On <Emphasis Type="Italic">osp</Emphasis>(<Emphasis Type="Italic">M</Emphasis>∣2<Emphasis Type="Italic">n</Emphasis>) Integrable Open Spin Chains

We consider open spin chains based on osp(M2n) Yangians and solve the reflection equations for some classes of reflection matrices, including the diagonal ones. Having then integrable open spin chains, we write the analytical Bethe Ansatz equations. More details and references can be found in D. Arnaudon et al.: Nucl. Phys B 668 (2003) 469 and 687 (2004) 257.     

碳原子线的电子传输特性

单分子电子器件的电子传输特性是当前分子电子学领域研究的热点.本文采用第一原理的ab inito法与格林函数方法,对Au电极-碳原子线-Au电极体系的电子结构以及电子传输等特性进行了分析,给出了C5、C10与C15原子线的电导 -电压曲线与伏安曲线.研究结果表明:碳原子线与Au电极之间的"接触"(结合)既有共价键的成分,又有离子键的成分;碳原子线的电导率及伏安特性具有特殊的量子效应和尺寸效应.     

Higher-loop integrability in gauge theory

The dilatation operator measures scaling dimensions of local operator in a conformal field theory. Algebraic methods of constructing the dilatation operator in four-dimensional N=4 gauge theory are reviewed. These led to the discovery of novel integrable spin chain models in the planar limit. Making use of Bethe ansätze a superficial discrepancy in the AdS/CFT correspondence was found, we discuss this issue and give a possible resolution. To cite this article: N. Beisert, C. R. Physique 5 (2004).

Résumé

L'opérateur de dilatation mesure les dimensions d'échelles des opérateurs locaux des théories conformes des champs. Nous passons en revue les méthodes algébriques de construction de l'opérateur de dilatation pour la théorie de jauge N=4 en quatre dimensions. Ceci nous a conduit à découvrir, dans la limite planaire, de nouveaux modèles intégrables de chaînes de spin. En utilisant l'ansätze de Bethe une incompatibilité avec la correspondance AdS/CFT fut découverte, nous discutons ce problème et une résolution possible. Pour citer cet article : N. Beisert, C. R. Physique 5 (2004).     

Factorization of Markov Chains

Existence of following factorization is proved:

Geometric Convergence Rates for Time-Sampled Markov Chains

We consider time-sampled Markov chain kernels, of the form P = _n n P ⁿ . We prove bounds on the total variation distance to stationarity of such chains. We are motivated by the analysis of near-periodic MCMC algorithms.     

Continuous-Time Controlled Markov Chains with Discounted Rewards

This paper studies denumerable state continuous-time controlled Markov chains with the discounted reward criterion and a Borel action space. The reward and transition rates are unbounded, and the reward rates are allowed to take positive or negative values. First, we present new conditions for a nonhomogeneous Q(t)-process to be regular. Then, using these conditions, we give a new set of mild hypotheses that ensure the existence of -optimal (0) stationary policies. We also present a martingale characterization of an optimal stationary policy. Our results are illustrated with controlled birth and death processes.     

Exactly Solvable su(N) Mixed Spin Ladders

It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin- spin-1 ladder, a mixed spin- spin- ladder and a spin-1 ladder with biquadratic interactions.     

Old and new from SOR

From the long history of Successive Over Relaxation (SOR) between the end of second world war and today three points are considered: (1) Classical results of Young and Varga are described. (2) It is shown how results on semiiterative methods can be used to derive these classical results in a unifying way and to compare SOR with other iterative methods. (3) In the last 15 years the application of SOR to compute the stationary distribution of a homogeneous Markov chain has been discussed. These results are reported, considering especially the term extended convergence introduced by Kontovasilis, Plemmons and Stewart.     

Carbon linear chains inside multiwalled nanotubes

Multiwalled carbon nanotubes have been deposited on graphite cathodes by using an arc discharge technique in He atmosphere, with the insertion of a catalytic Ni-Cr mixture as well as without catalysers. The topography of such deposition has been investigated by SEM, while a parallel micro-Raman study has revealed, in particular regions of the deposited cathodes, strong bands in the range 1780-1860 cm⁻¹, assignable to linear carbon chains inside the nanotubes. The variation of intensity, frequency and bandwidth of such bands has been investigated, in relation with the spectral characters of the host multiwalled carbon nanotube. In the cathode deposited without catalyst a quite ordered configuration of multiwalled carbon nanotubes is obtained in the central zone, while the maximum concentration of linear carbon chains is found in a ring shaped zone just inside the border. In sample obtained with catalyst the deposited multiwalled carbon nanotubes appear always more disordered, and a remarkable concentration of carbon chains appears in some zones, with a more casual distribution.     

Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree

In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree.