共查询到20条相似文献,搜索用时 31 毫秒
1.
G. M. Saha 《Annals of the Institute of Statistical Mathematics》1973,25(1):605-616
Summary Recently Saha and Das [10] constructed partially balanced incomplete block (PBIB) designs of two and more associate classes
by using confounded designs for 2
n
factorials. Several new designs of two associate classes were obtained through those methods. This paper generalizes one
of the earlier methods of construction to obtain several series ofT
m
-type (m≧2) PBIB designs, i.e., the designs havingm-dimensional triangular association schemes. Some more new designs of two associate classes (i.e.,T
2-type) are obtained through the generalized methods of construction. 相似文献
2.
In this article, the existence of additive BIB designs is discussed with direct and recursive constructions, together with investigation of a property of resolvability. Such designs can be used to construct infinite families of BIB designs. In particular, we obtain a series of B(sn, tsm, λt (tsm ? 1) (sn‐m ? 1)/[2(sm ? 1)]) for any positive integer λ, such that sn (sn ? 1) λ ≡ 0 (mod sm (sm ? 1) and for any positive integer t with 2 ≤ t ≤ sn‐m, where s is an odd prime power. Connections between additive BIB designs and other combinatorial objects such as multiply nested designs and perpendicular arrays are discussed. A construction of resolvable BIB designs with v = 4k is also proposed. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 235–254, 2007 相似文献
3.
Beiliang Du 《组合设计杂志》2004,12(6):404-420
Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e., (v, 3k, λ)‐splitting BIBDs; we give the spectrum of (v, 3 × 2, λ)‐splitting BIBDs. As an application, we obtain an infinite class of 2‐splitting A‐codes. © 2004 Wiley Periodicals, Inc. 相似文献
4.
Sanpei Kageyama 《Annals of the Institute of Statistical Mathematics》1987,39(1):661-669
Summary This paper investigates locally resistant balanced incomplete block (LRBIB) designs of degree one. A new necessary condition
for the existence of such an LRBIB design is presented. This condition yields a complete characterization of affine α-resolvable
LRBIB designs of degree one. Furthermore, regarding construction methods of LRBIB designs of degree one, it is shown that
Shah and Gujarathi's method (1977,Sankhy?, B39, 406–408) yields the same parameters as Hedayat and John's method (1974,Ann. Statist.,2, 148–158), but their block structures are different and interesting.
Partially supported by Grants 59540043 (C) and 60530014 (C). 相似文献
5.
In this paper we consider experimental situations requiring usage of a row-column design where v treatments are to be applied to experimental units arranged in b
1 rows and b
2 columns where row i has size k
1i
, i=1,..., b
1 and column j has size k
2j
, j=1,..., b
2. Conditions analogous to those given in Kunert (1983, Ann. Statis., 11, 247–257) and Cheng (1978, Ann. Statist., 6, 1262–1272) are given which can often be used to establish the optimality of a given row-column design from the optimality of an associated block design. In addition, sufficient conditions are derived which guarantee the existence of an optimal row-column design which can be constructed by appropriately arranging treatments within blocks of an optimal block design.Visiting from the Indian Statistical Institute. 相似文献
6.
Yanxun Chang 《数学学报(英文版)》2000,16(1):103-112
Abstract
Given any positive integers k≥ 3 and λ, let c(k, λ) denote the smallest integer such that v∈B(k, λ) for every integer v≥c(k, λ) that satisfies the congruences λv(v− 1) ≡ 0(mod k(k− 1)) and λ(v− 1) ≡ 0(mod k− 1). In this article we make an improvement on the bound of c(k, λ) provided by Chang in [4] and prove that
. In particular,
.
Supported by NSFC Grant No. 19701002 and Huo Yingdong Foundation 相似文献
7.
A defining set of a t-(v, k, λ) design is a partial design which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining
set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given
t-design. The complete list of minimal defining sets of 2-(6, 3, 6) designs, 2-(7, 3, 4) designs, the full 2-(7, 3, 5) design,
a 2-(10, 4, 4) design, 2-(10, 5, 4) designs, 2-(13, 3, 1) designs, 2-(15, 3, 1) designs, the 2-(25, 5, 1) design, 3-(8, 4,
2) designs, the 3-(12, 6, 2) design, and 3-(16, 8, 3) designs are given to illustrate the efficiency of the algorithm. Also,
corrections to the literature are made for the minimal defining sets of four 2-(7, 3, 3) designs, two 2-(6, 3, 4) designs
and the 2-(21, 5, 1) design. Moreover, an infinite class of minimal defining sets for 2-((v) || 3){v\choose3} designs, where v ≥ 5, has been constructed which helped to show that the difference between the sizes of the largest and the smallest minimal
defining sets of 2-((v) || 3){v\choose3} designs gets arbitrarily large as v → ∞. Some results in the literature for the smallest defining sets of t-designs have been generalized to all minimal defining sets of these designs. We have also shown that all minimal defining
sets of t-(2n, n, λ) designs can be constructed from the minimal defining sets of their restrictions when t is odd and all t-(2n, n, λ) designs are self-complementary. This theorem can be applied to 3-(8, 4, 3) designs, 3-(8, 4, 4) designs and the full 3-(8 || 4)3-{8 \choose 4} design using the previous results on minimal defining sets of their restrictions. Furthermore we proved that when n is even all (n − 1)-(2n, n, λ) designs are self-complementary. 相似文献
8.
