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应用数学学报  1993, Vol. 16 Issue (4): 442-451    DOI:
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偶数阶循环拉丁方型均匀设计的构作
陈瑞琛
扬州师范学院数学系, 扬州市 225002
CONSTRUCTION OF HOMOGENEOUS DESIGNS OF CYCLIC LATIN SQUARE TYPE WITH EVEN ORDER
CHEN RUI-CHEN
Department of Mathematics, Yangzhou Teacher's College, Yangzhou 225002
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摘要 均匀设计是一种适用于多因素、多水平面试验次数较少的设计,方开泰[1]曾用数论方法进行了系统的研究,其基本思想是力求使布点达到极大的均匀.
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陈瑞琛
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Abstract: In this paper, the author introduces a tool called the dual transformation, and by using it we can reduce to half the computational work of constructing homogeneous designs of Latin square type. Specially, for the even order and cyclic case, she devises a reduced method by means of quadratic roots and a chain of sets. As an application, all the homogeneous designs of cyclic Latin square type of order 10 are obtained; the homogeneity of these designs is obviously better than that of the known table U10(108).
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收稿日期: 1990-03-07;
基金资助:江苏省科研基金
引用本文:   
陈瑞琛. 偶数阶循环拉丁方型均匀设计的构作[J]. 应用数学学报, 1993, 16(4): 442-451.
CHEN RUI-CHEN. CONSTRUCTION OF HOMOGENEOUS DESIGNS OF CYCLIC LATIN SQUARE TYPE WITH EVEN ORDER[J]. Acta Mathematicae Applicatae Sinica, 1993, 16(4): 442-451.
 
[1] 方开泰,均匀设计——数论方法在试验设计中的应用,应用数学学报.3 (1980), 363-372.
[2] 蒋声、陈瑞璨,拉丁方型均匀设计,高校应用数学学报.2 (1987), 532-541.
[3] L.A.Cherkas.Stability of Heteroclinic cycle.Differential Equation (Russian),1968,4:
[4] Gibbons,D,G.,A Simulation Study of Some Ridge Estimators,J.Amer.Statiat.Aeeoc.,76(1981),131-139.
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