Mathematical Study Research Articles

Peirce on the Normative Basis of Deductive Logic

Abstract: I analyze Peirce's reply in the 1903 Lowell Lectures to the "defendant argument" and show how his response provides a key to interpreting his later philosophy of logic and his views on the normative role of deductive logic in inquiry. I argue that in Peirce's discussion of self-control in reasoning and evaluation of reasoning, we find an underappreciated position on logical revision and how to understand rational choice between deductive theories. To defend this point, I reconstruct Peirce's reply by providing an interpretation of his comments on higher-order criticism and the soundness of our reasoning, arguing that the resulting position's ability to separate questions involving the role of logic in inquiry from questions better suited to the mathematical study of a logical theory provides a fruitful pragmatist reframing of problems in the epistemology of logic.

Exploring Student Algebraic Thinking to Solve TIMSS Problems in Terms of Accommodator Learning Styles

This study aims to explore students' algebraic thinking skills in solving Trends International Mathematics and Science Study (TIMSS) problems in terms of accommodator learning styles. The research design used is a case study with a qualitative analysis approach. The results showed that accommodating subjects were able to meet the indicators of algebraic thinking, namely generalization, abstraction, analytical thinking, dynamic thinking, and modeling. However, the lack of accuracy in performing calculation operations causes the answers obtained by the subject to be less precise on abstraction, analytical thinking, and dynamic thinking problems. The characteristics of subjects with accommodator learning styles who are more likely to use intuition in solving problems influence students' ability to solve problems related to algebraic thinking.

Regulation of tissue growth in plants - A mathematical modeling study on shade avoidance response in Arabidopsis hypocotyls.

Plant growth is a plastic phenomenon controlled both by endogenous genetic programs and by environmental cues. The embryonic stem, the hypocotyl, is an ideal model system for the quantitative study of growth due to its relatively simple geometry and cellular organization, and to its essentially unidirectional growth pattern. The hypocotyl of Arabidopsis thaliana has been studied particularly well at the molecular-genetic level and at the cellular level, and it is the model of choice for analysis of the shade avoidance syndrome (SAS), a growth reaction that allows plants to compete with neighboring plants for light. During SAS, hypocotyl growth is controlled primarily by the growth hormone auxin, which stimulates cell expansion without the involvement of cell division. We assessed hypocotyl growth at cellular resolution in Arabidopsis mutants defective in auxin transport and biosynthesis and we designed a mathematical auxin transport model based on known polar and non-polar auxin transporters (ABCB1, ABCB19, and PINs) and on factors that control auxin homeostasis in the hypocotyl. In addition, we introduced into the model biophysical properties of the cell types based on precise cell wall measurements. Our model can generate the observed cellular growth patterns based on auxin distribution along the hypocotyl resulting from production in the cotyledons, transport along the hypocotyl, and general turnover of auxin. These principles, which resemble the features of mathematical models of animal morphogen gradients, allow to generate robust shallow auxin gradients as they are expected to exist in tissues that exhibit quantitative auxin-driven tissue growth, as opposed to the sharp auxin maxima generated by patterning mechanisms in plant development.

A META-ANALYTIC EXAMINATION OF THE EFFECT OF INDIVIDUAL AND SCHOOL-AVERAGE ACHIEVEMENT ON STUDENTS' SELF-CONCEPT IN SCIENCE

The purpose of the present study was to examine the effect of individual and school average achievement on students’ self-concept in science. The data of the last four Trends in International Mathematics and Science Study (TIMSS) cycles were used, and a two-stage individual data meta-analysis was conducted to examine the relationship between achievement and self-concept in science. In the first stage, multilevel structural equation modeling was performed for each dataset. Furthermore, the effect sizes were synthesized via meta-analysis with a three-level random-effect model. In addition, moderation analysis was conducted for the year, grade, and degree of stratification in countries. The results suggested a positive and significant effect of individual science achievement on the self-concept of students in science. On the other hand, the relation of the average school achievement was negative. The results were discussed by considering the big-fish-little-pond effect. Keywords: big fish little pond effect, TIMSS, self-concept, science education

