非齐次的

We give several sufficient conditions of NA and NSD properties of random variables, compare the closeness of distribution functions of order statistics between NA and independent rv's, investigate properties of NSD defined by supermodular functions, study the dependence structure of stationary Markov process and order statistics and their spacings from two samples, establish stochastic comparisons of order statistics of heterogeneous rv's in the hazard rate and the reversed hazard rate orders, and give the first analytic proof of the closure property of the up shifted likelihood ratio order under convolution.

给出判定一组随机变量NA性质的几个充分条件，并给出NA和独立随机变量的次序统计量之间"贴近性"的比较，系统地研究基于特殊函数类所定义的NSD负相依概念，给出一些判别NSD性质的结构定理和一些有用概率不等式。系统研究平稳马氏过程的相依结构。研究两样本次序统计量及其问题隔的相依结构。在失效率、反向失效率序和似然序意义下给出非齐次随机变量次序统计量的比较。给出上漂移似然序卷积封闭性的第一个解析证明。

What differ from that of the researchers in the past is the consideration of the direction of Hopf bifurcation with Dirichlet boundary condition , that is, the conditions when the Hopf bifurcation periodic solutions are orbitally asymptotically stable with asymptotic phase.Our basic idea come from the results given by Tang[30]. We adopt the method used by Hassard in the Hopf bifurcation theorem in [24], which is to judge the existence and the direction of Hopf bifurcation, and the stability of the Hopf bifurcation periodic solutions.

与以前的研究者不同的是，本文不仅讨论了在Dirichlet边界条件下系统的Hopf分支在以扩散系数为分支参数的情况下的存在性和分支周期解的空间非齐次性，而且更多的关注了系统在Dirichlet边界条件下Hopf分支解的稳定性及Hopf分支的方向，也即系统定态解在何种条件下，当分支参数如何变化时产生Hopf分支且分支周期解是带渐近位相轨道渐近稳定的。

The influence of initial imperfections on the stability ofcomposite laminated plates was studied by solving the nonlinear governing equations for laminated plates with elastical restraints subject to in-plane loading using the energy variational principle and nonlinear geometric equations incorporating the initial imperfection. The governing equations were solved using generalized Fourier series to obtain the effect of the non-uniform order term.

为深入研究初始缺陷对复合材料层板稳定性的影响，利用能量变分原理和考虑初始缺陷的非线性几何方程，建立了具有弹性约束的层合板在面内载荷作用下的非线性稳定性控制方程组，运用广义傅立叶级数法对其进行求解，并进一步获得了影响非线性稳定性控制方程组的性质的非齐次项。

An inhomogeneous Benjamin-Davis-Ono-Burgers equation including topographic forcing and turbulent dissipation is derived in terms of the quasi-geostrophic vorticity equation, an approximate analytic solution of the BDO-Burgers equation with a small dissipation is obtained, the time variations of mass and energy of the algebraic solitary waves are discussed, and finally, the forced BDO-Burgers equation is integrated numerically and the numerical solutions are given for a given basic flow with a weak shear and a localized topographic forcing.

利用包括地形外源和湍流耗散的准地转涡度方程导出了包含强迫项和湍流耗散项的非齐次强迫BDO-Burgers方程，求出了小耗散存在情况下BDO-Burgers方程的近似解析解，讨论了代数孤立波的质量和能量的守恒关系，最后，对给定的弱切变基本气流和局地地形强迫，数值积分强迫BDO-Burgers方程，求得了不同参数下的数值解。

Furthermore, as a deduction, it obtains a strong law of large numbers for non-homogeneous Markov chain functions.

这里的结果推广了经典的独立随机变量序列的强大数定律，同时也推广了前人关于非齐次马尔可夫链函数强大数定律的结果。

Under the Lipschitz conditions,using Morrey space and Campanatospace methods and filling-hole technique to clear off the difficulty,whicharoused by that monotonic inequalities are no longer true and blow-uptechnique are very difficult to be used again,we obtain that the weaksolutions or the very weak solutions to systems(3)are locally Holdercontinuous.

对方程组（3），我们增加了Lipschitz条件，利用Morrey空间法和Campanato空间法和补洞技巧等来克服非齐次项带来的，单调不等式不再成立和Blow-up技巧难于适用的困难，得出了方程组（3）在一定的条件下的很弱解和弱解是局部〓连续的。

V Roytburb′s results are generalized to inhomogeneous cases.Firstly,a monotone approximation to the flat function p is constructed,then the solutions of corresponding mudification system are estimated.

将V Roytburb的结果推广到非齐次情形，先对平坦函数p进行单调修正，再对修正方程组的解进行估计，最后比较原方程组的解和修正方程组解之间的关系。

The scattering wave velocity potential to the flexible circle pile was the solution of the Laplace equation, which satisfied the cylindrical surface non-homogeneous boundary condition.

采用动力Winkler弹性地基梁模型模拟桩土动力的相互作用，通过求解满足柱面非齐次边界条件的Laplace方程，直接构造波浪对柔性桩的散射速度势，考虑了流体和桩体的相互作用，由解析法给出了埋置圆桩在波浪荷载下的动力响应。

This paper discusses the strong laws of large numbers for random variable functions, and proves a strong law of large numbers for random variable functions by the analytical method.

文章主要讨论了任意随机变量序列泛函的强大数定律，并采用分析的方法证明了任意随机变量序列泛函的强大数定律，作为推论，得到了有关非齐次马尔可夫链函数的一个强大数定律。

Specially,at lower power density of laser,quasi static model is used to simulate the radial heat dissipation from irradiated region to nonirradiated regions.

在数值计算中，应用部分线性法处理非线性非齐次热传导方程，得到相应的隐格式差分方程，再用追赶法求解隐格式差分方程，得出绝热边界条件下的温度的时间和空间分布，从而得出激光退火的再结晶厚度。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。