Fields Of Mathematics Research Articles

Antipodal Turiyam Neutrosophic Graphs

Graph theory, a mathematical field, investigates the relationships between entities through vertices and edges [29]. Within this discipline, Uncertain Graph Theory emerges to model uncertainties in realworld networks. This paper presents the concept of the Antipodal Turiyam Neutrosophic Graph. In an Antipodal Graph, two nodes are connected if their shortest path distance equals the graph's diameter, emphasizing connections between the farthest nodes. Turiyam Neutrosophic Graphs extend traditional graphs by introducing four membership values-truth, indeterminacy, falsity, and liberal state-assigned to each vertex and edge, enabling a more nuanced representation of complex relationships.

Translating Indian Algebra in the Seventeenth Century: ʿAtāʾollāh Roshdi’s Persian Version of Bhāskara II’s Bījagaṇita

Abstract One of the most important works in the field of medieval Indian mathematics corresponding to algebra is Bījagaṇita (Seed Calculation), a Sanskrit treatise by the famous mathematician and astronomer Bhāskara II (or Bhāskarācārya, c. 1114–aft. 1183). This paper is a general overview of the Tarjoma-ye Bij ganet (The Translation of the Bījagaṇita, 1634), a Persian text composed by the mathematician ʿAtāʾollāh Roshdi (or Rashidi), who served at the court of the Mughal emperor Shāh Jahān (r. 1628–58). The translation is divided into an introduction, subdivided in six chapters (bāb), and five books (maqāla). After discussing both Bhāskara II and Roshdi, I compare the latter’s translation with the original Sanskrit text on the basis of available English translations. I will also demonstrate how an intermediate language, which played an important role in the connection of South Asian scientific sources, facilitated this translation.

Solving Partial Differential Equations Using Fourier Series

This research paper aims to study the methods of solving partial differential equations using Fourier series. Partial differential equations are a powerful and practical tool in mathematics and physics to describe many phenomena and processes that involve continuous change at the level of equations and functions. The basic concepts related to the Fourier series and how to represent functions using it in the field of mathematics will be reviewed. Application examples of partial differential equations, such as waves, heat and diffusion, and how to use the Fourier series to solve them will also be presented. The steps of solving the partial differential equation using the Fourier series will be explained. The importance of Fourier series in the theory of partial differential equations is that periodic functions f(x) defined on (-∞,∞) or functions defined on a finite interval can be represented by an infinite interval of sines and cosines. In this research, the solution of the partial differential equation using the Fourier series was studied with the solution of an example.

Interval Time Series Forecasting: An Innovative Approach Transforming Interval to Single Time Series

ABSTRACTInterval Time Series are present in everyday life. An example is the opening and closing value of some stock in a market for certain time intervals. The forecasting plays an essential role in many financial organisations. The development of new mathematical tools or improving the existing ones will lead to more accurate forecasting techniques. Interval Arithmetic is a mathematical field that uses intervals by nature and algorithms that use it are involved in the solution of Interval Time Series. Another classical algorithm is VAR models. In this paper, a method that comes from the insurance sector is used to forecast Brent Oil monthly values. The innovation of what we propose is that it converts the Interval Time Series system into a single time series and can propagate the results back to each time series of the system. This way the researcher works with only one time series instead of two (or more). The forecasting algorithm is a choice of the researcher, expediting the development of forecasting (even ARIMA can be applied). We demonstrate our methodology in forecasting the Brent Oil monthly prices by applying the ANFIS algorithm.

