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.     

A New One-dimensional Dicyanamide Bridged Zinc(II) Complex Containing Nitronyl Nitroxide Radicals:Synthesis,Crystal Structure and Magnetic Properties

A new one-dimensional dicyanamide bridged zinc(II) complex containing nitronyl nitroxide radicals Zn(NO3)(NIT-1'-MeBzIm)(dca)n·(H2O)n(NIT-1'-MeBzIm = 2-{2'-(l'-me-thyl)benzimidazolyl}-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide, dca = dicyanamide anion) has been prepared and structurally characterized by single-crystal X-ray diffraction.The complex crystallizes in triclinic, space group P1, with a = 7.428(3), b = 9.839(3), c = 16.708(6), α = 93.270(4), β = 101.642(4), γ = 100.632(4)°, C17.5H21N8O5.5Zn, Mr = 496.79, V = 1169.7(7) 3, Dc = 1.411 g/cm3, μ(MoKα) = 1.096 mm-1, Z = 2, F(000) = 512, R = 0.0583 and wR = 0.1663 for 4295 observed reflections with I > 2σ(I).X-ray analysis reveals that the zinc(II) ion is six-coordinated with a distorted octahedral geometry.These units develop as 1D species where dicyanamide ligands bridge zinc(II) ions.In addition, molecules are linked by π-π piling interactions to form 1-D double-chains.Magnetic investigation indicates that the weak intramolecular interactions are antiferromagnetic with J =-0.27 cm?1, where the spin Hamitonian is defined as H =-2∑i,jJi,jSiS within the complex.     

Solutions to the reflection equation and integrable systems for N = 2 SQCD with classical groups

Integrable systems underlying the Seiberg-Witten solutions for the N = 2 SQCD with gauge groups SO(n) and Sp(n) are proposed. They are described by the inhomogeneous XXX spin chain with specific boundary conditions given by reflection matrices. We attribute reflection matrices to orientifold planes in the brane construction and briefly discuss its possible deformations.     

Superstochastic matrices and magic Markov chains

A brief account of the conceptual formulation of the two entities in this paper’s title, plus an initial preliminary investigation of some of their mathematical properties, is given.     

Some identities between basic hypergeometric series deriving from a new Bailey-type transformation

We prove a new Bailey-type transformation relating WP-Bailey pairs. We then use this transformation to derive a number of new 3- and 4-term transformation formulae between basic hypergeometric series.     

交互式马尔科夫链上弱模拟关系的计算

对交互式马尔可夫链模型(IMCs)上的弱模拟前序关系的计算算法进行讨论.在IMCs上判断弱模拟关系时,重点对概率转移关系进行弱模拟前序关系的判断,同时考虑内部动作对系统的影响.通过引入适当的变量,将IMCs上弱模拟定义中的马尔可夫转移条件转化为求解一个线性规划问题的解.利用该线性规划问题的数值求解方法,可在多项式时间内求得该线性规划问题的解.从而得到判定IMC上两个进程是否弱模拟的多项式时间算法.     

隐马尔可夫模型在被动声信号分类中的应用

为了提高被动声目标识别率，该文研究了隐马尔可夫模型在被动声信号分类中的应用问题，然后，又提出了２种混合分类器：特征矢量混合的ＨＭＭ分类器和ＨＭＭ／ＭＬＰＮＮ（多层感知机神经网络）混合模型分类器。结果表明，这２种混合分类器在性能上都优于单个特定的分类器，它们在被动声信号分类中具有良好的应用前景。     

均聚物结晶与熔融化转变的稳态和亚稳态统计理论III. 分子分凝统计结晶动力学～熔体内结晶增长速率的一般化表征和它们对生长机制的依赖性

首先对微晶粒尺寸增长速率的表征进行总结.从微晶核和粒—高分子链组网络结构特点(高分子链组是微晶核和微晶粒同连接链段的复合体)同增长速率间的三个相关性的特征: ①晶核和晶粒加大同连接链段缩短的并存性; ②微晶核和粒表面上连接链段的缩短机制存有简并性; ③微晶粒内和粒表面上stem的反顺式构象共存性出发.建议了一种评估和计算微晶粒尺寸增长速率的新方法和原则,基于该种计算方法和原则用统计力学和动力学相结合法推导出了高分子熔体内几种不同结晶生长机制(近邻折叠、近邻伸直分凝和近邻折叠同近邻伸直分凝并存等生长方式)下微晶粒—高分子链组中微晶粒数增长速率和微晶粒尺寸增长速率动力学方程.