论多目标分式规划

论多目标分式规划徐增堃（浙江师范大学数学系，金华３２１００４）基金项目：浙江省教委自然科学基金资助课题．１９９０年１０月２９日收到，１９９１年１０月５日收到第一次修改稿．１９９２年９月７日收到第二次修改稿，１９９３年２月１３日收到第三次修改、压缩稿．...     

Hiriart—Urruty问题与Clarke广义梯度的若干性质

Ｈｉｒｉａｒｔ—Ｕｒｒｕｔｙ问题与Ｃｌａｒｋｅ广义梯度的若干性质刘晓华（湖南财经学院信息系，长沙４１００７９）１９８８年５月２６日收到，１９９２年４月２９日收到第一次修改稿，１９９３年４月２３日收到第二次修改稿．一、引言Ｈｉｒｉａｒｔ－Ｕｒｒｕｔｙ等...     

求解粘性系数的迭代方法及其收敛性

求解粘性系数的迭代方法及其收敛性丛文相（黑龙江大学，哈尔滨１５００８０）１９９１年８月３０日收到．１９９２年８月２５日收到第一次修改稿．１９９２年１２月４日收到第二次修改稿．一、引言研究地震正、反问题时，一般把地球假设为完全弹性体，而实际地球介质并非...     

油藏盆地发育数值模拟中的偏微分方程组的有限元方法和理论分析

油藏盆地发育数值模拟中的偏微分方程组的有限元方法和理论分析袁益让，王文洽，羊丹平（山东大学数学系，济南２５０１００）国家教委博士点基金资助项目．１９９０年４月２日收到，１９９０年８目２７日收到第一次修改压缩稿．１９９０年１２月１４日收到第二次修改稿．...     

一类三次系统的定性分析

一类三次系统的定性分析陈文灯（中央财政金融学院信息系，北京１０００８１）国家自然科学基金资助项目．１９９２年６月５日收到．１９９３年６月１６日收到修改稿．本文对一类三次系统进行了定性分析，得出系统（１）的极限环的存在性、唯一性及不存在性的条件．定理１...     

鲁棒稳定多项式的摄动界

鲁棒稳定多项式的摄动界安森建,王恩平（中国科学院系统科学研究所,北京１０００８０）基金项目：国家自然科学基金资助项目．１）作者现在通讯地址：北京大学力学系,邮政编码：１００８７１．１９９２年１月００４日收到,１９９２年４月７日收到第一次修改稿,１９９...     

混合序列强大数定律的收敛速度

混合序列强大数定律的收敛速度薛留根（河南许昌师范高等专科学校数学系，许昌４６１０００）河南省自然科学基金资助项目．１９９０年１２月３日收到，１９９１年１１月１１日收到第一次修改稿．一、引言和引理关于独立同分布的随机变量序列｛Ｘｎ｝的强大数定律的收敛速...     

截断族中参数与半参数估计

截断族中参数与半参数估计陈桂景（安徽大学，合肥２３００３９）赵忠柏（吉林工业大学，长春１３００２５）丁元耀（安徽大学，合肥２３００３９）基金项目：国家自然科学基金资助项目１９９１年１月９日收到，１９９２年７月１３日收到第一次修改稿，１９９３年毛月１３...     

非等谱Lax算子族的Virasoro代数

非等谱Ｌａｘ算子族的Ｖｉｒａｓｏｒｏ代数马文秀（复旦大学数学研究所，上海２００４３３）国家博士后科学基金资助项目．１９９１年７月２５日收到．１９９２年７月６日收到修改稿．一、引言Ｌａｘ算子方法［１］在可积系统理论中有着广泛的应用．从一个谱问题出发我们...     

Briot-Bouquet方程与一类积分算子

Ｂｒｉｏｔ－Ｂｏｕｑｕｅｔ方程与一类积分算子高建福（山西省忻州师专数学科，山西０３４０００）１９９０年１０月１６日收到，１９９１年９月１１日收到修改稿．一、引言设ｓ和ｔ是复数，在单位圆盘中正则，微分方程称为Ｂｒｌｏｔ－Ｂｏｕｑｕｅｔ方程．在的情况下，...     

