Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.     

The Crystal Structure of Sr2TiSi2O8

Sr₂TiSi₂O₈ single crystals were grown by Czochralski pulling and from a high-temperature solution. X-ray diffractometry revealed the modulated crystal structure of Sr₂TiSi₂O₈ to belong to the 5D superspace group P4bm (−α, α, 1/2; α, α, 1/2) with α=0.3. Atomic positions, anisotropic displacement factors and positional modulation parameters for Sr₂TiSi₂O₈ are determined and discussed. The positional modulation is further investigated by electron diffraction and high-resolution transmission electron microscopy. In the latter experiments, the 2D modulation appears to be superimposed by some 1D modulation waves. This effect is discussed in terms of growth conditions.     

一类四元零相关区非周期互补序列集构造法

零相关区非周期互补序列集在多载波码分多址通信系统中有着重要应用.已有的四元零相关区非周期互补序列集构造方法都是基于二元或四元零相关区互补序列集,得到的序列集参数受到初始互补序列集参数的限制.该文给出了一种构造法,利用四元正交序列集来构造四元非周期互补序列集.本文方法得到的序列集参数达到理论界限,并且零相关区长度可以灵活设定以满足不同的应用场合.另外给出了两类基于二元正交矩阵的四元正交序列集的构造方法,得到的四元正交序列集可以用于构造四元零相关区非周期互补序列集.二元正交矩阵存在数目很多,因此本文方法可以为多载波码分多址系统提供大量四元非周期互补序列集.     

GS算法在多输入多输出雷达信号集设计中的应用

为了高效地设计出性能良好的多输入多输出(Multiple Input Multiple Output,MIMO)雷达正交相位编码信号集,提出一种改进的Gerchberg-Saxton(GS)算法,将最小化信号集旁瓣能量的代价函数转化为适合求解的极小化问题;将原始GS算法扩展至多维,并改进其物面和频谱面的约束条件,以适应文中优化问题的求解;利用改进的GS算法迭代优化设计出信号集.仿真实验表明:该算法可以有效改善所得信号集的积分旁瓣和相关性能.     

Three‐Phase Barker Arrays

A 3‐phase Barker array is a matrix of third roots of unity for which all out‐of‐phase aperiodic autocorrelations have magnitude 0 or 1. The only known truly two‐dimensional 3‐phase Barker arrays have size 2 × 2 or 3 × 3. We use a mixture of combinatorial arguments and algebraic number theory to establish severe restrictions on the size of a 3‐phase Barker array when at least one of its dimensions is divisible by 3. In particular, there exists a double‐exponentially growing arithmetic function T such that no 3‐phase Barker array of size with exists for all . For example, , , and . When both dimensions are divisible by 3, the existence problem is settled completely: if a 3‐phase Barker array of size exists, then .     

三进制互补集及其在UWB中的应用

针对DS-UWB在室内高速短距离通信上的诸多优势,文章介绍了基于采用一组正交脉冲UWB信号的三进制互补集。文章首先建立了多用户通信传输的系统模型,分析了三进制互补集及其递归构造方法,进而提出了一种利用Rake接收的三进制互补集多用户通信性能评估结构。由于三进制互补集有良好的非周期自相关和互相关函数,因此减轻了多用户和多径干扰。仿真结果表明,在SV/IEEE802.15.3a信道模型下三进制互补集相对于其它随机序列而言具有更好的性能。     

Effects of potential functions on stochastic resonance

In this paper, the effects of a bistable potential function U(x)=-ax²/2+b|x|^2γ/(2γ) on stochastic resonance (SR) is discussed. We investigate the effects of index γ on the performance of the SR system with fixed parameters a and b, and with fixed potential barriers, respectively. To measure the performance of the SR system in the presence of an aperiodic input, the bit error rate is employed, as is commonly used in binary communications. The numerical simulations strongly support the theoretical results. The goal of this investigation is to explore the effects of the shape of potential functions on SR and give a guidance of nonlinear systems in the application of information processing.     

A Homeomorphism Invariant for Substitution Tiling Spaces

We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of ech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as of intuitive value.     

Symmetries of Quasicrystals

We consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant—rings instead of Bragg peaks. They can be distinguished from glasses by self-similarity of the pattern of radii of the rings.     

随机介质ZnO激光的一种整体效应模型

从实验现象出发建立了无序介质激光的一种整体散射效应物理模型，认为无序介质激光是无序介质中局域-非周期-类结构与相匹配的抽运光相互作用的结果.并以ZnO粉末激光参数为例进行数值模拟，结果与实验定性符合. 关键词： 无序增益介质 局域-非周期-类结构