Nombres transcendents

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Santiago Zarzuela[en] This project is a chronologic summary of several methods to find if a number is transcendental or not. Some of these results will guide us to very interesting others, such as, that $\pi+e$ or $e \cdot \pi$ is a transcendental number, but never both at the same time. And other methods will provide us the existence of at least a transcendental number in a specific set of numbers

A methodological framework for identifying potential sources of soil heavy metal pollution based on machine learning: a case study in the Yangtze Delta, China

It is a great challenge to identify the many and varied sources of soil heavy metal pollution. Often little information is available regarding the anthropogenic factors and enterprises that could potentially pollute soils. In this study we use freely available geographical data from a search engine in conjunction with machine learning methodologies to identify and classify potentially polluting enterprises in the Yangtze Delta, China. The data were classified into 31 separate and five integrated industry types by five different machine learning approaches. Multinomial naive Bayesian methods achieved an accuracy of 86.5% and Kappa coefficient of 0.82 and were used to classify the geographic data from more than 250 000 enterprises. The relationship between the different industry classes and measurements of soil cadmium and mercury concentrations was explored using bivariate local Moran's I analysis. The analysis revealed areas where different industry classes had led to soil pollution. In the case of cadmium, elevated concentrations also occurred in some areas because of natural sources. This study provides a new approach to investigate the interaction between anthropogenic pollution and natural sources of soil heavy metals to inform pollution control and planning decisions regarding the location of industrial sites

Identification of the potential risk areas for soil heavy metal pollution based on the source-sink theory

International audienceFrom the perspective of the mechanism of soil pollution, it is difficult to explain the process of predicting the spatial distributions of soil heavy metal pollution using traditional geostatistical methods at a regional scale. Furthermore, few methods are available to proactively identify potential risk areas for preventing soil contamination. In this study, we selected 13 environmental factors related to the accumulation of soil heavy metals based on the source-sink theory. Then, the fuzzy k-means method in combination with the random forest (RF) method was used to classify potential risk areas. The concentrations and spatial distributions of the heavy metals were well predicted by RF, and the average values of the root mean square error of the prediction and R-2 were 4.84 mg kg(-1) and 0.57, respectively. The results indicated that the soil pH, fine particulate matter, and proximity to polluting enterprises significantly influenced the heavy metal pollution in soils, and the environmental variables varied significantly across the identified subregions. This study provides a theoretical basis for the sustainable management and control of soil pollution at the regional scale

Improved Mapping of Potentially Toxic Elements in Soil via Integration of Multiple Data Sources and Various Geostatistical Methods

Soil pollution by potentially toxic elements (PTEs) has become a core issue around the world. Knowledge of the spatial distribution of PTEs in soil is crucial for soil remediation. Portable X-ray fluorescence spectroscopy (p-XRF) provides a cost-saving alternative to the traditional laboratory analysis of soil PTEs. In this study, we collected 293 soil samples from Fuyang County in Southeast China. Subsequently, we used several geostatistical methods, such as inverse distance weighting (IDW), ordinary kriging (OK), and empirical Bayesian kriging (EBK), to estimate the spatial variability of soil PTEs measured by the laboratory and p-XRF methods. The final maps of soil PTEs were outputted by the model averaging method, which combines multiple maps previously created by IDW, OK, and EBK, using both lab and p-XRF data. The study results revealed that the mean PTE content measured by the laboratory methods was as follows: Zn (127.43 mg kg−1) > Cu (31.34 mg kg−1) > Ni (20.79 mg kg−1) > As (10.65 mg kg−1) > Cd (0.33 mg kg−1). p-XRF measurements showed a spatial prediction accuracy of soil PTEs similar to that of laboratory analysis measurements. The spatial prediction accuracy of different PTEs outputted by the model averaging method was as follows: Zn (R2 = 0.71) > Cd (R2 = 0.68) > Ni (R2 = 0.67) > Cu (R2 = 0.62) > As (R2 = 0.50). The prediction accuracy of the model averaging method for five PTEs studied herein was improved compared with that of the laboratory and p-XRF methods, which utilized individual geostatistical methods (e.g., IDW, OK, EBK). Our results proved that p-XRF was a reliable alternative to the traditional laboratory analysis methods for mapping soil PTEs. The model averaging approach improved the prediction accuracy of the soil PTE spatial distribution and reduced the time and cost of monitoring and mapping PTE soil contamination

