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1.
《偏微分方程通讯》2013,38(9-10):1811-1859
We consider the resonances for the transmission problem associated with a strictly convex transparent obstacle. Under some natural assumptions we show that there is a free of resonances region in the complex upper half plane given by {C ≤ Im λ ≤ C 1|λ|1/3 ? C 2}, where C, C 1 and C 2 are positive constants. Moreover, we obtain asymptotics for the number of resonances counted with multiplicities in the region {0 < Im λ ≤ C, 0 < Re λ ≤ r} as r → ∞, where C > 0 is the same constant as above. 相似文献
2.
Richard Warlimont 《Mathematische Nachrichten》1998,193(1):211-234
Given sequences g, λ: IN0 → C, g (0) = 1, linked by the convolution λ g = g′1 (g′1(n)= (n + 1) g (n + 1)) we study what can be inferred about λ (n → ∞) from some concrete information about the behaviour of g (n → ∞). 相似文献
3.
Rolf S. Rees 《Journal of Combinatorial Theory, Series A》2000,90(2):257
A truncated transversal design TTD of type gkm1 is a {k, k+1}-GDD of type gkm1 in which each point on the group of size m lies only in blocks of size k+1. Thus a TTD of type gkm1 is equivalent to a transversal design TD (k, g) having m disjoint parallel classes of blocks. We employ a new construction developed by the author (1993, J. Combin. Des.1, 15–26) to show that if g1<g2 and if there exists a TD (k, g1) and a TD (k+1, g2), then there exists a TTD of type (g1g2)km1 for any 0m(g2 div g1) g21. As a corollary, we obtain a new lower bound on the number of mutually orthogonal idempotent latin squares of side g: if g1<g2 and there exist r MOLS of side g1 and r+1 MOLS of side g2 , then N(1 g1g2)r. 相似文献
4.
Improper choosability of planar graphs has been widely studied. In particular, ?krekovski investigated the smallest integer gk such that every planar graph of girth at least gk is k‐improper 2‐choosable. He proved [9] that 6 ≤ g1 ≤ 9; 5 ≤ g2 ≤ 7; 5 ≤ g3 ≤ 6; and ? k ≥ 4, gk = 5. In this article, we study the greatest real M(k, l) such that every graph of maximum average degree less than M(k, l) is k‐improper l‐choosable. We prove that if l ≥ 2 then . As a corollary, we deduce that g1 ≤ 8 and g2 ≤ 6, and we obtain new results for graphs of higher genus. We also provide an upper bound for M(k, l). This implies that for any fixed l, . © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 181–199, 2006 相似文献
5.
M. A. Fiol 《Journal of Graph Theory》1993,17(1):31-45
This paper studies the relation between the connectivity and other parameters of a digraph (or graph), namely its order n, minimum degree δ, maximum degree Δ, diameter D, and a new parameter lpi;, 0 ≤ π ≤ δ ? 2, related with the number of short paths (in the case of graphs l0 = ?(g ? 1)/2? where g stands for the girth). For instance, let G = (V,A) be a digraph on n vertices with maximum degree Δ and diameter D, so that n ≤ n(Δ, D) = 1 + Δ + Δ 2 + … + ΔD (Moore bound). As the main results it is shown that, if κ and λ denote respectively the connectivity and arc-connectivity of G, . Analogous results hold for graphs. © 1993 John Wiley & Sons, Inc. 相似文献
6.
Wenjie He Xiaoling Hou Ko‐Wei Lih Jiating Shao Weifan Wang Xuding Zhu 《Journal of Graph Theory》2002,41(4):307-317
Let G be a planar graph and let g(G) and Δ(G) be its girth and maximum degree, respectively. We show that G has an edge‐partition into a forest and a subgraph H so that (i) Δ(H) ≤ 4 if g(G) ≥ 5; (ii) Δ(H) ≤ 2 if g(G) ≥ 7; (iii) Δ(H)≤ 1 if g(G) ≥ 11; (iv) Δ(H) ≤ 7 if G does not contain 4‐cycles (though it may contain 3‐cycles). These results are applied to find the following upper bounds for the game coloring number colg(G) of a planar graph G: (i) colg(G) ≤ 8 if g(G) ≥ 5; (ii) colg(G)≤ 6 if g(G) ≥ 7; (iii) colg(G) ≤ 5 if g(G) ≥ 11; (iv) colg(G) ≤ 11 if G does not contain 4‐cycles (though it may contain 3‐cycles). © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 307–317, 2002 相似文献
7.
Assume that a dam has a capacity V. Its water input I={It, t ? [0, ∞)}], is assumed to be a diffusion process. The water is released at one of two rates 0 and M units of water per unit of time. The release rate is 0 until the water reaches level λ(0 < λ < V), when the water is released at rate M until it reaches level λ, (0 ≤ τ < λ). Once the level λ is reached, the release rate remains at zero until level λ is reached again, and the cycle is repeated. Under general cost structure, we discuss and review some of the most recent work in the area of optimal control of dams with release policies of the above type; we also discuss some new results and corrections to some existing results. 相似文献
8.
