Mathematical Processing Research Articles

Recursive identification of kernel-based hammerstein model for online energy efficiency estimation of large-scale chemical plants

Accurate energy efficiency prediction is crucial for decision-making in large-scale chemical production, especially considering energy management and environmental concerns. The complexity of chemical processes, characterized by strong nonlinearities, dynamics, and uncertainties, challenges traditional prediction methods. This paper introduces KHSM (Kernel-based Hammerstein Subspace Model), which models nonlinear static and linear dynamic processes in series by embedding kernel function-based nonlinear mapping into subspace modeling for energy efficiency estimation. KHSM identifies nonlinear process models without explicit nonlinear mapping functions, constructing dynamic models that encompass both energy input and product output variables. An adaptive KHSM variant dynamically updates the energy efficiency model, improving accuracy by iteratively selecting and excluding samples. Comparative analysis shows KHSM outperforms existing methods, achieving a coefficient of determination (R2) closest to 1 and reducing the root-mean-square error (RMSE) by up to an order of magnitude, with the smallest mean and standard deviation. Additionally, modeling efficiency increases by an order of magnitude. The developed model enables ongoing energy efficiency estimation and proactive identification of efficiency trends. Validation through mathematical and real-world ethylene process cases demonstrates KHSM's efficacy and applicability. These estimates facilitate informed adjustments to energy management strategies and optimization of production approaches in energy-intensive chemical processes.

Emotional attitude and motives of dislike as predictors of discriminatory attitudes

The emotional attitude towards outgroup representatives may differ depending on the target of discrimination. Establishing the role of emotional relationships and the motivation of dislike in adherence to certain combined types of discriminatory attitudes will contribute to the development of measures to counteract them. The aim of the study is to establish emotional attitudes towards representatives of outgroups and the motives of dislike, which are predictors of discriminatory attitudes. The study involved 190 people of both sexes (men — 36.6%), aged 20–40 years. The survey methods of direct and indirect assessment of discriminatory attitudes, affective reactions towards representatives of discriminated groups, motives of dislike, methods of mathematical data processing (descriptive statistics, correlation and regression analyses, modeling method) were used. The combination of forms of emotional attitude and motivation in the prediction of types of discriminatory attitudes, as well as direct and indirect effects of emotional relationships on generalized forms of discriminatory attitudes, has been revealed. Anger and anxiety act as emotional attitudes towards representatives of outgroups, causing a general discriminatory attitude, while interest and disgust contribute to its reduction. The predictors of discriminatory attitudes towards socially vulnerable groups are fear (positive), interest and pity (negative); dissident groups — anger and fear; outsider groups — anger and disgust; social status groups — irritation and aggression (positive), disgust and interest (negative). The strongest motivational predictors of discriminatory attitudes are the motivation of competition in the labor market in the case of dissident, socially-status and even socially unprotected groups, as well as hostility based on an emotional attitude in the case of dissident and socially-outsider groups. Various emotional attitudes and motivations of rejection towards outgroup representatives explain a significant part of the dispersion of generalized forms of discriminatory attitudes. Generalized discriminatory attitudes are characterized by heterogeneous emotional conditioning and polymotivation.

Designing Mini Modeling Projects

This paper is written as a guide for any instructor seeking to develop the mathematical modeling process or open-ended problem solving in their courses. We describe a pedagogical approach to create mini modeling problems to develop the modeling process. These are problems that fall between traditional homework problems and open-ended modeling problems, and focus on specific aspects of the modeling process. Implementing such mini modeling problems is a means of scaffolding the modeling process to engage the students in smaller stages of modeling and prepare them for the full modeling process. This is intended as a means to empower the students so they can engage confidently in the modeling process.