Gender, Racial-Ethnic, and Cohort Effects on STEM Interests: A Fourteen-Year Comparison

Gender and racial-ethnic disparities continue to exist in participation within science, technology, engineering, and mathematics (STEM) fields. Because vocational interests predict career choice and educational interventions to help promote STEM interest among underrepresented groups have increased, research is needed to assess if meaningful changes have occurred with STEM-related interests, particularly among women and people of color who have historically been underrepresented in the STEM workforce. The present study examines vocational interests in large samples of college students across two cohorts who completed the Strong Interest Inventory in 2005 ( N = 6,496) and 2019 ( N = 21,146). Results indicate that STEM-related interest levels have increased both across gender (i.e., men and women) and racial-ethnic groups, specifically for Black, Latinx, Asian, and White college students over this period. Notably, STEM-related interests declined or stayed the same across cohorts for Native American students. Additionally, the gap between women and men narrowed for the Investigative General Occupational Theme and STEM-related Basic Interest Scales. Finally, these results are discussed within the context of vocational interest development and societal STEM-related initiatives and focus on increasing STEM interests among underrepresented youth living in the United States.

Gender parity in African science.

Africa has seen a notable increase in young women's participation in science, technology, engineering, and mathematics (STEM) fields over the past two decades. In 2019, the continent boasted the greatest share of female STEM students globally-47% across 49 universities-according to a report from the United Nations Educational, Scientific and Cultural Organization. Sadly, much of this talent is underutilized. Traditional gender expectations and domestic roles pose substantial obstacles, restricting African women from accessing STEM career opportunities. In sub-Saharan Africa, for example, only 31% of professional researchers are women. Without closing the gender gap in African science, progress on widespread problems such as maternal and child health, and food security, is unlikely.

An Overview of the Basic Theory of Probability Theory and its Commercial Application

Abstract. Probability theory is a key field of mathematics that focus on developing theoretical models and mathematical frameworks to describe and analyze random events or processes. As a part of basic science, probability theory holds a central place in pure mathematics while also serving a crucial function across various domains, including natural science, social science and engineering technology. This paper summarizes the main concepts, basic theories and commercial applications of probability theory. Probability theory encompasses ideas such as random experiment, sample space, event, probability, conditional probability, independence, Bayes Theorem, random variable, probability distribution, expected value and variance, law of large numbers and central limit theorem. This paper provides an overview of key concepts and theorems from probability theory, along with their practical applications in everyday life, in order to make people deeply recognize the broad and profound contents and research fields of probability theory and its wide application in various fields as an academic tool, which has a great relation with people.

Euler’s Formula and Its Applications in Modern Mathematics

This article examines the various uses of Euler‘s formula in complex analysis, topology, number theory, and other mathematical fields. Renowned for its mathematical elegance, exponential and trigonometric functions are closely related according to Euler‘s formula. acting as a fundamental basis for various key developments in these fields. By conducting a thorough analysis, the study reveals the extensive significance and lasting impact of Euler’s formula in both theoretical and applied mathematics. The research employs a comprehensive literature review, enhanced by rigorous mathematical derivations and practical examples, to demonstrate the widespread applicability and versatility of Euler’s formula in a wide range of contexts. The findings underscore that Euler’s formula not only holds a central position in theoretical mathematics but also plays a crucial role in engineering, quantum mechanics, signal processing, and physics. This study contributes to a deeper understanding of the intrinsic relationships within mathematical formulas, emphasizing their far-reaching practical relevance and potential for future research and technological innovation.

Cauchy’s Residue Theorem and Its Application

One of the key theorems in complex analysis, Cauchy’s Residue Theorem, which refers to the integral value of an analytic function along any simple closed contour surrounding an isolated singularity in a certain ring domain divided by 2πi, will greatly simplify the process of computing integrals on contour surrounding singularities. In the field of basic mathematics, the Cauchy’ Residue Theorem plays a key role in the integral calculation of analytic functions, nonuniform complex functions and the argument principle, which establishes a connection between a curve’s winding number and the quantity of zeros and poles inside the curve. Furthermore, Residue Theorem can combine with various subjects, including electromagnetism. This paper gives an overview of the Cauchy’s Residue Theorem and its application. Firstly, it talks about the definition and proof of the Cauchy’ Residue Theorem, along with the definition of residue. Then two examples of using Residue Theorem to integrate functions will be given. Finally, this paper involves application of Residue Theorem in trigonometric sum identities and a remark on the method.

