代数几何

First we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator corresponding to the model, second prove that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity and algebraic multiplicity one,last by using theabove results we obtain that the time-dependent solution of the model str.

首先证明在虚轴上除了0以外其他所有点都属于该算子的豫解集，其次证明0是对应于该系统的主算子及其共轭算子的几何与代数重数为1的特征值，由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解。

We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition , substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

Specify what status the spatial operator algebra locates at in many methods of multibody systems dynamics formulations and what the relations are between the spatial operator algebra and other dynamics formulations.We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition, substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

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。

Mathematics An algebraic or geometric expression from which another expression is derived.

原始的：一种代数的或几何的表达，基于此派生出另一种表达

An algebraic or geometric expression from which another expression is derived.

原始的一种代数的或几何的表达，基于此派生出另一种表达

Mathematics being an algebraic or geometric expression from which another expression is derived.

指其他表达式是从中派生出来的代数或者几何表达式。

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。

There were many champions of synthetic geometry , Euclid-style development of projective geometry, in the nineteenth century, Jakob Steiner being a particularly brilliant figure.

该模型的欧几里得的要素，发展的几何连接作为一个不言自明的制度，是在紧张与笛卡尔的减少几何代数通过坐标系统。

There are three main methods in face localization: localization according to face outline, localization according to complexion and localization according to templates constructed by some standard sample images. As to feature extraction, it can be divided into two parts because face features can be divided into geometrical features and algebraic features. While extracting geometrical features, the features of eyes, nose, mouth, eyebrows can be gained by some image processes: binary, sharpen, smooth, projection, calculating gradient and so on. In order to extract algebraic features, we can do some mathematical transformation for the digital images such as singular value decomposition, K-L transformation.

在人脸检测部分，目前存在的方法有利用人脸的几何轮廓进行检测、利用人脸的肤色信息进行检测、构造标准人脸模板进行匹配检测等等；在人脸特征提取部分，可以用一些图像处理的方法如投影、二值化、求梯度图像等提取人脸中各特征器官如眼睛、鼻子、嘴巴等的几何特征，另外也可以借助于数学变换，求取人脸图像的一些代数特征，如对图像进行奇异值分解，以奇异值代表图象的特征，或对图像进行K-L变换，以图像在构造的特征空间上的投影系数作为图像的特征等；在识别部分，可以通过距离度量或相似度来判断输入图像与样本图像的匹配程度，还可以通过神经网络方法进行人脸的识别。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。