摘要翻译：
每个分式都是点的并集，这些点是平凡的正则分式。为了刻画非平凡分解，我们导出了包含正则分式的一个条件，如下所示。设$f=\sum_\alpha b_\alpha x^\alpha是一个泛型分数的指示多项式，参见Fontana et al,JSPI 2000,149-172。正则分式的特征为$R=\frac1L\sum_{\alpha\in\mathcal L}E_\alpha X^\alpha$,其中$\alpha\mapsto E_\alpha$是从$\mathcal L\子集\mathbb Z_2^d$到$\{-1,+1\}$的群同胚。规则$R$是分数$F$的子集，如果$fr=R$，它又相当于$\sum_t F(t)R(t)=\sum_t R(t)$。如果$\mathcal H=\{\alpha_1>...\alpha_k\}$是$\mathcal l$的生成集，且$r=\frac1{2^k}(1+e_1x^{\alpha_1}）...(1+e_kx^{\alpha_k}）$,$e_j=\pm 1$,$j=1...k$,则$b_\alpha$的包含条件为%\begin{方程}b_0+e_1 b_{\alpha_1}+>...+e_1...e_k b_{\alpha_1+...+\alpha_k}=1。\tag{*}\end{方程}%本文的最后一部分将讨论一些例子来研究前面条件(*)的实际适用性。本文是美国铝业公司158号欧盟研究合同的成果，该合同涉及旅游统计抽样调查的序贯设计规划。
---
英文标题：
《2-level fractional factorial designs which are the union of non trivial
  regular designs》
---
作者：
Roberto Fontana and Giovanni Pistone
---
最新提交年份：
2007
---
分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
--

---
英文摘要：
  Every fraction is a union of points, which are trivial regular fractions. To characterize non trivial decomposition, we derive a condition for the inclusion of a regular fraction as follows. Let $F = \sum_\alpha b_\alpha X^\alpha$ be the indicator polynomial of a generic fraction, see Fontana et al, JSPI 2000, 149-172. Regular fractions are characterized by $R = \frac 1l \sum_{\alpha \in \mathcal L} e_\alpha X^\alpha$, where $\alpha \mapsto e_\alpha$ is an group homeomorphism from $\mathcal L \subset \mathbb Z_2^d$ into $\{-1,+1\}$. The regular $R$ is a subset of the fraction $F$ if $FR = R$, which in turn is equivalent to $\sum_t F(t)R(t) = \sum_t R(t)$. If $\mathcal H = \{\alpha_1 >... \alpha_k\}$ is a generating set of $\mathcal L$, and $R = \frac1{2^k}(1 + e_1X^{\alpha_1}) ... (1 + e_kX^{\alpha_k})$, $e_j = \pm 1$, $j=1 ... k$, the inclusion condition in term of the $b_\alpha$'s is % \begin{equation}b_0 + e_1 b_{\alpha_1} + >... + e_1 ... e_k b_{\alpha_1 + ... + \alpha_k} = 1. \tag{*}\end{equation} % The last part of the paper will discuss some examples to investigate the practical applicability of the previous condition (*).   This paper is an offspring of the Alcotra 158 EU research contract on the planning of sequential designs for sample surveys in tourism statistics.
---
PDF链接：
https://arxiv.org/pdf/710.5838