A framework for curriculum transformation in quantum information science and technology education

The field of Quantum Information Science and Technology (QIST) is booming. Due to this, many new educational courses and university programs are needed in order to prepare a workforce for the developing industry. Owing to its specialist nature, teaching approaches in this field can easily become disconnected from the substantial degree of science education research which aims to support the best approaches to teaching in Science, Technology, Engineering and Mathematics fields. In order to connect these two communities with a pragmatic and repeatable methodology, we have synthesised this educational research into a decision-tree based theoretical model for the transformation of QIST curricula, intended to provide a didactical perspective for practitioners. The Quantum Curriculum Transformation Framework consists of four steps: (1) choose a topic, (2) choose one or more targeted skills, (3) choose a learning goal and (4) choose a teaching approach that achieves this goal. We show how this can be done using an example curriculum and more specifically quantum teleportation as a basic concept of quantum communication within this curriculum. By approaching curriculum creation and transformation in this way, educational goals and outcomes are more clearly defined which is in the interest of the individual and the industry alike. The framework is intended to structure the narrative of QIST teaching, and with future testing and refinement it will form a basis for further research in the didactics of QIST.

Preface to “Geometry and Topology with Applications”

Geometry is a very active research field in pure mathematics, with a history and tradition going back to the antiquity [...]

Investigation of Classification Validity in Terms of Various Variables in TIMSS 2019 International Benchmarks of Students

In this study, it was aimed to determine the variables affecting students' proficiency classification by using the data of 4th-grade students participating in the TIMSS 2019 application in the fields of mathematics and science. For this purpose, it was tried to provide evidence for classification validity with the variables of school belonging, bullying, home resources for learning, self-efficacy for computer use, disorderly behavior in Math lessons, like learning Math/Science, confident in Math/Science and instructional clarity in Math/Science lessons. The study was conducted with a correlational design. The sample of the study consisted of 3887 students in both lessons, which remained as a result of the missing data deletion and assignment processes from 4028 students who originally participated in the application. Logistic regression and discriminant analysis were used to analyze the data. As a result of the study, it was determined that 41.6% for Mathematics and 43% for Science in logistic regression analysis and 42.5% for Mathematics and 45% for Science in discriminant analysis were correctly classified through independent variables.

Optimizing predictive models for evaluating the F-temperature index in predicting the π-electron energy of polycyclic hydrocarbons, applicable to carbon nanocones

In the fields of mathematics, chemistry, and the physical sciences, graph theory plays a substantial role. Using modern mathematical techniques, quantitative structure-property relationship (QSPR) modeling predicts the physical, synthetic, and natural properties of substances based only on their chemical composition. For a chemical graph, the temperature of a vertex is a local property introduced by Fajtlowicz (1988). A temperature-based graphical descriptor is structured based on temperatures of vertices. Involving a non-zero real parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}, the general F-temperature index Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} is a temperature index having strong efficacy. In this paper, we employ discrete optimization and regression analysis to find optimal value(s) of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} for which the prediction potential of Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} and the total π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document}-electron energy Eπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\pi }$$\\end{document} of polycyclic hydrocarbons is the strongest. This, in turn, answers an open problem proposed by Hayat & Liu (2024). Applications of the optimal values for Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} are presented a two-parametric family of carbon nanocones in predicting their Eπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\pi }$$\\end{document} with significantly higher accuracy.

