两类关于二项式系数倒数的级数(英文)

By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.     

一类新的非线性比式和问题的分枝定界算法(英文)

对一类新的非线性比式和问题(SNR)提出分枝定界算法,该问题的研究还很少.首先,通过两层线性化技术,构造一个松弛线性规划,求解该线性规划问题,得到问题(SNR)最优值的下界.其次,介绍新的下界更新技术,证明所给算法的收敛性.数值试验显示了算法的可行性和有效性     

一类由切比雪夫多项式和$q$-微分算子定义的双单叶解析函数的初始系数估计

本文介绍了一类由切比雪夫多项式和$q$-微分算子定义的双单叶解析函数,得到了相关系数估计和Fekte-Szego不等式,所得结果改进或推广了已有部分作者的结论.     

一类变系数微分方程差分格式的收敛性(英文)

本文首先对一类变系数微分方程建立有限差分格式.然后利用矩阵的特征值和范数理论,讨论该格式解的收敛性和唯一性.通过数值算例,说明该格式既有效又便于模拟.并且文中所用方法还能用于高阶微分方程和某些非线性微分方程问题的研究.     

一类带扰动风险模型的Gerber-Shiu函数(英文)

本文研究了一类带扰动风险模型, 得到了此过程下Gerber-Shiu函数的微分积分方程, 并得到了推广Erlang(2)情形下Gerber-Shiu函数满足的更新方程.     

Banach空间中广义的Sturm-Liouville m点边界值问题的正解(英文)

By applying the fixed-point theorem of strict-set-contraction,this paper establishes the existence of one solution or one positive solution to the generalized Sturm-Liouville m-point boundary value problem in Banach spaces.     

一类含广义p-Laplace算子的积分微分方程的单调方法(英文)

利用极大单调算子和伪单调算子值域的结论,研究一类与广义p-Laplace算子相关的、具混合边值条件的积分微分方程.证明了这个方程解的存在唯一性.本文所研究的问题及所用方法是对以往一些研究工作的推广和补充.     

一类具欧指积系数微分算子谱的离散性(英文)

利用算子直和分解的方法和二次型估计的方法,研究了一类具欧指积系数微分算子谱的离散性,得到了其谱是离散的一些充分条件.     

一类临界情况的广义非线性奇摄动时滞模型近似解析解(英文)

Based on the boundary layer corrective method, a class of generalized nonlinear perturbed model in the critical case is studied. The asymptotic solution for the original equation is constructed. And the method is of significance to seek approximate solutions to other nonlinear models.     

带非凸二次约束的二次比式和问题的全局优化算法(英文)

对带非凸二次约束的二次比式和问题(P)给出分枝定界算法,首先将问题(P)转化为其等价问题(Q),然后利用线性化技术,建立了(Q)松弛线性规划问题(RLP),通过对(RLP)可行域的细分及求解一系列线性规划问题,不断更新(Q)的上下界,从理论上证明了算法的收敛性,数值实验表明了算法的可行性和有效性.     

General Gaussian Quadrature Formulas on Chebyshev Nodes

本文给出了基于（第一类及第二类）Ｃｈｅｂｙｓｈｅｖ节点的广义Ｇａｕｓ求积公式的Ｃｏｔｅｓ数的明显公式及其渐进性态．     

关于一般Guass-Birlhoff求积公式的注(英文)

本文证明了对于关联矩阵E＝（E1，E2），其中E1满足Polya条件，在其内行不含奇序列，E2是正则的，一般Guass-Birkhoff求积公式的存在性。     

一类广义Gauss型求积公式

基于被积函数在n次第一类和第二类Chebyshev多项式的零点处的差商,该本构造了两种Gauss型求积公式. 这些求积公式包含了某些已知结果作为特例.更重要的是这些新结果与Gauss-Turan求积公式有密切的联系.     

Quadrature Formulas Based on the Scaling Function

The scaling function corresponding to the Daubechies wavelet with two vanishing moments is used to derive new quadrature formulas. This scaling function has the smallest support among all orthonormal scaling functions with the properties M ₂ = M ₁ ² and M ₀ = 1. So, in this sense, its choice is optimal. Numerical examples are given.This work was partially supported by DFG grant GR 1777/2, by the Grant No 201/01/1200 of the CSF, by the grant MSMT 113200007 and by the grant IGS 116/5130/1 of FP TUL.     

Convergence of Gaussian Quadrature Formulas for Power Orthogonal Polynomials

In classical theorems on the convergence of Gaussian quadrature formulas for power orthogonal polynomials with respect to a weight w on I =（a,b）,a function G ∈ S（w）:= { f:∫_I | f（x）| w（x）d x < ∞} satisfying the conditions G ^2j（x） ≥ 0,x ∈（a,b）,j = 0,1,...,and growing as fast as possible as x → a + and x → b,plays an important role.But to find such a function G is often difficult and complicated.This implies that to prove convergence of Gaussian quadrature formulas,it is enough to find a function G ∈ S（w） with G ≥ 0 satisfying sup n ∑λ0knG（xkn） k=1 n<∞ instead,where the xkn ’s are the zeros of the n th power orthogonal polynomial with respect to the weight w and λ0kn ’s are the corresponding Cotes numbers.Furthermore,some results of the convergence for Gaussian quadrature formulas involving the above condition are given.     

Novel weak form quadrature element method with expanded Chebyshev nodes

Based on the principle of minimum potential energy and the differential quadrature rule, novel weak form quadrature element method is proposed. Different from the existing ones, expanded Chebyshev grid points are used as the element nodes. A simple but general way is proposed to compute the strains at the integration points explicitly by using the differential quadrature rule. For illustration and verification, quadrature bar and beam elements are established. Several examples are given. Numerical results indicate that the proposed quadrature element method allows a longer time step as compared to elements with other nodes and is an accurate and efficient method for structural analysis.     

扰动Chebyshev结点上的Hermite－Fejer插值

本文发现当Ｃｈｅｂｙｓｈｅｖ结点产生某些扰动时，只要扰动量不超过，则基于扰动后的Ｃｈｅｂｙｓｈｅｖ结点的Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值过程仍然保持对［－１，１］上任意连续函数的一致收敛性，此外，文中还给出了这种收敛性的收敛速度估计。     

The Bernstein Constant and Polynomial Interpolation at the Chebyshev Nodes

In this paper, we establish new asymptotic relations for the errors of approximation in L_p[−1,1], 0<p∞, of x^λ, λ>0, by the Lagrange interpolation polynomials at the Chebyshev nodes of the first and second kind. As a corollary, we show that the Bernstein constant

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is finite for λ>0 and .     

带重结点的三角求积公式的迭代构造

本文以三角多项式类作为工具讨论了偶数个结点情况下的带重结点的具有最大三角精度的三角求积公式,由拟正交三角多项式的性质给出了求积公式系数的迭代构造。     

Gaussian Quadrature Rules with Simple Node-Weight Relations

In this paper, we consider the symmetric Gaussian and L-Gaussian quadrature rules associated with twin periodic recurrence relations with possible variations in the initial coefficient. We show that the weights of the associated Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 4. We also show that the weights of the associated L-Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 5. Special cases of these quadrature rules are given. Finally, an easy to implement procedure for the evaluation of the nodes is described.