Vector Spaces and Kirchhoff Graphs

该项目涉及化学，电化学和生化反应网络，通过这些网络的反应路线（反应途径），以及使用Kirchhoff图描述这些网络。这项工作将建立在反应路径的向量空间方法上，以确定任何给定的反应网络存在一个或多个基尔霍夫图，并开发构建这些图的方法。对于任意反应网络，这两个结果都不明显。该项目的结果将大大有助于对反应网络的基本理解，并有可能应用于燃料电池和其他涉及复杂化学反应网络的设备的设计。

This project concerns chemical, electrochemical, and biochemical reaction networks, reaction routes (reaction pathways) through these networks, and the depiction of these networks using Kirchhoff graphs. This work will build on a vector space approach to reaction routes to establish that one or more Kirchhoff graphs exist for any given reaction network and to develop a method for constructing these graphs. Neither of these results is obvious for arbitrary reaction networks. Results of the project will significantly aid fundamental understanding of reaction networks and have potential application to the design of fuel cells and other devices involving complicated chemical reaction networks.