombination of
water molecules, and Joule heating of the solution and
heat transport through membranes. We have
constructed a mathematical model of two-dimensional
non-stationary ion transport binary salt in a smooth
rectangular channel desalting electrodialysis device
using equations Nernst-Planck-Poisson, heat
conduction and Navier-Stokes equations and the
natural boundary conditions. For numerical solution
we use the finite element method, with the splitting of
task at each new time layer into three subtasks:
electrochemical, thermal conductivity, hydrodynamic.
Such approach to the development of numerical
methods is the original and can solve arising in
modeling boundary-value problems for a nonlinear system of partial differential equations
We consider the methods for estimation of the
effectiveness and quality of the scientific activities
of the researcher, of the organization, of the
magazine. Performance indicators of scientific
activity are used as an important part in the
estimation of higher education institutions, the
innovative capacity of enterprises, etc. To estimate
the effectiveness of scientific activity is natural to
use intellectual tools which are well-established in
other subject areas. This will include, in particular,
the balanced scorecard, based on key performance
indicators (hence the title of this article), as well as
controlling, primarily controlling of research
activities. There are two more developed and
widely used types of tools for estimation the
effectiveness of the scientific activity - the
scientometric indicators and the expert estimators.
Their critical analysis is the subject of this article.
The goal - to choose the most effective tool.
Different versions of manipulating of values of
scientometric indicators in the Russian Federation,
in our estimation, are still relatively rare. Perhaps
this is due to the relatively short period of their use
in the management of science. Since an indicator
such as citation index (the number of citations of
publications) of researcher, allows estimating its
contribution to science, the use of this
scientometric indicator for the management of
science is justified. At the same time, the number
of publications and especially h-index is not
possible to objectively estimate the effectiveness of
research activities, particularly in view of the
properties of the real bibliometric databases. Expert
procedures have several disadvantages. In this
article we discuss the real effectiveness of expert
procedures in the areas of their application, as
conferring academic degrees and elections to the
National Academy of Sciences (primarily in the
Russian Academy of Sciences), as well as
appointments to senior positions. The basic
principles of expertise in these areas remain the
same for the past 70 years. Based on an analysis of
practice it is necessary to ascertain the lack of
efficacy of expert estimators in these areas. Rationale to what has been said is given in the
article
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 article presents the model of the large-scale clustering
of the matter in the universe. The base for mathematical
calculations is interval mathematics
Today, infectious diseases remain a leading cause of
premature deaths in the world. Agent-based
modeling can play an important role in predicting the
spread of disease and to assess the containment
measures. The aim is to construct a multi-agent
simulation model for the formation of epidemic
measures to reduce effectively their incidence. Using
the multi-agent simulation approach to modeling of
epidemics due to the fact that the approach allows us
to consider a number of factors influencing the
epidemic process, makes it possible to carry out
numerical experiments. The processes of the spatial
distribution and temporal variation of these two
groups of epidemics of infectious the author calls
dynamics. Usually hard-implemented spatial
components of the dynamics in the proposed model
can be substituted by predfractal topology of the
graph, which is built up by voluminous graphs -
primers, and the dynamics of compounding
prefractal graph, called its recognition, is responsible
for the timing of the process component. Under the
term of agent, we consider an elementary study
participant. An agent is active; it is in a state that
may change under the influence of factors. The
properties of the agent are attributed characteristics
that form the level of immunity: height, weight,
gender, income, marital status, education, geography
This article focuses on the mathematical modeling of
evaluation of financial and economic activities of a
company and on definition (based on this model) of
such balance settings (line F1 and F2) which would
make financial-economic indicators of the activities of
the organization optimal, and the total cumulative
score was the maximum. The knowledge and the use
of the optimal parameters of the balance will allow the
managers to plan strategy for the future development
of the company. The article analyzes the dependencies
of each of the 15 basic indicators (profitability,
turnover, financial stability, liquidity and solvency) of
financial and economic activity of the organization on
the balance parameters. The optimal values of the
parameters of the balance and the main indicators of
financial and economic activities of the organization
have been found. We have also built a mathematical
model of optimal control of financial and economic
indicators in the form of a problem of mathematical