Negotiating Knowledge Through Mathematical Activities in Classroom Interactions

What students are learning in mathematics classrooms can be analysed from a wide range of perspectives, focusing on the mathematical content, the mathematical processes or the mathematical activities. There is also a social dimension intertwined with this cognitive dimension that focuses on what mathematical activities in particular are established as socio-mathematical norms within a classroom. It is through these norms that students learn what it is to both learn mathematics and what it means to do mathematics. In this article I add a further epistemic dimension to illustrate how these socio-mathematical norms are co-constructed through interactions in a dynamic way. The analysis reported in this paper draws on video data of 65 lesson segments where students made their thinking explicit, taken from an original sample of 133 naturally occurring mathematics lessons with 81 teachers identified as including cognitively demanding mathematics. Using ethnomethodological conversation analysis and the epistemic dimensions of interaction initially outlined by Heritage and colleagues, a fine-grained sequential analysis of the interactions including students’ detailed contributions around cognitively demanding activities within these lessons illustrates how epistemic access, primacy and responsibilities are continually negotiated in interaction. Students’ rights to make knowledge claims or obligations to demonstrate their knowledge are negotiated in ways that influence students’ and teachers’ epistemic authority and stance. The analysis shows how the cognitive and social dimensions are intertwined both at an individual level but also at the classroom level that establish and reinforce the norms around the access and primacy of ideas and knowledge in interaction. These epistemic negotiations have consequences on the nature of mathematical activities that students experience and participate in, and subsequently their opportunities to learn mathematics.

Use of Language By generative AI Tools in Mathematical Problem Solving: The Case of ChatGPT

Texts generated by artificial intelligence agents have been suggested as tools supporting students’ learning. The present research analyses the language of texts generated by ChatGPT when solving mathematical problems related to the quadratic equation. We use the functional grammar theoretical framework that includes three meta-functions: the ideational meta-function, the interpersonal meta-function and the textual meta-function. The results indicated that in at least one of six problem-solving tasks ChatGPT provided a mathematically incorrect answer. The processes appearing in ChatGPT texts, aiming at developing students’ understanding of mathematical concepts, included verbal, mental, existential, relational and behavioural processes but no material processes. Specifically, ChatGPT performed a mathematically incorrect existential process. ChatGPT generally used the first plural pronoun ‘we’ when describing the processes of solving mathematical problems, while it generally used the first-person singular pronoun when taking responsibility for a specific mistake or when expressing happiness for the actions of the user. Moreover, generally the text of the solution did not include direct imperatives but used ‘let us do’. The advancement of the ChatGPT textual solution was made usually through steps like ‘first’, ‘second’, etc. The research results indicated that the way ChatGPT responded to the mathematical problems would be useful in supporting learners’ understanding of ways to solve quadratic equations, but only if the teacher critically accompanies the student in the problem-solving process. Self-study with ChatGPT could lead to or confirm students’ mathematical misconceptions.

Ethnomathematics-based Problem Based Learning (PBL) Model to Increase Students’ Critical Thinking in Mathematics Learning

Process of learning mathematics in the school that the researcher is aiming for tends to be theoretical, less contextual and pseudo. Applies mathematical concepts in learning with local cultural wisdom able to touch aspects in the daily lives of students. This study aims to apply the ethnomathematics-ground Problem Based Learning (PBL) model to ameliorate critical thinking in mathematics literacy. This explored was type of quasi-experimental explored (pseudo-experiment), with The Non-Equivalent Control Group type design. The population of this study was all fourth grade students at SD Insan Mandiri Bandar Lampung, totaling 121 students. The sample of this studied was determined by intentional slice fashion, which is a sample determination fashion with consideration in opting for the class to be studied and attained by as numerous as 49 students. Data collection technique used valid and dependable test instruments. The data analysis fashion uses a mated t- test with the results attained for the experimental class with a significance value of 0.000 (p<0.05) passing significant changes and in the control class which is not applied to the Ethnomathematics-based PBL model gets a value of 0.070 (p>0.05) indicating that the results of the original test and final test do not witness significant changes. Grounded on the data attained is from the results of this study, the ethnomathematics-ground Problem Based Learning (PBL) model to ameliorate thinking is significant.

