代数形式

This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering.

本书试图提供外微分形式、微分几何、代数拓扑、微分拓扑、李群、向量丛、Chern公式等前沿知识，它们对于深入理解经典物理、现代物理以及工程都是必需的。

It is sometimes easier to use quaternions with complex elements, leading to a form that is not a division algebra.

有时候采用带有复数元素之四元数会比较容易，导得结果不为除法代数之形式。

Applying the vector representation of formula for definite proportional division point in vector algebra,this paper obtains a new useful method of compunction for segment ratio in volume ratio .

利用向量代数中定比分点公式的向量形式，给出了一种非常简明有用的求容积比中线段比的新方法。

For example,a generalization of linear algebra is developed in which "convex bifunctions" are the analogues of linear transformations,and "inner products" of convex sets and functions are defined in terms of the extremal values in Fenchel's Duality Theorem.

例如，一类线性代数的推广形式在凸双重函数中发展起来，而凸双重函数是线性变换的类似情况，凸集和凸函数的内积是根据 Fenchel 对偶理论的极值定义的。

Meanwhile this dissertation points out the form and properties of basic symmetric function、simple symmetric function and basic CRM symmetric function in OR-Coincidence algebra system, discusses the relations and transform methods among the coefficients of the three kinds of symmetric functions.

提出了在或、符合代数系统中基本对称函数、简单对称函数及基本CRM对称函数的形式及性质，并详细讨论了对称函数三种展开式系数之间的关系和各种转换方法。

Based on the Saint-venant equations describing the channel flow movement, the nonlinear algebraic equations derived by the use of Preissmann weighted implicit four-point scheme are solved with the Netwon-Raphson method. A combined Gauss main-element elimination method with compress-storage technique is proposed. The relaxation iterative method for solving branch river networks is extended, which can turn the problem of any complex river networks into the problem of a series of single rivers. The coupling of hydraulic model with water quality model is built up. The combined model was applied to a large complicated river networks with numerical hydraulic structure which influenced by strong tide, storm and heave rain. Visualization of computational results is realized by means of MapInfo, which displays the computational results in fast, convenient and accurate way.

水力模型以描述河道洪水波运动的Saint-Venant方程组为基础，用Newton-Raphson方法直接求解按Preissmann加权四点格式进行离散所得的非线性代数方程组，提出了压缩存贮形式的Gauss列主元消去法并对数值解的收敛性进行了讨论；将支流流量的松弛迭代方法从树状河系推广到了环状河网，使任意复杂河网水力计算的问题都可化为一系列的单一河道的水力计算问题；建立了水力模型与水质模型的联接，初步应用于既有洪水、暴雨、强潮等综合影响，又存在多种水工建筑物及水力调度问题的大型复杂河网中的非恒定流水力、水质计算问题；利用MapInfo对计算结果的可视化进行了研究，有利于决策者快速、方便、准确地作出决策。

By use of the relationships between the hermite polynomial and the laguerre polynomial, the eigenequations of one-dimensional harmonic oscillator and hydrogen atom are conversed into the same equations in form.

同时本文利用SU(1，1)代数将二维、三维情况下的谐振子同加了反平方势的氢原子分别表示成具有相同形式的两算符下的本征值方程，从而得出

By using the techniques of an explicit criterion to determine the number of real roots of a univariate polynomial in ( [13] , [73] ); B-net form of bivariate splines function; discriminant sequence of polynomial (cf. [13] , [73] ) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence, this paper determines the number of real intersection points two piecewise algebraic curves whose common points are finite.

3：利用杨路，张景中，侯晓荣在文献（[13]，[73]）中关于一元多项式实根的显式判准，以及二元样条函数的B-网形式，多项式的判别序列和Sturm序列的最高次数项系数序列的变号数，本文给出了两个分片代数曲线的实交点数的计算公式。

In order to introduce the formal techniques such as stepwise refinement, automatic transformation and testing based on formal specification to the multimedia field, we first present a powerful subset of Allen's interval algebra as the temporal specification language to multimedia program.

为了在多媒体领域中应用逐步求精、程序自动生成和面向形式规范的并发系统测试等形式化技术，本文首先研究一个表达能力足够的Allen区间代数的子集合，以它作为多媒体对象时序关系的描述语言。

So, in the past decade the single-, two- and multi-mode bosonic realizations of the SU(1,1) Lie algebra have been receiving a lot of attention.

因此，在过去几十年内，人们大量讨论了单模，双模和多模SU(1，1)李代数的玻色子算符实现形式。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。