As solar energy is a low-cost and clean energy source, there has been a great deal of interest in how to harvest it. To absorb solar energy efficiently, we designed a broadband metamaterial absorber based on the principle of Fabry–Pérot (FP) cavities and surface plasmon resonance (SPR). We propose a broadband perfect absorber consisting of a four-layer structure of silica–tungsten–silica–titanium (SiO2–W–SiO2–Ti) for the incident light wavelength range of 300–2500 nm. The structure achieves perfect absorption of incident light in the wavelength range of 351.8–2465.0 nm (absorption > 90%), with an average absorption of 96.3%. The advantage of our proposed structure is that it combines the characteristics of both high and broadband absorption, and has high overall absorption efficiency for solar radiation. It is also independent of polarization and insensitive to incident angle. We investigated how absorption was affected by different structures, materials, geometric parameters, and refractive indices for different dielectric materials, and we explored the reasons for high absorption. This structure is refractory and ultrathin, and it offers a good tradeoff between bandwidth and absorption. It therefore has premium application prospects and value.

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The Silk Road is a land artery connecting China and the West, an important passage for East-West trade, and glass products are one of the treasures of early exchanges. Due to different production techniques, the composition and performance of Eastern and Western glass are often very different, but the identification of glass has always been a problem in ancient times. Aiming at the analysis of the composition and source of ancient glass products, this paper designs a mathematical model to avoid duplication of work. Based on the data, this paper calculates the classification rules of the main components of high potassium glass, lead-barium glass; and by selecting the appropriate chemical components as the subcomponents for each category, the specific division methods and division results are given, and the rationality and sensitivity of the classification results are analyzed. And the chemical composition of the unknown category of glass artifacts is identified by the model to identify the type they belong to, and the sensitivity of the classification results is analyzed.

After two years of the Newcastle epidemic, the emergence of a mutant strain of Omicron virus has once again raised a high level of alarm worldwide, and it has rapidly replaced the Delta strain as the major strain in the world epidemic with high infectivity. In order to study the spread of the epidemic in a qualitative and quantitative manner, this paper uses relevant mathematical modeling ideas and methods, combined with the background of big data, to conduct relevant research and analysis in order to provide guidance for the actual fight against the epidemic and facilitate scientific research and response measures. In this paper, a gray prediction algorithm is used to predict the future epidemic data. A metabolic algorithm is introduced to recursively correct the prediction residuals and build a multilevel gray model. In this paper, to investigate the role of vaccines on epidemics, the R values under each dose of vaccine were calculated by selecting data from several countries and regions using fitted curve idealization. The prediction of the data yields the conclusion that vaccination is indeed directly effective in controlling the spread of the epidemic.

The Silk Road was a key channel for trade and cultural exchange between China and the West in ancient times, and one of the gems of the early exchange was glass products. The composition and properties of glass from the East and the West often differ greatly because of the different production processes, but the problem of glass identification has been an ancient challenge. For the analysis of the composition and origin of ancient glass products, this paper is a mathematical approach to model design, avoiding the duplication of labor into this area. This paper uses chi-square test and correspondence analysis to first determine which factors are significantly correlated with glass products, and then further determine the correlation with the factors. The use of box-line plots allows for a very visual analysis of the statistical patterns of the presence or absence of chemical composition content on the surface of artifact samples. For predicting the chemical composition content before weathering, the approximate chemical composition content was first estimated based on the average rate of change of each chemical composition before and after weathering, and then a multiple linear regression model was used to correct for the chemical composition content. It was finally concluded that the weathering of glass surface was significantly correlated with glass type, and high potassium glass was not easily differentiated, while lead-barium glass was easily weathered; the silica content changed most significantly before and after weathering of high potassium glass, with an average change rate of 25.98%, and the silica and lead oxide content changed most significantly before and after weathering of lead-barium glass, with average change rates of 29.75% and 23.77%, respectively.