共查询到20条相似文献,搜索用时 31 毫秒
1.
Douglas R. Woodall 《Journal of Graph Theory》2004,45(1):51-56
It is proved that, if s ≥ 2, a graph that does not have K2 + K s = K1 + K1, s as a minor is (s, 1)*‐choosable. This completes the proof that such a graph is (s + 1 ? d,d)*‐choosable whenever 0 ≤ d ≤ s ?1 © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 51–56, 2004 相似文献
2.
F. M. Dong K. M. Koh K. L. Teo C. H. C. Little M. D. Hendy 《Journal of Graph Theory》2001,37(1):48-77
Given a graph G and an integer k ≥ 1, let α(G, k) denote the number of k‐independent partitions of G. Let ???s(p,q) (resp., ??2?s(p,q)) denote the family of connected (resp., 2‐connected) graphs which are obtained from the complete bipartite graph Kp,q by deleting a set of s edges, where p ≥ q ≥ 2. This paper first gives a sharp upper bound for α(G,3), where G ∈ ?? ?s(p,q) and 0 ≤ s ≤ (p ? 1)(q ? 1) (resp., G ∈ ?? 2?s(p,q) and 0 ≤ s ≤ p + q ? 4). These bounds are then used to show that if G ∈ ?? ?s(p,q) (resp., G ∈ ?? 2?s (p,q)), then the chromatic equivalence class of G is a subset of the union of the sets ???si(p+i,q?i) where max and si = s ? i(p?q+i) (resp., a subset of ??2?s(p,q), where either 0 ≤ s ≤ q ? 1, or s ≤ 2q ? 3 and p ≥ q + 4). By applying these results, we show finally that any 2‐connected graph obtained from Kp,q by deleting a set of edges that forms a matching of size at most q ? 1 or that induces a star is chromatically unique. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 48–77, 2001 相似文献
3.
Luis Silvestre 《纯数学与应用数学通讯》2007,60(1):67-112
Given a function φ and s ∈ (0, 1), we will study the solutions of the following obstacle problem:
- u ≥ φ in ?n,
- (??)su ≥ 0 in ?n,
- (??)su(x) = 0 for those x such that u(x) > φ(x),
- lim|x| → + ∞ u(x) = 0.
4.
Let F ∈ C([0,∞)) be a positive increasing function such that Φ(s):= |s|F(|s|) is a Young function. In general, the F-Sobolev inequality and the Φ-Orlicz-Sobolev inequality are not equivalent. In this paper, a growth condition on F is presented for these two inequalities to be equivalent. The main result generalizes the corresponding known one for F(s) = logδ(1 + s) (δ > 0). As an application, some criteria are presented for the F-Sobolev inequality to hold. 相似文献
5.
For an integer s ≥ 0, a graph G is s‐hamiltonian if for any vertex subset with |S′| ≤ s, G ‐ S′ is hamiltonian. It is well known that if a graph G is s‐hamiltonian, then G must be (s+2)‐connected. The converse is not true, as there exist arbitrarily highly connected nonhamiltonian graphs. But for line graphs, we prove that when s ≥ 5, a line graph is s‐hamiltonian if and only if it is (s+2)‐connected. 相似文献
6.
Yong HE Yi Wei JIANG Hao ZHOU 《数学学报(英文版)》2007,23(1):165-174
In this paper, we consider the seml-online preemptive scheduling problem with known largest job sizes on two uniform machines. Our goal is to maximize the continuous period of time (starting from time zero) when both machines are busy, which is equivalent to maximizing the minimum machine completion time if idle time is not introduced. We design optimal deterministic semi-online algorithms for every machine speed ratio s ∈ [1, ∞), and show that idle time is required to achieve the optimality during the assignment procedure of the algorithm for any s 〉 (s^2 + 3s + 1)/(s^2 + 2s + 1). The competitive ratio of the algorithms is (s^2 + 3s + 1)/(s^2 + 2s + 1), which matches the randomized lower bound for every s ≥ 1. Hence randomization does not help for the discussed preemptive scheduling problem. 相似文献
7.
For any s ≥ 1 and t ≥ (S2), we prove that among all graphs with n vertices the graph that contains the maximal number of induced copies of Kt, t+s for any fixed s ≥ 1 and t ≥ (s2) is K(n/2)+α(n/2)-α for some function α = o(n). We show that this is not valid for t < (s2). Analogous results for complete multipartite graphs are also obtained. 相似文献
8.
For s < 3/2, it is shown that the Cauchy problem for the Degasperis-Procesi equation (DP) is ill-posed in Sobolev spaces H s . If 1/2 ≤ s < 3/2, then ill-posedness is due to norm inflation. This means that there exist DP solutions who are initially arbitrarily small and eventually arbitrarily large with respect to the H s norm, in an arbitrarily short time. Since DP solutions conserve a quantity equivalent to the L 2-norm, there is no norm inflation in H 0 for these solutions. In this case, ill-posedness is caused by failure of uniqueness. For all other s < 1/2, the situation is similar to H 0. Considering that DP is locally well-posed in H s for s > 3/2, this work establishes 3/2 as the critical index of well-posedness in Sobolev spaces. 相似文献
9.
