A baire approach to quantitative resonance principles

The main purpose of this paper is to give a proof of quantitative resonance and condensation principles via Baire category arguments in contrast to the gliding hump method used previously. Thereby a new nonquantitative resonance principle is established which is concerned with dominated convergence in Frechet spaces, by the way yielding more detailed information on the structure of the underlying spaces. On the other hand, Baire's approach is an easy tool to develop condensation principles by considering residual sets. Finally, some typical applications concerning trigonometric Fourier partial sums may illustrate the result received.     

On integro quartic spline interpolation

In this paper, we use quartic B-spline to construct an approximating function to agree with the given integral values of a univariate real-valued function over the same intervals. It is called integro quartic spline interpolation. Our interpolation method is new and easy to implement. Moreover, it can work successfully even without any boundary conditions. The interpolation errors are studied. The super convergence (sixth order and fourth order, respectively) in approximating function values and second-order derivative values at the knots is proved. Numerical examples illustrate that our method is very effective and our integro-interpolating quartic spline has higher approximation ability than others.     

一种新的细分小波及其应用

在图形图像数据传输与数据处理过程中,数据鼍过大是造成不便的主要原因,因此用少量的数据更好地表现图形图像特征是人们追求的目标．图形简化的任务是在保留图形特征的同时删除过多的采样点．简化的中心问题是简化模板的选择,王国谨等人介绍了基于球面多边形逼近的曲面简化技术等方法．用小波技术进行图形简化也是目前图形图像处理过程中的常用方法,如孙延奎等人研究了B样条曲线的多分辨率表示,LounsberyM．等人研究了任意拓扑结构的曲面多分辨分析问题等等．     

An Affirmative Result of the Open Question on Determining Function Jumps by Spline Wavelets

We study the open question on determination of jumps for functions raised by Shi and Hu in 2009. An affirmative answer is given for the case that spline-wavelet series are used to approximate the functions.     

Galerkin-FEM for obtaining the numerical solution of the linear fractional Klein-Gordon equation

In this paper, an efficient numerical method for solving the linear fractional Klein-Gordon equation (LFKGE) is introduced. The proposed method depends on the Galerkin finite element method (GFEM) using quadratic B-spline base functions and replaces the Caputo fractional derivative using $L2$ discretization formula. The introduced technique reduces LFKGE to a system of algebraic equations, which solved using conjugate gradient method. The study the stability analysis to the approximation obtained by the proposed scheme is given. To test the accuracy of the proposed method we evaluated the error norm $L_{2}$. It is shown that the presented scheme is unconditionally stable. Numerical example is given to show the validity and the accuracy of the introduced algorithm.     

X-CT噪音条件下数字体积相关算法评测

数字体积相关是通过分析具有相关关系的两组三维图像,获得物体变形过程中位移场和应变场的计算方法。了解该算法在实际噪音下的表现,对这种方法的应用具有十分重要的意义。利用爬山法、最小二乘法,结合三次B样条插值,建立了一套数字体积相关计算方法,用两组具有真实噪音的三维X射线CT数据对该算法进行了系统评测。在没有噪音的理想情况下,该算法的位移误差为0.0065voxel;在真实X-CT噪音的情况下,位移误差增加到0.008voxel,应变误差约为100με。结果表明,本方法可对真实物体变形进行三维位移场、应变场分析。     

变系数单指标模型的B-样条估计

变系数单指标模型结合和单指标和变系数模型的优点,在许多领域中有着重要的应用。本文我们基于B-样条逼近,提出了两种估计方法：第一种方法是利用Newton-Raphson迭代方法同时获得参数和非参数部分的估计;第二个方法是剖面方法获得了相应的估计。当模型中有许多参数时,我们建议使用第二种估计方法,而当参数个数较少时采用第一种方法更方便。两个模拟例子用来验证本文提出的估计方法。