Mathematical Sciences Research Articles

UJI ASYMPTOTIC KORELASI DUA VARIABEL ACAK MENGGUNAKAN METODE DELTA

The purpose of this study is to obtain the limit distribution of the sample correlation coefficient, to test the population correlation coefficient and furthermore to apply the derived method in testing the correlation of the weight (BB) and the height (TB) of the students of Mathematics Department, Faculty of Mathematics and Natural Sciences, Halu Oleo University. The limit distribution of the sample correlation coefficient is derived by means of the central limit theorem and the delta method. Random samples (X_i,Y_j) are assumed to follow a bivariate normal distribution. Based on these assumptions by using the Delta method, it is obtained that (√n (r-ρ))/(1-ρ^2 )→N(0,1). Furthermore, a test for the hypotheses H_0:ρ=0 against H_1:ρ≠0 is to reject H_0 at a level of significance α, if Z_count>Z_(1-α/2) or Z_count<Z_(α/2). The application of the asymptotic test method in testing the correlation between BB and TB leads to the conclusion of the rejection of H_0.

Demographic factors and university mathematics performance during Covid-19

This research considers the academic performance of all students undertaking mathematical sciences modules at the University of the West of Scotland in the years immediately before and during Covid-19-induced learning and assessment changes. Each student's first attempt at each module was considered, and we investigated what demographic factors affected their grades. The statistical analysis showed that on average, the performance of young, male students from ethnic minority backgrounds deteriorated the most during this period. We present statistics which illustrate that not all demographic groups' scores deteriorated throughout the pandemic; however, there was an alarming increase in non-engagement of assessment across the entire student body. We conclude with possible next steps to further this investigation and hence provide reflection for university executives and support teams alike.

Optimizing Portfolio Risk through Diversification: Application of The Black-Litterman Model

Aim: The study investigates how the risk reduction strength of different assets and their impact on minimizing portfolio risk. It seeks to recommend an optimal investment strategy using the Black-Litterman model to balance risk and return, helping investors make informed decisions to enhance portfolio stability and financial resilience. Study Design: We adopt a quantitative approach, by employing the Black-Litterman model to analyze portfolio risk reduction. Monthly financial data from 2018 to 2022 is used to evaluate the impact of asset allocation on risk minimization, focusing on assessing various asset combinations to determine the most effective diversification strategy. Place and Duration of Study: The study took place at the Department of Mathematical Sciences, Adekunle Ajasin University, Akungba Akoko, Nigeria, where we explored data from Yahoo finance of Gold, Oil and Gas which span from 2018 to 2022. Methodology: Data from Yahoo Finance (2018-2022) covering Gold, Oil, and Natural Gas was analyzed. The Black-Litterman model was used to compute portfolio risk. The Augmented Dickey Fuller test verified stationary conditions of time series data before the model implementation. Mean-variance optimization techniques determined asset allocation. Various portfolios were compared to identify those with the lowest risk levels. Results: Gold exhibited the highest risk reduction strength (8.7%), followed by oil (8.37%) and natural gas (0.47%). Portfolios containing gold had significantly lower risk levels. The benchmark portfolio had 0.0038 risk, while portfolios excluding gold had higher risks, confirming gold’s effectiveness in minimizing overall portfolio risk. Conclusion: The study confirms that diversification alone does not guarantee risk minimization unless optimal asset selection is applied. Portfolios with high-risk reduction assets like gold significantly lower overall risk. Investors should prioritize assets with strong risk reduction capabilities to enhance portfolio stability, particularly during economic downturns or financial crises.

