Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.     

Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations

This article focuses on discontinuous Galerkin method for the two‐ or three‐dimensional stationary incompressible Navier‐Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007     

小长径比垂直管气液两相流动特性分析

实验观察了小长径比垂直上流管内流型及特点,并对管入口处的压力波动特性和系统的压差波动特性进行了试验研究.结果表明:小长径比(L/D)垂直管内流型表现为泡状流、塞状流、乳沫状流、环状流和液束环状流;分别增加管线中的气量、液量,或者同时增加气液流量,均会造成垂直管入口处压力波动的均值和最大压力的增加;压力信号的概率密度(PDF)大部分呈双峰分布,也存在单峰和多峰分布;差压信号的概率密度符合正态分布,其功率谱密度同压力信号相比具有频率波动范围宽、幅值小的特点.     

Linear least squares problems with data over incomplete grids

The paper addresses bivariate surface fitting problems, where data points lie on the vertices of a rectangular grid. Efficient and stable algorithms can be found in the literature to solve such problems. If data values are missing at some grid points, there exists a computational method for finding a least squares spline by fixing appropriate values for the missing data. We extended this technique to arbitrary least squares problems as well as to linear least squares problems with linear equality constraints. Numerical examples are given to show the effectiveness of the technique presented. AMS subject classification (2000)  65D05, 65D07, 65D10, 65F05, 65F20     

几种基于散乱数据拟合的局部插值方法

本文首先针对散乱数据拟合的Shepard方法,结合截断多项式、B样条基函数和指数函数来构造其权函数,使新的权函数具有更高的光滑度和更好的衰减性,并且其光滑性和衰减性可以根据实际需要自由调节,从而提高了曲面的拟合质量．同时还给出一种类似的局部插值方法．另外,本文还基于多重二次插值,结合多元样条的思想,给出了两个局部插值算法．该算法较好地继承了多重二次插值曲面的性质,从而保证了拟合曲面具有好地光顺性和拟合精度．曲面整体也具有较高的光滑性．     

关于由衍射片的背面反射光形成的衍射图样的讨论

在光的衍射实验中,我们看到的一般是由通过衍射片的直射光形成的衍射图样,但在衍射片的另一面,同样存在着另一个衍射图样,它是由衍射片的背面反射光形成的,两个衍射图样关于衍射片对称.本文给出了这种实验现象,并用巴比涅原理解释了这种现象.     

双相干点光源干涉的一般分析

讨论了双相干点光源的三维空间干涉场的一般数学描述,分析了3个不同截面处的干涉强度的空间分布情况,并给出了相干相长点的计算机模拟图样.该结果也适用于其他类型波的相干叠加场分布.     

扫描隧道显微镜研究石墨表面的莫尔图

利用扫描隧道显微镜研究石墨表面的大尺度周期性图样．研究结果表明,莫尔图起源于石墨深层的缺陷,实验结果与理论完全吻合,并且第一次在实验上证明了纳米波可以穿透多层石墨而没有明显衰减．     

改进形态学相关算法以识别高相似度灰度图像

从形态学角度定义了灰度联合图像相似度，提出两种基于位表示法形态学相关算法的改进算法，通过提取位表示法的图像片边缘特征或二元化位表示法的图像片功率谱，以提高位表示法形态学相关算法对高相似度灰度图像的识别能力。     

数值孔径与数字剪切散斑干涉条纹亮度的关系

分析了数字剪切散斑干涉条纹图的形成理论，并获得了条纹亮度与摄象机数值孔径等参数的精确关系式，从理论分析和实验验证均得出在采用小的摄象机数值孔径和３ｍＷ Ｈｅ－Ｎｅ激光器的情况下，仍可获得比较满意的数字剪切散斑干涉条纹图，理论工作及其结论对于进行数字剪切散斑干涉实验的最佳参数选择具有指导作用。