一类排序问题的求解及效果评估

对一类排序问题给出了一种有效的排序方法.我们将该类排序问题中的属性分为正向属性和负向属性,建立了属性规范化处理的数学模型,得到属性之间无差异的偏好比重,并对偏好比重进行汇总,得到对象之间的排序.最后,利用带自然边界条件的三次样条插值的三弯矩算法对该排序方法进行误差估计.     

Stieltjes-Newton型有理插值

Stieltjes型分叉连分式在有理插值问题中有着重要的地位，它通过定义反差商和混合反差商构造给定结点上的二元有理函数，我们将Stieltjes型分叉连分式与二元多项式结合起来，构造Stieltje- Newton型有理插值函数，通过定义差商和混合反差商，建立递推算法，构造的Stieltjes-Newton型有理插值函数满足有理插值问题中所给的插值条件，并给出了插值的特征定理及其证明，最后给出的数值例子，验证了所给算法的有效性．     

B-值鞅Hardy空间与BMO空间的实内插

研究了B值鞅Hardy空间与BMO空间的实内插，并利用所得结果，讨论了鞅Hardy空间的内插空间的共轭问题。     

闭区间[0,1]上的分形插值函数的分数阶积分

介绍了分形插值函数和迭代函数系统以及v阶黎曼-刘准尔分数阶积分的概念及相关定理.利用这些概念及定理讨论了分形插值函数的分数阶积分在[0,1]上连续性及判定[0,1]上的分形插值函数的分数阶积分也是[0,1]上的分形插值函数,并给予了证明.     

求解二维Poisson方程的重心插值配点法

采用重心Lagrange插值配点法计算了二维Poisson方程.采用重心Lagrange插值法构造近似函数,由配点法离散Poisson方程及其边界条件.数值算例表明方法具有理论简单、计算精度高的特点.     

Constrained moving least‐squares immersed boundary method for fluid‐structure interaction analysis

A numerical method is presented for the analysis of interactions of inviscid and compressible flows with arbitrarily shaped stationary or moving rigid solids. The fluid equations are solved on a fixed rectangular Cartesian grid by using a higher‐order finite difference method based on the fifth‐order WENO scheme. A constrained moving least‐squares sharp interface method is proposed to enforce the Neumann‐type boundary conditions on the fluid‐solid interface by using a penalty term, while the Dirichlet boundary conditions are directly enforced. The solution of the fluid flow and the solid motion equations is advanced in time by staggerly using, respectively, the third‐order Runge‐Kutta and the implicit Newmark integration schemes. The stability and the robustness of the proposed method have been demonstrated by analyzing 5 challenging problems. For these problems, the numerical results have been found to agree well with their analytical and numerical solutions available in the literature. Effects of the support domain size and values assigned to the penalty parameter on the stability and the accuracy of the present method are also discussed.     

Spectrum is periodic for n-intervals

In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case.     

Wavelets with differential relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.     

Conservative Means of Orthogonal Series and the Spaces $$L^p [0;1] $$ , $$p \in (1;\infty ) $$

Necessary and sufficient conditions for an orthogonal series to be the Fourier series of a function in the space , , are obtained. In the special case of regular summation methods we recover the classical results of Orlicz and Lomnicki.