Mathematical Representation Research Articles

Dynamic chaos unveiled: enhancing ship’s attitude time series prediction through spatiotemporal embedding and improved transformer model

Abstract During ship operations at sea, the vessel's attitude undergoes continuous changes due to various factors such as wind, waves, and its own motion. These influences are challenging to mathematically describe, and the changes in attitude are also influenced by multiple interconnected factors. Consequently, accurately predicting the ship's attitude presents significant challenges. Previous studies have demonstrated that phenomena like wind speed and wave patterns exhibit chaotic characteristics when affecting attitude changes. However, research on predicting ship attitudes lacks an exploration of whether chaotic characteristics exist and how they can be described and applied. This paper initially identifies the chaotic characteristics of ship attitude data through phase space reconstruction analysis and provides mathematical representations for them. Based on these identified chaotic characteristics, a
Transformer model incorporating feature embedding layers is employed for time series prediction. Finally, a comparison with traditional methods validates the superiority of our proposed approach.

KEMAMPUAN REPRESENTASI MATEMATIS SISWA DALAM MENYELESAIKAN SOAL OLIMPIADE TINGKAT SMP

Mathematical representation abilities can be in the form of expressions, ideas or mathematical ideas, which originate from students' thoughts that emerge during learning in an effort to find mathematical solutions. There are three indicators of mathematical representation ability, namely verbal, pictorial and symbolic. The process of developing students' potential and thinking can be done by holding mathematics competitions or olympiads. The approach used in this research is qualitative with descriptive methods. Purposive sampling technique was used in this research to select samples with certain considerations. The aim of this research is to describe students' mathematical representation abilities in solving Olympiad questions. This research used a sample of 3 students each representing each high, medium and low representation ability group. Based on the results of research on visual representation abilities, some students already have high abilities, although there are some who are still medium or low. Meanwhile, in symbolic ability, there are many students whose abilities are high and only a few whose abilities are medium or low. For verbal representation, most students already have high abilities and only a few students have medium or low abilities

The hidden lessons in textbooks: Gender representation and stereotypes in European mathematics and language books

AbstractThis cross‐national European comparison examined gender representation and stereotypes in mathematics and language textbooks from Germany, Italy, Lithuania, the Netherlands and Romania. The results showed that female characters were numerically underrepresented. Female characters were also less often a main character or individually portrayed compared to male characters, but not proportionally to the overall lower number of female characters. Characters in occupational roles were less often female than male, whereas among characters with gender non‐conform characteristics, these were more often female than male in some textbooks. There was no sexual diversity among characters. The differences in gender representation are found within each country, but gender differences were smaller in more gender‐egalitarian countries. If textbooks are to offer the same learning benefits to both boys and girls, students should be equally represented in a diversity of roles and occupations.

Guest Editorial: Connecting Mathematical Representations from Algebra to Calculus

Guest Editorial: Connecting Mathematical Representations from Algebra to Calculus

Efektivitas Model Eliciting Activitis (Meas) Terhadap Kemampuan Representasi Matematis Siswa MTs

The purpose of this research is to describe and obtain data on the influence of Model-Eliciting Activities (MEAs) on the representational ability of MTs students. This type of research is an experimental study with control and experimental groups by observing the results of pretests and posttests. The research instrument is a mathematical representation ability test. The population of this research consists of all students at MTs Madrasah Miftahul Ulum II Punggur Kecil, with the sample being two eighth-grade classes selected purposively from the seven existing classes. Data analysis was conducted using a two-population mean difference test. The results of the study show that the mathematical representation ability of students who received Model-Eliciting Activities is better than that of students who received conventional teaching. The improvement in the mathematical representation ability of students who received Model-Eliciting Activities in both the upper and lower groups is statistically better than that of students who received conventional teaching.

