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| 1 | 扩大设计的中心化L_2-偏差的新下界显示文摘在构造两水平因子设计时,折叠反转是非常有用的技巧.折叠反转设计是通过改变初始设计中一个或多个因子的符号产生的跟随设计.通过把折叠反转设计中的处理加到初始设计中所得到的设计称为扩大设计.本文中,我们应用条件极值的方法得到了一般折叠反转方案下扩大设计在中心化L_2-偏差下一个新的下界,它可以作为寻找最优折叠反转方案的一个基准. | 雷轶菊 欧祖军 | 2017 | 应用数学学报2017，40，6： | 1 |
| 2 | A Note on Optimal Foldover Four-level Factorials显示文摘The foldover is a quick and useful technique in construction of fractional factorial designs,which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L2-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L2-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided,where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient algorithms for searching the optimal four-level foldover plans. | A.M.ELSAWAH M.A.AL-AWADY M.A.ABD ELGAWAD Hong QIN | 2016 | Acta Mathematica Sinica,English Series2016，32，3： | 1 |
| 3 | Effective Lower Bounds of Wrap-Around L_2-Discrepancy on Three-Level Combined Designs显示文摘How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions.This paper takes the wrap-around L_2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L_2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs. | ELSAWAH A.M. HU Jianwei QIN Hong | 2017 | Journal of Systems Science & Complexity2017，30，6： | 0 |
| 4 | 两水平扩大设计基于中心化L2-偏差的均匀性显示文摘基于中心化L2-偏差讨论了两水平扩大设计的均匀性,获得了两水平扩大设计中心化L2-偏差的一个新的下界,该下界可作为寻找最优折叠反转方案的一个基准. | 李洁 欧祖军 | 2020 | 吉首大学学报(自然科学版)2020，41，2： | 0 |
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