Geometrical constructions and analysis in population capture cohorts

Introduction. The article examines the problem of assessing students' academic performance in the current situation. The purpose of the paper is to evaluate the influence of e-learning and some social and behavioral parameters on students’ academic performance. Materials and Methods. The author employed the machine learning procedures in order to identify and assess the current problems of the educational system, students’ behavior, and universities’ policy. Methods of mathematical analysis and statistics as well as ensemble methods (gradient boosting and the random forest algorithms) were used in order to achieve high accuracy of the research. Results. The author conducted the analysis of the following datasets devoted to academic performance at higher and secondary educational institutions in a number of countries: Students’ Performance in Portugal, E-learning Student Reactions and Students’ Academic Performance. The purposes of the current study were to identify statistical correlations between social parameters of students and the level of their academic performance and to understand how academic performance is determined by the implementation of online learning and blended learning. The research findings suggest that mathematical statistics and data analysis methods allow to identify correlations between students’ performance data and reveal hidden relationships which can be important for university staff. Conclusions. In conclusion, the author summarizes the results of evaluating the impact of the introduction of e-learning elements and some social parameters on students’ academic performance. Keywords Clustering students; Blended learning; Academic performance evaluation; Digitalization of education; Digital technologies in education; Correlation of features; performance improvement.

Introduction. Mountains territories play a key role in the sustainable development of the Russian economy, since the economy of flat territories largely depends on mountain resources. The successful solution of this problem largely depends on the methods used to form and implement the state financial policy. The purpose of the article is to develop a simulation management model that helps improve the efficiency of public financial decisions for sustainable development of mountainous areas of Russia using economic and mathematical methods of multidimensional data analysis. Statement of the problem and solution method. The task is to decompose regions of Russia, including mountainous territories, into clusters according to a vector assessment indicator that determines their ability to self-development, based on the application of the c-means method. Assessment of the development of mountainous territories. Currently, mountainous regions are lagging far behind in economic development. The authors have presented a list of subjects with mountainous terrain that are subject to subsidies. It is concluded that interbudgetary regulatory measures have a significant impact on changing the economic level of development of these territories. Research areas on the concepts of hard and soft budget constraints. It is shown that the works of Russian and foreign authors focus on issues of fiscal policy in solving spatial development problems. At the same time, the phenomenon of decentralization of public goods is considered as the most important factor in economic development. The author's position is formulated, which consists in assessing the feasibility of using an individual approach to the application of the concepts of «soft» and «hard» budget constraints based on the use of mathematical methods of multidimensional data analysis. Results and discussion. As a result of decomposition of Russian federal districts using the c-means method, clusters were built, which include territories with a high, medium and low degree of self-development. Recommendations are given for each cluster regarding the application of budget constraints concepts. Conclusion. The article proposes and tests an approach based on the use of economic and mathematical methods of multidimensional data analysis, which made it possible to develop a simulation model for making predictive decisions on interbudgetary regulation that contribute to increasing the effectiveness of financial policy for the sustainable development of mountainous areas in Russia. Suggestions for practical applications and directions for future research. The proposed approach, based on the application of economic and mathematical methods, allows for scientific and quantitative justification of decisions taken in the sphere of interbudgetary regulation and can be used in the process of financial policy forming aimed at sustainable development of mountainous regions of Russia.

Aims To understand the reasons for the decline in the birth rate of our country, the effects of the decline in the birth rate and the countermeasures needed to reduce the birth rate, as well as the urgency of the reform of education, especially art education. Methods Using a mathematical statistical analysis method, the decline of the birth rate in our country was statistically analysed, and the influence of education, especially art education, was discussed. Results The results show that the birth rate of China's population decreased significantly, that is, from 36% in 1949 to 23.3% in 1987 and from 12.95% in 2016 to 10.8% at present. This has a significant impact on the manpower of all walks of life. Students at all levels and all kinds of schools have brought about a greater impact. Higher education, especially art education, has a greater impact. Conclusions In the face of the decline in the birth rate, corresponding countermeasures must be taken to strengthen the development of maternal and child health care and medical resources. In-depth reform or correction of the current compulsory education must be assessed in order to relieve the worries of women who have given birth so that the birth rate increases within the framework of a reasonable, normal span of time and demonstrates smooth development. In order to ensure that China has sufficient human resources and enough students at all levels and all kinds of schools, the reform of art education is deepened, thus facilitating training of the talents of world-class masters.

