For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation inde...For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.展开更多
This paper is made out of necessity as a doctoral student taking the exam from Lie groups. Using the literature suggested to me by the professor, I felt the need to, in addition to that literature, and since there was...This paper is made out of necessity as a doctoral student taking the exam from Lie groups. Using the literature suggested to me by the professor, I felt the need to, in addition to that literature, and since there was more superficial in that book with some remarks about the examples given in relation to the left group. I decided to try a little harder and collect as much literature as possible, both for the needs of me and the others who will take after me. Searching for literature in my mother tongue I could not find anything, in English as someone who comes from a small country like Montenegro, all I could find was through the internet. I decided to gather what I could find from the literature in my own way and to my observation and make this kind of work. The main content of this paper is to present the Lie group in the simplest way. Before and before I started writing or collecting about Lie groups, it was necessary to say something about groups and subgroups that are taught in basic studies in algebra. In them I cited several deficits and an example. The following content of the paper is related to Lie groups primarily concerning the definition of examples such as <i>The General Linear Group GL(n, R)</i>, The <i>Complex General Linear Group GL(n, C)</i>, <i>The Special Linear Group SL(n, R)=SL(V)</i>, <i>The Complex Special Linear Group SL(n, C)</i>, <i>Unitary and Orthogonal Groups</i>, <i>Symplectic Group</i>, <i>The groups R*, C*, S<sup>1</sup> and R<sup>n</sup></i> and others. In addition, invariant vector fields and the exponential map and the lie algebra of a lie group. For me, this work has the significance of being useful to all who need it.展开更多
In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
In this paper,some existence results for the fourth order nonlinear subelliptic equations on the Heisenberg group are given by means of variational methods.
The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we ...The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.展开更多
村庄规划基础数据库涉及大量的空间数据,并且来源较广,通常采用遥感、测量等手段获取,存在一定的误差和不确定性。为此,提出基于三维地理信息系统(Geographic Information System,GIS)建模的实用型村庄规划基础数据库设计。遵循相关的...村庄规划基础数据库涉及大量的空间数据,并且来源较广,通常采用遥感、测量等手段获取,存在一定的误差和不确定性。为此,提出基于三维地理信息系统(Geographic Information System,GIS)建模的实用型村庄规划基础数据库设计。遵循相关的编码标准对村庄规划基础数据编码,采用多元组构建编码的村庄规划基础数据模型,并对村庄规划基础数据模型中的每类数据属性进行设定。以村庄规划图为底图,根据数据模型中各类村庄规划的基础数据属性,对空间数据进行矢量化处理,提取村庄规划二维坐标信息;采用三维GIS建模技术构建村庄规划地理空间三维模型,并对其进行消差处理,通过ArcCatalog导入数据库中,完成实用性村庄规划基础数据库设计。实验结果表明,设计数据库响应时间在123.42~142.65 ms范围内,输出点与真实点误差为±0.01 m,具有良好的适应性。展开更多
文摘For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.
基金Supported by National Basic Research Program of China （973 Program） （2005CB321902） National Natural Science Foundation of China （90916024,60727002,60774003）+1 种基金 the Ph.D. Programs Foundation of Ministry of Education of China （20030006003） the Commission on Science,Technology,and Industry for National Defense （A2120061303）
文摘This paper is made out of necessity as a doctoral student taking the exam from Lie groups. Using the literature suggested to me by the professor, I felt the need to, in addition to that literature, and since there was more superficial in that book with some remarks about the examples given in relation to the left group. I decided to try a little harder and collect as much literature as possible, both for the needs of me and the others who will take after me. Searching for literature in my mother tongue I could not find anything, in English as someone who comes from a small country like Montenegro, all I could find was through the internet. I decided to gather what I could find from the literature in my own way and to my observation and make this kind of work. The main content of this paper is to present the Lie group in the simplest way. Before and before I started writing or collecting about Lie groups, it was necessary to say something about groups and subgroups that are taught in basic studies in algebra. In them I cited several deficits and an example. The following content of the paper is related to Lie groups primarily concerning the definition of examples such as <i>The General Linear Group GL(n, R)</i>, The <i>Complex General Linear Group GL(n, C)</i>, <i>The Special Linear Group SL(n, R)=SL(V)</i>, <i>The Complex Special Linear Group SL(n, C)</i>, <i>Unitary and Orthogonal Groups</i>, <i>Symplectic Group</i>, <i>The groups R*, C*, S<sup>1</sup> and R<sup>n</sup></i> and others. In addition, invariant vector fields and the exponential map and the lie algebra of a lie group. For me, this work has the significance of being useful to all who need it.
文摘In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
文摘In this paper,some existence results for the fourth order nonlinear subelliptic equations on the Heisenberg group are given by means of variational methods.
文摘The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.
文摘村庄规划基础数据库涉及大量的空间数据,并且来源较广,通常采用遥感、测量等手段获取,存在一定的误差和不确定性。为此,提出基于三维地理信息系统(Geographic Information System,GIS)建模的实用型村庄规划基础数据库设计。遵循相关的编码标准对村庄规划基础数据编码,采用多元组构建编码的村庄规划基础数据模型,并对村庄规划基础数据模型中的每类数据属性进行设定。以村庄规划图为底图,根据数据模型中各类村庄规划的基础数据属性,对空间数据进行矢量化处理,提取村庄规划二维坐标信息;采用三维GIS建模技术构建村庄规划地理空间三维模型,并对其进行消差处理,通过ArcCatalog导入数据库中,完成实用性村庄规划基础数据库设计。实验结果表明,设计数据库响应时间在123.42~142.65 ms范围内,输出点与真实点误差为±0.01 m,具有良好的适应性。