Preface to the Proceedings of the International Conference on Physics and Technology of Advanced Materials (ICPTAM) 2024 in conjunction with 8th Nanoscience and Nanotechnology Symposium (NNS)

The International Conference on Physics and Technology of Advanced Materials (ICPTAM) 2024, held in conjunction with the 8th Nanoscience and Nanotechnology Symposium (The 8th NNS), took place from 7-10 October 2024 in Bali, Indonesia. With the overarching theme of “Advanced materials for future technology”, this event brought together leading scientists, engineers, and professionals to discuss cutting-edge advancements in materials science and nanotechnology in celebration of international year of quantum science and technology. The event features 2 keynote speakers, 6 plenary speakers, 14 Invited speakers, and 90 contributed oral presenters, which come from several countries: Japan, Malaysia, Indonesia, South Korea, United Kingdom, Thailand, Taiwan, China, and India. This year’s conference provided a unique platform for participants to exchange knowledge, foster collaboration, and showcase innovative research on topics ranging from functional advanced materials, nanomaterials and nanotechnology, computational materials and modelling, nanoelectronics and nanodevices, energy materials, environmental and green materials, biomaterials and biodevices, quantum computing. This event also highlighted the crucial intersection of physics and materials science in shaping the future of technology and society. We would like to express our sincere appreciation to Prof. Ir. Wahyu Srigutomo, Dean of the Faculty of Mathematics and Natural Sciences (FMIPA), Bandung Institute of Technology (ITB), for his invaluable support and guidance in preparing this scientific event. We also extend our heartfelt gratitude to the Physical Society of Indonesia, MRS-id, and the Department of Electrical Engineering, Udayana University, for their generous support and collaboration, which played a pivotal role in ensuring the success of this conference and creating an engaging and stimulating environment. List of Advisory Board, Organizing Committee and Co-Organizing Committee are available in this Pdf.

A new hierarchical control for the wave equation

A new hierarchical control for the wave equation

Research on bench dragon motion based on Runge-Kutta algorithm

"The Bench Dragon" is a distinctive folk art form originating from the Fujian and Zhejiang regions of China. It plays a pivotal role in cultural preservation and serves as a vital conduit for cultural exchange, both within China and globally. A well-executed "Bench Dragon" performance significantly bolsters national cultural identity and is a prominent display of China's cultural allure. The study focuses on enhancing the performance's fluidity and safety by precisely determining the real-time location of the dragon dance team and anticipating potential collisions. The research employs a mathematical approach to model the dragon's movement as a spiral curve, utilizing differential equations and the Runge-Kutta algorithm to describe the position of the dragon head's front handle at any moment. This methodological innovation offers a scientific basis for the performance, optimizing it through mathematical modeling to improve both its visual appeal and safety. Additionally, the cosine iteration method is applied to calculate the positions of the dragon body and tail handles, based on the known position of the head's front handle, ensuring the performance's synchronicity. The study also delves into the analysis of potential collisions using the SAT algorithm, which, after simplifying the judgment criteria, accurately forecasts the timing of collisions. This analysis is crucial for ensuring the performance's safety and smooth progression. The integration of mathematical and physical sciences with the "Bench Dragon" tradition not only enriches its research domain but also provides novel scientific methodologies and technical support for the continuation and evolution of this traditional folk art. This interdisciplinary approach underscores the potential for blending traditional practices with modern scientific techniques to foster cultural heritage while ensuring performances are conducted with enhanced safety and aesthetic quality.

SPECIAL CURVES ACCORDING TO TYPE-2 QUATERNIONIC FRAME IN R4

Quaternions, which were defined by William Rowan Hamilton in 1843, are a number system in four-dimensional space and are analogous to complex numbers. However, quaternion multiplication is not commutative, distinguishing them from complex numbers. Quaternions are special mathematical tools used in computer science, robotics, and many other mathematical sciences. From this point of view, they also get attention in differential geometry. In particular, their characterizations given by the Serret-Frenet apparatus are challenging. For this reason, Bharathi and Nagaraj obtained Serret-Frenet formulas for spatial quaternionic and quaternionic curves in R3and R4, respectively. Inspired by this work, the geometers obtained quaternionic frames in 4-dimensional Semi-Euclidean space R_2^4, dual quaternionic space, and lately type -2 quaternionic frame in R4. Their features are also examined. On the other hand, studying the characterizations of the curves is a significant research area for differential geometers because of having used various branches of applied sciences. Particularly, the features of the specially defined curves, such as Bertrand, Smarandache, rectifying, and osculating curves, are curiously studied. In four-dimensional spaces, rectifying curves are defined as a curve whose position vector fully lies in {T,N2,N3}. Similarly, the osculating curve defined as first and second kind became of having two different binormals {T,N1,N2} and {T,N1,N3}, respectively. In this study, inspired by the definitions above, we define rectifying, osculating first kind, and osculating second kind curves according to the type-2 quaternionic frame in R4. Their characterizations are also examined.

A Review of the Chebyshev Inequality Pertaining to Fractional Integrals

In this article, we give a brief review of a well-known integral inequality that gives information about the integral of the product of two functions using synchronous functions, the Chebyshev inequality. We have compiled the most relevant information about fractional and generalized integrals, which are one of the most dynamic topics in today’s mathematical sciences. After presenting the classical formulation of the inequality using Lebesgue integrable functions, the most general results known from the literature are collected in an attempt to present the reader with a current overview of this research topic.

Systematic Literature Review dengan Metode Prisma: Pembelajaran Berdiferensiasi pada Pendidikan Dasar

Since the implementation of the Merdeka Curriculum, differentiated instruction has increasingly become the focus of educators in Indonesia. Differentiated instruction is considered highly relevant to the current condition of students. This research investigates the trends and main findings from studies on differentiated instruction in elementary and middle school. A systematic literature review followed the PRISMA protocol to achieve this goal, focusing on articles published from 2020 to May 2024. The initial search on Google Scholar yielded 2,460 relevant article titles. Several inclusion and exclusion criteria were applied during the screening process, resulting in the analysis and qualitative synthesis of only 12 articles. The findings of this review indicate that the number of comparative studies on differentiated instruction in Indonesia has increased since 2022. Research on differentiated learning is mainly carried out in Mathematics and Natural Sciences subjects. The main findings from the reviewed articles show that differentiated instruction has a more significant impact than traditional instruction in enhancing the learning outcomes of elementary and junior high school students in areas such as conceptual understanding, critical thinking, and problem-solving skills. However, one article found different results regarding students’ autonomy. Most reviewed articles did not elaborate on the content, process, and product aspects used in the differentiated instruction under investigation.

The botization of science? Large‐scale study of the presence and impact of Twitter bots in science dissemination

AbstractThe rise of social media has brought new dynamics to the dissemination of scientific research, with Twitter (X) playing a significant role. This study focuses on the role of social bots—automated accounts designed to mimic human behavior and amplify content—in scientific communication. By analyzing over 3.7 million papers published between 2017 and 2021 and their 51 million Twitter mentions. Using a novel hybrid method that includes BotometerLite and specific activity parameters, with verification via a robustness check, it was found that 0.23% of accounts were bots. Despite their small numbers, these bots contributed to 4.72% of all mentions, indicating a significant presence, but with varied impact. Bots were particularly active in Mathematics, Physics, and Space Sciences, where they generated over 70% of tweets in some cases. Automated accounts disproportionately influence the visibility and perceived impact of research in these disciplines, which underscores the need for discipline‐specific analysis when considering Twitter's role in scientific communication. This large‐scale study highlights the potential for bots to skew altmetric indicators, misleading stakeholders about true engagement.

Identifying academic phrases in self-compiled corpora: A case study from mathematical sciences

Multi-word combinations are a key component of a variety of academic genres. Student writers thus need to master control of these expressions to communicate effectively in their specific contexts. However, multi-word patterns often present a challenge to students at various levels of academic study. This paper reports on a case study exploring how a data-driven learning approach drawing on self-compiled corpora can enhance student writing in preparation for their doctoral study at a British university. The participant was an international student in mathematical sciences who utilized a self-build corpus throughout a ten-week pre-sessional programme to acquire and incorporate multi-word expressions in their writing. The effectiveness of this approach was investigated through a ‘talk around text’ technique in an interview on completion of the pre-sessional programme. The findings show that a self-compiled corpus is a valuable resource for students mastering writing in specific disciplinary contexts. This article was published open access under a CC BY-NC-ND licence: https://creativecommons.org/licenses/by-nc-nd/4.0/ .