A transversal cover is a set of gk points in k disjoint groups of size g and a minimum collection of transversal subset s, called blocks, such that any pair of points not contained in the same group appear in at least one block. The case g = 2 was investigated and completely solved by Sperner, Renyi, Katona, Kleitman, and Spencer. For all g, asymptotic results are known, but little is understood for small values of k. Sloane and others have initiated the investigation of g = 3. The present article is concerned with constructive techniques for all g and k. One of the principal constructions generalizes Wilson's theorem for transversal designs. This article also discusses a simulated annealing algorithm for finding transversal covers and gives a table of the best known transversal covers at this time. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 185–203, 1999 相似文献
9.
Let M = {m1, m2, …, mh} and X be a v-set (of points). A holey perfect Mendelsohn designs (briefly (v, k, λ) - HPMD), is a triple (X, H, B), where H is a collection of subsets of X (called holes) with sizes M and which partition X, and B is a collection of cyclic k-tuples of X (called blocks) such that no block meets a hole in more than one point and every ordered pair of points not contained in a hole appears t-apart in exactly λ blocks, for 1 ≤ t ≤ k − 1. The vector (m1, m2, …, mh) is called the type of the HPMD. If m1 = m2 = … = mh = m, we write briefly mh for the type. In this article, it is shown that the necessary condition for the existence of a (v, 4, λ) - HPMD of type mh, namely, is also sufficient with the exception of types 24 and 18 with λ = 1, and type m4 for odd m with odd λ. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 203–213, 1997 相似文献
10.
《Quaestiones Mathematicae》2013,36(3):291-303
Abstract Most homotopies considered in the literature are linear homotopies of the form h i (λ) = λx i + (1—λ)y i , 0 ≤ λ ≤ 1. Although these prove to be adequate in most instances, they lack direct geometric significance because {h i (λ) | 0 ≤ λ ≤ 1} are not orbits of a vector field. On the other hand, the nonlinear homotopy g i (s) = e s x i + (1—e s )y i ,—∞ ≤ s ≤ 0, are orbits of a vector field (i.e., dg i /ds = g i —y i , g i (0) = x i ), and thus have direct geometric significance. This suggests that useful results can be obtained by replacing linear homotopy by transport along flows of smooth vector fields. The purpose of this paper is to elaborate on this simple idea. We define prehomotopy operators induced by vector fields on a manifold. These allow us to obtain finite transport relations and pre-Poincaré lemmas that generalize the classical results. They are shown to reproduce the classical results as asymptotic limits and to obtain representations of all solutions of complete systems of exterior differential equations on a star shaped region of a manifold. 相似文献
11.
An incomplete t‐wise balanced design of index λ is a triple (X,H,??) where X is a υ–element set, H is a subset of X called the hole, and B is a collection of subsets of X called blocks, such that, every t‐element subset of X is either in H or in exactly λ blocks, but not both. If H is a hole in an incomplete t‐wise balanced design of order υ and index λ, then |H| ≤ υ/2 if t is odd and |H| ≤ (υ ? 1)/2 if t is even. In particular, this result establishes the validity of Kramer's conjecture that the maximal size of a block in a Steiner t‐wise balanced design is at most υ/2 if t is odd and at most (υ?1)/2 when t is even. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 269–284, 2001 相似文献
12.
X is a nonnegative random variable such that EXt < ∞ for 0≤ t < λ ≤ ∞. The (l??) quantile of the distribution of X is bounded above by [??1 EXt]1?t. We show that there exist positive ?1 ≥ ?2 such that for all 0 <?≤?1 the function g(t) = [?-1EXt]1?t is log-convex in [0, c] and such that for all 0 < ? ≤ ?2 the function log g(t) is nonincreasing in [0, c]. 相似文献
13.
K. L. Patra 《Linear and Multilinear Algebra》2013,61(4):381-397
Consider a tree Pn-g,g , n≥ 2, 1≤ g≤ n-1 on n vertices which is obtained from a path on [1,2,?…?,n-g] vertices by adding g pendant vertices to the pendant vertex n-g. We prove that over all trees on n?≥?5 vertices, the distance between center and characteristic set, centroid and characteristic set, and center and centroid is maximized by trees of the form Pn-g,g , 2?≤?g?≤?n-3. For n≥ 5, we also supply the precise location of the characteristic set of the tree Pn-g,g , 2?≤?g?≤?n-3. 相似文献
14.
Michael A. Henning 《Journal of Graph Theory》2000,34(1):60-66
For integers m, n ≥ 2, let g(m, n) be the minimum order of a graph, where every vertex belongs to both a clique Km of order m and a biclique K(n, n). We show that g(m, n) = 2(m + n − 2) if m ≤ n − 2. Furthermore, for m ≥ n − 1, we establish that ≡ 0 mod(n − 1) or, if m is sufficiently large and is not an integer. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 60–66, 2000 相似文献
15.
Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λmin=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λmin≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009 相似文献
16.