Psychological Characteristics of Internet Addiction in Students in Problem Life Situations (COVID, War)

The relevance of this research lies in the fact that the number of Internet addicts in the world is constantly growing (the premise of which we consider the possibilities of Internet content that open up to a person in the virtual space), and the situation can turn into a public health problem. The purpose of the article is to carry out a theoretical analysis of the phenomenon of Internet addiction and, based on it, conduct an empirical study of Internet addiction of students, its connection with their personal traits and their satisfaction with life in difficult life situations: during the COVID-19 pandemic (n=88) and war (n=87). The research used the following methods: Internet Addiction Test (K. Young), CIAS, Chen-Internet-Addiction-Scale (S.-H. Cnen), Techniques for diagnosing predisposition to 13 types of addictions (G.V. Lozova), Test T. Leary, Questionnaire “Life Satisfaction Index” (B. Neugarten, R. Havighurst, Sh. Tobin), Oxford Happiness Inventory, OHI. Mathematical processing of research results was carried out using statistical package SPSS 17.0. The analysis of approaches to the understanding of Internet addiction by scientists leads to the conclusion that it is a behavioral deviation that manifests itself in a person’s excessive spending of time in the Internet space due to reluctance to return to real life; this is exactly information addiction. The main symptoms of Internet addiction: the tendency of an individual to choose being on the Internet before any other types of his activity; a change in his/her state of consciousness, a gradual increase in the time spent on the Internet, the lack of an objective assessment of the negative consequences of Internet addiction. As a result of the study, it was found that: Internet addiction can be combined with other types of addiction, Internet addicts are characterized by certain types of attitude towards others and a lack of feeling of satisfaction with life; Respondents who are less dependent on the Internet tend to positively evaluate themselves, be consistent in achieving their goals, fall into other addictions less often, and activate situationally necessary types of attitude towards others.

Gamification and problem-based learning (PBL): Development of creativity in the teaching-learning process of mathematics in university students

This study aims to determine whether the combination of techniques such as gamification along with problem-based learning (PBL) can significantly enhance the problem-solving abilities of university students and their academic performance compared to those who do not receive this educational approach. An experimental design was employed, incorporating the administration of tests, data collection, non-participant observation directed at teachers, and a survey administered to students. The study was conducted with 42 students in the treatment group and 37 students in the control group. As a result of the analysis, it was identified that the combination of gamification and PBL significantly improves the problem-solving capabilities of the treatment group, as well as the average grades. This suggests that these techniques can increase the engagement, motivation, and academic performance of university students in the context of mathematics. This holds significant implications for the design of educational programs and underscores the importance of integrating innovative approaches in teaching to foster holistic student development. It is recommended that educational programs and teachers consider the implementation of techniques that promote active student participation and the integration of technological resources to enhance the teaching and learning process of mathematics in university students.

Practicality of Student-Centered Assessment/Learning using Mathematics Modeling Process Worksheets to Improve the Quality of Education

It is necessary to consider reforms to improve the quality of education through assessment/learning. The problem formulation of this research is how to design student-centered assessment/learning using practical mathematical modeling process worksheets to improve the quality of education? This research uses a development research approach developed by Akker, Gravemeijer, McKenney and Nieveen. This development research consists of 3 steps, namely analysis, design and evaluation. In the analysis step, student analysis, curriculum, mathematical modeling and real world problems are implemented. Second step, design and product. In the final step, researchers used a formative evaluation design consisting of self-evaluation, one-to-one, expert review, small group, and field test. Data were analyzed using descriptive analysis methods: (1) walk through, analysis based on solutions and student comments in small groups to obtain student-centered assessment/learning using mathematical modeling process worksheets using the best practical transportation context to improve the quality of education; (2) analyzing the results of the review of small group results. Based on the results of the small group worksheet, the mathematical modeling process is practical for improving the quality of education. Students commented that this mathematical modeling process worksheet was interesting, confusing but challenging and had never been found in their classrooms. Students can solve problems on process worksheets even though the mathematization process has not yet appeared, because students only solve them using informal methods. So, this is a golden opportunity to implement in order to improve the quality of education through assessment/learning. So, a practical mathematical modeling process worksheet is obtained to implement student-centered assessment/learning in order to improve the quality of education.

