物理学中两个非线性积分算子的固有值

对于辐射传输理论与核物理学中的两类非线性积分算子的不动点,Leggett R.W.、刘清荣、作者以及Stuart C.H.、郭大钧和张庆雍等分别进行过研究;而物理与力学工作者更为关心的是这些算子的固有值与固有元。本文对二者作了构造性研究,且假设条件易于检验。     

三维有限体中平片裂纹的超奇异积分方程方法—Ⅱ.数值方法

超奇异积分方程方法的理论分析已在本文的第Ｉ部分中给出，这一部分是经的数值方法，及用此方法求解的若干典型的平片裂纹问题。     

为什么把perturbation翻译为"摄动"?

英文科学名词perturbation在不同学科中有不同的定名.在原子物理叫"微扰",在天文学、数学、力学里称为"扰动",更多场合用"摄动".     

多重调和Dirichlet问题奇异正解的对称性

我们在穿孔单位球上研究下面多重调和Dirichlet问题{(-Δ)ku=f(u),在B\{0)内,u＞0,在B\{0)内,u=(e)u/(e)v=…=(e)k-1u/(e)vk-1=0,在(e)B上,其中,B是RN中的单位球,v是(e)B的单位外法向量,N＞2k,k≥2.在f满足适当假设条件下,如果0是不可去奇点,我们...     

一类非奇异H-矩阵判定的新条件

非奇异H-矩阵是在许多领域具有广泛应用的重要矩阵类,但实际判定一个非奇异H-矩阵是十分困难的.在本文中,我们给出了一类关于非奇异H-矩阵新的判定条件,改进了近期的相关结果,并用数值例子说明了文中结果判定范围的更广泛性.     

一类带停时的奇异型随机控制问题的研究

以随机分析的知识和最优控制理论为基础,讨论了一类带停时的奇异型随机控制的折扣费用模型,在原模型的状态过程的基础上添加了漂移因子和扩散因子,并在λ＜δα的情况下讨论了该问题相应的变分方程的解,给出了此随机控制问题的最优策略,即最优控制和最优停时,并且证明了变分方程的解即为最优费用函数.     

Positive solution of singularly perturbed Dirichlet problem with singularities

A class of singularly perturbed boundary value problem with singularities is considered. Introducing the stretched variables, the boundary layer corrective terms near x = 0 and x = 1 are constructed. Under suitable conditions, by using the theory of differential inequalities the existence and asymptotic behavior of solution for boundary value problem are proved, uniformly valid asymptotic expansion of solution with boundary layers are obtained,     

A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Let h be a measurable function defined on R+×R+. LetΩ∈ L(log L+)νq(Sn1-1×Sn2-1)(1 ≤νq≤ 2) be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral T f(x1, x2) = p. v.∫ Rn1+n2Ω(y′1, y′2)h(|y1|, |y2|)|y1|n1|y2|n2f(x1- y1, x2- y2)dy1dy2maps from Sα1, α2p, q˙F(Rn1× Rn2) boundedly to itself for 1 p, q ∞, α1, α2 ∈ R.     

LIMIT CYCLES BIFURCATION FOR A CLASS OF DEGENERATE SINGULARITY

In this paper, bifurcation of limit cycles for the degenerate equilibrium to a three- dimensional system is investigated. Firstly, we use formal series to calculate the focal values at the high-order critical point on center manifold. Then an example is studied, and the existence of 3 limit cycles on the center manifold is proved. In terms of high- order singularities in high-dimensional systems, our results are new.     

Rough singular integrals associated with surfaces of Van der Corput type简

In this paper,the authors establish the Lp-mapping properties for a class of singular integrals along surfaces in Rn of the form {φ(|u|)u : u ∈ Rn} as well as the related maximal operators provided that the function φ satisfies certain oscillatory integral estimates of Van der Corput type,and the integral kernels are given by the radial function h ∈Δγ(R+) for γ 1 and the sphere function Ω∈ Fβ(Sn.1) for some β 0,which is distinct from H1(Sn.1).