非经典Ekman方程的解和演化条件

建立了一个Ekman边界层的随机方程和非经典Ekman方程，研究了非经典Ekman流的频率响应、解和演化条件．有关研究结果表明，当经典Ekman流的切变足够大时，非经典Ekman流将发展起来，而且在相似条件和普适条件下，非经典Ekman流将分别朝最可几态(U3，V3)或(-fV3,fU2)演化．     

我校大学生课外体育活动现状的调查分析

本文通过对我校大学生课外体育活动的调查分析，指出我校学生的体育锻炼存在自觉性不够、活动时间与次数偏少等问题，建议在今后的教学中把培养学生的自我锻炼的能力、兴趣放在重要的位置，使学生逐步形成较稳定的活动兴趣，并养成经常锻炼的良好习惯。     

P-拉普拉斯方程正解和多解的存在性

研究在RN中的一般形式的P-拉普拉斯方程-div(|Du|p-2Du)=f(x,u)(N>P>1).在一定的条件下得到正确和多解.首先建立相应的变分范函,利用H lder和Sobolev不等式证明此范函满足Palais-Smale条件,然后利用爬山原理证明了解的存在性.最后利用严格最大值原理证明了正解的存在性.     

预优矩阵及其构造技术

为达到预处理共轭梯度法(PCG)提高收敛速度，克服数值不稳定性目的，给出了构造预优矩阵的条件，并构造了三个典型的预优矩阵。它们是不完全Cholesky因子预优矩阵，对角预优矩阵和利用SSOR法导出的预优矩阵，且在PCG中是应用效果很好的预优矩阵。     

B-样条曲面的G1连续性

得到了关于两个双三次内部重结点B-样条曲面片G1连续的充分必要条件和在公共边界线上控制向量的本征条件,这些条件直接由两个B-样条曲面的控制向量表示.利用本文所给的条件,得到了具有局部性质且是真正G1光滑的曲面模型.     

边界曲线摄动的双解析函数的Riemann边值问题

讨论了双解析函数Riemann边值问题的解在区域边界L发生光滑摄动时的稳定性问题。     

M带多尺度函数逼近阶的频域条件

在小波理论中，精度或逼近阶是刻划尺度函数最重要的特征之一。就肘带多小波的多尺度函数逼近阶在频域里进行研究，给出了肘带多尺度函数具有逼近阶m的频域充要条件。     

弱条件线性方程组的一种迭代方法

设A为m×n矩阵、线性方程组AX=b相容,其解集为C。给出了求X∈C的迭代方法。对序列{X(k)},其中λit(k)X(k)满足: X0,X(k+1)=X(k)+ mi=[bi-(Ai,X(k))]/‖Ai‖2,k=0,1,2,…。证明了{X(k)}收敛,设i,Ai,t(k)i=1X(k)=X ,则X ∈C。若取X0=0,则X ∈R(AT),其中R(AT)={ATX｜X∈Rm}。limk→∞     

Relations among gauge functions, metrics and Hausdorff measures

In this paper we discuss the relations among the doubling condition, equivalence of the Hausdorff measures and equivalence of metrics. We will show that H ρ,g1 and H ρ,g2 are equivalent for any compact metric space (X,ρ) if and only if g1 and g2 are equivalent gauge functions. Then, we prove that for given c∈(0,∞)＼{1}, H ρ,g and H cρ,g are equivalent for any compact metric space (X,ρ) if and only if the gauge function g satisfies the doubling condition, where H ρ,g is the Hausdorff measure with respect to the metric ρ and gauge function g.     

Compact difference approximation with consistent boundary condition

For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.