Search Results (1,900)

The aim of this study is to develop a valid and reliable scale for measuring the self-efficacy of primary school and mathematics teachers regarding dyscalculia. Grounded in Bandura’s Social Cognitive Theory, the study followed established scale development procedures. In the initial phase, a pool of 42 items was generated to assess teachers’ self-efficacy regarding dyscalculia. The items were reviewed by a panel of seven experts in the fields of psychometrics, mathematics education, special education, and psychology to ensure content validity. Based on expert evaluations, four items were removed due to overly technical phrasing that could lead to misinterpretation, reducing the pool to 38 items. Subsequently, Exploratory Factor Analysis (EFA) conducted with 273 teachers indicated that four additional items exhibited inadequate factor loadings or problematic cross-loadings; these items were also excluded. The resulting Dyscalculia Self-Efficacy Scale (DSES) comprises 34 items organized into four factors: “Dyscalculia Symptoms”, “Providing Psychological Support to Children with Dyscalculia”, “Diagnosing Dyscalculia”, “Providing Support in the Teaching Process”. Confirmatory Factor Analysis conducted with a separate sample of 242 teachers yielded strong model fit indices, supporting the construct validity of the scale. The overall scale demonstrated high internal consistency (Cronbach’s α = 0.980, McDonald’s ω = 0.980). Correlation analyses with established instruments provided evidence of convergent and discriminant validity. The findings indicate that the DSES is a valid and reliable instrument for assessing teachers’ self-efficacy regarding dyscalculia. Full article

Formative assessment is widely seen as a key teaching strategy to support student learning; however, evidence about its connection with self-regulated learning and the alignment between teachers’ and students’ perceptions remains mixed. This study explored the role of formative assessment in promoting self-regulated learning in lower secondary mathematics by incorporating both students’ and teachers’ viewpoints. From a co-regulatory perspective, formative assessment is considered a process developed through ongoing interactions between teachers and students and shared views of assessment practices. The sample included 305 students from Grades 5–9 and 39 mathematics teachers. Students reported their perceptions of formative assessment practices and self-regulated learning, while teachers reported their own practices. Analyses included Pearson correlation and multiple regression at the student level, along with class-level comparisons of teacher–student perceptions and analyses of perceptual agreement. Results revealed that students’ perceptions of formative assessment were positively linked to cognitive, metacognitive, behavioral, and motivational dimensions of self-regulated learning. Multiple regression results showed that different aspects of formative assessment significantly predicted students’ self-regulation, with the greatest explained variance in behavioral self-regulation. Teachers believed they used more formative assessment practices than students perceived. Additionally, higher levels of perceptual agreement between teachers and students, especially in clarifying learning goals and gathering evidence of learning, were associated with increased behavioral regulation and motivational independence among students. These findings emphasize formative assessment in mathematics as a relational and co-regulatory process that relies on shared understanding between teachers and students. Full article

Integration of artificial intelligence (AI) into mathematics education holds significant potential to enhance learning outcomes; however, its effectiveness in resource-constrained higher education contexts remains uneven due to persistent digital divide barriers. This quantitative study investigates how socioeconomic status shapes first-level (technology access) and second level (digital skills and institutional support) digital divide barriers, and how these factors relate to students’ perceptions of AI-driven mathematics learning. Grounded in van Dijk’s digital divide theory, a cross-sectional survey was administered to 121 undergraduate mathematics students at a historically disadvantaged higher education institution. Descriptive statistics, Pearson correlation, and Chi-square analyses were employed to examine associations among socioeconomic status, access, skills, institutional support, and AI perceptions. The findings indicate that material access barriers, such as limited devices and internet connectivity, remain prevalent among disadvantaged students but show weak or inconsistent associations with perceptions of AI. In contrast, institutional support demonstrates a statistically significant positive relationship with students’ perceptions of AI training (r = 0.212, p < 0.05), highlighting its central role in shaping readiness for AI-enhanced learning. Overall, the results suggest that second-level digital divide factors, particularly structured institutional support, are more influential than access alone in determining students’ engagement with AI in mathematics education. The study implies the need for universities to move beyond infrastructure provision toward comprehensive and sustained institutional strategies that foster confidence, guided engagement, and equitable AI adoption. Full article

