This study aims to apply mathematical modelling methods focusing on the fishing songs of Poyang Lake for its conservation and digital reform. Through the principles of abstraction, model building and parameter estimation of mathematical modelling, we will quantitatively analyse the efficiency of cultural heritage and the degree of influence of digital reform. Specific methods include time series analysis, data mining and optimisation models. These tools will provide theoretical support and quantify the complexity of the problem by introducing corresponding mathematical models and formulas.

This research focuses on patients’ perceptions regarding the accessibility of dental services in Slovenia across four dimensions: financial accessibility, time accessibility, geographical accessibility, and service quality. We observed how specific factors impact accessibility dimensions of dental services in Slovenia, that patients perceive important. A cross-sectional quantitative survey was conducted using proportionate stratified sampling. Data was collected through an online questionnaire, and 599 completed responses were received from patients regarding their experiences and perceptions of accessibility to dental care. A SEM (structural equation model) approach was used to examine the data. The analysis revealed that patients perceive all four dimensions of accessibility: financial, time, geographical, and service quality important and they all constitute the perception of dental accessibility. The findings of this study can assist policymakers in developing a more accessible dental health system by considering the results proposed in our model.

The present research is on the propagation of Rayleigh waves in a homogenous thermoelastic solid half-space by considering the compact form of six different theories of thermoelasticity. The medium is subjected to an insulated boundary surface that is free from normal stress, tangential stress, and a temperature gradient normal to the surface. After developing a mathematical model, a dispersion equation is obtained with irrational terms. To apply the algebraic method, this equation must be converted into a rational polynomial equation. From this, only those roots are filtered out, which has satisfied both of the above equations for the propagation of waves decaying with depth. With the help of these roots, different characteristics are computed numerically, like phase velocity, attenuation coefficient, and path of particles. Various particular cases are compared graphically by using phase velocity and attenuation coefficient. The elliptic path of surface particles in Rayleigh wave propagation is also presented for the different theories using physical constants of copper material for different depths and thermal conductivity.

Uncontrolled economic development often leads to land degradation, a decline in ecosystem services, and negative impacts on community welfare. This study employs water yield (WY) modeling as a method for environmental management, aiming to provide a comprehensive understanding of the relationship between Land Use Land Cover (LULC), Land Use Intensity (LUI), and WY to support sustainable natural resource management in the Cisadane Watershed, Indonesia. The objectives include: (1) analyzing changes in WY for 2010, 2015, and 2021; (2) predicting WY for 2030 and 2050 under two scenarios—Business as Usual (BAU) and Protected Forest Area (PFA); (3) assessing the impacts of LULC and climate change on WY; and (4) exploring the relationship between LUI and WY. The Integrated Valuation of Ecosystem Services and Trade-offs (InVEST) model calculates actual and predicted WY conditions, while the Coupling Coordination Degree (CCD) analyzes the LULC-WY relationship. Results indicate that the annual WY in 2021 was 215.8 × 108 m³, reflecting a 30.42% increase from 2010. Predictions show an increasing trend in WY under both scenarios for 2030 and 2050 with different magnitudes. Rainfall contributes 88.99% more dominantly to WY than LULC. Additionally, around 50% of districts exhibited unbalanced coordination between LUI and WY in 2010 and 2020. This study reveals the importance of ESs in sustainable watershed management amidst increasing demand for natural resources due to population growth.

This paper mainly uses the idea of pedigree clustering analysis, gray prediction and principal component analysis. The clustering analysis model, GM (1,1) model and principal component analysis model were established by using SPSS software to analyze the correlation matrices and principal component analysis. MATLAB software was used to calculate the correlation matrices. In January, The difference in price changes of major food prices in cities is calculated, and had forecasted the various food prices in June 2016. For the first issue, the main food is classified and the data are processed. After that, the SPSS software is used to classify the 27 kinds of food into four categories by using the pedigree cluster analysis model and the system clustering. The four categories are made by EXCEL. The price of food changes over time with a line chart that analyzes the characteristics of food price volatility. For the second issue, the gray prediction model is established based on the food classification of each kind of food price. First, the original data is cumulated, test and processed, so that the data have a strong regularity, and then establish a gray differential equation, and then use MATLAB software to solve the model. And then the residual test and post-check test, have C <0.35, the prediction accuracy is better. Finally, predict the price trend in June 2016 through the function. For the third issue, we analyzed the main components of 27 kinds of food types by celery, octopus, chicken (white striped chicken), duck and Chinese cabbage by using the data of principal given and analyzed by principal component analysis. It can be detected by measuring a small amount of food, this predict CPI value relatively accurate. Through the study of the characteristics of the region, select Shanghai and Shenyang, by looking for the relevant CPI and food price data, using spss software, principal component analysis, the impact of the CPI on several types of food, and then calculated by matlab algorithm weight, and then the data obtained by the analysis and comparison, different regions should be selected for different types of food for testing.

The Organic Rankine Cycle (ORC) is an electricity generation system that uses organic fluid instead of water in the low temperature range. The Organic Rankine cycle using zeotropic working fluids has wide application potential. In this study, data mining (DM) model is used for performance analysis of organic Rankine cycle (ORC) using zeotropik working fluids R417A and R422D. Various DM models, including Linear Regression (LR), Multi-Layer Perceptron (MLP), M5 Rules, M5 Model Tree, Random Committee (RC), and Decision Tree (DT) models are used. The MLP model emerged as the most effective approach for predicting the thermal efficiency of both R417A and R422D. The MLP’s predicted results closely matched the actual results obtained from the thermodynamic model using Genetron software. The Root Mean Square Error (RMSE) for the thermal efficiency was exceptionally low, at 0.0002 for R417A and 0.0003 for R422D. Additionally, the R-squared (R²) values for thermal efficiency were very high, reaching 0.9999 for R417A and R422D. The findings demonstrate the effectiveness of the DM model for complex tasks like estimating ORC thermal efficiency. This approach empowers engineers with the ability to predict thermal efficiency in organic Rankine systems with high accuracy, speed, and ease.