论文标题
部分可观测时空混沌系统的无模型预测
Square-weighted zero-sum constants
论文作者
论文摘要
令$ a \ subseteq \ mathbb z_n $为子集。 $ s =（x_1，\ ldots，x_k）$ in $ \ mathbb z_n $中的$ a $ a $ a $ a _1，\ ldots，a_k \ a_k \ a_1x_1+a_1x_1+\ cdots+a_kx_kx_kx_kx_k = 0 $。在正方形的情况下，我们是指$ \ mathbb z_n $中的非零平方。我们确定了最小的自然数$ k $，以便每序列为$ k $的$ \ mathbb z_n $中的每个序列，都有一个平方加权的零和子序列。我们还确定了最小的自然数量$ k $，以便每个序列的长度为$ k $中的$ \ mathbb z_n $，具有一个平方加权的零和子序列，其术语是给定序列的连续项。
Let $A\subseteq \mathbb Z_n$ be a subset. A sequence $S=(x_1,\ldots,x_k)$ in $\mathbb Z_n$ is said to be an $A$-weighted zero-sum sequence if there exist $a_1,\ldots,a_k\in A$ such that $a_1x_1+\cdots+a_kx_k=0$. By a square, we shall mean a non-zero square in $\mathbb Z_n$. We determine the smallest natural number $k$, such that every sequence in $\mathbb Z_n$ whose length is $k$, has a square-weighted zero-sum subsequence. We also determine the smallest natural number $k$, such that every sequence in $\mathbb Z_n$ whose length is $k$, has a square-weighted zero-sum subsequence whose terms are consecutive terms of the given sequence.