Exploring impact of student attitude, parental involvement, and teacher competence on mathematics performance in selected schools in Northern Ghana

The purpose of this study was to see how students’ attitudes towards mathematics influenced their academic achievement in the Savelugu Municipality in the Northern Region of Ghana. The study employed the pragmatic paradigm and quantitative methodology. A 41-item semi-structured questionnaire rated using 5-points Likert scale, and document reviews were used to collect data. A combination of purposive and simple random sampling procedures was used to select 35 junior high school (JHS) in the Savulugu Municipality, questionnaires were administered to 350 JHS students, however, 315 questionnaires were returned. Data obtained from questionnaire were analyzed using Pearson product moment correlation coefficient, t-test, means, standard deviation, and percentages. The results revealed that educational institutions should develop programs to help parents become more active in their children’s education. To influence students’ attitudes towards mathematics study, policymakers and the Ghanaian Educational Service should promote programs such as National Mathematics Day to raise students’ awareness of the importance of mathematics in their daily lives. The Ministry of Education and non-governmental organizations should endeavor to offer enough instructional resources and financial incentives to instructors to help them make teaching relevant in the classroom.

TIMSS vs. PISA: what can they tell us about student success?—a comparison of Swedish and Norwegian TIMSS and PISA 2015 results with a focus on school factors

This paper explores the measurement capabilities of the Trends in International Mathematics and Science Study (TIMSS) and the Program for International Student Assessment (PISA) in assessing school factors that influence student performance. We specifically focus on the 2015 assessments of the science performance of eighth graders in Sweden and Norway. This was the latest year when the two assessments were conducted in the same year and science was the major subject area in the PISA assessment, which was essential for maximizing the assessments’ comparability. Using multilevel models, the study identifies common and unique factors across the assessments and investigates the factors that influence student performance at different proficiency levels. The findings highlight the importance of school-level factors, which are significant in both assessments. Moreover, both assessments provide information on overlapping sets of factors that have varying influence on the performance of students with different proficiency levels. Overall, there are limited common factors between TIMSS and PISA. School factors vary between low-performing and high-performing schools, with differing significance in Norway and Sweden. The results indicate that TIMSS and PISA assessments offer complementary information, particularly for low-performing schools. Our findings suggest that different school types may benefit or suffer from distinct school factors. The findings are relevant for both educational professionals and policy-makers.

Systematic Literature Review: Implementation of Ethnomodelling in Mathematics Learning

The increase in research on ethnomathematics in mathematics education, along with the rise in research on ethnomodelling. It triggers an increasing need and interest in how ethnomodelling is applied in mathematics learning. This study aims to review the literature on implementing ethnomodelling in mathematics learning. This research method is a systematic literature review with the PRISMA model. The research data are ethnomodelling-themed studies in mathematics learning published from 2019 to 2023 and obtained through the Google Scholar database. The articles obtained were 17 articles published in various countries. The results showed the implementation of ethnomodelling in mathematics learning, including different mathematical concepts, cultural objects, and ethnomodelling approaches. Also presented are contributions from various researchers and countries that have applied ethnomodelling in mathematics learning. The results of this study contribute to researchers, teachers, and practitioners in the form of a review of various ethnomodelling studies within the scope of mathematics concepts. So, they can be used as guidelines in developing culture-based mathematics learning strategies.

Factors Influencing the Attitude of Students Towards the Study of Mathematics among Secondary Schools in Uyo, Akwa Ibom State Nigeria

