论文标题
部分可观测时空混沌系统的无模型预测
On symmetric Tetranacci polynomials in mathematics and physics
论文作者
论文摘要
在本手稿中，我们通过考虑非统一系数和递归定义中的非统一初始值，引入（对称）四acci多项式$ξ_j$作为对普通Tetranacci数字的双重概括。这些多项式的问题出现在凝结物理学和对角线的对角线化矩阵中，总共具有四个非对角线的四个非零。对于后者，对称四acci多项式是相关特征向量的基本实体。因此，处理递归结构也决定了特征值。随后，我们为任何对称四acci多项式提供了完整的闭合形式表达式。关键特征是在广义斐波那契多项式方面的分解。
In this manuscript, we introduce (symmetric) Tetranacci polynomials $ξ_j$ as a twofold generalization of ordinary Tetranacci numbers, by considering both non unity coefficients and generic initial values in their recursive definition. The issue of these polynomials arose in condensed matter physics and the diagonalization of symmetric Toeplitz matrices having in total four non-zero off diagonals. For the latter, the symmetric Tetranacci polynomials are the basic entities of the associated eigenvectors; thus, treating the recursive structure determines the eigenvalues as well. Subsequently, we present a complete closed form expression for any symmetric Tetranacci polynomial. The key feature is a decomposition in terms of generalized Fibonacci polynomials.
