New existence of multi-spike solutions for the fractional Schrödinger equations

Science China Mathematics - We consider the following fractional Schrödinger equation: (0.1) $${\left( { - \Delta } \right)^s}u + V\left( y \right)u = {u^p},\,\,\,\,\,\,u >...     

Two-Dimensional MOF and COF Nanosheets: Synthesis and Applications in Electrochemistry

Metal–organic framework (MOF) and covalent organic framework (COF) nanosheets are a new type of two-dimensional (2D) materials with unique design principles and various synthesis methods. They are considered ideal electrochemical devices due to the ultrathin thickness, easily tunable molecular structure, large porosity and other unique properties. There are two common methods to synthesize 2D MOF/COF nanosheets: bottom-up and top-down. The top-down strategy mainly includes ultrasonic assisted exfoliation, electrochemical exfoliation and mechanical exfoliation. Another strategy mainly includes interface synthesis, modulation synthesis, surfactant-assisted synthesis. In this Review, the development of ultrathin 2D nanosheets in the field of electrochemistry (supercapacitors, batteries, oxygen reduction, and hydrogen evolution) is introduced, and their unique dimensional advantages are highlighted.     

Graphene Saturable Absorber Mirror for Mode-Locked Orange Pulse Laser

Journal of Russian Laser Research - We demonstrate a passively-mode-locked Pr3+: LuLiF4 laser operated at the 604 nm orange wave-length, using monolayer graphene as a saturable absorber. The...     

Effect of cationic surfactant cetyltrimethylammonium bromide on the enzymatic hydrolysis of cellulose

Effect of cationic surfactants alkyltrimethylammonium bromide (C_nTAB) with varied alkyl chain lengths on the enzymatic hydrolysis of Avicel and the surface charge of cellulase was investigated. Enzymatic hydrolysis of Avicel increased linearly from 42.1 to 61.4 % with the increase of the concentration of cetyltrimethylammonium bromide (C₁₆TAB) logarithmically from 0.0001 to 0.01 mM, and reached a maximum value at the concentration of 0.01–0.03 mM. When the concentration was increased further, the cellulase solution became positively charged and the enzymatic hydrolysis of Avicel decreased rapidly. With the increasing alkyl chain length, C_nTAB provided more proton and neutralized the negative charge of cellulase more obviously. Therefore, the required concentration of C_nTAB could be less to enhance the enzymatic hydrolysis of Avicel. In addition, C₁₆TAB could enhance enzymatic hydrolysis efficiency of corncob at high solid content from 35.0 to 56.3 %; C₁₆TAB could reduce about 60 % of the cellulase loading in the enzymatic hydrolysis of corncob to obtain the same glucose yield. Effect of C₁₆TAB on the enzymatic hydrolysis of typical pretreated softwood and hardwood was also investigated. This study laid the foundation for using C_nTAB to recover cellulase, and provided the design direction for cellulase with higher activity and better stability by adjusting its hydrophilicity and chargeability.     

关于半clean群环

环$R$称为是半clean的, 是指环中的每个元素都是一个单位与一个周期元的和. clean环是半clean的. 刻画半clean群环的一般情形是不容易的. 我们的目的是考虑如下问题：若$G$ 是局部有限群或者是阶是3的循环群, 群环$RG$何时是semiclean的. clean群环上的一些已有结果被推广.     

Volterra算子及其伴随算子线性组合的数值域

经典Volterra算子$V$及其伴随算子$V^*$在复空间$L^2[0,1]$中起着关键作用. 关于$V$和$V^*$的线性组合的性质, 我们给出了确保$z_1V+z_2V^*(z_1,z_2\in\mathbb{C})$满足增生性质的等价条件. 本文描述了$(u+iv)I+mV+nV^*(u,v,m,n\in\mathbb{R},m+n\geq0)$数值域的精确表示.     

探讨利用在线平台对我院数学教学改革

本文探讨在大数据时代下,如何将在线教育平台介入到我院的大学数学教学改革中,并针对军队院校的特殊性,给出利用在线教育平台进行数学教学改革的具体措施和一些建议.     

Polarization-controlled leakage current and photovoltaic effect in highly preferentially oriented BiFeO3 film

Highly preferentially oriented polycrystalline BiFeO₃ thin film was grown on FTO/glass substrate by a sol–gel method annealed at 500 °C. XRD result showed that the film adopts highly (100) preferential orientation. SEM results indicate that the film is composed of large grains of 40–200 nm and the thickness is about 320 nm. Room temperature saturated polarization and large Pr ~55 μC/cm² were obtained. Leakage current was substantially reduced by the controlling of ferroelectric polarization. Polarization-modulated conduction mechanism was studied. Moreover, substantial photovoltaic effect was observed.