Sampling numbers and function spaces

We want to recover a continuous function using only its function values. Let us assume, that f is from the unit ball of some function space (for example a fractional Sobolev space or a Besov space) and the precision of the reconstruction is measured in the norm of another function space of this type. We describe the rate of convergence of the optimal sampling method (linear as well as nonlinear) in this setting.     

A method for indefinite integration of oscillatory and singular functions

We propose a general method for computing indefinite integrals of the form

需求弹性在价格决策中的应用

将着眼点由总收益改变为总利润,对于需求弹性用于价格决策,利用微积分方法,分5种情况进行推导,得到的结论修正和补充了现行"经济数学"、"市场营销学"和"管理经济学"等教科书里讲的内容,并在此基础上进一步研究了最佳调价量问题.     

利用近红外及中红外融合技术对小麦产地和烘干程度的同时鉴别

小麦是制作馒头的主要原料之一,小麦中水、蛋白质、淀粉会因产地以及烘干程度的差异而不同,进而影响到加工成馒头的品质。所以实现对小麦产地和烘干程度的快速鉴别就显得尤为重要。感官评定是鉴别小麦产地和烘干程度常用的方法,对比感官评定,光谱分析可以识别样品中的分子结构等信息。基于此,尝试利用近红外和中红外光谱融合技术实现对不同产地和不同烘干程度的小麦同时鉴别。首先选取了两个不同产地的小麦,再利用微波干燥法对两个不同产地的小麦做烘干预处理,使烘干的小麦水含量为12%±0.5%,原麦水含量为18%±0.5%。分别标记为原麦A,烘干A,原麦B,烘干B,再将小麦研磨成粉末,过100目筛网筛选后,置于自封袋中备用。随后分别采集四种小麦样品的近红外和中红外光谱信息,在Matlab 7.10的环境下使用标准正态变量变换(standard normal variable transformation, SNVT)对采集到的原始光谱数据进行预处理,利用主成分分析对预处理后的数据进行降维处理,再结合线性判别分析（linear discriminant analysis,LDA）和支持向量机（support vector machine, SVM）分别建立小麦近红外、中红外光谱数据识别模型。另外利用联合区间偏最小二乘法（synergy interval partial least square, SiPLS）筛选出利用标准正态变量变换(SNVT)预处理后的小麦近红外和中红外光谱数据特征光谱区间,将筛选出的近红外和中红外光谱数据特征光谱区间融合后再结合线性判别分析（LDA）和支持向量机（SVM）建立小麦融合光谱信息的识别模型。然后比较同种光谱数据下利用线性判别分析（LDA）和支持向量机（SVM）建立的小麦识别模型识别率、比较同种建模方法下近红外和中红外光谱数据建立小麦识别模型识别率、比较同种建模方法下光谱数据融合和单一光谱数据建立小麦识别模型识别率。结果表明,同种光谱分析方法,利用SVM建立的四种小麦识别模型识别率高于利用LDA建立的小麦识别模型识别率。同种建模方法,近红外光谱数据建立的小麦识别模型识别率优于中红外光谱数据建立的小麦识别模型识别率。而在同种建模方法下,利用SiPLS筛选出近红外和中红外光谱数据的特征光谱区间数据融合后建立小麦识别模型识别率最高,光谱数据融合后结合LDA建立的小麦识别模型校正集识别率为98.75%,预测集识别率为97.50%;而将此选择的变量结合SVM建立的小麦识别模型的校正集和预测集识别率都达到100.0%。对比利用单一光谱数据建立的小麦识别模型识别率,光谱数据融合之后建立的小麦识别模型识别率得到显著提高,该研究从纵向和横向上全面地比较了光谱数据建立的小麦模型识别率,结果可为更准确地运用光谱融合技术建立小麦产地以及烘干程度识别模型提供参考。     

陕西关中地区生态弹性计量模型与测算

关中地区是关中-天水经济区的主要部分,生态环境面临来自社会经济、自然环境等方面的压力,研究关中地区的生态弹性及其影响因素具有重要意义.通过GIS和RS技术,运用生态弹性度计算模型,测算了2000-2015年15 a间陕西省关中地区的生态弹性度,分析了市区间生态弹性度和生态弹性动态度的时空特征;探讨了土地利用变化和植被净初级生产力对生态弹性度的影响.研究结果表明：关中地区生态弹性度总体在4~8,从2000年的4.17~7.67升至2015年的5.94~7.52,总体呈上升趋势,生态环境有所改善.区域生态弹性受土地利用方式和NPP的影响,其中林地对区域生态弹性的提高影响最大,草地、耕地次之.通过植树造林增加建成区植被覆盖面积,有益于改善区域生态环境,提高区域生态弹性度.     

花生种子品质的可见-近红外光谱分析

利用600～1 100 nm波段研究花生品种的可见-近红外反射光谱,对选取的三种具有代表性的花生种子进行实验。使用近红外光纤光谱仪采集光谱数据,对原始光谱进行小波分析以提取光谱特征,再用主成分分析方法进行聚类分析,最后把每一个样品的前4个主成分得分作为识别模型的输入,品种类别作为模型的输出,以马氏距离作为判别函数,建立了线性判别分析模型。对于每个品种的50个样品,随机挑选30个样本作为训练集,剩余的20个样本作为预测集。该识别模型对3个花生品种的平均正确识别率为95%。表明该方法能有效的识别花生种子,得到较好的分类效果,为花生种子品质的区分和鉴别提供了一种新方法。     

Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order −1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.     

Three-dimensional elastostatic solutions for transversely isotropic functionally graded material plates containing elastic inclusion

Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied. The general solutions of the governing equations are expressed by four analytic functions α(ζ), β(ζ), φ(ζ), and ψ(ζ) when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite func-tionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional (3D) elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one, the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.