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1.
Norihide Tokushige 《组合设计杂志》2006,14(1):52-55
Let be a k‐uniform hypergraph on n vertices. Suppose that holds for all . We prove that the size of is at most if satisfies and n is sufficiently large. © 2005 Wiley Periodicals, Inc. J Combin Designs 相似文献
2.
Stefano Bianchini 《纯数学与应用数学通讯》2006,59(5):688-753
We consider the special Jin‐Xin relaxation model We assume that the initial data ( ) are sufficiently smooth and close to ( ) in L∞ and have small total variation. Then we prove that there exists a solution ( ) with uniformly small total variation for all t ≥ 0, and this solution depends Lipschitz‐continuously in the L1 norm with respect to time and the initial data. Letting , the solution converges to a unique limit, providing a relaxation limit solution to the quasi‐linear, nonconservative system These limit solutions generate a Lipschitz semigroup on a domain containing the functions with small total variation and close to . This is precisely the Riemann semigroup determined by the unique Riemann solver compatible with (0.1). © 2005 Wiley Periodicals, Inc. 相似文献
3.
A k‐digraph is a digraph in which every vertex has outdegree at most k. A ‐digraph is a digraph in which a vertex has either outdegree at most k or indegree at most l. Motivated by function theory, we study the maximum value Φ (k) (resp. ) of the arc‐chromatic number over the k‐digraphs (resp. ‐digraphs). El‐Sahili [3] showed that . After giving a simple proof of this result, we show some better bounds. We show and where θ is the function defined by . We then study in more detail properties of Φ and . Finally, we give the exact values of and for . © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 315–332, 2006 相似文献
4.
In this paper we give a necessary and sufficient condition for the oscillation of the second order linear differential equation where p is a locally integrable function and either or where We give some applications which show how these results unify and imply some classical results in oscillation theory. 相似文献
5.
An asymmetric covering is a collection of special subsets S of an n‐set such that every subset T of the n‐set is contained in at least one special S with . In this paper we compute the smallest size of any for We also investigate “continuous” and “banded” versions of the problem. The latter involves the classical covering numbers , and we determine the following new values: , , , , and . We also find the number of non‐isomorphic minimal covering designs in several cases. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 218–228, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10022 相似文献
6.
Nicolas Bougard 《组合设计杂志》2006,14(5):333-350
An (n,k,p,t)‐lotto design is an n‐set N and a set of k‐subsets of N (called blocks) such that for each p‐subset P of N, there is a block for which . The lotto number L(n,k,p,t) is the smallest number of blocks in an (n,k,p,t)‐lotto design. The numbers C(n,k,t) = L(n,k,t,t) are called covering numbers. It is easy to show that, for n ≥ k(p ? 1), For k = 3, we prove that equality holds if one of the following holds:
- (i) n is large, in particular
- (ii)
- (iii) 2 ≤ p ≤ 6.
7.
Let be integers, , , and let for each , be a cycle or a tree on vertices. We prove that every graph G of order at least n with contains k vertex disjoint subgraphs , where , if is a tree, and is a cycle with chords incident with a common vertex, if is a cycle. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 87–98, 2009 相似文献
8.
Massimo Gobbino 《Mathematical Methods in the Applied Sciences》1999,22(5):375-388
We investigate the evolution problem where H is a Hilbert space, A is a self‐adjoint linear non‐negative operator on H with domain D(A), and is a continuous function. We prove that if , and , then there exists at least one global solution, which is unique if either m never vanishes, or m is locally Lipschitz continuous. Moreover, we prove that if for all , then this problem is well posed in H. On the contrary, if for some it happens that for all , then this problem has no solution if with β small enough. We apply these results to degenerate parabolic PDEs with non‐local non‐linearities. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
9.
Vaclav Linek 《组合设计杂志》2009,17(1):36-38
For , a S(t,K,v) design is a pair, , with |V| = v and a set of subsets of V such that each t‐subset of V is contained in a unique and for all . If , , , and is a S(t,K,u) design, then we say has a subdesign on U. We show that a S(3,{4,6},18) design with a subdesign S(3,4,8) does not exist. © 2007 Wiley Periodicals, Inc. J Combin Designs 17: 36–38, 2009 相似文献
10.
Ross G. Pinsky 《Random Structures and Algorithms》2006,29(3):277-295
Let the random variable Zn,k denote the number of increasing subsequences of length k in a random permutation from Sn, the symmetric group of permutations of {1,…,n}. We show that Var(Z) = o((EZ)2) as n → ∞ if and only if . In particular then, the weak law of large numbers holds for Z if ; that is, We also show the following approximation result for the uniform measure Un on Sn. Define the probability measure μ on Sn by where U denotes the uniform measure on the subset of permutations that contain the increasing subsequence {x1,x2,…,x}. Then the weak law of large numbers holds for Z if and only if where ∣∣˙∣∣ denotes the total variation norm. In particular then, (*) holds if . In order to evaluate the asymptotic behavior of the second moment, we need to analyze occupation times of certain conditioned two‐dimensional random walks. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 相似文献
11.
