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1.
For m ≥ 1 and p ≥ 2, given a set of integers s1,…,sq with for and , necessary and sufficient conditions are found for the existence of a hamilton decomposition of the complete p-partite graph , where U is a 2-factor of consisting of q cycles, the jth cycle having length sj. This result is then used to completely solve the problem when p = 3, removing the condition that . © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 208–214, 2003 相似文献
2.
H. Kharaghani 《组合设计杂志》2000,8(3):166-173
A set of square real matrices is said to be amicable if for some permutation σ of the set . An infinite number of arrays which are suitable for any amicable set of eight circulant matrices are introduced. Applications include new classes of orthogonal designs. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 166–173, 2000 相似文献
3.
Massimo Giulietti 《组合设计杂志》2007,15(5):420-436
A new family of small complete caps in PG(N,q), q even, is constructed. Apart from small values of either N or q, it provides an improvement on the currently known upper bounds on the size of the smallest complete cap in PG(N,q): for N even, the leading term is replaced by with , for N odd the leading term is replaced by with . © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 420–436, 2007 相似文献
4.
Michael Capalbo 《Random Structures and Algorithms》2010,37(4):437-454
For any integer n, let be a probability distribution on the family of graphs on n vertices (where every such graph has nonzero probability associated with it). A graph Γ is ‐almost‐universal if Γ satisifies the following: If G is chosen according to the probability distribution , then G is isomorphic to a subgraph of Γ with probability 1 ‐ . For any p ∈ [0,1], let (n,p) denote the probability distribution on the family of graphs on n vertices, where two vertices u and v form an edge with probability p, and the events {u and v form an edge}; u,v ∈ V (G) are mutually independent. For k ≥ 4 and n sufficiently large we construct a ‐almost‐universal‐graph on n vertices and with O(n)polylog(n) edges, where q = ? ? for such k ≤ 6, and where q = ? ? for k ≥ 7. The number of edges is close to the lower bound of Ω( ) for the number of edges in a universal graph for the family of graphs with n vertices and maximum degree k. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010 相似文献
5.
Camil Muscalu 《纯数学与应用数学通讯》1999,52(10):1213-1230
In this paper we prove the following theorem (for notation and definitions, see the paragraphs below): “Let Ω ⊆ ℝn be a domain, m ∈ ℕ, and λ, q > 0. Then, there exists r (= r(λ, q)) > 1 such that for every 0 < p < q, whenever are weak solutions of a strongly elliptic system with m equations of ellipticity λ satisfying ∈ 𝒫r a.e. and Ω′ ⊆ Ω subdomain, the following inequalities hold: where C (= C(n,m,λ,q,p,Ω,Ω′)) is a positive constant.” © 1999 John Wiley & Sons, Inc. 相似文献
6.
Heungju Ahn 《Mathematische Nachrichten》2007,280(4):343-350
We introduce a notion of q ‐pseudoconvex domain of new type for a bounded domain of ?n and prove that for given a ‐closed (p, r)‐form, r ≥ q, that is smooth up to the boundary, there exists a (p, r – 1)‐form smooth up to the boundary which is a solution of ‐equation on a bounded q ‐pseudoconvex domain. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
A p‐list assignment L of a graph G assigns to each vertex v of G a set of permissible colors. We say G is L‐(P, q)‐colorable if G has a (P, q)‐coloring h such that h(v) ? L(v) for each vertex v. The circular list chromatic number of a graph G is the infimum of those real numbers t for which the following holds: For any P, q, for any P‐list assignment L with , G is L‐(P, q)‐colorable. We prove that if G has an orientation D which has no odd directed cycles, and L is a P‐list assignment of G such that for each vertex v, , then G is L‐(P, q)‐colorable. This implies that if G is a bipartite graph, then , where is the maximum average degree of a subgraph of G. We further prove that if G is a connected bipartite graph which is not a tree, then . © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 190–204, 2008 相似文献
8.