REMEDIAL PRACTICES AND STUDENTS COMPETENCES IN MATHEMATICS IN PUBLIC SECONDARY SCHOOLS IN RWANDA A CASE OF GICUMBI DISTRICT

Background: Mathematics plays a crucial role in both vocational success (Jetter, 2017) and everyday life (Umameh, 2011), yet many students face challenges in mastering it. Globally, educational equity remains a priority, with persistent disparities in math education, especially among low-SES students (UNESCO, OECD). Tanzania and Rwanda are actively addressing these challenges to enhance educational outcomes. Materials and Methods: This descriptive survey study involved 171 participants from 32 secondary schools in Gicumbi District: 105 mathematics instructors, 50 subject leaders, 35 head teachers, and 110 students. Data collection employed random sampling, with Slovenes method used to select the study sample. SPSS version 21.0 facilitated analysis, encompassing descriptive statistics (frequency, percentage, mean, standard deviation) and inferential statistics (correlation, regression coefficients). Results and Discussions: Findings revealed strong consensus among respondents on the efficacy of modifying instructional methods (80.0%), using personalized learning materials (63.1%), integrating visual and auditory resources (60.0%), and creating tailored exercises (68.0%) to improve math competencies. Key indicators such as problem-solving (64.3%), method application (96.6%), reasoning (92.3%), and mathematical representation (92.3%) demonstrated significant improvements. Enhanced physical facilities also correlated positively with student outcomes, underscoring the role of supportive environments in fostering mathematical competence. Conclusion: The study emphasizes the effectiveness of adapting teaching methods and environments to enhance students math skills. Customized approaches, including personalized materials and multimedia integration, proved instrumental in improving competencies like problem-solving and reasoning. Statistical analyses consistently supported these findings, highlighting the importance of personalized and diversified teaching strategies in enhancing math education in Gicumbi, Rwanda.

PENGGUNAAN MEDIA SOFTWARE GEOGEBRA UNTUK MENINGKATKAN KEMAMPUAN REPRESENTASI MATEMATIS SISWA SMA

Mathematical representation ability is an important ability in understanding mathematical concepts as an effort to obtain clarity of meaning and understanding in solving problems. Technology-based learning media can simplify the learning process thereby helping students in representing mathematical problems. This research aims to determine the increase in students' mathematical representation abilities using Geogebra software. This research is quantitative research with a quasi-experimental type. The population is students of class XI MIPA at SMA Negeri 1 Lhoong Aceh Besar for the 2023/2024 academic year consisting of 2 classes totaling 60 people. There are 30 people in Class XI MIPA 1 as an experimental class with the Geogebra software learning media, and 30 people in XI MIPA 2 as a control class without the Geogebra program learning media. The data collection technique in this research is using Pretest and Posttest. Meanwhile, the data analysis techniques used in this research are descriptive statistical analysis and inferential statistical analysis. The results of the research showed that there was an increase in students' mathematical representation abilities who were taught using Geogebra software media in class XI MIPA students at SMA Negeri 1 Lhoong. Most students answered the questions according to indicators of mathematical representation ability in the form of visual, symbolic and verbal representations.

The Influence of Mathematical Beliefs on The Mathematical Representation Ability of Students in Class VII

The Influence of Mathematical Beliefs on The Mathematical Representation Ability of Students in Class VII

MATHEMATICAL REPRESENTATION ABILITY OF HIGH SCHOOL STUDENTS IN SOLVING PROBABILITY MATERIAL PROBLEMS BASED ON HONEY MUMFORD LEARNING STYLE

This study aims to describe the mathematical representation ability of grade XII high school students in solving permutation subsubject probability material problems based on Honey Mumford's learning style. This type of research is qualitative research with a descriptive method. The data collection techniques used were Honey Mumford's learning style questionnaire, mathematical representation ability test, and interview. The source of data in this research is grade XII students of science 5 MAN 2 Pamekasan for the 2023/2024 school year. The subjects selected were 2 students who each had a theorist learning style and an activist learning style based on questionnaires and considerations with mathematics teachers. The data analysis techniques used are data reduction, data presentation, and conclusion drawn. The results of the study show that students with a theorist learning style can meet all indicators in the aspect of representation, both visual, symbolic, and verbal representation. Meanwhile, students with activist learning styles have not been able to meet the indicators in the aspect of visual representation but can meet all indicators in the aspect of symbolic representation and verbal representation.

