查询词典 algebraic geometry

In this paper, we discuss effect algebra and related topics. The main results are the following:1. Effect algebra is a commutative algebraic structure. To get a non-commutative algebraic structure.we introduced the concepts of left difference and right difference, and we also introduced the concept of the Bi-difference sets, the concept of pseudo-difference poset, and proved that pseudo-difference poset is equivalent to pseudo-effect algebra.

效应代数描述的是具有交换性的量子系统，我们借助于差运算的思想研究了不可交换的量子逻辑结构，建立了左差、右差、伪差偏序集、双差集等概念，证明了伪差偏序集与伪效应代数等价，并得到了双差集的幺半群表示定理。

By using properties of scalar matrices over semirings,we generalize algebraic properties for the automorphisms of matrix algebras over commutative rings and obtain some algebraic properties for the automorphisms of matrix algebras over commutative semirings.

在这一章中，我们首先利用半环上常量矩阵的性质把环上矩阵代数的性质拓广到半环上，获得了交换半环上矩阵代数自同构的一些代数性质，接下来采用积和式的方法证明任意非负交换半环上n阶矩阵代数Tn的自同构的n次幂必为内自同构。

This book provides an introduction to abstract algebraic geometry using the methods of schemes and cohomology.

代数几何学是数学中的重要分支之一，编码理论则是起源于工程技术的应用数学分支，本书是研究这两个分支的完美结合――代数几何码的一本专著。

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。

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。

In this paper, multivariate Lagrange interpolation problems are systemically discussed,and through amending Cramer Strange Proposition and proving interpolation theory, the geometry construction of the properly posed sets of nodes along the plane algebraic curve is studied, at the same time, a number of practical constructing methods are given.

本文系统阐述了多元Lagrange插值问题，通过修正Cramer奇论并用插值法加以证明，进一步对沿平面代数曲线插值唯一可解点组的几何结构进行深入的研究，同时得到了一些实用性较强的构造方法。

The findings show how the students understanding the concept of complex number and other related concepts:(1) The concepts of complex number is understood from the perspective of algebraic expression;(2) The concepts of complex number is understood from the perspective of geometry;(3) The concepts of complex number is understood comprehensively.

结果显示，学生对复数及其一些概念的理解呈现三个侧面：（1）代数式子意义上理解的复数；（2）几何意义上理解的复数；（3）整体意义上理解的复数。

Or think of it as an algebraic extension of your geometry system.

或者考虑把该软件作为几何系统的代数扩展。

This is a genuine introduction to algebraic geometry.

这是一个真正介绍代数几何。

It is important to study the interpolation by multivariatesplines and algebraic geometry etc.

因此，研究分片代数簇是很重要的。

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。