概率统计教学的几点建议

概率统计是大学数学的基础课程之一,我们通过具体的例子分析了概率统计课程教学应该重视的几个问题,并提出了解决问题的建议．这对概率统计课程的教学有一定的借鉴意义．     

处处不可导连续函数的构造法

为了方便向大学生介绍处处不可导的连续函数的构造,对van derWaerden的级数构造法和Bush直接定义函数的构造法分别进行推广并给出证明.     

图的Smarandachely邻点无圈边色数的一个上界

提出了图的Smarandachely邻点无圈边染色的概念,讨论了图的Smarandachely 邻点无圈边染色与邻点可区别无圈边染色之间的关系,并运用概率方法得到了图G的Smarandachely邻点无圈边色数的一个上界,其中G为无孤立边的图.     

环F_p+uF_p+vF_p+uvF_p上的循环码

讨论了非有限链环R=F_p+uF_p+vF_p+uvF_p上的循环码.通过环R上的循环码与多项式环R_n=(F_p+uF_p+vF_p+uvF_p)[x]/(xⁿ-1)的理想的对应关系及对R_n的研究给出了R上循环码的刻画.最后定义了一个Gray映射,并刻画了F_p+uF_p+vF_p+uvF_p上的循环码在该映射下的像.     

Experimental validation of domain-level gradient-based and hierarchical PCE-based routing and control in heterogeneous optical networks

A domain-level gradient-based routing （DLR） algorithm for heterogeneous optical networks with syn- chronous digital hierarchy and optical transport network domains is proposed and experimentally vali- dated. This algorithm classifies domains into groups with incremental levels on the basis of domain-level partitioning, and guides paths level by level along a gradient on the basis of interdomain routing tree evolution. The proposed algorithm is implemented in the hierarchical path computation element-based control architecture for connection provisioning. Testbeds with commercial and emulated nodes are es- tablished to verify the feasibility and performance of the algorithm. Experimental and emulation results show that DLR effectively performs in terms of network blocking probability, real time characteristics, and scalability.     

Enhanced NIR emission in Ce^3＋/Er^3＋-doped YAG induced by Bi^3＋ doping

Ce^3＋/Er^3＋/Bi^3＋ triply-doped yttrium aluminum garnet （YAG） is synthesized using co-precipitation method. The Bi^3＋ concentration-dependent near-infrared （NIR） emission behavior is systemically in- vestigated. The NIR emission of Er^3＋ ions at 1531 nm is enhanced threefold by the addition of 7 mol% Bi^3＋. Bi^3＋doping results in the formation of exciton in YAG and the variation in the local environment of the doped rare-earth ions. The enhancement in NIR luminescence is ascribed to the combined effects of the sensitization of exciton→Ce^3＋ →Er^3＋ and the Bi^3＋ doping-induced adjustment of the local environment for Ce^3＋ and Er^3＋ ions.     

Self-accelerating and self-breathing Bessel-like beams along arbitrary trajectories

We theoretically and experimentally study self-accelerating and self-breathing Bessel-like beams that fol- low arbitrary trajectories, including hyperbolic, hyperbolic secant, and three-dimensional （3D） spiraling trajectories. The beams have an overall Bessel-like profile in transverse dimensions; however, the intensity of their central main lobe breathes while traveling along a curved trajectory. Such beams can be readily generated experimentally through appropriate phase modulation of the optical wavefront. The beams con- tribute to the design of new families of self-accelerating beams.     

Improving attosecond pulse reflection by large angle incidence for a periodic multilayer mirror in the extreme ultraviolet region

The improvement of attosecond pulse reflection by large angle incidence for a periodic multilayer mirror in the extreme ultraviolet region has been discussed. Numerical simulations of both spectral and temporal reflection characteristics of periodic multilayer mirrors under various incident angles have been analyzed and compared. It was found that the periodic multilayer mirror under a larger incidence angle can provide not only higher integrated reflectivity but also a broader reflection band with negligible dispersion, making it possible to obtain better a reflected pulse that has a higher pulse reflection efficiency and shorter pulse duration for attosecond pulse reflection. In addition, by increasing the incident angle, the promotion of attosecond pulse reflection capability has been proven for periodic multilayer mirrors with arbitrary layers.     

Cryptanalysis and improvement of a digital image encryption method with chaotic map lattices

A digital image encryption scheme using chaotic map lattices has been proposed recently. In this paper, two fatal flaws of the cryptosystem are pointed out. According to these two drawbacks, cryptanalysts could recover the plaintext by applying the chosen plaintext attack. Therefore, the proposed cryptosystem is not secure enough to be used in the image transmission system. Experimental results show the feasibility of the attack. As a result, we make some improvements to the encryption scheme, which can completely resist our chosen plaintext attack.     

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.