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1.
We study the asymptotic distribution of the fill‐up level in a binary trie built over n independent strings generated by a biased memoryless source. The fill‐up level is the number of full levels in a tree. A level is full if it contains the maximum allowable number of nodes (e.g., in a binary tree level k can have up to 2k nodes). The fill‐up level finds many interesting applications, e.g., in the internet IP lookup problem and in the analysis of level compressed tries (LC tries). In this paper, we present a complete asymptotic characterization of the fill‐up distribution. In particular, we prove that this distribution concentrates on one or two points around the most probably value k = ?log1/qn ? log log log n + 1 + log log(p/q)?, where p > q = 1 ? p is the probability of generating the more likely symbol (while q = 1 ? p is the probability of the less likely symbol). We derive our results by analytic methods such as generating functions, Mellin transform, the saddle point method, and analytic depoissonization. We also present some numerical verification of our results. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004  相似文献   
2.
We consider noncommutative line bundles associated with the Hopf fibrations of SUq(2) over all Podle? spheres and with a locally trivial Hopf fibration of S3pq. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SUq(2) and S3pq. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).  相似文献   
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Research supported by the NSF Grant DMS-8602672  相似文献   
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The Hidden Markov Chains (HMC) are widely applied in various problems. This succes is mainly due to the fact that the hidden process can be recovered even in the case of very large set of data. These models have been recetly generalized to ‘Pairwise Markov Chains’ (PMC) model, which admit the same processing power and a better modeling one. The aim of this note is to propose further generalization called Triplet Markov Chains (TMC), in which the distribution of the couple (hidden process, observed process) is the marginal distribution of a Markov chain. Similarly to HMC, we show that posterior marginals are still calculable in Triplets Markov Chains. We provide a necessary and sufficient condition that a TMC is a PMC, which shows that the new model is strictly more general. Furthermore, a link with the Dempster–Shafer fusion is specified. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 275–278.  相似文献   
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Summary Bidentate complexes of dimolybdenum tetraacetate with 1,3-diaxial diols show Cotton effects around 490–540 nm (CD band I), 400–440 nm (II), 350–380 nm (III), 320 nm (IV) and 280 nm (V). The sign of the Cotton effect II can be predicted by a proposed sector rule. It seems that from the Cotton effects for cyclic 1,3-diols the absolute configurations or conformations can be obtained.A part of this material was presented at III-rd International Conference on CD Spectroscopy [1]  相似文献   
7.
1H,13C,14N and15N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.  相似文献   
8.
Conclusions Nonradiative energy transfer between similar and different rare-earth ions in LiNbO3 has been evidenced for the first time. The contribution of nonradiative energy transfer to the decay of the1G4 and3H4 levels of thulium and the4S3/2 and4I13/2 levels of erbium is significant for activator concentrations of the order of several thousand ppm in LiNbO3. The excitation of higher-lying levels of both activators is transferred faster in codoped crystal to the lowest luminescent levels, from which the luminescence in the 1–2-μm spectral region occurs. This accelerated relaxation is advantageous for broadband optical pumping since the contribution of radiative transitions competing with the3F43H6 laser transition of thulium is reduced. On the other hand, it appears that erbium ions will influence adversely the efficiency of a laser-diode-pumped LiNbO3∶Er, Tm laser operating near 1.8 μm since the part of the3H4 excitation transferred to erbium ions is emitted from the long-lived4I11/2 level of Er3+. Furthermore, the4I13/2 excitation is not transferred fully to thulium ions and is lost in4I13/24I15/2 emission. Lithium niobate singly doped with thulium is more promising since the cross-relaxation process that transfers the excitation from the3H4 level to the3F4 level appears to be efficient in this host. Published in Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 5, pp. 125–133, September–October, 1995.  相似文献   
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