Mathematical Sciences Research Articles

Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations

In this study, solutions of random complex partial differential equations were found using the two-dimensional Sumudu transformation method(STM). The initial conditions of a deterministic equation or the non-homogeneous part of the equation are transformed into random variables to obtain a random complex partial differential equation. With the help of the properties of two-dimensional Sumudu and inverse Sumudu transformation, an approximate analytical solution of a complex partial differential equation with random constant coefficients was obtained by selecting a random variable with an initial condition of Normal and Gamma distribution. The probability characteristics of the resulting solutions, such as expected value and variance, were obtained and graphically shown with the help of the Maple package program.

Умови екстремальності допустимого елемента для задачі відшу-кання узагальненого чебишовського центра кількох точок деякого полінормованого простору відносно множини цього простору

The problems related to the need to approximate complex mathematical objects in the best possible way with simpler and more convenient ones arise in various sections of mathematical science. An important class of approximation theory problems is the best simultaneous approximation of several elements. The problem of finding the Chebyshev center of several points of a linear normalized space relative to the set of this space can be attributed to the problems of best simultaneous approximation of several elements. This task consists in finding in a given set of linear normed space such a point (the relative Chebyshev center) the maximum distance to which from several fixed points of space would be the smallest, in other words not exceeding the maximum distance from the given points to any other point of this set. The problems of the best simultaneous approximation of several elements of a linear normed space by convex sets of this space from single positions were considered, in particular, in works [1, 2]. In practice, one has to deal with such problems, in which, when finding the Chebyshev's center of several given points of a linear normed space relative to the set of this space, appear weighted distances. The task of finding the weighted distances of the Chebyshev’s center was considered, in particular, in the paper [3]. In this work, the criteria of generalized Chebyshov’s center in the sense of the weighted distances of the of several points of a linear normed space relative to the convex set of this space, based on the duality ratio for the corresponding extremal problem, are established. If in the problem of the Chebyshev's center of several points of a linear normed space, in which the distances between points are determined by weighted norms, the weighted norms are replaced, generally speaking, by different norms given on the corresponding linear space, then we obtain the problem of the Chebyshev's center of several points of some polynormed space, which is considered in this work. It is clear that the problems about the Chebyshev's center of several points of a linear normed space, which were discussed above, are partial cases of the problem about the Chebyshev center of several points of some polynormed space.

Standardizing Excellence: Metric Assemblages in Mathematics Research in Chile

This study investigates the development, implementation, and establishment of evaluation metrics within the mathematics research community in Chile, a discipline where the use of bibliometric indicators for quality assessment has been highly controversial. Using a mixed-methods approach, the study conducted focus groups with mathematicians at different stages of their academic careers and analyzed the ANID Mathematics Studies Group's method for assessing researcher productivity. The findings reveal that the evaluation metrics in mathematics remain in a state of “magmatic flow,” fluid and solid, constantly changing yet stable enough to articulate multiple social worlds. The study highlights the challenges faced in three closely linked spheres: mathematical research, science and higher education governance, and organizational management. The functioning of this metrics assemblage as boundary infrastructure, which meets the information needs of diverse social worlds while maintaining the integrity of the interests involved, is a temporal achievement of situated practices that provide continuous adjustment and stabilization. The study suggests that academic metric assemblages are made unstable through practical politics involving controversies and qualitative deliberation. Concurrently, they achieve stability through translation and blackboxing practices.

Generative Artificial Intelligence on Mobile Devices in the University Preparation of Future Teachers of Mathematics

The integration of artificial intelligence (AI) is revolutionizing the field of education. The possibilities of AI in education range from providing intelligent tutoring to facilitating computational thinking, a key skill in an AI-based society. As education systems around the world adapt to technological advances, the need for teachers to develop AI skills becomes crucial. This paper explores the use of AI on mobile devices to improve the preparation of future mathematics teachers. We acknowledge the need for teachers to be skilled in the use of AI tools to foster collaborative, effective, and ethical learning environments. We also provide a case study of our implementation of the generative AI ChatGPT in the preparation of future mathematics teachers at the Faculty of Mathematics, Physics and Computer Science at Comenius University in Bratislava. After this implementation, we analyzed students’ opinions on the application of AI in selected areas. We present the results of this analysis and the implications for the practical use of AI in the university education of future mathematics teachers. Finally, based on our study results, we highlight the possibilities of the successful use of AI in different aspects of teaching and its temporary limitations, which are likely to be reduced by further technological developments.

