The unified processing and research of multiple network models are implemented, and a new theoretical advance has been made, which sets up two new theorems on evaluating the exact electrical characteristics (potential and resistance) of the complex m × n resistor networks by the recursion-transform method with potential parameters, and applies to a variety of different types of lattice structure with arbitrary boundaries such as the nonregular m × n rectangular networks and the nonregular m × n cylindrical networks. Our research gives the analytical solutions of electrical characteristics of the complex networks (finite, semi-infinite and infinite), which has not been solved before. As applications of the theorems, a series of analytical solutions of potential and resistance of the complex resistor networks are discovered.

中文翻译：

---

m×n电阻网络的基本原理

实现了多种网络模型的统一处理和研究，并取得了新的理论进展，它建立了两个新的定理，用于通过递归计算评估复杂的m×n电阻器网络的精确电气特性（电势和电阻）。具有潜在参数的变换方法，并应用于具有任意边界的各种不同类型的晶格结构，例如非规则m×n矩形网络和非规则m×n圆柱网络。我们的研究给出了复杂网络（有限，半无限和无限）的电气特性的解析解，这是以前从未解决过的。作为定理的应用，发现了一系列复杂电阻网络的电势和电阻的解析解。