The correlation and determination coefficients are widely used in statistical data analysis. According to measurement theory, Pearson's linear paired correlation coefficient is applicable to variables measured on an interval scale. It cannot be used in the analysis of ordinal data. The nonparametric Spearman and Kendall rank coefficients estimate the relationship of ordinal variables. The critical value when testing the significance of the difference of the correlation coefficient from 0 depends on the sample size. Therefore, using the Chaddock Scale is incorrect. When using a passive experiment, the correlation coefficients are reasonably used for prediction, but not for control. To obtain probabilistic-statistical models intended for control, an active experiment is required. The effect of outliers on the Pearson correlation coefficient is very large. With an increase in the number of analyzed sets of predictors, the maximum of the corresponding correlation coefficients — indicators of approximation quality noticeably increases (the effect of “inflation” of the correlation coefficient). Four main regression analysis models are considered. Models of the least squares method with a determinate independent variable are distinguished. The distribution of deviations is arbitrary, however, to obtain the limit distributions of parameter estimates and regression dependences, we assume that the conditions of the central limit theorem are satisfied. The second type of model is based on a sample of random vectors. The dependence is nonparametric, the distribution of the two-dimensional vector is arbitrary. The estimation of the variance of an independent variable can be discussed only in the model based on a sample of random vectors, as well as the determination coefficient as a quality criterion for the model. Time series smoothing is discussed. Methods of restoring dependencies in spaces of a general nature are considered. It is shown that the limiting distribution of the natural estimate of the dimensionality of the model is geometric, and the construction of an informative subset of features encounters the effect of "inflation coefficient correlation". Various approaches to the regression analysis of interval data are discussed. Analysis of the variety of regression analysis models leads to the conclusion that there is no single “standard model”
Among the widely used economic-mathematical models, dynamic programming plays an important role, and among them, models with discounting. The most famous example is the model for calculating the net present value (NPV) as an estimate of the efficiency of the investment project. In the article, it is clarified which features are distinguished by models with discounting among all models of dynamic programming. In models with discounting, the comparison of plans does not change when the time of the beginning of the implementation of plans changes, ie. there is a stability of the results of comparing plans. It is proved that if the results of comparing plans for 1 and 2 steps are stable in the dynamic programming model, then this model is a model with discounting. This theorem shows that the introduction of discounted functions for the estimation of the effect is justified only in stable economic conditions in which the orderliness of managerial decisions does not change from year to year. In other words, if at the beginning of the period under consideration the first solution is better than the second, then at all other times, up to the end of the period under consideration, the first solution is better than the second. Stable economic conditions are rarely found in the modern economy with its constant changes, including those caused by innovations. Therefore, the decision to choose (to implement) an investment project from a set of possible ones can not be based solely on the calculation of discounted project performance indicators, such as net present value and internal rate of return. Such indicators can only play a supporting role. Decide on the choice of an investment project for implementation is necessary on the basis of the whole range of social, technological, environmental, economic, political factors
The article provides a comparative analysis of assessments of the socio-economic development of the Krasnodar region from such well-known rating agencies as Standard & Poors, Moody’s, Fitch Ratings, which belong to the United States of America. The studied ratings are compared with the ratings of the national agency of the Russian Federation called “Expert RA”. The values of the established ratings are examined, as well as number of possible reasons why the ratings of the United States of America differ from the ratings of the Russian Federation, for example, economic and political reasons, and, subsequently, how these ratings affect the investment attractiveness of the Krasnodar region. The article explains positive and negative aspects of the integrated methodology used by international rating agencies, consisting of software and expert opinion, the level of access to it for study and analysis. We study another (local) source of information on the investment attractiveness of the Krasnodar region, which is a state institution, namely the Department of Investments and Development of Small and Medium Enterprises of the Krasnodar region. Options are proposed for improving the system of analysis of statistical data through methods that are based on a clear mathematical approach to provide an adequate assessment of the region and municipalities without the influence of subjective expert opinion
The article studies the influence of the plant growth regulator of the retardant type called HEFK (AS 480 g/l of etephone) on the yield and structural elements of winter wheat of Moskovskaya 39 variety under the conditions of the OAO Veryakushi Agricultural Entreprise, located in the north-eastern part of Diveyevo region on gray forest medium loamy soil. Field studies were being carried out for three years: from 2016 to 2019. We studied different application rates of HEFK: 0.5; 1.0; 1.5; and 2.0 l / ha. The processing of winter wheat crops was performed in the phase of the beginning of exit into the tube. On average, over 3 years, the indicators of field germination of seeds and the survival rate of plants at harvest were good and amounted to 88.4-89.2% and 80.1 - 81.3%, respectively. The processing crops by HEFK in doses of 0.5 and 1.0 l / ha, showed the highest crop yield of - 4.07 and 4.12 t / ha, which exceeded the control rate by 0.29 and 0.34 t / ha, respectively. The growth regulator did not showed a significant effect on the density of the productive stem. At the same time, the treatment of HEFK crops in doses of 0.5 and 1.0 l / ha showed an increase in the spike productivity by 0.121-0.133 g due to an increase in spike grains by 3 pcs. In the variant with a HEFK use rate of 1.0 l / ha, the weight of 1000 grains increased by 0.6 g compared to the control rate. An increase in the dose of the growth regulator significantly reduced the height of wheat plants from 72.1 cm in the control group to 48.0 cm in the variant with a product application rate of 2.0 l / ha. The spike length in the variants with the application rate of HEFK of 0.5 and 1.0 l / ha was at the control level - 7.0-7.1 cm, whereas an increase in the dose of the growth regulator to 1.5-2.0 l / ha showed the decrease in the length of the spike by 0.5-0.8 cm. When using growth regulator HEFK resistance of crops to lodging varied from 4.7 till 5.0 points
