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We report simulations concerning optical amplification in Er:Ti:LiNbO3 curved waveguides. The derivation and the evaluation of the spectral optical gain, the spectral noise figure, the amplified spontaneous emission photon number, and the signal to noise ratio are performed under the small gain approximation. The simulations show the evolution of these parameters under various pump regimes, Er concentration profiles and waveguide lengths. The results obtained are of significant interest for the design of complex, rare earth-doped integrated optics structures involving bent waveguides. 相似文献
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Roland Grappe 《Discrete Applied Mathematics》2008,156(1):138-144
We define a new set of functions called semi-monotone, a subclass of skew-supermodular functions. We show that the problem of augmenting a given graph to cover a symmetric semi-monotone function is NP-complete if all the values of the function are in {0,1} and we provide a minimax theorem if all the values of the function are different from 1. Our problem is equivalent to the node to area augmentation problem. Our contribution is to provide a significantly simpler and shorter proof. 相似文献
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João Gouveia Roland Grappe Volker Kaibel Kanstantsin Pashkovich Richard Z. Robinson Rekha R. Thomas 《Linear algebra and its applications》2013
In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack matrix. The underlying decision problem is equivalent to the polyhedral verification problem whose complexity is unknown. 相似文献
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Laurent Beaudou Antoine Gerbaud Roland Grappe Frédéric Palesi 《Graphs and Combinatorics》2010,26(4):471-481
We prove that two disjoint graphs must always be drawn separately on the Klein bottle in order to minimize the crossing number of the whole drawing. 相似文献
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Given a hypergraph, a partition of its vertex set, and a nonnegative integer k, find a minimum number of graph edges to be added between different members of the partition in order to make the hypergraph k‐edge‐connected. This problem is a common generalization of the following two problems: edge‐connectivity augmentation of graphs with partition constraints (J. Bang‐Jensen, H. Gabow, T. Jordán, Z. Szigeti, SIAM J Discrete Math 12(2) (1999), 160–207) and edge‐connectivity augmentation of hypergraphs by adding graph edges (J. Bang‐Jensen, B. Jackson, Math Program 84(3) (1999), 467–481). We give a min–max theorem for this problem, which implies the corresponding results on the above‐mentioned problems, and our proof yields a polynomial algorithm to find the desired set of edges. 相似文献
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Barbato Michele Grappe Roland Lacroix Mathieu Lancini Emiliano 《Mathematical Programming》2023,197(1):307-336
Mathematical Programming - Given a graph $$G=(V,E)$$ and an integer $$k\ge 1$$ , the graph $$H=(V,F)$$ , where F is a family of elements (with repetitions allowed) of E, is a k-edge-connected... 相似文献
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Mathematical Programming - Box-totally dual integral (box-TDI) polyhedra are polyhedra described by systems which yield strong min-max relations. We characterize them in several ways, involving the... 相似文献
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