Pattern formation in a variable diffusion predator–prey model with additive Allee effect

This paper deals with a variable diffusion predator–prey model with additive Allee effect. A good understanding of the existence of steady states is gained for the case  $\sigma =0$. The result shows that the reduce problem has multiple solutions. Moreover, by applying the singular perturbation method, we give a proof of existence of large amplitude solutions when  $\sigma$ is sufficiently small.     

A Hardy–Trudinger–Moser Inequality Involving LpNorm in the Hyperbolic Space

Let B be the unit disc in R~2, H be the completion of C_0∞(B) under the norm■ .By the method of blow-up analysis and an argument of rearrangement with respect to the standard hyperbolic metric ■, we prove that, for any fixed■ ,the supremum■ .This is an analog of early results of Lu–Yang(Discrete Contin. Dyn. Syst., 2009) and Yang(Trans.Amer. Math. Soc., 2007), and extends those of Wang–Ye(Adv. Math., 2012) and Yang–Zhu(Ann.Global Anal. Geom., 2016).     

Nucleophilic Activation of Sulfur Hexafluoride by N-Heterocyclic Carbenes and N-Heterocyclic Olefins: A Computational Study

Sulfur hexafluoride (SF₆) is considered as a potent greenhouse gas, whose effective degradation is challenging. Here we report a computational study on the nucleophilic activation of sulfur hexafluoride by N-heterocyclic carbenes and N-heterocyclic olefins. The result shows that the activation of SF₆ is both thermodynamically and kinetically favorable at mild condition using NHOs with fluoro-substituted azolium and sulfur pentafluoride anion being formed. The Gibbs free energy barrier during the activation of SF₆ has a linear relationship with the energy of HOMO of substrates, which could be a guideline for applying those compounds that feature higher energy in HOMO to activate SF₆ in high efficiency.     

An Intrinsic Photothermal Liquid for Light Detection and Energy Storage

Photothermal materials (PTMs) have been intensively investigated in the fields of photothermal conversion. Superior to solid PTMs, liquid PTMs are leading the trends in satisfying the demands of high flexibility and easy recycling. Successful examples of liquid PTMs are mostly formulated by dispersing solid PTMs in solvents, but suffer from the problems of phase segregation and solvent pollution. In this work, a low-cost formulation is proposed, which involves an oxidative product of ethyl oleate by iodine. It is an intrinsic liquid PTM, preserving the fluidic nature as well as possessing considerable ability for photothermal conversion. In addition to understanding the mechanism of light absorption in the visible and even near infrared windows, two examples are presented to demonstrate the great potential of liquid PTMs in broad areas such as light sensing and energy storage.     

多种分布下选择后变量显著性分析及其在CEPS数据中的应用

在使用变量选择方法选出模型后,如何评价模型中变量系数的显著性是统计学重点关注的前沿问题之一.文章从适应性Lasso变量选择方法的选择结果出发,在考虑实践中误差分布多样性的前提下,基于选择事件构造了模型保留变量系数的条件检验统计量,并给出了该统计量的一致收敛性质的证明过程.模拟研究显示,在多种误差分布下所提方法均可进一步优化变量选择结果,有较强的实用价值.应用此方法对CEPS学生数据进行了实证分析,最终选取了学生认知能力等10个变量作为影响中学生成绩的主要因素,为相关研究提供了有益的参考.     

Nonseparating Independent Sets and Maximum Genus of Graphs

Acta Mathematicae Applicatae Sinica, English Series - A subset I of vertices of an undirected connected graph G is a nonseparating independent set (NSIS) if no two vertices of I are adjacent and G...     

An Electrochemical Nanosensor for Monitoring the Dynamics of Intracellular H2O2 Upon NADH Treatment

Reactive oxygen species (ROS)-based therapeutic strategies play an important role in cancer treatment. However, in situ, real-time and quantitative analysis of intracellular ROS in cancer treatment for drug screening is still a challenge. Herein we report one selective hydrogen peroxide (H₂O₂) electrochemical nanosensor, which is prepared by electrodeposition of Prussian blue (PB) and polyethylenedioxythiophene (PEDOT) onto carbon fiber nanoelectrode. With the nanosensor, we find that the level of intracellular H₂O₂ increases with NADH treatment and that increase is dose-dependent to the concentration of NADH. High-dose of NADH (above 10 mM) can induce cell death and intratumoral injection of NADH is validated for inhibiting tumor growth in mice. This study highlights the potential of electrochemical nanosensor for tracking and understanding the role of H₂O₂ in screening new anticancer drug.