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.     

Enantiopure Aminopyrans by a Lewis Acid Promoted Rearrangement of 1,2‐Oxazines: Versatile Building Blocks for Oligosaccharide and Sugar Amino Acid Mimetics

1,3‐Dioxolanyl‐substituted 1,2‐oxazines, such as syn‐ 1 and anti‐ 1 , rearrange under Lewis acidic conditions to provide bicyclic products 2 – 5 . Subsequent reductive transformations afforded enantiopure 3‐aminopyran derivatives such as 7 and 9 or their protected diastereomers 16 and 18 , which can be regarded as carbohydrate mimetics. An alternative sequence of transformations including selective oxidation of the primary hydroxyl groups in 21 and 24 led to two protected β‐amino acid derivatives with carbohydrate‐like backbone (sugar amino acids). Treatment of bicyclic ester 23 with samarium diiodide cleaved the N? O bond and furnished the unusual β‐lactam 27 in excellent yield. Alternatively, γ‐amino acid derivative 29 was efficiently prepared in a few steps. Fairly simple transformations gave azides 32 and 35 or alkyne 30 which are suitable substrates for the construction of oligosaccharide mimetics such as 34 by copper iodide catalyzed cycloadditions. With this report we demonstrate that enantiopure rearrangement products 2 – 5 are protected precursors of a variety of polyfunctionalized pyran derivatives with great potential for chemical biology.     

Development of a high-sensitivity chromatographic separation system for pyridylaminated aldopentoses and aldohexoses

A rare sugar is considered to be a monosaccharide rarely found in nature. To investigate their natural distribution and biological roles, a robust analytical system must be used to isolate, identify, and quantify them. Herein, we report the development of such a system that can specifically quantify and chromatographically separate four aldopentoses and eight aldohexoses tagged with 2-aminopyridine. Purified monosaccharides derivatized with a pyridylamino moiety (PA–monosaccharides) are first chromatographed over a high-performance anion-exchange resin. But, because two of the PA–aldohexoses used in this study, PA–talose and PA–idose, co-elute with the common saccharides, PA–glucose and PA–mannose, respectively, a second chromatographic step, reversed-phase high-performance liquid chromatography, is used to completely separate them. Thus, as shown by the results of this study, chromatographic separation of PA–monosaccharides is achievable and provides a quantitative measurement of common and rare isomeric aldopentoses and aldohexoses.     

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.     

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.     

Irradiation of cane sugar spirit

The present study deals with the effect of irradiation on the gas-chromatographic profile of irradiated cane sugar spirit irradiated in glass containers in the presence of oak chops with doses of 0–10 kGy. Volatile constituents were analyzed in a CG gas chromatographer with a flame ionization detector using a Megabore CG-745 column. The results are discussed considering the contribution of irradiation to the quality of the spirit and the contribution of the irradiated oak wood.     

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.     

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.