Urbanization is a key determinant of fine particulate matter (PM_2.5) pollution variability. However, there is a limited understanding of different urbanization factors’ roles in PM_2.5 pollution. Using satellite-derived PM_2.5 data from 2002 to 2017, we investigated the spatiotemporal evolution and the spatial autocorrelation of PM_2.5 pollution in the Yangtze River Delta (YRD) region. Afterwards, the impacts of three urbanization factors (population urbanization, land urbanization and economic urbanization) on PM_2.5 pollution were estimated by a spatial Durbin panel data model (SDM). Obtained results showed that: (i) PM_2.5 pollution was larger in the north than in the south of YRD; (ii) Lianyungang and Yancheng cities had significant increasing trends in PM_2.5 pollution from 2002 to 2017; (iii) the regional median center of PM_2.5 pollution was observed in the Nanjing city, with gradual shifting to the northwest during the 16-year period; (iv) PM_2.5 pollution showed significant and positive spatial autocorrelation and spillover effect; (v) population urbanization contributed more to the increase in PM_2.5 pollution than land urbanization, while economic urbanization had no significant impact. The present study highlights the impacts of three urbanization factors on PM_2.5 pollution which represent valuable and relevant information for air pollution control and urban planning.

China is facing pressure to reduce carbon emissions and control pollution. Promoting the synergy between pollution reduction and carbon reduction has become an inevitable choice to achieve the construction of a beautiful China and meet the dual carbon target. This study examines the main factors influencing industrial pollution and carbon reduction in the Pearl River Delta (PRD) and Yangtze River Delta (YRD) urban agglomerations based on data on industrial CO₂ and local air pollutants (LAP) from 2002 to 2021, using the random forest regression model. The results indicate that (1) industrial CO₂ emissions have increased overall, while intensity has decreased. Additionally, both industrial LAP emissions and intensity have decreased. (2) The main factor influencing industrial CO₂ and LAP emissions is the proportion of industrial value added above the scale. Additionally, the proportion of R&D internal expenditure in GDP and total trade imports and exports are the main influencing factors of industrial CO₂ emissions. The industrial fume and dust removal rate mainly affects industrial LAP emissions. (3) There is a clear non-linear relationship between industrial CO₂- and LAP-influencing factors and emissions, which can be attributed to the scale effect factor, the lagging effect of R&D expenditure, and the inappropriate treatment of the “three wastes” by relevant departments that is non-linear. The urban agglomerations of PRD and YRD should prioritize the reduction of carbon emissions, upgrading and transforming their industrial structures, promoting the impact of foreign trade on pollution and carbon reduction, and achieving a balance between sustainable economic development and environmental protection.

The synergetic reduction of CO₂ and PM_2.5 emissions has received much attention in China in recent years. A comprehensive evaluation of the synergy between CO₂ emission reduction (CER) and PM_2.5 emission reduction (PER) would provide valuable information for developing synergetic control policies. Thus, we constructed a comprehensive CO₂-PM_2.5-emission-reduction index system and evaluated the synergy between CER and PER, using the coupling coordination degree (CCD) and relative development degree (RDD) model in China’s 329 cities from 2003 to 2017. The spatiotemporal characteristics of the CCD were analyzed on the national, regional, and urban scales. Furthermore, we used the spatial autocorrelation analysis, kernel density estimation, and Dagum Gini coefficient to investigate the spatial autocorrelation, evolutionary characteristics, and regional differences of the CCD. The results indicate that (1) the synergy between CO₂ and PM_2.5 emissions’ reductions showed an upward trend, and the lowest CCD values occurred in NW and Shanghai on the regional and urban scales, respectively; (2) the CCD showed obvious spatial clustering characteristics, with 75% of the cities located in the “High–High” or “Low–Low” clustering zones in the Moran scatter plots in 2017; (3) the polarization of CCD in SC, MYR, and SW showed intensified trends; (4) and the hypervariable density was the largest contributor to the overall difference in the CCD. Our findings suggest that more attention should be paid to the top-level design of the policies, technological innovation, and cross-regional or intercity cooperation.

Variational autoencoders (VAEs) are popular for their robust nonlinear representation capabilities and have recently achieved notable advancements in the problem of missing data imputation. However, existing imputation methods often exhibit instability due to the inherent randomness in the sampling process, leading to either underestimation or overfitting, particularly when handling complex missing data types such as images. To address this challenge, we introduce a conditional iterative sampling imputation method. Initially, we employ an importance-weighted beta variational autoencoder to learn the conditional distribution from the observed data. Subsequently, leveraging the importance-weighted resampling strategy, samples are drawn iteratively from the conditional distribution to compute the conditional expectation of the missing data. The proposed method has been experimentally evaluated using classical generative datasets and compared with various well-known imputation methods to validate its effectiveness.

Although economic growth brings abundant material wealth, it is also associated with serious PM_2.5 pollution. Decoupling PM_2.5 emissions from economic development is important for China’s long-term sustainable development. In this paper, the generalized Divisia index method (GDIM) is extended by introducing innovation indicators to investigate the main drivers of PM_2.5 pollution in China and its four subregions from 2008 to 2017. Afterwards, a GDIM-based decoupling index is developed to examine the decoupling states between PM_2.5 emissions and economic growth and to identify the main factors leading to decoupling. The obtained results show that: (1) Innovation input scale and GDP are the main drivers for increases in PM_2.5 emissions, while innovation input PM_2.5 intensity, emission intensity, and emission coefficient are the main reasons for reductions in PM_2.5 pollution. (2) China and its four subregions show general upward trends in the decoupling index, and their decoupling states turn from weak decoupling to strong decoupling. (3) Innovation input PM_2.5 intensity, emission intensity, and emission coefficient contribute largely to the decoupling of PM_2.5 emissions. Overall, this paper provides valuable information for mitigating haze pollution.

In this paper, we consider the symmetry properties of the positive solutions of a $ p $-Laplacian problem of the form \begin{document}$ \begin{eqnarray*} \begin{cases} -{{\Delta}}_p u = f(x,u),\ \ \ \ \ \ \ \mathrm{in}\ \ \ \ \ {{\Omega}},\\ \ \ \ \ \ \ \ u = g(x), \ \ \ \ \ \ \ \ \ \ \mathrm{on}\ \ \ \ \partial{{\Omega}}, \end{cases} \end{eqnarray*} $\end{document} where $ {{\Omega}} $ is an open smooth bounded domain in $ R^N, N\geq2 $, and symmetric w.r.t. the hyperplane $ T_0^\nu (\nu $ is a direction vector in $ R^N, |\nu| = 1 $$) $, $ f $: $ {{\Omega}}\times R^+\rightarrow R^+ $ is a continuous function of class $ C^1 $ w.r.t. the second variable, $ g\geq 0 $ is continuous, and both $ f $ and $ g $ are symmetric w.r.t. $ T^\nu_0 $, respectively. Introducing some assumptions on nonlinearities, we get that the positive solutions of the problem above are symmetric w.r.t. the direction $ \nu $ by a new simple idea even if $ {{\Omega}} $ is not convex in the direction $ \nu $.