Optical Recording Properties of Metal-Azo Dye as Recording Medium with Super-Resolution Near-Field Structure

A novel metallized azo dye has been synthesized. The absorption spectra of the thin film and thermal characteristic are measured. Static optical recording properties with and without the Bi mask layer super-resolution near-field structure （Super-RENS） of the metal-azo dye are investigated. The results show that the metal-azo dye film has a broad absorbance band in the region of 450-650 nm and the maximum absorbance wavelength is located at 603 nm. It is also found that the new metallized azo dye occupies excellent thermal stability, initiatory decomposition temperature is at 270℃ and the mass loss is about 48% in a narrow temperature region （15℃）. The complex refractive index N （N = n ＋ iκ） is measured. High refractive index （n = 2.45） and low extinction coefficient （κ = 0.2） at the recording wavelength 65Ohm are attained. Static optical recording tests with and without Super-RENS are carried out using a 65Ohm semiconductor diode laser with recording power of 7mW and laser pulse duration of 200ns. The AFM images show that the diameter of recording mark on the dye film with the Bi mask layer is reduced about 42%, compared to that of recorded mark on the dye film without Super-RENS. It is indicated that Bi can well performed as a mask layer of the dye recording layer and the metallized azo dye can be a promising candidate for recording media with the super-resolution near-field structure.     

Metaheuristics can solve sudoku puzzles

In this paper we present, to our knowledge, the first application of a metaheuristic technique to the very popular and NP-complete puzzle known as ‘sudoku’. We see that this stochastic search-based algorithm, which uses simulated annealing, is able to complete logic-solvable puzzle-instances that feature daily in many of the UK’s national newspapers. We also introduce a new method for producing sudoku problem instances (that are not necessarily logic-solvable) and use this together with the proposed SA algorithm to try and discover for what types of instances this algorithm is best suited. Consequently we notice the presence of an ‘easy-hard-easy’ style phase-transition similar to other problems encountered in operational research.     

Thin-walled Beams: A Derivation of Vlassov Theory via Γ-Convergence

This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order ε and ε ², as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams.      

Uniform non-amenability of free Burnside groups

The aim of this paper is to show that free Burnside groups of sufficiently large odd exponent are non-amenable in a certain strong sense. More precisely their left regular representations are isolated from the trivial representation uniformly on finite generating sets. It follows that free Burnside groups are of uniform exponential growth. This answers a question of de la Harpe. This work has been partially supported by the NSF grant DMS-0605093 and by the RFBR Grant # 05-01-00892. Received: 25 April 2006     

流动注射化学发光抑制法测定尼群地平

基于尼群地平在碱性条件下对铁氰化钾鲁米诺化学发光体系有较强的抑制作用,联用流动注射技术建立了测定尼群地平的新方法.本法的线形范围为0.1～100.0 μg/mL,检出限0.02 μg/mL ,此法用于尼群地平片剂含量测量和药典法对照结果满意.     

Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.     

Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Topological Properties of Urban Public Traffic Networks in Chinese Top-Ten Biggest Cities

We investigate the topological characteristics of complex networks as exemplified by the urban public traffic network （UPTN） in Chinese top-ten biggest cities. It is found that the UPTNs have small world behaviour, by the examination of their topological parameters. The quantitative analysis of the transport efficiency of the UPTNs reveals their higher local efficiency El and lower global efficiency Eg, which coincide well with the status quo of those Chinese cities still at their developing stage. Furthermore, the topological properties of efficiency in the UPTNs are also examined, and the findings indicate that, on the one hand, the UPTNs show robustness to random attacks and frangibility to malicious attacks on a global scale; on the other hand, the interrelation between UPTN efficiency and network motifs deserves our attention. The motifs which interrelate the UPTN efficiency are always triangular-formed patterns, e.g. motifs ID 238, ID 174 and ID 102, etc.