Mathematical Processing Research Articles

Editorial: Mathematical thinking, practices, and processes in non-formal learning environments

Editorial: Mathematical thinking, practices, and processes in non-formal learning environments

Experience of integrating lean technologies into the quality management system of a medical organization providing primary medical and sanitary care

Objective. To evaluate the effectiveness of implementation of lean production methods into the practical activity of primary health care on the example of the State Institution of Health Care «Saratov City Polycli nic № 2». Materials and methods. The study was divided into three stages: data collection through anonymous sociological surveys using phones or tablets, timing and improvement of the process, and a follow-up questioning of participants to assess their satisfaction. 296 residents of Saratov receiving primary health care at the polyclinic took part in the survey. The survey was conducted using a specially developed electronic questionnaire via Google Form. For mathematical processing, the results of the study were initially transferred into an electronic database; the results of the study were analyzed using the descriptive statistics method. Results. According to the survey, the majority of respondents are satisfied with the quality of outpatient medical care. This shows that organization of the medical care is focused on the patients` needs and desire to meet their demands. The organization of the front office and the premises of the polyclinic in accordance with the requirements for the new model of the organization providing primary medical care made it possible to achieve a high evaluation of the information stands and the waiting area. The study showed that ineffective organization of the registry office contributed significantly to the patients` low assessment. In our opinion, in order to solve the problem, it is necessary to optimize the work of the registry office by introducing modern technologies and equal distribution of duties among the employees. Conclusions. In order to improve the quality and accessibility of medical services, it is necessary to make certain changes in the organization of medical care. The level of patient satisfaction with the work of medical institutions may depend on various factors, such as waiting time for a doctor, the timing of medical services provision after the appointment, the availability of necessary diagnostic tests and specialists.

An investigation of students’ mathematical connection and metacognitive skills in the mathematical modelling process

The purpose of the study is to investigate the changing mathematical connection and metacognitive skills of students in the process of applying mathematical modelling. The data used for the study were collected from modelling activities, students’ written responses to modelling activities, audio recordings, semi-structured interviews, and observation notes. The data obtained were analysed using content analysis. As a result of the data analysis, it was found that metacognitive skills were used in each activity in the mathematical modelling process and were developed in interaction with each other. Although inter-concept and real-world connection skills are most commonly used in mathematical connection skills, modelling activities were found to enhance connection skills by allowing students to use connection skills with different disciplines and between different representations of the concept. It was found that metacognitive skills and mathematical connection skills develop interdependently, and it was found that mathematical modelling activities can be used as a tool for developing both of these skills.

Metacognitive strategies in mathematical modelling: a case study with engineering students

During the last years, mathematical modelling has been entering the field of engineering education because it is a bridge between mathematics and industry that also promotes the development of skills that require the engineer of the twenty-first century. Nevertheless, the modelling process is involved and requires the deployment of cognitive skills of superior level, particularly metacognitive skills. This contribution presents the results of a multiple qualitative case study on metacognitive strategies used by groups of engineering students associated with each transition of the mathematical modelling process. During the development of the course, observations and retrospective interviews were carried out, which evidenced the use of metacognitive planning strategies from simplification to interpretation; metacognitive monitoring strategies throughout the modelling process, metacognitive regulation strategies from mathematization to mathematical work and metacognitive evaluation strategies during simplification, mathematization and validation. The results expand the classification framework of metacognitive strategies for engineering students.

Development of coordination abilities of mentally retarded children in physical education lessons

The aim of the study to develop a methodology for improving the level of development of the coordination abilities of mentally retarded children aged 8-9 years in the lessons of adaptive physical education. Methods The study was organized at a special correctional school from September 13 to December 16, 2023. 14 schoolchildren aged 8-9 took part in the experiment. Children from the control group studied according to the usual program, and children from the experimental group performed complexes of coordination exercises and used outdoor games during lessons on adaptive physical culture. The level of development of coordination abilities of mentally retarded children aged 8-9 years was determined by three tests: 3x10m shuttle run, one-leg stand, obstacle course. The Student’s T-Test was the main method of mathematical processing of the research results. Results Prior to the start of the study, the difference in performance in control tests in both groups was not significant and not reliable (p>0.05), which indicates the homogeneity of the groups. After the end of the pedagogical experiment, the indicators of coordination abilities of children from the control group improved, but not significantly or significantly (p>0.05). Significant positive changes occurred in the experimental group for all tests. In the shuttle run, the indicators became higher by 0.5 seconds (p>0.05), in the one-leg stand test, the indicators improved by 1.1 seconds (p>0.05), and in the obstacle course test, the indicators improved by 1.2 seconds (p<0.05). An intergroup comparison showed a difference in two of the three indicators of coordination abilities when the significant difference is the shuttle run (p<0.05) and the obstacle course (p<0.05). Conclusion The developed experimental methodology for the development of coordination abilities for mentally retarded children aged 8-9 years in the lessons of adaptive physical education has proven its effectiveness and is recommended for use in correctional schools in working with mentally retarded children. Bangladesh Journal of Medical Science Vol. 23 No. 04 October’24 Page : 1219-1226