The purpose of the study is to assess and predict the adaptation of workers of coke-chemical production to working conditions. An assessment is presented to the influence of harmful production factors on the body of workers of coke-chemical production in the process of adaptation to working conditions. The level of influence on the body of harmful production factors was estimated with using a method of multidimensional mathematical analysis of experimental data - solid correlation analysis. For this, intrasystem and intersystem links of physiological systems (PhS) were determined. With using the method of mathematical analysis, the diagnosis was carried out and the evaluation criteria were specified making possible to evaluate and predict the current state of health and level of efficiency of physiological systems. Quantitative criteria are specified for identifying the groups of "risk" and disability depending on the share of participation in professional and production activities, age and experience. Analysis of the systemic interaction of the PhS showed the predominance of intrasystem links over intersystems. The factor disperse analysis showed that the PhS stress indicators reflecting the condition of the body's functions were worsened with an increase in not only age, but also professional experience. Indicators of the age - length of service categories of the surveyed workers completely repeat a set of compensatory connections formed in the studied age groups, which made it possible to assume the existence of a single regulatory mechanism that ensures the sustainable functioning of the body as a biological system. It is shown that the low level and premature performance decrement, the exhaustion of functional reserves of the body's adaptation to the effects of a complex of harmful factors of the production environment significantly reduce occupational fitness of workers in the system "Man - labor factors - health". Keywords: working conditions, adaptation, factor analysis, diagnosis, intersystem and intrasystems links.

The use of mathematical methods in economic analysis is the most important direction for improving control systems. Mathematical methods speed up economic analysis, increase the accuracy of calculations, and more fully take into account the influence of factors on productivity. Using mathematical methods requires the following: 1. Development of mathematical models reflecting the quantitative indicators of the systemic activity of employees of the organization, processes occurring in complex systems such as enterprises; 2. A systematic approach to the study of a given object, taking into account its relationships and connections with other objects (enterprise, firm); 3. Improvement of the enterprise management information system using an electronic computer. The solution of problems of economic analysis by mathematical methods is possible only when constructing mathematical ones, i.e. real economic relations and dependencies of expressions using mathematical analysis. This necessitates the development of mathematical models. Mathematical methods play an important role in economic analysis, since they can provide accurate calculations and a complete account of the influence of factors using short-term forecasting methods and making management decisions at the enterprise. The thesis reflects the results of research and development in the field of analysis of economic processes and systems based on the use of economic and mathematical methods and tools. The mathematical apparatus of economic research is being developed, and it is proposed to integrate applied methods and solutions into efficiency improvement tools. The model approach, which arose in ancient sciences in antiquity, gradually turned into a universal method of scientific knowledge. Currently, the importance of using mathematical methods in the analysis of economic processes is indispensable both from the point of view of a more serious substantiation of theoretical concepts, and the ability to quantify economic relations. The research presented in the thesis will be useful to everyone who is interested in the theory of mathematical methods of economics. Some of the presented methods and models can be used directly by practitioners in this field.

