Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.     

T型微混合器混合特性的浓度分布评价法

提出一种微混合器混合性能的评价方法.在样品盒中注入不同浓度罗丹明B溶液并用体视显微镜观察捕获图像,通过Image J软件读取图像灰度值,建立不同深度下溶液的浓度-灰度值函数关系,运用此关系式将T型微混合器3种不同深度(0.1、 0.2和0.4 mm,质量浓度0.05 %的罗丹明B溶液和去离子水作为配对流体)混合实验中捕获的图像中各像素点上的灰度值转换为浓度值,绘制浓度等高线图及浓度频数分布图,分析各自混合情况,最后引入浓度混合指数概念及计算公式,分析3种深度混合器内不同截面上的混合程度.此方法从定性和定量两方面分析了微尺度下混合腔深度对微混合的影响程度,具有一定的应用价值.     

An Encryption Algorithm for Region of Interest in Medical DICOM Based on One-Dimensional eλ-cos-cot Map

Today, with the rapid development of the Internet, improving image security becomes more and more important. To improve image encryption efficiency, a novel region of interest (ROI) encryption algorithm based on a chaotic system was proposed. First, a new 1D eλ-cos-cot (1D-ECC) with better chaotic performance than the traditional chaotic system is proposed. Second, the chaotic system is used to generate a plaintext-relate keystream based on the label information of a medical image DICOM (Digital Imaging and Communications in Medicine) file, the medical image is segmented using an adaptive threshold, and the segmented region of interest is encrypted. The encryption process is divided into two stages: scrambling and diffusion. In the scrambling stage, helical scanning and index scrambling are combined to scramble. In the diffusion stage, two-dimensional bi-directional diffusion is adopted, that is, the image is bi-directionally diffused row by column to make image security better. The algorithm offers good encryption speed and security performance, according to simulation results and security analysis.     

A Hierarchy of Integrable Lattice Soliton Equations and New Integrable Symplectic Map

Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure. A new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a Bäcklund transformation for the resulting integrable lattice equations. At last, conservation laws of the hierarchy are presented.     

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. 关键词： 图胞映射方法 不变流形 Henon映射     

Multi-user cognitive radio network resource allocation based on the adaptive niche immune genetic algorithm

Multi-user cognitive radio network resource allocation based on the adaptive niche immune genetic algorithm is proposed, and a fitness function is provided. Simulations are conducted using the adaptive niche immune genetic algorithm, the simulated annealing algorithm, the quantum genetic algorithm and the simple genetic algorithm, respectively. The results show that the adaptive niche immune genetic algorithm performs better than the other three algorithms in terms of the multi-user cognitive radio network resource allocation, and has quick convergence speed and strong global searching capability, which effectively reduces the system power consumption and bit error rate.     

自适应间断有限元方法求解双曲守恒律方程

研究自适应Runge-Kutta间断Galerkin (RKDG)方法求解双曲守恒律方程组,并提出两种生成相容三角形网格的自适应算法.第一种算法适用于规则网格,实现简单、计算速度快.第二种算法基于非结构网格,设计一类基于间断界面的自适应网格加密策略,方法灵活高效.两种方法都具有令人满意的计算效果,而且降低了RKDG的计算量.     

Newton trajectories for the tilted Frenkel–Kontorova model

ABSTRACT

Newton trajectories are used for the Frenkel–Kontorova model of a finite chain with free-end boundary conditions. We optimise stationary structures, as well as barrier breakdown points for a critical tilting force were depinning of the chain happens. These special points can be obtained straight forwardly by the tool of Newton trajectories. We explain the theory and add examples for a finite-length chain of a fixed number of 2,?3,?4,?5 and 23 particles.     

Bi-f-harmonic map equations on singly warped product manifolds

Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extension of f-harmonic maps but also an extension of bi-harmonic maps, and that there should exist many examples of proper bi-f-harmonic maps.In order to find some concrete examples of proper bi-f-harmonic maps, we study the basic properties of bi-f-harmonic maps from two directions which are conformal maps between the same dimensional manifolds and some special maps from or into a warped product manifold.     

The localized longitudinal index theorem for Lie groupoids and the van Est map

We define the “localized index” of longitudinal elliptic operators on Lie groupoids associated with Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of the localized index, is an action of the Hopf algebroid of jets around the unit space, and the characteristic map it induces on Lie algebroid cohomology. This map can be globalized to differentiable groupoid cohomology, giving a definition of the “global index”, that can be computed by localization. This correspondence between the “global” and “localized” index is given by the van Est map for Lie groupoids.