Wolfgang Knirsch 《Mathematische Nachrichten》2002,245(1):94-103
On bounded pseudoconvex domains Ω the orthogonal projection Pq : L2(p,q) (Ω) → ker q is given by Pq = Id – Sq+1 q = Id – *q+1Nq+1 q, where Sq is the canonical solution operator of the ‐equation and Nq is the ‐Neumann operator. We prove a formula for the solution operator Sq restricted on (0, q)‐forms with holomorphic coefficients. And as an application we get a characterization of compactness of the solution operator restricted on (0, q)‐forms with holomorphic coefficients. On general (0, q)‐forms we show that this condition is necessary for compactness of the solution operator. 相似文献
9.
Ryszard Mazur 《Mathematische Nachrichten》1980,99(1):355-361
Let Q(D) be a class of functions q, q(0) = 0, |q(z)| < 1 holomorphic in the Reinhardt domain D ? C n, a and b — arbitrary fixed numbers satisfying the condition — 1 ≤ b < a ≤ 1. ??(a, b; D) — the class of functions p such that p ? ??(a, b; D) iff for some q ? Q(D) and every z ? D. S*(a, b; D) — the class of functions f such that f ? S*(a, g; D) iff Sc(a, b; D) — the class of functions q such that q ? Sc(a, b; D) iff , where p ε ??(a, b; D) and K is an operator of the form for z=z1,z2,…zn. The author obtains sharp bounds on |p(z)|, f(z)| g(z)| as well as sharp coefficient inequalities for functions in ??(a, b; D), S*(a, b; D) and Sc(a, b; D). 相似文献
10.
The distribution of the ground state eigenvalue λ0(Q) of Hill's operator Q = −d2/dx2 + q(x) on the circle of perimeter 1 is expressed in two different ways in case the potential q is standard white noise. Let WN be the associated white noise measure, and let CBM be the measure for circular Brownian motion p(x), 0 ≤ x < 1, formed from the standard Brownian motion b(x), 0 ≤ x ≤ 1, starting at b(0) = a, by conditioning so that b(1) = a, and distributing this common level over the line according to the measure da. The connection is based upon the Ricatti correspondence q(x) = λ + p′ (x) + p2(x). The two versions of the distribution are (1) in which $\overline{p}$ is the mean value ∫ pdx, and (2) the left‐hand side of (2) being the density for (1) and CBM0 the conditional circular Brownian measure on $\overline{p}$ = 0. (1) and (2) are related by the divergence theorem in function space as suggested by the recognition of the Jacobian factor the outward‐pointing normal component of the vector field v(x) = ∂Δ(λ)/∂q(x), 0 ≤ x < 1, Δ being the Hill's discriminant for Q. The Ricatti correspondence prompts the idea that (1) and (2) are instances of the Cameron‐Martin formula, but it is not so: The latter has to do with the initial value problem for Ricatti, but it is the periodic problem that figures here, so the proof must be done by hand, by finite‐dimensional approximation. The adaptation of 1 and 2 to potentials of Ornstein‐Uhlenbeck type is reported without details. © 1999 John Wiley & Sons, Inc. 相似文献
11.
In this article we give the definition of the class ??1 and prove: (1) ??1(v) ≠ ? for v ∈ ?? = ??1 ∪ ??2 ∪ ??3 where (2) there exists 2 ? {2q2; q2 ± q, q2;q2 ± q} supplementary difference sets for q2 ∈ ??; (3) there exists an Hadamard matrix of order 4v for v ∈ ??; (4) if t is an order of T-matrices, there exists an Hadamard matrix of order 4tv for v ∈ ??. © 1994 John Wiley & Sons, Inc. 相似文献
12.
For a finite projective plane , let denote the maximum number of classes in a partition of the point set, such that each line has at least two points in the same partition class. We prove that the best possible general estimate in terms of the order of projective planes is , which is tight apart from a multiplicative constant in the third term :
- (1) As holds for every projective plane of order q.
- (2) If q is a square, then the Galois plane of order q satisfies .
13.
