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The main question discussed in this paper is how well a finite metric space of size n can be embedded into a graph with certain topological restrictions.
The existing constructions of graph spanners imply that any n -point metric space can be represented by a (weighted) graph with n vertices and n
1 +O(1/r)
edges, with distances distorted by at most r . We show that this tradeoff between the number of edges and the distortion cannot be improved, and that it holds in a much
more general setting. The main technical lemma claims that the metric space induced by an unweighted graph H of girth g cannot be embedded in a graph G (even if it is weighted) of smaller Euler characteristic, with distortion less than g/4 - 3/2 . In the special case when |V(G)| =|V(H)| and G has strictly less edges than H , an improved bound of g/3 - 1 is shown. In addition, we discuss the case χ(G) < χ(H) - 1 , as well as some interesting higher-dimensional analogues. The proofs employ basic techniques of algebraic topology.
Received September 26, 1995, and in revised form March 18, 1996. 相似文献
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Graham LA Fout AR Kuehne KR White JL Mookherji B Marks FM Yap GP Zakharov LN Rheingold AL Rabinovich D 《Dalton transactions (Cambridge, England : 2003)》2005,(1):171-180
The manganese(I) tricarbonyl complexes (Bm(R))Mn(CO)3(R = Me, Bz, But, p-Tol) and (PhBmMe)Mn(CO)3, the first bis(mercaptoimidazolyl)borate derivatives for this metal, have been readily prepared and fully characterized. In particular, the presence of three-center-two-electron Mn...H-B interactions in these species, both in solution and in the solid state, has been investigated using a combination of IR and NMR spectroscopies and, in the case of the methyl-, tert-butyl- and para-tolyl-substituted derivatives, by X-ray crystallography. To complement these synthetic and structural studies, the tris(mercaptoimidazolyl)borate complexes (TmMe)Mn(CO)3(R = Me, Bz, But, p-Tol) and (PhTm(Me))Mn(CO)3, as well as the related pyrazolylbis(mercaptoimidazolyl)borate (pzBmMe)Mn(CO)3, have also been synthesized and characterized by a combination of analytical and spectroscopic techniques. 相似文献
18.
We present a new, simple, inexpensive, and highly precise approach to excited-state fluorescence-lifetime-based measurements. The detection system consists of a closed-loop optoelectronic arrangement containing a radio frequency resonance amplifier, a fluorescence excitation light source, a fiber-optic delay line, and a photodetector. The system exhibits auto-oscillations in the form of intensity modulation. The oscillation frequency varies with the modulation phase shift of the fluorescent light. This frequency is used as the detection parameter, which is advantageous because frequency may be measured easily, inexpensively, and with high precision. This technique is well suited for chemical or biosensor applications. 相似文献
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A. N. Karapetyants V. S. Rabinovich N. L. Vasilevski 《Integral Equations and Operator Theory》2001,40(3):278-308
We describe the Fredholm symbol algebra for theC
*-algebra generated by two dimensional singular integral operators, acting onL
2(2), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin.These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.Rostov State University RussiaPartially supported by Russian Fund for Fundamental Investigations, RFFI-98-01-01-023, and by CONACYT project 32424-EPartially supported by CONACYT Project 27934-E, México. 相似文献
20.
The Helmholtz equation describing the propagation of acoustic and electromagnetic waves in a nonhomogeneous media slowly varying
in the horizontal direction is considered. The contribution of the discrete and continuous spectra of the transversal Sturm-Liouville
problem to the asymptotics is studied. A uniform asymptotics for the Green function in neighborhoods of thresholds is obtained. 相似文献