代数化

Tai Chi has algebra contains the contents of the dialectic, and Tai Chi is dialectical logic of algebra and math.

太极代数里包含有辩证的内客，而太极代数是辩证逻辑的数学化。

For a general parametric curve/surface, we usually cannot compute its exact implicit form. Even though its exact implicit form can be computed, the curve/surface implicitization involves relatively complicated computation and the degree is higher. Moreover, it may have unexpected components and self-intersections. All these unsatisfied properties limit the applications of the exact implicitization. So finding curve/surface approximate implicitization has become a practical problem. In this paper, we present an algorithm to solve the approximate implicitization of a given parametric curve by using a quadratic algebraic spline curve.

由于精确隐式化过程不一定可以实现，即使可以实现隐式曲线曲面的阶数高计算复杂，并且具有不希望的自交点和奇异分支，从而限制了隐式化的运用，所以寻求参数曲线曲面的近似隐式化问题成为很实际又重要的问题，提出利用二次代数样条曲线来实现一般平面参数曲线近似隐式化的一种算法。

We present a general method to construct blinding functions of discrete-logarithm-based (simply DL-based) blind signature schemes by analyzing the algebraic form of blinding function, thus solve the problem of blinding DL-based signature schemes completely.

从盲化函数的代数形式入手给出盲化函数的构造方法，完整地解决了基于离散对数数字签名的盲化问题，对可盲化的情况给出统一的最一般的盲化方案，对不可盲化的情况证明其不可盲化。

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。

If the surface isrepresented by an implicit algebraic equation,the mapping can be constructed bythe theory of parametrization of algebraic surfaces;If the surface is represented byan parametric equation,the parameter values on the parameter plane can be solvedby numerical method or Grobner Basis method.

若曲面由代数隐式方程给出，可通过代数曲面参数化理论构造映射；若曲面由参数方程给出，可通过数值方法或Grobner基方法求解参数型值点。

Let L and P be Lie color algebras and let M be a graded module over P, the crossed modules which make M as their kernal and P as their cokernal are considered. It is shown that under a suitable equivalent relation, there is a bijection between the set of the equivalent classes CML and the homogeneous components of degree zero of H~3.

从交叉模的定义出发，对于给定的Lie color代数L，P以及阶化P模M，考虑所有以M为核、以P为余核的L的交叉模，在这些交叉模之间定义了一个等价关系，由此得到交叉模的等价类集CML，证明了CML与三维上同调群H~3的零次齐次部分之间存在一一对应，从而可以利用三维上同调群对Lie color代数的交叉模进行分类。

In [3], Kassel gaveHopf *-algebra structures on GL_q(2) and SL_q (2), and also described those on thequantum enveloping algebra U_qsl(2 in detail.

Kassel在[3]中给出了GL_q(2)和SL_q(2)上的Hopf *-代数结构，并且对量子化包络代数U_q sl

It is shown that if L is a subalgebra of a Lie color algebra Q, then Q is an algebra of quotients of L if and only if Q is ideally absorbed into L.

利用没有非零零化子的理想对Lie color代数的商代数进行刻画，证明了：若L为Lie color代数Q的子代数，则Q为L的商代数当且仅当Q理想吸收于L。

We introduce the notion of characteristic pairs and give the definition of dual characteristic pairs of Dirac structures on Lie bialgebroids. Using the dual characteristic pairs, we give the if and only if conditions for which a maximally isotropic subbundle of the double of a Lie bialgebroid is a Dirac structure.

本文在李双代数胚上，引入了Dirac结构的特征对并给出对偶特征对的概念，利用对偶特征对，给出李双代数胚double的极大迷向子丛是Dirac结构的充要条件；其次，分别利用特征对与对偶特征对，将可约Dirac结构分为第一类可约与第二类可约，在此基础上，建立Poisson流形的两类对应约化定理。

Let 〓 be a finite-dimensional Z-graded Lie superalgebra.Weprove that if L has a non-degenerate trace form then s=r.Using the result,weobtain that the Killing forms of Lie superalgebras of Cartan type are degenerate.

本文得出如果有限维单Z-阶化李超代数L=〓具有非退化迹型〓，则s=r，由此可推出Cartan型李超代数的killing型是退化的。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