论文标题
基希霍夫（Kirchhoff）关于网络双曲线保护法的第一定律证明
A Proof of Kirchhoff's First Law for Hyperbolic Conservation Laws on Networks
论文作者
论文摘要
网络是许多应用程序中的重要模型，例如信息技术，化学，电力系统，运输，神经科学和社会科学。鉴于如此广泛的适用性，网络上动态系统的一般理论可以捕获共享的概念，并为推导抽象属性提供了设置。为此，我们为建模为抽象度量空间的网络开发了一个演算，并得出了基希霍夫（Kirchhoff）的第一定律的双曲线保护法律。在网络上的动态系统中，基尔乔夫的第一定律通过陈述其等效性来连接抽象全局对象的研究以及计算偏边的欧几里得观点的研究。特别是，我们的结果表明，可以在没有明确的Kirchhoff型边界条件的情况下说明网络上的双曲线保护法。
Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on networks may capture shared concepts, and provide a setting for deriving abstract properties. To this end, we develop a calculus for networks modeled as abstract metric spaces and derive an analog of Kirchhoff's first law for hyperbolic conservation laws. In dynamical systems on networks, Kirchhoff's first law connects the study of abstract global objects, and that of a computationally-beneficial edgewise-Euclidean perspective by stating its equivalence. In particular, our results show that hyperbolic conservation laws on networks can be stated without explicit Kirchhoff-type boundary conditions.
