Mathematical Representation Research Articles

Gender representations in school mathematics: a study of primary textbooks in the Republic of Cyprus

ABSTRACT Several studies indicate that gender is often portrayed stereotypically in mathematics textbooks worldwide. Based on the premise that such representations need to be examined with particular attention to the cultural context within which they exist, this study focuses on the upper-primary mathematics textbooks of the Republic of Cyprus, which are nationally produced and mandatory for all public schools. Specifically, the eight individual parts of grades 5 and 6 (four for each grade) were examined. By approaching both written and visual references from a critical discourse analysis perspective, the findings highlight that (a) gender is represented within the binary system, and (b) there are essential differences in depictions of men and women across three dimensions: professional status, everyday activities, and references to real people. These differences allude to stereotypical performative aspects of gender in this specific socio-cultural context. In closing, I make recommendations for future research directions in this area.

Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials.

Numerical solutions to partial differential equations (PDEs) are instrumental for material structural design where extensive data screening is needed. However, traditional numerical methods demand significant computational resources, highlighting the need for innovative optimization algorithms to streamline design exploration. Direct gradient-based optimization algorithms, while effective, rely on design initialization and require complex, problem-specific sensitivity derivations. The advent of machine learning offers a promising alternative to handling large parameter spaces. To further mitigate data dependency, researchers have developed physics-informed neural networks (PINNs) to learn directly from PDEs. However, the intrinsic continuity requirement of PINNs restricts their application in structural mechanics problems, especially for composite materials. Our work addresses this discontinuity issue by substituting the PDE residual with a weak formulation in the physics-informed training process. The proposed approach is exemplified in modeling digital materials, which are mathematical representations of complex composites that possess extreme structural discontinuity. This article also introduces an interactive process that integrates physics-informed loss with design objectives, eliminating the need for pretrained surrogate models or analytical sensitivity derivations. The results demonstrate that our approach can preserve the physical accuracy in data-free material surrogate modeling but also accelerates the direct optimization process without model pretraining.

Biophysical Drivers of Seasonal Hysteresis of Urban Heat Islands Across Climates and Urban Landscapes

AbstractThe phenomenon of seasonal hysteresis between urban heat islands (UHIs) and background surface temperature was reported in many studies, but a unifying explanation for the causes of its magnitude, shape and looping direction remained less clear, and the impacts of urban landscapes and background climate on such hysteresis were also the subject of enquiry. Here we performed a systematic study based on a long‐term offline simulation for surface energy budgets, surface air and skin temperature of the urban‐biosphere system in East China. It was carried out with an up‐to‐date land surface model — the CLM5‐LCZs (the Community Land Model version 5 (CLM5) coupled with a newly developed urban canopy model representing diverse urban landscapes with the local climate zones classification scheme). To isolate the causes of UHIs hysteresis, a simplified framework was constructed by combining a mathematical representation of grid/subgrid model outputs, the two‐resistance mechanism method and the time‐lagged cross correlation analysis. The results exhibited distinct hysteresis patterns of UHIs such as twisted, concave‐down, concave‐up and convex‐up curve across diverse background climates and urban landscapes. The basic shapes of hysteresis depict a gradual transition from concave/convex‐up to concave/convex‐down by characterized by a larger winter UHIs from a wetter and warmer climate to a drier and colder climate. Magnitude and seasonality of surface UHIs are separately dominated by the urban‐rural contrast of evapotranspiration and heat storage at daytime and nighttime, whereas across‐climate variations of daytime and nighttime surface UHIs hysteresis are regulated by the phase shift of convection efficiency and anthropogenic heat. Urban landscapes affect the hysteresis mainly by altering the amplitude rather than the shape of looping curves. Our work could provide a fuller picture of how to mitigate urban warming considering inter‐seasonal tradeoffs over a broader region.

