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This paper studies the properities of weakly invertible Linear finite automata through zero state,and obtains some results of weakly invertibility of Linear finite automata and description of the minimal linear finite sub-automata.

通过零状态研究了线性有限自动机的一些性质，得到了线性有限自动机弱可逆的一些结果，并给出了最小线性子有限自动机的描述，最后给出了算法实现。

In chapter 2, we prove that sn—first countable spaces are preserved by the finite subsequence-covering mappings.By this result, we prove that the finite subsequence-covering, quotient mappings preserve g—metrizable spaces, also prove that the finite subsequence-covering, closed mappings preserve sn—metrizable spaces, g-metrizable spaces, metrizable spaces, point-countable bases.

在第二章中，我们主要证明了有限子序列覆盖映射保持sn-第一可数空间，作为它的应用，又证明了有限子序列覆盖、商映射保持g-第一可数空间，也证明了有限子序列覆盖闭映射保持sn-度量空间，g-度量空间，度量空间，点可数基。

A rational procedure is presented to solve finite element problem mixing nonlinear and elastoplastic materials. To avoid numerical problem, the incremental finite element analysis of geometrically altered structures is adopted, and a corresponding automatic finite element mesh strategy is proposed for simulating construction process of excavation.

本文采用变结构有限元分析方法，建立了一种可以灵活模拟基坑工程各种施工工况的有限元网格方法，该方法克服了现有的一些网格方法无法模拟加支撑、加锚杆或拆支撑的缺点，以及不便于计算机自动生成有限元网格的不足，可以更全面、准确地模拟施工过程，大大方便了有限元前处理工作。

The formulas derived show that FAM is more accurate and reasonable than finite difference method and finite element method , also, on the element partial differentiation of dynamic Reynolds equations with respect to circumferential and axial direction is directly obtained by finite analytic solution.

本文在详细分析目前流体润滑轴承层流、紊流润滑理论及轴承-转子系统稳定性理论的基础上，提出了将有限分析法用于计算动压、静压、动静压轴承的静特性和动特性系数，并推导了相应的计算公式。

We constructed a finite volume scheme of fifth order Hermite type with high accuracy for twopoint boundary value problems, choosing trial and test spaces as the fifthorder finite element space of Hermite type and the piecewise linear function space respectively. We didn't use higher derivatives as interpolation conditions, which is the same as the thirdorder finite element of Hermite type, but the scheme obtained had higher accuracy.

构造求解两点边值问题的一种Hermite型五次元高精度有限体积法，其中试探函数空间取Hermite型五次有限元空间，与Hermite型三次元相同，未引入更高阶导数作为插值条件，检验函数空间取分段线性函数空间，这样构造的格式求解精度更高。

The plane adopts the joint method of both the finite element and the finite difference to divide plane domain by means of irregular triangular net in order to fit topography and coastal line complicated sea zone; Vertical application σcoordinate conversion and the finite difference method.

平面采用有限元法和有限差分法相结合的方法，用不规则三角形网格剖分计算域，以适应地形和岸线复杂的海区；垂向应用σ-坐标变换及有限差分法。

Based on the virtual displacement principle of finite element method, a weak variation of GAO-YONG turbulence equations is put forward. The subroutine of the element and the integrated finite element code are generated by the finite element program generator successfully.

基于有限元方法中的虚位移原理，写出了不可压流Gao-Yong湍流方程组弱形式的微分方程表达式，利用有限元程序自动生成系统得到了全部有限元计算程序。

Using the Updated Lagrange finite element method and the elastic-plastic large deformation finite element formula based on virtual work-rate principle of finite deformation, the author studies in detail the plastic flow rule of MPF, including the influence of the work hardening index, friction, thickness of sheet, material, number and position of the punch.

作者采用逐级更新Lagrange法以及有限变形虚功率增率原理的弹塑性大变形有限元法，详细研究了金属板材多点成形的塑性流动规律，包括加工硬化指数、摩擦系数、板料厚度、材料、冲头个数及位置等对成形的影响，同时探讨了分段成形时的金属流动规律。

Two finite element analyses were conducted. First, the poroelastic dynamic equations were transformed to Laplace domain and the Galerkin finite element approach is applied to derive the stiffness matrix of rectangular porous element for conducting the finite element frequency domain analysis.

为探讨空间声场之特性，本文将分析方法归纳为二部份，第一部份应用拉普拉斯转换后之多孔线性弹性动态方程以二维矩形多孔弹性元素及 Galerkin有限元素法推导并进行有限元素频域分析。

Divide the whole region D into finite units and corresponding link points may be obtained. Constructing the equation of variation calculation about every element leads to the finite number of equations. Further more, algebra equation group for general synthesis are gained by adding these finite number of equations, that is,{T}={P} where is the coefficient matrix of the equation group, or say the temperature rigidity matrix,{T} is the row vector of unknown temperature and {P} is the row vector of the terms on the right side of the equation.

然后将整体区域D划分成有限个单元并得到相应的有限个节点，从而可以得到关于每个单元的变分计算方程，将这有限个方程相加就得到了总体合成的代数方程组，即{T}={P}，其中为方程组的系数矩阵，也称温度刚度矩阵，{T}为未知温度值的列向量，{P}为等式右端项组成的列向量。

It is also known as one of the most poisonous naturally occurring substances.

它也被称为一个最自然发生的有毒物质。

The greatest stress is found at the location on the cross section where V is the largest.

最大应力出现在横截面上V为最大的地方。