Elementary students' argumentative and explanatory mathematical writing about fractions

AbstractMathematical writing (MW) is an important yet underutilized form of mathematics discourse. Given the lack of attention to MW, there are few resources to support the implementation and assessment of MW. This study responds to the lack of resources by describing a MW unit focused on fractions that was implemented during a summer school program to support rising fourth grade students with explanatory and argumentative writing. Findings from the study revealed that students used different forms of reasoning about fractions to compose their mathematical argument and explanation. We also identified five categories that captured how students communicated a mathematical argument and explanation: writing organization, precise mathematical vocabulary, mathematics content, mathematical representation, and characteristics specific to a mathematical argument/explanation. The five categories led to the development of an analytic rubric for argumentative and explanatory writing.

Teachers’ practice of mathematical representation, and its relationship to the preschooler’s utilization of it in expressing mathematical ideas

هدفت الدراسة إلى الكشف عن العلاقة بين مستوى ممارسة المعلمات لعملية التمثيل الرياضي وتوظيف طفل ما قبل المدرسة له في التعبير عن الأفكار الرياضية. اتّبعت الدراسة المنهج الوصفي الارتباطي، واشتملت الأدوات على بطاقتي ملاحظة مغلقة لكل من المعلمة والطفل. تم اختيار العينة بطريقة قصدية، وتكونت من (15) معلمة في مرحلة ما قبل المدرسة، يعملن في مدارس رياض الأطفال التي تطبق برنامج رياضيات خلال البرنامج اليومي في مدينة الأحساء و(120) طفل من الأطفال في فصولهن، وتم معالجة البيانات إحصائيًا باستخدام البرنامج (SPSS)، خلصت النتائج إلى وجود علاقة ارتباطية موجبة دالة إحصائيًا بين درجات ممارسات المعلمات للتمثيل الرياضي وتوظيف الطفل له في التعبير عن الأفكار الرياضية، كما أظهرت أنّ مستوى ممارسات المعلمات لعملية التمثيل الرياضي جاء بمستوى منخفض، ومستوى توظيف الطفل لعملية التمثيل الرياضي في التعبير عن أفكاره الرياضية جاء بمستوى منخفض. وفي ضوء النتائج توصي الدراسة بتوفير برامج تطوير مهني لمعلمات الطفولة المبكرة تتضمن طرق استخدام التمثيلات الرياضية في تقديم وشرح مفاهيم الرياضيات، وتوفير الوقت الكافي والأنشطة الملائمة نمائيًا لجميع الأطفال للانخراط في أنشطة الرياضيات عامةً والتمثيل الرياضي خاصة.

Improving fake news detection on social networks through a novel machine learning approach

Recent years have seen an increase in societal information, such as commercial advertisements, celebrity information, political news, etc., due to the growth of online social networks. Some social media sites including Facebook, Instagram, and Twitter, were impacted by Fake News (FN) spread by their users. Nevertheless, some individuals propagate false information using words, images, and videos to increase their connections and reputation. The most current information is unreliable and misleads other members on an online social network. Because FN is circulated to encourage users to trust disinformation, it’s hard for detection algorithms to recognize false information according to uploaded material. In this research, we will provide an autonomous false news detection strategy called Grey Wolf optimized Adaptive Bidirectional Gated Recurrent Unit (GWO+ABi-GRU) that can identify FN on Twitter. The TF-IDF method translates textual material into a mathematical representation that accurately captures the value of terms and their context in the dataset. We improve the overall efficiency of the BiGRU by applying this GWO, which leads to increased accuracy when spotting false news. The experimental examination of real-world data shows that the proposed FN detection strategy GWO+ABi-GRU outperforms traditional approaches regarding recall, accuracy, F1 score, and precision. This enhanced performance proves essential in preventing the circulation of false news on social media, protecting the integrity of information sources, and mitigating the potential damage caused by false information.