Accurate prediction of submitochondrial localization is fundamental to understanding mitochondrial biogenesis and cellular metabolic pathways. While deep representations from pre-trained protein language models (pLMs) have significantly advanced the field, traditional global average pooling methods often fail to capture critical, localized N-terminal targeting signals, particularly in long sequences where these motifs are mathematically diluted. To resolve this “signal dilution” bottleneck, we developed a multi-scale architecture that explicitly integrates high-resolution N-terminal features with global evolutionary context derived from ESM-2 embeddings. The proposed framework utilizes an orthogonal mixing strategy consisting of Token-mixing and Channel-mixing. Token-mixing is specifically designed to detect spatial rhythmic patterns across residue positions, while Channel-mixing refines the biochemical signatures within the latent feature space. Extensive benchmarking across diverse datasets demonstrates that our approach effectively maintains signal integrity. Compared to existing state-of-the-art methods, the model achieves a superior overall Generalized Correlation Coefficient (GCC) of 0.7443 on the SM424-18 dataset and 0.7878 on the SubMitoPred dataset, outperforming the latest benchmarks by 9.4% and 16.1%, respectively. Furthermore, on the independent M983 test set, our method maintained a high GCC of 0.6945, demonstrating a 9.9% improvement relative to the state-of-the-art methods. This robust and efficient framework provides a high-precision tool for large-scale mitochondrial proteomics. Full article

In this work, a study of the chemical composition of the compound Sb₂(S_1−xSe_x)₃ used in thin-film solar cell fabrication, based on correlating data obtained from XRD and XPS analyses, is presented. This approach enables us to propose a mathematical expression for evaluating stoichiometric variations in the material, showing how the variable x evolves as a function of the diffraction angle 2θ. To establish this model, we analyzed the most intense diffraction peak, corresponding to the (221) plane. To validate the proposed method, a series of Sb₂(S_1−xSe_x)₃ thin films with different compositions were synthesized using RF-magnetron sputtering followed by conventional heat treatments in a controlled-atmosphere reaction furnace. The XRD results reveal a systematic 2θ shift in the crystalline diffraction peaks toward the positions of the binary precursor phases—from Sb₂Se₃ to Sb₂S₃—caused by the increased sulfur content during synthesis. XPS measurements confirm the presence of Sb, Se, and S, and high-resolution spectra indicate a decrease in selenium content as the sulfur fraction increases. These results allowed us to elucidate the stoichiometric behavior of antimony sulfoselenide Sb₂(S_1−xSe_x)₃ using trend curves fitted to the characterization data. Full article

Operations scheduling of mass customized products is vital in the modern make-to-order (MTO) supply chains. In these systems, order acceptance decisions should be coordinated with available capacity in different sections of the supply chain while considering their potential correlations and interactions. One of the fundamental challenges in optimization of these systems is the computation time of solving models with multiple coupling constraints between supply chain units. This paper addresses this issue by proposing a game-based framework that decomposes the related mixed integer programming mathematical model and it is coordinated and solved using integrated game-based Alternating Direction Method of Multipliers (ADMM). The proposed Stackelberg Leader-Follower game optimizes order acceptance decisions while considering the requirements in supply, production planning, maintenance, inventory, and distribution units. To validate the efficiency of the proposed framework, the model is tested with a simulated four-layer supply chain. The results of experiments proved that decompositions of the model to smaller subsections and solving it in a distributed manner not only optimizes supply chain participating units but also coordinate their movements to achieve the global optimal solution. The proposed framework offers managers a practical decision layer that preserve local autonomy of the supply chain units and reduce their data sharing and computation burdens and concerns. Full article

Engineering education requires pedagogical approaches that integrate sustainability with the development of core technical competencies. This study develops, implements, and evaluates a Sustainability-Integrated Problem-Based Learning (SI-PBL) approach in an undergraduate mechanical vibration course. The approach anchors the learning process in the inherent sustainability characteristics of an engineering problem, requiring students to explicitly negotiate trade-offs between technical performance and sustainability objectives. A quasi-experimental study with 121 mechanical engineering students compared the SI-PBL approach to traditional lecture-based instruction through a compressor redesign project in which students redesigned the balancing system of a single-stage air compressor. Analysis of covariance showed that the SI-PBL cohort achieved significantly larger gains in conceptual understanding ($d=0.74$, $p<0.001$), mathematical proficiency ($d=0.77$, $p<0.001$), complex problem-solving ($d=0.56$, $p<0.001$), and sustainability-oriented decision-making ($d=0.61$, $p<0.001$). A positive correlation between gains in complex problem-solving and sustainability reasoning within the SI-PBL group ($r=0.41$, $p=0.001$) indicated related competency development. The study provides empirical evidence for using sustainability as an integrating context for developing both technical and sustainability competencies in engineering education. Full article

