Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.     

Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.     

Cycloparaphenylene (CPP) series are molecular models for graphene armchair edges: trends in their aromaticity and cyclic conjugation are evaluated

Cycloparaphenylene ([r]CPP) and cyclacene ([r]CA) series are models for short carbon nanotubes. It is shown that armchair edges in model cycloparaphenylenes possess greater aromaticity and cyclic conjugation than do zigzag edges in model cyclacenes. According to Aihara’s bond resonance energy (BRE) and Bosanac and Gutman energy effect (ef) measurements, cycloparaphenylenes are twice as aromatic as cyclacenes. The general solution of all eigenvalues of all members of the cycloparaphenylene series is given. The origin of the recurrence of some eigenvalues are determined.     

Autonomous system for data collection: Location and mapping issues in post-disaster environment

Disaster relief requires many resources. Depending on the circumstances of each event, it is important to rapidly choose the suitable means to respond to the emergency intervention. A brief review of the conditions and means demonstrated the usefulness of an autonomous stand-alone machine for these missions. If many techniques and technologies exist, their relevant combination to achieve such a system presents several challenges. This communication tries to outline the possible achievement of an autonomous vehicle under these particular circumstances. This paper focuses on the specific working conditions and welcomes future contributions from robotics and artificial intelligence.In the necessarily limited scope of this article, the authors focus on a particularly critical aspect: location. Indeed, this machine is intended to evolve in heterogeneous and dangerous environment and without any outside contacts that could last up to several days. This blackout, due to the propagation difficulties of electromagnetic waves in the ground, induces an independence of the localisation process and makes the use of any radio navigation support system (GNSS), most of the time, impossible. The knowledge of the position of the system, both for navigation of the autonomous system (Rover) and location of targets (victims buried under debris) must be able to be estimated without contributions from external systems. Inertial classical techniques, odometer, etc., have to be adapted to these conditions during a long period without external support. These techniques also have to take into account that energy optimisation requests the use of low-power processors. Consequently, only poor computing capacity is available on-board.The article starts with a presentation of the context of a post-disaster situation as well as the main missions of Search and Rescue (SaR). It is followed by the analysis of autonomous navigation located in a post-earthquake situation. We will then discuss means to determine the attitude of the autonomous system and its position. The interest of hybridisation with external systems – whenever possible –, will be evaluated with a view to correcting deviations suffered by the system during its mission. Finally, prospects and future work are presented.     

Gas-phase 21Ne NMR studies and the nuclear magnetic dipole moment of neon-21

Gas-phase ²¹Ne nuclear magnetic resonance spectra were measured at the natural abundance of ²¹Ne isotope for samples consisting of pressurized neon up to 60 bar at room temperature and applying the magnetic field of the strength B₀ = 11.7574 T. It showed that the nuclear magnetic resonance frequency is linearly dependent on the density of gaseous neon. The resonance frequency was extrapolated to the zero-density point, and it permitted the determination of the ²¹Ne nuclear magnetic moment, μ(²¹Ne) = 0.6617774(10) μ_N. The present value of μ(²¹Ne) is not influenced by the bulk magnetic susceptibility of neon and interactions between neon atoms; therefore, it is more precise and reliable than the previous result obtained for μ(²¹Ne).     

腔光子-自旋波量子耦合系统中各向异性奇异点的实验研究

通过耦合三维微波腔中光子和腔内钇铁石榴石单晶小球中的自旋波量子形成腔-自旋波量子的耦合系统,并通过精确调节系统参数在该实验系统中观测到各向异性奇异点.奇异点对应于非厄米系统中一种特殊状态,在奇异点处,耦合系统的本征值和本征矢均简并,并且往往伴随着非平庸的物理性质.以往大量研究主要集中在各向同性奇异点的范畴,它的特征是在系统参数空间中沿着不同参数坐标趋近该奇异点时具有相同的函数关系.在这篇文章中,主要介绍实验上在腔光子-自旋波量子耦合系统中通过调节系统的耦合强度和腔的耗散衰减系数两条趋近奇异点的路径而实现了各向异性奇异点,具体分别对应于在趋近奇异点时,本征值的虚部的变化与耦合强度和腔的衰减系数的变化会有线性和平方根不同的行为.各向异性奇异点的实现有助于基于腔光子-自旋波量子耦合系统的量子信息处理和精密探测器件的进一步研究.     

Preparation and Characterization of Activated Carbon from Microwave and Conventional Heated Almond Shells Using Phosphoric Acid Activation

Activated carbon production from almond shells using phosphoric acid activation agent was achieved by applying both conventional heating and microwave heating in succession. The morphology and surface properties of activated carbon were studied using thermogravimetric and differential gravimetric analysis, Fourier-transform infrared spectroscopy, scanning electron microscopy, and Brunauer–Emmett–Teller analysis. A surface area of 1128 m²/g was achieved by optimizing the microwave power (500?W), microwave application time (15?minutes), conventional heating time (45?minutes), conventional heating temperature (500?°C), and the phosphoric acid:sample ratio (0.7:1). An adsorption capacity of methylene blue of 148?mg/g and an iodine value of 791?mg/g was obtained for the prepared activated carbon.     

The antidepressant effect of 4-hydroxybenzyl alcohol 2-naphthoate through monoaminergic,GABAergic system and BDNF signaling pathway

Abstract

Gastrodigenin, also known as 4-hydroxybenzyl alcohol (HBA), is one of the main components of Gastrodia elata, which is a perfect lead compound of natural products. In order to get new active compounds, we modified the structure of HBA through esterification with carboxylic acid, and got a series of derivatives in which 4-hydroxybenzyl alcohol 2-naphthoate (NHBA) showed stronger antidepressant activity than HBA. In this paper, we firstly evaluated the antidepressant activity of NHBA by tail suspension test (TST) and forced swimming test (FST). Then, we carried out the biochemical assay and western blot to determine its mechanism. The results displayed that NHBA could increase the content of serotonin, dopamine, norepinephrine, γ-aminobutyric acid, brain-derived neurotrophic factor (BDNF) and tropomyosin receptor kinase B (TrkB) in mice brain. It suggested that NHBA exhibited an antidepressant-like effect through monoaminergic system, GABAergic system and BDNF/TrkB signaling pathways.