Mathematical Representation of Peterson’s Rules for Fuzzy Peterson’s Syllogisms

Mathematical Representation of Peterson’s Rules for Fuzzy Peterson’s Syllogisms

Dynamic characteristic analysis and key parameter optimization of throttling orifice type air damping air spring

Abstract The unique hysteretic characteristic of rubber bellows and the nonlinear flow of internal airflow in the system results in the significant nonlinear dynamic characteristic of throttling orifice type air damping air springs (OADASs). To solve the problem of mathematical representation of dynamic characteristic and key parameters optimization of throttling OADAS, this paper comprehensively considers the hysteretic characteristic of rubber bellows under variable pressure, the nonlinear dynamic characteristic model and linear model of throttling OADAS are established based on the concepts of gas thermodynamics and fluid mechanics. The static and dynamic characteristic tests of the throttling OADAS are conducted, to verify the accuracy and effectiveness of the proposed model, and to reveal the influence laws of excitation amplitude, excitation frequency, and throttling orifice diameter on the quantitative characterization indexes. Finally, a complete throttling orifice diameter optimization method is proposed based on the eight-degree-of-freedom model of the entire vehicle. Optimization results illustrate that the RMS values of the vertical acceleration of the body and the vertical acceleration of the driver are decreased by 19.02% and 38.44%, respectively. Overall, the outcomes of this paper can provide the design idea and theoretical basis for air damping matching and active suspension control.

Mathematical Representation Ability of Middle School Students in the REMAP-TPS Learning Model and Student Activeness

Kemampuan representasi matematis siswa kelas VIII SMPN 1 Way Bungur masih rendah. Aktivitas belajar yang bervariasi antar siswa menimbulkan perbedaan kemampuan pada setiap siswa. Hal ini menyoroti perlunya revitalisasi pendekatan pengajaran dengan menggunakan model pembelajaran yang berpusat pada peserta didik, yang mendorong peningkatan aktivitas siswa dan pemahaman materi. Model pembelajaran REMAP-TPS hadir sebagai pendekatan inovatif yang melibatkan siswa secara dominan dalam proses pembelajaran dan membantu eksplorasi materi melalui penggunaan peta konsep. Penelitian ini bertujuan untuk menilai keefektifan model pembelajaran REMAP-TPS dalam meningkatkan kemampuan representasi siswa. Desain penelitian yang digunakan adalah quasi eksperimen Posttest-Only Control Group Design. Instrumen yang digunakan untuk mengukur kemampuan representasi matematis meliputi soal deskriptif terkait geometri sisi data dan angket untuk menilai aktivitas pembelajaran. Tes diberikan kepada siswa setelah proses pembelajaran selesai, dilanjutkan dengan analisis menggunakan ANOVA. Temuan penelitian menunjukkan bahwa model pembelajaran REMAP-TPS unggul dalam mengembangkan kemampuan representasi matematis siswa. Hal ini terlihat dari rata-rata nilai posttest kelompok eksperimen sebesar 79,56, melampaui rata-rata kelas kontrol sebesar 68,52.

Edge dependent fault-tolerance in certain carbon-based crystal structures

The field of chemical graph theory encompasses interdisciplinary studies that utilize mathematical methods in exploring the attributes and arrangement of chemical compounds. Chemical graphs, in which atoms are vertices and bonds are edges, offer influential mathematical representations for portraying the molecular structures of chemical compounds. A smallest subset of vertices of a graph from which the vector of distances to each vertex of the graph is unique is known as metric basis for that graph and cardinality of a metric basis is known as metric dimension of that graph. In this paper, an important variant of metric dimension known as fault-tolerant edge metric dimension (FTEMD) is taken into consideration and computed it for most important possible allotrope of carbon family, known as crystal cubic carbon (denoted by G(n)). We prove that the FTEMD value of the molecular graph of crystal cubic carbon is unbounded for large n. Also, the comparison between several variants of metric dimension and FTEMD for the molecular graph G(n) has also been incorporated in the paper.

