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过去超饱和设计的研究集中在2水平设计的范围内,Lu and Sun(2000)首次讨论了高于2水平因子的超饱和设计问题,该文提出了用E(d^2)作为构造超饱和设计的准则,并给出了E(d^2)最优的一些设计,本文讨论了以给定的Max(d^2)为前提构造超饱和设计的方法,并给出了一些三水平和四水平的超饱和设计。 相似文献
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超饱和设计是一种试验次数不足以同时估计其设计矩阵的列所代表的主效应的因子设计, 在这样的设计中因子各水平等重复出现且没有全混杂的因子. 这种设计因其在因子筛选试验中的优势而得到了越来越多的关注. 而填充设计是组合设计理论中一类重要的研究对象. 本文建立起了这两种不同设计之间的紧密联系. 提出了比较超饱和设计的几个准则, 讨论了它们的性质及与现有准则的关系, 给出了构造最优超饱和设计的一种组合方法, 即填充方法, 研究了所构造设计的性质并与现有的其他设计做了比较, 结果表明所构造的方法和新构造的设计具有优良的性质. 相似文献
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均衡随机分组设计是一种把随机抽样设计与显著性检验相结合的试验设计方法.试验设计可以避免完全随机抽样(或完全随机分组)设计可能会造成所分组间存在较大差异的缺点,保证所分组或样本间具有均衡性,确保抽样的科学性和可比性,以增强对处理效果反应的灵敏度,提高试脸的准确度. 相似文献
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Kite-可分组设计的相交数问题是确定所有可能的元素对$(T,s)$, 使得存在一对具有相同组型 $T$ 的Kite-可分组设计 $(X,{\cal H},{\cal B}_1)$ 和$(X,{\cal H},{\cal B}_2)$ 满足$|{\cal B}_1\cap {\cal B}_2|=s$. 本文研究组型为 $2^u$ 的Kite-可分组设计的相交数问题, 设 $J(u)=\{s:\exists$ 组型为 $2^u$ 的Kite-可分组设计相交于$s$ 个区组\}, $I(u)=\{0,1,\ldots,b_{u}-2,b_{u}\}$,其中 $b_u=u(u-1)/2$ 是组型为$2^u$ 的Kite-可分组设计的区组个数. 我们将给出对任意整数 $u\ge 4$ 都有$J(u)=I(u)$ 且 $J(3)= \{0,3\}$. 相似文献
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主要研究基于(v,k,2)光正交码的最优超单严格循环填充,即(v,k,λ)-OSCP的存在性问题,解决了λ=2,3,4的(v,3,λ)-OSCP的存在性,得到了一些k≥4的(v,k,λ)-OSCP的无穷类. 相似文献
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遗传算法作为一种随机化优化搜索方法,已经在很多领域得到了成功应用,但其存在控制参数多且配置困难的问题.本文采用一类最新试验设计方法-计算机试验设计,对遗传算法的参数配置进行优化.结果表明,基于正交拉丁超立方设计的参数配置,其算法的计算精度和速度表现最佳.模拟结果进一步讨论了不同试验设计方案在遗传算法中的差别. 相似文献
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Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. In
this article, we investigate the existence of a super-simple (ν, 5, 5) balanced incomplete block design and show that such
a design exists if and only if ν ≡ 1 (mod 4) and ν ≥ 17 except possibly when ν = 21. Applications of the results to optical orthogonal codes are also mentioned.
