Dynamic Model of Impact Energy Absorption by a Conveyor Belt in Interaction with the Support System

Measurements of the dynamic load of conveyor belts of identical strengths were used to evaluate and compare the data for belts with and without a support system. The goal was to identify the effects of the support system in terms of a relative amount of impact energy absorbed by a conveyor belt. A dynamic model was designed based on selected parameters of the impact process. Damage to conveyor belts, caused by the absorption of impact energy, was evaluated using the applied methods of mathematical statistics.

Investigation of piston ring wear engines by the mathematical statistics method

Improving the reliability and durability of internal combustion engines makes it possible to increase productivity and reduce the cost of operation. The study of nature and magnitude of piston rings wear is relevant and represents a scientific novelty. During the operation of internal combustion engines, it is almost impossible to determine the influence of various factors on the wear rate and the resource of piston rings. One of the most accurate ways to study the wear intensity and the service life values of internal combustion engines piston rings during operation is the statistical method. The method of mathematical statistics allows us to study the nature and magnitude of individual parts wear with a sufficient degree of accuracy, to determine the main causes of wear, to outline ways of increasing the parts wear resistance, to establish durability criteria, to reasonably assign standard service life of parts and plan the parts need for any period with a given probability, with climatic conditions being taking into account. The article presents the collected statistical material on the internal combustion engines piston rings wear of construction and road vehicles operated at construction sites of Rostov region. It has been processed according to the normal Gauss law and data on the wear and service life of piston rings are obtained. The obtained experimental data on the wear of piston rings in height are reliable to the distribution law and can be used to determine the intensity of engines piston rings wear at repair enterprises.

On the Use of the Wilcoxon Criterion in the Practice of Pedagogical Research

The article discusses the use of nonparametric measures of influence in pedagogical research. The Wilcoxon criterion for comparing indicators obtained as a result of measurements in a connected sample is highlighted. The necessary conditions for the application of the criterion, as well as the advantages of its use are indicated. The possibility of using the Wilcoxon criterion is illustrated by the example of determining the effectiveness of the proposed teaching methodology using the Uchi.ru online platform in educational activities. Most modern studies in the field of pedagogy and psychology, along with qualitative descriptions of the results of the research, actively use quantitative analysis. Last analysis includes processing of the data using methods of mathematical statistics. In order to show the effectiveness of the developed methodology for the learning process, it should be considered as a factor influencing changes in the studied trait. Further study of these changes allows the researcher to determine the statistical reliability (significance) of the influence of the factor under consideration. The subsequent analysis of the reliability of the influence of a particular factor, the comparison of the measure of influence of various factors is carried out using parametric (variance analysis) and nonparametric measures of influence (the sign criterion, the Wilcoxon criterion). This article discusses the use of nonparametric measures of influence in pedagogical research. The Wilcoxon criterion is selected for comparing the indicators obtained as a result of measurement in a connected sample and allowing to diagnose not only the direction of changes, but also their severity. The necessary conditions for the application of the criterion, as well as the advantages of its use, are indicated. The possibility of using the Wilcoxon criterion is illustrated by the example of determining the effectiveness of the proposed teaching methodology using the Uchi.ru online platform in educational activities. Conclusions are made about its inefficiency for mastering the material in mathematics for younger schoolchildren.

Effect of Different Intensity Outdoor Tennis Training on Cardiac Load

Starting from the outdoor tennis competition, this paper studies the load characteristics of tennis competition through the experimental test of outdoor tennis players. This paper mainly adopts four research methods: literature, experimental test, mathematical statistics and logical analysis. This paper analyzes the load characteristics of outdoor tennis players in singles through experiments on the characteristics of competition time, the changes of center rate in the process of competition and the changes of creatine kinase, blood urea and urinary protein before and after competition. The results showed that the content of creatine kinase in blood increased significantly and the protein in urine increased significantly. This shows that outdoor tennis competition is more intense. The increase of blood urea after competition shows that there is a certain load in outdoor tennis competition, but the load is relatively small. The small load is mainly due to the short time of outdoor tennis competition, so the content of blood urea will not increase significantly.

Towards the Calculation of Jack Polynomials

<p>Jack polynomials are useful in mathematical statistics, but they are awkward to calculate, and their uses have chiefly been theoretical. In this thesis a determinantal expansion of Jack polynomials in elementary symmetric polynomials is found, complementing a recent result in the literature on expansions as determinants in monomial symmetric functions. These results offer enhanced possibilities for the calculation of these polynomials, and for finding workable approximations to them. The thesis investigates the structure of the determinants concerned, finding which terms can be expected to dominate, and quantifying the sparsity of the matrices involved. Expressions are found for the elementary and monomial symmetric polynomials when the variates involved assume the form of arithmetic and geometric progressions. The latter case in particular is expected to facilitate the construction of algorithms suitable for approximating Jack polynomials.</p>

Towards the Calculation of Jack Polynomials

<p>Jack polynomials are useful in mathematical statistics, but they are awkward to calculate, and their uses have chiefly been theoretical. In this thesis a determinantal expansion of Jack polynomials in elementary symmetric polynomials is found, complementing a recent result in the literature on expansions as determinants in monomial symmetric functions. These results offer enhanced possibilities for the calculation of these polynomials, and for finding workable approximations to them. The thesis investigates the structure of the determinants concerned, finding which terms can be expected to dominate, and quantifying the sparsity of the matrices involved. Expressions are found for the elementary and monomial symmetric polynomials when the variates involved assume the form of arithmetic and geometric progressions. The latter case in particular is expected to facilitate the construction of algorithms suitable for approximating Jack polynomials.</p>

VOICE-BASED IDENTIFICATION AND CONTRIBUTION TO THE EFFICIENCY OF CRIMINAL PROCEEDINGS

Today, forensic voice identification is a powerful tool in the fight against crime, in situations where it is necessary to identify a suspect or to acquit an innocent person. In this type of expertise, multidisciplinary approach is applied in which several scientific disciplines are included - linguistics, phonetics, acoustics, psychology, mathematical statistics, law and criminalistics. The perpetrator’s voice is characterized by pitch, volume, timbre, or tone of the sound produced i.e., a series of individual characteristics that make each individual's voice, regardless of the variations expressed, suitable for identification. Some of these characteristics are natural features, determined by hereditary and physiological factors, and some are acquired habits. The aim of this paper is to present the most commonly used procedures and methods of analysis-assessment of voice and speech in order to identify persons as well as more modern approaches to the analysis of the speech signal.

Computer Mathematical Statistics and Analysis on Automobile HFCs Reduction Path Using Big Data Technology

China has submitted an application to join the Kigali amendment to the Montreal Protocol. As the second largest hydrofluorocarbons (HFCs) consumer industry in China, the automotive industry is facing enormous pressure to reduce HFCs. This paper analyzes the current situation of HFCs use in the domestic automotive industry, and makes a simulation prediction of HFCs use data in the automotive industry from 2024 to 2030, analyze and evaluate the advantages and disadvantages of different technical routes. The relevant contents of this paper will provide reference for the formulation of HFCs reduction policy.