Multiple exp-function method for soliton solutions of nonlinear evolution equations

We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.     

周期脉冲作用下Logistic映射的复杂动力学行为及其分岔分析

研究了两种周期脉冲作用下Logistic映射的复杂动力学行为. 随着参数的变化, 该系统产生平衡解、周期解、混沌等现象, 且该系统可经级联倍周期分岔到达混沌. 通过构造Poincaré 映射, 对周期脉冲作用下Logistic映射进行了分岔分析. 最后基于Floquet理论揭示了该系统周期解的分岔机理. 关键词： Logistic映射 脉冲 周期解 分岔机理     

A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions

One of the main difficulties in the application of the method of fundamental solutions (MFS) is the determination of the position of the pseudo-boundary on which are placed the singularities in terms of which the approximation is expressed. In this work, we propose a simple practical algorithm for determining an estimate of the pseudo-boundary which yields the most accurate MFS approximation when the method is applied to certain boundary value problems. Several numerical examples are provided.     

Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi emptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.     

String Cosmological Solutions with O(d,d) Duality Symmetry and Matter Coupling

The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.     

扩展的(G’/G)展开法和Zakharov方程组的新精确解

对(G’/G)展开法进行了扩展, 引入了新的辅助方程, 对(G’/G)展开式附加了负指数幂, 并利用扩展的(G’/G)展开法求出了Zakharov方程组的一些新精确解. 该方法还可被应用到其他非线性演化方程中去. 关键词： G’/G)展开法')" href="#">(G’/G)展开法 Zakharov方程组 精确解     

Novel Wronskian Condition and New Exact Solutions to a （3＋1）-Dimensional Generalized KP Equation

Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.     

Er3＋-Yb3＋-Mo6＋共掺杂ZrO2-Al2 O3固溶体的上转换发光

采用共沉淀法制备了一系列Al2 O3含量由低到高的ZrO2-Al2 O3固溶体,并研究了固溶体的晶相结构以及稀土Er3＋在固溶体中的上转换发光增强机制。XRD结果表明固溶体为四方晶相ZrO2结构,Al2 O3的最高固溶度约为20 mol％。上转换发光光谱分析表明,Er3＋掺杂ZrO2室温下具有绿色上转换荧光发射,通过共掺杂Yb3＋和M o6＋离子,使得Er3＋掺杂ZrO2的绿色上转换发光强度增强了约20倍,获得了明亮的黄绿色上转换发光。基质ZrO2通过与Al2 O3固溶形成复合氧化物,由于产生的大量氧空位缺陷的能级与Er3＋的4 F7/2能级高度相接近,增强了Yb3＋-MoO2-4基团（2 F7/2,3 T2）能级向Er3＋的4 F7/2能级的能量传递。通过形成固溶体复合氧化物基质材料,使得Er3＋的绿色上转换发光在获得20倍增强的基础上又提高了8倍。绿色与红色上转换发光比例的变化也提高了材料的色纯度,上转换发光由黄绿色变为纯绿色。     

基于激光诱导击穿光谱技术的土壤快速分类方法研究

为实现不同种类土壤的快速分类鉴别,实验研究了基于激光诱导击穿光谱技术的土壤快速分类方法。由于不同类型的土壤在元素组成上会存在较大差异,所以利用激光诱导击穿光谱技术进行土壤分类具有可行性。不同土壤在相同实验条件下产生的等离子体温度会存在较大差异,可以作为分类的重要依据,所选择的7类土壤中,赤红壤的等离子体温度最高。选取土壤中6种常量元素Si,Fe,Al,Mg,Ca和Ti的光谱强度作为分类指标,利用主成分分析(principal component analysis,PCA)对7种土类的25个样品进行了分类,其中砖红壤和赤红壤分类出现了交叠,而不同高山草甸土样品之间元素差异较大,并没有实现较好的聚类。利用反向传播神经网络(back-propagation artificial neural network)结合土壤的LIBS光谱对土壤进行了分类,分类结果与PCA结果相近,赤红壤与砖红壤出现了识别错误。当用PCA分析获得三个主成分值作为BP神经网络的输入量时,获得了较好的分类结果,因为简化了输入量,降低了BP神经网络的误差,此时只有一个高山草甸土被识别成褐土,而高山草甸土的等离子体温度显著低于褐土,所以结合不同土壤类型的等离子体温度差异,能够实现不同土壤的分类识别。实验证明激光诱导击穿光谱技术可以应用于土壤分类,为土壤普查和合理利用提高了一种新的技术。     

应用遗传算法结合连续投影算法近红外光谱检测土壤有机质研究

应用遗传算法结合连续投影算法近红外光谱检测土壤有机质研究。采集浙江省文城地区农田土壤样品近红外光谱数据,土壤样品数为394个。为简化模型,采用遗传算法结合连续投影算法挑选出18个特征波长建模,应用偏最小二乘回归建立有机质预测模型,建模集的决定系数为0.81,均方根预测误差为0.22, 剩余预测偏差为2.31,预测集的决定系数为0.83,均方根预测误差为0.20,剩余预测偏差为2.45。研究发现,遗传算法结合连续投影算法在简化模型同时,模型的预测评价指标同采用全谱波长建模并没有明显降低。因此,遗传算法结合连续投影算法挑选的特征波长可以应用于近红外光谱检测土壤有机质含量。