变量有界半定最小二乘问题

<正>1引言设A_i∈S~n,i=1,…,m,定义线性算子A:S~n→R~m,AX=(A_1·X,…,A_m·X)~T,其相应的伴随算子为A~*:R~m→S~n,且A~*y=sum from i=1 to my_iA_i.X∈S~n,b∈R~m.Malick.J在[6]中讨论了如下标准半定最小二乘问题(SDLS):     

Iterative methods for a forward-backward heat equation in two-dimension

A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis.     

水-气界面参数和二向性影响因素交互作用研究

基于光学辐射传输软件HYDROLIGHT,模拟不同外界和水质条件下水气界面透射率T,Gordon模型参数f和二向性因子Q,研究风速、太阳天顶角、单次反照率和拉曼散射对T、f和Q及其组合f/Q的影响和交互作用,确定T、f、Q和f/Q的主导影响因子,以期为确定水色反演算法误差来源以及减小反演误差提供定量的依据。研究结果表明,T、f和Q的主导影响因素为太阳天顶角,单次反照率和风速对T、f和Q的影响相对较小,而对f/Q影响最大是单次反照率,其次是太阳天顶角,风速最小,且各影响因素之间具有较强的交互作用。高散射特性水体中,拉曼散射对f、f/Q和T的影响可忽略不计;黄质(CDOM)和叶绿素的荧光特性对f和f/Q的影响随着叶绿素和CDOM浓度的增加不断减小,但在高CDOM和叶绿素浓度的富营养化水体中该影响仍难以忽略。     

基于近红外光谱技术检测除草剂胁迫下油菜叶片中脯氨酸含量的方法

应用近红外光谱技术实现除草剂胁迫下油菜叶片中脯氨酸含量的检测。对248个经过除草剂丙酯草醚处理后的油菜叶片,经过烘干、磨碎后进行光谱扫描。经过Savitzky-Golay平滑、变量标准化(SNV)、二阶求导预处理后,应用偏最小二乘法(PLS)建立脯氨酸含量的预测模型,同时提取有效特征变量作为神经网络(BPNN)和最小二乘-支持向量机(LS-SVM)的输入值,并建立相应的模型。用186个样本建模,62个样本预测。结果表明,最小二乘-支持向量机能够获得最优的预测效果,预测的相关系数(r)、预测标准差(RMSEP)和偏差分别为0.995,0.041和0.000。说明应用近红外光谱技术结合最小二乘-支持向量机能够定量获得油菜叶片中脯氨酸的含量。     

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.     

广角镜头桶形畸变的二元二次多项式修正法

为了修正广角镜头的桶形畸变,提出了一种基于二元二次多项式的修正方法,阐述了其图像的像素坐标校正和像素灰度恢复方法。该方法首先用模板对广角镜头进行对准相对标定,然后用二元二次多项式拟合畸变图像与非畸变图像像素坐标之间的规律,最后把该方法应用于某广角镜头拍摄的图像,并采用最小二乘法对校正效果进行评价。结果表明:在不考虑视觉系统具体参数的情况下,该方法能够有效地对广角镜头桶形畸变进行修正。     

LAMOST光纤单元定位参数研究

大天区多目标光纤光谱天文望远镜LAMOST是世界上光谱获取量最大的望远镜,4000个双回转光纤单元的精确定位是关键因素之一。根据对星像观测的要求以及单元的定位方式,确立了所需的7个定位参数,研究了在复杂现场环境下获取定位参数的具体流程和可行性算法,包括光重心法、摄像机快速标定算法、基于最小二乘拟合圆算法、空间坐标旋转算法等。通过模拟星像观测仿真测试和现场星像试观测证明,定位参数精度能很好地满足观测需求。目前LAMOST望远镜观测光谱获取率已达到90%以上。     

二维光子晶体T型波导分支器数值模拟研究

采用平面波展开法和时域有限差分法,对GaAs二维正方晶格光子晶体的色散特性和带隙结构进行了数值模拟研究,并对GaAs二维光子晶体线缺陷构成的T型波导分支器的微波传输特性进行了模拟和优化。数值模拟结果表明,光子晶体填充比对带隙结构有显著地影响。通过在拐角处插入额外的电介质棒对GaAs二维正方光子晶体T型波导分支器进行优化,数值模拟的结果表明,优化的GaAs二维正方光子晶体T型波导分支器在一阶带隙范围内透射系数将提高到0.96以上。     

基于纠缠交换和团簇态实现二粒子任意态的可控隐形传态

提出一个对二粒子任意态的可控隐形传态方案,利用四粒子团簇态作为量子信道,用EPR态实现控制.首先,发送者向控制者提出申请,控制者再对其拥有的2个粒子做Bell基测量,并把结果通知发送者,实现纠缠交换.然后,发送者对自己手中的四个粒子做适当的幺正变换,接着进行纽曼测量,并把结果通知接受者.接受者根据发送者的测量结果,对自己拥有的粒子做适当的幺正变换,就可以重建发送者的二粒子任意态.方案成功的概率为100%.     

近红外光谱法快速评定牛肉品质

应用近红外反射光谱技术(NIRS),采用偏最小二乘法(PLS),建立了牛肉理化特性的近红外预测模型。从屠宰加工厂选取经48 h排酸后的里脊、眼肉、腿肉、臀肉、外脊等部位的牛肉样品114份,采用多元散射校正(MSC)、一阶导数、标准正态变量(SNV)预处理方法,谱区为950～1 650 nm,建立牛肉水分、脂肪、蛋白质3个化学参数以及pH、肉色(CEI L*,a*, b*)和剪切力(WBSF)3个物理参数的校正模型。其校正相关系数(R2)分别为0.947 2(水分),0.924 5(脂肪),0.934 6(蛋白质),0.620 2(pH),0.820 3(L*),0.864 6(a*),0.753 0(b*),0.475 9(WBSF)。校正标准差(RMSEC)分别为0.313 3(水分), 0.221 0(脂肪), 1.243 2(蛋白), 0.744 6(pH),1.778 3(L*),1.394 2(a*),1.763 9(b*),1.074 3(WBSF)。应用所建立的模型对30个实际牛肉样品的理化参数进行预测,并对预测值与实测值进行t检验,检验结果显示预测值与实测值差异不显著,说明模型适合于快速评价牛肉的品质。从预测的准确度看,化学指标预测的精确度明显高于物理指标。