Within the Feynman–Kac path integral representation, the equilibrium quantities of a quantum plasma can be represented by Mayer graphs. The well known Coulomb divergencies that appear in these series are eliminated by partial resummations. In this paper, we propose a resummation scheme based on the introduction of a single effective potential that is the quantum analog of the Debye potential. A low density analysis of shows that it reduces, at short distances, to the bare Coulomb interaction between the charges (which is able to lead to bound states). At scale of the order of the Debye screening length
–1D, approaches the classical Debye potential and, at large distances, it decays as a dipolar potential (this large distance behaviour is due to the quantum nature of the particles). The prototype graphs that result from the resummation obey the same diagrammatical rules as the classical graphs of the Abe–Meeron series. We give several applications that show the usefulness of to account for Coulombic effects at all distances in a coherent way. 相似文献
The accumulation of the Jacobian matrix F of a vector function can be regarded as a transformation of its linearized computational graph into a subgraph of the directed complete bipartite graph Kn,m. This transformation can be performed by applying different elimination techniques that may lead to varying costs for computing F. This paper introduces face elimination as the basic technique for accumulating Jacobian matrices by using a minimal number of arithmetic operations. Its superiority over both edge and vertex elimination methods is shown. The intention is to establish the conceptual basis for the ongoing development of algorithms for optimizing the computation of Jacobian matrices. 相似文献
We solve a problem proposed by Jacobson, Kézdy, and Lehel [4] concerning the existence of forbidden induced subgraph characterizations of line graphs of linear k-uniform hypergraphs with sufficiently large minimal edge-degree. Actually, we prove that for each k3 there is a finite set Z(k) of graphs such that each graph G with minimum edge-degree at least 2k2–3k+1 is the line graph of a linear k-uniform hypergraph if and only if G is a Z(k)-free graph.Acknowledgments. We thank the anonymous referees, whose suggestions helped to improve the presentation of the paper.Winter 2002/2003 DIMACS Award is gratefully acknowledged2000 Mathematics Subject Classification: 05C65 (05C75, 05C85) 相似文献
Let F be a graph of order at most k. We prove that for any integer g there is a graph G of girth at least g and of maximum degree at most 5k13 such that G admits a surjective homomorphism c to F, and moreover, for any F-pointed graph H with at most k vertices, and for any homomorphism h from G to H there is a unique homomorphism f from F to H such that h=fc. As a consequence, we prove that if H is a projective graph of order k, then for any finite family of prescribed mappings from a set X to V(H) (with ||=t), there is a graph G of arbitrary large girth and of maximum degree at most 5k26mt (where m=|X|) such that and up to an automorphism of H, there are exactly t homomorphisms from G to H, each of which is an extension of an f.Supported in part by the National Science Council under grant NSC89-2115-M-110-012Final version received: June 9, 2003 相似文献
Let be a class of graphs on n vertices. For an integer c, let be the smallest integer such that if G is a graph in with more than edges, then G contains a cycle of length more than c. A classical result of Erdös and Gallai is that if is the class of all simple graphs on n vertices, then . The result is best possible when n-1 is divisible by c-1, in view of the graph consisting of copies of Kc all having exactly one vertex in common. Woodall improved the result by giving best possible bounds for the remaining cases when n-1 is not divisible by c-1, and conjectured that if is the class of all 2-connected simple graphs on n vertices, thenwhere , 2tc/2, is the number of edges in the graph obtained from Kc+1-t by adding n-(c+1-t) isolated vertices each joined to the same t vertices of Kc+1-t. By using a result of Woodall together with an edge-switching technique, we confirm Woodall's conjecture in this paper. 相似文献
Clustering applications dealing with perception based or biased data lead to models with non-disjunct clusters. There, objects to be clustered are allowed to belong to several clusters at the same time which results in a fuzzy clustering. It can be shown that this is equivalent to searching all maximal cliques in dynamic graphs like Gt = (V,Et), where Et – 1Et, t = 1,...,T; E0 = . In this article algorithms are provided to track all maximal cliques in a fully dynamic graph. 相似文献
It is shown explicitly how self-similar graphs can be obtained as `blow-up' constructions of finite cell graphs . This yields a larger family of graphs than the graphs obtained by discretising continuous self-similar fractals.
For a class of symmetrically self-similar graphs we study the simple random walk on a cell graph , starting at a vertex of the boundary of . It is proved that the expected number of returns to before hitting another vertex in the boundary coincides with the resistance scaling factor.
Using techniques from complex rational iteration and singularity analysis for Green functions, we compute the asymptotic behaviour of the -step transition probabilities of the simple random walk on the whole graph. The results of Grabner and Woess for the Sierpinski graph are generalised to the class of symmetrically self-similar graphs, and at the same time the error term of the asymptotic expression is improved. Finally, we present a criterion for the occurrence of oscillating phenomena of the -step transition probabilities.
This is a summary of the most important results presented in the authors PhD thesis (Spanjaard 2003). This thesis, written in French, was defended on 16 December 2003 and supervised by Patrice Perny. A copy is available from the author upon request. This thesis deals with the search for preferred solutions in combinatorial optimization problems (and more particularly graph problems). It aims at conciliating preference modelling and algorithmic concerns for decision aiding.Received: March 2004, MSC classification:
91B06, 90C27, 90B40, 16Y60 相似文献