TOBACCO CONSUMPTION DYNAMICS BEFORE AND AFTER THE COVID-19 PANDEMIC

In 2022, 2,453 residents were surveyed (men - 1137, women - 1316) aged from 15 to 86 years (average age - 43,0 ± 16,4 years). There were 58,9% city dwellers, 41,1% villagers. The GATS technique was used. The results of the 2022 survey were compared with 2019. Mathematical and statistical processing included descriptive statistics and calculation of the χ2 distribution. Over the past three years, the share of smokers has not changed (19,0% in 2022 vs 19,9% in 2019). At the same time, there were significantly more women smoking (7,4% vs 5,4%), and fewer men smoking (32,4% vs 36,7%). The number of smokers has significantly increased in the age group 65+, among women, as well as among persons aged 45-64 years. In 2022, smokers made fewer attempts to quit smoking. The number of users of electronic nicotine delivery systems increased (7.1% vs 5.4%), especially among men (9.5% vs 6.0%); a noticeable increase was observed in the 45-64 age group (2.8% vs 0.9%). During the COVID-19 pandemic, the proportion of smokers of both sexes in the older age group has increased significantly. The number of users of electronic nicotine delivery systems has increased. Many indicators of assistance to the population in quitting tobacco use and prevention of smoking among the adult population have worsened.

FEATURES OF EMOTIONAL MANIFESTATIONS OF PROFESSIONAL DEFORMATIONS (BURNOUT) OF HEALTHCARE WORKERS IN THE POST-COVID PERIOD

The purpose of the study is to identify the features of the emotional component of professional deformation (burnout) of healthcare workers in the post-covid period. A survey was conducted of 658 healthcare workers with characteristics of the emotional component of professional deformation (burnout) in the post-covid period. Questionnaires of emotional burnout and self-assessment of emotional states were used. Mathematical and statistical processing included the K. Pearson correlation criterion and the Chaddock-Snedecor scale.

Delving into division

When teaching the multiplicative domain in New Zealand primary schools, teachers tend to spend a greater proportion of time on the meaning and processes of multiplication, to the detriment of a specific focus on understanding the concept of division. When division is taught, it tends to be by reversing the context and turning the division scenarios into multiplication problems. While this article stems from wider research based on teaching division in Years 5 and 6, it is relevant to all primary school teachers as they teach the mathematical process of division to the students in their classroom.

Dynamic analysis of six-bar tensegrity-based robot

Abstract The tensegrity-based robot is a hot research topic in the research field of robotics. The dynamics of the robot, describing the specific motion patterns under the influence of forces and torques, play an important role in the application of robotics. In addition, the dynamics should be considered when revealing the internal mechanisms of robots and predicting their dynamic behaviors. In this work, a dynamic model for a rolling six-bar tensegrity-based robot is established. In terms of kinematic representation, quaternions are chosen as the tool for attitude description, simplifying the derivation process of the complex three-dimensional rotational kinematics calculations. Quaternions play a crucial role in mathematical processing for robot attitude control and path planning due to their effective representation of three-dimensional space rotations. The classic Newton-Euler dynamic framework was adopted to conduct in-depth and detailed studies on the dynamic characteristics of the robot under various force conditions and motion states, with a particular focus on rolling dynamic analysis. Special attention was paid to the dynamic response mechanisms of each component of the robot under the combined action of internal and external forces and torques.