Improved Mapping of Potentially Toxic Elements in Soil via Integration of Multiple Data Sources and Various Geostatistical Methods

International audienceSoil pollution by potentially toxic elements (PTEs) has become a core issue around the world. Knowledge of the spatial distribution of PTEs in soil is crucial for soil remediation. Portable X-ray fluorescence spectroscopy (p-XRF) provides a cost-saving alternative to the traditional laboratory analysis of soil PTEs. In this study, we collected 293 soil samples from Fuyang County in Southeast China. Subsequently, we used several geostatistical methods, such as inverse distance weighting (IDW), ordinary kriging (OK), and empirical Bayesian kriging (EBK), to estimate the spatial variability of soil PTEs measured by the laboratory and p-XRF methods. The final maps of soil PTEs were outputted by the model averaging method, which combines multiple maps previously created by IDW, OK, and EBK, using both lab and p-XRF data. The study results revealed that the mean PTE content measured by the laboratory methods was as follows: Zn (127.43 mg kg(-1)) > Cu (31.34 mg kg(-1)) > Ni (20.79 mg kg(-1)) > As (10.65 mg kg(-1)) > Cd (0.33 mg kg(-1)). p-XRF measurements showed a spatial prediction accuracy of soil PTEs similar to that of laboratory analysis measurements. The spatial prediction accuracy of different PTEs outputted by the model averaging method was as follows: Zn (R-2 = 0.71) > Cd (R-2 = 0.68) > Ni (R-2 = 0.67) > Cu (R-2 = 0.62) > As (R-2 = 0.50). The prediction accuracy of the model averaging method for five PTEs studied herein was improved compared with that of the laboratory and p-XRF methods, which utilized individual geostatistical methods (e.g., IDW, OK, EBK). Our results proved that p-XRF was a reliable alternative to the traditional laboratory analysis methods for mapping soil PTEs. The model averaging approach improved the prediction accuracy of the soil PTE spatial distribution and reduced the time and cost of monitoring and mapping PTE soil contamination

Pollution Characteristics, Spatial Patterns, and Sources of Toxic Elements in Soils from a Typical Industrial City of Eastern China

Soil pollution due to toxic elements (TEs) has been a core environmental concern globally, particularly in areas with developed industries. In this study, we sampled 300 surface (0–0.2 m) soil samples from Yuyao City in eastern China. Initially, the geo-accumulation index, potential ecological risk index, single pollution index, and Nemerow composite pollution index were used to evaluate the soil contamination status in Yuyao City. Ordinary kriging was then deployed to map the distribution of the soil TEs. Subsequently, indicator kriging was utilized to identify regions with high risk of TE pollution. Finally, the positive matrix factorization model was used to apportion the sources of the different TEs. Our results indicated that the mean content of different TEs kept the order: Zn > Cr > Pb > Cu > Ni > As > Hg ≈ Cd. Soil pollution was mainly caused by Cd and Hg in the soil of Yuyao City, while the content of other TEs was maintained at a safe level. Regions with high TE content and high pollution risk of TEs are mainly located in the central part of Yuyao City. Four sources of soil TEs were apportioned in Yuyao City. The Pb, Hg, and Zn contents in soil were mainly derived from traffic activities, coal combustion, and smelting. Meanwhile, Cu was mainly sourced from industrial emissions and atmospheric deposition, Cr and Ni mainly originated from soil parental materials, and Cd and As were produced by industrial and agricultural activities. Our study provides important implications for improving the soil environment and contributes to the development of efficient strategies for TE pollution control and remediation