Characterization of patterns in rimming flow

Patterns were generated inside a horizontal cylinder rotating at low speeds. The cylinder was filled with a very low volume liquid fraction of 1.8% of Newtonian fluid and the rotation speed ranged between 0.08 and 5.2 s⁻¹. A novel laser-plane technique was utilized to obtain time series from each pattern. This enabled the characterization of fluid patterns using Fourier spectral (FS) and dynamical-systems (chaotic) techniques such as the recurrence map, correlation dimension (D₂) and Hurst exponent (H). Four patterns were found (fingers, furrows, waterfall and smooth tooth) before annular flow was reached. The results indicate that the FS technique not is suitable for flow pattern characterization; and H only has the ability to indicate a possible pattern change. The best tool for indicating the pattern transitions and the inner coat liquid evolution was found to be recurrence maps and D₂.     

Hash function based on the generalized Henon map

A new Hash function based on the generalized Henon map is proposed. We have obtained a binary sequence with excellent pseudo-random characteristics through improving the sequence generated by the generalized Henon map, and use it to construct Hash function. First we divide the message into groups, and then carry out the Xor operation between the ASCII value of each group and the binary sequence, the result can be used as the initial values of the next loop. Repeat the procedure until all the groups have been processed, and the final binary sequence is the Hash value. In the scheme, the initial values of the generalized Henon map are used as the secret key and the messages are mapped to Hash values with a designated length. Simulation results show that the proposed scheme has strong diffusion and confusion capability, good collision resistance, large key space, extreme sensitivity to message and secret key, and it is easy to be realized and extended.     

Cascades with coupled map lattices in preferential attachment community networks

In this paper, cascading failure is studied by coupled map lattice （CML） methods in preferential attachment community networks. It is found that external perturbation R is increasing with modularity Q growing by simulation. In particular, the large modularity Q can hold off the cascading failure dynamic process in community networks. Furthermore, different attack strategies also greatly affect the cascading failure dynamic process. It is particularly significant to control cascading failure process in real community networks.     

Chaotic motion of the dynamical system under both additive and multiplicative noise excitations

With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map.     

图胞映射的一种改进方法

通过引入新的概念，提出了图胞映射动力系统中瞬态胞的新的分类方法，基于新的分类方法研究了动力系统中不变流形的胞映射逼近问题；并结合计算机的计算速度与内存特点，建立了完成上述压缩分类的有效算法.通过对典型算例Henon映射的应用分析，证实了该方法的有效性.     

Banach空间中全纯映射的若干性质

本文将全纯映射的若干性质推广到Ｂａｎａｃｈ空间，并应用这些性质研究有界域中的凸映射与星形映射．     

Similarity-Invariant Subspaces and Similarity-Preserving Linear Maps

In this paper, the similarity-invariant subspaces of B(H), which is the Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given. Received November 3, 1999, Revised September 20, 2000, Accepted February 5, 2001     

Sur l'' application de réciprocité pour une surface fibrée en coniques définie sur un corps local

For a proper smooth variety X defined over a local field k, unramified class field theory investigates the reciprocity map _X: SK₁(X) ^ab ₁(X) as introduced by S. Saito. We study this map in the case when X is a surface admitting a proper surjection onto a smooth geometrically connected curve C with a smooth conic as generic fibre. Without any assumption on the reduction of C, we prove that _X is injective modulo n for all n invertible in k and its cokernel is the same as that of _C.