The use of mathematical methods in economic analysis is the most important direction for improving management systems. Mathematical methods speed up economic analysis, increase the accuracy of calculations and more fully take into account the impact of factors on productivity. The use of mathematical methods requires: - development of mathematical models reflecting quantitative indicators of system activity of the organization's employees, processes occurring in complex enterprise-type systems; - a systematic approach to the study of this object, taking into account its relationships and connections with other objects (enterprise, firm); - improvement of the enterprise management information system with the help of IT technologies. Solving tasks of economic analysis by mathematical methods is possible only when constructing mathematical, that is, real economic relations and dependencies of expressions using mathematical analysis. This calls for the development of mathematical models. Mathematical methods play an important role in economic analysis, as they can provide accurate calculations and full accounting of the influence of factors using short-term forecasting methods and management decision-making at the enterprise. The article highlights the results of research and development in the field of analysis of economic processes and systems based on the use of economic and mathematical methods and tools. The mathematical apparatus of economic research was developed and it was proposed to integrate applied methods and solutions into efficiency improvement tools. The model approach, which arose in the ancient sciences, gradually turned into a universal method of scientific knowledge. Currently, the use of mathematical methods in the analysis of economic processes is indispensable both from the point of view of a more serious substantiation of theoretical concepts and the ability to quantitatively determine economic relations. The research presented in the article will be useful for everyone who is interested in the theory of mathematical methods of economics. Some of the presented methods and models can be used directly by practitioners in this field.

Productivity rate (Q) or production rate is one of the important indicator criteria for industrial engineer to improve the system and finish good output in production or assembly line. Mathematical and statistical analysis method is required to be applied for productivity rate in industry visual overviews of the failure factors and further improvement within the production line especially for automated flow line since it is complicated. Mathematical model of productivity rate in linear arrangement serial structure automated flow line with different failure rate and bottleneck machining time parameters becomes the basic model for this productivity analysis. This paper presents the engineering mathematical analysis method which is applied in an automotive company which possesses automated flow assembly line in final assembly line to produce motorcycle in Malaysia. DCAS engineering and mathematical analysis method that consists of four stages known as data collection, calculation and comparison, analysis, and sustainable improvement is used to analyze productivity in automated flow assembly line based on particular mathematical model. Variety of failure rate that causes loss of productivity and bottleneck machining time is shown specifically in mathematic figure and presents the sustainable solution for productivity improvement for this final assembly automated flow line.

This paper deals with development of a method for the data analysis of medical expert system by pulse diagnosis. One of the main directions of an application for artificial intelligence in medical practice is attempts to build a new clinical decision-making support system at the expert-level. Medical diagnosis is based on the pathophysiological process, which is a not very common in compared to other approaches, as described by several disease symptoms. As a result, scientists were developed different methods for the medical data analysis. Among these methods, mathematical methods for medical data analysis have been actively developed with compare to other working methods.

The aims of this research was to develop learning device of Advanced Calculus 1 subject with scaffolding-based problem-solving abilities that include syllabi, lesson plan, learning media, student worksheets and assessment, and determine the effectiveness of the implementation of scaffolding-based learning problem-solving abilities in the subject Advanced Calculus 1.This research was a Research and Development (R & D). Methods of data analysis done by using triangulation mix-design method by simultaneously analyze data from quantitative and qualitative data as well as data combined. The results showed that the development of the learning course Advanced Calculus 1 with scaffolding based problem solving ability using learning device development of Borg and Gall models which has been modified. Results of learning device development course Advanced Calculus 1 consists of a syllabi, lesson plan, student worksheet, observation sheets and feasible achievement test used. Furthermore limited trial obtained tvalue ?»Oe¼?¢7,440 ?»Oe¼?¥ ttable ?»Oe¼?¢1,645 so H0 is rejected. This shows that the average learning outcomes with scaffolding better than conventional learning. ?e?a Key w ords : Scaffolding, Learning devices, Advanced Calculus 1

The compressibility and shear strength of soil play a crucial role in engineering design and construction. For this study, samples were collected from the indoor geotechnical tests conducted on the fourth layer of the third series of the Haikou Formation. By conducting a correlation analysis of various physical properties of soil and utilizing the random forest algorithm, we developed a predictive model for the compressibility and shear strength of coastal soft soil. Initially, we proposed an empirical formula that utilizes mathematical statistical analysis methods to characterize the correlation between the indicators of this soil. Subsequently, we employed the feature selection guided by the aforementioned data analysis results to establish a random forest model. This model predicts the compressive modulus, compressibility coefficient, cohesion, and internal friction angle of the soil. The results indicate that the established model exhibits strong predictive capabilities, with the mean squared error values of compression modulus (0.012), compression coefficient (1.21× 10−6), cohesion (0.081), and internal friction angle (0.003). The data analysis methods, fitting parameters, empirical formulas, and random forest model employed in this study hold substantial value in guiding the preliminary evaluation stage of engineering projects with limited data. This study helps to save time and cost of geotechnical investigation for soft soils in the area.

