查询词典 algebraic fraction

The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a number of basic concepts and examples.

全书共分七章，前三章是基础知识部分；后四章是本书的核心部分，总结了近年来代数几何码的最新研究成果，并且包含了作者的一些尚未发表的结果。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

Difference from other algebraic structures which are introduced for some logic system, Implication Algebra is a abstraction of one logic connective, i. e. implicative operator, and other operators in it are all introduced by implicative operator.

特别值得提出的是，与其它为研究逻辑系统而引入的代数结构不同，蕴涵代数是对一个逻辑联结词，即蕴涵算子抽象而得到的，其它算子均是由蕴涵算子诱导而得到。

In this paper, we discuss some kinds of special filters and congruence relation in fuzzy algebraic system MTL which is used extensively. The conceptions of the special filter are fuzzified in terms of the fuzzy set of Zadehs theories and further study them by way of logic algebra of n-value.

本文在具有广泛应用的模糊逻辑代数系统MTL-代数中，讨论了几类特殊滤子和同余关系，并且进一步用多值逻辑代数的方法研究它们。

It reflects the algebra in other algebraic structure of the basic idea.

它体现了代数学中研究其他代数结构的基本思路。

As an important algebraic tool, DG algebra turns out to be very important.

作为一个重要的代数工具，日益显示出其重要价值。

They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations.

它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。

They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differ tial equations.

它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。

Since there are special courses devoted to commutative algebra and algebraic geometry, these parts are not included in the present course.

因此选择的内容应有普适性、示范性、基础性、重要性和可教性。过于专门化的理论或细节不是这门课的任务。

The thesis studies the formation of several basic algebraic terms such as "algebra","equation" in the book of Elements of Algebra and Algebra.

本文的研究表明，术语与其所表述的数学内容之间的差异反映当时数学术语在翻译时不能保证单义性和系统性。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。