GF(2)上本原多项式的三项倍式的次数研究

研究了二元域上本原多项式的三项倍式的计数问题,通过对三项倍式进行分类,导出了本原多项式三项倍式最低次数的一个上界.利用这一结果,使构造本原多项式的次数最低的三项倍式的计算复杂性降到原来的九分之一.     

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

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NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

各向异性材料中共线刚性线夹杂的纵向剪切问题

本文研究各向异性材料中共线刚性线夹杂，（有时称作“硬裂纹”或“反裂纹”问题）的纵向剪切问题。利用复变函数方法，提出了一般问题的公式和某些实际重要问题的封闭形式解，考察了刚性线端点附近的应力分布．从本文解答的特殊情形，可以直接导出各向同性材料相应问题的公式和结果，包括某些已有的结果￣［７］．     

具有两层基片的微带线的混合模分析

给出了有两层基片的微带线与频率有关的混合模分析，应用傅里叶交换域分析及新的矩阵研究推导出色散特性．除了波导波长以外，还根据功率一电流的定义计算了特征阻抗，波导波长和特征阻抗与频率的关系及其数据值结果，并将其与有关文献的结果相比较，其一致性很好．     

Instability of Fabry-Perot interferometer with a multilayered paramagnetic filling

The results of the analysis of the stability of stationary solutions of wave equations discribing a behavior of the nonlinear Fabry-Perot interferometer with a saturated paramagnetic filling are presented in this paper. The cases when paramagnetic medium is characterized by a homogeneously and nonhomogeneously broadened line of the magnetic resonance have been considered. Areas of unstable behavior of these characteristics of the resonance structure have been found.     

Numerical analysis of finite amplitude motion of waves and a moored floating body under severe storm conditions

The motion of a moored floating body under the action of wave forces, which is influenced by fluid forces, shape of the floating body and mooring forces, should be analysed as a complex coupled motion system. Especially under severe storm conditions or resonant motion of the floating body it is necessary to consider finite amplitude motions of the waves, the floating body and the mooring lines as well as non-linear interactions of these finite amplitude motions. The problem of a floating body has been studied on the basis of linear wave theory by many researchers. However, the finite amplitude motion under a correlated motion system has rarely been taken into account. This paper presents a numerical method for calculating the finite amplitude motion when a floating body is moored by non-linear mooring lines such as chains and cables under severe storm conditions.     

DISTRIBUTION OF THE（0，∞）ACCUMULATIVE LINES OF MEROMORPHIC FUNCTIONS

Suppose that f(z)is a meromorphic function of order λ（0<λ<+∞）and of lower order μ in the plane.Let ρ be a positive number such that μ≤ρ≤λ.(1)If f^(l)(z)(0≤l<+∞）has p(1≤p<+∞）finite nonzero deficient valnes αi(i=1,…，p)with deficiencies δ（αi,f^(l)),then f(z)has a (0,∞）accumulative line of order ≥ρin any angular domain whose vertex is at the origin and whose magnitude is larger than max(π/ρ，2π-4/ρ ∑i=1^p arcsin √δ（αi,f^(l))/2).(2)If f(z) has only p(0<p<+∞）（0,∞）,accumulative lines of order≥ρ：arg z=θk(0≤θ1<θ2<…<θp<2π，θp+1=θ1+2π）,then λ≤π/ω，where ω=min I≤k≤p(θk+1-θk),provided that f^(l)(z)(0≤l<+∞）has a finite nonzero deficient value.     

结构—饱和土壤相互作用的固结有限元分析

讨论了结构与饱和土壤相互作用的固结分析问题.对于结构利用多重子结构分析技术实现向饱和土交界面上的凝聚.从而建立了结构与饱和土壤相互作用的固结控制方程.文中给出了问题求解的一次性算法方案,采取压力主从关系的手段处理边界上的不排水条件.文末给出数值算例.本文工作为大型结构与土体相互作用固结分析研究工作的深入创造了条件.