Good Prophets Know When the End Is Near

We consider a class of online decision-making problems with exchangeable actions, where in each period a controller is presented an input type drawn from some stochastic arrival process. The controller must choose an action, and the final objective depends only on the aggregate type-action counts. Such a framework encapsulates many online stochastic variants of common optimization problems with knapsack, bin packing, and generalized assignment as canonical examples. In such settings, we study a natural model-predictive control algorithm. We introduce general conditions under which this algorithm obtains uniform additive loss (independent of the horizon) compared with an optimal solution with full knowledge of arrivals. Our condition builds on the recently introduced compensated coupling technique, providing a unified view of how uniform additive loss arises as a consequence of the geometry of the underlying decision-making problem. Our characterization allows us to derive uniform loss algorithms for several new settings, including the first such algorithm for online stochastic bin packing. It also lets us study the effect of other modeling assumptions, including choice of horizon, batched decisions, and limited computation. In particular, we show that our condition is fulfilled by the above-mentioned problems when the end of the time horizon is known sufficiently long before the end. In contrast, if at a late stage, there is still uncertainty about the end of the time horizon we show that such uniform loss guarantees are impossible to achieve. We use real and synthetic data to illustrate our findings. This paper was accepted by J. George Shanthikumar, data science. Funding: This work was supported by the Division of Mathematical Sciences [Grant 1839346]; the Division of Electrical, Communications and Cyber Systems [Grant 1847393]; and the Army Research Laboratory [Grant W911NF-17-1-0094]. The authors also gratefully acknowledge support from the NSF [Grants ECCS-1847393, CNS-195599, and DMS-1839346], AFOSR [Grant FA9550-23-1-0068], an ARL award [Grant W911NF-17-1-0094], and ARO MURI [Grant W911NF-19-1-0217]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.04307 .

Effect of Ethanolic Extract of Avocado (Persea americana Mill.) Seed on the Testis Histology (Mus musculus l.) Induced Monosodium Glutamate (MSG)

Monosodium Glutamate (MSG) is a substance that is able to produce free radicals such as ROS (Reactive Oxygen Species), which can cause oxidative stress in the body and damage reproductive organs such as the testes. The purpose of this study was to determine the effect of avocado seed ethanol extract (Persea americana Mill.) on the histology of the testes of mice (Mus musculus L.) induced monosodium glutamate (MSG). This research is an experimental study that was conducted in October 2023 – January 2024 at Biology Laboratory, Faculty of Mathematics and Natural Sciences, Universitas Negeri Padang. The design used is a Complete Randomized Design (CRD) with 4 treatments and 6 repeats. The data obtained were analyzed using the ANOVA test (Analysis of variance) using the SPSS 23 application. The results showed that the administration of avocado seed ethanol extract showed a noticeable effect on the diameter of the testes of male mice exposed to MSG. However, it showed no noticeable influence on testicular weight, seminiferous tubule diameter and Leydig cell count. Ethanol extract avocado seed dose 0.84 mg /g body weight / day (P1) was able to improve the diameter of mice testes that had been induced MSGKeyword: Avocado seed extract, Histology of testis, Mice, MSG

Vyacheslav Fedorovych Klepikov (to his 75th birthday)

07.13.2024 75 years have passed since the birthday of Vyacheslav Fedorovych Klepikov, a well-known theoretical physicist, Doctor of physical and mathematical sciences, Professor, Correspondent member of the National Academy of Sciences of Ukraine.