Research supported by NSERC grant 239135-01. 相似文献
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Haitao Cao 《Discrete Mathematics》2009,309(9):2808-2814
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v,4,λ)-BIBDs have been determined for λ=2,3,4 and 6. When λ=5, the necessary conditions of such a design are that and v≥13. In this paper, we show that there exists a super-simple (v,4,5)-BIBD for each and v≥13. 相似文献
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A design is said to be super-simple if the intersection of any two blocks has at most two elements. A super-simple design \({\mathcal{D}}\) with point set X, block set \({\mathcal{B}}\) and index λ is called completely reducible super-simple (CRSS), if its block set \({\mathcal{B}}\) can be written as \({\mathcal{B}=\bigcup_{i=1}^{\lambda} \mathcal{B}_i}\), such that \({\mathcal{B}_i}\) forms the block set of a design with index unity but having the same parameters as \({\mathcal{D}}\) for each 1 ≤ i ≤ λ. It is easy to see, the existence of CRSS designs with index λ implies that of CRSS designs with index i for 1 ≤ i ≤ λ. CRSS designs are closely related to q-ary constant weight codes (CWCs). A (v, 4, q)-CRSS design is just an optimal (v, 6, 4)q+1 code. On the other hand, CRSS group divisible designs (CRSSGDDs) can be used to construct q-ary group divisible codes (GDCs), which have been proved useful in the constructions of q-ary CWCs. In this paper, we mainly investigate the existence of CRSS designs. Three neat results are obtained as follows. Firstly, we determine completely the spectrum for a (v, 4, 3)-CRSS design. As a consequence, a class of new optimal (v, 6, 4)4 codes is obtained. Secondly, we give a general construction for (4, 4)-CRSSGDDs with skew Room frames, and prove that the necessary conditions for the existence of a (4, 2)-CRSSGDD of type g u are also sufficient except definitely for \({(g,u)\in \{(2,4),(3,4),(6,4)\}}\). Finally, we consider the related optimal super-simple (v, 4, 2)-packings and show that such designs exist for all v ≥ 4 except definitely for \({v\in \{4,5,6,9\}}\). 相似文献
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In this paper we study (4,2μ)-GDDs of type gn possessing both the pan-decomposable property introduced by Granville, Moisiadis, Rees, On complementary decompositions of the complete graph, Graphs and Combinatorics 5 (1989) 57-61 and the pan-orientable property introduced by Grüttmüller, Hartmann, Pan-orientable block designs, Australas. J. Combin. 40 (2008) 57-68. We show that the necessary condition for a (4,2μ)-GDD satisfying both of these properties, namely (1) n≥4, μg(n−1)≡0 (mod 3), and (2) g−1,n are not both even if μ is odd are sufficient. When λ=2, our designs are super-simple.We also determine the spectrum of (4,2)-GDDs which are super-simple and possess some of the decomposable/orientable conditions, but are not pan-decomposable or pan-orientable. In particular, we show that the necessary conditions for a super-simple directable (4,2)-GDD of type gn are sufficient. 相似文献
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R.J.R. Abel 《Discrete Applied Mathematics》2008,156(5):780-793
A Steiner pentagon system of order v(SPS(v)) is said to be super-simple if its underlying (v,5,2)-BIBD is super-simple; that is, any two blocks of the BIBD intersect in at most two points. In this paper, it is shown that the necessary condition for the existence of a super-simple SPS(v); namely, v?5 and v≡1 or is sufficient, except for v=5, 15 and possibly for v=25. In the process, we also improve an earlier result for the spectrum of super-simple (v,5,2)-BIBDs, removing all the possible exceptions. We also give some new examples of Steiner pentagon packing and covering designs (SPPDs and SPCDs). 相似文献
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Iliya Bluskov 《Journal of Geometry》2000,67(1-2):42-49
Optimization algorithms perform well in many construction problems. We describe several algorithms used in recent research on designs. These include algorithms for generating cyclic 2-designs, studying the number of mutually disjoint cyclic designs (with application in the search for large sets of designs) and constructing super-simple designs. 相似文献
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The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 4, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient. 相似文献
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Constant-composition codes are a special type of constant-weight codes and have attracted recent interest due to their numerous applications. In a recent work, the authors found that an optimal (n, 5, [2, 1, 1])4-code of constant-composition can be obtained from a Room square of side n with super-simple property. In this paper, we study the existence problem of super-simple Room squares. The problem is solved leaving only two minimal possible n undetermined. 相似文献
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A twofold pentagon system of order v is a decomposition of the complete undirected 2-multigraph 2K v into pentagons. A twofold Steiner pentagon system of order v [TSPS(v)] is a twofold pentagon system such that every pair of distinct vertices is joined by a path of length two in exactly two pentagons of the system. A TSPS(v) is said to be super-simple if its underlying (v, 5, 4)-BIBD is super-simple; that is, if any two blocks of the BIBD intersect in at most two points. In this paper, it is shown that the necessary conditions for the existence of a super-simple TSPS(v); namely, v ≥ 15 and v ≡ 0 or 1 (mod 5) are sufficient. For these specified orders, the main result of this paper also guarantees the existence of a very special and interesting class of twofold and fourfold Steiner pentagon systems of order v with the additional property that, for any two vertices, the two or four paths of length two joining them are distinct. 相似文献
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PERIODIC SOLUTIONS OF SCALAR NEUTRAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH INFINITE DELAY 总被引:1,自引:0,他引:1
This paper deals with the existence and uniqueness of periodic solutions of the following scalar neutral Volterra integro-differential equation with infinite delaywhere a, C, D, f are continuous functions, also a(t + T) = a(t), C(t + T,s + T) = C(t, s), D(t + T,s + T) = D(t, s), f(t + T) = f(t). Sufficient conditions on the existence and uniqueness of periodic solution to this equation are obtained by the contraction mapping theorem. 相似文献