Inspection of the nonlinear instability of electrified Casson fluids: a novel approach

The nonlinear electrohydrodynamic (EHD) instability of a circular cylindrical interface, separating two Casson prototypes is the aim of the present inspection. The motivation for the issue is owing to the increasing significance of several engineering and practicle physics. Because of the complicated mathematical processes, the contribution is performed through the viscous potential theory (VPT). The methodology resulted in a nonlinear characteristic equation of the interface displacement. This equation is transformed to simulate a hybrid Rayleigh-Helmholtz Duffing oscillator (HRDO) with complex coefficients. Guaranteeing the stability of fluid interfaces is crucial in industrial coating operations to provide consistent and even coatings. Gaining comprehension of the nonlinear stability criterion helps to enhance the management of coating thickness and uniformity. A novel methodology via the Non-perturbative approach (NPA) is employed. Through the case of the real coefficients, the later form is validated using a numerical solution (NS). It is concluded that the Ohnesorge contribution has a destabilizing effect on the stability zone in contrast with permeability factor. The electrical coefficients are found to be decaying factors in the stability configuration. It is also established that the viscosity decays the nonlinear steadiness requirement of the structure. The approach is a simple, promising, effective, and interesting.

A future classroom lab with active and gamified STEAM proposal for mathematics and science disciplines: Analyzing the effects on pre-service teacher’s affective domain

The recent emergence of innovative learning spaces, Future Classroom Lab (FCL), provides educators the use of physical learning spaces (to research, interact, exchange, develop, create, and present) and diverse technological tools to work according to active methodologies. Learners become more active in the learning process with the introduction of innovative learning environments that enable the application of interdisciplinary STEAM methodology and foster the development of 21st century competences. This study aims to uncover the probable link between application active and gamified STEAM educational interventions in the FCL and Pre-Service Teachers’ (PSTs) affective domain. The findings obtained showed statistically significant variations and, therefore, positive effects on the PSTs’ affective domain (self-efficacy, attitude, and emotion) after performing the intervention. The sample consisted of a total of 54 PSTs enrolled in the second year of Primary Education. Limited studies regarding the affective domain in the FCL were found, which restricted the comparison with prior research. This study has several implications, such as the introduction of innovative educational proposals to PSTs at the university level and, consequently, the implementation of similar interventions in elementary schools. This research intended to reveal how the different variables work as a support system for students’ learning process in mathematics and science disciplines.

ANALYSIS OF THE POSSIBILITIES OF MODERN RESEARCH METHODS FOR THE DIAGNOSTIC OF HEMORRAGE IN THE SUBSTANCE OF THE HUMAN BRAIN (LITERATURE REVIEW)

Traumatic brain injury is one of the most widespread and complex types of mechanical injury today, which involves many fields of medical practice, including neurosurgery, neurology, rehabilitation, forensic medicine, etc., and requires a multidisciplinary approach to its solution. Aim of the work: to analyse, on the basis of data from literary sources, the possibilities of modern research methods for the diagnosis of haemorrhages in the substance of the human brain and their genesis. Research results. The gold standard for verification of the diagnosis in forensic medicine is a forensic histological examination, however, the classical technique of histological differential diagnosis of the genesis and time of formation of a haemorrhage in the brain substance is not effective. The diagnosis of traumatic brain injury can be complicated in cases where there are no macroscopic signs of head trauma and little information is available about the circumstances of death. Therefore, a number of researchers have explored the possibility of using biomarkers to provide objective evidence of traumatic brain injury as the cause of death or to estimate the survival and post-mortem time of the deceased. Biophysical studies using a laser have shown potential success in the field of traumatic brain injury diagnostics. Preliminary conclusions regarding the possibility of differentiating the genesis of cerebral haemorrhage using the method of reconstructing distributions of the magnitude of linear dichroism fluctuations gave positive results. Conclusion. It was found that biochemical studies show significant success in the diagnosis of traumatic brain injury, some markers even make it possible to differentiate the genesis of brain haemorrhage, but forensic medical practice requires the development of easy-to-use, highly effective methods to verify the type of human brain injury. This role can potentially be fulfilled by physical-optical methods based on laser irradiation of biological objects followed by mathematical and statistical processing of the obtained data.

Mathematical modelling and covariational reasoning: a multiple case study

This research aims to investigate the relationships between the mathematical modelling process and the levels of covariational reasoning through a multiple instrumental case study with six college students solving a task in the context of science. We designed a modelling task based on a problem faced by Newton: obtaining higher temperature values than a thermometer could register; and analysed the participants’ modelling processes and covariational reasoning as they solved the task. The results show that the modelling task promoted covariational reasoning. The results also show that participants used covariational reasoning to solve the task, and the participants were unaware of nonlinear covariational reasoning which prevented them from making mathematical models closer to reality. Furthermore, participants required specific levels of covariational reasoning at specific steps in the mathematical modelling process, and as they advanced in the mathematical modelling process they exhibited more sophisticated levels of covariational reasoning.