Soil heavy metal pollution caused by mineral resource extraction activities poses a serious threat to the ecological environment within and surrounding mining areas. As a highly concealed toxic heavy metal, arsenic (As) urgently requires the establishment of efficient pollution monitoring methods to achieve pollution prevention and control, as well as environmental remediation in mining areas. This study investigated the feasibility of hyperspectral remote sensing inversion for soil heavy metal arsenic based on ZY-1 02E hyperspectral satellite imagery, focusing on a mining area and its surrounding soils in Sanlisha’an, Wuxuan County, Guangxi. Full Constrained Least Squares (FCLS) was employed to separate mixed pixels and enhance soil spectral contributions in ZY-1 02E imagery, thereby mitigating vegetation interference. Six mathematical transformations, including RT, AT, FD, RTFD, ATFD, and SD, were applied to both the original and enhanced spectra to enhance spectral features. The correlations between the transformed spectra, as well as the original image spectra (S), and soil As concentration were analyzed; then the spectra strongly correlated with soil As concentration were selected to construct Ratio Spectral Index (RSI) and Normalized Difference Spectral Index (NDSI). Correlation matrices were calculated between RSI/NDSI indices and As concentration. Sensitive features were screened using an improved Successive Projection Algorithm (SPA). As concentration inversion was also performed with four models: traditional regression models, PLSR and MLR, and ensemble learning models (RF and XGBoost). In the soil contribution-enhanced spectral modeling results, the optimal transformation–index combination is ATFD-NDSI. The performance indicators of each model are as follows: MLR test set R² = 0.65, PLSR test set R² = 0.62, RF test set R² = 0.7, and XGBoost test set R² = 0.64. The results indicate that the ATFD-NDSI-RF ensemble model provides the best performance. By integrating multiple decision trees, RF effectively handles complex nonlinear relationships, thus enhancing the accuracy and generalization ability of predication. The analysis of NDSI–ATFD–RF inversion results based on sampling points indicates that model error correlates with the pollution intensity gradient, showing greater errors, especially in high-concentration areas, but still maintaining strong correlations (tailings reservoir: r = 0.92, forested areas: r = 0.96, and cropland: r = 0.83). The spatial distribution reveals that the inversion results are closely similar to the spatial distribution of IDW interpolation. Areas with high As concentrations are concentrated in the tailings reservoir and in the southeastern part of the study area. The correlation coefficient between the inversion results and IDW interpolation is 0.6, which further verifies that the inversion results effectively reproduce the spatial distribution trend of highly polluted areas. Full article

Math anxiety, or a student’s lack of confidence in learning mathematics, is one of the emotional dimensions with the greatest impact on mathematics education. Sociological factors such as sex and age, demographic aspects like cultural characteristics, and emotional variables such as general anxiety have been identified as significantly influencing math anxiety. This study conducts quantitative, descriptive, correlational, and regression analyses of the influence of sex, age, and general anxiety on math anxiety in a sample of 185 Spanish elementary students. It also examines whether the effects of age and general anxiety on math anxiety differ by sex. For this purpose, students’ responses to a quantitative questionnaire are analyzed. The instrument combines two validated scales: (i) STAIC T-Anxiety, measuring general anxiety, and (ii) AMAS, measuring math anxiety. Results show that students exhibit moderate average math anxiety, which is not significantly affected by sex. However, significant correlations between math anxiety, age, and general anxiety were found, independent of sex. The study highlights the need to design corrective measures for math anxiety and suggests lines for future research. Full article