In this chapter, advanced mathematical modeling, simulation, and data analysis methods are described, which are applied to biological problems at the molecular level. An introduction to molecular mechanics is given and fundamental principles are described such as chemical formulas, molecular structure, and polarity. Then, the significant role of molecular bioengineering in areas critical to human health is presented focusing on the effect of computational modeling at molecular level on cell biology, diagnostic medicine, preventive medicine, and therapeutic medicine.

Chromatographic dispersion corrections utilizing the generalized exponential function

Objectives. COVID-19 has a number of specific characteristics that distinguish it from past pandemics. In addition to the high infection rate, the high spread rate is due to the increased mobility of contemporary populations. The aim of the present work is to construct a mathematical model for the spread of the pandemic and identify patterns under the assumption that Moscow comprises the main source of viral infection in Russia. For this purpose, a twoparameter kinetic model describing the spatial spread of the epidemic is developed. The parameters are determined using theoretical constructions alongside statistical vehicle movement and population density data from various countries, additionally taking into account the development of the first wave on the examples of Russia, Italy and Chile with verification of values obtained from subsequent epidemic waves. This paper studies the development of epidemic events in Russia, starting from the third and including the most recent fifth and sixth waves. Our twoparameter model is based on a kinetic equation. The investigated possibility of predicting the spatial spread of the virus according to the time lag of reaching the peak of infections in Russia as a whole as compared to Moscow is connected with geographical features: in Russia, as in some other countries, the main source of infection can be identified. Moscow represents such a source in Russia due to serving as the largest transport hub in the country.Methods. Mathematical modeling and data analysis methods are used.Results. A predicted time lag between peaks of daily infections in Russia and Moscow is confirmed. Identified invariant parameters for COVID-19 epidemic waves can be used to predict the spread of the disease. The checks were carried out for the wave sequence for which predictions were made about the development of infection for Russia and when the recession following peak would occur. These forecasts for all waves were confirmed from the third to the last sixth waves to confirm the found pattern, which can be important for predicting future events.Conclusions. The confirmed forecasts for the timing and rate of the recession can be used to make good predictions about the fifth and sixth waves of infection of the Omicron variant of the COVID-19 virus. Earlier predictions were confirmed by the statistical data.

Chapter 16 - High-throughput phenotyping: the latest research tool for sustainable crop production under global climate change scenarios

This article studies the convergence characteristics of a genetic algorithm (GA) in which individuals of different age groups in the population possess different survival and birth rates. The inclusion of this feature into the algorithm makes the algorithm mimic the natural evolutionary process more closely than the conventional GA. Although numerical experiments have demonstrated that the proposed algorithm tends to perform better than the conventional GA when used as a function optimizer, the population size of the algorithm is affected by the survival and birth rates of the individuals, which may lead to an unstable search process. Hence, this research develops the condition which governs the birth and survival rates for maintaining a stationary population size during the search process. The Markov chain approach is also used to analyze the convergence characteristics of the algorithm. The proposed algorithm is shown to converge to the global optimal solution if the best candidate solution is maintained over time. The mathematical analysis thus provides a theoretical foundation for the application of the proposed approach as a function optimizer. The performance of the proposed algorithm is tested by solving two benchmark test problems and the results are compared to those obtained by using the conventional GA. Indeed, comparison of the results clearly shows that the proposed approach is superior to the canonical genetic algorithm in terms of the quality of the final solution. The algorithm is described in some detail in the hope of thus stimulating the use of the proposed genetic approach to the solution of important problems in industrial engineering practice.