Alan V. Lair 《Applicable analysis》2013,92(5):431-437
We show that the equation Δu = p(x)f(u) has a positive solution on R N , N ≥ 3, satisfying <artwork name="GAPA31011ei1"> <artwork name="GAPA31011ei2"> if and only if <artwork name="GAPA31011ei3"> when ψ(r) = min{p(x): |x| = r}. The nondecreasing continuous function f satisfies f(0) = 0, f (s) > 0 for s > 0, and sup s ≥ 1 f(s)/s<∞, and the nonnegative continuous function p is required to be asymptotically radial. This extends previous results which required the function p to be constant or radial. 相似文献
10.
We study a quasilinear parabolic–elliptic Keller–Segel system involving a source term of logistic type ut = ? ? (?(u) ? u) ? χ ? ? (u ? v) + g(u), ? Δv = ? v + u in Ω × (0,T), subject to nonnegative initial data and the homogeneous Neumann boundary condition in a bounded domain with smooth boundary, n ≥ 1, χ > 0, ? ≥ c1sp for s ≥ s0 > 1, and g(s) ≤ as ? μs2 for s > 0 with a,g(0) ≥ 0, μ > 0. There are three nonlinear mechanisms included in the chemotaxis model: the nonlinear diffusion, aggregation and logistic absorption. The interaction among the triple nonlinearities shows that together with the nonlinear diffusion, the logistic absorption will dominate the aggregation such that the unique classical solution of the system has to be global in time and bounded, regardless of the initial data, whenever , or, equivalently, , which enlarge the parameter range , or , required by globally bounded solutions of the quasilinear K‐S system without the logistic source. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
Let Ls 1 (s ∈ ?) be the s-th differential group, that is the set {(x1,…,xs): x1 ≠ 0, xn ∈ K, n =1,2,…,s} (K ∈ {?,?}) together with the group operation which describes the chain rules (up to order s) for Cs-functions with fixed point 0. We consider homomorphisms Φs, Φs = (f1,…,fs) from an abelian group (G,+) into Ls 1 such that f1 = 1, f2 = … = fp+2 = 0, 0p+2 ≠ 0 for a fixed, but arbitrary p ≥ 0 such that p + 2 ≤ s (then fp+2 is necessarily a homomorphism from (G, +) to (K, +). Let l ∈ ? or l = ∞. We present a criterion for the extensibility of Φs to a homomorphism Φs+l from (G, +) to Ls+1 1 (L∞ 1, if l = ∞), by proving that such an extension (continuation) exists iff the component functions fn of Φs with s - p ≤ n ≤ min(s - p + l - 1,s) are certain polynomials in fP+2 (see Theorem 1). We also formulate the problem in the language of truncated formal power series in one indeterminate X over K. The somewhat easier situation f 1 ≠ 1 will be studied in a separate paper. 相似文献
12.
We consider the long‐time behavior and optimal decay rates of global strong solution to three‐dimensional isentropic compressible Navier–Stokes (CNS) system in the present paper. When the regular initial data also belong to some Sobolev space with l?4 and s∈[0, 1], we show that the global solution to the CNS system converges to the equilibrium state at a faster decay rate in time. In particular, the density and momentum converge to the equilibrium state at the rates (1 + t)?3/4?s/2 in the L2‐norm or (1 + t)?3/2?s/2 in the L∞‐norm, respectively, which are shown to be optimal for the CNS system. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
13.
Kazuhide Hirohata 《Journal of Graph Theory》1998,29(3):177-184
For a graph G and an integer k ≥ 1, let ςk(G) = dG(vi): {v1, …, vk} is an independent set of vertices in G}. Enomoto proved the following theorem. Let s ≥ 1 and let G be a (s + 2)-connected graph. Then G has a cycle of length ≥ min{|V(G)|, ς2(G) − s} passing through any path of length s. We generalize this result as follows. Let k ≥ 3 and s ≥ 1 and let G be a (k + s − 1)-connected graph. Then G has a cycle of length ≥ min{|V(G)|, − s} passing through any path of length s. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 177–184, 1998 相似文献
14.
Sigmund Selberg Achenef Tesfahun 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(3):1055-1063
Recently, Grünrock and Pecher proved global well-posedness of the 2d Dirac–Klein–Gordon equations given initial data for the spinor and scalar fields in H s and H s+1/2 × H s-1/2, respectively, where s ≥ 0, but uniqueness was only known in a contraction space of Bourgain type, strictly smaller than the natural solution space C([0,T]; H s × H s+1/2 × H s-1/2). Here we prove uniqueness in the latter space for s ≥ 0. This improves a recent result of Pecher, where the range s > 1/30 was covered. 相似文献
15.
