Overdetermined boundary value problems with strongly nonlinear elliptic PDE

We consider the strongly nonlinear elliptic Dirichlet problem in a connected bounded domain, overdetermined with the constant Neumann condition F(∇u) = c on the boundary. Here F is convex and positively homogeneous of degree 1, and its polar F ∗ represents the anisotropic norm on R n. We prove that, if this overdetermined boundary value problem admits a solution in a suitable weak sense, then Ω must be of Wulff shape

On a nonlocal problem for a confined plasma in a Tokamak

summary:The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms $u'_{\ast }(|u>u(x)|)$ and $|u>u(x)|$, which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem

DISCUSSION ON THE CHARACTERISTICS OF UU-XIANG'S HURDLING TECHNIQUES

By using the, methods of experiment and documentary, the data and motor photo of liu Xiang attending Olympic and pre-Olympic games were collected and digitized. Based on the sport training practice, Liu-Xiang 110m hurdle sport techniques were investigated. Results show that the performance showing the technique characteristics of short flight time, long offending hurdle distance, short landing distance, high sprint pace frequency and the hip-hurdling style which postponed hold-down-hurdle time, enhanced hold-downhurdle speed and decreased landing time. His knee conceding angle was small and pelvis swung rapidly

The observation of quantum fluctuations in a kagome Heisenberg antiferromagnet

The search for the experimental evidence of quantum spin liquid (QSL) states is critical but extremely challenging, as the quenched interaction randomness introduced by structural imperfection is usually inevitable in real materials. YCu$_3$(OH)$_{6.5}$Br$_{2.5}$ (YCOB) is a spin-1/2 kagome Heisenberg antiferromagnet (KHA) with strong coupling of $\langle J_1\rangle\sim$ 51 K but without conventional magnetic freezing down to 50 mK $\sim$ 0.001$\langle J_1\rangle$. Here, we report a Br nuclear magnetic resonance (NMR) study of the local spin susceptibility and dynamics on the single crystal of YCOB. The temperature dependence of NMR main-line shifts and broadening can be well understood within the frame of the KHA model with randomly distributed hexagons of alternate exchanges, compatible with the formation of a randomness-induced QSL state at low temperatures. The in-plane spin fluctuations as measured by the spin-lattice relaxation rates ($1/T_1$) exhibit a weak temperature dependence down to $T$ $\sim$ 0.03$\langle J_1\rangle$. Our results demonstrate that the majority of spins remain highly fluctuating at low temperatures despite the quenched disorder in YCOB.Comment: NMR work on YCu3(OH)6.5Br2.5, accepted in Communications Physic

Is more use of electricity leading to less carbon emission growth? An analysis with a panel threshold model

Abstract(#br)Electricity plays a key role in modern energy service and climate mitigation. Electricity is becoming more accessible and it is substituted for fossil fuel in more scenarios. Generating electricity from clean energy instead of traditional coal and improving the efficiency of electricity generation, transmission, distribution, and utilization are making it possible for a carbon emission growth reduction. Here we explored the question of whether more use of electricity will lead to less carbon emission growth. Firstly, based on the panel data of 114 countries from 2000 to 2014, we applied a STIRPAT model and then analyzed the relationship between carbon emission and electricity use level with fixed effects panel model and adopted a panel threshold regression model considering electricity-generating source heterogeneity. The results show that electricity use level has a significant negative effect on carbon emission especially when clean energy-based electricity takes a bigger portion. Population, economic growth, urbanization, and industrialization have significant positive impacts on carbon emission. We came up with policy implications based on the results in the end

Heat transport of the kagom\'{e} Heisenberg quantum spin liquid candidate YCu3_3(OH)6.5_{6.5}Br2.5_{2.5}: localized magnetic excitations and spin gap

The spin-1/2 kagom\'{e} Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which unfortunately suffers from the notorious orphan spins problem caused by magnetic disorders. Here we turn to YCu$_3$(OH)$_{6.5}$Br$_{2.5}$, recently recognized as another host of a globally undistorted kagom\'{e} Cu$^{2+}$ lattice free from the orphan spins, thus a more feasible system for studying the intrinsic kagom\'{e} quantum spin liquid physics. Our high-resolution low-temperature thermal conductivity measurements yield a vanishing small residual linear term of $\kappa/T$ ($T\rightarrow 0$), and thus clearly rule out itinerant gapless fermionic excitations. Unusual scattering of phonons grows exponentially with temperature, suggesting thermally activated phonon-spin scattering and hence a gapped magnetic excitation, consistent with a $\mathbb{Z}_2$ quantum spin liquid ground state. Additionally, the analysis of magnetic field impact on the thermal conductivity reveals a field closing of the spin gap, while the excitations remain localized.Comment: 4 figure

Integrated transcriptome and metabolome analysis reveals the anthocyanin biosynthesis mechanisms in blueberry (Vaccinium corymbosum L.) leaves under different light qualities

IntroductionBlueberry (Vaccinium corymbosum L.) is a popular fruit with an abundance of anthocyanins in its leaves and fruits. Light is one of the pivotal environmental elements that affects plant growth and development, but the regulatory mechanism between light quality and anthocyanin formation is poorly understood.MethodsAn integrated transcriptome and metabolome analysis was performed to investigate the effects of white (control), blue (B), red (R), and red/blue (60R/40B) light on blueberry growth and reveal the potential pathway controlling anthocyanin biosynthesis in blueberry leaves.ResultsThe anthocyanin content was significantly improved by the blue and red/blue light when compared with white light, whereas there was a significant reduction in the photosynthesis under the blue light, showing an inverse trend to that of anthocyanin accumulation. Transcriptomic analysis resulted in the assembly of 134,709 unigenes. Of these, 22 were differentially expressed genes (DEGs) that participate in the anthocyanin biosynthesis pathway, with the majority being significantly up-regulated under the blue light. Most of the photosynthesis-related genes that were down-regulated were expressed during anthocyanin accumulation. Targeted metabolome profiling identified 44 metabolites associated with anthocyanin biosynthesis. The contents of most of these metabolites were higher under blue light than the other light conditions, which was consistent with the transcriptome results. The integrated transcriptome and metabolome analysis suggested that, under blue light, leucoanthocyanidin dioxygenase (LDOX), O-methyltransferase (OMT), and UDP-glucose flavonoid glucosyltransferase (UFGT) were the most significantly expressed, and they promoted the synthesis of cyanidin (Cy), malvidin (Mv), and pelargonidin (Pg) anthocyanidins, respectively. The expression levels of dihydroflavonol 4-reductase (DFR) and OMT, as well as the accumulation of delphinidin (Dp), peonidin (Pn), and petunidin (Pt), were significantly increased by the red/blue light.DiscussionThe blue and red/blue lights promoted anthocyanin biosynthesis via inducing the expression of key structural genes and accumulation of metabolites involved in anthocyanin synthesis pathway. Moreover, there was a possible feedback regulating correlation between anthocyanin biosynthesis and photosynthesis under different light qualities in blueberry leaves. This study would provide a theoretical basis for elucidating the underlying regulatory mechanism of anthocyanin biosynthesis of V. corymbosum