The Effectiveness of Puzzle Game-Based Learning Media in Improving Mathematics Science Problem Solving Skills

Problem solving ability is an important skill in learning mathematics, especially in geometry material that requires conceptual understanding and spatial analysis. This study aims to test the effectiveness of puzzle games in improving mathematical science problem solving abilities. The method used in this study was a quasi-experimental design with a pretest-posttest control group design. The research sample consisted of 60 grade XII students who were divided into two groups, an experimental group using ethnomathematics puzzle games and a control group using conventional methods. Data were obtained through problem solving tests before and after treatment, then analyzed using N-gain and t-test with SPSS to determine the significance of differences in learning outcomes between the two groups. The results showed that the experimental group experienced a significant increase compared to the control group (p <0.001). The average N-gain value in the experimental group was 0.70 in the high category, while in the control group it was 0.46 in the moderate category. In addition, the effect size analysis of 1.39 showed that the use of ethnomathematics puzzle games had a major impact on improving students' mathematical science problem solving abilities. Puzzle games are an effective learning medium in improving students' mathematical science problem-solving abilities in geometry material. In addition, this approach can enrich students' learning experiences by connecting mathematical concepts with relevant cultural contexts. Therefore, the use of ethnomathematics puzzle games is recommended as an innovative learning strategy that can be applied in teaching mathematics at MAN 1 Tanggamus.

Prediction of Student Major Selection at High School Using a Machine Learning Approach

The primary objective of this research was to develop and evaluate a machine learning prediction system that matches Senior High School (SMA) Nusa Putra Kota Tangerang students with their potential school majors based on their academic interests and performance levels. This research method employs machine learning algorithms, including Random Forest, Support Vector Machine (SVM), logistic regression, K-Nearest Neighbor (K-NN), and Naive Bayes, using academic records, interest tests, and questionnaires for data collection. The data was processed and analyzed to train and test the algorithm. The findings of this study indicate that the Random Forest algorithm achieved the best performance among the models, with an accuracy of 85%, a precision of 82%, a recall of 88%, and an AUC score of 0.92. The factors that affected the prediction of major selection were Grade XII Mathematics scores and Science Interest Test results. The research implications suggest that Random Forest technology within Machine Learning (ML) enhances major selection accuracy while promoting fairness, providing superior educational choices and increased student satisfaction. Future studies should investigate additional factors that influence this phenomenon.

A new look at the formation of functional literacy of students in the context of digitalization of education

The article is devoted to the study of the process of forming functional literacy of students in a comprehensive school. In the modern world, where digital technologies penetrate into all vital structures, the formation of functional literacy of students has become one of the core tasks of the education system, opening up new horizons for the educational process in the context of digitalization. The article proves the thesis that functional literacy includes not only academic knowledge in the main academic disciplines of the humanitarian, mathematical and natural science cycle, but also the skills and abilities to effectively use this knowledge in solving practical non-standard problems, the ability to think critically and creatively, and readiness to adapt to rapidly changing conditions. The formation of functional literacy in the context of digitalization requires a new approach based on rethinking traditional methods and techniques. The integration of digital technologies, the use of interactive methods, the development of digital competencies and the individualization of learning - all this contributes to the creation of an effective educational environment where students become active participants in their learning. It is necessary to remember that the main goal of education is not only the transfer of academic knowledge, but also the preparation of students for adult independent life in a rapidly changing world, where functional literacy occupies a key place. With the digitalization of the educational environment, it became possible to implement the technology of individualization of learning, which is especially important for the formation of functional literacy. With the help of adaptive educational programs, it is possible to take into account the individual needs and interests of students when forming their functional literacy, which contributes to a deeper assimilation of the material and the development of the necessary skills.

