四阶微分方程奇异边值问题的正解

本文利用锥上的不动点指数理论,在更一般的边界条件下讨论了一类四阶奇异边值问题正解的存在性并给出了应用．     

PRACTICAL STABILITY IN TERMS OF TWO MEASURES FOR DISCRETE SYSTEMS

Practical stability in terms of two measures for difference equations is discussed by using the Lyapunov function and a new comparison theorem.     

The Newton filtration and d-determination of bifurcation problems related to C~0 contact equivalence

In this paper, from the Newton filtration's point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C0 contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

在SQUID心磁测量中基于奇异值分解和自适应滤波的噪声消除法

采用矩阵奇异值分解(singular value decomposition, SVD)的方法，对高温射频超导量子干涉仪(HTc rf-SQUID)采集到的单通道心磁信号进行处理.证明了对于近似周期性的心磁信号，在无参考噪声的情况下矩阵奇异值分解的方法与自适应窄带陷波相结合有较好的消除广谱噪声的效果. 关键词： 高温射频超导量子干涉仪 心磁信号 奇异值分解 噪声消除     

四阶半线性椭圆型积分微分方程的奇摄动

本文研究了一个四阶椭圆型积分微分方程的奇摄动问题。证明了相应的比较定理并得到了解的一致有效的渐近展开式。     

n维广义函数的集值导数

本文将文献［9］中给出的一维广义函数的集值导数的某些结果，推广到n维情形，并给出一些与优化有关的其他结果．     

ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS

In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.     

Some Oscillatory Singular Integrals on Herz-type Spaces (Ⅱ)

In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).     

THE ASYMPTOTIC SOLUTION FOR A CLASS OF SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR SINGULAR EQUATION

The singularly perturbed boundary value problem for a class of semilinearsingular equation is considered. Using a simple and special method the asym-ptotic behavior of solution is studied.     

关于有限Abel群直接因子的平均数

对于有限Ａｂｅｌ群Ｇ，ｔ（Ｇ）定义为其直接因子的个数，在［５］中，Ｅ．Ｋｒａｔｚｅｌ对于和式得到一渐近公式，对应余项为△＿１（ｘ）．本文利用Ｅ．Ｆｏｕｖｒｙ和Ｈ　．Ｉｗａｎｉｅｃ的方法，得到了关于△＿１（ｘ）的一个新的估计，改进了Ｈ．Ｍｅｎｚｅｒ等人的结果．