Predicting CO₂ absorption behavior in aqueous amine systems is a critical challenge for optimizing carbon capture technologies. This research develops a high-precision Artificial Neural Network (ANN) to simulate equilibrium data across various amine classes, including primary (MEA, DGA), secondary (DEA, DPA), and tertiary (MDEA) amines. The model architecture utilizes a Multi-Layer Perceptron (MLP) trained on a dataset split into 70% training, 15% validation, and 15% testing segments to prevent overfitting and ensure reliable generalization. By employing a Sigmoid activation function, the network achieved a coefficient of determination (R²) exceeding 0.98 and an absolute average relative deviation (AARD) below 5%. Furthermore, this study evaluates the efficacy of classical isotherms (Langmuir, Freundlich, and Temkin) strictly as empirical curve-fitting correlations for liquid-phase behavior. Results indicate that while these models are traditionally surface-adsorption based, the Langmuir form provides a mathematically robust fit for the tertiary amine MDEA (R² = 0.9673). Experimental observations indicate that Monoethanolamine (MEA) maintains the highest capacity for CO₂ uptake. Since the model relies on categorical descriptors for amine types, it offers a rapid and efficient framework for assessing specific solvents in post-combustion capture infrastructure. Full article

Auxiliary line construction has been identified as a crucial approach to fostering mathematical creative thinking. However, existing studies have only focused on the correlations between auxiliary line construction tasks and mathematical creative thinking, without investigating whether engaging in auxiliary line construction can improve mathematical creativity. As a well-established research paradigm, cognitive priming can elicit changes in thinking within a short period. Based on this idea, the present study adopted the cognitive priming paradigm combined with functional near-infrared spectroscopy (fNIRS) technology, and randomly assigned 42 Chinese college students to an auxiliary line group or a control group. The students’ brain activity was monitored in real time during the priming phase (the auxiliary line group completed geometric problems requiring auxiliary line construction, while the control group finished proof problems with pre-set auxiliary lines) and the post-test phase (both groups completed a mathematical creative thinking test). The behavioral results showed that the auxiliary line group achieved significantly higher scores in fluency and originality of mathematical creative thinking than the control group in the post-test phase. The fNIRS data revealed that during the priming phase, the auxiliary line group exhibited stronger activation of the right superior frontal gyrus and higher variability in dynamic functional connectivity; meanwhile, in the post-test phase, the right superior frontal gyrus and right middle frontal gyrus maintained robust neural activation, and brain functional connectivity exhibited a lower clustering coefficient and attenuated small-world network properties. This study confirms that short-term engagement in auxiliary line construction exerts a priming effect on the fluency and originality of mathematical creative thinking, which may be associated with the enhanced activation of specific brain regions and the dynamic adjustment of brain functional connectivity. These findings provide theoretical and empirical evidence for the cultivation of mathematical creative thinking. Full article

This paper presents the development and analysis of a planar microwave sensor designed for detecting adulteration in milk by evaluating the purity of milk in a water-based solution. The sensor comprises a pair of complementary split-ring resonators (CSRRs) fabricated on an FR4 substrate, measuring 30 mm × 50 mm × 1.6 mm, with a dielectric constant of 4.4 and a loss tangent of 0.022. The device’s performance was assessed using a vector network analyzer (VNA) by varying the ratio of full-cream milk to water in a 50 mL solution, starting from 60% and increasing in 10% increments up to 100%. Measurements focused on return loss (RL) at resonant frequency 1.5425 GHz, which exhibited minimal frequency shifts but significant variations in RL magnitude with changing milk concentration (M). To establish a mathematical relationship between RL and M, we segmented the data into two ranges—60% to 80% and 80% to 100% milk concentrations—and applied second-order polynomial regression for each segment. The quadratic equations derived from this regression allowed us to express M in terms of RL. Verification of this method was conducted using arbitrary samples of milk concentrations: 61%, 62%, 72%, 88%, 93%, and 95%. Discrepancies between different quadratic solutions for the same RL values were resolved by normalizing the return losses against pure water and comparing the resulting normalized values with those from known concentrations. This comparison allowed for the accurate selection of the appropriate quadratic equation based on the closest match. Our normalization approach revealed distinct patterns correlating RL magnitudes, enabling us to select the appropriate quadratic equation segment based on minimal discrepancies. The analysis confirmed that by excluding negative and complex solutions and solutions which are beyond the stipulated range of the curve segment, the accuracy of the sensor in determining milk concentration exceeded 83.5%. This study demonstrates the potential of the proposed microwave sensor in ensuring milk quality by effectively quantifying milk purity. Full article