The circular chromatic index of a graph G, written , is the minimum r permitting a function such that whenever e and are incident. Let □ , where □ denotes Cartesian product and H is an ‐regular graph of odd order, with (thus, G is s‐regular). We prove that , where is the minimum, over all bases of the cycle space of H, of the maximum length of a cycle in the basis. When and m is large, the lower bound is sharp. In particular, if , then □ , independent of m. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 7–18, 2008 相似文献
12.
De‐Jun Feng 《Mathematische Nachrichten》2002,241(1):65-72
For each 0 < s < 1, define where , denote respectively the s‐dimensional packing measure and Hausdorff measure, and the infimum is taken over all the sets E ⊂ R with . In this paper we give a nontrivial estimation of c(s), namely, for each 0 < s < 1, where . As an application, we obtain a lower density theorem for Hausdorff measures. 相似文献
13.
Let consist of all simple graphs on 2k vertices and edges. For a simple graph G and a positive integer , let denote the number of proper vertex colorings of G in at most colors, and let . We prove that and is the only extremal graph. We also prove that as . © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 135–148, 2007 相似文献
14.
In this paper we prove a Tauberian type theorem for the space L ( H n ). This theorem gives sufficient conditions for a L ( H n ) submodule J ? L ( H n ) to make up all of L ( H n ). As a consequence of this theorem, we are able to improve previous results on the Pompeiu problem with moments on the Heisenberg group for the space L∞( H n ). In connection with the Pompeiu problem, given the vanishing of integrals ∫ z m L g f ( z , 0) dσ ( z ) = 0 for all g ∈ H n and i = 1, 2 for appropriate radii r1 and r2, we now have the (improved) conclusion f ≡ 0, where = · · · and form the standard basis for T(0,1)( H n ). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
We prove the uniqueness of weak solutions of the 3‐D time‐dependent Ginzburg‐Landau equations for super‐conductivity with initial data (ψ0, A0)∈ L2 under the hypothesis that (ψ, A) ∈ Ls(0, T; Lr,∞) × (0, T; with Coulomb gauge for any (r, s) and satisfying + = 1, + = 1, ≥ , ≥ and 3 < r ≤ 6, 3 < ≤ ∞. Here Lr,∞ ≡ is the Lorentz space. As an application, we prove a uniqueness result with periodic boundary condition when ψ0 ∈ , A0 ∈ L3 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
We study the number of n‐vertex graphs that can be written as the edge‐union of k‐vertex cliques. We obtain reasonably tight estimates for in the cases (i) k = n ? o(n) and (ii) k = o(n) but . We also show that exhibits a phase transition around . We leave open several potentially interesting cases, and raise some other questions of a similar nature. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 87–107, 2006 相似文献
17.
Given a basis for 2‐cocycles over a group G of order , we describe a nonlinear system of 4t‐1 equations and k indeterminates over , whose solutions determine the whole set of cocyclic Hadamard matrices over G, in the sense that ( ) is a solution of the system if and only if the 2‐cocycle gives rise to a cocyclic Hadamard matrix . Furthermore, the study of any isolated equation of the system provides upper and lower bounds on the number of coboundary generators in which have to be combined to form a cocyclic Hadamard matrix coming from a special class of cocycles. We include some results on the families of groups and . A deeper study of the system provides some more nice properties. For instance, in the case of dihedral groups , we have found that it suffices to check t instead of the 4t rows of , to decide the Hadamard character of the matrix (for a special class of cocycles f). © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 276–290, 2008 相似文献
18.
Let be bounded Lipschitz and relatively open. We show that the solution to the linear first order system 1 : (1) vanishes if and , (e.g. ). We prove to be a norm if with , for some p, q > 1 with 1/p + 1/q = 1 and . We give a new proof for the so called ‘in-finitesimal rigid displacement lemma’ in curvilinear coordinates: Let , satisfy for some with . Then there are and a constant skew-symmetric matrix , such that . (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
We consider the half‐linear boundary value problem where and the weight function q is assumed to change sign. We prove the existence of two sequences , of eigenvalues and derive asymptotic estimates for as . 相似文献
20.
A spanning subgraph G of a graph H is a k‐detour subgraph of H if for each pair of vertices , the distance, , between x and y in G exceeds that in H by at most k. Such subgraphs sometimes also are called additive spanners. In this article, we study k‐detour subgraphs of the n‐dimensional cube, , with few edges or with moderate maximum degree. Let denote the minimum possible maximum degree of a k‐detour subgraph of . The main result is that for every and On the other hand, for each fixed even and large n, there exists a k‐detour subgraph of with average degree at most . © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 55–64, 2008 相似文献