Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.     

关于三维各向同性谐振子径向矩阵元计算的讨论

根据广义Laguerre多项式的数学性质，导出了较为简单的三维各向同性谐振子径向矩阵元的普遍公式,并在这基础上计算了一些重要特殊情形的径向矩阵元: 矢径r整数次幂的平均值，电偶极跃迁矩阵元和电四极跃迁矩阵元. 关键词： 三维各向同性谐振子 径向矩阵元 广义Laguerre多项式 偶极跃迁 四极跃迁     

Multiscale kernels

This paper reconstructs multivariate functions from scattered data by a new multiscale technique. The reconstruction uses standard methods of interpolation by positive definite reproducing kernels in Hilbert spaces. But it adopts techniques from wavelet theory and shift-invariant spaces to construct a new class of kernels as multiscale superpositions of shifts and scales of a single compactly supported function φ. This means that the advantages of scaled regular grids are used to construct the kernels, while the advantages of unrestricted scattered data interpolation are maintained after the kernels are constructed. Using such a multiscale kernel, the reconstruction method interpolates at given scattered data. No manipulations of the data (e.g., thinning or separation into subsets of certain scales) are needed. Then, the multiscale structure of the kernel allows to represent the interpolant on regular grids on all scales involved, with cheap evaluation due to the compact support of the function φ, and with a recursive evaluation technique if φ is chosen to be refinable. There also is a wavelet-like data reduction effect, if a suitable thresholding strategy is applied to the coefficients of the interpolant when represented over a scaled grid. Various numerical examples are presented, illustrating the multiresolution and data compression effects.     

天然树脂局部结构的径向分布函数研究

本工作用x射线衍射技术分析计算了二种天然树脂的局部结构参数,由测得的衍射强度数据求出了它们的结构因子I(r)和径向分布函数RDF(r),并由此得到了分子链内临近原子和次临近原子平均间距、配位数和短程有序畴。     

Adaptive Interpolation by Scaled Multiquadrics

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.     

KrVI离子能级和振子强度的理论计算

利用组态相互作用理论和参数外推法,计算了KrVI离子4s~24p—4s4p~2、4s~24p—4s~24d和4s4p~2—4p~3跃迁的能级、谱线波长和振子强度。与已有实验结果比较表明:波长的理论计算值与观测值在0.7A内很好符合,振子强度的理论计算值较大的跃迁均是实验中观测到的跃迁。     

一种非刚性医学图像点匹配方法

提出了一种非刚性点匹配的算法并把其运用于医学图像配准．该算法采用信号滤波的方法来获得点集间的匹配信息，并运用松弛标记法将各点邻域关系对模糊的匹配信息进行迭代获得明确的匹配关系．在此基础上，利用高斯径向基函数来描述点模式间的弹性形变，在基本的迭代框架下实现问题的求解．实验结果显示在形变程度为5％、出格点比率50％和噪声标准差为5％的情况下该算法的匹配误差能控制在0．13以下，表明了该算法的鲁棒性和有效性，较好地解决了医学非刚性形变的点匹配问题．     

微型圆光栅刻划偏心量的控制

对微型圆光栅刻划偏心误差问题进行了讨论。提出了微型圆光栅刻划时偏心调试误差的公差范围。     

Microwave and RF surface wave sustained discharges as plasma sources for plasma chemistry and plasma processing

The surface wave produced plasma belongs to a class of RF and microwave induced plasmas. It results from the propagation of an electromagnetic wave which uses the plasma column it sustains and the plasma tube as its sole propagating media. This type of plasma offers several advantages compared to the positive column plasma of dc discharges or to other RF and microwave produced plasmas. Surface wave plasmas require no internal electrodes, and they can be applied over an extremely broad range of wave frequencies (27 MHz to 10 GHz demonstrated) and gas pressures (about 10^–4 Torr to a few times the atmospheric pressures). Using the surface wave plasma technique, a large variety of plasma column diameters have been created (0.5–150 mm demonstrated) and no limitation on plasma column length (column up to 6 m long demonstrated) has been found. The surface wave produced plasma is used in elemental analysis and to sustain emission in lasing media. This article is intended as a guide for potential users of surface wave plasmas in the field of plasma processing and plasma chemistry.     

径向基-偏最小二乘-贝叶斯方法及其在化学模式分类中的应用

提出一种用于模式分类的RBF-PLS—Bayes方法。它集成地应用径向基(RBF)变换与偏最小二乘(PLS)方法，从原有模式中提取出分类能力甚强的成分，然后进行贝叶斯(Bayes)判别。这种集成方法尤其适用于复杂化学信息的模式分类，本文将其应用于两种类型的化学模式分类问题，均取得了令人满意的效果。与经典的判别分析方法和单纯的神经网络方法相比，具有明显的优越性。