共查询到20条相似文献,搜索用时 93 毫秒
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J.R. Cannon 《Journal of Mathematical Analysis and Applications》2005,311(1):147-161
The authors study the problem , and u(0,t)=u(1,t)=ψ(t), where ψ(t)=u0 for t2k<t<t2k+1 and ψ(t)=0 for , with t0=0 and the sequence tk is determined by the equations , for , and , for k=2,4,6,… and where 0<m<M. Note that the switching points , are unknown. Existence and uniqueness are demonstrated. Theoretical estimates of the tk and tk+1−tk are obtained and numerical verifications of the estimates are presented. The case of ux(0,t)=ux(1,t)=ψ(t) is also considered and analyzed. 相似文献
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Florian Luca 《Journal of Number Theory》2003,102(2):298-305
In this paper, we prove two results. The first theorem uses a paper of Kim (J. Number Theory 74 (1999) 307) to show that for fixed primes p1,…,pk, and for fixed integers m1,…,mk, with , the numbers (ep1(n),…,epk(n)) are uniformly distributed modulo (m1,…,mk), where ep(n) is the order of the prime p in the factorization of n!. That implies one of Sander's conjectures from Sander (J. Number Theory 90 (2001) 316) for any set of odd primes. Berend (J. Number Theory 64 (1997) 13) asks to find the fastest growing function f(x) so that for large x and any given finite sequence , there exists n<x such that the congruences hold for all i?f(x). Here, pi is the ith prime number. In our second result, we are able to show that f(x) can be taken to be at least , with some absolute constant c1, provided that only the first odd prime numbers are involved. 相似文献
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Abey López García 《Advances in Mathematics》2008,218(4):1081-1106
We prove ratio asymptotic for sequences of multiple orthogonal polynomials with respect to a Nikishin system of measures N(σ1,…,σm) such that for each k, σk has constant sign on its support consisting on an interval , on which almost everywhere, and a set without accumulation points in . 相似文献
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Hong-Gwa Yeh 《Discrete Applied Mathematics》2009,157(7):1663-1668
We show that there is a curious connection between circular colorings of edge-weighted digraphs and periodic schedules of timed marked graphs. Circular coloring of an edge-weighted digraph was introduced by Mohar [B. Mohar, Circular colorings of edge-weighted graphs, J. Graph Theory 43 (2003) 107-116]. This kind of coloring is a very natural generalization of several well-known graph coloring problems including the usual circular coloring [X. Zhu, Circular chromatic number: A survey, Discrete Math. 229 (2001) 371-410] and the circular coloring of vertex-weighted graphs [W. Deuber, X. Zhu, Circular coloring of weighted graphs, J. Graph Theory 23 (1996) 365-376]. Timed marked graphs [R.M. Karp, R.E. Miller, Properties of a model for parallel computations: Determinancy, termination, queuing, SIAM J. Appl. Math. 14 (1966) 1390-1411] are used, in computer science, to model the data movement in parallel computations, where a vertex represents a task, an arc uv with weight cuv represents a data channel with communication cost, and tokens on arc uv represent the input data of task vertex v. Dynamically, if vertex u operates at time t, then u removes one token from each of its in-arc; if uv is an out-arc of u, then at time t+cuv vertex u places one token on arc uv. Computer scientists are interested in designing, for each vertex u, a sequence of time instants {fu(1),fu(2),fu(3),…} such that vertex u starts its kth operation at time fu(k) and each in-arc of u contains at least one token at that time. The set of functions is called a schedule of . Computer scientists are particularly interested in periodic schedules. Given a timed marked graph , they ask if there exist a period p>0 and real numbers xu such that has a periodic schedule of the form fu(k)=xu+p(k−1) for each vertex u and any positive integer k. In this note we demonstrate an unexpected connection between circular colorings and periodic schedules. The aim of this note is to provide a possibility of translating problems and methods from one area of graph coloring to another area of computer science. 相似文献
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Edith Hemaspaandra Lane A. Hemaspaandra Stanis?aw P. Radziszowski 《Discrete Applied Mathematics》2007,155(2):103-118
We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c?1 of deletion:
