Mathematical Sciences: The Variational Bicomplex: Theory and Applications
Mathematical Sciences: The Variational Bicomplex: Theory and Applications
批准号:
9100674
负责人:
Ian Anderson
金额:
$6.37万
依托单位:
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1991
资助国家:
美国
项目状态:
已结题
起止时间:
1991-06-01 至 1994-05-31
中文摘要
首席研究员将继续他对变分双复合体的研究。这个理论最初是在大约15年前提出的,它为变分学中的多重积分问题提供了一个统一的方法。双复形也被用于求解变分法中的逆问题。变分复合体在微分方程的几何理论中所起的作用有点类似于有限维流形中deRham复合体所起的作用。这个主题将在研究中发展,应用到具体的例子是动机的主要来源。创建一个“微积分”或形式主义通常是有用的,它可以应用于一个类的大量问题。本研究中所研究的形式主义适用于被称为变分问题的一类问题。这些问题在自然科学的各种情况下都会自然出现。一个简单的例子是,在连接两点的曲面上的所有曲线中,确定一条曲线的长度最短。
英文摘要
The principal investigator will continue his research on the variational bicomplex. This theory was first introduced approximately fifteen years ago to provide a uniform approach to multi-integral problems in the calculus of variations. The bicomplex has also been used to solve inverse problems in calculus of variations. The variational bicomplex plays a role in the geometric theory of differential equations somewhat analogous to the role played by the deRham complex in finite dimensional manifolds. This theme will be developed in the research with application to specific examples a primary source of motivation. It is often useful to create a "calculus" or formalism which can be applied to a large number of problems of a class. The formalism being studied in this research applies to the class of problems known as variational problems. These problems arise naturally in a very wide range of circumstances in natural science. A simple example would be the problem of determining, among all curves on a surface connecting two points, the one with the shortest length.
期刊论文(0)
专著(0)
科研奖励(0)
会议论文
SI2- SSE: Symbolic Toolboxes for Differential Geometry and Mathematical Physics
-
批准号:1642404
-
项目类别:Standard Grant
-
资助金额:$31.42万
-
财政年份:2016
-
负责人:Ian Anderson
-
依托单位:
SI2-SSE: Interdisciplinary Software Infrastructure for Differential Geometry, Lie Theory and their Applications
-
批准号:1148331
-
项目类别:Standard Grant
-
资助金额:$36.08万
-
财政年份:2012
-
负责人:Ian Anderson
-
依托单位:
Collaborative Doctoral 2010 Grant - Reconsidering Access to Material Culture at the Digital Boundary
-
批准号:AH/I505296/1
-
项目类别:Training Grant
-
资助金额:$7.01万
-
财政年份:2010
-
负责人:Ian Anderson
-
依托单位:
The neural basis of treatment-induced remission in depression: an fMRI and pharmacoMRI study
-
批准号:G0601526/1
-
项目类别:Research Grant
-
资助金额:$90.3万
-
财政年份:2007
-
负责人:Ian Anderson
-
依托单位:
Geometric methods for the symbolic integration of differential equations
-
批准号:0713830
-
项目类别:Standard Grant
-
资助金额:$18.46万
-
财政年份:2007
-
负责人:Ian Anderson
-
依托单位:
Multidimensional visualisation of archival finding aids
-
批准号:119340/1
-
项目类别:Research Grant
-
资助金额:$5.4万
-
财政年份:2006
-
负责人:Ian Anderson
-
依托单位:
Symbolic Methods for Classification Problems In Lie Theory and Differential Geometry
-
批准号:0410373
-
项目类别:Standard Grant
-
资助金额:$0.0万
-
财政年份:2004
-
负责人:Ian Anderson
-
依托单位:
Topics in Formal Geometry
-
批准号:9804833
-
项目类别:Continuing Grant
-
资助金额:$12.79万
-
财政年份:1998
-
负责人:Ian Anderson
-
依托单位:
Mathematical Sciences: Constrained Variational Bicomplexes
-
批准号:9403788
-
项目类别:Continuing Grant
-
资助金额:$8.39万
-
财政年份:1994
-
负责人:Ian Anderson
-
依托单位:
Mathematical Sciences: Cohomological Problems in Differential Equations and Mathematical Physics
-
批准号:8702832
-
项目类别:Continuing Grant
-
资助金额:$5.86万
-
财政年份:1987
-
负责人:Ian Anderson
-
依托单位:
Mathematical Sciences: Research Conference On Symmetry Methods In Differential Equations, June 17-23, 1987
-
批准号:8617331
-
项目类别:Standard Grant
-
资助金额:$0.77万
-
财政年份:1987
-
负责人:Ian Anderson
-
依托单位:
Mathematical Sciences: The Variational Bicomplex: Its Role in Differential Geometry and Mathematical Physics
-
批准号:8503768
-
项目类别:Continuing Grant
-
资助金额:$3.17万
-
财政年份:1985
-
负责人:Ian Anderson
-
依托单位:
Research in Applied Mathematics: Further Study of the Inverse Problem in the Calculus of Variations
-
批准号:8104410
-
项目类别:Standard Grant
-
资助金额:$1.02万
-
财政年份:1981
-
负责人:Ian Anderson
-
依托单位:
The Inverse Problem in the Calculus of Variations
-
批准号:8002328
-
项目类别:Standard Grant
-
资助金额:$0.83万
-
财政年份:1980
-
负责人:Ian Anderson
-
依托单位:
国内基金
海外基金
登录
查看更多内容
Handbook of the Mathematics of the Arts and Sciences的中文翻译
-
批准号:12226504
-
项目类别:数学天元基金项目
-
资助金额:20.0万元
-
批准年份:2022
-
负责人:黄朝凌
-
依托单位:
SCIENCE CHINA: Earth Sciences
-
批准号:41224003
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2012
-
负责人:魏建晶
-
依托单位:
Journal of Environmental Sciences
-
批准号:21224005
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2012
-
负责人:冯庆彩
-
依托单位:
SCIENCE CHINA Information Sciences
-
批准号:61224002
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2012
-
负责人:宋扉
-
依托单位:
SCIENCE CHINA Technological Sciences
-
批准号:51224001
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2012
-
负责人:安梅
-
依托单位:
SCIENCE CHINA Life Sciences (中国科学 生命科学)
-
批准号:81024803
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2010
-
负责人:李纪元
-
依托单位:
Journal of Environmental Sciences
-
批准号:21024806
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2010
-
负责人:冯庆彩
-
依托单位:
SCIENCE CHINA Earth Sciences(中国科学:地球科学)
-
批准号:41024801
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2010
-
负责人:魏建晶
-
依托单位:
SCIENCE CHINA Technological Sciences
-
批准号:51024803
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2010
-
负责人:安梅
-
依托单位: