Enhancement of Biodiesel Production via Ultrasound Technology: A Mathematical Study.

Biodiesel is one of the alternative renewable energy sources that has received a lot of attention since it is clean, green energy. Different sources can be used for the production of biodiesel, but the most appropriate and economical method relies on the transesterification of methanol with the nonedible vegetable oil from the fruit of the Jatropha curcas plant. Molar ratio, vessel diameter, catalyst concentration, and ultrasound all have a substantial influence on the synthesis of biodiesel by the transesterification process. Among these factors, the diameter of the vessel and the ultrasonic effect through mass transfer limitations have a significant impact on successful reaction completion. In this research work, we have developed a mathematical model to analyze the three-step transesterification process and side saponification reaction in the presence of a potassium hydroxide catalyst. The model considers the influence of mixing intensity variations, including ultrasound, on the mass transfer in different phases. The mass transfer rate is calculated using the modified Dittus-Boelter correlation. An optimal control approach through the minimum principle by Pontryagin is applied to maximize the production of biodiesel at minimal cost. The novelty of this research, which we have derived from our analytical as well as numerical results, considering industrial processes, is that more than 97% biodiesel yield conversion is to be obtained at 50 kHz ultrasound frequency, a 6:1 methanol-to-Jatropha-oil molar ratio, and 1 m of vessel diameter within 50 min using optimal control theory.

Multi-classification of national fitness test grades based on statistical analysis and machine learning.

Physical fitness is a key element of a healthy life, and being overweight or lacking physical exercise will lead to health problems. Therefore, assessing an individual's physical health status from a non-medical, cost-effective perspective is essential. This paper aimed to evaluate the national physical health status through national physical examination data, selecting 12 indicators to divide the physical health status into four levels: excellent, good, pass, and fail. The existing challenge lies in the fact that most literature on physical fitness assessment mainly focuses on the two major groups of sports athletes and school students. Unfortunately, there is no reasonable index system has been constructed. The evaluation method has limitations and cannot be applied to other groups. This paper builds a reasonable health indicator system based on national physical examination data, breaks group restrictions, studies national groups, and hopes to use machine learning models to provide helpful health suggestions for citizens to measure their physical status. We analyzed the significance of the selected indicators through nonparametric tests and exploratory statistical analysis. We used seven machine learning models to obtain the best multi-classification model for the physical fitness test level. Comprehensive research showed that MLP has the best classification effect, with macro-precision reaching 74.4% and micro-precision reaching 72.8%. Furthermore, the recall rates are also above 70%, and the Hamming loss is the smallest, i.e., 0.272. The practical implications of these findings are significant. Individuals can use the classification model to understand their physical fitness level and status, exercise appropriately according to the measurement indicators, and adjust their lifestyle, which is an important aspect of health management.

Heavy element contents of vegetables and health-risk assessment in China.

This study analyzed five heavy elements (HEs), including cadmium (Cd), chromium (Cr), mercury (Hg), lead (Pb), and arsenic (As), in fresh vegetables (i.e., legume, rhizome and potato, gourd, bulb, solanaceous fruit, leafy, and brassica; total: 7214) collected from 31 provinces in China from 2016 to the first half of 2017. By analyzing the concentration level of the five HEs in seven regions (the Northeast, North China, East China, South China, Central China, the Northwest, and the Southwest), except for As, average HEs concentrations were higher in the Southwest than that in the other six regions. According to the maximum permissible limit (MPL), the highest rate of HEs concentration above the MPL was found in the Southwest (11.038%). Analysis of variance (ANOVA) showed varying degrees of variability between regions and categories. By using principal component analysis (PCA), it was found that two principal components account for 73.79% of the total variance in the data. Together with hierarchical cluster analysis (HCA), concluded that Tibet was significantly different from the other 30 provinces. By calculating estimated daily intake (EDI) and the target hazard quotient (THQ), the EDI of Cr in the Southwest was the highest, with results of 1.2119 µg/kg/day for children and 0.8073 µg/kg/day for adults. North China had the highest total target hazard quotient (TTHQ) for HEs in vegetables ingested by children, with a result of 0.933.

Physicochemical parameter based estimation of discarding points for frying oil using data interpolation and principal component transformation.

Data interpolation and principal component transformation (PCT) were used to compute the discarding points of a frying oil by measuring the physicochemical parameters-acid value, carbonyl value, and total polar compounds. Herein, the discarding point refers to the time point (associated with the value of each physicochemical parameter) at which the frying oil should be discarded. First, a primary visual analysis was performed for the obtained data by using line charts. Second, a curve interpolation method was used to compute the discarding points for each parameter and thus determine the discarding points for the frying oil. At 190, 205, and 220°C, the frying oil reached the discarding points at 22.1, 17.7, and 13 hr, respectively. The discarding area was also visualized on the corresponding surfaces for the originally obtained data and the interpolated data to investigate the discarding points. Third, the PCT was conducted for the three parameters at each temperature; the discarding point estimation for the three parameters could be reduced to the estimation from the first principal component (FPC), thereby simplifying this process. At 190, 205, and 220°C, the frying oil reached the discarding points when the FPCs were 10.4524, 6.2881, and -1.7629 at the time points 22.1, 17.7, and 13 hr, respectively. Finally, a verification experiment revealed that the correlation between the results obtained by our interpolation method or PCT and the verified data was higher than 0.98, which demonstrates the effectiveness of our method.