programming. For example, for the company called "Nika" it is shown the possibility of improving
estimation of financial and economic condition of the
organization. Knowledge of the optimal parameters of
the balance will allow the managers to plan strategy
for the future development of the organization. To
solve this problem we have used the method of
generalized reduced gradient implemented in Excel,
with which there was found a maximum of the
objective function for the article restrictions. The
article describes the analysis algorithm of the
optimization problem. A common assessment was
carried out in stages, based on the calculation
algorithm of sequentially improved target functions
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
When considering the ecological safety of industrial productions, territory, etc., we usually allocate the constant (permanent) risk and the accident (emergency) risk. Permanent risk is given by the used technology, and cannot be changed substantially. Emergency risks are associated with uncertainty, in contrast to the constant risks. Let in adopted mathematical model the uncertainty is probabilistic in nature, and the loss describes as one-dimensional random variable. The distribution function of the loss, as a rule, is not normal. We have discussed in detail the seven characteristics of accidental loss: expectation; median and, more generally, quantile; dispersion; standard deviation; coefficient of variation; a linear combination of the expectation and standard deviation; the expectation of the loss function. Risk management may be to minimize these characteristics and their combinations (in different variants of multicriteria optimization). For example, in the two-criteria formulation it is required to minimize the expectation of loss and the standard deviation. Two-criteria formulation one way or another is reduced to a one-criteria formulation. In addition to probabilistic methods of risk modeling, sometimes we consider methods for describing risk using by means of objects of non-numeric nature, in particular qualitative characteristics, concepts of the theory of fuzzy sets, interval mathematical and econometric models and other mathematical tools. The main problems of the theory and practice of ecological insurance have been discussed
The Euler function is very important in number theory
and in Mathematics, however, the range of its values in
the natural numbers has not been written off. The
greatest value of the Euler function reaches on Prime
numbers, furthermore, it is multiplicative. The value of
the Euler function is closely associated with the values
of the Moebius function and the function values of the
sum of the divisors of the given natural number. The
Euler function is linked with systems of public key
encryption. The individual values of the Euler function
behave irregularly because of the irregular distribution
of primes in the natural numbers. This tract is
illustrated in the article with charts; summatory
function for the Euler function and its average value
are more predictable. We prove the formula of
Martinga and, based on it, we study the approximation
accuracy of the average value of the Euler function
with corresponding quadratic polynomial. There is a
new feature associated with the average value of the
Euler function and calculate intervals of its values. We
also introduce the concept of density values of the
Euler function and calculate its value on the interval of
the natural numbers. It can be noted that the results of
the behavior of the Euler function are followed by the
results in the behavior of functions of sums of divisors
of natural numbers and vice versa. We have also given
the results of A.Z.Valfish and A.N.Saltykov on this
subject
The article is devoted to the discussion of the
organization of clinical-statistical studies and
experiments. We have considered the examples of
the application of statistical methods in scientific
medical research. Under the clinical-statistical
research we understand specially organized
collection and analysis of medical data about the
course of disease in patients, research of the
dynamics of objective and subjective indicators of
the state of reaction to these or other therapeutic
effects. We study one, two or more groups of
individuals (patients or healthy), conclusions are
drawn on the whole group, but not for each
individual patient. The purpose of research - to
transfer the conclusions reached for the sample to
the general population, i.e., clinical and statistical
study focused on the production of useful
recommendations concerning those patients who fall
into the field of view of doctors after the end of the
study. There are two main types of research -
prospective and retrospective. The first related to the
analysis of the last patients, the second - to
monitoring the course of their disease in the future.
We have considered typical mistakes in the
organization of clinical-statistical studies. When
planning a research, we usually distinguish the
experimental and control groups, which are identical
or similar in all respects except for the studied
factors (exposure). We discuss the various options
for blind methods and consider the application of
statistical models and methods in scientific medical
research. We have analyzed examples of confidence
estimation of proportion (probability) and the
homogeneity test of probabilities. For statistical
modeling we use the Poisson distribution in the case
of small probability. With its help, we analyze
statistical data on the opisthorchiasis