A Novel Computational Paradigm for Reconstructing Solid CAD Features from a Segmented Manifold Triangular Mesh

We introduce a novel computational paradigm for reconstructing solid computer-aided design (CAD) features from the surface of a segmented manifold triangular mesh. This paradigm addresses the challenge of capturing high-level design semantics for manifold triangular meshes and facilitates parametric and variational design capabilities. We categorize four prevalent features, namely extrusion, rotation, sweep, and loft, as generalized swept bodies driven by cross-sectional sketches and feature paths, providing a unified mathematical representation for various feature types. The numerical optimization-based approach conducts geometric processing on the segmented manifold triangular mesh patch, extracting cross-sectional sketch curves and feature paths from its surface, and then reconstructing appropriate features using the Open CASCADE kernel. We employ the personalized three-dimensional (3D) printed model as a case study. Parametric and variant designs of the 3D-printed models are achieved through feature reconstruction of the manifold triangular mesh obtained via 3D scanning.

Network analysis of students’ conceptual understanding of mathematical expressions for probability in upper-division quantum mechanics

One expected outcome of physics instruction is for students to be capable of relating physical concepts to multiple mathematical representations. In quantum mechanics (QM), students are asked to work across multiple symbolic notations, including some they have not previously encountered. To investigate student understanding of the relationships between expressions used in these various notations, a survey was developed and distributed to students at six different institutions. All of the courses studied were structured as “spins-first,” in which the course begins with spin-1/2 systems and Dirac notation before transitioning to include continuous systems and wave function notation. Network analysis techniques such as community detection methods were used to investigate conceptual connections between commonly used expressions in upper-division QM courses. Our findings suggest that, for spins-first students, Dirac bras and kets share a stronger identity with vectorlike concepts than are associated with quantum state or wave function concepts. This work represents a novel way of using well-developed network analysis techniques and suggests such techniques could be used for other purposes as well. Published by the American Physical Society 2024

Biological Basis and Computer Vision Applications of Image Phase Congruency: A Comprehensive Survey.

The concept of Image Phase Congruency (IPC) is deeply rooted in the way the human visual system interprets and processes spatial frequency information. It plays an important role in visual perception, influencing our capacity to identify objects, recognize textures, and decipher spatial relationships in our environments. IPC is robust to changes in lighting, contrast, and other variables that might modify the amplitude of light waves yet leave their relative phase unchanged. This characteristic is vital for perceptual tasks as it ensures the consistent detection of features regardless of fluctuations in illumination or other environmental factors. It can also impact cognitive and emotional responses; cohesive phase information across elements fosters a perception of unity or harmony, while inconsistencies can engender a sense of discord or tension. In this survey, we begin by examining the evidence from biological vision studies suggesting that IPC is employed by the human perceptual system. We proceed to outline the typical mathematical representation and different computational approaches to IPC. We then summarize the extensive applications of IPC in computer vision, including denoise, image quality assessment, feature detection and description, image segmentation, image registration, image fusion, and object detection, among other uses, and illustrate its advantages with a number of examples. Finally, we discuss the current challenges associated with the practical applications of IPC and potential avenues for enhancement.

Generation of optical dromions to generalized stochastic nonlinear Schrödinger equation with Kerr effect and higher order nonlinearity

Stochastic nonlinear Schrödinger equation is a mathematical model, used in the study of complex systems especially nonlinear optics and quantum mechanics. It explains the evolution of a quantum field with stochastic and nonlinear terms. A stochastic or random process is a mathematical representation that outlines the progression of a system in a way that incorporates probability. This is in contrast to a deterministic process, where the future states are strictly defined by initial conditions. In mathematical model, stochastic term is usually represent by variable or a function that involves random variable or a noise. In this paper, we study the generalized nonlinear Schrödinger equation by adding stochastic term for the first time to retrieve different types of optical solitons. To the best of our knowledge, no one work on this model with stochastic term. Our aim is to find optical solitons like bright and dark solitons, also solitary wave solutions for this model like bell type, hyperbolic functions, Jacobi Elliptic Function, Weierstrass Elliptic Function, periodic and rational solutions. These solutions will be obtained using the sub-ode method, subject to certain constraint conditions. Finally, we will use Jupyter as a machine learning tool and also mathematica to plot some obtained solutions in various dimensions like 3D, 2D and contour plots by using some libraries of PYTHON like numpy, scipy.integrate and matplotlib.pyplot. For the first time, we use this approach for this model and our results are new and novel [1].