Mechanism and Application of Attitude and Orbit Coupling Dynamics for Spacecraft Proximity Relative Motion

This paper analyzes the root causes of attitude-orbit coupling effects of spacecraft proximity relative motion in space precision collaborative tasks from three aspects: mathematical representation, physical definition, and engineering applications. At first, taking mathematical representation as the context, spacecraft proximity relative motion representations such as particle relative dynamic model, extended particle relative dynamic model, and dual-spiral-based relative dynamic model are investigated in detail. On this basis, the mechanism of attitude-orbit coupling effects originating from different mathematical representations is further investigated. Second, spiral theory–based attitude-orbit coupling relative dynamics is developed. The innovation of this work is extending the dual number representation from rigid body to flexible body, which makes it possible to describe the proximity relative motion between two rigid-flexible coupling spacecraft. Third, the application value of attitude-orbit coupling relative dynamic model in precision collaborative mission such as precision formation, rendezvous and docking, space manipulation, and on-orbit assembly is provided. Finally, simulation results verify the engineering significance of the attitude-orbit coupling relative dynamic model.

A Simplified Method for Determining Mathematical Representation of Microwave Oscillator Load Characteristics

A Simplified Method for Determining Mathematical Representation of Microwave Oscillator Load Characteristics

Enhancing generative adversarial network

The paper provides a comprehensive review of various GAN methods from the perspectives of theory, and applications. GAN algorithms' mathematical representations, and structures are detailed. The commonalities and differences among these GANs methods are compared. Theoretical issues related to GANs are explored, and typical applications in various fields are showcased. Future scope of research problems for GANs are also discussed in the paper.

Analisis Kemampuan Representasi Matematis Siswa dalam Menyelesaikan Soal Matematika Ditinjau dari Tipe Kepribadian Florence Littauer

This research purpose to describe students' mathematical representation abilities in solving mathematics problems in terms of Florence Littauer's personality type. This type of research is descriptive qualitative with the research subjects being class VIII students at SMPN 2 Sukodadi, totaling 8 students. This research uses technical triangulation, a Florence Littauer questionnaire to determine students' personality types and tests used to determine students' mathematical representation abilities. The results of this research show that students with a sanguine personality with high ability can complete visual and symbolic representations, students with moderate ability are less able to complete verbal representations, and students with moderate ability are less able to complete all indicators of mathematical representation ability. Choleric personality students with medium ability are less able to complete visual and symbolic representation indicators, low ability students are not able to complete verbal representations, and students with low ability are not able to complete all indicators of mathematical representation ability. Melancholic personality students with high abilities can complete all mathematical representation abilities. Phlegmatic personality students with low abilities have not been able to complete all mathematical representation skills

The gene “degrees of kevin bacon” (dokb) regulates a social network behaviour in Drosophila melanogaster

Social networks are a mathematical representation of interactions among individuals which are prevalent across various animal species. Studies of human populations have shown the breadth of what can spread throughout a social network: obesity, smoking cessation, happiness, drug use and divorce. ‘Betweenness centrality’ is a key property of social networks that indicates an individual’s importance in facilitating communication and cohesion within the network. Heritability of betweenness centrality has been suggested in several species, however the genetic regulation of this property remains enigmatic. Here, we demonstrate that the gene CG14109, referred to as degrees of kevin bacon (dokb), influences betweenness centrality in Drosophila melanogaster. We identify strain-specific alleles of dokb with distinct amino acid sequences and when the dokb allele is exchanged between strains, flies exhibit the betweenness centrality pattern dictated by the donor allele. By inserting a GAL4 reporter into the dokb locus, we confirm that dokb is expressed in the central nervous system. These findings define a novel genetic entry point to study social network structure and thereby establish gene-to-social structure relationships. While dokb sequence homology is exclusive to Diptera, we anticipate that dokb-associated molecular pathways could unveil convergent neural mechanisms of social behaviour that apply in diverse animal species.

