d-dominating sets in graphs are very important in system and network engineering. Their constructions is thus an important research topic. An heuristic which forms such sets by using a given criterion is proposed. We simplify the heuristic presented elsewhere. We extend it and prove the correctness of the extended heuristic. This heuristic has the advantage of being distributed and scalable. To cite this article: A. Delye de Clauzade de Mazieux et al., C. R. Mecanique 334 (2006).相似文献
We consider a cluster system in which each cluster is characterized by two parameters: an "order" i , following HortonStrahler rules, and a "mass" j following the usual additive rule. Denoting by c i,j ( t ) the concentration of clusters of order i and mass j at time t , we derive a coagulation-like ordinary differential system for the time dynamics of these clusters. Results about the existence and the behavior of solutions as t are obtained; in particular, we prove that c i,j ( t ) 0 and N i ( c ( t )) 0 as t , where the functional N i (·) measures the total amount of clusters of a given fixed order i . Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that suggest the existence of self-similar solutions to these approximate equations and discuss their possible relevance for an interpretation of Horton's law of river numbers. 相似文献
This paper deals with existence results for a Vlasov-Poisson system, equipped with an absorbing-type law for the Vlasov equation and a Dirichlet-type boundary condition for the Poisson part. Using the ideas of Lions and Perthame [21], we prove the existence of a weak solution having good Lp estimates for moment and electric field, by a good control on the higher moments of the initial data. As an application, we establish a homogenization result in the Hilbertian framework for this type of problem in non-homogeneous media, following the work by Alexandre and Hamdache [2] for general kinetic equations, and Cioranescu and Mural [11] for the Laplace problem. 相似文献
One of the most pervasive laws in biology is the allometric scaling, whereby a biological variable Y is related to the mass M of the organism by a power law, Y=Y0Mb, where b is the so-called allometric exponent. The origin of these power laws is still a matter of dispute mainly because biological laws, in general, do not follow from physical ones in a simple manner. In this work, we review the interspecific allometry of metabolic rates, where recent progress in the understanding of the interplay between geometrical, physical and biological constraints has been achieved.
For many years, it was a universal belief that the basal metabolic rate (BMR) of all organisms is described by Kleiber's law (allometric exponent b=3/4). A few years ago, a theoretical basis for this law was proposed, based on a resource distribution network common to all organisms. Nevertheless, the 3/4-law has been questioned recently. First, there is an ongoing debate as to whether the empirical value of b is 3/4 or 2/3, or even nonuniversal. Second, some mathematical and conceptual errors were found these network models, weakening the proposed theoretical arguments. Another pertinent observation is that the maximal aerobically sustained metabolic rate of endotherms scales with an exponent larger than that of BMR. Here we present a critical discussion of the theoretical models proposed to explain the scaling of metabolic rates, and compare the predicted exponents with a review of the experimental literature. Our main conclusion is that although there is not a universal exponent, it should be possible to develop a unified theory for the common origin of the allometric scaling laws of metabolism. 相似文献
We consider Farey series of rational numbers in terms of fractal sets labeled by the Hausdorff dimension with values defined in the interval 1<h<2 and associated with fractal curves. Our results come from the observation that the fractional quantum Hall effect-FQHE occurs in pairs of dual topological quantum numbers, the filling factors. These quantum numbers obey some properties of the Farey series and so we obtain that the universality classes of the quantum Hall transitions are classified in terms ofh. The connection between Number Theory and Physics appears naturally in this context. 相似文献
The flexibility of weights assigned to inputs and outputs is a key aspect of DEA modeling. However, excessive weight variability and implausible weight values have led to the development of DEA models that incorporate weight restrictions, reflecting expert judgment. This in turn has created problems of infeasibility of the corresponding linear programs. We provide an existence theorem that establishes feasibility conditions for DEA multiplier programs with weight restrictions. We then propose a linear model that tests for feasibility and a nonlinear model that provides minimally acceptable adjustments to the original restrictions that render the program feasible. The analysis can be applied to restrictions on weight ratios, or to restrictions on virtual inputs or outputs. 相似文献
The nth Bell number Bn is the number of ways to partition a set of n elements into nonempty subsets. We generalize the “trace formula” of Barsky and Benzaghou [1], which asserts that for an odd prime p and an appropriate constant τp, the relation Bn=-Tr(n-1-τp)Bτp holds in , where is a root of and is the trace form. We deduce some new interesting congruences for the Bell numbers, generalizing miscellaneous well-known results including those of Radoux [4]. 相似文献
Several novel tin(IV) adducts of amidines, [SnClPh3L], [SnCl2Ph2L] and [SnBr4L] {L=N,N-diphenylacetamidine (Hdpac) or N,N-diphenylbenzamidine (Hdpba)}, were prepared and investigated by Mössbauer spectroscopy which was an important tool for the elucidation of bonding and structural features. The resulting Mössbauer data also led to the conclusion that the tin(IV) centre for the adduct [SnClPh3L] is pentacoordinated in a trigonal bipyramidal arrangement and hexacoordinated for [SnCl2Ph2L] and [SnBr4L] in a geometric patterns of an octahedral. The amidines act as monodentate ligands to the metal centre for the former and bidentate for the latter. 相似文献
A matrix whose entries consist of elements from the set {+, −, 0} is a sign pattern matrix. Using a linear algebra theoretical
approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign
matrices. 相似文献