Existence and multiplicity of positive solutions for an elastic beam equation

This paper investigates the boundary value problem for elastic beam equation of the form

大型粮仓温度分布反演数学模型的研究

采用有限元数值模拟方法,以响应面模型RSM(Response surface model)理论为基础对大型粮仓冬、夏两季的温度分布进行了深入分析,推导了粮仓温度反演数学模型。将采集的温度值导入RSM模型中,并结合单因素轮换法、正交实验和统计方法,通过构造一个具有明确表达形式的多项式来预测粮仓温度分布反演数学模型。在数学模型的基础上给出各因子交互作用下的设计空间、各因素对粮温影响的主效应及交互效应。实验证明该数学模型误差小,精度高,具有良好的计算性能,在大型粮仓温度监控系统中采用该模型能够解决布线少、预测空间范围广的问题。     

An Alternate [2×2] Grid Constructed Around TiO4N2 Units

The formation of a tetranuclear self-assembled species constructed around a TiO₄N₂ motif is reported. This aggregate is generated from Ti(OⁱPr)₄, 2,2’-bipyrimidine (bpym) and a bis-biphenol strand (L²H₄) where two 2,2’-biphenol units are connected with a biphenyl spacer. The solid-state structure of the [Ti₄(L²)₄(bpym)₄] architecture reveals the formation of an unprecedented chiral alternate [2×2] grid. In addition to the structural characterization of the [Ti₄(L²)₄(bpym)₄] architecture, geometry optimisation on various possible isomeric tetrameric assemblies ([2×2] grid, alternate [2×2] grid, circular helicate or cyclic hemihelicate) is performed using DFT calculations. These results confirm the higher stability of the alternate [2×2] grid over the other possible tetranuclear isomers and allow examining the replacement of the bpym ligands by two novel diimine chelates within the tetranuclear assembly (2,2’-bipyridine=bipy and 2,2’-bipyrazine=bipyraz). From this initial theoretical investigation, the competition between these three nitrogen ligands in the course of the self-assembly process is next evaluated. Overall, this investigation shows that the exclusive formation of the alternate [2×2] grid is driven by CH⋅⋅⋅N interactions.     

Photoelectrocatalytic Reduction of Cr（Vl） over TiO2 Nanotube Arrays under Half-wave Pulsed Direct Current

报道了在半波脉冲直流电（h-DC）作为电压驱动下,以阳极氧化法制备的TiO2纳米管（TNT）为工作电极,紫外光光电催化（PEC）还原Cr（VI）的研究.半波脉冲直流电相比稳压直流电（DC）和交流电（AC）具有更佳的载流子分离和光电催化作用.探讨了电压大小、频率及电解质NaCl浓度对Cr（VI）催化还原反应的影响.TNT光电催化和电催化还原Cr（VI）效率随外加电压和频率的增大而增大,但是频率过高对反应有一定的抑制作用.电解质NaCl对反应的影响不显著,这是因为在重金属还原体系中,NaCl作为活性氯物种的母体和增强溶液导电性的作用体现得不明显.     

Use of symmetry plane fragmentation and graph squaring techniques to express the eigenspectra for some vertex-weighted graphs of linear chains and cycles in analytical form

Three types of graphs of linear chains, viz. linear chains with unit increment or decrement in weight on one terminal vertex, linear chains with unit increment or decrement in weight on both the terminal vertices and linear chains with unit increment in weight on one terminal vertex and decrement in that on the other terminal vertex, have been considered. The symmetry plane fragmentation and graph squaring techniques have been exploited to express the eigenspectra of such graphs of linear chains in analytical form, and have subsequently been used to express the eigenspectra of graphs of linear chains and cycles with alternant vertex weights. The derived expressions for the eigenspectra have been used to obtain the eigenspectra of linear polyacenes, methylene-substituted linear polyacenes and cylindrical polyacene strips in analytical form.     

基于微波法制备纳米银胶的三种病菌的SERS光谱初步研究

使用激发光为785 nm的便携式拉曼光谱仪分别对赤星病菌、谷镰刀病菌和香蕉炭疽悬浮液进行了普通拉曼光谱和表面增强拉曼散射(SERS)光谱检测。实验结果显示,微波法制备的纳米银胶对三种植物病菌均具有较好的增强效果,同时获得了三种病菌信噪比较好的SERS光谱。从整体上看,三种菌谱峰峰强分布具有一定的相似性,如在481 cm-1处均为最强谱峰,500～1 000 cm-1谱峰较弱和1 000～1 600 cm-1谱峰较强。但三者在谱峰的分布和峰形上仍有明显不同,因此通过比较三种病菌的不同SERS谱峰可对其进行快速区分和鉴别。     

Diameter preserving surjection on alternate matrices

Let F be a field with ｜F｜ ≥ 3, Km be the set of all m × m （m ≥ 4） alternate matrices over F. The arithmetic distance of A, B ∈ Km is d（A, B） ：= rank（A - B）. If d（A, B） = 2, then A and B are said to be adjacent. The diameter of Km is max{d（A, B） ： A, B ∈ km}. Assume that φ ： Km→Km is a map. We prove the following are equivalent： （a） φ is a diameter preserving surjection in both directions, （b） φ is both an adjacency preserving surjection and a diameter preserving map, （c） φ is a bijective map which preserves the arithmetic distance.     

一类有理交错样条曲线的逼近性及形状修改

本文提出一类Ｃ＾２连续的四阶有理交错样条曲线，它能整体或局部逼近于控制多边形。     

Mathematical methods for a class of mixed boundary-value problems of planar pentagonal quasicrystal and some solutions

The mathematical theory of elasticity for planar pentagonal quasicrystals is developed and some analytic solutions for a class of mixed boundary-value problems (corresponding to a Griffith crack) of the theory are offered. An alternate procedure and a direct integral approach are proposed. Some analytical solutions are constructed and the stress and displacement fields of a Griffith crack in the quasicrystals are determined. A basis for further studying the mechanical behavior of the material related to planar defects is provided. Project supported by the Foundation of State Education Commission of China for Doctorate Station.