In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg–de Vries (KdV) equation in the homogeneous Sobolev spaces Ḣs for s ≥ 0. Specifically, we prove the global existence, uniqueness, and Lipschitz‐continuous dependence on the initial data of the solutions of the periodic KdV. For the case where the initial data is in L2 we also show the Lipschitz‐continuous dependence of these solutions with respect to the initial data as maps from Ḣs to Ḣs for s ∈(−1,0]. © 2010 Wiley Periodicals, Inc. 相似文献
16.
For a continuous function s\sigma defined on [0,1]×\mathbbT[0,1]\times\mathbb{T}, let \ops\op\sigma stand for the (n+1)×(n+1)(n+1)\times(n+1) matrix whose (j,k)(j,k)-entries are equal to \frac1 2pò02p s( \fracjn,eiq) e-i(j-k)q dq, j,k = 0,1,...,n . \displaystyle \frac{1} {2\pi}\int_0^{2\pi} \sigma \left( \frac{j}{n},e^{i\theta}\right) e^{-i(j-k)\theta} \,d\theta, \qquad j,k =0,1,\dots,n~. These matrices can be thought of as variable-coefficient Toeplitz matrices or as the discrete analogue of pseudodifferential operators. Under the assumption that the function s\sigma possesses a logarithm which is sufficiently smooth on [0,1]×\mathbbT[0,1]\times\mathbb{T}, we prove that the asymptotics of the determinants of \ops\op\sigma are given by det[\ops] ~ G[s](n+1)E[s] \text as n?¥ , \det \left[\op\sigma\right] \sim G[\sigma]^{(n+1)}E[\sigma] \quad \text{ as \ } n\to\infty~, where G[s]G[\sigma] and E[s]E[\sigma] are explicitly determined constants. This formula is a generalization of the Szegö Limit Theorem. In comparison with the classical theory of Toeplitz determinants some new features appear. 相似文献
17.
《偏微分方程通讯》2013,38(7-8):1391-1436
Abstract Studied here is an initial- and boundary-value problem for the Korteweg–de Vries equation posed on a bounded interval with nonhomogeneous boundary conditions. This particular problem arises naturally in certain circumstances when the equation is used as a model for waves and a numerical scheme is needed. It is shown here that this initial-boundary-value problem is globally well-posed in the L 2-based Sobolev space H s (0, 1) for any s ≥ 0. In addition, the mapping that associates to appropriate initial- and boundary-data the corresponding solution is shown to be analytic as a function between appropriate Banach spaces. 相似文献
18.
We report a new unconditionally stable implicit alternating direction implicit (ADI) scheme of O(k2 + h2) for the difference solution of linear hyperbolic equation utt + 2αut + β2u = uxx + uyy + f(x, y, t), αβ ≥ 0, 0 < x, y < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where α > 0 and β ≥ 0 are real numbers. The resulting system of algebraic equations is solved by split method. Numerical results are provided to demonstrate the efficiency and accuracy of the method. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 684–688, 2001 相似文献
19.
In this paper, we introduce an inverse problem of a Schrödinger type variable nonlocal elliptic operator (???(A(x)?))s+q), for 0<s<1. We determine the unknown bounded potential q from the exterior partial measurements associated with the nonlocal Dirichlet-to-Neumann map for any dimension n≥2. Our results generalize the recent initiative [18] of introducing and solving inverse problem for fractional Schrödinger operator ((?Δ)s+q) for 0<s<1. We also prove some regularity results of the direct problem corresponding to the variable coefficients fractional differential operator and the associated degenerate elliptic operator. 相似文献
20.
YANG Dachun Department of Mathematics Beijing Normal University Beijing China 《中国科学A辑(英文版)》2005,48(1):12-39
Let(X,p,μ)d,θ be a space of homogeneous type,(?) ∈(0,θ],|s|<(?) andmax{d/(d+(?)),d/(d+s+(?))}<q≤∞.The author introduces the new Triebel-Lizorkin spaces (?)_∞q~s(X) and establishes the framecharacterizations of these spaces by first establishing a Plancherel-P(?)lya-type inequalityrelated to the norm of the spaces (?)_∞q~s(X).The frame characterizations of the Besovspace (?)_pq~s(X) with|s|<(?),max{d/(d+(?)),d/(d+s+(?))}<p≤∞ and 0<q≤∞and the Triebel-Lizorkin space (?)_pq~s(X)with|s|<(?),max{d/(d+(?)),d/(d+s+(?))}<p<∞ and max{d/(d+(?)),d/(d+s+(?))}<q≤∞ are also presented.Moreover,the au-thor introduces the new TriebeI-Lizorkin spaces b(?)_∞q~s(X) and H(?)_∞q~s(X) associated to agiven para-accretive function b.The relation between the space b(?)_∞q~s(X) and the spaceH(?)_∞q~s(X) is also presented.The author further proves that if s=0 and q=2,thenH(?)_∞q~s(X)=(?)_∞q~s(X),which also gives a new characterization of the space BMO(X),since (?)_∞q~s(X)=BMO(X). 相似文献