论文标题
部分可观测时空混沌系统的无模型预测
Harrison center and products of sums of powers
论文作者
论文摘要
本文主要与\ [（x_1^d + x_2^d + \ cdots + x_r^d）（y_1^d + y_2^d + y_2^d + \ cdots y_n^d）= z_1^d + z_2 + z_2^d + cdots + cdots + z_n^d \ \ cdots $ d> d> d> 2，$ x__________________________________________________1， $ y =（y_1，y_2，\ dots，y_n）$是不确定的系统，每种$ z_k $都是$ y $的线性形式，在$ y $中具有合理函数字段中的系数$ \ k（x）$上的任何字段$ \ k $ \ k $ \ k $ 0 $ 0 $或大于$ d。和Pfister。我们表明，至少$ 3 $的学位能力总和的构图身份是微不足道的，即，如果$ d> 2，$ r = 1。
This paper is mainly concerned with identities like \[ (x_1^d + x_2^d + \cdots + x_r^d) (y_1^d + y_2^d + \cdots y_n^d) = z_1^d + z_2^d + \cdots + z_n^d \] where $d>2,$ $x=(x_1, x_2, \dots, x_r)$ and $y=(y_1, y_2, \dots, y_n)$ are systems of indeterminates and each $z_k$ is a linear form in $y$ with coefficients in the rational function field $\k (x)$ over any field $\k$ of characteristic $0$ or greater than $d.$ These identities are higher degree analogue of the well-known composition formulas of sums of squares of Hurwitz, Radon and Pfister. We show that such composition identities of sums of powers of degree at least $3$ are trivial, i.e., if $d>2,$ then $r=1.$ Our proof is simple and elementary, in which the crux is Harrison's center theory of homogeneous polynomials.
