论文标题
部分可观测时空混沌系统的无模型预测
An Infinite 2-Dimensional Array Associated With Electric Circuits
论文作者
论文摘要
除了Koshy专门针对斐波那契数字应用于电路的Koshy外，大多数书籍和Fibonacci季刊都对图形和电路的应用相对静默，以对纤维纳基数字。本文通过介绍和研究电路阵列（一个无限的二维阵列，其条目是电阻标记与图形家族相关的电路的电阻边缘值，该论文延续了研究图，电路和斐波那契数的相互作用的论文趋势。电路阵列具有几个功能，将其与其他更熟悉的阵列（例如二项式阵列和Wythoff数组）区分开。例如，可以证明Modulo是一个有力支持的猜想，即其最左侧对角线的分子不能满足任何线性，同质的，递归，并具有恒定系数（LHRCC）。但是，我们在支持数值证据的情况下猜想了涉及电路阵列左侧对角线满足的$π$的渐近公式。
Except for Koshy who devotes seven pages to applications of Fibonacci Numbers to electric circuits, most books and the Fibonacci Quarterly have been relatively silent on applications of graphs and electric circuits to Fibonacci numbers. This paper continues a recent trend of papers studying the interplay of graphs, circuits, and Fibonacci numbers by presenting and studying the Circuit Array, an infinite 2-dimensional array whose entries are electric resistances labelling edge values of circuits associated with a family of graphs. The Circuit Array has several features distinguishing it from other more familiar arrays such as the Binomial Array and Wythoff Array. For example, it can be proven modulo a strongly supported conjecture that the numerators of its left-most diagonal do not satisfy any linear, homogeneous, recursion, with constant coefficients (LHRCC). However, we conjecture with supporting numerical evidence an asymptotic formula involving $π$ satisfied by the left-most diagonal of the Circuit Array.