The Effect of Training Program Based on Instructional Practices According to the (NCTM) Standards on Improving the Pedagogical Knowledge among Mathematics Teachers in Jordan

The current study aims at revealing the effect of a training program based on teaching practices according to NCTM standards in improving the pedagogical knowledge of mathematics teachers. The study followed the semi- experimental method. To achieve the aims of the research, a training program that is based on the standards of NCTM was designed. The program consists of eight packages which are (Establish mathematics goals to focus learning, implement tasks that promote reasoning and problem solving, Use and connect mathematical representations, facilitate meaningful mathematical discourse, pose purposeful questions, build procedural FLuency from conceptual understanding, support productive struggle in learning mathematics, Elicit and use evidence of student thinking). After confirming the validity of the tool, a sample of (20) male and female teachers from Deir Ala Directorate of Education in the academic year 2020-2021.To reveal the effectiveness of the program, a test in pedagogical knowledge was prepared. The test consists of six respects which are identification of mathematics content, the pedagogical knowledge of the mathematical content and knowing students' thinking. The test validity and reliability were checked. The results of the study showed that there were statistically significant differences between measuring averages in the post application of the test. These results were pro- sample in all dimensions and in the total degree. Depending on these results, the study asserted the necessity for the training department in the Jordanian Ministry of Education to benefit from the suggested and used program in the study to focus more on the teaching practices.

Exploring Dynamic Spalling Behavior in Rock–Shotcrete Combinations: A Theoretical and Numerical Investigation

Spalling is a widespread dynamic disaster during blasting excavation in underground engineering. To clarify the coupled dynamic response and spalling behavior of an underground tunnel with a spray anchor, an investigation based on the rock–shotcrete combination was conducted using theoretical and numerical methods. The mathematical representation of stress wave propagation between rock and shotcrete was deduced based on the elastic stress wave theory. A novel method for predicting the location and time of initial spalling in a rock–shotcrete combination was proposed. A numerical simulation was conducted to verify the validity of the proposed theoretical method. In addition, the effect of the material’s tensile strength, the loading amplitude, and the thickness of shotcrete on the stress evolution and spalling characteristics was studied. The results demonstrate that the initial spalling locations are sensitive to the relationship between the normalized tensile strength of the rock, shotcrete, and interface. A high incident amplitude can cause the initial spalling in rock, and the shotcrete or rock–shotcrete interface can cause initial spalling due to a low incident amplitude. The stress evolution and spalling characteristics are sensitive to the thickness of shotcrete. The location of the initial spalling failure changes with the thickness of the shotcrete. An appropriate increment in thickness and normalized strength of the shotcrete is beneficial to the dynamic stability of underground engineering.

Stability analysis and conserved quantities of analytic nonlinear wave solutions in multi-dimensional fractional systems

The (3+1)-dimensional generalized nonlinear fractional Konopelchenko–Dubrovsky–Kaup–Kupershmidt [Formula: see text] model represents the propagation and interaction of nonlinear waves in complex multi-dimensional physical media characterized by anomalous dispersion and dissipation phenomena. By incorporating fractional derivatives, this model introduces non-locality and memory effects into the classical [Formula: see text] equations, commonly utilized in phenomena such as shallow water waves, nonlinear optics, and plasma physics. The fractional approach enhances mathematical representations, allowing for a more realistic depiction of the intricate behaviors observed in numerous modern physical systems. This study focuses on the development of accurate and efficient numerical techniques tailored for the computationally demanding [Formula: see text] model, leveraging the Khater II and generalized rational approximation methods. These methodologies facilitate stable time-integration, effectively addressing the model’s stiffness and multi-dimensional nature. Through numerical analysis, insights into the stability and convergence of the algorithms are gained. Simulations conducted validate the performance of these methods against established solutions while also uncovering novel capabilities for exploring complex wave dynamics in scenarios involving complete fractional formulations. The findings underscore the potential of integrating fractional calculus into higher-dimensional nonlinear partial differential equations, offering a promising avenue for advancing the modeling and computational analysis of complex wave phenomena across a spectrum of contemporary physical disciplines.

