Probabilistic models for stochastic elliptic partial differential equations

Mathematical requirements that the random coefficients of stochastic elliptical partial differential equations must satisfy such that they have unique solutions have been studied extensively. Yet, additional constraints that these coefficients must satisfy to provide realistic representations for physical quantities, referred to as physical requirements, have not been examined systematically.     

Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

We show by an extensive method of quasi-discrete multiple-scale approximation that nonlinear multi-dimensional lattice waves subjected to intersite and external on-site potentials are found to be governed by (N +1)-dimensional nonlinear Schro¨dinger (NLS) equation. In particular, the resonant mode interaction of (2+1)-dimensional NLS equation has been identified and the theory allows the inclusion of transverse effect. We apply the exponential function method to the (2+1)-dimensional NLS equation and obtain the class of soliton solutions with a purely algebraic computational method. Notably, we discuss in detail the effects of the external on-site potentials on the explicit form of the soliton solution generated recursively. Under the action of the external on-site potentials, the model presents a rich variety of oscillating multidromion patterns propagating in the system.     

荧光光谱结合支持向量机测定食用色素纯度

采用一种由原点矩法改造所得的特征压缩算法对荧光光谱数据进行预处理,将处理后的数据与加权最小二乘支持向量机(WLS-SVM)算法结合,建立鲁棒回归模型,用以预测实际食用色素粉末的纯度。以亮蓝和胭脂红这2种色素为例论述该方法对实际食用色素粉末纯度的预测效果。首先,利用FLS920荧光光谱仪测量获得两种色素的标准样本和实际样本在最佳激发波长下的荧光发射光谱数据,利用由原点矩法改造所得的特征压缩算法对获取的荧光光谱数据进行压缩和变换,一方面缩短了算法的运算时间,另一方面也提高了模型的预测精度。将预处理后的荧光光谱数据输入加权最小二乘支持向量机中建立浓度预测模型,该模型对亮蓝、胭脂红实际样本溶液给出的预测光谱与它们的实测光谱吻合程度好,半高峰宽区间内的平均决定系数分别为0.662和0.931。所有亮蓝、胭脂红溶液的预测浓度和标称浓度之间具有良好的线性关系,相关系数分别为0.997和0.992。由此通过多项式拟合得到的亮蓝、胭脂红粉末的预测纯度分别为61.0%和72.3%。     

用偶幂级数处理Abel变换问题

本文提出了用偶幂级数代替对称分布函数,使其线积分成为递推可积,从而简化了Abel逆变换。引进权函数使本方法简单地过渡到非对称问题。对一组假想相移信号进行变换,获得了可靠的密度分布结果,并对影响变换精度的各种因素作了讨论。     

Ab initio multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule, including Σ , Ⅱ, and △ symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method.The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present.Three quintet states are reported for the first time.Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.     

有耗孤子的最小作用量原理及其在二维光子带隙结构中的应用

采用变分方法对于二维矩形光子带隙结构中X点孤子的耗散以及相干作用进行了动力学分析.通过对由作用量原理得到的孤子参量联立方程组的分析可知，除了耗散作用导致孤子的幅度衰减，并引起孤子横向的展宽以外，同向孤子的相互作用负势函数为耗散作用所减弱，从而使得孤子在x方向的束缚态被削弱.孤子中心间距随x的增加呈现出增幅变化且波动周期增大，当纵向距离增大到一定值后，孤子中心间距将一直增大下去.     

利用异或运算和编码约束的降维LDP人脸识别方法

为了有效表示面部特征,在局部方向模式(LDP)的基础上,提出降维局部方向模式(RDLDP)。首先,修改LDP编码模式约束以完成模式的重构,通过对LDP码进行异或运算来计算每个块的单一码;然后,将所得编码图像划分为生成直方图,连接所有区域的直方图块以形成最终描述符。最后,计算特征向量间的卡方相异性度量值,并使用最近邻分类器完成最终的人脸识别。实验采用了三个公开的标准数据库FERET、扩展YALE-B和ORL。实验结果验证了提出算法的有效性。与其他基于局部描述符的先进方法相比,提出方法在准确度和错误识别率等方面更优。     

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。