Improved Caffarelli-Kohn-Nirenberg Inequalities and Uncertainty Principle

In this paper we prove some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on $\mathbb R^n$, which is a further study of the results in \cite{Dang-Deng-Qian}. Moreover, we also extend the extra-strong uncertainty principle given in \cite{Dang-Qian-Chen} to cases for complex- and vector-valued functions defined on $\mathbb S^n,n\geq 2.

Microbial Diversity of Liquan’s Laozao, Sweet Fermented Glutinous Rice

In this study, MiSeq high-throughput sequencing technology was used to analyze the bacterial and fungal diversity in Laozao produced in Liquan. The results showed that the dominant bacterial phyla in Liquan’s Laozao were Firmicutes (97.20%) and Proteobacteria (2.29%), accounting for 99.49% of the total abundance, and the dominant bacterial genera were Lactobacillus (85.25%), Pediococcus (5.50%), Leuconostoc (1.68%), Streptococcus (1.63%) and Lactococcus (1.12%). The dominant fungal phyla were Mucoromycota (56.90%) and Ascomycota (43.10%), and the dominant fungal genera were Rhizopus (56.66%), Saccharomyces (23.28%), Saccharomycopsis (12.24%) and Candida (5.35%). Diversity analysis found that the microbial community of Liquan’s Laozao could be divided into two groups, which showed significant differences in bacterial diversity and fungal richness (P < 0.05). Gene and phenotype prediction showed that the relative expression levels of amino acid transport and metabolism, potential pathogenicity and mobile elements were significantly different between the two groups (P < 0.05)

Gastrodia elata powder capsule enhances anti-epileptic effect of carbamazepine by decreasing P-gp expression

Purpose: To investigate the influence of Gastrodia elata powder capsule (GC) or gastrodin (GTD) on the anti-epileptic effect of carbamazepine (CBZ) on penicillin (PG)-induced epilepsy in rats. Methods: A total 116 rats were used in this study. Rats in the control group (n = 8) were injected with normal saline (NS) in place PG. Epilepsy was induced in the remaining 108 rats on the first day via PG injection. The rats were then divided randomly into six groups (18 rats per group): PG group, CBZ group, CBZ + GC group, CBZ + GTD group, GC group, and GTD group, which were given (p.o.) NS, CBZ (100 mg/kg), CBZ (100 mg/kg.) + GC (350 mg/kg), CBZ (100 mg/kg) + GTD (100 mg/kg), GC (350 mg/kg), and GTD (100 mg/kg), respectively, once a day for 15 days. The behavioral characteristics of the rats were observed and used to assess the anti-epileptic effect of the test drugs. Real-time quantitative reverse transcription-PCR and Western blot assays were employed for the determination of the effect of CBZ, GC and GTD on the expression levels of P-gp. Results: CBZ significantly reduced the symptoms of epilepsy, while GC and GTD enhanced the antiepileptic effect of CBZ, and reversed the CBZ-induced increases in the protein expressions of mrd1a and P-gp (p &lt; 0.05). Conclusion: GC reverses CBZ drug resistance, probably through downregulation of P-gp expression. This finding indicates that GC is a potential anti-epilepsy drug, but it merits further studies

Hardy-Hodge decomposition of vector fields on compact Lipschitz hypersurfaces

For M a compact Lipschitz Riemannian manifold of dimension at least 2, we prove a Helmholtz-Hodge decomposition of tangent $L p$ vector fields as a sum of a gradient and a divergence free fields; the result holds for restricted range of p around 2, and for all $p ∈ (1, ∞)$ when M is V M O-smooth. If, moreover, M is a compact and connected hypersurface having the local Lipschitz graph property, embedded in $R n+1$ with the natural metric, we also establish a Hardy-Hodge decomposition of a $R n+1$-valued vector field of L p class on M as the sum of a tangent divergence free field and of two (traces of) harmonic gradients of Hardy class with exponent p, one from inside and one from outside M. The latter holds for restricted range of p, and for all $p ∈ (1, ∞)$ when M is $C 1$-smooth