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Let G be a graph. The connectivity of G, κ(G), is the maximum integer k such that there exists a k-container between any two different vertices. A k-container of G between u and v, Ck(u,v), is a set of k-internally-disjoint paths between u and v. A spanning container is a container that spans V(G). A graph G is k∗-connected if there exists a spanning k-container between any two different vertices. The spanning connectivity of G, κ∗(G), is the maximum integer k such that G is w∗-connected for 1≤w≤k if G is 1∗-connected.Let x be a vertex in G and let U={y1,y2,…,yk} be a subset of V(G) where x is not in U. A spanningk−(x,U)-fan, Fk(x,U), is a set of internally-disjoint paths {P1,P2,…,Pk} such that Pi is a path connecting x to yi for 1≤i≤k and . A graph G is k∗-fan-connected (or -connected) if there exists a spanning Fk(x,U)-fan for every choice of x and U with |U|=k and x∉U. The spanning fan-connectivity of a graph G, , is defined as the largest integer k such that G is -connected for 1≤w≤k if G is -connected.In this paper, some relationship between κ(G), κ∗(G), and are discussed. Moreover, some sufficient conditions for a graph to be -connected are presented. Furthermore, we introduce the concept of a spanning pipeline-connectivity and discuss some sufficient conditions for a graph to be k∗-pipeline-connected. 相似文献
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This paper studies a variation of domination in graphs called rainbow domination. For a positive integer k, a k-rainbow dominating function of a graph G is a function f from V(G) to the set of all subsets of {1,2,…,k} such that for any vertex v with f(v)=0? we have ∪u∈NG(v)f(u)={1,2,…,k}. The 1-rainbow domination is the same as the ordinary domination. The k-rainbow domination problem is to determine the k-rainbow domination number of a graph G, that is the minimum value of ∑v∈V(G)|f(v)| where f runs over all k-rainbow dominating functions of G. In this paper, we prove that the k-rainbow domination problem is NP-complete even when restricted to chordal graphs or bipartite graphs. We then give a linear-time algorithm for the k-rainbow domination problem on trees. For a given tree T, we also determine the smallest k such that . 相似文献
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A discrete function f defined on Zn is said to be logconcave if for , , . A more restrictive notion is strong unimodality. Following Barndorff-Nielsen [O. Barndorff-Nielsen, Unimodality and exponential families, Commun. Statist. 1 (1973) 189-216] a discrete function is called strongly unimodal if there exists a convex function such that if . In this paper sufficient conditions that ensure the strong unimodality of a multivariate discrete distribution, are given. Examples of strongly unimodal multivariate discrete distributions are presented. 相似文献
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Jie Xiao 《Journal of Differential Equations》2006,224(2):277-295
Let u(t,x) be the solution of the heat equation (∂t-Δx)u(t,x)=0 on subject to u(0,x)=f(x) on Rn. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t2,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞). 相似文献
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Gerard J. Chang Jer-Jeong Chen David Kuo Sheng-Chyang Liaw 《Discrete Applied Mathematics》2007,155(8):1007-1013
For positive integers j?k, an L(j,k)-labeling of a digraph D is a function f from V(D) into the set of nonnegative integers such that |f(x)-f(y)|?j if x is adjacent to y in D and |f(x)-f(y)|?k if x is of distance two to y in D. Elements of the image of f are called labels. The L(j,k)-labeling problem is to determine the -number of a digraph D, which is the minimum of the maximum label used in an L(j,k)-labeling of D. This paper studies -numbers of digraphs. In particular, we determine -numbers of digraphs whose longest dipath is of length at most 2, and -numbers of ditrees having dipaths of length 4. We also give bounds for -numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining -numbers of ditrees whose longest dipath is of length 3. 相似文献
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Angelika Hellwig 《Discrete Applied Mathematics》2008,156(17):3325-3328
Let G be a graph with minimum degree δ(G), edge-connectivity λ(G), vertex-connectivity κ(G), and let be the complement of G.In this article we prove that either λ(G)=δ(G) or . In addition, we present the Nordhaus-Gaddum type result . A family of examples will show that this inequality is best possible. 相似文献