Let D be a bounded and smooth domain in RN, N ≥ 5, P ∈ D. We consider the following biharmonic elliptic problemin Ω = D \Bδ (P), with p supercritical, namely . We find a sequence of resonant exponents such that if is given, with p ≠ pj for all j, then for all δ > 0 sufficiently small, this problem is solvable (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
Xiaohui Yu 《Mathematical Methods in the Applied Sciences》2011,34(10):1236-1242
In this paper, we study the multiple solutions for the semilinear elliptic equation where , 1<p<(N + 2)/(N ? 2) for and p>1 for N = 2. We will prove that the problem possesses infinitely many solutions under some assumptions on Q(x). Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
The expansion of f ∈ Lp(0, 1) Fourier series of Bessel functions of order converges to f in Lp whenever Let be the space of p-integrable functions with respect to the measure t dt and where {sn}, n = 1, 2, …, is the set of positive zeros of Jv. Then, the expansion of in a Fourier series of functions ψn, ?1 < ν < ?½, converges to in whenever 相似文献
16.
Nakao Hayashi Masahiro Ikeda Pavel I. Naumkin 《Mathematical Methods in the Applied Sciences》2011,34(8):896-910
We prove the existence of the wave operator for the system of the massive Dirac–Klein–Gordon equations in three space dimensions x∈ R 3 where the masses m, M>0. We prove that for the small final data , (?, ?)∈ H 2 + µ, 1 × H 1 + µ, 1, with and , there exists a unique global solution for system (1) with the final state conditions Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
17.
K. C. Chang Luis Sanchez P. Rabinowitz 《Mathematical Methods in the Applied Sciences》1982,4(1):194-205
We consider the existence of a nontrivial solution of the following equation: where g is a nondecreasing function defined on R1, satisfies g(O) = O, and some other additional conditions. Our results and methods are quite similar to those associated with recent work on the nonlinear wave equation [1]-[8]: . 相似文献
18.
Given graphs G and H, an edge coloring of G is called an (H,q)‐coloring if the edges of every copy of H ? G together receive at least q colors. Let r(G,H,q) denote the minimum number of colors in a (H,q)‐coloring of G. In 9 Erd?s and Gyárfás studied r(Kn,Kp,q) if p and q are fixed and n tends to infinity. They determined for every fixed p the smallest q (denoted by qlin) for which r(Kn,Kp,q) is linear in n and the smallest q (denoted by qquad) for which r(Kn,Kp,q) is quadratic in n. They raised the problem of determining the smallest q for which we have . In this paper by using the Regularity Lemma we show that if , then we have . © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 39–49, 2003 相似文献
19.
In this paper, we study the multiplicity of non‐negative solutions for the quasilinear p‐Laplacian equation with the nonlinear boundary condition (1) where Δp denotes the p‐Laplacian operator, defined by △ pu = div( | ? u | p ? 2 ? u),1 < p < N, Ω is a smooth exterior domain in . is the outward normal derivative, . The parameters p,q,r are either or . The weight functions a(x),h(x),g(x) satisfy some suitable conditions. Using the decomposition of the Nehari manifold and the variational methods, we prove that problem (1) has at least two positive solutions provided 0 < | λ | < λ1 for some λ1. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
20.
Jeong Han Kim 《Random Structures and Algorithms》2003,23(2):111-132
Let ??k(n, p) be the random k‐uniform hypergraph on V = [n] with edge probability p. Motivated by a theorem of Erd?s and Rényi 7 regarding when a random graph G(n, p) = ??2(n, p) has a perfect matching, the following conjecture may be raised. (See J. Schmidt and E. Shamir 16 for a weaker version.) Conjecture. Let k|n for fixed k ≥ 3, and the expected degree d(n, p) = p(). Then (Erd?s and Rényi 7 proved this for G(n, p).) Assuming d(n, p)/n1/2 → ∞, Schmidt and Shamir 16 were able to prove that ??k(n, p) contains a perfect matching with probability 1 ? o(1). Frieze and Janson 8 showed that a weaker condition d(n, p)/n1/3 → ∞ was enough. In this paper, we further weaken the condition to A condition for a similar problem about a perfect triangle packing of G(n, p) is also obtained. A perfect triangle packing of a graph is a collection of vertex disjoint triangles whose union is the entire vertex set. Improving a condition p ≥ cn?2/3+1/15 of Krivelevich 12 , it is shown that if 3|n and p ? n?2/3+1/18, then © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 111–132, 2003 相似文献