Computational Thinking Processes in Solving the Corona Epidemic Model: Pre-service Maths Teachers

In the 21st century, pre-service mathematics teachers are expected to have problem-solving skills that are effective, efficient, and solutive and are in line with the mindset of computer experts. In learning mathematics, the concept of computational thinking (CT) is also needed and at this time, many still have difficulty solving mathematical problems in general, especially in solving problems in epidemic mathematical models. The subjects of this study were twenty-seven pre-service mathematics teacher students who took mathematical modeling courses. The researcher used the purposive sampling technique to select two research samples. The research method used was a descriptive qualitative research method in exploring the thinking process of pre-service mathematics teacher students in solving the problem of modeling the epidemic spread of disease. The results showed that the thinking process of the first subject began with identifying the problem and existing information by writing down the data in the form of a graph so as to get a certain pattern, which was then used as the basis for the process of transforming the problem into mathematical language. By adding assumptions related to the existence of environmental limitations in the next epidemic model, the concept of differential equations, in which there are integral properties and natural logarithms, can be used to find the solution to the epidemic model. The second subject was unable to solve the integral at hand. The researcher discovered that pre-service mathematics teacher students who correctly solved the problem in the mathematical model used CT components, namely decomposition, abstraction, pattern recognition, algorithm and mathematical literacy.

Psychological aspects of aggression among police personnel

The article presents psychological aspects of aggression in the context of professional activity of police personnel. The nature and manifestations of aggression in the working environment of police officers are investigated, the factors that cause aggressive behaviour are considered, and its impact on the efficiency and safety of performance of official duties is analysed. The theoretical analysis has shown that everyday stress and dangerous situations in wartime create a favourable environment for the development of aggressive tendencies, which can negatively affect the quality of official duties performance. It has been found that aggression among police personnel can take various forms such as verbal conflict and physical force, which calls into question the credibility of law enforcement agencies and can have serious legal and ethical consequences. The purpose of the study is to examine and analyse various manifestations of aggression among police personnel in order to identify possible differences in their characteristics and ability to display such behaviour. The sample consisted of 200 police officers, divided into two groups by gender, 100 in each group. The first group was represented by men, the second by women. The study used the “Aggression Level Questionnaire” by A. Bass and A. Darky. Mathematical and statistical processing of the results was carried out using Student’s t-test for independent samples and Fisher's angular transformation criterion (φ). An empirical study of aggression among police officers of different gender groups has revealed significant differences in the manifestation of aggressive behaviour. Male police officers are more likely to use physical force and verbal aggression compared to female police officers. At the same time, both groups have a similar tendency to indirect aggression and negativism, which indicates a general tendency towards indirect forms of aggression and oppositional behaviour among police personnel. Female police officers show a higher level of irritability, suspicion and resentment, which may affect their interaction with others and their overall psychological state.

Влияние жизнестойкости на психологическую безопасность пожарных-спасателей

Introduction. The professional activity of a firefighter is inseparable from psychological states associated with risks and challenges. Performing the tasks of extinguishing fires, eliminating emergency situations and man-made disasters, firefighters act in a team. Their hardiness, the ability to use adaptive strategies in difficult situations, the skill of constructive interpersonal interaction depends on their psychological safety. The aim of the study is to examine firefighters' resilience and its contribution to psychological safety. Materials and methods. The following methods were used: The Hardiness Survey (S. Muddy), The Security Questionnaire (Ch. Kong and L. Ahn), The Portrait Values Questionnaire (Sh. Schwartz). The study on the basis of IPSA GPSA of the Ministry of Emergency Situations of Russia involved firefighters studying in the master's programme in the direction of “Fire Safety”. Methods of mathematical data processing (descriptive statistics, Spearman rank correlation, regression analysis) were implemented in IBM SPSS Statistics 26 package. Results. The mean scores of resilience, personal psychological safety of firefighters were above the normative values. Significant correlations were found between psychological safety and resilience of firefighters, and involvement as a component of resilience is a predictor of psychological safety with the dominance of values of caring for people and nature. Conclusion. Firefighters' willingness to take risks, sense of confidence and control, and engagement enable adaptive, resilient coping mechanisms. Firefighters' higher sense of psychological safety reflects their ability to better cope with stress, make informed decisions, work effectively as a team, and maintain their psychological well-being in high-risk and highresponsibility environments. Job involvement and commitment to the values of the profession enhance their sense of psychological safety in a teamwork environment and confidence in control. It is important for leaders of fire and rescue organisations to understand the psychological benefits based on resilience and firefighters' sense of psychological safety and to employ practices to develop them.