Subject Advisors’ Understanding of their Curriculum Leadership Roles for Mathematics Improvement in South African Schools

The study aimed to investigate the curriculum leadership role of Mathematics subject advisors in enhancing Mathematics education in South Africa. Using a case study design, seven Mathematics subject advisors and ten Mathematics educators were sampled from all seven districts of the Free State province. Data collection methods included in-depth semi-structured interviews, observations, and document analysis. Data analysis followed Tesch’s (1990) eight-step coding technique. The field study revealed that Mathematics subject advisors’ leadership roles encompassed providing support and guidance to educators, conducting educator appraisals, monitoring and overseeing educators’ and learners’ workbooks, mentoring, and professional development. They also handled administrative tasks findings like resource provision and paperwork using monitoring tools. While all subject advisors aimed to improve Mathematics achievement, their approaches varied. Some reviewed past strategies while others adapted based on resource availability. Individual educational philosophies also influenced their strategies. Moreover, subject advisors operate within a network that includes principals, educators, learners, and the broader context. Effective curriculum leadership depends on these interactions. Interestingly, none of the subject advisors claimed comprehensive knowledge of their subject area. Some lacked specialization in Mathematics or related fields in which they were operating. Many expressed a need for training, particularly in managing and supporting progressed learners. These findings suggest the need for a standardized model to guide leadership training for Mathematics subject advisors. Such a model could enhance curriculum leadership, thereby improving teaching practices and student performance. Future research could use these insights to develop this model. Keywords: Curriculum Leadership, Subject Advisors, Mathematics, Curriculum, Assessment Policy Statement (CAPS), Cognitive Theory

A phenomenological study of women’s everyday lived experiences and perceptions in science research organizations in India

There has been a significant paucity of representation of women in the fields of science, technology, engineering, mathematics, and medicine (STEMM) on a worldwide scale. Women are more likely to be at a disadvantage than men due to the existence of gender prejudices as well as other social and cultural variables. This tendency is also present in India. Feminist scholars within the Science, Technology, and Society field have conducted thorough examinations of the gender component, despite their relatively small representation. This study aims to examine the challenges faced by female scientists in higher education institutions in India to comprehend these issues. It employs a phenomenological approach, using primary data to investigate how female scientists perceive their day-to-day lives and the world around them, and it focuses on the perceptions and experiences of these women. The study finds that women who work in STEMM fields face a wide variety of challenges and roadblocks both on the personal and professional front. In addition, it highlights certain attitudes that have a negative impact on women working in the field of science, such as the rationalization of institutional prejudices and unwillingness to recognize discrimination. It concludes with a few policy implications.

Stern-Gerlach centennial: Parity, gradient effect, and an analogy with the Higgs field

In this article, which celebrates 100 years of the Stern-Gerlach experiment, we identify and discuss some limitations of the mathematical field we intend to represent as the Stern-Gerlach magnetic field. We extend some recent theoretical results concerning Stern-Gerlach eigenenergies, where what we call “the gradient effect” manifests itself: the contribution of the magnetic field gradient to the self-energies. Finally, based on an analogy with the Stern-Gerlach effect, we visualized that the Higgs field must be homogeneous in its minimum energy configuration within the context of the Higgs mass generation mechanism.

Recent advances in branching problems of representations

How does an irreducible representation of a group behave when restricted to a subgroup? This is part of branching problems, which are one of the fundamental problems in representation theory, and also interact naturally with other fields of mathematics. This expository paper is an up-to-date account on some new directions in representation theory highlighting the branching problems for real reductive groups and their related topics ranging from global analysis of manifolds via group actions to the theory of discontinuous groups beyond the classical Riemannian setting. This article is an outgrowth of the invited lecture that the author delivered at the commemorative event for the 70th anniversary of the re-establishment of the Mathematical Society of Japan, and originally appeared in Japanese in Sugaku 71 (2019).

