论

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 paper applies algebraic geometry, computational geometry, approximation theory to study the following problems: the Nother type theory and the Riemann-Roch type theory of the piecewise algebraic curve; the number of real intersection points of piecewise algebraic curves; the real piecewise algebraic variety and the B-net resultant of polynomials.

本文应用代数几何，计算几何，函数逼近论等学科的基本理论，分别就分片代数曲线的Nother型与Riemann-Roch型定理；分片代数曲线的实交点数；实分片代数簇以及多项式的B-网结式进行研究。

It's really the natural setting for algebraic topology because the traditional algebraic invariants (fundamental group, homolog group,etc.) arc isomorphic not only for homeomorphic spaces but for spaces of the same homotopy type. Homtopy epimorphisms and monomorphisms are special morphisms in the category of topological spaces and the initial research of them may be traceable to S.T.

同伦论的本质是利用比同胚关系更广泛的等价关系—同伦关系来对拓扑空间进行研究，这也是代数拓扑研究中一种自然的考虑，因为传统的代数不变量不仅在同胚的空间之间保持同构，而且在具有相同伦型的空间之间也保持同构。

Prime ideal decomposition is an important problem in algebraic number theory and is relative closely with the class field theory and so on.

素理想分解问题是代数数论中的一个重要课题，它与类域论的关系极为密切，因而如何判断K的素理想在K的有限扩张中的分解状况是一个十分有意义的问题。

In this thesis we investigate the algebraic structure of the plus cupping degrees.

在这篇论文中，我们主要致力于研究加杯度的代数结构。

The purpose of this thesis is to collect the known results in graph theory with algebraic techniques involved.

这篇论文的目的主要是收集了已知的图论上使用的代数方法。

In this thesis, we propose a new algorithm to overcome the problem.

在本论文中，我们将提出一个新的演算法来解决这个问题。

In the course of algorithmization, we should select arithmetic with high numerical stability and controlling error and computational effort little and saving memory space.

建立模块化仿真模型时，本文通过模型算法的模块化平台一仿真支撑系统BLINK，把算法进行单独的模块太原理工大学硕士学位论文化处理，通过算法来构造仿真模块，实现模块的搭建和组合。

Huxley says that the doctrine of Biogenesis is victorious all along the line, and Tyndall is compelled to say:'I affirm that no shred of trustworthy evidence exists to prove that life in our day has ever appeared independent of antecedent life.

赫胥黎说过，生源论的信条放诸四海而皆准，丁铎尔也不得不宣布："我承认，没有一丝一缕的确凿证据，可以证明我们今天所能见到的生命是与更早的生命毫不相关的。"

Through the argument, we can see that "Allais paradox" has an important influence on the development of expected utility theory.

通过论述可以看出，"Allais悖论"对于期望效用理论的发展具有重大而深远的影响。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新