Locally constrained curvature flows and geometric inequalities in hyperbolic space

In this paper, we first study the locally constrained curvature flow of hypersurfaces in hyperbolic space, which was introduced by Brendle, Guan and Li [7]. This flow preserves the $m$th quermassintegral and decreases $(m+1)$th quermassintegral, so the convergence of the flow yields sharp Alexandrov-Fenchel type inequalities in hyperbolic space. Some special cases have been studied in [7]. In the first part of this paper, we show that h-convexity of the hypersurface is preserved along the flow and then the smooth convergence of the flow for h-convex hypersurfaces follows. We then apply this result to establish some new sharp geometric inequalities comparing the integral of $k$th Gauss-Bonnet curvature of a smooth h-convex hypersurface to its $m$th quermassintegral (for $0\leq m\leq 2k+1\leq n$), and comparing the weighted integral of $k$th mean curvature to its $m$th quermassintegral (for $0\leq m\leq k\leq n$). In particular, we give an affirmative answer to a conjecture proposed by Ge, Wang and Wu in 2015. In the second part of this paper, we introduce a new locally constrained curvature flow using the shifted principal curvatures. This is natural in the context of h-convexity. We prove the smooth convergence to a geodesic sphere of the flow for h-convex hypersurfaces, and provide a new proof of the geometric inequalities proved by Andrews, Chen and the third author of this paper in 2018. We also prove a family of new sharp inequalities involving the weighted integral of $k$th shifted mean curvature for h-convex hypersurfaces, which as application implies a higher order analogue of Brendle, Hung and Wang's [8] inequality.Comment: 38 pages, accepted version for Mathematische Annalen, add Corollary 1.10 to describe the application of the new locally constrained flow (1.11

The fruits of Xanthium sibiricum Patr: A review on phytochemistry, pharmacological activities, and toxicity

In recent years, drug development and research have gradually shifted from chemical synthesis to biopharmaceutical and natural drugs. Natural medicines, such as traditional Chinese medicine, have been among the first studied because of their long medicinal history, simplicity, and the relatively low cost of research. Among them, Xanthii Fructus (XF) is famous for the treatment of sinusitis. In this article, the achievements of research on XF from 1953 to 2020 are systematically reviewed, focusing on the aspects of chemical constituents, pharmacological effects, clinical applications, toxicity and side effects, and processing methods. To date, there have been significant advances in both the phytochemistry and pharmacology of XF. Some traditional uses have been validated and clarified in modern pharmacological studies. However, its mechanism of action in the treatment of allergic diseases has not been satisfactorily explained. Further in vitro and in vivo studies are required to rationally develop new drugs and to elucidate the therapeutic potential of XF. A comprehensive evaluation of XF and an understanding of network pharmacology are also needed. © 2020 World Journal of Traditional Chinese Medicine | Published by Wolters Kluwer ‑ Medknow

Study on Microstructure Differences of Coal Samples before and after Loading

The microscopic pore structure of coal affects the content of adsorbed gas. The microstructure of coal sample before and after loading is different, which will affect the adsorption and permeability of coal seam gas. In order to study this difference, the authors carried out mercury intrusion experiments on coal containing different coal samples and used nondestructive nuclear magnetic resonance (NMR) techniques, scanning electron microscopy, and transmission electron microscopy, to study the microstructure of coal samples before and after loading. The experimental results show that the pores of coal samples are mainly micropores and small pores, and the mesopores and macropores are relatively few. The T2 spectrum area of the coal sample is significantly increased after loading, and the parallel-layer coal samples’ T2 spectrum area is 46735, which is 9112 more than the vertical layer coal samples. The T2 spectrum of the vertical coalbed of saturated water samples shows a three-peak shape, the peak of the T2 spectrum is 12692, and the parallel bedding shows a bimodal morphology. The peak area of the T2 spectrum is 11277. The permeability of the parallel bedding coal sample is good, and the coal sample exhibits anisotropic properties. The pores and cracks of the coal samples increased after loading, and the localized area of the coal sample collapsed and formed a fracture zone, which was not conducive to the occurrence of coal seam gas. Further explanation of the changes in the permeability of the coal sample before and after loading will affect the gas storage and transportation

Multiporous carbon allotropes transformed from symmetry-matched carbon nanotubes

Carbon nanotubes (CNTs) with homogeneous diameters have been proven to transform into new carbon allotropes under pressure but no studies on the compression of inhomogeneous CNTs have been reported. In this study, we propose to build new carbon allotropes from the bottom-up by applying pressure on symmetry-matched inhomogeneous CNTs. We find that the (3,0) CNT with point group C3v and the (6,0) CNT with point group C6v form an all sp3 hybridized hexagonal 3060-Carbon crystal, but the (4,0) CNT with point group D4h and the (8,0) CNT with point group D8h polymerize into a sp2+sp3 hybridized tetragonal 4080-Carbon structure. Their thermodynamic, mechanical and dynamic stabilities show that they are potential carbon allotropes to be experimentally synthesized. The multiporous structures, excellently mechanical properties and special electronic structures (semiconductive 3060-Carbon and semimetallic 4080-Carbon) imply their many potential applications, such as gases purification, hydrogen storage and lightweight semiconductor devices. In addition, we simulate their feature XRD patterns which are helpful for identifying the two carbon crystals in future experimental studies

Preparation and Characterization of Antioxidative and UV-Protective Larch Bark Tannin/PVA Composite Membranes

In order to prepare functional materials for antioxidant and ultraviolet (UV)-protective green food packaging, condensed tannin, previously extracted from larch bark, was mixed with polyvinyl alcohol (PVA), and then the mixture was used to cast composite membranes. An antioxidative assay using 1,1-diphenyl-2-picrylhydrazyl (DPPH)—a free radical scavenger—and starch–potassium iodide oxidation–discoloration analyses showed that the composite membranes have good antioxidative activities. The low UV transmission and protective effect of the composite films on vitamin E indicated the UV protection ability of the composite membranes. Both larch bark tannin and PVA are rich in hydroxyl groups; scanning electron microscopy analysis demonstrated their compatibility. Also, the mechanical and crystallization properties of the composite membranes did not significantly decrease with the addition of larch bark tannin

ADEPT: Autoencoder with differentially expressed genes and imputation for robust spatial transcriptomics clustering

Summary: Advancements in spatial transcriptomics (ST) have enabled an in-depth understanding of complex tissues by quantifying gene expression at spatially localized spots. Several notable clustering methods have been introduced to utilize both spatial and transcriptional information in the analysis of ST datasets. However, data quality across different ST sequencing techniques and types of datasets influence the performance of different methods and benchmarks. To harness spatial context and transcriptional profile in ST data, we developed a graph-based, multi-stage framework for robust clustering, called ADEPT. To control and stabilize data quality, ADEPT relies on a graph autoencoder backbone and performs an iterative clustering on imputed, differentially expressed genes-based matrices to minimize the variance of clustering results. ADEPT outperformed other popular methods on ST data generated by different platforms across analyses such as spatial domain identification, visualization, spatial trajectory inference, and data denoising