Development of Interactive Learning Media Assisted by Desmos Based on RME to Improve Mathematical Representation Abilities and Resilience of Class VIII Students at SMPN 1 Idi

Development of Interactive Learning Media Assisted by Desmos Based on RME to Improve Mathematical Representation Abilities and Resilience of Class VIII Students at SMPN 1 Idi

Development of Geogebra Assisted Learning Modules to Improve Mathematical Representation Abilities and Self Regulated Learning of Senior High School

Development of Geogebra Assisted Learning Modules to Improve Mathematical Representation Abilities and Self Regulated Learning of Senior High School

Exact Transport Coefficients from the Inelastic Rough Maxwell Model of a Granular Gas

Granular gases demand models capable of capturing their distinct characteristics. The widely employed inelastic hard-sphere model (IHSM) introduces complexities that are compounded when incorporating realistic features like surface roughness and rotational degrees of freedom, resulting in the more intricate inelastic rough hard-sphere model (IRHSM). This paper focuses on the inelastic rough Maxwell model (IRMM), presenting a more tractable alternative to the IRHSM and enabling exact solutions. Building on the foundation of the inelastic Maxwell model (IMM) applied to granular gases, the IRMM extends the mathematical representation to encompass surface roughness and rotational degrees of freedom. The primary objective is to provide exact expressions for the Navier–Stokes–Fourier transport coefficients within the IRMM, including the shear and bulk viscosities, the thermal and diffusive heat conductivities, and the cooling-rate transport coefficient. In contrast to earlier approximations in the IRHSM, our study unveils inherent couplings, such as shear viscosity to spin viscosity and heat conductivities to counterparts associated with a torque-vorticity vector. These exact findings provide valuable insights into refining the Sonine approximation applied to the IRHSM, contributing to a deeper understanding of the transport properties in granular gases with realistic features.

Analysis of Student's Mathematical Representation Abilities on Plane Figures Subject in the New Normal Era

This study aims to analyze the mathematical representation ability of junior high school students on plane figures subject in the new normal era. To prevent the spread of Covid-19 in schools, learning was carried out alternately with 50% face-to-face learning and 50% independently at home. This research is a qualitative descriptive study. The subjects of this study were 20 students studying in seventh-grade students, in the second semester, at Dharmasraya West Sumatra for the academic year 2020/2021. The instruments used in this study were tests of students’ mathematical representation abilities and interviews. The indicators measured are visual representation, expression representation, and word representation. Based on the research conducted, it was found that the level of students’ mathematical representation ability was still low (52.65). In general, students still experience problems in using their mathematical representation skills; therefore, students must be able to hone their representation skills in visual, symbol, and verbal representations. Mastering mathematical representation skills can make it easier for students to solve mathematical problems, and there will be fewer conceptual errors. Moreover, it is necessary to conduct additional research to enhance students’ mathematical representation skills. Keywords: mathematical representation abilities, new normal era, plane figures subject

UJI VALIDITAS KONTEN INSTRUMEN KEMAMPUAN REPRESENTASI MATEMATIS DALAM MENYELESAIKAN MASALAH BANGUN DATAR

Planar material is one of the materials that will be found again in several subsequent materials. In plane material, students' mathematical representation abilities need to be considered so that students are able to solve problems well. The aim of this research is to analyze the level of validity and reliability of the test instrument for junior high school students' mathematical representation abilities in solving flat shape problems. The research method used is a quantitative descriptive method. By using the Aiken's V formula, the expert validation results obtained an average V value of 0.93, which means that the questions have a very high level of validity and can be used. Meanwhile, the results of the reliability calculation show that the r value is 0.94, which means that the question has a very strong correlation coefficient and can be used. So this instrument can be used by teachers to measure the level of students' mathematical representation abilities in solving flat shape problems.

Mathematical Representation for speech signal based on ‎polynomial equation

The sound is an important vital information that it relies to recognize the character when lessening to it. Therefore, the audio signal adopted into many important applications. Sound forming and synthesizing in addition to distinguishing the speaker are so important in fields of digital signal processing. In this paper, work is done to represent acquired acoustic signal based on mathematical techniques. Mathematical representation provides deal with the sound signal which lead to smoothing, amplification or compression, in addition to the sound filtering process. In the proposed algorithm, polynomials of various degrees were adopted as a mathematical representation for speech signal, then the retrieved speech was studied based on level of clarity and the possibility of adopting it as an alternative signal in terms of the proximity to the original sound and the amount of noise added to it. The results shows that the proposed algorithm with degree of polynomial 20 and segment length 25 had the best sound representation and so closed to the original, which clearly seen from the evaluation parameters (Correlation=0.9993, Mean squared error(MSE) =1.32e-06, Standard deviation(STD)=1.80e-05 and the Euclidean dimension(ED) =0.1703).