Marco Buratti 《组合设计杂志》1999,7(6):406-425
Let X =((x1,1,x1,2,…,x1,k),(x2,1,x2,2,…,x2,k),…,(xt,1,xt,2,…,xt,k)) be a family of t multisets of size k defined on an additive group G. We say that X is a t-(G,k,μ) strong difference family (SDF) if the list of differences (xh,i-xh,j∣h=1,…,t;i≠ j) covers all of G exactly μ times. If a SDF consists of a single multiset X, we simply say that X is a (G,k,μ) difference multiset. After giving some constructions for SDF's, we show that they allow us to obtain a very useful method for constructing regular group divisible designs and regular (or 1-rotational) balanced incomplete block designs. In particular cases this construction method has been implicitly used by many authors, but strangely, a systematic treatment seems to be lacking. Among the main consequences of our research, we find new series of regular BIBD's and new series of 1-rotational (in many cases resovable) BIBD's. 相似文献
9.
Tamar Ziegler 《Journal d'Analyse Mathématique》2006,99(1):249-266
We use ergodic theoretic tools to solve a classical problem in geometric Ramsey theory. LetE be a measurable subset of ℝ
m
, with
. LetV = {0,v
1,...,v
k} ⊂ ℝm. We show that fort large enough, we can find an isometric copy oftV arbitrarily close toE. This is a generalization of a theorem of Furstenberg, Katznelson and Weiss [FuKaW] showing a similar property form=k=2. 相似文献
10.
Ching-Shui Cheng 《Annals of the Institute of Statistical Mathematics》1981,33(1):155-164
A method to compare two-associate-class PBIB designs is discussed. As an application, it is shown that ifd
* is a group-divisible design withλ
2=λ1+1, a group divisible design with group size two andλ
2=λ1+1>1, a design based on a triangular scheme andv=10 andλ
1=λ2+1, a design with anL
2 scheme andλ
2=λ1+1, a design with anL
s scheme,v=(s+1)
2, andλ
2=λ1+1, wheres is a positive integer, or a design with a cyclic schemev=5, andλ
1=λ2±1, thend
* is optimum with respect to a very general class of criteria over all the two-associate-class PBIB designs with the same values
ofv, b andk asd
*. The best two-associate-class PBIB design, however, is not necessarily optimal over all designs.
This paper was prepared with the support of Office of Naval Research Contract No. N00014-75-C-0444/NR 042-036 and National
Science Foundation Grant No. MCS-79-09502. 相似文献
11.
Splitting t-designs were first formulated by Huber in recent investigation of optimal (t − 1)-fold secure splitting authentication codes. In this paper, we investigate the construction and existence of splitting
t-designs t-(v, u × k, 1) splitting designs and, show that there exists a 3-(v, 3 × 2, 1) splitting design if and only if v ≡ 2 (mod 8). As its application, we obtain a new infinite class of optimal 2-fold secure splitting authentication codes. 相似文献
12.
Evidence is presented to suggest that, in three dimensions, spherical 6-designs withN points exist forN=24, 26,≥28; 7-designs forN=24, 30, 32, 34,≥36; 8-designs forN=36, 40, 42,≥44; 9-designs forN=48, 50, 52,≥54; 10-designs forN=60, 62, ≥64; 11-designs forN=70, 72,≥74; and 12-designs forN=84,≥86. The existence of some of these designs is established analytically, while others are given by very accurate numerical
coordinates. The 24-point 7-design was first found by McLaren in 1963, and—although not identified as such by McLaren—consists
of the vertices of an “improved” snub cube, obtained from Archimedes' regular snub cube (which is only a 3-design) by slightly
shrinking each square face and expanding each triangular face. 5-designs with 23 and 25 points are presented which, taken
together with earlier work of Reznick, show that 5 designs exist forN=12, 16, 18, 20,≥22. It is conjectured, albeit with decreasing confidence fort≥9, that these lists oft-designs are complete and that no other exist. One of the constructions gives a sequence of putative sphericalt-designs withN=12m points (m≥2) whereN=1/2t
2(1+o(1)) ast→∞. 相似文献
13.
Charles J. Colbourn Sosina S. Martirosyan Tran Van Trung Robert A. Walker II 《Designs, Codes and Cryptography》2006,41(1):33-57
A covering array CA(N;t,k,v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t-sets of component interactions. Recursive constructions for covering arrays of strengths 3 and 4 are developed, generalizing
many “Roux-type” constructions. A numerical comparison with current construction techniques is given through existence tables
for covering arrays.
相似文献
14.
It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order v by removing the edges of two vertex disjoint complete subgraphs of orders u and w if and only if u,w, and v are odd, (mod 3), and . Such decompositions are equivalent to group divisible designs with block size 3, one group of size u, one group of size w, and v – u – w groups of size 1. This result settles the existence problem for Steiner triple systems having two disjoint specified subsystems, thereby generalizing the well‐known theorem of Doyen and Wilson on the existence of Steiner triple systems with a single specified subsystem. © 2005 Wiley Periodicals, Inc. J Combin Designs 相似文献
15.
