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11.
We study perturbations of the Erdös–Renyi model for which the statistical weight of a graph depends on the abundance of certain geometrical patterns. Using the formal correspondance with an exactly solvable effective model, we show the existence of a percolation transition in the thermodynamical limit and derive perturbatively the expression of the threshold. The free energy and the moments of the degree distribution are also computed perturbatively in that limit and the percolation criterion is compared with the Molloy–Reed criterion. 相似文献
12.
We consider optimal control problems for systems described by stochastic differential equations with delay. We state conditions
for certain classes of such systems under which the stochastic control problems become finite-dimensional. These conditions
are illustrated with three applications. First, we solve some linear quadratic problems with delay. Then we find the optimal
consumption rate in a financial market with delay. Finally, we solve explicitly a deterministic fluid problem with delay which
arises from admission control in ATM communication networks. 相似文献
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Carsten Franz 《Proceedings of the American Mathematical Society》2006,134(8):2437-2446
A method to approximate the eigenvalues of linear operators depending on an unknown distribution is introduced and applied to weighted sums of squared normally distributed random variables. This area of application includes the approximation of the asymptotic null distribution of certain degenerated U- and V-statistics.
15.
When a stretched elastomer is laminated to a flat plastic frame, a complex shape is formed, which is termed a minimum-energy structure. It is shown how self-organized structures can be applied in the development of actuators with complex, out-of-plane actuationmodes. This unusual concept is then demonstrated in the case of dielectric elastomer actuators. Among advantages of this approach are the simplicity in manufacturing, the potential complexity and sophistication of the manufactured structures, and the general benefits of the concept when applied to other electro-mechanically active materials. PACS 46.32.+x; 77.65.-j; 83.80.Va 相似文献
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Carsten Thomassen 《Journal of Combinatorial Theory, Series B》1997,70(2):306-311
We give a simple proof of the fact (which follows from the Robertson–Seymour theory) that a graph which is minimal of genusgcannot contain a subdivision of a large grid. Combining this with the tree-width theorem and the quasi-wellordering of graphs of bounded tree-width in the Robertson–Seymour theory, we obtain a simpler proof of the generalized Kuratowski theorem for each fixed surface. The proof requires no previous knowledge of graph embeddings. 相似文献