联噻吩桥联双三联吡啶的合成、质子化及其与金属离子的配位

以2,5-二溴噻吩为底物, 经醛基化、Kröhnke吡啶合成反应、Suzuki偶联三步制备了联噻吩桥联双三联吡啶 (BTTPY,总产率13%).通过紫外吸收及荧光光谱研究了其在酸性介质中的质子化效应, BTTPY在乙酸和三氟乙酸中的吸收及荧光光谱较非质子溶剂中均有明显红移.借助紫外吸收滴定法研究了其与过渡金属离子(Ni²⁺、Zn²⁺、Cd²⁺、Cu²⁺)的配位作用.结果表明BTTPY可与这些金属离子形成1:1的配合物,原子力显微镜 (AFM)图像显示, BTTPY与铬离子所形成的配位聚合物主要呈现一维堆积.     

Solitons for a generalized variable-coefficient nonlinear Schrdinger equation

In this paper,we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear Schrdinger 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.     

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.     

New explicit exact solutions for a generalized Hirota—Satsuma coupled KdV system and a coupled MKdV equation

In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota--Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.     

Travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms

Applying the general projective Riccati equations method, we consider the exact travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms using symbolic computation.From our results, we not only can successfully recover some previously known travelling wave solutions found by using various tanh methods, but also can obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.     

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.