共查询到20条相似文献,搜索用时 15 毫秒
1.
Yury J. Ionin 《Journal of Geometry》2000,67(1-2):164-172
An (m, n, k, 1,2) divisible difference set in a groupG of ordermn relative to a subgroupN of ordern is ak-subsetD ofG such that the list {xy–1:x, y D} contains exactly 1 copies of each nonidentity element ofN and exactly 2 copies of each element ofG N. It is called semi-regular ifk >
1 and k2=mn2. We develop a method for constructing a divisible difference set as a product of a difference set and a relative difference set or a difference set and a subset ofG which we call a relative divisible difference set. The method results in several parametrically new families of semi-regular divisible difference sets. 相似文献
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Partial geometric difference sets (PGDSs) were defined in Olmez (J Combin Des 22(6):252–269, 2014). They are used to construct partial geometric designs. We use the framework of extended building sets to find infinite families of PGDSs in abelian groups. Included in our new families of PGDSs are generalizations of the Hadamard, McFarland, Spence, Davis-Jedwab, and Chen difference sets. 相似文献
3.
《Discrete Mathematics》2021,344(12):112589
Let be the set of positive integers. For a nonempty set A of integers and every integer u, denote by the number of with such that . For a sequence S of positive integers, let be the counting function of S. The set is called a perfect difference set if for every positive integer u. In 2008, Cilleruelo and Nathanson (2008) [4] constructed dense perfect difference sets from dense Sidon sets. In this paper, as a main result, we prove that: let be an increasing function satisfying for any positive integer n, then for every Sidon set B and every function , there exists a set such that for every positive integer u and for all . 相似文献
4.
John O. Dow Michael S. Jones Shawn A. Harwood 《Numerical Methods for Partial Differential Equations》1990,6(2):137-152
Procedures are developed that improve the applicability of the finite difference method to problems in solid mechanics. This is accomplished by formulating the coefficients of the Taylor series expansion used to approximate derivative quantities in terms of physically interpretable strain gradients. Improvements realized include modeling of boundary conditions that has intuitive appeal and the use of irregular grids in a natural manner. These developments are demonstrated for the analysis of plane stress problems with traction boundary conditions. The results compare well with finite element solutions. The approach suggests further generalization of the finite difference method. 相似文献
5.
Edward Spence 《Journal of Combinatorial Theory, Series A》1977,22(1):103-106
A construction is given for difference sets with parameters , in certain noncyclic groups of order v. For s = 1 it is shown that the construction yields all possible difference sets with parameters (36, 15, 6, 9) in an abelian group of order 36. 相似文献
6.
Difference systems of sets (DSSs) are combinatorial structures that are generalizations of cyclic difference sets and arise in connection with code synchronization. In this paper, we give a recursive construction of DSSs with smaller redundancy from partition-type DSSs and difference sets. As applications, we obtain some new infinite classes of optimal DSSs from the known difference sets and almost difference sets. 相似文献
7.
Marco Buratti 《Designs, Codes and Cryptography》1995,5(1):13-25
In this paper we proceed in the way indicated by R. M. Wilson for obtaining simple difference families from finite fields [28]. We present a theorem which includes as corollaries all the known direct techniques based on Galois fields, and provides a very effective method for constructing a lot of new difference families and also new optimal optical orthogonal codes.By means of our construction—just to give an idea of its power—it has been established that the only primesp<105 for which the existence of a cyclicS(2, 9,p) design is undecided are 433 and 1009. Moreover we have considerably improved the lower bound on the minimumv for which anS(2, 15,v) design exists. 相似文献
8.
Viorel Gh. Vodă 《Applications of Mathematics》2009,54(5):417-431
In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. 47 (1976), pp. 395–412. The construction makes use of the so-called “conservability approach” (see Kybernetika 25 (1989), pp. 209–215) namely, if X is a positive continuous random variable with a finite mean-value E(X), then a new density is set to be f
1(x) = xf(x)/E(X), where f(x) is the probability density function of X. The new generalized Rayleigh variable is obtained using a generalized form of the exponential distribution introduced by
Isaic-Maniu and the present author as f(x). 相似文献
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10.
S. L. Ma 《Designs, Codes and Cryptography》1994,4(4):221-261
LetG be a finite group of order . Ak-element subsetD ofG is called a (,k, , )-partial difference set if the expressionsgh
–1, forg andh inD withgh, represent each nonidentity element inD exactly times and each nonidentity element not inD exactly times. IfeD andgD iffg
–1D, thenD is essentially the same as a strongly regular Cayley graph. In this survey, we try to list all important existence and nonexistence results concerning partial difference sets. In particular, various construction methods are studied, e.g., constructions using partial congruence partitions, quadratic forms, cyclotomic classes and finite local rings. Also, the relations with Schur rings, two-weight codes, projective sets, difference sets, divisible difference sets and partial geometries are discussed in detail. 相似文献
11.
H.A Wilbrink 《Journal of Combinatorial Theory, Series A》1985,38(1):94-95
It is proven that if G is an abelian regular automorphism group of a projective plane of order n and if p is a prime dividing n exactly once, then a certain identity holds in the group algebra p|G|. As a corollary we obtain that n = p if p = 2 or 3. 相似文献
12.
Jennifer Wallis 《Aequationes Mathematicae》1973,9(2-3):306-306
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Clement W.H Lam 《Journal of Combinatorial Theory, Series A》1975,19(1):51-65
This is the first of two papers on addition sets. In this paper, the basic properties of addition sets are given. It also contains examples of addition sets arising from natural central groupoids, (0, 1)-matrices satisfying the equation M2 = dI+λJ and Nth power residues. Their relationship with difference sets is also explained. 相似文献
18.
A family of skew Hadamard difference sets 总被引:1,自引:0,他引:1
Cunsheng Ding 《Journal of Combinatorial Theory, Series A》2006,113(7):1526-1535
In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley-Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and further progress in favor of this conjecture was made in the past 50 years. However, the conjecture remains open until today. In this paper, we present a family of new perfect nonlinear (also called planar) functions, and construct a family of skew Hadamard difference sets using these perfect nonlinear functions. We show that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamard difference sets. These new examples of skew Hadamard difference sets discovered 70 years after the Paley construction disprove the longstanding conjecture on skew Hadamard difference sets. The class of new perfect nonlinear functions has applications in cryptography, coding theory, and combinatorics. 相似文献
19.
Gerold Wagner 《Discrete and Computational Geometry》1993,9(1):111-129
We use quadrature formulas with equal weights in order to constructN point sets on spheres ind-space (d 3) which are almost optimal with respect to a discrepancy concept, based on distance functions (potentials) and distance functionals (energies). By combining this approach with the probabilistic method, we obtain almost best possible approximations of balls by zonotopes, generated byN segments of equal length.Editors' note: We learned with sadness of Gerold Wagner's untimely death as a result of an avalanche in the Alps shortly after the submission of this paper. When one of the referees, Joram Lindenstrauss, suggested that Wagner's results might be extended to dimensions >6, we invited Professor Lindenstrauss to submit a paper containing that extension which we would publish alongside the Wagner paper. The result is the paper by Bourgain and Lindenstrauss that follows the present one. 相似文献
20.
In this paper we present a numerical method for a generalized Black-Scholes equation, which is used for option pricing. The method is based on a central difference spatial discretization on a piecewise uniform mesh and an implicit time stepping technique. Our scheme is stable for arbitrary volatility and arbitrary interest rate, and is second-order convergent with respect to the spatial variable. Furthermore, the present paper efficiently treats the singularities of the non-smooth payoff function. Numerical results support the theoretical results. 相似文献