Wronskian Form Solutions for a Variable Coefficient Kadomtsev–Petviashvili Equation

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili （vKP） equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.     

伏安特性实验中电压表的改进应用

改进了传统电压表的面板设计,使电压表不仅能测两端的电压,还能测量自身的电流.于是在测量元件的伏安特性实验中,使用该电压表可以不考虑被测器件电阻的大小,均采用电流表外接的接线方式,即让电压表分流.再利用电压表的电流测量功能,测出自身分流电流的大小,从而可以准确得出被测器件的电流与两端的电压.     

Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.     

高斯拟合算法在光谱建模中的应用研究

采用高斯拟合算法对光谱进行特征提取,利用拟合得到的特征参量表征光谱信息,并结合多元校正方法对光谱模型进行优化和解释,建立了样品快速准确的测定方法。实验以玉米活体叶片为研究对象,建立叶片光谱与叶绿素含量之间的关系模型,采用三个高斯峰对原始光谱的1 551个数据拟合后,光谱数据转换为9个高斯特征量(约为整个波段的0.58%),进而利用该高斯特征量来预测叶绿素含量。实验结果显示,采用高斯拟合分别与偏最小二乘法和主成分回归结合建模,其预测集相关系数分别为0.960和0.962;不采用高斯拟合算法而直接采用偏最小二乘法和主成分回归对全光谱建模,其预测集相关系数分别为0.957和0.919。可见,将高斯拟合算法运用到定量分析模型中是可行的,该方法不仅简化了模型参数,而且提高了模型的可解释性。     

高平均功率电光开关晶体热畸变分析

 深入分析了方板构型的电光开关晶体在高功率载荷条件下的热畸变行为,讨论了光强分布对热效应的影响。以KDP晶体为例,分别计算了激光束光强为高斯分布和均匀分布时晶体的温升、相应的热应力分布、波前畸变以及热退偏。结果表明,光强的分布形式对波前畸变和热退偏的影响是不同的。相对于光强均匀分布的激光束,高斯光束减缓了光斑边沿处的温度梯度,产生的热应力较小,因此可以减弱热退偏效应;另一方面,在光束口径范围内,高斯光束产生了附加的温度分布非均匀性,因而波前畸变会大一些。     

New solitary wave solutions for nonlinear evolution equations

Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system.Maple,using the direct algebraic method proposed recently,We explicitly obtain several new solutions of physical interest in addition to rederiving all the known solutions.     

追踪问题轨迹的解析解

关于追踪目标问题,一般文献仅计算了追上所用的时间,或者在给定位置追上的条件下,追踪者与目标的速度比的取值.而获得追踪者运动轨迹的解析解,显然更重要也更困难.本文在追踪问题一般表述的基础上,通过建立并求解追踪者运动的二阶微分方程,得到追踪轨迹的解析解,最后顺便简捷地推导了追上的地点、时间以及在给定位置追上时二者的速度比.     

基于遗传算法的安溪铁观音品质快速评价研究

为探究一种快速无损的安溪铁观音品质评价方法,利用遗传算法(GA)对茶样的近红外光谱特征波长进行筛选,结合偏最小二乘(PLS),建立全谱段的PLS定量模型与GA-PLS模型。结果表明,傅里叶变换近红外(FT-NIR)全谱段光谱在经过平滑+二阶导数+归一化处理后,PLS模型预测性能最高,建模结果为：校正集相关系数R_C=0.921,校正集均方根误差RMSEC=0.543,验证集相关系数R_P=0.913,验证集均方根误差RMSEP=0.665。选用近红外光谱6 670～4 000 cm-1谱区,采用遗传算法进行特征波长筛选,参与建模数据点数从1 557缩减到408个。优选波段后,GA-PLS建模结果为：校正集相关系数R_C=0.959,校正集均方根误差RMSEC=0.413,验证集相关系数R_P=0.940,验证集均方根误差RMSEP=0.587。可见,GA-PLS模型的校正集和验证集的预测结果均优于全谱段PLS模型。结果说明,在传统的近红外光谱技术结合化学计量学方法的建模基础上,加入遗传算法进行波长筛选,能有效提高模型预测能力,实现方法学的创新研究,且GA-PLS品质评价模型具有较强的参考和推广价值,为提高我国茶叶品质的检测技术水平提供新的方法借鉴。     

Rotating polarizer,compensator, and analyzer ellipsometry

In this paper we propose theoretically a set of ellipsometric configurations using a rotating polarizer, compensator, and analyzer at a speed ratio of N1ω：N2ω：N3ω. Different ellipsometric configurations can be obtained by giving different integral values to N1, N2, and N3. All configurations are applied to bulk c-Si and GaAs to calculate the real and imaginary parts of the refractive index of the samples. The accuracies of all ellipsometric configurations are investigated in the presence of a hypothetical noise and with small misalignments of the optical elements. Moreover, the uncertainties in the ellipsometric parameters as functions of the uncertainties of the Fourier coefficients are studied. The comparison among different configurations reveals that the rotating compensator–analyzer configuration corresponds to the minimum error in the calculated optical parameters.     

高校椭偏测厚实验的计算机辅助教学

分析了高校椭偏测厚实验中存在的问题，成功研制出具有教学特点的多功能智能椭偏测厚仪和编制了一套该实验的CAI课，实验表明：椭偏测厚实验的计算机辅助教学效果良好。