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1.
A (k,λ)‐semiframe of type gu is a (k,λ)‐group‐divisible design of type gu (??, ??, ??), in which the collection of blocks ?? can be written as a disjoint union ??=??∪?? where ?? is partitioned into parallel classes of ?? and ?? is partitioned into holey parallel classes, each holey parallel class being a partition of ??\Gj for some Gj∈??. In this paper, we shall prove that the necessary conditions for (3,λ)‐semiframes of type 3u are also sufficient with one exception. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 253–265, 2009 相似文献
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In this article, a kind of auxiliary design BSA* for constructing BSAs is introduced and studied. Two powerful recursive constructions on BSAs from 3‐IGDDs and BSA*s are exploited. Finally, the necessary and sufficient conditions for the existence of a BSA(v, 3, λ; α) with α = 2, 3 are established. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 61–76, 2007 相似文献
3.
Nonsymmetric designs, with , admitting a solvable flag‐transitive automorphism group of affine type not contained in are classified. 相似文献
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When basic necessary conditions for the existence of a balanced incomplete block design are satisfied, the design may still not exist or it may not be known whether it exists. In either case, other designs may be considered for the same parameters. In this article we introduce a class of alternative designs, which we will call virtually balanced incomplete block designs. From a statistical point of view these designs provide efficient alternatives to balanced incomplete block designs, and from a combinatorial point of view they offer challenging new questions. © 1995 John Wiley & Sons, Inc. 相似文献
5.
It is shown that the necessary condition for a given Sλ(2,4,u) to be embedded in some Sλ(2,4,v) as a subdesign, namely v ≥ 3u + 1, is also sufficient for the case of λ = 6. Combining this with the previously known results gives the same sufficiency for any positive integer λ. © 1994 John Wiley & Sons, Inc. 相似文献
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Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao, and Stufken in 1988. In this paper, we generalize the concept of a cyclic BSEC to a cyclic balanced sampling plan to avoid the selection of adjacent units (or CBSA for short) and use Langford and extended Langford sequences to construct a cyclic BSA(ν, 3, λ; α) with α = 2, 3. We finally establish the necessary and sufficient conditions for the existence of a cyclic BSA(ν, 3, λ; α) where α = 2, 3. © 2005 Wiley Periodicals, Inc. J Combin Designs. 相似文献
7.
Joseph Hershenov 《Studies in Applied Mathematics》1976,55(4):301-314
This paper deals with the solutions of the differential equation u?+λ2zu+(α?1)λ2u=0, in which λ is a complex parameter of large absolute value and α is an arbitrary constant, real or complex. After a discussion of the structure of the solutions of the differential equation, an integral representation of the solution is given, from which the series solutions and their asymptotic representations are derived. A third independent solution is needed for the special case when α?1 is a positive integer, and two derivations for this are given. Finally, a comparison is made with the results obtained by R. E. Langer. 相似文献
8.
(v, 6,1) BIBDs are given for several new values of v. This reduces to 55 the number of v values for which existence of a (v,6,1) BIBD is in doubt. A new resolvable (565,5,1) BIBD is also given. © 1995 John Wiley & Sons, Inc. 相似文献
9.
R.J.R. Abel 《组合设计杂志》1996,4(1):27-50
This article is in two main parts. The first gives some (q,k, 1) difference families with q a prime power and 7 ≤ k ≤ 9; it also gives some GD(k, 1, k,kq)s which are extendable to resolvable (kq,k, 1) BIBDs for k E {6,8,10} and q a prime power equal to 1 mod 2(k − 1). The second uses some of these plus several recursive constructions to obtain some new (v,k,, 1) BIBDs with 7 ≤ k ≤ 9 and some new (v,8,1) resolvable BIBDs. © 1996 John Wiley & Sons, Inc. 相似文献
10.
A λ‐design is a family of subsets of such that for all and not all are of the same size. Ryser's and Woodall's λ‐design conjecture states that each λ‐design can be obtained from a symmetric block design by a certain complementation procedure. Our main result is that the conjecture is true when λ < 63. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 408–431, 2012 相似文献
11.