Exploring How Female Scientists are Uplifted in Research Networks in STEM Fields in Public Universities in Uganda

Participation in research networks is inevitable for the female scientists in the Science Technology Engineering and Mathematics (STEM) fields because they provide a platform for collaborative activities. New research communities of women are created to support each other through mentoring, advancing shared research interests, co-organizing conferences with men, participating in the editorial and the publications. It was on this basis that this study explored how female scientists were uplifted by research networks in STEM fields in public universities in Uganda. This study was anchored on the existential phenomenology by Martin Heidegger in the interpretive world view. Eight female scientists in research networks in STEM fields in public universities in Uganda were interviewed and they were selected from the hard applied and hard pure disciplines as classified in Becher and Biglan’s typology of academic disciplines. Using thematic analysis, two themes such as research collaboration activities and capacity development emerged in this study. This qualitative study set out to explore how female scientists were uplifted in research networks in public universities in Uganda.The public universities included Makerere University, Mbarara University of Science and Technology, Gulu University and Busitema University. Both semi-structured interviews and document check data generation strategies were used in this study. In semi-structured interviews, a sample comprising eight female academics with not less than five years in research networks in public universities were selected, while documents such as the annual reports and strategic plans were used. This study concludes that research networks are uplifting the female scientists in STEM fields in public universities in Uganda because they were internationally exposed, networked, funded, research skills were strengthened, and progressed in career. This study concludes that it was important for female scientists to access physical and human resource in their research networks as this increased their research performance and outputs in STEM fields in public universities in Uganda. This study therefore recommends that, to uplift female scientists in research networks in STEM fields in public universities in Uganda, female scientists in the research networks and senior colleagues should act as ambassadors and mentors to young female scientists in STEM fields

Didactic Innovation in Mathematics Using Technologies

The continuous progress of society requires all the actors to be dynamic and constantly updated, both in terms of monitoring as well as in the need to adapt. Regarding education, no matter how updated we are in relation to the contents, didactic strategies, and technological resources, we are still inevitably forced to adapt to new paradigms, leading us to reformulate traditional teaching methods. In this context, the contribution of e-learning platforms emerges, where teachers and students have at their disposal new means of empowering the teaching and learning process, since these platforms can be defined as a virtual teaching support environment. Currently, our students, in general, have many difficulties in problem-solving and mathematical reasoning, which often reflects in the performance of very simple tasks, with a growing disinterest towards Mathematics. It is also possible to argue that our students' "poor preparation" is a contributing factor in their failure (many did not attend Mathematics in Secondary Education and/or have not studied for several years, as is the case of those who entered through special contingents, as the “aged 23 and over”). In order to promote a distinct, alternative and supportive pathway that may help to solve this issue, a project on the Moodle learning management system (LMS) platform has been developed with the goal of assisting students in their study and the development of their skills in a way that is directly related to the curricular units (CU) in the scientific field of Mathematics, in an online learning environment. To increase students’ engagement into their learning process in a collaborative environment, a flipped model was employed into a Financial Mathematics/Financial Calculus Course (FCC). This paper's primary goal is to examine the effects of implementing the flipped classroom paradigm on students' performance, learning, and classroom instruction. The results from employing this approach have indicated a beneficial effect on the overall academic progress of students.

On a Class of Generalized Multivariate Hermite–Humbert Polynomials via Generalized Fibonacci Polynomials

This paper offers a thorough examination of a unified class of Humbert’s polynomials in two variables, extending beyond well-known polynomial families such as Gegenbauer, Humbert, Legendre, Chebyshev, Pincherle, Horadam, Kinnsy, Horadam–Pethe, Djordjević, Gould, Milovanović, Djordjević, Pathan, and Khan polynomials. This study’s motivation stems from exploring polynomials that lack traditional nomenclature. This work presents various expansions for Humbert–Hermite polynomials, including those involving Hermite–Gegenbauer (or ultraspherical) polynomials and Hermite–Chebyshev polynomials. The proofs enhanced our understanding of the properties and interrelationships within this extended class of polynomials, offering valuable insights into their mathematical structure. This research consolidates existing knowledge while expanding the scope of Humbert’s polynomials, laying the groundwork for further investigation and applications in diverse mathematical fields.