The study of the city of Rudny as a “heat island”

The annual increase in surface air temperatures contributes to climate change. This phenomenon is widespread over the entire surface of the Earth and is typical for any point of the planet. The purpose of this study was to identify patterns of changes in meteorological indicators in the city of Rudny, Kostanay region, Republic of Kazakhstan over the summer period 2018–2022. The scientific novelty of the work lies in the fact that for the first time the spatial distribution of the heat index in the territory of the city of Rudny was determined. To conduct the study, data from local automated weather stations were used, meteorological data was analyzed, compared for each year of the study, and the heat index was calculated. The reliability of the results is ensured by mathematical processing of daily empirical temperature and humidity data (calculation of the average for the day, the average for the month), coefficient of variation, coefficient of dispersion. The conducted research provides a clear description of climate changes in the city of Rudny, which can be used by municipal authorities to form measures to reduce the thermal impact on public health, heat loss in the housing and communal services system, and to improve air quality when planning urban infrastructure in the territory of the studied city.

Accurate Modelling of AFM Force-Indentation Curves with Blunted Indenters at Small Indentation Depths.

When testing biological samples with atomic force microscopy (AFM) nanoindentation using pyramidal indenters, Sneddon's equation is commonly used for data processing, approximating the indenter as a perfect cone. While more accurate models treat the AFM tip as a blunted cone or pyramid, these are complex and lack a direct relationship between applied force and indentation depth, complicating data analysis. This paper proposes a new equation derived from simple mathematical processes and physics-based criteria. It is accurate for small indentation depths and serves as a viable alternative to complex classical approaches. The proposed equation has been validated for ℎ < 3R (where h is the indentation depth and R is the tip radius) and confirmed through simulations with blunted conical and pyramidal indenters, as well as experiments on prostate cancer cells. It is a reliable method for experiments where the tip radius cannot be ignored, such as in shallow indentations on thin samples to avoid substrate effects.

Analysis and design of voltage-source parallel resonant class [formula omitted] inverter

In this paper, a detailed mathematical analysis process of the voltage-source parallel resonant (VSPR) class E/F3 inverter at 50% duty ratio is proposed. Combining the advantages of VSPR class E and F inverters, the performance of the proposed inverter can be improved greatly compared to the traditional. The transistor in the VSPR class E/F3 inverter is satisfied with zero-voltage switching(ZVS) and zero-voltage derivative switching(ZVDS) conditions. Moreover, two design freedoms can be obtained and the proposed analysis process is based on them, which can provide more flexible selections. Finally, a VSPR class E/F3 inverter is fabricated and the experiment is carried out. The measured normalized peak transistor voltage decreases by 25.6%. The output power reaches 5.06 W, and the efficiency reaches 93.75%. The measured results are well agreed with the theoretical and simulated.

Current Status of Research on Fault Diagnosis Using Machine Learning for Gear Transmission Systems

Gear transmission system fault diagnosis is crucial for the reliability and safety of industrial machinery. The combination of mathematical signal processing methods with deep learning technology has become a research hotspot in fault diagnosis. Firstly, the development and status of gear transmission system fault diagnosis are outlined in detail. Secondly, the relevant research results on gear transmission system fault diagnosis are summarized from the perspectives of time-domain, frequency domain, and time-frequency-domain analysis. Thirdly, the relevant research progress in shallow learning and deep learning in the field of fault diagnosis is explained. Finally, future research directions for gear transmission system fault diagnosis are summarized and anticipated in terms of the sparsity of signal analysis results, separation of adjacent feature components, extraction of weak signals, identification of composite faults, multi-factor combinations in fault diagnosis, and multi-source data fusion technology.

ANALYSING THE EFFICIENCY OF USING POROUS METALS IN HEAT EXCHANGERS

This study focuses on analysing the effectiveness of porous metals in heat exchangers, focusing on their effect on improving heat transfer processes. Porous metals, due to their unique structure, have high thermal conductivity and increased contact surface area, which contributes to more efficient heat transfer. As part of the study, experiments and theoretical analyses were carried out to evaluate the effect of porosity coefficient on heat exchange performance. The plotted dependence of Freon mass flow rate and heat quantity on porosity coefficient demonstrate the linear nature of these dependencies. Mathematical processing of the data showed that an increase in the porosity coefficient leads to an increase in both the amount of heat transferred by Freon and Freon mass flow rate, indicating an increase in heat exchange efficiency. The results confirmed that porous metals can significantly improve the performance of heat exchangers and energy saving. Based on the study, further investigation and implementation of porous metals in heat exchangers is recommended to optimise their performance and improve the overall system efficiency. These results open new perspectives for the application of porous metals in various industries including power and mechanical engineering.