In this work we present a study of the Pearson discrete distributions generated by the hypergeometric function 3F2(α1, α2, α3;γ1, γ2; λ), a univariate extension of the Gaussian hypergeometric function, through a constructive methodology. We start from the polynomial coefficients of the difference equation that lead to such a function as a solution. Immediately after, we obtain the generating probability function and the differential equation that it satisfies, valid for any admissible values of the parameters. We also obtain the differential equations that satisfy the cumulants generating function, moments generating function and characteristic function, From this point on, we obtain a relation in recurrences between the moments about the origin, allowing us to create an equation system for estimating the parameters by the moment method. We also establish a classification of all possible distributions of such type and conclude with a summation theorem that allows us study some distributions belonging to this family. © 1997 by John Wiley & Sons, Ltd. 相似文献
12.
Let be a symmetric (ν,κ,λ) design with λ ≤ 100. If G is a flag‐transitive and point‐primitive automorphism group of , then G must be an affine or almost simple group. 相似文献
13.
In this article, two necessary conditions for a graph to have an equality of the second largest Laplacian eigenvalue λ2 ( G ) and its lower bound d 2 ( G ) are presented. Some of the graphs who satisfy λ2 ( G )= d 2 ( G ) are also described. 相似文献
14.
Shiro Iwasaki 《组合设计杂志》1997,5(2):95-110
Let p be an odd prime number such that p − 1 = 2em for some odd m and e ≥ 2. In this article, by using the special linear fractional group PSL(2, p), for each i, 1 ≤ i ≤ e, except particular cases, we construct a 2-design with parameters v = p + 1, k = (p − 1)/2i + 1 and λ = ((p − 1)/2i+1)(p − 1)/2 = k(p − 1)/2, and in the case i = e we show that some of these 2-designs are 3-designs. Likewise, by using the linear fractional group PGL(2,p) we construct an infinite family of 3-designs with the same v k and λ = k(k − 2). These supplement a part of [4], in which we gave an infinite family of 3-designs with parameters v = q + 1, k = (q + 1)/2 = (q − 1)/2 + 1 and λ = (q + 1)(q − 3)/8 = k(k − 2)/2, where q is a prime power such that q − 1 = 2m for some odd m and q > 7. Some of the designs given in this article and in [4] fill in a few blanks in the table of Chee, Colbourn, and Kreher [2]. © 1997 John Wiley & Sons, Inc. 相似文献
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Dian-hua Wu Jian-xiao Yang Bi-chang Huang 《应用数学学报(英文版)》2008,24(4):643-648
A (v, k, λ) difference family ((v, k, λ)-DF in short) over an abelian group G of order v, is a collection F=(Bi|i ∈ I} of k-subsets of G, called base blocks, such that any nonzero element of G can be represented in precisely A ways as a difference of two elements lying in some base blocks in F. A (v, k, λ)-DDF is a difference family with disjoint blocks. In this paper, by using Weil's theorem on character sum estimates, it is proved that there exists a (p^n, 4, 1)-DDF, where p = 1 (rood 12) is a prime number and n ≥1. 相似文献
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Christiane Tretter 《Mathematische Nachrichten》2000,214(1):129-172
This paper deals with the spectral properties of boundary eigenvalue problems for systems of first order differential equations with boundary conditions which depend on the spectral parameter polynomially. It is not assumed that is injective or surjective. The main results concern the completeness minimality and Riesz basis properties of the corresponding eigenfunctions and associated functions. 相似文献
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《Journal of Combinatorial Theory, Series A》1986,43(2):334-337
We study a method of Lonz and Vanstone which constructs an S3(3, 4, 2n) from any given 1-factorization of K2n. We show that the resulting designs admit at least 3 mutually orthogonal resolutions whenever n ⩾ 4 is even. In particular, the necessary conditions for the existence of a resolvable S3(3, 4, ν) are also sufficient. Examples without repeated blocks are shown to exist provided that n ≢ 2 mod 3. 相似文献