A Study of Mathematical Models Used in Anaerobic Digestion of Organic Refuse

The mathematical computation and process evaluation of anaerobic digestion (AD) treatment of organic refuse (OR) has become quite common in process designing. Furthermore, the modelling of AD process is considered as well established and mature, and largely known as a mechanistic model structure. There are various mathematical models being used to comprehend the biochemical variations, rate of decomposition, and the methane or biogas production potentials. Moreover, these mathematical analyses of the models determine the computation of equilibrium points, helping to understand their internal stability with respect to feeding parameters, and compatibility to the output static characteristics of the entire AD process. Whereas numerical simulations are also carried out for specific biodegradation on web-based software. These simulations are useful to demonstrate the dynamic responses of the mathematical models to present the most mathematical viable solutions. However, the major issues lie in the application of AD in lab-based modelling needs improvement in characterization and the adaptation of new approaches to optimize bioenergy recoveries. Hence, this review paper discusses the selection and utilization of mathematical models for different conditions in AD treatment of OR for the best mathematical representations.

An unsupervised adversarial autoencoder for cyber attack detection in power distribution grids

Detection of cyber attacks in smart power distribution grids with unbalanced configurations poses challenges due to the inherent nonlinear nature of these uncertain and stochastic systems. It originates from the intermittent characteristics of the distributed energy resources (DERs) generation and load variations. Moreover, the unknown behavior of cyber attacks, especially false data injection attacks (FDIAs) in the distribution grids with complex temporal correlations and the limited amount of labeled data increases the vulnerability of the grids and imposes a high risk in the secure and reliable operation of the grids. To address these challenges, this paper proposes an unsupervised adversarial autoencoder (AAE) model to detect FDIAs in unbalanced power distribution grids integrated with DERs, i.e., PV systems and wind generation. The proposed method utilizes long short-term memory (LSTM) in the structure of the autoencoder to capture the temporal dependencies in the time-series measurements and leverages the power of generative adversarial networks (GANs) for better reconstruction of the input data. The advantage of the proposed data-driven model is that it can detect anomalous points for the system operation without reliance on abstract models or mathematical representations and data labels. To evaluate the efficacy of the approach, it is tested on IEEE 13-bus and 123-bus systems with historical meteorological data (wind speed, ambient temperature, and solar irradiance) as well as historical real-world load data under three types of data falsification functions. The comparison of the detection results of the proposed model with other data-driven methods verifies its superior performance in detecting cyber attacks in unbalanced power distribution grids.

Evolutionary graph theory beyond single mutation dynamics: on how network-structured populations cross fitness landscapes.

Spatially resolved datasets are revolutionizing knowledge in molecular biology, yet are under-utilized for questions in evolutionary biology. To gain insight from these large-scale datasets of spatial organization, we need mathematical representations and modeling techniques that can both capture their complexity, but also allow for mathematical tractability. Evolutionary graph theory utilizes the mathematical representation of networks as a proxy for heterogeneous population structure and has started to reshape our understanding of how spatial structure can direct evolutionary dynamics. However, previous results are derived for the case of a single new mutation appearing in the population and the role of network structure in shaping fitness landscape crossing is still poorly understood. Here we study how network-structured populations cross fitness landscapes and show that even a simple extension to a two-mutational landscape can exhibit complex evolutionary dynamics that cannot be predicted using previous single-mutation results. We show how our results can be intuitively understood through the lens of how the two main evolutionary properties of a network, the amplification and acceleration factors, change the expected fate of the intermediate mutant in the population and further discuss how to link these models to spatially resolved datasets of cellular organization.