Modelling the Spectrum of Potency a Stationary Random Process in the Form of Spline First Order at the Random Number of Data in Instant of Time

The spectrum of potency as same the function of correlation is one of the most important characteristic of the second process random order. The spectrum of potency allows to judge about, that structure of process gives opportunity to take estimation of spectrum composition of useful signals and hindrances, allows to produce synthesis (reconstruction) the signals and to build filters and to obtain the estimates filtration. The purpose of this presenting work is modeling of process random stationary potency spectrum by random dates number in measurement moments. Using by probability theory methods and mathematical statistics was derived unbiased estimator of the potency spectrum in the form of spline first order, and were researched statistic characteristics estimation

The Simulation of the Trend of the Time Series in the form of the Spline of Third-Order With a Random Number of Data at the Moments of Measurement

The possibility of simulation of trend of a time series as a spline of third-order with a random number of data at the moments of measurement is discussed. Estimations of coefficients of the spline are obtained in the explicit form. The statistical characteristics of the received estimations are studied in details

Application of the "Fishbone" Technology in the Organization of Independent Work of Students in Higher Mathematics

Formation of a creative personality able to self-development, self-education, and innovative activity is the main objective of graduate education. In this regard, a special attention should be paid to the organization of independent work of students in a university educational process management. One of the most recognized types of independent work of students is a functional conspectus. “Fishbone” technology (a type of functional conspectus) is a method of cause-effect relationships structural analysis, which allows developing students' skills to work with information and their ability to formulate and to solve the problems. This paper deals with the application of this technology to the practical work on higher mathematics in order to increase the efficiency of the organization of independent work of students. Thus we have two objectives: first, to test the effectiveness of “Fishbone” technology in the organization of independent work, and second, to explore the possibility of using this technology in the higher mathematics university course. Comparative analysis of the test results of students who were trained with “Fishbone” technology application and without it demonstrates that its use can significantly increase the level of new information assimilation (in 19.8438%). Therefore, in future work we plan to consider applying other types of functional conspectus, such as insert, text markings, clusters, conceptual table and Bloom's chamomile to the course of higher mathematics in order to compare their efficiency in the organization of independent work of students and identify the most productive of them

Poster: The role of mathematical disciplines in engineering practice

The article describes mathematical education as an essential part of modern engineers' fundamental training system. The research determines the role of mathematics for engineering practice by analyzing responds of survey experts: engineers with PhD and doctoral degrees in the fields of natural sciences and technology and representatives of acting industrial enterprises of Russia. The purpose of this study is to analyze the role of mathematics in engineering practice. Additionally, the task of the paper is to analyze the relationship between students 'experience with school mathematics and their choice of an engineering career. The research uses the Likert scale as the ground basis. As a result of the study, a link was established between the level of proficiency in mathematics at school and the subsequent choice of an engineering specialty by respondents. Over 80% of responding engineers were successful in mathematics at school. High school students, who are successful in mathematics, continue their success as university students. The quality of mathematical education both in high school and at university has a great influence on future engineers. The study showed that professional engineers constantly use mathematical knowledge in their work

Probabilistic-statistical models of the dynamics of climatic changes in the Altai Mountains

A probabilistic-statistical parameterization of time series characterizing geological and climatic processes allows determining some regularities by an autocorrelation analysis of signals which differ in nature. The use of the autocorrelation method for analyzing data related to solar and tectonic activity and characterizing the level of stratospheric ozone (total ozone content), hydrothermal regimes (De Martonne aridity index), and wood structure (maximum density of annual rings) allows us to find regularities in time series of various natural processes. Data on the maximum density of Siberian larch trees growing in the Altai Mountains made it possible to calculate the past changes in total ozone content and the aridity index in the Altai Mountains from 1900 to 2014 based on some similarities in the series and a separation of a dendrochronological signal into its main components

Additive singular spectral model of a dendrochronological signal

Relevance. Allocation of structural components in a dendrochronological signal of annual rings of coniferous trees expands the possibilities of the bioindication method and allows obtaining information about changes in environmental conditions in the past for extended territories. Aim. Creation of an additive singular spectral model based on the frequency trigonometric components of the dendrochronological signal; reconstruction of changes in the total ozone content in the atmosphere in the past, affecting the level of ultraviolet radiation in the B range radiation. Objects. Time series of total ozone content in the atmosphere (data from 1932), width and density of annual rings (data from 1686–2004) on the example of the territory near the observatory in Arosa, Switzerland, time series of stable oxygen isotopes δ18Oc, France. Methods. Time series analysis (decomposition of a time series, identification of model parameters, prediction of a time series), statistical analysis (F-criterion, χ2 – Pearson criterion), experimental measurements of the percentage components of the wood of annual rings, correlation analysis, spectral singular analysis. Results. Decomposition of the dendrochronological signal of individual chronologies into trigonometric components in the Caterpillar program. Correlation analysis of the sensitivity of trees to atmospheric effects. Reconstruction of the ozone level in the stratosphere using the first trigonometric component of the dendrochronological signal. In cellulose, the first low-frequency component of the signal and the structural component of wood, a reliable response of trees to long-period fluctuations in the total ozone content is recorded. This allows assessment of the impact of the stress factor on conditions of exploitation of forest resources. The use of data on the width of the annual rings allows you to expand the territorial boundaries of the method

Justification of the identification of threats and problematic components of sustainable regional development in the security dimension

The issue of substantiation of the problematic components of sustainable development in the security dimension and threat identification methodology is investigated. The methodology consists of directly combining the identification of threats with the need to observe the limits of the safe existence of dynamic economic systems, which connects the problem of sustainable development with the problem of security. The explanation of the extended homeostatic plateau, which explains the conditions for the transition to a higher technological system, or the complication of functioning and the loss of the main functions of the existing technological system, has gained further development. A theoretical substantiation of the limits of secure existence in terms of security gradations is proposed: critical, threshold, and optimal on both sides of the “extended homeostatic plateau”. Quantitative values of security gradations are associated with the extension of the “t-criterion” method for the formal determination of bifurcation points for characteristic types of distribution, that is, threats. The identification, classification, and analysis of problematic components and critical threats at the level of components and indicators were carried out, which made it possible to identify only four strategic directions of institutional measures that allow covering almost all indicators of sustainable development at the regional level

Project activity in the formation of subject competencies

The project-based learning has long established itself as one of the most stimulating methods of mastering the educational program. However, to study in depth of mathematical disciplines, project tasks must be specifically formulated for the topic being studied. The purpose of this work is to study the methodological relationship between the declared projects and the studied topic of mathematics, as well as a comparative analysis of the results of the development of three mathematical disciplines using the project method and without it. The work on the projects has been carried out for three years at our university and it is aimed at activating the independent cognitive activity of students. In 2018-2019, these were applied and educational projects, the topics for which were selected by teachers. In 2019-2020, students were given the right to independently choose a project topic based on their scientific interests and develop it. In one experimental group, students had the opportunity to consult with the teacher to find a solution to the project problem, in the other such an opportunity was not available. The results of both groups were roughly the same. The conclusion that we came to as a result of this work: project activity increases the horizons of students and allows us to see interdisciplinary connections. Project activity is more effective only if the student works closely with the teacher