代数形式

Using the substitution-elimination method affine algebraic variety can be resolved to pure d-dimensional subvariety and expressed by an algebraic hypersurface on d+1-dimensional space with a sequence of elimination-polynomial systems. All 0-dimensional solution can be found, too.

利用变换消元法可以把代数簇分解成纯d维的子簇，并把代数簇表示为d+1维子空间上的超曲面形式和一系列的消元多项式组，且能求出全部孤立解，同时给出了算法及其在多项式因式分解中的应用。

Since the visualization of implicit algebraic surface is still a difficult problem, it is doubtlessly meaningful to construct some convenient and effective parameterization method for some kind of concrete implicit surfaces.

由于隐式代数曲面的显示问题始终是困扰人们的一个关键性难题，从而针对具体形式的代数曲面，能给出方便有效的参数化方法无疑是有意义的。

Applying the techniques of real radical ideal, P-radical ideal , decomposition of semi-algebraic set in ( [72] ), affine Hilbert polynomial and B-net form of polynomials on simplex, this paper obtains two theorems of real C〓 piecewise algebraic variety dimensions and the real Nullstellensatz in C〓 spline ring.

4：应用多项式在单纯形上的B-网形式以及文献（[72]）中的实根理想，锥根理想，半代数簇分解定理，本文得出了实C〓分片代数簇的二个维数定理和C〓样条空间的实零点定理。

Secondly,we firstly study the properties of functions with values in a uni-versal Clifford algebra 〓,and we obtain the following very important basictheorems in universal Clifford analysis:Cauchy's integral formula,Cauchy's inte-gral theorem,the mean value theorem,the three versions of the maximum mod-ulus theorem,the Taylor's expansion,the Laurent's expansion and the residuetheorem etc..All of these results generalized the classical results.

第二，本文所讨论的各种函数性质以及所得的结果都在泛Clifford代数〓上所做的工作，它一方面包含了从前在泛Clifford代数〓上所做的工作，所得到的结果更广泛、更漂亮、更自然，另一方面，本文也是迄今为止第一次建立起来了在泛Clifford分析中与经典函数论相对照处基础地位的LR正则函数在特异边界上的Cauchy积分公式、Cauchy积分定理、平均值定理、极大模原理的三种表达形式、Taylor展式、Laurent展式留数定理等深刻的结果。

In this paper,some properties of automorphisms of classical Lie algebras was given first and then a classification of conjugacy automorphisms using only the matrix theory was presented.

首先给出了典型李代数自同构的一些性质，接着用矩阵的形式具体给出典型李代数自同构共轭的充要条件，并计算了任意阶自同构的不动点集。

The paper expounded internal difference between 0/0 of the derivative and of algebra, and discussed in detail the dual nature of 0/0 about algebraic substance of derivative on the basis of the philosophical thought about the concept of the differential quotient of Marx and Engels, and thus answered how derivative itself is converted to differential quotient logically.Then the discussion was extended to the Concept of the partial derivative, and proved that the form of differential quotient converted f...

本文依据马克思、恩格斯关于微商概念的哲学思想，阐述了代数的0/0与导数的0/0的内在差异，并详细讨论了导数的代数实体0/0的双重性质，从而回答了导数本身是如何合平逻辑地转化为微商的问题；其次，把这一讨论推广到偏导数的概念中去，论证了偏导数转化为微商形式的合理性，以及偏微商表述的意义，文中还就微商所牵涉到的形式逻辑与辩证逻辑的问题做了具体分析。

The paper expounded internal difference between 0/0 of the derivative and of algebra, and discussed in detail the dual nature of 0/0 about algebraic substance of derivative on the basis of the philosophical thought about the concept of the differential quotient of Marx and Engels, and thus answered how derivative itself is converted to differential quotient logically.Then the discussion was extended to the Concept of the partial derivative, and proved that the form of differential quotient converted from pa...

本文依据马克思、恩格斯关于微商概念的哲学思想，阐述了代数的0/0与导数的0/0的内在差异，并详细讨论了导数的代数实体0/0的双重性质，从而回答了导数本身是如何合平逻辑地转化为微商的问题；其次，把这一讨论推广到偏导数的概念中去，论证了偏导数转化为微商形式的合理性，以及偏微商表述的意义，文中还就微商所牵涉到的形式逻辑与辩证逻辑的问题做了具体分析。

D Whyte is the first attempt to create a general symbol algebra mathematician, he created the algebraic symbols, by Descartes improved as a modern form.

韦达是第一个试图创立一般符号代数的的数学家，他开创的符号代数，经笛卡尔改进后成为现代的形式。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

We give another form of the infinitesimal time translation operator in algebraic dynamical algorithm so that it is more easy to use new operator to solve evolution equations.

我们给出了求解偏微分演化方程的代数动力学解法中关于时间平移的无穷小算子的构造的另一个形式，使得在应用代数动力学方法求解偏微分方程时更简洁更方便。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了