In this paper, we develop a new adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method for solving multidimensional spatiotemporal integrodifferential equations in unbounded domains. By devising adaptive techniques for sparse mapped Jacobi spectral expansions defined in a hyperbolic cross space, our proposed AHMJ method can efficiently solve various spatiotemporal integrodifferential equations such as the anomalous diffusion model with reduced numbers of basis functions. Our analysis of the AHMJ method gives a uniform upper error bound for solving a class of spatiotemporal integrodifferential equations, leading to effective error control.
Wetlands are major microplastic sinks with a large atmospheric input. However, many details of such deposited atmospheric microplastics entering into wetlands remain unclear, including temporal patterns of input and ecological effects. We monitored the aerial microplastics during four seasons in eleven economically developed cities along the lower reaches of the Yangtze River Basin, China. The average microplastic deposition rate was 512.31 items m−2 d−1, equivalent to an annual contribution of 17.46 metric tons of plastic to the surveyed wetlands with a total area of 1652 km2. These microplastics were predominantly composed of polyamide and polyethylene terephthalate with 61.85 ± 92.29 µm sized pellets, and we obtained similar results for microplastics intercepted on moss in wetlands. Microplastic input varied between wet and dry periods, primarily influenced by wind, rainfall and ozone concentration. Civilian vehicle density and textile industry were the primary socioeconomic factors driving microplastic deposition. Further indoor microcosm experiments revealed that moss phyllosphere bacterial community structure and function were influenced by microplastic abundance and size, exemplifying the unique ecological risks of aerially deposited microplastics to wetlands. These results indicate that mosses and their phyllosphere microbiota could serve as bio-indicators of aerial microplastic characteristics and impacts.
As a judicious correspondence to the classical maxcut, the anti-Cheeger cut has more balanced structure, but few numerical results on it have been reported so far. In this paper, we propose a continuous iterative algorithm (CIA) for the anti-Cheeger cut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the objective function values are monotonically updated and the iteration points converge to a local optimum in finite steps via an appropriate subgradient selection. It can also be easily combined with the maxcut iterations for breaking out of local optima and improving the solution quality thanks to the similarity between the anti-Cheeger cut problem and the maxcut problem. The performance of CIAs is fully demonstrated through numerical experiments on G-set from two aspects: one is on the solution quality where we find that the approximate solutions obtained by CIAs are of comparable quality to those by the multiple search operator heuristic method; the other is on the computational cost where we show that CIAs always run faster than the often-used continuous iterative algorithm based on the rank-two relaxation.
In the context of supply chain digitization and green development in full swing, it is crucial to clarify the impact of the former on green energy innovation. Using exogenous shocks deriving from supply chain innovation and application pilot events, this study examines the impact of supply chain digitization on green energy innovation based on the data of Chinese listed companies from 2012 to 2021. The findings show that supply chain digitization significantly enhances corporate green energy innovation and that receivable asset management is a path mechanism for supply chain digitization to drive green energy innovation. Moreover, there is a significant positive intra-city spillover. Supply chain digitization contributes significantly to corporate green energy innovation in state-controlled manufacturing firms with effective internal controls in the eastern region. This study has important policy implications for promoting green energy innovation and accelerating the development of modern supply chain systems.
Numerical resolution of moderately high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality for the classical numerical methods including finite difference, finite element and spectral methods. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by tracking the deterministic motion, random jump, resampling and reweighting of particles. Real-valued weighted particles are adopted by SPM to approximate the high-dimensional solution, which automatically adjusts the point distribution to intimate the relevant feature of the solution. A piecewise constant reconstruction with virtual uniform grid is employed to evaluate the nonlinear terms, which fully exploits the intrinsic adaptive characteristic of SPM. Combining both, SPM can achieve the goal of adaptive sampling in time. Numerical experiments on the 6-D Allen-Cahn equation and the 7- D Hamiltonian-Jacobi-Bellman equation demonstrate the potential of SPM in solving moderately high-dimensional nonlinear PDEs efficiently while maintaining an acceptable accuracy