Students’ attitude towards mathematics has been a factor that is known to influence students’ achievement in mathematics. This paper explored factors influencing the attitude of students towards the study of mathematics in Nigeria. This study used a descriptive survey design. A simple random sampling technique was further applied to obtain Mathematics teachers, junior and senior staff, and principals targeted in this research, equal to 273 staff. The study sampled 162 respondents. The collected data was analyzed using descriptive statistics, correlation, and regression analysis through the Statistical Package for Social Science (SPSS) version 21. The data collected were analyzed using descriptive statistics and multiple regression. The findings indicated that the teaching approach in teaching Mathematics was more correlated with students ‘attitudes in Uyo, Akwa Ibom State (r = 0.738; p= 0.000). Multiple linear regression analysis showed that the problem-solving method contributed to 57.2% of the variation in the performance, hence playing a vital role in students ‘attitudes towards Mathematics subjects in public secondary schools. It was also inferred that the teaching approach increases positive attitudes toward learning Mathematics subject. The study recommended that the maximum effort should be given to improve the students‟ attitude toward mathematics by organizing forums such as seminars and workshops where teachers and other education stakeholders can support, motivate, and cultivate positive attitudes among their students.

Modeling and techno-economic optimization of the supercritical drying of silica aerogels

Supercritical drying is the only effective method for producing aerogels. Aerogels are innovative materials that found various applications in the range of industries. At the same time, supercritical drying is a technologically complex and expensive process, and an important goal is to optimize the production process to reduce costs and energy consumption. In this paper, the following aspects are considered: Investigation of the influence of parameters on the supercritical drying of silica aerogels on a laboratory scale; Modeling and simulation of the supercritical drying process; Developing a methodology for calculating the cost of manufacturing of silica aerogels; Creating a software module for calculating the cost of manufacturing of silica aerogels and performing techno-economic optimization of the supercritical drying process; Techno-economical optimization of the supercritical drying of silica aerogels on a pilot scale. With the aid of the developed software, techno-economic optimization of the pilot plant of silica aerogels was carried out. The developed mathematical model, optimization approach, and studies of the intensification of the supercritical drying process make it possible to reduce the cost of manufacturing in the existing production of aerogels by 26.4%.

Mathematical study of the mechanical properties of NOL rings with different winding process parameters

This study investigates the impact of different winding tension parameters (40 N, 45 N, and 50 N) on the quality of fiber-wrapped products using the Navy Ordnance Laboratory (NOL) composite rings. Design Expert software was utilized to analyze the response surface of fiber winding process parameters, including winding tension, winding speed, and curing temperature, which significantly influence the mechanical properties of the fiber. Mathematical models were developed to understand the combined effects of these process parameters on the mechanical properties of NOL rings. Furthermore, a satisfaction function was employed to synthesize the two mechanical response variables into a comprehensive index for parameter optimization. Experimental validation was conducted to verify the reliability of the proposed design scheme.

The public health impact and cost-effectiveness of the R21/Matrix-M malaria vaccine: a mathematical modelling study

The R21/Matrix-M vaccine has demonstrated high efficacy against Plasmodium falciparum clinical malaria in children in sub-Saharan Africa. Using trial data, we aimed to estimate the public health impact and cost-effectiveness of vaccine introduction across sub-Saharan Africa. We fitted a semi-mechanistic model of the relationship between anti-circumsporozoite protein antibody titres and vaccine efficacy to data from 3 years of follow-up in the phase 2b trial of R21/Matrix-M in Nanoro, Burkina Faso. We validated the model by comparing predicted vaccine efficacy to that observed over 12-18 months in the phase 3 trial. Integrating this framework within a mathematical transmission model, we estimated the cases, malaria deaths, and disability-adjusted life-years (DALYs) averted and cost-effectiveness over a 15-year time horizon across a range of transmission settings in sub-Saharan Africa. Cost-effectiveness was estimated incorporating the cost of vaccine introduction (dose, consumables, and delivery) relative to existing interventions at baseline. We report estimates at a median of 20% parasite prevalence in children aged 2-10 years (PfPR2-10) and ranges from 3% to 65% PfPR2-10. Anti-circumsporozoite protein antibody titres were found to satisfy the criteria for a surrogate of protection for vaccine efficacy against clinical malaria. Age-based implementation of a four-dose regimen of R21/Matrix-M vaccine was estimated to avert 181 825 (range 38 815-333 491) clinical cases per 100 000 fully vaccinated children in perennial settings and 202 017 (29 868-405 702) clinical cases per 100 000 fully vaccinated children in seasonal settings. Similar estimates were obtained for seasonal or hybrid implementation. Under an assumed vaccine dose price of US$3, the incremental cost per clinical case averted was $7 (range 4-48) in perennial settings and $6 (3-63) in seasonal settings and the incremental cost per DALY averted was $34 (29-139) in perennial settings and $30 (22-172) in seasonal settings, with lower cost-effectiveness ratios in settings with higher PfPR2-10. Introduction of the R21/Matrix-M malaria vaccine could have a substantial public health benefit across sub-Saharan Africa. The Wellcome Trust, the Bill & Melinda Gates Foundation, the UK Medical Research Council, the European and Developing Countries Clinical Trials Partnership 2 and 3, the NIHR Oxford Biomedical Research Centre, and the Serum Institute of India, Open Philanthropy.