带变系数的第二类奇异积分方程的Galerkin解法

基于对未知函数用适当的正交多项式进行逼近，本文讨论了带变系数的第二类奇异积分方程的Galerkin解法，证明了逼近解的存在唯一性，给出了逼近解在带权L^2模和一致模下的误差估计．     

干线网络的选址问题研究

考虑平面上和三维空间中同时确定多条干线的干线网络选址问题.对于平面上情形,通过最小化每个点到离它最近干线的加权距离之和,给出了一种有限步终止算法和基于k-means聚类分析、加权全最小一乘和重抽样方法的线性类算法;对于空间情形,给出了线性聚类算法.通过计算机仿真说明以上算法可以有效地确定平面和空间中干线网络位置.     

Weighted singular decomposition and weighted pseudoinversion of matrices

For a rectangular real matrix, we obtain a decomposition in weighted singular numbers. On this basis, we obtain a representation of a weighted pseudoinverse matrix in terms of weighted orthogonal matrices and weighted singular numbers.     

An efficient spectral method and rigorous error analysis based on dimension reduction scheme for fourth order problems

In this paper, we propose an effective spectral method based on dimension reduction scheme for fourth order problems in polar geometric domains. First, the original problem is decomposed into a series of one‐dimensional fourth order problems by polar coordinate transformation and the orthogonal properties of Fourier basis function. Then the weak form and the corresponding discrete scheme of each one‐dimensional fourth order problem are derived by introducing polar conditions and appropriate weighted Sobolev spaces. In addition, we define the projection operators in the weighted Sobolev space and give its approximation properties, and further prove the error estimation of each one‐dimensional fourth order problem. Finally, we provide some numerical examples, and the numerical results show the effectiveness of our algorithm and the correctness of the theoretical results.     

Mean convergence of Fourier-Dunkl series

In the context of the Dunkl transform a complete orthogonal system arises in a very natural way. This paper studies the weighted norm convergence of the Fourier series expansion associated to this system. We establish conditions on the weights, in terms of the Ap classes of Muckenhoupt, which ensure the convergence. Necessary conditions are also proved, which for a wide class of weights coincide with the sufficient conditions.     

Lower bounds of error estimates for singular perturbation problems with Jacobi-Spectral approximations

With weighted orthogonal Jacobi polynomials, we study spectral approximations for singular perturbation problems on an interval. The singular parameters of the model are included in the basis functions, and then its stiff matrix is diagonal. Considering the estimations for weighted orthogonal coefficients, a special technique is proposed to investigate the a posteriori error estimates. In view of the difficulty of a posteriori error estimates for spectral approximations, we employ a truncation projection to study lower bounds for the models. Specially, we present the lower bounds of a posteriori error estimates with two different weighted norms in details.     

An efficient spectral‐Galerkin method based on a dimension reduction scheme for eigenvalue problems of Schrödinger equations

In this paper, we propose an efficient spectral‐Galerkin method based on a dimension reduction scheme for eigenvalue problems of Schrödinger equations. Firstly, we carry out a truncation from a three‐dimensional unbounded domain to a bounded spherical domain. By using spherical coordinate transformation and spherical harmonic expansion, we transform the original problem into a series of one‐dimensional eigenvalue problem that can be solved effectively. Secondly, we introduce a weighted Sobolev space to treat the singularity in the effective potential. Using the property of orthogonal polynomials in weighted Sobolev space, the error estimate for the approximate eigenvalues and corresponding eigenfunctions are proved. Error estimates show that our numerical method can achieve spectral accuracy for approximate eigenvalues and eigenfunctions. Finally, we give some numerical examples to demonstrate the efficiency of our algorithms and the correctness of the theoretical results.     

A simple characterization of weighted Sobolev spaces with bounded multiplication operator

In this paper we give a simple characterization of weighted Sobolev spaces (with piecewise monotone weights) such that the multiplication operator is bounded: it is bounded if and only if the support of μ₀ is large enough. We also prove some basic properties of the appropriate weighted Sobolev spaces. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain the asymptotic behavior of Sobolev orthogonal polynomials.     

Numerical solution of nonlinear three‐point boundary value problem on the positive half‐line

In this paper, we present an efficient numerical algorithm to solve the three‐point boundary value problem on the half‐line based on the reproducing kernel theorem. Considering the boundary conditions including a limit form, a new weighted reproducing kernel space is established to overcome the difficulty. By applying reproducing property and existence of the orthogonal basis in the weighted reproducing kernel space, the approximate solution is constructed by the orthogonal projection of the exact solution. Convergence has also been discussed. We demonstrate the accuracy of the method by numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.     

Some new results on orthogonal polynomials for Laguerre type exponential weights

We prove some results on the root-distances and the weighted Lebesgue function corresponding to orthogonal polynomials for Laguerre type exponential weights.