The Influence of Edugame Wordwall Media on Students’ Ability to Solve Mathematical Problems

The ability of mathematical problem-solving is a crucial element in a mathematical learning process that allows learners to deepen their understanding comprehensively. To overcome the various challenges that arise in this process, effective learning solutions are needed, including the use of tools or media such as Wordwall edugame. This study aims to investigate how Wordwall educational games affect the improvement of students' abilities in solving mathematical problems. The study adopted a quantitative experimental method utilizing a Pretest-Posttest Control and quasi-experimental Design, each class consisted of 40 grade VII students selected through a purposive sampling technique. The research utilizes a test as its measuring tool for mathematical problem-solving ability. The statistical test results revealed that using Wordwall edugame had a profound impact on enhancing mathematical problem-solving ability, with a paired sample t-test value of <0.001. After the treatment was applied, the average scores increased significantly, with the experimental class averaging from 18.85 to 53.2 and the control class from 22.83 to 41.83. The experimental class showed a significant improvement before and after the treatment, while the control class did not show a significant change in this study, indicating that using Wordwall edugame media significantly improved math problem-solving ability.

Features of body balance in 12-year-old schoolchildren with visual deprivation compared to their relatively healthy peers

Purpose. The purpose of the presented scientific research was to carry out a comparative analysis of the state of functional balance of the body of 12-year-old schoolchildren with visual deprivation in accordance with their relatively healthy peers. Material & Methods. The scientific study involved 23 schoolchildren aged 12 years, of which 13 were with visual deprivation and 10 were relatively healthy. The pedagogical research took place at the Educational and Rehabilitation Center “Zorozvit” in Odessa and at the Basic Educational Institution “Vypasnyansky Institution of General Secondary Education” of the Mologovo Village Council of the Bilhorod-Dnistrovsky District, Odessa Region. The follo wing methods were used in the study: theoretical (analysis and synthesis of scientific and methodological literature); pedagogical research (experiment and testing of the development of body balance using the Flamingo test), mathematical static data processing. Results. A scientific study found that among schoolchildren without visual deprivation, only 10% had a low ability to maintain body balance. In turn, 90% of schoolchildren with visual deprivation had a sufficient, satisfactory and high level of development of body balance. It should be noted that schoolchildren with visual deprivation demonstrate a low level of ability to maintain balance, which distinguishes them from their peers without visual deprivation.

Computational synthesis of locomotive soft robots by topology optimization.

Locomotive soft robots (SoRos) have gained prominence due to their adaptability. Traditional locomotive SoRo design is based on limb structures inspired by biological organisms and requires human intervention. Evolutionary robotics, designed using evolutionary algorithms (EAs), have shown potential for automatic design. However, EA-based methods face the challenge of high computational cost when considering multiphysics in locomotion, including materials, actuations, and interactions with environments. Here, we present a design approach for pneumatic SoRos that integrates gradient-based topology optimization with multiphysics material point method (MPM) simulations. This approach starts with a simple initial shape (a cube with a central cavity). The topology optimization with MPM then automatically and iteratively designs the SoRo shape. We design two SoRos, one for walking and one for climbing. These SoRos are 3D printed and exhibit the same locomotion features as in the simulations. This study presents an efficient strategy for designing SoRos, demonstrating that a purely mathematical process can produce limb-like structures seen in biological organisms.

Students' Mathematical Literacy in the Process of Teaching Problem Solving Strategies

The purpose of the study is to investigate the mathematical competence of 8th grade students in the context of teaching problem solving strategies. In the study, students were taught problem-solving strategies and were asked to solve problems prepared on these strategies using the appropriate strategy. The study was conducted with 32 eighth grade students in an elementary school. The data were analyzed using the content analysis method. The results of the pretest and posttest on mathematical competence suggest that the exercise in which problem-solving strategies were taught increased the level of mathematical competence of the students. In addition, data from the semi-structured interview sheets, student solution sheets, and observation notes identified progress in the students' problem-solving process and implementation of mathematical processes.