What COVID-19 Vaccine Distribution Disparity Reveals About Solidarity

What COVID-19 Vaccine Distribution Disparity Reveals About Solidarity

Health systems impacts of the COVID-19 pandemic on malaria control program implementation and malaria burden in Benin: A mixed-method qualitative and mathematical modelling and study.

The COVID-19 pandemic has sent ripple effects across health systems and impacted the burden of many other diseases, such as malaria in sub-Saharan Africa. This study takes a mixed method approach to assess the impact of COVID-19 on malaria control programs in three rural communes in Benin. We conducted individual semi-structured interviews with key informants who play important roles in malaria control in Benin at three levels of the health system-national, health zone, and commune. Using a purposive sampling technique, informants were interviewed regarding their roles in malaria control, the impact of the pandemic on their activities, and the mitigation strategies adopted. Relevant themes were identified by content analysis. We then formulated an agent-based model of malaria epidemiology to assess the impacts of treatment disruption on malaria burden. The key informant interviews revealed that essential aspects of malaria control were upheld in Benin due to the close collaboration of public health practitioners and health care providers at all levels of the health system. There were some disruptions to case management services for malaria at the start of the pandemic due to the public avoiding health centers and a brief shortage of malaria treatment that may not be entirely attributable to the pandemic. Results from the agent-based model suggest that duration, severity, and timing of treatment disruption can impact malaria burden in a synergistic manner, though the effects are small given the relatively mild disruptions observed. This study highlights the importance of top-down leadership in health emergencies, as well as the critical role of community health workers in preventing negative health outcomes for their communities. We also showcased the integration of qualitative research and mathematical models-an underappreciated form of mixed methods research that offer immense value in the continued evaluation of rapidly evolving health emergencies.

Etnomatematika pada Pakaian Adat Ulos Batak Toba dan Implementasi dalam Rancangan Pembelajaran Matematika

The country of Indonesia is rich in culture where there are elements of mathematics in it. One of these cultures is Ulos cloth with various motifs. The results of this study of mathematics in culture can then be implemented in contextual mathematics learning by paying attention to cultural background, which is expected to facilitate and motivate students. The purpose of this research is to explain and expose the existence of ethnomathematics-based learning methods that associate elements of a culture with mathematical learning. With the existence of a culture, every person or individual can know everything that is contained in that culture. By choosing a topic about the cultural diversity of communities in the region of North Sumatra about the customary clothing of Ulos Batak, which in this study explains the existence of ethnomatematics contained in the motifs of the fabric of the Ulos of the Tribe of Batak Toba used in the wedding ceremony. The research method used is descriptive qualitative. The research also reveals how mathematical concepts are reflected in the fabric motifs of the outline, such as transformation, symmetry, and balance. This research uses data analysis techniques i.e. reduction, presentation and drawing conclusions. The data collection technique is carried out with the method of literature study where it is done by searching from various sources about Batak Toba's Modern Clothing then reduced by selecting the necessary information. Research results show that ethnomatematics is present in a variety of fabric motifs, including Passamot, Pengantin, Holong, and Sadum. By understanding the interrelationship between mathematics and culture in the context of the textile fabric, mathematical learning can become more interesting and meaningful for students. The research also emphasizes the importance of understanding and preserving the cultural heritage of the Batak Toba tribe.

