符号矩阵和某些Jacobi行列式的行列式展开式
Determinant Expansions of Signed Matrices and of Certain Jacobians
摘要：
本文讨论两个问题：矩阵的符号模式和雅可比矩阵的某些映射。主要的题目是计算正负号模式的行列式展开式和雅可比行列式中正负系数的个数。本文的动机是由Craciun和Feinberg发起的化学网络的方法。我们还给出了一个图论测试确定时的雅可比矩阵的化学反应动力学有一个符号模式。
英文摘要：
This paper treats two topics: matrices with sign patterns and Jacobians of certain mappings. The main topic is counting the number of plus and minus coefficients in the determinant expansion of sign patterns and of these Jacobians. The paper is motivated by an approach to chemical networks initiated by Craciun and Feinberg. We also give a graph-theoretic test for determining when the Jacobian of a chemical reaction dynamics has a sign pattern.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