Research on Mathematical Model and Process Parameter Optimization of Rotary Hearth Furnace Process Toward Energy and Cost Saving

Research on Mathematical Model and Process Parameter Optimization of Rotary Hearth Furnace Process Toward Energy and Cost Saving

Cycle-based high-intensity sprint exercise elicits acute cognitive dysfunction in psychomotor and memory task performance

PurposeTo examine the impact of an acute high-intensity sprint exercise protocol (HISEP) for eliciting post-exercise cognitive dysfunction in psychomotor, attentional, executive, and memory tasks.MethodsTwenty-four recreationally active adults (22 ± 4 yrs, 169.39 ± 10.07 cm, 75.80 ± 14.73 kg, 27.03 ± 9.55 BF%) performed a HISEP on a cycle ergometer. Average psychomotor reaction time (avgRT; Dynavision D2 Mode A & Mode B), mood (Profile of Mood States Questionnaire; POMS), and cognition (Automated Neuropsychological Assessment Metrics; ANAM) were assessed pre- (PRE), post- (POST) and 60-min post (60POST) HISEP. One-way repeated measures ANOVAs were used to assess changes across time.ResultsFatigue (main effect: p < 0.001, ηp2 = 0.309) was significantly higher at POST compared to PRE (p = 0.007). Tension (main effect: p = 0.021, ηp2 = 0.154) was significantly lower at 60POST compared to PRE (p = 0.029). Mode A avgRT (main effect: p = 0.022, ηp2 = 0.153) was significantly slower at POST compared to PRE (p = 0.026). Throughput (TP) scores for ANAM code substitution-delayed (CSD) task (main effect: p < 0.001, ηp2 = 0.284) and matching to sample (M2S) tasks (main effect: p = 0.014, ηp2 = 0.169) were significantly lower at POST compared to PRE (p = 0.001 and p = 0.025, respectively), while mathematical processing (main effect: p = 0.002, ηp2 = 0.232) was significantly higher at 60POST compared to both PRE (p = 0.019) and POST (p = 0.005). No other significant changes in cognitive task performance were observed (p's > 0.05).ConclusionsThe HISEP is a feasible and time-effective fatiguing exercise stimulus capable of eliciting acute cognitive dysfunction in psychomotor and memory task performance. NCT05100589.

ПОЧВЕННЫЕ БАКТЕРИИ ИЗ АВТОХТОННЫХ МИКРОБНЫХ СООБЩЕСТВ ЦЕНТРАЛЬНОЙ СИБИРИ В БИОЛОГИЧЕСКОЙ ЗАЩИТЕ ПШЕНИЦЫ ОТ ALTERNARIA TENUISSIMA

The most powerful soil bacteria from autochthonous microbial communities of Central Siberia against phytopathogenic fungi Alternaria tenuissima were selected. Isolation from soil samples and cultivation of bacterial isolates were performed on the artificial nutrient medium for bacteria PD-agar. Antagonistic activity was measured on GRM Saburo. In this case, Alternaria tenuissima was sown in a dish on GRM Saburo, and the selected bacterial strains were sown around the micromycete. As a result of joint growth of the test culture and soil bacteria, the most powerful antagonists in the suppression zone of Alternaria tenuissima were identified. The most powerful bacteria-antagonists in reducing the intensity and prevalence of root rot were identified by the method of artificial infection of Alternaria tenuissima. Before infection with micromycete, bacterization of spring wheat seeds Novosibirskaya-15 with the studied bacterial isolates was carried out. Mathematical processing of the obtained results was fulfilled by one-way variance analysis and two-sample F-test for variance. The results of the study on the use of soil autochthonous antagonist microorganisms in biological protection of spring wheat from the causative agents of root rot Alternaria tenuissima showed that the studied bacterial isolates statistically significantly (p < 0.01) reduced the intensity and prevalence of this disease. The maximum effect in reducing the intensity and prevalence of the disease was shown by isolates B2 and B4 (according to preliminary identification of Bacillus sp.). Also, the studied bacterial strains showed a positive effect on the length of sprouts. At the same time, isolate B2 showed a statistically significant (p < 0.001) effect on the length of spring wheat sprouts. The stimulating effect was manifested in an increase in the length of sprouts compared to the control. Therefore, this strain can be recommended not only for protection against Alternaria tenuissima, but also for stimulating wheat growth.