Критическая рефлексия системного подхода к изучению взаимодействия формальной логики и обоснования математики

It should be noted that many modern works on logical research use a complex technical apparatus, which can only be understood by a well-prepared logic, it is impossible without studying mathematics. On the other hand, feedback from logic in the study of mathematics is important, since logical principles are intrinsically present in the basis constructions of mathematics and in mathematical logic. The principles of logic are adopted in mathematics in order to develop mathematical thinking through critical reflection, although formal logical analysis does not always reflect the real rules of mathematical argumentation. Understanding this contributes to the fundamentality of university mathematical education, as well as the need for a systematic approach to justification for mathematics.

Research trends in critical thinking skills in mathematics: a bibliometric study

<span lang="EN-US">This study systematically reviews and analyzes previous studies’ literature to identify the research gaps and the steps that must be taken for research on critical thinking in further mathematics education. Two methods, namely bibliometric analysis and descriptive content analysis, were used to achieve this goal. Data for the bibliometric analysis was obtained from the Scopus database, with the keywords “critical thinking” and “mathematics” Documents accessed are limited to the publication range of 2012-2022. The results show that the number of critical thinking research in mathematics has increased significantly, with a peak in 2021 of 65 articles; the United States has the most research and citations. The source that received the most citations was the journal Educational Studies in Mathematics. The evolution of the theme of critical thinking in mathematics began to link critical thinking with collaboration learning, mathematics education, teacher education, engineering, education, and collaborative learning. The quantitative approach with a student sample, tests as data collection instruments, and the analysis of variance (ANOVA) method is the methodology most often used by researchers. The results of this study are likely helpful for other researchers who will examine critical thinking skills in mathematics, namely as a research guide that they will develop. In addition, the existence of several research gaps can motivate other researchers to fill these gaps to contribute to improving the quality of critical thinking in mathematics.</span>

Smart performance optimization of energy‐aware scheduling model for resource sharing in 5G green communication systems

AbstractThis paper presents an analysis of the performance of the Energy Aware Scheduling Algorithm (EASA) in a 5G green communication system. 5G green communication systems rely on EASA to manage resource sharing. The aim of the proposed model is to improve the efficiency and energy consumption of resource sharing in 5G green communication systems. The main objective is to address the challenges of achieving optimal resource utilization and minimizing energy consumption in these systems. To achieve this goal, the study proposes a novel energy‐aware scheduling model that takes into consideration the specific characteristics of 5G green communication systems. This model incorporates intelligent techniques for optimizing resource allocation and scheduling decisions, while also considering energy consumption constraints. The methodology used involves a combination of mathematical analysis and simulation studies. The mathematical analysis is used to formulate the optimization problem and design the scheduling model, while the simulations are used to evaluate its performance in various scenarios. The proposed EASM reached a 91.58% false discovery rate, a 64.33% false omission rate, a 90.62% prevalence threshold, and a 91.23% critical success index. The results demonstrate the effectiveness of the proposed model in terms of reducing energy consumption while maintaining a high level of resource utilization.

Review of research on performance indicators for water utilities

Abstract Water utilities are affected by various social, environmental, and technological factors and are increasingly required to enhance their infrastructure and long-term efficiency. Performance indicators are useful tools for assessing the operational, financial, environmental, and social aspects of water systems. Given this background, the author reviewed the literature on performance indicators for the water sector and summarized the research trends as follows. As a perspective, there are a lot of good mathematical and theoretical studies on distribution pipes and leakage management. Future research should address the problems of water utilities, by using multiple levels of performance indicators including social and environmental context in the long term. Asset management and utility management studies address diverse and current problems faced by water utilities. However, there is still room for improvement in standardizing the methodology for data collection, processing, and integration. In addition, it is recommended for future research, to include carbon neutrality aspect, to include pipeline materials and soil information in leakage management, to extend asset management studies to treatment plants, with including additional indicators about human and financial resources.

