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Metric mean dimension and mean Hausdorff dimension depend on metrics. In this paper, we investigate the continuity of the metric mean dimension and mean Hausdorff dimension concerning the metrics for amenable group actions, which extends recent results by Muentes, Becker, Baraviera et al.. Moreover, we give proof of the product formulas for the mean Hausdorff dimension and the metric mean dimension for amenable group actions.

For the countable discrete amenable group actions, we calculate the mean Hausdorff dimensions of three types of infinite dimensional fractal systems, the self-similar systems, homogeneous systems in the infinite-dimensional torus, and the infinite dimensional-carpets., Comment: 38 pages

The Forbush Decrease (FD) represents the rapid decrease of the intensities of charged particles accompanied with the coronal mass ejections (CMEs) or high-speed streams from coronal holes. It has been mainly explored with ground-based neutron monitors network which indirectly measure the integrated intensities of all species of cosmic rays by counting secondary neutrons produced from interaction between atmosphere atoms and cosmic rays. The space-based experiments can resolve the species of particles but the energy ranges are limited by the relative small acceptances except for the most abundant particles like protons and helium. Therefore, the FD of cosmic ray electrons and positrons have just been investigated by the PAMELA experiment in the low energy range ($<5$ GeV) with limited statistics. In this paper, we study the FD event occurred in September, 2017, with the electron and positron data recorded by the Dark Matter Particle Explorer. The evolution of the FDs from 2 GeV to 20 GeV with a time resolution of 6 hours are given. We observe two solar energetic particle events in the time profile of the intensity of cosmic rays, the earlier and weak one has not been shown in the neutron monitor data. Furthermore, both the amplitude and recovery time of fluxes of electrons and positrons show clear energy-dependence, which is important in probing the disturbances of the interplanetary environment by the coronal mass ejections., Comment: This article is dedicated to the 72nd anniversary of People's Republic of China

In general, perovskite solar cells (PSC) with a sensitized or thin film architecture absorb light from a single illumination. This paper reported a PSC architecture with a semitransparent Au/ITO counter electrode, which allows light to pass it partially. When the device was illuminated simultaneously from both the FTO and Au/ITO sides, the PSC has achieved an overall power conversion efficiency (PCE) as high as 20.1% under high light intensity (1.4 sun), which is much higher than that of the single-irradiation system.