A Tool to Visualise and Interact with Probability Density Functions - Development and Case Study

This article is an overview of the design, implementation and testing of a tool to visualise and interact with probability density functions. The tool is a desktop application implemented entirely in Python using the tkinter library for the graphical user interface. The project was undertaken as part of a collaboration between Mathematics and Computer Science. The goal of the application is to provide a simple user interface for teaching staff and students to visualise and interact with probability density functions. The application should help improve students’ understanding of the concepts involved and its simple design should reduce the complexity barrier that often faces users when using technology in the classroom. Following initial testing, a variety of teaching staff were involved with trialling the tool, together with student volunteers from a first-year and second-year statistics module at Swansea University. Feedback was obtained and evaluated from all participants. For the teaching staff group, we found that all four participants strongly agreed that the application is easy to use and that the user interface was not distracting. Furthermore, all teaching staff stated that they would consider using the application in their own teaching and all would recommend using the application to a colleague/friend. For the student volunteer group, all twelve participants either agreed or strongly agreed with the statements that the application is easy to use, useful and not distracting. Similar to the teaching staff group, all the student participants stated that they would consider using the application in their own learning and all would recommend the application to a friend. A full analysis of the survey results is provided in the Feedback section.

Towards a Better Transition to University: A Student-Centric Welcome Day for the New Undergraduate Students in a Mathematics Department

This case study delves into a Welcome Day event organised by the Department of Mathematical Sciences at a UK university for the incoming first year students in the department. This report reflects some of the practicalities and the evaluation of the event. The event, primarily focused on student engagement activities along with reduced amount of traditional presentations, was aimed at facilitating peer networking and smoothing the transition from school to university, hence nurturing a sense of belonging within the student community. The structure of the event was crafted to align with the department's unique ethos, with an emphasis on activities that resonate with the field of mathematics. Evaluation of the event is done based on the responses from the students during the event via an online questionnaire. The event not only demonstrated high levels of student satisfaction but also served as a good example of department-specific orientation programs. These localized events can complement university-wide initiatives, offering a more tailored setting for new students to acclimate to their specific academic environment. This paper has the prospect to guide others and to reinforce the notion of seeking to tailor welcome days to match the needs of new cohorts.

Mikania micrantha Kunth leaf Methanol Extract as Bioherbicide Againts The Growth of Amaranthus spinosus L. Weeds

The presence of weeds on plantation land causing a decrease in growth and productivity of cultivated plants. Thorny amaranth (Amaranthus spinosus L.) is broadleaf weeds that have high competitiveness. This study aims to determine the influence of the application of bitter vine (Mikania micrantha Kunth) leaf extracts against the growth of thorny amaranth and the best concentration that can inhibit the growth of thorny amaranth weed. This study has been carried out for October 2023 - March 2024 in the Biology Screen House and Chemistry Laboratory, Faculty of Mathematics and Natural Sciences, Tanjungpura University. This study used a completely randomized design (CRD) with four levels concentration treatment of bitter vine leaf extracts with five replications. The treatment consisted of bitter vine leaf extract with a concentration 0% (0g/ml) as a control, 15% (0,15 g/ml), 20% (0,2 g/ml) and 25% (0,25 g/ml). Data was analysed using Kruskal Wallis test followed by Mann-Whitney test. The results showed giving bitter vine leaf extracts can inhibited the growth of thorny amaranth weeds. Application of bitter vine leaf extract concentration 15% was the best treatment that can inhibited the growth of thorny amaranth on parameters weeds height (2,53 cm), number of leaves (2,65 strands), root length (1,74 cm), wet weight (0,13 grams) and dry weight (0,01 grams).

Implementation of Demand and Supply Functions Related to The Application of Mathematical Science to MSME Products in Pelawi Utara Village, Babalan, Langkat Regency

Implementation of Demand and Supply Functions Related to The Application of Mathematical Science to MSME Products in Pelawi Utara Village, Babalan, Langkat Regency

Analysis the Implementation of Independent Learning-Independent Campus Program based on Students’ Perceptions

Investigations of the independent learning-independent campus program still encounter obstacles in its implementation. This research is research that is motivated by the phenomenon of certain obstacles and problems faced by students when implementing independent learning-independent campus program in the mathematics department, FMIPA UNM, so it needs to be reviewed and carried out further analysis as material for further improvements. This research aims to explore student perceptions regarding the implementation of independent learning-independent campus program which is focused on the implementation of existing programs at independent learning-independent campus program which is implemented in the Mathematics Department of FMIPA UNM. This research is quantitative descriptive research using survey methods. The research was carried out at the Mathematics Education Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Makassar. The sample in this study were students in semester IV and semester VI from the FMIPA mathematics department who were selected purposively based on research interests and needs, namely students who took part in the independent learning-independent campus program. Data was analyzed descriptively to see students' perceptions of the implementation of the independent learning-independent campus program. Research finds that students majoring in mathematics at FMIPA UNM responded well to the MBKM program, it can be seen that the majority of students were interested in joining the program.