Tobias Povel 《Probability Theory and Related Fields》1999,114(2):177-205
Consider Brownian motion among random obstacles obtained by translating a fixed compact nonpolar subset of ℝ
d
, d≥ 1, at the points of a Poisson cloud of constant intensity v <: 0. Assume that Brownian motion is absorbed instantaneously upon entering the obstacle set. In SZN-conf Sznitman has shown
that in d = 2, conditionally on the event that the process does not enter the obstacle set up to time t, the probability that Brownian motion remains within distance ∼t
1/4 from its starting point is going to 1 as t goes to infinity. We show that the same result holds true for d≥ 3, with t
1/4 replaced by t
1/(
d
+2). The proof is based on Sznitmans refined method of enlargement of obstacles [10] as well as on a quantitative isoperimetric
inequality due to Hall [4].
Received: 6 July 1998 相似文献
16.
Mike Jacroux 《Annals of the Institute of Statistical Mathematics》1985,37(1):557-566
Summary It is well known that in experimental settings wherev treatments are being tested inb blocks of sizek, a group divisible design having parametersλ
2=λ2+1 and whose correspondingC-matrix has maximal trace is both E and MV-optimal among all possible competing designs. In this paper, we show that under
certain conditions, the E and MV-optimal group divisible block designs mentioned in the previous sentence can be used to construct
E and MV-optimal row-column designs to handle experimental situations in which heterogeneity is to be eliminated in two directions
and wherev treatments are being tested inb columns andk rows. Examples are given to illustrate how the results obtained can be applied.
Research sponsored in part by National Science Foundation Grant No. DMS-8401943. 相似文献
17.
The basic necessary conditions for the existence of a (v, k, λ)-perfect Mendelsohn design (briefly (v, k, λ)-PMD) are v ≥ k and λ v(v − 1) ≡ 0 (mod k). These conditions are known to be sufficient in most cases, but certainly not in all. For k = 3, 4, 5, 7, very extensive investigations of (v, k, λ)-PMDs have resulted in some fairly conclusive results. However, for k = 6 the results have been far from conclusive, especially for the case of λ = 1, which was given some attention in papers
by Miao and Zhu [34], and subsequently by Abel et al. [1]. Here we investigate the situation for k = 6 and λ > 1. We find that the necessary conditions, namely v ≥ 6 and λ v(v − 1)≡0 (mod 6) are sufficient except for the known impossible cases v = 6 and either λ = 2 or λ odd.
Researcher F.E. Bennett supported by NSERC Grant OGP 0005320. 相似文献
18.
A directed balanced incomplete block design (or D
B(k,;v)) (X,) is called self-converse if there is an isomorphic mapping f from (X,) to (X,–1), where –1={B
–1:B} and B
–1=(x
k
,x
k
–1,,x
2,x
1) for B=(x
1,x
2,,x
k
–1,x
k
). In this paper, we give the existence spectrum for self-converse D
B(4,1;v).
AMS Classification:05BResearch supported in part by NSFC Grant 10071002 and SRFDP under No. 20010004001 相似文献
19.
Teruhiro Shirakura 《Annals of the Institute of Statistical Mathematics》1986,38(1):145-159
Summary For a given fractional 2
m
factorial (2
m
-FF) designT, the constitution of a block plan to divideT intok (2
r−1<k≦2
r
) blocks withr block factors each at two levels is proposed and investigated. The well-known three norms of the confounding matrix are used
as measures for determining a “good” block plan. Some theorems concerning the constitution of a block plan are derived for
a 2
m
-FF design of odd or even resolution. Two norms which may be preferred over the other norm are slightly modified. For each
value ofN assemblies with 11≦N≦26, optimum block plans fork=2 blocks with block sizes [N/2] andN−[N/2] minimizing the two norms are presented forA-optimal balanced 24-FF designs of resolutionV given by Srivastava and Chopra (Technometrics,13, 257–269). 相似文献
20.
Marco Buratti 《组合设计杂志》1998,6(3):165-182
We present a new recursive construction for difference matrices whose application allows us to improve some results by D. Jungnickel. For instance, we prove that for any Abelian p-group G of type (n1, n2, …, nt) there exists a (G, pe, 1) difference matrix with e = Also, we prove that for any group G there exists a (G, p, 1) difference matrix where p is the smallest prime dividing |G|. Difference matrices are then used for constructing, recursively, relative difference families. We revisit some constructions by M. J. Colbourn, C. J. Colbourn, D. Jungnickel, K. T. Phelps, and R. M. Wilson. Combining them we get, in particular, the existence of a multiplier (G, k, λ)-DF for any Abelian group G of nonsquare-free order, whenever there exists a (p, k, λ)-DF for each prime p dividing |G|. Then we focus our attention on a recent construction by M. Jimbo. We improve this construction and prove, as a corollary, the existence of a (G, k, λ)-DF for any group G under the same conditions as above. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 165–182, 1998 相似文献