非局部边界条件的Jaulent-Miodek算子的迹公式

利用Jaulent-Miodek方程初值解的渐进估计,构造一个整函数ω(λ),借助积分恒等式,采用留数的方法,对Jaulent-Miodek算子的特征值做出了估计,得到了问题的渐进迹公式.     

一个特征值问题的迹

本文获得了Jauknt-Miodek特征值问题的迹公式.     

一类迹占优矩阵的特征值分布

基于迹占优矩阵给出了一类广义迹占优矩阵,得到了这一类广义迹占优矩阵的一些性质,并且给出它的特征值估计和分布。     

两个非负定矩阵乘积的特征值的新估计

本文得出如下矩阵特征值的不等式：设Ａ，Ｂ为阶数ｎ的非负定的实矩阵，Ａ，Ｂ和ＡＢ的特征值分别为：λ＿１≥λ＿２≥……≥λ＿ｎ；μ＿１≥μ＿２≥…≥μ＿ｎ和θ＿１≥θ＿２≥……≥θ＿ｎ，则对任意正整数γ，均有：这是￣【２】中关于￣【１】中的公开问题的肯定回答的高次幕的情形。     

一类常微分方程特征值的上界估计

考虑一类常微分方程特征值的上界估计,利用分部积分、Rayleigh定理和不等式估计等方法,获得了用前n个特征值来估计第n+1个特征值的上界的不等式,其估计系数与区间的几何度量无关,其结果在物理学和力学等领域中应用广泛.     

周期边界条件下Sturm-Liouville问题的一个注记

证明了周期边界条件下Sturm-Liouville问题特征值的集合和一整函数w(λ)零点的集合一致,且特征值的秩和其作为零点的重数一致.作为应用,给出了与此问题相关的特征展开定理及特征值的迹公式的精确表述.     

常微分方程特征值问题的求解器解法

许多工程计算归结为常微分方程(ODE)特征值问题.近代的高效能的ODE求解器为一般的线性及非线性ODE问题的求解提供了强有力的武器,但通常不具备求解特征值问题的功能,难以直接应用.本文提出了一个用标准的ODE求解器求解ODE特征值问题的算法,使得大批ODE特征值问题能够凭借ODE求解器的功效得以方便有效、精确可靠地求解.     

高阶常微分方程特征值的上界估计

考虑高阶常微分方程特征值的上界估计，利用试验函数，Rayleigh定理和不等式估计等方法，获得了用前n个特征值来估计第n 1个特征值的上界的不等式，其估计系统与区间的几何度量无关，其结果在物理学和力学等领域中应用广泛。     

一类常微分方程特征值的带权估计

考虑一类常微分方程的特征值的带权估计,利用分部积分、Rayleigh定理和不等式估计等方法,获得了用前n个特征值来估计第n＋1个特征值的上界的不等式,其估计系数与区间的几何度量无关,其结果在物理学和力学等领域中应用广泛。     

Singularly perturbed first-order differential equations with integral boundary condition

In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the uniformly valid asymptotic solution of the original problem is obtained.     

具双曲动力边界的Laplace方程解的爆破

讨论了具非线性双曲动力边界条件的Laplace方程解的爆破.在边界条件为半线性双曲型且初始能量为负及边界源项满足一定条件下,利用凸性方法得到了解的爆破性。     

A Novel Absorbing Boundary Condition for the Frequency—Dependent Finite—Difference Time—Domain Method

A new absorbing boundary condition(ABC) for frequency-dependent finite-difference time-domain algorithm for the arbitrary dispersive media is presented.The concepts of the digital systems are introduced to the (FD)^2TD method.On the basis of digital filter disigning and vector algebra,the absorbing boundary condition under arbitrary angle of incidence are derived.The transient electromagnetic problems in two-dimensions and three-dimensions are calculated and the validity of the ABC is verified.     

奇性三阶非线性微分方程的边值问题的微分不等式

研究奇性三阶非线性微分方程的边值问题 ,通过构造上下解并利用nagumo的思想和截段函数的技巧 ,得到了解的存在性及微分不等式     

非Nagumo条件的三阶微分方程的三点边值问题

研究满足一个简单条件,但可能不满足Nagumo条件的三阶微分方程三点边值问题的微分不等式的解的存在性及其唯一性．     

Analytical solution for 1D consolidation of unsaturated soil with mixed boundary condition

Based on consolidation equations proposed for unsaturated soil, an analytical solution for 1D consolidation of an unsaturated single-layer soil with nonhomogeneous mixed boundary condition is developed. The mixed boundary condition can be used for special applications, such as tests occur in laboratory. The analytical solution is obtained by assuming all material parameters remain constant during consolidation. In the derivation of the analytical solution, the nonhomogeneous boundary condition is first transformed into a homogeneous boundary condition. Then, the eigenfunction and eigenvalue are derived according to the consolidation equations and the new boundary condition. Finally, using the method of undetermined coefficients and the orthogonal relation of the eigenfunction, the analytical solution for the new boundary condition is obtained. The present method is applicable to various types of boundary conditions. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with mixed boundary condition.     

A necessary and sufficient condition for positive solutions of singular fourth order boundary value problems

This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3[0,1] positive solution is given by means of the monotone terative technique.Furthermore,the uniqueness of the C3[0,1]positive solution,and the iterative sequence of the C3[0,1]positive solution are also obtained.     

代数特征问题的一个注记

改进了求代数特征值与特征向量的传统方法,给出了一种用初等变换来求代数特征值与特征向量的方法.     

一类微分方程(组)的公式解

利用分式性质 ,给出一类微分方程及方程组的公式解法 ,较一般微分方程教材上的方法简洁 ,便于应用。     

Symmetric solutions of singular nonlocal boundary value problems for systems of differential equation

In this paper, we investigate the existence of symmetric solutions of singular nonlocal boundary value problems for systems of differential equations. Our analysis relies on a nonlinear alternative of Leray - schauder type. Our results presented here unify, generalize and significantly improve many known results in the literature.