Comparative Study of Bioactive Compounds of Several Varieties of Sembalun Garlic, Lombok, West Nusa Tenggara

Indonesia is known as a rich country in herbs, which are utilized as a source of natural herbal medicine, including garlic. This research aims to achieve a comparative study of the bioactive compounds retained in several varieties of Sembalun garlic. The research was conducted at the Integrated Laboratory of Mataram State Islamic University and Laboratory of Biology, Faculty of Mathematics and Natural Sciences, University of Nahdlatul Wathan Mataram. Three varieties of Sembalun Garlic were used in this research, namely the Nunggal, Jamak and Sanggah varieties, which were extracted using 96% ethanol. The research results show bioactive compounds in flavonoids, saponins, steroids and phenolics in the three varieties of Sembalun garlic (Nunggal, Jamak, and Sanggah).

PENERAPAN PENDEKATAN STEM UNTUK MENINGKATKAN PEMAHAMAN KONSEP SISWA SD DI KABUPATEN PASURUAN

This study aims to improve the understanding of concepts with Science, Technology, Emgineering, and Mathematics (STEM) approaches in mathematics learning in elementary school students. The subjects of this study were Class IV teachers and 12 MI Riyadlul Ulum students for the even semester 2023/2024 academic year. Data collection techniques are observation, tests and documentation. Data analysis techniques are carried out through three stages, namely data condensation, data presentation, and concluding data. Based on the results of research on the learning process in cycle I, teacher activities obtain good qualifications (B) and student activities obtain sufficient qualifications (C). while in cycle II teacher activities have good qualifications (B) and student activities obtain good qualifications (B). Furthermore, students' understanding of concepts in the first cycle reached a percentage of 75%, in the second cycle it increased to 93%. So it can be concluded that students experience an increase in understanding concepts using a STEM approach. These findings support the integration of STEM approaches in the Merdeka curriculum in basic education to improve the quality of education.

Mathematical Data Science with Applications in Business, Industry, and Medicine

Mathematical data science is a field that combines mathematical techniques with data science methods to extract insights and knowledge from data [...]

Mathematical sciences as symbolic form: the objects and objectivity of science in Ernst Cassirer’s philosophy of science and culture

AbstractIn this paper, I explore how Cassirer’s early and mature epistemology, philosophy of science, and philosophy of culture make up a coherent and comprehensive view of the mathematical sciences that is fruitful for understanding contemporary science. In Cassirer’s first systematic work, Substanzbegriff und Funktionsbegriff, the mathematical sciences are understood through the concept of function. This implies that scientific investigation aims at increased unity in a system of functional concepts, rather than at answering the substance-rooted question of what is. In his mature work, Philosophie der symbolischen Formen, Cassirer expands his inquiry to diverse notions of objects and principles of symbolic forming, recognizing the mathematical sciences as one of many ways of structuring experience, alongside other symbolic forms such as myth and ordinary language. Together, Cassirer’s early and mature works detail the preconditions and idiosyncrasies of the unfolding of scientific objects and situate the mathematical sciences within the totality of human experience. Applying these insights to contemporary interpretations of science suggests connecting common misconceptions of science to challenges in translating objects between symbolic forms. I propose the concepts of domestication and mythification of science as instructive for clearing up such misunderstandings.

THE EFFECT OF PROBLEM-BASED LEARNING MODEL ON STUDENTS' PHYSICS LEARNING OUTCOMES

The purpose of this study is to measure student learning outcomes using problem-based learning models on students' physics learning outcomes. The research method is using experimental research. The research design used is Posttest-Only Control Design. The sampling technique used in the study was simple random sampling, so one class was obtained as a control class, namely class X mathematics science 2 and one class as an experimental class. With Data Analysis Techniques using Descriptive Analysis and inferential analysis. The results of the study showed that students who were taught with problem-based learning models had high average physics learning outcomes scores, while students who were not taught with this model had average physics learning outcomes scores that were in the low and sufficient categories. This study also found a significant difference in physics learning outcomes between the two groups, indicating that problem-based learning models have a positive effect on students' physics learning outcomes. This study provides a new perspective in measuring the effectiveness of problem-based learning models, especially in improving students' physics learning outcomes, which have not previously been widely studied in the context of physics learning in Indonesia.

