一维的

Different models for different structure sections are established, namely, one-dimensional piping model for laneway or large hole, two-dimensional structure plane model for absciss layer and contacting weathering zone, three-dimensional seeping fracture section model.

分区建立了采空区不同注浆结构部位的理论模型，包括采空区空洞或巷道的一维"管道"模型、离层与接触风化带等结构面二维模型、导水裂隙带三维模型。

We develop his ideas by finding some algebraic invariants under the adjoint actions of the group in addition to the Killing form and give a rigorous proof of the optimality of the one-parameter systems for the symmetry group of the given equations.

本文系统地研究了1+2维非线性发展方程的对称代数，证明了该方程容许一个七维李点对称群，利用Olver提出的方法，详细地建构了1+2维非线性发展方程的一维最优系统，在此基础上我们发展了他的方法，发现了除Killing型之外的其它六个在群伴随作用下的代数不变量，利用这些不变量证明了该最优系统的最优性。

However the computation of the finite element method is very complex when dealing high-dimensional problems. So that in order to solve the multi-variables problems, the alternating- direction method appears. It can lower the dimension.

有限元方法虽然具有高精度的优点，但是在处理高维问题时计算很复杂，因此为求解多变量的复杂问题，出现了交替方向法，可以把多维问题降维，分解成连续解几个一维问题。

In this paper , for a co-dimension two-bifurcation system that is on a three-dimensional central manifold and subjected to a parametric excitation by a white noise , the asymptotic expansion of the maximal Lyapunov exponent is evaluated.

为了分析白噪声参数激励对三维中心流形上一类余维2分岔系统的影响，本文基于一维扩散过程的奇异点理论，通过使用 L。

Through the numerical computation and comparison with the exact solutions of one dimensional linear convection equation and nonlinear equation, accuracy of the first order upwind scheme is analyzed in detail.

摘 要：通过对一维线性对流方程和一维非线性对流方程的数值求解，对一阶迎风差分格式的精度作了较详细的分析。

The 3D wavelet sampling theorem has been obtained from 1D wavelet sampling theorem using scalar product method and then it is used to improve ART in direct volume reconstruction. In the other hand, the 1D wavelet sampling theorem is applied for the analytic direct reconstruction algorithm too.

7将一维小波取样定理推广到高维情形，并以此给出了一种改进的直接体积重建的ART方法，并进行了计算机模拟；将一维小波取样定理应用到了解析类的直接体积重建算法之中。

According to the primary principles of the half division method and Newton method ,a new method called horizontal secant method was presented for one dimension search.

根据经典的一维搜索算法———对分法和Newton 切线法的基本原理，提出了一种新的一维搜索算法———水平割线法。

Use of tensor product can be from one-dimensional analysis directly from the two-dimensional multiresolution analysis, thus conveniently be constructed of two-dimensional wavelet and wavelet packet and the corresponding decomposition and synthesis algorithms.

利用张量积方法可以从一维多分辨分析直接得到二维的多分辨分析，从而方便地构造得到二维小波和小波包以及相应的分解和合成算法。

3D effect is analyzed and the average velocity of wave propagating in the pile, which mainly influences inverse interpretation, is discussed. Finally, the theory results are verified by model experiment. It is shown that 3D results have the same phase with ID results. The pile radius, the duration of impulse, the ratio of hammer radius to pile radius and shear velocity of the soil around the pile have influences on 3D effect. The best position of receiver is 0.55R from the pile center. The average velocity of wave propagating in the pile reduces due to transversal inertia effect and 3D effect.

结果表明：三维曲线与一维结果在相位特征上一致；波场图直观地反映了波在桩中的传播规律；三维效应与桩径、激振脉冲宽度、相对激振半径及桩周土剪切波速有关；传感器放在0.55R处可以得到干扰较小的信号；三维效应和横向惯性效应的存在会使桩中的波速减小，土的性质对波速影响不大；反演精度与缺陷的性质、激振条件有关。

One manufacturer defines types as lead-acid versus NiCad, while another refers to 1D, 3D, 4D and 8D, or group number batteries as sizes.

一制造商的定义类型式铅酸银两nicad ，而另一个是指一维，三维，四维和为8 D ，或一组号码电池的大小。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。