Some estimators of the probability density function
in spaces of arbitrary nature are used for various
tasks in statistics of non-numerical data. Systematic
exposition of the theory of such estimators has been
started in our articles [3, 4]. This article is a direct
continuation of these works [3, 4]. We will regularly
use references to conditions and theorems of the
articles [3, 4], in which introduced several types of
nonparametric estimators of the probability density.
We have studied linear estimators. In this article, we
consider particular cases - kernel density estimates in
discrete spaces. When estimating the density of the
one-dimensional random variable, kernel estimators
become the Parzen-Rosenblatt estimators. Under
different conditions, we prove the consistency and
asymptotic normality of kernel density estimators.
We have introduced the concept of "preferred rate
differences" and are studied nuclear density
estimators based on it. We have introduced and
studied natural affinity measures which are used in
the analysis of the asymptotic behavior of kernel
density estimators. Kernel density estimates are
considered for sequences of spaces with measures.
We give the conditions under which the difference
between the densities of probability distributions and
of the mathematical expectations of their nuclear
estimates uniformly tends to 0. Is established the
uniform convergence of the variances. We find the
conditions on the kernel functions, in which take
place these theorems about uniform convergence. As
examples, there are considered the spaces of fuzzy
subsets of finite sets and the spaces of all subsets of
finite sets. We give the condition to support the use
of kernel density estimation in finite spaces. We
discuss the counterexample of space of rankings in
which the application of kernel density estimators
can not be correct
Parameters describing periodic trends in the formation of nuclear shells have been established based on the theory of nuclear interactions and data on the binding energy of nucleons for the set of known nuclides
Parameters describing periodic trends in the formation of nuclear shells have been established based on the theory of nuclear interactions and data on the binding energy of nucleons for the set of known nuclides
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
Following the absence of a definite treatment for the human immunodeficiency virus (HIV) or the acquired immune deficiency syndromes (AIDS) since their appearance, many scientific studies with the help of mathematical models have been formulated to the extent possible to prevent and eradicate the disease. In this article we have formulated a mathematical model that explores the dynamics of the impact of the use of condom and therapeutic treatment simultaneously, as a means (tools) against the spread of HIV/AIDS in the heterosexual population. The proposed model uses a nonlinear differential equation system consisting of seven (7) differential equations in seven (7) groups of the population. The model takes into account natural birth rate of the studied population, and the proportion of infected males, which simultaneously uses condom and antiretroviral therapy. The model explores the behavioral change of proportion of infected individuals in the population following the application of control measures (condom use and antiretroviral therapy). It is proved that the effectiveness of preventive measures greatly depends on a number of parameters described. In addition, the results of numerical experiments showed that in the absence of both preventive measures, the entire population is contaminated with the infection. The interaction of the model parameters show that the population with high levels of condom use in the presence of significant adherence to antiretroviral therapy as prophylaxis significantly reduces the level of HIV/AIDS. Thus, prevention of infection is significantly improved with the increasing number of the infected population using condoms and antiretroviral therapy simultaneously
In this article we consider a mathematical model of effect of non-compliance with the prevention of HIV/AIDS among a heterogeneous population based on known model by Kimbir et al (2006). The effectiveness of a condom use and implications of non-compliance with a population of preventive measures (condoms) are the aim of this research work. In this work, with definite coefficients, nonlinear model is used, which consists of system of six differential equations for different population groups (six groups of the population) to obtain the model equations. Compared with the existing model by Kimbir, the proposed model to a large extent, takes into account the birth rate of the studied population. Numerical simulation of the model equations shows that reducing the rate of transmission of HIV/AIDS can be effectively achieved within a certain time, and only where relatively high condom efficacy and high compliance by susceptible and infected are observed. From the obtained results, we can see that the control of HIV/AIDS in the heterosexual population depends on the net compliance and effectiveness of the recommended prevention (condom use). As a recommendation, the model focuses on intensive training and ongoing campaigns to raise the awareness of the population by governmental and non-governmental agencies on the effective use of the condom
Small business is an important part of modern Russian economy. We give a wide panorama developed by us of possible approaches to the construction of economic-mathematical models that may be useful to describe the dynamics of small businesses, as well as management. As for the description of certain problems of small business can use a variety of types of economic-mathematical and econometric models, we found it useful to consider a fairly wide range of such models, which resulted in quite a short description of the specific models. In this description of the models brought to such a level that an experienced professional in the field of economic-mathematical modeling could, if necessary, to develop their own specific model to the stage of design formulas and numerical results. Particular attention is paid to the use of statistical methods of non-numeric data, the most pressing at the moment. Are considered the problems of economic-mathematical modeling in solving problems of small business marketing. We have accumulated some experience in application of the methodology of economic-mathematical modeling in solving practical problems in small business marketing, in particular in the field of consumer goods and industrial purposes, educational services, as well as in the analysis and modeling of inflation, taxation and others. In marketing models of decision making theory we apply rankings and ratings. Is considered the problem of comparing averages. We present some models of the life cycle of small businesses - flow model projects, model of capture niches, and model of niche selection. We discuss the development of research on economic-mathematical modeling of small businesses
There is a widely known problem regarding the
ordering of the partially ordered sets (Linear Ordering
Problem). It boils down to finding the numerations of
such sets. The main result of this article is a
generalization of one of the known S. S. Kislitsyn's
results about finding the number of numerations of
finite partially ordered sets
In this article, we discuss various issues related to the
formulas approximating the distribution function of
prime numbers pi(x). This question has occupied many
scholars, but the exact function is well approximated
function pi(x) over the number of positive integers not.
Based on certain hypotheses, we present a new
function s(x) is very well approximated pi(x). The
above article hypotheses are so important that their
numerical validation and refinement for the lengths of
the segments more in 1014 - one of the main areas
related to the problem of approximation of the function
pi(x) throughout the series of natural numbers. After
analyzing the behaviors and constructs many
functions, we are building the basis of the function
s(x), which is well approximates the function pi(x)
throughout the series of natural numbers. We also
present a table of values for x, less or equal 1022 for the
difference of s(x) - pi(x)
Inventory management (in other words, logistics) is an integral part of the work of firms, companies and organizations. We are talking about stocks of raw materials, fuel, tools, components, semi-finished products, finished products for industrial (or agricultural) firms, about stocks of goods to distribution centers, warehouses, shops, workplaces sellers, finally consumers. Stocks spent all the time and supplemented on various rules adopted in the firm. Optimization of these rules, ie, optimal inventory management, gives a big economic effect. The mathematical theory of inventory management, based on the models of movement of flows of goods, is an important area of economic-mathematical research. The classical model of inventory management proposed in 1915 by F. Harris is one of the simplest and most illustrative examples of application of the mathematical apparatus for decision-making in the economic field. This model is commonly referred to as the Wilson model, because this model became known after the publication of R.G. Wilson in 1934. The formula of the optimum batch size (the so-called "the formula of the square root"), obtained in the Wilson model, is widely used on various stages of production and distribution, since this formula is practically useful for decision-making in the inventory management, in particular, for generating significant economic effect. However, contrary to popular belief, by means of this formula it is impossible to calculate the optimal batch size (although it is a necessary step on the path of its finding). In strict economic-mathematical analysis of Wilson model, conducted in the article, it is shown that the formula of square root does not give the optimal batch size. We have given the algorithm for calculating the optimal batch size. It has been found that the formula of the square root gives asymptotically optimal plan. We have studied the stability of the conclusions in the economic-mathematical model and considered an example of the practical application of the classical model of inventory management