On–Off Intermittency and Long-Term Reactivity in a Host–Parasitoid Model with a Deterministic Driver

Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host–parasitoid systems. We explore the impact of environment on the host–parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental fluctuations on the average host population growth rate. We hence focus on the discrete host–parasitoid Beddington–Free–Lawton model and show that a more comprehensive mathematical study of the dynamics behind the onset of on–off intermittency in host–parasitoid systems may be achieved by considering a deterministic, chaotic system that represents the dynamics of the environment. To this aim, some of the key model parameters are allowed to vary in time according to an evolution law that can exhibit chaotic behavior. Fixed points and stability properties of the resulting 3D nonlinear discrete dynamical system are investigated and on–off intermittency is found to emerge strictly above the blowout bifurcation threshold. We show, however, that, in some cases, this phenomenon can also emerge in the sub-threshold. We hence introduce the novel concept of long-term reactivity and show that it can be considered as a necessary condition for the onset of on–off intermittency. Investigations in the time-dependent regimes and kurtosis maps are provided to support the above results. Our study also suggests how important it is to carefully monitor environmental variability caused by random fluctuations in natural factors or by anthropogenic disturbances in order to minimize its effects on throphic interactions and protect the potential function of parasitoids as biological control agents.

Preface

Preface The present volume constitutes the proceedings of the First workshop on Soliton Theory, Nonlinear Dynamics and Machine Learning held in Varna (Bulgaria) from 12 to 17 August 2023 which is organized by the Institute for Advanced Physical Studies (Bulgaria) and the Institute for Physical and Mathematical Studies of the Varna Free University (VFU).The purpose of the workshop was to bring together qualified scientists, young researchers and students with expertise and interests in mathematics and physics. In this way the workshop was intended to offer an opportunity to discuss recent developments and achievements, as well as future perspectives in these modern and fast developing areas and their interface.Contemporary science, mainly due to its complexity, uses more and more elaborate techniques and methods, thus achieving sometimes amazing results. The numerous conferences often involve large number of scientists which should be able to explain their results in rather short time. Hence, only a limited number of participants, who already have mastered the relevant field, are able to understand these results. A beginner in the field has practically no chances to understand which are the main ideas and techniques in it. Our aim with this workshop was to avoid these difficulties and to help a group of beginners do their start in science. In order to achieve practical results with our Workshop to have more young people as participants. Every speaker had 45 minutes for presentation and 15 minutes for questions and discussions. This is an ample time to explain in detail the main ideas in the talk so that even a beginner could understand it. In addition there was extra time during the coffee and lunch breaks for contacts among the people on site. Of course for the online participants this was more difficult, though they were given optimal chances to ask questions during and after the reports.It is our belief that in such atmosphere the beginners will have the best chance to understand a certain subject and get introduced to a given scientific field. During the Workshop we had 28 reports (see the list of reports and the list of participants). Some of the younger participants were also given the chance to report on their results and to gain experience for their future participation in conferences.The workshop greatly benefited from the dedicated involvement of the renowned experts in their fields of science Vladimir Gerdjikov (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences), Peter Hristov (CERN), Radu Constantinescu (University of Craiova, Romania), Rossen Ivanov (Technological University Dublin, Ireland), Stoytcho Yazadjiev (St. Kliment Ohridski University of Sofia, Bulgaria) who were the scientific committee members.We would like to thank the President of VFU Dr. Krasimir Nedyalkov and the Rector of VFU Prof. Dr. Peter Hristov for the collaboration and continuous attention.The success of every conference is based on the activity and the competence of its participants. We are grateful to all participants for their efforts to produce high quality reports and for their activity in the discussions after every talk.The Workshop was held at the VFU campus, close to the Black Sea with the financial support of the Bulgarian National Science Fund contract BG-175467353-2023-02-0006 and Varna Free University.The Editors:R. Constantinescu, V. Gerdjikov, S. Mishev, S. YazadjievList of Scientific Committee, Local Organizing Committee are available in this pdf.