Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation

Nonlinear Dynamics - A new method named bilinear neural network is introduced in this paper, and the corresponding tensor formula is proposed to obtain the exact analytical solutions of nonlinear...     

激光剥蚀-电感耦合等离子体-原子发射光谱/质谱法分析中国古代钾玻璃组分

利用激光剥蚀电感耦合等离子体原子发射光谱(LA-ICP-AES)和激光剥蚀电感耦合等离子体质谱(LA-ICP-MS)分析了一批中国古代钾玻璃。样品表面磨去100μm以上,并通过预剥蚀去除风化影响,设计剥蚀路径以消除元素分布不均匀影响。通过钙铝及其它微量元素将钾玻璃分成3个亚类,它们可能有不同的配方及制造中心;研究发现,钾玻璃着色剂类型多样化,有单质Cu,Mn2+,Cu2+,Co2+等;系统研究了钾玻璃的稀土元素特征,成功区分了九只岭地区及风门岭地区的钾玻璃;对两种方法在古代玻璃分析中的特点进行了探讨。     

直流辉光放电质谱法测定多晶硅中关键杂质元素的相对灵敏度因子

采用直流辉光放电质谱(dc-GD-MS)测定多晶硅中关键杂质元素的相对灵敏度因子(RSF).标样制作过程中主要是在连续通入氩气条件下将固定量的非标准多晶硅样品熔化,向硅熔体中均匀掺入浓度范围为1～30 μg/g的关键杂质元素(如B和P),采用快速固化法制成标样;再将制成的标准样品加工成一系列适合GD-MS扁平池(Flat Cell)的片状样品(20 mm×20 mm×2mm).采用二次离子质谱法(SI-MS)对标准样品中关键掺杂元素进行多次定量测定,取平均值作为关键杂质元素的精确含量.优化一系列质谱条件后,运用GD-MS对标样中关键掺杂元素的离子强度进行多次测定,计算平均结果,得到未校正的表观浓度,利用标准曲线法计算出关键杂质元素的相对灵敏度因子.     

An extended simplest equation method and its application to several forms of the fifth-order KdV equation

In this paper, an extended simplest equation method is proposed to seek exact travelling wave solutions of nonlinear evolution equations. As applications, many new exact travelling wave solutions for several forms of the fifth-order KdV equation are obtained by using our method. The forms include the Lax, Sawada-Kotera, Sawada-Kotera-Parker-Dye, Caudrey-Dodd-Gibbon, Kaup-Kupershmidt, Kaup-Kupershmidt-Parker-Dye, and the Ito forms.     

Solving Huxley equation using an improved PINN method

Although many effective methods for solving partial differential equations (PDEs) have been proposed, there is no universal method that can solve all PDEs. Therefore, solving partial differential equations has always been a difficult problem in mathematics, such as deep neural network (DNN). In recent years, a method of embedding some basic physical laws into traditional neural networks has been proposed to reveal the dynamic behavior of equations directly from space-time data [i.e., physics-informed neural network (PINN)]. Based on the above, an improved deep learning method to recover the new soliton solution of Huxley equation has been proposed in this paper. As far as we know, this is the first time that we have used an improved method to study the numerical solution of the Huxley equation. In order to illustrate the advantages of the improved method, we use the same network depth, the same hidden layer and neurons contained in the hidden layer, and the same training sample points. We analyze the dynamic behavior and error of Huxley’s exact solution and the new soliton solution and give vivid graphs and detailed analysis. Numerical results show that the improved algorithm can use fewer sample points to reconstruct the exact solution of the Huxley equation with faster convergence speed and better simulation effect.

     

Investigation of Ancient Chinese Potash Glass by Laser Ablation Inductively Coupled Plasma Atomic Emission Spectroscopy

In the present study, laser ablation inductively coupled plasma atomic emission spectroscopy (LA-ICP-AES) was successfully used to classify 26 ancient potash glass beads. These samples, mainly dated from the Han Dynasty to the Jin Dynasty, were from several provinces of both China and Vietnam. Quantitative analyses were done with both weathered and polished samples in order to consider the effects of surface weathering. Based on the characteristics of major, minor, and trace elements, we divided the samples into three subgroups (the percentage for each subgroup was 50%, 42%, and 8%, respectively) and also determined their main colorants. The results obtained provide new clues to trace the possible producing centers of ancient potash glasses in Asia. This study also reveals a complex network related to the trade of ancient potash glasses.     

人工晶体中掺杂元素分析方法进展

晶体材料的合成中,通过特定掺杂可以提高晶体质量、改善晶体性能,而掺杂元素的种类、浓度和分布对于人工晶体结构、性能等也有非常重要的影响。因此,准确测定晶体中各种元素的含量,对于改进晶体材料配方、生长工艺以及质量控制具有重要指导意义。目前,人工晶体中掺杂元素表征的主要方法包括原子光谱法,X射线荧光光谱法,无机质谱法和电子探针显微分析法等,对各种方法的原理、特点与局限性进行了综合论述,由于每种方法都有其各自的优缺点和适用范围,可根据不同的分析需求选择合适的方法以提高分析的效率与准确性。对人工晶体中掺杂元素分析方法的发展趋势进行了展望。     

The application of improved physics-informed neural network (IPINN) method in finance

Nonlinear Dynamics - With the development of computers and neural networks, the traditional methods of solving differential equations have been greatly developed. Typical examples are the...     

对称分类在非线性偏微分方程组边值问题中的应用

研究了微分方程对称分类在非线性偏微分方程组边值问题中的应用.首先,利用偏微分方程(组)完全对称分类微分特征列集算法确定了给定非线性偏微分方程组边值问题的完全对称分类;其次,利用一个扩充对称将非线性偏微分方程组边值问题约化为常微分方程组初值问题;最后,利用龙格-库塔法求解了常微分方程组初值问题的数值解.     

Lump solutions of a ( $$2+1$$ 2 + 1 )-dimensional bSK equation

Nonlinear Dynamics - In this paper, we obtained a kind of lump solutions of ( $$2+1$$ )-dimensional bSK equation with the assistance of Mathematica by using the Hirota bilinear method. These lump...