Sobolev-Hardy不等式与临界双重调和问题

该文讨论一类带有奇异系数的双重调和方程{△^2u-μu/|x|^s=f(x,u),x∈Ω,u=δu/δv=0,x∈δΩ，这里Ω包含R^N是包含0的有界光滑区域，u∈H0^2(Ω），μ∈R是参数，0≤s≤2,△^2=△△表示双重拉普拉斯算子，当f(x,u)=u^p,p=2N/N-4时，上述问题就是一个临界双重调和问题，该文运用Sobolev-Hardy不等式和变分方法，得到它的解的存在性的一些结果。     

四元数矩阵方程AXAH=B的最小二乘解

引入了四元数矩阵范数的概念，通过使用四无数矩阵的奇异值分解，给出了四元数矩阵方程AXA^H＝B在最小二乘意义下的Hermitian解以及Skew-Hermitian解．     

高阶微分方程允许解的存在性

本文主要目的是利用值分布理论研究复高阶微分方程(Ω(z,w)/w^k0(w’)^k1…(w^(n)^kn)^m=aw^p ∑j=0^s bj(z)w^j,(p≥m）亚纯允许解的存在性问题．证明了一个在适当的条件下，该微分方程的亚纯解一定不是允许解的结果．实例表明该文的结果是最佳的．     

均布荷载作用下压电材料简支梁的解析解

采用逆解法求解了均布荷载作用下压电材料简支梁的解析解。首先给出应力函数和电位移函数的多项式表达式,进而根据相容方程以及应力和电位移、位移和电势的边界条件,求得了同时考虑材料弹性参数、密度参数和压电参数呈梯度变化时,简支梁在均布荷载作用下的解析解。作为特例还得到了常体力以及材料参数为常数时的解答。并对结果进行了讨论。     

谱半径前六位的n阶单圈图

恰含一个圈的简单连通图称为单圈图。Cn记n个顶点的圈。△（i,j,κ）记C3的三个顶点上分别接出i,j,κ条悬挂边所得的图，其中i≥j≥κ≥0.Sl^n-l记Cl的某一顶点上接出n-l条悬挂边所得到的图。△（n-4 1,0,0)记△（n-4,0,0)的某个悬挂点上接出一条悬挂边所得到的图。本文证明了：若把所有n(n≥12）阶单圈图按其最大特征值从大到小的顺序排列，则排在前六位的依次是S3^n-3，△（n-4,1,0),△（n-4 1,0,0),S4^n-4,△（n-5,2,0),△（n-5,1,1)。     

拟线性抛物型方程广义解的局部有界性

本文给出了一类较广泛的拟线性抛物型方程广义解的局部有界性,进而也得到了解的Holder连续性.     

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

θ-Fuzzy关系方程的分解与求解

在有限论域上首先给出θ-Fuzzy关系方程的分解，然后针对NR-蕴涵θ，探讨θ-Fuzzy关系方程的求解问题，基于解矩阵给出解的存在性的几个新判据，并在解集非空时，证明θ-Fuzzy关系方程的每一个解都存在一个极大解。     

Algebraic and Geometric Properties of Matrix Solutions of Nonlinear Wave Equations

We improve the construction of exact matrix solutions for nonlinear wave equations by using unitary anti-Hermitian and anticommuting matrices. We prove the theorem that constructs the matrix functions u _n satisfying the nonlinear wave equation for a set of special potentials. In this case, the graph of complex solution u ₁ has a soliton-like form with a finite number of coils. Exponential representation of matrix solutions u _n is associated with continuous rotations that can be used for describing intrinsic rotations and state changes of elementary particles. We also prove the theorem on the decomposition of continuous rotation (described by solution u ₂) onto three simultaneous rotations about coordinate vectors. Each of the three constructed matrix solutions u ₃ is also decomposed into the triplet of elementary matrix solutions.     

A superdense star model as charged analogue of Schwarzschild’s interior solution

A charged analogue of Schwarzschilds interior solution has been derived by considering the non-gravitational energy density to be constant along with a special choice of electric intensity. The charged fluid sphere so obtained is seen to be more general than that of P.S. Florides and joins smoothly with the Reissner-Nordström metric at the pressure-free interface. Also the new charged fluid sphere is capable of representing a superdense star with surface density of 2×10¹⁴ g cm^–3 which can occupy maximum mass 1.502408 times the solar mass. In the process of deriving the solution, the authors have also come across A. L. Mehras gaseous charged fluid model which is found to be unphysical as it has negative pressure at least at the center of the model.This revised version was published online in April 2005. The publishing date was inserted.