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1.
研究一类高阶两项微分方程的振荡原则,利用变分原理及微分方程振荡性的扰动理论得到了此类微分方程的振荡与非振荡原则.  相似文献   

2.
陈庆益 《应用数学》1989,2(1):23-30
本文给出一些充分条件,使振荡函数的含参量积分保持振荡性。  相似文献   

3.
电磁、声波散射问题的研究涉及一类数学物理问题, 此类问题具有深刻的理论价值和重要的应用背景, 亟待解决. 高振荡微分、积分方程是刻画这些问题的重要的数学模型, 其数值计算存在许多挑战性研究课题. 本文从积分方程解法角度出发, 综述了求解这类高振荡问题的一些最新进展, 特别是针对广义Fourier 变换、Bessel 变换的高效算法、高振荡核Volterra 积分方程的数值解法作了详细介绍. 这些数值方法共有特点是振荡频率越高算法精度愈高, 且可望为电磁计算的研究提供一些新的高效算法.  相似文献   

4.
首先将常用类型的模糊矩阵都纳入到了二阶占优模糊矩阵的统一框架之内,然后利用模糊矩阵的有向伴随图,指出了强连通布尔矩阵振荡的一个充要条件,依次证明了强连通的二阶占优布尔矩阵的振荡指数为2n-2,非强连通的二阶占优布尔矩阵的振荡指数为3n-4.  相似文献   

5.
本文分析了一种非定常振荡的不稳定性问题。其特点是,应用偏微分方程特征理论以及O-S方程特征值的展开,求解扰动波的相函数而不是预先给定扰动波的波动形式。本文研究平面Poisettille流与其垂向振荡流的组合流动系统,对于连续振荡源导致的波包演化,该系统存在不稳定性。  相似文献   

6.
研究了磁场对具有非定常压力梯度的振荡自然对流的影响.假设流体是在两平行板内流动.由于在航天材料中的重要性,重点研究在微重力作用下由于矿振荡器诱发的低频振荡自然对流.得到了在非定常磁场下的振荡流体的一般解.还给出了一些特殊的振荡流和对作用磁场的响应.发现振荡流的性质依赖于频率、驱动浮力的振幅、温度梯度、磁场、壁面的导电情况.当没有磁场时,浮力在驱动流体振荡中起主导作用,并且速度的大小还受温度梯度的影响.为了控制振荡流,可以应用外磁场.还发现:当壁面是导体时,速度的减小与作用磁场的平方成反比;当壁面是绝缘体时,速度的减小与作用磁场成反比.一些详细的计算结果反映了真实的状态.  相似文献   

7.
聚类分析有效性问题是一个值得研究的问题.已有的一些方法计算量较大.本文在"子集度"概念基础上,提出一种简便方法ρ检验法.它以距离概念为基础,通过对贡献度的分析,检验相似系数或距离公式的选取是否恰当,分类数的选取是否为优.  相似文献   

8.
一种新型高效的振荡函数数值积分方法   总被引:7,自引:0,他引:7  
李毅夫 《计算数学》1992,14(4):506-512
§1.引言 目前,求振荡函数的数值积分的方法已有多种,如Lobatto法则,Filon法则和Price法则等.为了得到较精确的计算值,迄今各种方法需要的计算量都相当大. 本文给出一种新型高效的求解振荡函数数值积分的方法.与其他方法相比,具有简便易行、计算量小而求积精度高等特点.  相似文献   

9.
自1950年,人们开始研究时滞微分方程的动力学行为.主要研究带有分段常变量时滞微分方程解的振荡与非振荡性.基于唯一正平衡点的全局渐近稳定性,可以构造两个解:在一定条件下,其中一个单调递增趋向于该平衡点,另外一个单调递减趋向于该平衡点.有时所有解都是振荡的.从而给出对于这类带有一个分段常变量的时滞微分方程,其振荡与非振荡性的充分必要条件.结果也给出了当唯一正平衡点全局渐近稳定时解趋向于该平衡点时解的方式,同时也给出了该平衡点不稳定时,解振荡偏离平衡点的动力学行为.  相似文献   

