Multiplicity of solutions for a class of fourth elliptic equations

We show that there exist at least three nontrivial solutions for a class of fourth elliptic equations under Navier boundary conditions by linking approaches.     

交易者行为倾向与股市波动形态

分析一个具有基础价值均衡、非基础价值均衡、周期和混沌等四种市场波动形态的随机多主体股市模型,利用理论分析和数值实验的方法研究交易者模仿学习、价格追踪和策略转移三种行为倾向对股市场波动形态的影响,得出结论:当三类行为倾向都很小时,股市处于基础价值均衡形态;随着价格追踪和模仿学习倾向逐渐增大,股市进入周期形态;当模仿学习倾向足够大时,系统处于非基础价值均衡形态;混沌形态出现在周期和非基础价值均衡形态中间很窄的参数范围.     

On slightly P-coherent rings

A ring R is called left slightly P-coherent if C is P-injective, for every left R-module exact sequence 0→A→B→C→0 with A and B P-injective. The properties of slightly P-coherent rings and several examples are studied to show that left slightly P-coherent rings fall in between left P-coherent rings and left strongly P-coherent rings. In terms of some derived functors, some homological dimensions over these rings are investigated. As applications, some new characterizations of p.p.rings are given.     

Nonuniformly nonlinear elliptic equations of p-biharmonic type

This paper deals with the existence and multiplicity of weak solutions to nonlinear differential equations involving a general p-biharmonic operator (in particular, p-biharmonic operator) under Dirichlet boundary conditions or Navier boundary conditions. Our method is mainly based on variational arguments.     

概率与直觉

通过“免费抽奖问题”、“生日问题”、“肇事车认定问题”一个例子说明:在求某个事件的概率时,如果不经过认真分析,常常会被直觉误导。并分析了导致错觉的原因是错误地选择了样本空间,进而说明正确选择样本空间的重要性。     

Porous graphene-based electrodes: Advances in electrochemical sensing of environmental contaminants

Extravagant toxins release at an uncontrollable scale due to the continuous embarking of organic and inorganic contaminants has become a severe threat to the ecosystem’s healthy sustainability. The timely monitoring and determination of the environmental contaminants are crucial to take proper steps for environmental remediation. Among advanced nanomaterials, graphene is one of the extensively explored electrode materials for sensing environmental toxins. However, the graphene sheets' agglomeration due to weak wander Waals forces and the π–π interactions compromise its unique inherent features. The integration of graphene into porous structures can facilitate in exploiting its intrinsic properties. Graphene porous network offers highly conductive multiplexed pathways with a well-defined porous structure that provides a better diffusion of the electrolyte along with analytes to encounter the active electrode material. The pores in the 2D sheet or 3D architecture of graphene provide extensive active sites for various analytes' interaction. Rationally designed porous graphene-based materials and nanocomposites are promising advanced electrode materials for trace level quantification of environmental toxins. Herein, we critically discuss the advances in developing the porous graphene and its composites-based electrodes for electrochemical sensing of the environmental toxins.     

Source-type solutions of heat equations with convection in several variables space

In this paper we study the source-type solution for the heat equation with convection: ut = △u + ■· ▽un for (x,t) ∈ ST→ RN × (0,T] and u(x,0) = δ(x) for x ∈ RN, where δ(x) denotes Dirac measure in = RN,N 2,n 0 and b = (b1,...,bN) ∈ RN is a vector. It is shown that there exists a critical number pc = N+2 such that the source-type solution to the above problem exists and is unique if 0 N n < pc and there exists a unique similarity source-type solution in the case n = N+1 , while such a solution does not exist...     

Gradient estimate for exponentially harmonic functions on complete Riemannian manifolds

The notion of exponentially harmonic maps was introduced by Eells and Lemaire (Proceedings of the Banach Center Semester on PDE, pp. 1990–1991, 1990). In this note, by using the maximum principle we get the gradient estimate of exponentially harmonic functions, and then derive a Liouville type theorem for bounded exponentially harmonic functions on a complete Riemannian manifold with nonnegative Ricci curvature and sectional curvature bounded below.     

金属有机骨架Ni-BTC和Ni-BDC的溶剂效应形貌调控及超级电容器性能

储能材料的性能在很大程度上取决于它们的结构和形貌。我们使用简单的溶剂热方法,通过改变溶剂合成了不同形貌的Ni-1,3,5-苯三甲酸（Ni-BTC）和Ni-1,4-苯二甲酸（Ni-BDC）金属有机骨架材料。Ni-BTC有不规则块状、球状和八面体3种形貌,Ni-BDC有纳米片状、花状和不规则块状3种形貌。对Ni-BTC和Ni-BDC作为超级电容器电极材料的性能进行了研究。结果表明,通过溶剂热方法,在N,N-二甲基甲酰胺（DMF）溶剂中合成出的Ni-BTC和Ni-BDC电极材料的超级电容器性能要优于乙醇（EtOH）和DMF/EtOH （50：50,V/V）溶剂。     

一类非线性抛物型对流扩散方程的相似解

本文讨论对流扩散方程:的相似源型解．由于方程具有对流项且初始值为Ｄｉｒａｃ测度,特别当ｍ＞１时方程在{ｕ＝０}处退化,给求解造成实质的困难．本文基于作者以往研究的有关结果,应用特殊函数理论和微分方程极值原理等技巧,讨论了形如ｕ(ｘ,ｔ)＝ｔ－αｆ(ｘｔ－β)的相似解存在性、唯一性及其数学结构特征．指出当方程存在这种特殊解时ｍ与ｎ应满足某种关系,从量纲分析上看,此种条件是必要的．