Strain profile reconstruction of fiber Bragg grating with gradient using chaos genetic algorithm and modified transfer matrix formulation

In this paper, a new heuristic approach based on chaos genetic algorithm and modified transfer matrix method is presented to demodulate the fiber Bragg grating strain sensors. To facilitate accurate calculation of the grating reflected intensity spectrum, the modified transfer matrix approach is applied. The motivation for using the spline smooth function scheme is to provide nice approximation of strain profiles from a scattered data set and overcome the difficulty of calculating the strain gradients in local period function of the modified T-matrix formulation for the piecewise constant strain field assumption. The chaos genetic algorithm is developed to improve the performance of GA and optimize the data of control nodes of the spline smooth function, and more valuably, the reconstructed strain profile is continuous with discretionary spatial resolution. The proposed method is verified through numerical example reconstructions of Bragg grating sensor simulated strain profile cases.     

On the spectrum of the Cesàro operator on spaces of analytic functions

This paper concerns the Cesàro operator acting on various spaces of analytic functions on the unit disc. The remarkable fact that this operator is subnormal when acting on the Hardy space H² has lead to extensive studies of its spectral picture on other spaces of this type. We present some of the methods that have been used to obtain information about the spectrum of the Cesàro operator acting on Hardy and Bergman spaces and give a unified approach to these problems which also yields new results in this direction. In particular, we prove that the Cesàro operator is subdecomposable on H¹ and on the standard weighted Bergman spaces , α0.     

Representation of measures with polynomial denseness in , , and its application to determinate moment problems

It has been proved that algebraic polynomials are dense in the space , , iff the measure is representable as with a finite non-negative Borel measure and an upper semi-continuous function such that is a dense subset of the space    as equipped with the seminorm . The similar representation ( ) with the same and ( , and is also a dense

subset of ) corresponds to all those measures (supported by ) that are uniquely determined by their moments on ( ). The proof is based on de Branges' theorem (1959) on weighted polynomial approximation. A more general question on polynomial denseness in a separable Fréchet space in the sense of Banach has also been examined.

     

动态变系数回归模型的识别与非参数GMM估计

主要研究关于面板数据的有限阶固定效应的动态变系数回归模型(简称FDVCM)的统计推断问题.基于B-样条函数和广义矩估计(简称GMM)方法,首先建立了未知系数函数的非参数GMM估计,并证明大样本情形下该估计达到最优非参数收敛速度且具有渐近正态性质.然而实际问题中模型的动态阶数完全未知,也可能存在其它冗余的回归变量,文中借助文[Fan J,Li R.Variable selection via penalized likelihood and its oracle properties.Journal of the American Statistical Association,2001,96(456):1348-1360]中的smoothly clipped absolute deviation(简称SCAD)惩罚函数同时识别真实的动态阶数和显著的外生回归变量.同时建立了压缩估计的Oracle性质,即所识别的模型与真实模型中的参数估计具有相同的渐近分布.最后,无论是数值试验还是实例数据分析都验证了本文方法的合理性和可行性.     

几何光学传递函数及其计算方法

本文借助Bessel函数、数值积分和样条函数插值给出几何光学传递函数的数值计算方法,这种方法有益于保证精度和节省计算量。     

样条最小二乘法处理毛细管电泳数据的研究

毛细管电泳由于具有进样量少,分离效率高,分析速度快等优点而倍受关注［１～３］．目前商品化毛细电泳仪的检测器部分一般是光学敏感器,主要原因是光学检测受毛细管电泳的高压影响甚微,数据较为稳定,但是由于毛细管的内径很小,光程很短,大大限制了光学检测器的灵敏...     

多元弱样条空间和最小确定集

根据研究多元弱样条函数的B—网方法,给出了某些多元弱样条函数空间的最小确定集的构造方法,并从而求出了它们的维数．本文还讨论了对偶基的局部支集性质。     

On the Problem of Instability in the Dimensions of Spline Spaces over T-Meshes with T-Cycles

The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.     

样条变换集成罚函数偏最小二乘方法用于光谱数据重构和定量分析

针对高维小样本光谱数据所显现的函数型数据(Functional data)特性、与性质参数的非线性关系及变量间存有的严重共线性,采用了样条变换集成罚函数偏最小二乘回归新技术.它首先以三次B基样条变换实现非线性光谱数据的线性化重构,随后将重构的新光谱矩阵交由罚函数偏最小二乘法(Penalized PLS)构建其与性质参变量间的校正模型,其中罚函数中的光滑因子由交叉验证优化确定以调控模型的拟合精度.最后,通过小麦样品水分含量的近红外光谱定量分析,结果显示该技术光谱数据重构稳健,去噪明显,并有效解决高维小样本的过拟合和变量间的共线性,而预测集的均方根误差(RMSEP)为0.1808%,方法的非线性校正模型预测能力得到了明显提高.     

Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges

New quadrature formulas (QFs) for evaluating the singular integral (SI) of Cauchy type with unbounded weight function on the edges is constructed. The construction of the QFs is based on the modification of discrete vortices method (MMDV) and linear spline interpolation over the finite interval [−1,1]. It is proved that the constructed QFs converge for any singular point x not coinciding with the end points of the interval [−1,1]. Numerical results are given to validate the accuracy of the QFs. The error bounds are found to be of order O(h^α|lnh|) and O(h|lnh|) in the classes of functions H^α([−1,1]) and C¹([−1,1]), respectively.