FLUE GAS RECIRCULATION AS A WAY TO IMPROVE THERMAL EFFICIENCY AND REDUCE EMISSIONS IN POWER BOILERS

This study investigates the impact of flue gas recirculation on key parameters of the fuel combustion process, such as heat release and adiabatic combustion temperature. Based on the mathematical processing of experimental data, equations were obtained that reflect the dependence of useful heat release and adiabatic combustion temperature on the gas recirculation coefficient. According to the results of the study, the useful heat release in the furnace increases proportionally with the growth of the recirculation coefficient. This indicates that an increase in the level of recirculation contributes to an increase in combustion thermal efficiency, improving heat exchange processes within the furnace. A similar trend is observed for the adiabatic combustion temperature. It was found that the adiabatic combustion temperature also increases with an increase in the recirculation coefficient, which indicates the significant influence of recirculation on raising the temperature parameters of the combustion process. The rise in combustion temperature is associated with improved fuel combustion and more complete utilization of its energy potential. This, in turn, can contribute to a reduction in emissions of harmful substances such as nitrogen oxides and carbon, which is an important factor for environmental safety.Thus, the results of the study demonstrate that flue gas recirculation has a significant impact on heat exchange processes and combustion temperature. This makes recirculation an effective tool for increasing thermal efficiency and reducing the environmental impact. The application of this method in modern energy systems not only improves production performance but also ensures compliance with environmental requirements. The study results confirm the feasibility of implementing flue gas recirculation to enhance overall efficiency and environmental safety in energy installations.

Evaluation of Digital Technology Management in Mathematics Learning

The rapid advancement of digital technology necessitates that teachers enhance their competencies in the teaching and learning process of mathematics. This study aims to evaluate the demographic factors affecting teachers' use of digital technology and their digital skills, explore the frequency of online learning platform usage in relation to teachers' digital skills, and identify challenges while providing recommendations for integrating technology into mathematics instruction through a Sequential Explanatory Design mixed-methods approach. The quantitative sample consisted of 104 mathematics teachers, with 14 teachers selected as respondents for the qualitative phase. Data collection instruments included questionnaires, structured interviews, and non-participant observations, with quantitative data analyzed using Jamovi 2.4.8.0 software, and qualitative data manually coded and thematically analyzed using an inductive-deductive approach. The findings indicate that employment status, teaching experience, and school level significantly influence the use of digital technology in teaching mathematics. Teachers who are government employees under contract, have over 10 years of teaching experience, and teach at the middle or high school level tend to integrate technology more effectively. Consequently, government policies and educational programs for technology development should prioritize teachers irrespective of their employment status, offering continuous training (both online and offline) focused on mathematics.

Density, thermal expansion, dynamic viscosity of halogenated arenes

Purpose. Experimental study of the density, thermal expansion and dynamic viscosity of halogenated arenes at temperatures from 293.15 to 343.15 K and atmospheric pressure 97.992 kPa.Methods. Density was determined by the pycnometric method, viscosity by the capillary method. A quartz pycnometer type PZh2 with a nominal capacity of 10 ml and a glass capillary viscometer type VPZh-2 with a nominal capillary diameter of 0.34 mm were used. The mass of liquids was measured using an electronic scale VSL-200/0.1A with a division value of 0.0001 g. Numerical methods were used to process the experimental results.Results. Experimental data were obtained on the density, coefficient of volumetric thermal expansion and dynamic viscosity of liquid o-xylene, ethylbenzene, fluorobenzene, chlorobenzene, bromobenzene, toluene, o-fluorotoluene, mfluorotoluene, p-fluorotoluene, o-chlorotoluene, m-chlorotoluene, p-chlorotoluene, 2,4-dichlorotoluene, 2,6-dichlorotoluene. Density and dynamic viscosity data are approximated by a third-degree polynomial. Data on the coefficient of volumetric thermal expansion are obtained from approximated measured density data. The maximum estimate of the measurement error for density was 0.13 %, for dynamic viscosity – 3.5 %. The maximum calculation error for the coefficient of thermal expansion is estimated at 3 %.Conclusion. Mathematical processing of the obtained experimental data on density and dynamic viscosity made it possible to obtain analytical relations in the form of power polynomials that allow calculating the values of these quantities at any temperature from the studied temperature range and atmospheric pressure with an error not exceeding the error of experimental determination. The calculated values are in good agreement with the data provided in the reference and scientific literature. The experimental data obtained complement the information on the properties of some of the liquids under consideration, for which the dependences of density and viscosity on temperature are poorly understood. The substances under study are used in various sectors of the economy and are therefore technically important liquids. The measurement results can be used in condensed matter physics, for the analysis of liquid hydrocarbons, and can be useful in the chemical industry.