Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré

We study the relationship between two classical approaches for quantitative ergodic properties: the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one based on functional inequalities (of Poincaré type). We show that they can be linked through new inequalities (Lyapunov-Poincaré inequalities). Explicit examples for diffusion processes are studied, improving some results in the literature. The example of the kinetic Fokker-Planck equation recently studied by Hérau and Nier, Helffer and Nier, and Villani is in particular discussed in the final section.     

宽带卫星服务在亚洲的发展趋势

NSR（Northern Sky Research）公司为评估宽带卫星服务发展趋势，分别从企业IPVSAT宽带网络应用、单点接收用户（卫星宽带典型应用）和卫星IP中继应用这3部分进行了考察。这些应用都来自基于IP的典型用户。包括大型企业、政府和非政府组织、中小型企业、个人用户、SOHO一族和ISP服务商。以下市场趋势的调查研究来源于NSR公司的《全球卫星需求调查（第4版）》和《宽带卫星市场研究（第6版）》。     

Décodage par le treillis de codes polynomiaux: un écueil à éviter

We give a simple proof of a well known property of the maximum likelihood decoding of polynomial block codes: the systematic version of the code results in fewer decoding errors than the non systematic version. As a practical result, it is interesting to decode the systematic version of the code on the treillis of the non systematic version, because the non systematic version of the code exhibits a more regular trellis, and both version generate the same codewords.     

Factoring Algorithms for Computing K-Terminal Network Reliability

Let GK denote a graph G whose edges can fail and with a set K ? V specified. Edge failures are independent and have known probabilities. The K-terminal reliability of GK, R(GK), is the probability that all vertices in K are connected by working edges. A factoring algorithm for computing network reliability recursively applies the formula R(GK) = piR(GK * ei) + qiR(GK - ei) where GK * ei is GK, with edge ei contracted, GK - ei is GK with ei deleted and pi ? 1 - qi is the reliability of edge ei. Various reliability-preserving reductions can be performed after each factoring operation in order to reduce computation. A unified framework is provided for complexity analysis and for determining optimal factoring strategies. Recent results are reviewed and extended within this framework.     

Base-catalyzed tritium exchange between tritium-containing heavy water and deuterated chloroform–kinetics and equilibrium

We develop a kinetic model for the exchange of tritium and deuteriumbetween tritium-containing heavy water and deuterated chloroform in a two-phase liquid system, catalyzed by hydroxide ion (sodium hydroxide). For the exchange reaction yielding tritiated chloroform andheavy water, the measured equilibrium constant is 0.518 at 25–45°C, independent of temperature. The rate constant (for the controlling step, deuteron abstraction from chloroform) is 0.22 L/mol s at 25°C, 0.72 at 35°C, and 2.0 at 45°C, corresponding to an activation energy of 87 kJ/mol. Comparison is made with literature data, and effects of mass transfer on the apparent rate constant are discussed.