The Method of Moving spheres on Hyperbolic Space and Symmetry of Solutions to a Class of PDEs

The classification of solutions of semilinear partial differential equations, as well as the classification of critical points of the corresponding functionals, have wide applications in the study of partial differential equations and differential geometry. The classical moving plane method and the moving sphere method on $\mathbb{R}^n$ provide an effective approach to capturing the symmetry of solutions. As far as we know, the moving sphere method has yet to be developed on the hyperbolic space $\mathbb{H}^n$. In the present paper, we focus on the following equation \begin{equation*} P_k u = f(u) \end{equation*} on hyperbolic spaces $\mathbb{H}^n$, where $P_k$ denotes the GJMS operators on $\mathbb{H}^n$ and $f : \mathbb{R} \to \mathbb{R}$ satisfies certain growth conditions. We develop a moving sphere approach for integral equations on $\mathbb{H}^n$, to obtain the symmetry property as well as a characterization result towards positive solutions. Our methods also rely on Helgason-Fourier analysis and Hardy-Littlewood-Sobolev inequalities on hyperbolic spaces together with a Kelvin transform we introduce on $\mathbb{H}^n$ in this paper.Comment: Some references are added and typos fixe

Effect of Bordered Pit Torus Position on Permeability in Chinese Yezo Spruce

The effect of different bordered pit torus positions on wood permeability was studied by air-drying and ethanol-exchange drying for green wood and by soaking in water, then followed by ethanol-exchange drying for air-dried wood of Chinese yezo spruce (Picea jezoensis var. komarovii). The results showed that different treatments caused different pit torus positions and different wood permeability. The air-drying treatment resulted in pit torus aspiration and low permeability for sapwood. The ethanol-exchange drying treatment left the pit torus in an unaspirated position and resulted in high permeability for sapwood. Soaking in water followed by ethanol-exchange drying caused deaspiration of a part of pit torus and increased permeability for both sapwood and heartwood

Climatic Signals in Wood Property Variables of Picea Crassifolia

Little attention has been given to climatic signals in wood properties. In this study, ring width(RW), annual average microfibril angle (MFA), annual average tracheid radial diameter (TRD), andannual average density (DEN), as the annual and intra-annual wood property variables, were measured at high resolution by SilviScan-3 on dated Picea crassifolia trees. Dendroclimatological methods were used to analyze climatic signals registered in wood property variables. RW, MFA, and TRD negatively correlated with temperature and positively correlated with precipitation in the growing season, whereas the reverse was true for DEN. Climatic signals recorded in the earlywood were similar to those measured for the full width of the annual rings. Climatic signals recorded in latewood were very weak except for latewood MFA. This study showed that wood property variables could be extensive resources for learning more about the influences of climate on tree growth and how trees adapt to ongoing climate change

Time dependence of the orthotropic compression Young's moduli and Poisson's ratios of Chinese fir wood

The time dependency of the orthotropic compliance for Chinese fir wood [Cunninghamia lanceolata (Lamb.) Hook] has been investigated by performing compressive creep experiments in all orthotropic directions. Time evolution of the creep strain in the axial and lateral directions was recorded by means of the digital image correlation (DIC) technique, to determine the diagonal and nondiagonal elements of the viscoelastic compliance matrix. The results reveal the significant influence of time on the mechanical behavior. The orthotropic nature of the viscoelastic compliance is highlighted by the different time dependency of the Young's moduli and the Poisson's ratios obtained for the individual directions. Differences among the time-dependent stress-strain relationship determined at the 25, 50, and 75% stress levels indicate that the viscoelastic behavior of wood is also load-dependent. A Poisson's ratio values, which are increasing with time in νLR, νLT, νRT, νTR, and decreasing in νRL and νTL, demonstrate that the creep strain is influenced by loading directions. The substantially different time dependency of the nondiagonal elements of the compliance matrix further reveals the orthotropic compliance asymmetry and emphasizes the complexity of the viscoelastic character of wood

Sustained methane emissions from China after 2012 despite declining coal production and rice-cultivated area

China’s anthropogenic methane emissions are the largest of any country in the world. A recent study using atmospheric observations suggested that recent policies aimed at reducing emissions of methane due to coal production in China after 2010 had been largely ineffective. Here, based on a longer observational record and an updated modelling approach, we find a statistically significant positive linear trend (0.36 ± 0.04 ( $\pm1\sigma$ ) Tg CH _4 yr ^−2 ) in China’s methane emissions for 2010–2017. This trend was slowing down at a statistically significant rate of -0.1 ± 0.04 Tg CH _4 yr ^−3 . We find that this decrease in growth rate can in part be attributed to a decline in China’s coal production. However, coal mine methane emissions have not declined as rapidly as production, implying that there may be substantial fugitive emissions from abandoned coal mines that have previously been overlooked. We also find that emissions over rice-growing and aquaculture-farming regions show a positive trend (0.13 ± 0.05 Tg CH _4 yr ^−2 for 2010–2017) despite reports of shrinking rice paddy areas, implying potentially significant emissions from new aquaculture activities, which are thought to be primarily located on converted rice paddies