Socio-Economic Status of Students and Its Impact on the Quality of Studies

The research was done in order to highlight the connection between the socio-economic status (SES) of students and the quality of studies, as well as the connection between the organization of the teaching curriculum and the quality of studies. It has a quantitative descriptive design and falls in the field of theoretical-empirical research. The population is homogeneous and includes students from the faculties of Education throughout Kosovo and the Faculty of Mathematical and Natural Sciences in Pristina, who attended bachelor studies in the period 2019–2022. The research was conducted with a sample of 312 students, representing over 2800 students. The research instrument was a survey/questionnaire. The results of the research showed that the social and economic status of students is in stable correlation with the quality of studies. The research also highlighted that the organization and quality implementation of the teaching curriculum significantly correlates with the quality of studies. From the attitudes of the students, it was understood that there is a variable correlation depending on the variables (such as marital status, village-city residence, number of employees in the family, economic situation, etc.). The findings from the research serve as a recommendation for educational institutions so that during the drafting of policies on education, they take into consideration the qualitative organization of studies by institutions of higher education, as well as create mechanisms to help students with poor economic conditions, in order to raise of the quality of studies and the quality of education.

‘STEM belonging’: the association between stereotype vulnerability, COVID-19 stress, general self-efficacy, multidimensional perceived social support, and STEM interest among Physics, Chemistry, and Mathematical Science students

ABSTRACT This study aimed to develop and validate a theoretical framework elucidating the connections between general self-efficacy (GSE), multidimensional perceived social support (MPSS), STEM interest (SI), stereotype vulnerability (SVS-4), COVID-19 Student Stress (CSSQ), and STEM Belonging (SB) among a diverse group of students in England. An online survey was administered to 290 Mathematics (n = 83, 28.6%), Physics (n = 95, 32.8%), and Chemistry (n = 112, 38.6%) students in three Russell Group universities in England. The majority of participants (n = 115, 43.1%) were between 18 and 19 years old. Data were collected and analysed using a structural equation model and multigroup analysis. The study findings revealed that MPSS, GSE, and SI had a positive impact on students’ SB, while CSSQ and SVS-4 had a negative impact on students’ SB. The findings revealed that the influence of MPSS on SB and the effect of GSE on SI were found to be statistically significant among female, male, and non-binary students, as well as across A-level, undergraduate, master’s, and Ph.D. levels.

Interest in science and mathematics teaching among non-science/mathematics initial teacher education candidates

ABSTRACT Many countries are experiencing teacher shortages, with particularly long-standing issues in attraction and retention in secondary science and mathematics. Policy initiatives often focus on science and mathematics undergraduates, with the aim of encouraging them to consider teaching by offering scholarships into teacher education or fast-tracking into employment permanency. However, those who have already chosen to teach in non-science and mathematics teaching specialisations have already shown their interest in teaching and form a pool of candidates that may potentially be recruited into science and mathematics teaching pathways. While these non-science and mathematics teacher candidates could have the capacity to address in part longstanding science and mathematics teacher shortages, there is a lack of research examining their motivations from the perspective of initiatives that may attract them into science and mathematics teaching, and little that examines their science and mathematics backgrounds. We sought to address these gaps by surveying 349 initial teacher education (ITE) students from four Australian universities, examining their career motivations, interest in science and mathematics teaching, and science and mathematics backgrounds. We explored perceived barriers to secondary science and mathematics teaching, and responses to potential policy initiatives. We found that 61% of non-science/mathematics ITE candidates indicated high interest in secondary science or mathematics pathways. Policy options such as support for science and mathematics retraining after several years of teaching in their current subject area or level, were selected as likely to support this choice. Our results suggest considerable capacity for policymakers and tertiary institutions to design initiatives that may attract non-science/mathematics ITE candidates into science and mathematics teaching.