Recursion Operators of Two Supersymmetric Equations

From Lax representations, recursion operators for the supersymmetric KdV and the supersymmetric Kaup-Kupershimdt (SKK) equations are proposed explicitly. Under some special conditions, the recursion operator of the supersymmetricSawada-Kotera equation can be recovered by the one of the SKK equation.     

势Korteweg-de Vries方程的暗方程分类

通过要求势Korteweg-de Vries (KdV)方程和线性扩展方程具有高阶对称,获得了势KdV方程的完整的暗方程标量分类:8类具有若干自由参数的相互独立的暗方程.然后通过一个直接假设方法,获得了势KdV方程的8类暗方程的递归算子.     

Darboux Transformations,Higher-Order Rational Solitons and Rogue Wave Solutions for a(2+1)-Dimensional Nonlinear Schrdinger Equation

By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a modified KdV equation and an NLS equation. With the help of symbolic computation, some higher-order rational solutions and rogue wave(RW) solutions are constructed by its(1, N-1)-fold DTs according to determinants. From the dynamic behavior of these rogue waves discussed under some selected parameters, we find that the RWs and solitons are demonstrated some interesting structures including the triangle, pentagon, heptagon profiles, etc. Furthermore, we find that the wave structure can be changed from the higher-order RWs into higher-order rational solitons by modulating the main free parameter. These results may give an explanation and prediction for the corresponding dynamical phenomena in some physically relevant systems.     

PbF_2:Er~(3+),Yb~(3+)荧光粉的制备和多波长响应双向转换发光机理（英文）

采用高温固相法制备了PbF_2∶Er~(3+),Yb~(3+)双向转换荧光粉。通过X射线粉末衍射分析(XRD)、结构精修分析、功率-强度测试和荧光光谱分析对样品进行了表征。通过X射线衍射和精修结果分析了样品的相组成和晶胞参数的变化。荧光光谱分析表明,在紫外光(378 nm)和不同波长的红外光(808、980、1 064和1 550 nm)激发下,样品在540～550 nm范围内具有强绿光发射和在650～660 nm范围内的弱红光发射。最后,通过强度-功率测试讨论了样品在不同波长的红外光下激发的上转换发光机理,并分析了在378 nm激发的下转换发光机理。     

Solitons for a generalized variable-coefficient nonlinear SchrSdinger equation

In this paper, we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear SchrSdinger equation （NLS） with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions, one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results, some previous one- and two- soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one- and the two-soliton and the discussion about the integrability property and the Hirota method is given finally.     

上转换发光在染料敏化太阳能电池中的应用

以水热和高温煅烧相结合的方法制备了掺Er³⁺的TiO₂上转换发光层,并将其组装在染料敏化太阳能电池(DSSC)中。通过XRD﹑荧光光谱﹑UV-Vis和电池的光电性能测试,分析了上转换发光层的发光机理及其加入后对染料敏化太阳能电池性能的影响。结果表明,上转换发光层的引入有效地提高了DSSC的光电性能,在80 mW·cm^-2红外光照射下最高光电转换效率达到了0.14‰,比未加上转换发光层的DSSC提高了160%。     

中国国债市场收益率的统计特征分析

首先通过采用基于各个国债之间相关性的距离测度方法,对修正后的国债日收益率时间序列进行了聚类分析,将上海证券交易所的20只国债分成了5类,分类结果显示我国国债市场中的各个国债日收益率之间的相关性程度是很明显地依赖于它们的到期时间的。同时,研究了每一个国债修正后日收益率时间序列的价格波动结构,结果表明中国的国债市场也表现出非常明显的多标度分形特征,还发现属于同一类国债的多标度特征具有很强的自相似性,而不同类型国债之间的多标度特征则具有一定程度上的差异性。     

基于梯度优化物理信息神经网络求解复杂非线性问题

近年来,物理信息神经网络(PINNs)因其仅通过少量数据就能快速获得高精度的数据驱动解而受到越来越多的关注.然而,尽管该模型在部分非线性问题中有着很好的结果,但它还是有一些不足的地方,如它的不平衡的反向传播梯度计算导致模型训练期间梯度值剧烈振荡,这容易导致预测精度不稳定.基于此,本文通过梯度统计平衡了模型训练期间损失函数中不同项之间的相互作用,提出了一种梯度优化物理信息神经网络(GOPINNs),该网络结构对梯度波动更具鲁棒性.然后以Camassa-Holm(CH)方程、导数非线性薛定谔方程为例,利用GOPINNs模拟了CH方程的peakon解和导数非线性薛定谔方程的有理波解、怪波解.数值结果表明,GOPINNs可以有效地平滑计算过程中损失函数的梯度,并获得了比原始PINNs精度更高的解.总之,本文的工作为优化神经网络的学习性能提供了新的见解,并在求解复杂的CH方程和导数非线性薛定谔方程时用时更少,节约了超过三分之一的时间,并且将预测精度提高了将近10倍.