Traditional mean–variance portfolio optimization proves inadequate for cryptocurrency markets, where extreme volatility, fat-tailed return distributions, and unstable correlation structures undermine the validity of variance as a comprehensive risk measure. To address these limitations, this paper proposes a unified entropy-based portfolio optimization framework grounded in the Maximum Entropy Principle (MaxEnt). Within this setting, Shannon entropy, Tsallis entropy, and Weighted Shannon Entropy (WSE) are formally derived as particular specifications of a common constrained optimization problem solved via the method of Lagrange multipliers, ensuring analytical coherence and mathematical transparency. Moreover, the proposed MaxEnt formulation provides an information-theoretic interpretation of portfolio diversification as an inference problem under uncertainty, where optimal allocations correspond to the least informative distributions consistent with prescribed moment constraints. In this perspective, entropy acts as a structural regularizer that governs the geometry of diversification rather than as a direct proxy for risk. This interpretation strengthens the conceptual link between entropy, uncertainty quantification, and decision-making in complex financial systems, offering a robust and distribution-free alternative to classical variance-based portfolio optimization. The proposed framework is empirically illustrated using a portfolio composed of major cryptocurrencies—Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB)—based on weekly return data. The results reveal systematic differences in the diversification behavior induced by each entropy measure: Shannon entropy favors near-uniform allocations, Tsallis entropy imposes stronger penalties on concentration and enhances robustness to tail risk, while WSE enables the incorporation of asset-specific informational weights reflecting heterogeneous market characteristics. From a theoretical perspective, the paper contributes a coherent MaxEnt formulation that unifies several entropy measures within a single information-theoretic optimization framework, clarifying the role of entropy as a structural regularizer of diversification. From an applied standpoint, the results indicate that entropy-based criteria yield stable and interpretable allocations across turbulent market regimes, offering a flexible alternative to classical risk-based portfolio construction. The framework naturally extends to dynamic multi-period settings and alternative entropy formulations, providing a foundation for future research on robust portfolio optimization under uncertainty. Full article

Accurately estimating the steel reinforcement volume in hydropower plant structures requires a clear understanding of the statistical patterns of reinforcement ratios. Based on engineering data from 11 completed hydropower plant buildings, this study employs mathematical statistical methods to systematically analyze the reinforcement ratios of the overall plant structure and its sub-structures (main and auxiliary buildings). The results indicate significant differences in reinforcement ratios among substructures, which exhibit weak correlations with one another. In contrast, the overall plant reinforcement ratio demonstrates clear statistical regularity, following a normal distribution (mean 78 kg/m³, standard deviation 13 kg/m³). The study further identifies the concrete proportion in main and auxiliary buildings, plant type, and hydraulic turbine type as key influencing factors. Based on these findings, a practical formula for estimating the overall reinforcement ratio was developed. Validation demonstrated that this formula yields estimation errors below 5% in most cases. This study not only reveals the statistical distribution patterns of reinforcement ratios but also establishes a theory-based estimation formula that addresses the limitations of existing empirical methods. The proposed approach provides a unified reference framework for preliminary design, filling the gap in systematic statistical analysis of reinforcement ratios in hydropower plant buildings. Full article

The paper presents the development of a correlation model for initial tensile elastic modulus for flexible polymers as a function of Shore hardness in OO and A scale based on measurement. Measured polymers are in groups of silicone rubber, nitrile butadiene rubber (NBR), thermoplastic polyurethane (TPU) and silicone. The model is composed of piecewise exponential functions with fixed coefficients chosen to minimize the S₂ error norm and absolute value of relative error at the measured data points. Every chosen section of the hardness scale has one exponential function correlating the hardness to tensile elastic modulus with the argument in the form of a polynomial up to the fourth degree. The coefficients for the polynomial arguments were determined by enforcing interpolation conditions in a chosen set of points in the logarithmic scale for the elastic modulus. The correlation model possesses C0 continuity. For each material, five specimens were used for hardness measurements and five for the elastic modulus testing. The correlation model gives a positive value for elastic modulus of 0 for hardness, and a “finite”, “reasonable” value of 100 for hardness and is monotonic. Tensile properties were evaluated using true stress and logarithmic (Hencky) strain, with iterative correction of the changing cross-sectional area to account for large strain. The maximum relative error achieved in the correlation model for the OO scale is 13.4%, while for the A scale it is 7%. The developed model provides a practical and rapid method for estimating the initial tensile elastic modulus from non-destructive hardness measurements and is particularly useful in industrial applications and in the development of material models for dental surgery simulations. Full article