10.
1 引言 在物理学中常会遇到integral from n=-T to T(f(x)φ(x)dx)型的数值积分问题,其中φ(x)在[-T,T]上为奇函数,亦即φ(-x)=-φ(x),比如振荡函数的积分integral from n= x to -x(f(x)sinwxdx)就是最典型的情况,本文把此型积分称为带奇函数因子的积分,由于φ(x)在[-T,T]上符号有正有负,故在[-  相似文献   

11.
We investigate maximal functions involving averages over geodesics in three-dimensional Riemannian manifolds. We first show that one can easily extend the Euclidean results of Bourgain and Wolff if one assumes constant curvature. These results need not hold if this assumption is dropped. Nonetheless, we formulate a generic geometric condition which allows favorable estimates. Curiously, this condition ensures that one is in some sense as far as possible from the constant curvature case. Assuming this, one can prove dimensional estimates for Nikodym-type sets which are essentially optimal. Optimal estimates for the related maximal functions are still open though.

  相似文献   


12.
Let M be the multilinear maximal function and b =(b1,..., bm) be a collection of locally integrable functions. Denote by M b and [ b, M] the maximal commutator and the commutator of M with b, respectively. In this paper, the multiple weighted strong and weak type estimates for operators M b and [ b, M] are studied. Some characterizations of the class of functions bj are given, for which these operators satisfy some strong or weak type estimates.  相似文献   

13.
We study the maximal and fractional maximal functions and Riesz potentials that are generated by the generalized shift operator associated with the Laplace-Bessel operator. We obtain some pointwise and integral estimates that give a relation between the B-maximal and B-fractional maximal functions and B-Riesz potentials and extend the available results to the objects of a more general nature. Basing on these results, we prove interpolation theorems for the B-fractional maximal functions and B-Riesz potentials.  相似文献   

14.
A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted Lebesgue spaces equipped with multiple weights are obtained. Results for other multi(sub)linear maximal functions associated with bases of open sets are studied too. Bilinear interpolation results between distributional estimates, such as those satisfied by the multivariable strong maximal function, are also proved.  相似文献   

15.
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.  相似文献   

16.
Our main objective is to study Haj?asz type Sobolev functions with the exponent one on metric measure spaces equipped with a doubling measure. We show that a discrete maximal function is bounded in the Haj?asz space with the exponent one. This implies that every such function has Lebesgue points outside a set of capacity zero. We also show that every Haj?asz function coincides with a Hölder continuous Haj?asz function outside a set of small Hausdorff content. Our proofs are based on Sobolev space estimates for maximal functions.  相似文献   

17.
主要研究了拟度量测度空间(X,d,μ)中修正的极大函数,其中X表示集合,μ表示不满足二重性的Borel测度,d表示不满足对称性的拟度量,本文对修正的极大函数建立了弱(1,1)估计和(Φ,Φ)型估计,其中Φ比N函数更一般.作为应用,证明了拟度量测度空间中推广的Lebesgue微分定理.本文的结果也适用于与常系数Kolmogorov型算子对应的Lie群G=(R~(N+1),o).  相似文献   

18.
This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar's inequality and the sharp maximal function estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.  相似文献   

19.
We give a survey of research on the problem of single-weighted and double-weighted estimates of strong and weak types for the Hardy-Littlewood maximal function, Riesz potentials, singular integral operators, and harmonic functions. Necessary and sufficient conditions on the weight are given under which weighted estimates are valid (Muckenhoupt's Ap-condition, Sawyer's condition, etc.). Special attention is given to papers which appeared after 1980 and the latest results, published as reports and preprints.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 21, pp. 42–129, 1983.  相似文献   

20.
In this paper we study maximal sharp functions associated with arbitrary differential bases. The definition of these functions goes back to the papers by F. John (1965), and by C. Fefferman and E. M. Stein (1972), where the classical bases consisting of cubic intervals were considered. We obtain conditions imposed on the basis, under which inequalities, known earlier in the case of a basis of cubes, are valid for the considered maximal functions. The main results are formulated in terms of nonincreasing rearrangements. In the capacity of applications, we obtain estimates of the rearrangements of subadditive operators acting in BMO. In particular, the estimate for the Hilbert transform, obtained earlier by C. Bennett and K. Rudnick, follows.  相似文献   

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