Transverse Steiner quadruple systems with five holes are either of type g5 or g4u1. We concentrate on the systems of type g4u1 and settle existence except when g ≡ u ≡ 2 (mod 4) and all except 40 parameter situations when g ≡ u + 2 ≡ 0 (mod 4). The question of existence for transverse quadruple systems of type g4u1 with index λ > 1 is completely solved for all λ ≥ 13 and λ ∈ {4, 6, 8, 9, 10, 12}. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 315–340, 2007 相似文献
17.
Ahmed M. Assaf 《组合设计杂志》1993,1(6):453-458
A (v, k. λ) covering design of order v, block size k, and index λ is a collection of k-element subsets, called blocks, of a set V such that every 2-subset of V occurs in at least λ blocks. The covering problem is to determine the minimum number of blocks, α(v, k, λ), in a covering design. It is well known that $ \alpha \left({\nu,\kappa,\lambda } \right) \ge \left\lceil {\frac{\nu}{\kappa}\left\lceil {\frac{{\nu - 1}}{{\kappa - 1}}\lambda} \right\rceil} \right\rceil = \phi \left({\nu,\kappa,\lambda} \right) $, where [χ] is the smallest integer satisfying χ ≤ χ. It is shown here that α (v, 5, λ) = ?(v, 5, λ) + ? where λ ≡ 0 (mod 4) and e= 1 if λ (v?1)≡ 0(mod 4) and λv (v?1)/4 ≡ ?1 (mod 5) and e= 0 otherwise With the possible exception of (v,λ) = (28, 4). © 1993 John Wiley & Sons, Inc. 相似文献
18.
An affine α-resolvable PBD of index λ is a triple (V, B, R), where V is a set (of points), B is a collection of subsets of V (blocks), and R is a partition of B (resolution), satisfying the following conditions: (i) any two points occur together in λ blocks, (ii) any point occurs in α blocks of each resolution class, and (iii) |B| = |V| + |R| − 1. Those designs embeddable in symmetric designs are described and two infinite series of embeddable designs are constructed. The analog of the Bruck–Ryser–Chowla theorem for affine α-resolvable PBDs is obtained. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:111–129, 1998 相似文献
19.
We study the asymptotic, long-time behavior of the energy function where {Xs : 0 ≤ s < ∞} is the standard random walk on the d-dimensional lattice Zd, 1 < α ≤ 2, and f:R+ → R+ is any nondecreasing concave function. In the special case f(x) = x, our setting represents a lattice model for the study of transverse magnetization of spins diffusing in a homogeneous, α-stable, i.i.d., random, longitudinal field {λV(x) : x ∈ Zd} with common marginal distribution, the standard α-symmetric stable distribution; the parameter λ describes the intensity of the field. Using large-deviation techniques, we show that Sc(λ α f) = limt→∞ E(t; λ f) exists. Moreover, we obtain a variational formula for this decay rate Sc. Finally, we analyze the behavior Sc(λ α f) as λ → 0 when f(x) = xβ for all 1 ≥ β > 0. Consequently, several physical conjectures with respect to lattice models of transverse magnetization are resolved by setting β = 1 in our results. We show that Sc(λ, α, 1) ≈ λα for d ≥ 3, λagr;(ln 1/λ)α−1 in d = 2, and in d = 1. © 1996 John Wiley & Sons, Inc. 相似文献
20.
A λ‐design is a family ?? = {B1, B2, …, Bv} of subsets of X = {1, 2, …, v} such that |Bi∩Bj| = λ for all i≠jand not all Bi are of the same size. The only known example of λ‐designs (called type‐1 designs) are those obtained from symmetric designs by a certain complementation procedure. Ryser [J Algebra 10 (1968), 246–261] and Woodall [Proc London Math Soc 20 (1970), 669–687] independently conjectured that all λ‐designs are type‐1. Let g = gcd(r ? 1, r* ? 1), where rand r* are the two replication numbers. Ionin and Shrikhande [J Combin Comput 22 (1996), 135–142; J Combin Theory Ser A 74 (1996), 100–114] showed that λ‐designs with g = 1, 2, 3, 4 are type‐1 and that the Ryser–Woodall conjecture is true for λ‐designs on p + 1, 2p + 1, 3p + 1, 4p + 1 points, where pis a prime. Hein and Ionin [Codes and Designs—Proceedings of Conference honoring Prof. D. K. Ray‐Chaudhuri on the occasion of his 65th birthday, Ohio State University Mathematical Research Institute Publications, 10, Walter de Gruyter, Berlin, 2002, pp. 145–156] proved corresponding results for g = 5 and Fiala [Codes and Designs—Proceedings of Conference honoring Prof. D. K. Ray‐Chaudhuri on the occasion of his 65th birthday, Ohio State University Mathematical Research Institute Publications, 10, Walter de Gruyter, Berlin, 2002, pp. 109–124; Ars Combin 68 (2003), 17–32; Ars Combin, to appear] for g = 6, 7, and 8. In this article, we consider λ designs with exactly two block sizes. We show that in this case, the conjecture is true for g = 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, and for g = 10, 14, 18, 22 with v≠4λ ? 1. We also give two results on such λ‐designs on v = 9p + 1 and 12p + 1 points, where pis a prime. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:95‐110, 2011 相似文献