The Competition Complexity of Prophet Inequalities

We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the [Formula: see text]-competition complexity of different types of online algorithms. This metric asks for the smallest k such that the expected value of the online algorithm on k copies of the original instance is at least a [Formula: see text]-approximation to the expected off-line optimum on a single copy. We show that block threshold algorithms, which set one threshold per copy, are optimal and give a tight bound of [Formula: see text]. This shows that block threshold algorithms approach the off-line optimum doubly exponentially fast. For single threshold algorithms, we give a tight bound of [Formula: see text], establishing an exponential gap between block threshold algorithms and single threshold algorithms. Our model and results pave the way for exploring resource-augmented prophet inequalities in combinatorial settings. In line with this, we present preliminary findings for bipartite matching with one-sided vertex arrivals as well as in XOS combinatorial auctions. Our results have a natural competition complexity interpretation in mechanism design and pricing applications. Funding: J. Correa was partially funded by Anillo Information and Computation in Market Design [Agencia Nacional de Investigación y Desarrollo (ANID) Grant ACT210005] and the Center for Mathematical Modeling [ANID Grant FB210005]. T. Ezra is supported by the Harvard University Center of Mathematical Sciences and Applications. M. Feldman was partially funded by the European Research Council under the European Union’s Horizon 2020 research and innovation program [Grant 866132], by an Amazon Research Award, by the United States-Israel Binational Science Foundation [Grant 2020788], and by a grant from the TAU Center for AI and Data Science. V. Verdugo was partially funded by Anillo ICMD [ANID Grant ACT210005] and Fondecyt [ANID Grant 1241846].

Deskripsi Kesalahan Mahasiswa dalam Menyelesaikan Soal Geometri Analitik Menurut Teori Newman Ditinjau dari Kemampuan Matematika

Analytical geometry as a course that involves algebraic processes in solving problems requires students' accuracy and it is not uncommon for various errors to occur due to the varying levels of students' mathematical abilities. This study aims to describe students' errors in solving Analytical Geometry problems according to Newman's theory as viewed from their mathematical abilities. This research is a qualitative study with a descriptive approach. This research was conducted at the Mathematics Department, Faculty of Mathematics and Natural Sciences, Makassar State University in the even semester of 2023/2024. The subjects in this study were students of the Mathematics Department consisting of 3 people, namely students with high mathematical abilities, students with moderate mathematical abilities, and students with low mathematical abilities. The sampling technique used was purposive sampling by setting criteria for selecting research subjects. Data were collected through written tests and interviews. As well as data analysis techniques used qualitatively by collecting data, presenting data and drawing conclusions. The results obtained in this study were that the errors made by students with high mathematical abilities only made mistakes in the reading and endcoding processes, while at other stages according to Newman's theory, students did not make mistakes and were able to get the correct answers. Students with moderate mathematical abilities make reading errors, comprehension errors, transformation errors, process skill errors and endcoding errors. Students with low mathematical abilities make errors at every stage, at the reading stage, students also do not understand the meaning of the question (comprehension) so that students are unable to use the correct notation (transformationi) and ultimately are unable to continue the solution process.

Subclass of Analytic Functions Defined by Miller-Ross-Type Poisson Distribution Series

It is very well-known that the special functions and integral operators play a vital role in the research of applied and mathematical sciences. The main purpose of this paper is to introduce a new subclass of analytic functions involving Miller-Ross functions and obtain coefficient inequalities, distortion theorem, convex linear combination, partial sums, convolution, and neighborhood results for this class.

Studying the functional literacy of schoolchildren based on the use of educational content about Russia and Ethiopia: results of testing diagnostic tools

