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1.
Quasi-symmetric 3-designs with block intersection numbers x and y(0x<y<k) are studied, several inequalities satisfied by the parameters of a quasi-symmetric 3-designs are obtained. Let D be a quasi-symmetric 3-design with the block size k and intersection numbers x, y; y>x1 and suppose D′ denote the complement of D with the block size k′ and intersection numbers x′ and y′. If k −1 x + y then it is proved that x′ + y′ k′. Using this it is shown that the quasi-symmetric 3-designs corresponding to y = x + 1, x + 2 are either extensions of symmetric designs or designs corresponding to the Witt-design (or trivial design, i.e., v = k + 2) or the complement of above designs. 相似文献
2.
Let D be a set of positive integers. The distance graph G(Z,D) with distance set D is the graph with vertex set Z in which two vertices x,y are adjacent if and only if |x−y|D. The fractional chromatic number, the chromatic number, and the circular chromatic number of G(Z,D) for various D have been extensively studied recently. In this paper, we investigate the fractional chromatic number, the chromatic number, and the circular chromatic number of the distance graphs with the distance sets of the form Dm,[k,k′]={1,2,…,m}−{k,k+1,…,k′}, where m, k, and k′ are natural numbers with m≥k′≥k. In particular, we completely determine the chromatic number of G(Z,Dm,[2,k′]) for arbitrary m, and k′. 相似文献
3.
A numerical estimate is obtained for the error associated with the Laplace approximation of the double integral I(λ) = ∝∝D g(x,y) e−λf(x,y) dx dy, where D is a domain in
, λ is a large positive parameter, f(x, y) and g(x, y) are real-valued and sufficiently smooth, and ∝(x, y) has an absolute minimum in D. The use of the estimate is illustrated by applying it to two realistic examples. The method used here applies also to higher dimensional integrals. 相似文献
4.
Rajendra M. Pawale 《Designs, Codes and Cryptography》2011,58(2):111-121
Quasi-symmetric designs with intersection numbers x > 0 and y = x + 2 under the condition λ > 1 are investigated. If D(v, b, r, k, λ; x, y) is a quasi-symmetric design with above conditions then it is shown that either λ = x + 1 or x + 2 or D is a design with the parameters given in the Table 6 or complement of one of these designs. 相似文献
5.
In a recent paper, Pawale (Des Codes Cryptogr, 2010) investigated quasi-symmetric 2-(v, k, λ) designs with intersection numbers x > 0 and y = x + 2 with λ > 1 and showed that under these conditions either λ = x + 1 or λ = x + 2, or D{\mathcal{D}} is a design with parameters given in the form of an explicit table, or the complement of one of these designs. In this paper,
quasi-symmetric designs with y − x = 3 are investigated. It is shown that such a design or its complement has parameter set which is one of finitely many which
are listed explicitly or λ ≤ x + 4 or 0 ≤ x ≤ 1 or the pair (λ, x) is one of (7, 2), (8, 2), (9, 2), (10, 2), (8, 3), (9, 3), (9, 4) and (10, 5). It is also shown that there are no triangle-free
quasi-symmetric designs with positive intersection numbers x and y with y = x + 3. 相似文献
6.
M. Deza 《Journal of Combinatorial Theory, Series A》1976,20(3):306-318
Le nombre maximal de lignes de matrices seront désignées par:
- 1. (a) R(k, λ) si chaque ligne est une permutation de nombres 1, 2,…, k et si chaque deux lignes différentes coïncide selon λ positions;
- 2. (b) S0(k, λ) si le nombre de colonnes est k et si chaque deux lignes différentes coïncide selon λ positions et si, en plus, il existe une colonne avec les éléments y1, y2, y3, ou y1 = y2 ≠ y3;
- 3. (c) T0(k, λ) si c'est une (0, 1)-matrice et si chaque ligne contient k unités et si chaque deux lignes différentes contient les unités selon λ positions et si, en plus, il existe une colonne avec les éléments 1, 1, 0.
7.
Rajendra M. Pawale 《组合设计杂志》2007,15(1):49-60
The following results for proper quasi‐symmetric designs with non‐zero intersection numbers x,y and λ > 1 are proved.
- (1) Let D be a quasi‐symmetric design with z = y ? x and v ≥ 2k. If x ≥ 1 + z + z3 then λ < x + 1 + z + z3.
- (2) Let D be a quasi‐symmetric design with intersection numbers x, y and y ? x = 1. Then D is a design with parameters v = (1 + m) (2 + m)/2, b = (2 + m) (3 + m)/2, r = m + 3, k = m + 1, λ = 2, x = 1, y = 2 and m = 2,3,… or complement of one of these design or D is a design with parameters v = 5, b = 10, r = 6, k = 3, λ = 3, and x = 1, y = 2.
- (3) Let D be a triangle free quasi‐symmetric design with z = y ? x and v ≥ 2k, then x ≤ z + z2.
- (4) For fixed z ≥ 1 there exist finitely many triangle free quasi‐symmetric designs non‐zero intersection numbers x, y = x + z.
- (5) There do not exist triangle free quasi‐symmetric designs with non‐zero intersection numbers x, y = x + 2.
8.
Let k be fixed, 1 < k < 2. There exists an infinite word over a finite alphabet which contains no subword of the form xyz with |xyz | / | xy | ≥ k and where z is a permutation of x. 相似文献
9.
Quasi-symmetric designs are block designs with two block intersection numbersx andy It is shown that with the exception of (x, y)=(0, 1), for a fixed value of the block sizek, there are finitely many such designs. Some finiteness results on block graphs are derived. For a quasi-symmetric 3-design
with positivex andy, the intersection numbers are shown to be roots of a quadratic whose coefficients are polynomial functions ofv, k and λ. Using this quadratic, various characterizations of the Witt—Lüneburg design on 23 points are obtained. It is shown
that ifx=1, then a fixed value of λ determines at most finitely many such designs. 相似文献
10.
For a fixed integer m ≥ 0, and for n = 1, 2, 3, ..., let λ2m, n(x) denote the Lebesgue function associated with (0, 1,..., 2m) Hermite-Fejér polynomial interpolation at the Chebyshev nodes {cos[(2k−1) π/(2n)]: k=1, 2, ..., n}. We examine the Lebesgue constant Λ2m, n max{λ2m, n(x): −1 ≤ x ≤ 1}, and show that Λ2m, n = λm, n(1), thereby generalising a result of H. Ehlich and K. Zeller for Lagrange interpolation on the Chebyshev nodes. As well, the infinite term in the asymptotic expansion of Λ2m, n) as n → ∞ is obtained, and this result is extended to give a complete asymptotic expansion for Λ2, n. 相似文献
11.
M. Eshaghi Gordji H. Khodaei 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5629-5643
In this paper, we achieve the general solution and the generalized Hyers–Ulam–Rassias stability of the following functional equation
f(x+ky)+f(x−ky)=k2f(x+y)+k2f(x−y)+2(1−k2)f(x)