Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

基于有限状态的全周期序列混沌映射的研究

在有限长度的数字计算机中，混沌迭代序列是一个有限周期序列，其相关性能远远低于理想序列。基于skew tent映射，提出一种离散化的有限状态混沌映射，它允许精确的数值计算，没有舍入误差，通过选择合适的参数，映射能产生全周期长度的序列。仿真实验表明，归一化的序列平均周期对计算机精度不敏感，生成的二进制序列具有良好的相关性能。     

Patterns and Symmetries in the Visual Cortex and in Natural Images

As borders between different entities, lines are an important element of natural images. Indeed, the neurons of the mammalian visual cortex are tuned to respond best to lines of a given orientation. This preferred orientation varies continuously across most of the cortex, but also has vortex-like singularities known as pinwheels. In attempting to describe such patterns of orientation preference, we are led to consider underlying rotation symmetries: Oriented segments in natural images tend to be collinear; neurons are more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underlying topography. This is verified by direct statistical tests in both natural images and in cortical maps. Using the statistics of natural scenes we construct filters that are best suited to extracting information from such images, and find qualitative similarities to mammalian vision. PACS84.35+i 89.70.+c 87.57.Nk     

基于一种特定混沌映射的跳频序列

使用一种简单的分段线性映射构造混沌跳频序列。用于跳频通信中取代传统的伪随机序列（PN序列），分析了此混沌序列的周期性。平衡性，汉明相关特性和线性间隔，最后给出了混沌序列的神经网络实现。仿真和实验结果表明，此序列具有较好的统计特性。应用于跳频多址通信中，可获得较好的抗干扰。抗截获能力。     

瑞利与非瑞利杂波背景下单、双参数杂波图的性能分析

对瑞利和非瑞利杂波中的单、双参数杂波图的控制虚警性能和检测性能进行了比较分析，并得到了双参数杂波图门限调整值的取值范围，得出了几点有益的结论。     

强流脉冲高斯分布束在磁四极透镜中的非线性传输

用李代数方法分析了高斯分布下强流脉冲束在磁四极透镜中的非线性传输.在高斯分布下,束流的空间电荷势可利用Green函数算出,进而可以得到包含束流自场的粒子运动的Hamilton函数.再施加李变换,就可以得到粒子运动的各级近似解.本文给出二级近似下的结果,根据需要,还可以扩展到更高级近似.计算过程需要进行迭代,即根据每次算出的轨迹值,确定束团在三维实空间中的大小,然后再进行迭代,直到满足精度要求为止.     

Cyclic permutations and evolutionary trees

Given a tree with leaf set X, there are certain ways of arranging the elements of X in a circular order so that can be embedded in the plane and ‘preserve’ this ordering. We investigate some new combinatorial properties of these ‘circular orderings.’ We then use these properties to establish two results concerning dissimilarity maps on X that are induced by edge-weighted trees with leaf set X.     

Regular Balanced Cayley Maps for Cyclic, Dihedral and Generalized Quaternion Groups

A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and generalized quaternion groups are classified.