Introduction. In the context of developing cooperation between Russia and Ethiopia, projects are being implemented that provide Ethiopian teachers and students with access to modern educational resources that improve the standard of living of the population. One of such projects, related to the study of the functional literacy of African schoolchildren, is being implemented by the Ulyanovsk State Pedagogical University named after I.N. Ulyanov. Within the framework of the project, an original methodology for assessing the formation of functional literacy of students has been developed, which requires testing. The purpose of the article is to test a diagnostic tool for studying the functional literacy of schoolchildren, developed on the basis of educational content about Russia and Ethiopia on a Russian sample. Materials and methods. To form the educational content and tasks of the methodology, an analysis of texts reflecting current information about Russia and Ethiopia was used. The methodology was tested in the format of pedagogical testing, in which 59 10th-grade students of comprehensive schools in Ulyanovsk took part. The primary data were summarized using mathematical processing methods. KEYWORDS Results. It was found that the values of the development indicators (the average score for students completing assignments) of different types of literacy are close to each other. At the same time, for reading literacy they correspond to an advanced level of development (19.35 points out of 30 possible), and for mathematical literacy (17.86 points) and natural science literacy (16.93 points) – to the average. An insufficient level of development in all types of literacy was shown by an insignificant number of respondents (1.7% for reading and mathematical literacy, and 3.4% for natural science literacy). Together with schoolchildren who showed a low level of reading and mathematical literacy, their share (20.3% and 17.0%) is significantly inferior to the total share of students with an advanced and high level (33.9% each). In terms of scientific literacy, 25.4% of high school students have insufficient and low levels of development, 22.1% have increased and high levels. Most respondents have an average level of development in all types of functional literacy: 45.8% in reading, 49.1% in mathematics, and 52.5% in natural science. A comprehensive assessment of the developed functional literacy of schoolchildren was carried out by summing up the average scores for completing assignments for each type of literacy. The final score was 54.14 points, which allows us to conclude that the level of functional literacy development was average. Conclusion. The study yielded data close to the normal distribution of the sample of respondents with a tendency for the median indicators to shift toward an increased level of functional literacy development. This confirms the diagnostic capabilities of the author's methodology and provides grounds for its use in assessing and developing the functional literacy of Russian and Ethiopian schoolchildren.

ОТОБРАЖЕНИЕ НАУЧНЫХ ИССЛЕДОВАНИЙ ПО ТЕМЕ "МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ" В МАТЕМАТИЧЕСКОМ ОБРАЗОВАНИИ: ТЕМАТИЧЕСКОЕ ИССЛЕДОВАНИЕ SCOPUS

Mathematical modelling, as a universal language of modern science, is an indispensable mathematical skill that transforms complex real-world problems into quantitative and systematic frameworks, enhances prediction accuracy, optimizes decision-making processes, and guides the development of interdisciplinary solutions. This study conducts a bibliometric analysis to map scientific publications on mathematical modelling in mathematics education. Bibliometric analysis is a statistical method used to identify, evaluate, and track published literature through bibliometric data, including citation information related to authors, publications, institutions, journals, and countries. A total of 536 publications in the categories of Mathematics and Social Sciences from the Scopus database were analyzed. Findings reveal that the most prolific countries are the United States, Germany, and Spain, while the most influential journals are ZDM-Mathematics Education, ZDM-International Journal on Mathematics Education, and Journal of Engineering Education. Additionally, the conceptual structure of mathematical modelling is visualized and presented.

Preface

International Conference on Interdisciplinary Physics (ICIPs) in Conjunction with Bond21: Joint International Conference on Nanoscience & Nanoengineering 2024 (ICIPs - Bond21) On behalf of the organizing committee, it is our great pleasure to present the proceedings of Bond21 in Conjunction with the International Conference on Interdisciplinary Physics (ICIPs) 2024 . This biennial international conference, chaired by Dr. Erus Rustami from the Department of Physics IPB IPB University and co-organized by the Institute of Nano Electronic Engineering (INEE) and the Faculty of Mathematics and Natural Sciences, IPB University, Indonesia, continues to serve as a vital platform for fostering collaboration and advancing knowledge across diverse disciplines of physics and related sciences. The 2024 conference was successfully held on August 12-13, 2024, at the picturesque Swiss- Belresort, Belitung Island, Indonesia. With the theme, “Empowering Circularity through Advances in Sciences,” the event brought together researchers, academicians, and practitioners from around the globe, representing countries such as Singapore, Japan, and the UAE. The conference drew over 100 participants, highlighting its growing significance and international appeal. The proceedings reflect the rigorous academic standards upheld during the conference. A double-anonymous peer review process was employed to ensure the quality of submissions, facilitated by the Morressier submission management system. The conference received 37 submissions, of which 27 were sent for review and 22 subsequently accepted by the committee for further review by the IOP team. List of Organizing Committee and Scientific Committee are available in this Pdf.