线性模型中F-检验的稳健性

本文讨论了一般线性模型中关于均值参数β的线性假设基于广义最小二乘估计的F-检验统计量的稳健性问题.主要研究了当误差的协方差矩阵含有参数时,设计阵可以列降秩情况下的F-检验统计量的稳健性,得到了F(V(θ))为该假设下F-检验统计量的误差协方差矩阵的最大类.并讨论了分块线性模型中,关于分块参数的线性假设的F-检验统计量的稳健性.     

集值Vitali-Hahn-Saks-Nikodym定理

本文通过强可加集值测度的一个等价叙述引入集值测度一致强可加的概念,并建立了集值测度的Vitali-Hahn-Saks-Nikodym定理.     

沿齐次曲线的强奇异积分算子在调幅空间上的有界性

设Γ_θ(t)为R~n(n≥2)中的齐次曲线,定义沿齐次曲线的强奇异积分算子T_(n,α,β)f(x)=p.v.∫_(-1)~1f(x-Γ_θ(t))(e~((-2πi|t|)~(-β))/(t|t|~α))dt,α,β>0.本文讨论了上述奇异积分算子在广义调幅空间上的有界性.     

THE EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF SECOND ORDER DIFFERENTIAL EQUATIONS

In this paper, a fixed point theorem in C1[0,1] space is established using the properties of the fixed point index. This theorem is applied to prove the existence of positive solution to the boundary value problems of second order differential equations.     

Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coeffcients with Dissipation

Decay of the energy for the Cauchy problem of the wave equation of variable coeffcients with a dissipation is considered.It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coeffcients.In particular,some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.     

ON BLOCK MATRICES ASSOCIATED WITH DISCRETE TRIGONOMETRIC TRANSFORMS AND THEIR USE IN THE THEORY OF WAVE PROPAGATION

Block matrices associated with discrete Trigonometric transforms （DTT＇s） arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators with the Method of Moments, the Boundary Element Method, and the Method of Auxiliary Sources. The DTT＇s are represented by the Fourier, Hartley, Cosine, and Sine matrices, which are unitary and offer simultaneous diagonalizations of specific matrix algebras. The main tool for the investigation of the aforementioned wave applications is the efficient inversion of such types of block matrices. To this direction, in this paper we develop an efficient algorithm for the inversion of matrices with U-diagonalizable blocks （U a fixed unitary matrix） by utilizing the U- diagonalization of each block and subsequently a similarity transformation procedure. We determine the developed method＇s computational complexity and point out its high efficiency compared to standard inversion techniques. An implementation of the algorithm in Matlab is given. Several numerical results are presented demonstrating the CPU-time efficiency and accuracy for ill-conditioned matrices of the method. The investigated matrices stem from real-world wave propagation applications.     

L—Fuzzy拓扑空间中的可数F紧性与几乎可数F紧性

本文在Ｌ－ｕｚｚｙ拓扑空间中引入可数Ｆ紧性与几乎可数Ｆ紧性的概念，并讨论了它们的性质及其相互关系。     

SOME BLENDING INTERPOLATION METHODS IN CAGD

Some of the blending interpolation methods (which) stated by a convex combination technique are presented. This includes C1 ,C2 blending triangular interpolanls and C1 -blending quadrilateral inter polanls for surfaces. The mentioned methods can be generalized to the construction of C" blending interpolants.     

THE EIGENVALUE PROBLEM EQUIVALENT TO MULTIVARIATE POLYNOMIAL SYSTEM

In this paper, the authors proved that finding all solutions of a given multivariate polynomial system is equivalent to solving a relative joint eigenvalue problem(Theorem 1) and in some cases one can find all solutions of the given system from the eigenvalues and vectors of one matrix or matrix pencil (Theorem 2). Especially the situation that the ideal generated by the given system is 0-dimensional is discussed.     

不确定条件下多属性决策的比较因素法(英文)

本文针对不确定条件下多属性决策问题,扩展了原有多属性决策的概念,引入了比较因素与次比较因素,获得了其一些代数性质以及相应的定理。在此基础上,给出了不确定条件下多属性决策的比较因素法。