This article discusses the general principles of developing software applications for generating and verifying practical tasks in mathematical disciplines in the Visual Basic for Application development environment. The article describes the structure of computer programs, the main components of the implemented macros are also investigated, the algorithms of the basic procedures are given. A special place is given to the problems of identifying students and protecting the generated data. We have also given recommendations on the use of developed programs in the educational process
In the article, we develop the methodology of strategic planning and management of a holding, on the theoretical basis of automated system-cognitive analysis (ASC-analysis). This methodology provides scientific research of any holding by creating and researching its model. The methodology includes both the synthesis, adaptation and verification of system-cognitive models of the holding, and the use of these models for strategic planning and decision support for the management of the holding, as a complex, multiparametric, nonlinear system. The relevance of the research is due to the special role of holdings and other corporate integrated structures both in Russia as a whole and, in particular, in the Krasnodar region. Despite obvious system advantages, holdings face a wide range of problems related to management efficiency, ensuring their sustainable functioning, etc. The proposed methodology offers ways to solve these problems and can be successfully applied in holdings and other corporate integrated structures of various regions, volumes and areas of activity, which determines the relevance of the research topic. The level of significance and scientific novelty of the Research consists in the development of conceptual and theoretical and methodological provisions aimed at managing the development of holdings. The expected results and their significance are that the methodology developed as a result of the Research can be applied by holding companies and other corporate integrated structures and will significantly improve the quality of their management
As a result of the analysis of the scientific question, there is a steady trend of growth in food consumption, especially of plant origin. To this issue, it is also necessary to add the provision of food security of the country and the exclusion of dependence on foreign producers. Thus, before science and production is a serious question of a significant increase in the production of crop products with a slight increase in the cost of these types of work and the main thing is to ensure the preservation of soil fertility. This can be achieved by reducing the use of chemical means of protection, less intensive impact on the treated environment by the running systems of power facilities and the working bodies of machines, but in compliance with the primary requirements for the treated surface. The proposed design of a horizontally arranged spherical disk working body can be used in various tillage machines for shallow and surface tillage. The design of the working body allows reducing the passes of the unit to perform the necessary agricultural requirements for equalization and ridges of the soil. And these indicators have a significant impact on the quality of sowing, which will necessarily affect the yield in the end. Comparative studies of the proposed working body and the same devices used in production show a clear advantage of the new scheme
The work is devoted to studying the productivity of an ear of winter soft wheat samples from the collection of the All-Russian Institute of Plant Genetic Resources named after N.I. Vavilov (VIR). The study attempted to conduct a pre-selection study of collection material on the elements of spike productivity. The concept of pre-selection research is based on the study of initial collection material according to given characteristics in order to identify the best genotypes for further use in breeding practice. In the analysis of the collection material, the following characteristics were used as indicators of spike productivity: length of the main spike (cm), number of spikelets in the main spike (pcs), number of grains in the main spike (pcs), grain weight from the main spike (g), 1000-kernel weight (g). Plant height was one of the basic indicators of the studied material, because a number of samples differed in alleles of short-stem genes. According to the results of two years of research, according to the indicator «1000-kernel weight», the varietal sample Cologna lunga razza 188 (Italy) was identified as 71,20 g. According to the indicator «number of grains in an ear», the varietal sample Fenotipo 1 (Italy) was 57,3 g. Also according to the totality of indicators, the varietal sample Kaloyan (Bulgaria) with an average of two years of research with a 1000-kernel weight – 51,77 g, the number of grains in an ear – 51,6 pcs. and a mass of grains per ear – 2,71 g.
The review article describes the role of tomato gene mutations in the creation of new cultivars and hybrids suitable for mechanized harvesting. The work gives characteristic of different genes associated with morphological characteristics of tomato plants, types of fruit (flower) brush and peduncle. The genes controlling the shape and size of the fruit, its resistance to cracking and mechanical effects are noted, the value of these genes for the breeding of machine cultivars and hybrids is shown. The article emphasizes the need to create new cultivars and hybrids of tomato suitable for mechanized harvesting with high quality fruits, evenly colored, without green spots at the base, corresponding to the basic requirements of the processing industry. The figures illustrate gene mutants that are of the greatest interest for the breeding of cultivars, suitable for mechanized harvesting
In the process of formation of nonlinear dynamics, the scientific society was able to refute the classical mechanisms of Newton-Laplace by justifying the chaotic nature of the phenomena of the world. However, despite the emergence of new mathematical models and tools, forecasting of nonlinear systems is a difficult task, as not only the quantitative and qualitative characteristics of the factors affecting the system are unknown, but also there is a problem of a small amount of information for forecasting. In this article, the authors consider the linear cellular apparatus as a tool for prediction the final state, to which the system will come based only on its output indicators of previous years. Since the use of a linear cellular automaton for prediction of nonlinear systems is an assumption of the authors, it should be tested on the series of stochastic systems exposed to different risk factors, which together give either a positive response of the system or a negative one. An example of such series is the time series of yields, as it is affected by climatic conditions, the appearance of which, in turn, is also difficult to predict. Prediction of stochastic systems using linear cellular automaton really makes it possible to get adequate and visual models. Due to the fact that the forecast model has a discrepancy with the real result of 0-15% (both positive and negative), the conclusion is that the predicted value will help either to take measures to ensure that the real value in the future is not lower, or to make sure that the decisions and measures taken are correct, when a value is higher than the forecast