OCDMA SystemSignature Code Design Theory Via Finite Projective Geometry

Optical orthogonal code is the main signature code employed by optical CDMA system. Starting from modern mathematics theory, finite projective geometry and Galois theory, the essential connection between optical orthogonal code designing and finite geometry theory were discussed; find out the corresponding relationship between the parameter of OOC and that of finite geometry space. In this article, the systematic theory of OOC designing based on projective geometry is established in detail. The designing process and results of OOC on projective plane PG(2,q) and on m-dimension projective space are given respectively. Furthermore, the analytical theory for the corresponding relation between OOC with high cross-correlation and k-D manifold of projective space is set up. The OOC designing results given in this article have excellent performance, whose maximum cross-correlation is 1, and the cardinality reaches the Johnson upper bound, i.e. it realizes the optimization in both MUI and system capacity.

Vanishing Ideals of Projective Spaces over Finite Fields and a Projective Footprint Bound

We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obner basis of the ideal. Further we give a projective analogue for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre’s inequality for the number of points of projective hypersurfaces over finite fields is included.

Evaluating Local Approximations of the L^(2)-Orthogonal Projection Between Non-Nested Finite Element Spaces

We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).

杆件轴向受迫振动的Galerkin有限元EEP法自适应求解

基于单元能量投影(element energy projection,EEP)法自适应分析在杆件静力问题以及离散系统运动方程组中所取得的成果,以直杆轴向受迫振动为例,研究并建立了一种在时间域和一维空间域同时实现自适应分析的方法.该方法在时间和空间两个维度都采用连续的Galerkin有限元法(finite element method,FEM)进行求解,根据半离散的思想,由空间有限元离散将模型问题的偏微分控制方程转化为离散系统运动方程组,对该方程组进行时域有限元自适应求解;然后再基于空间域超收敛计算的EEP解对空间域进行自适应,直至最终的时空网格下动位移解答的精度逐点均满足给定误差限要求.文中对其基本思想、关键技术和实施策略进行了阐述,并给出了包括地震波输入下的典型算例以展示该法有效可靠.

面向大屏幕投影环境的场景漫游交互技术

为提高交互的自然性和降低认知负担,针对大屏幕投影环境提出一种无标识的基于人体空间定位和姿势识别的虚拟场景漫游交互方法。通过已标定的双摄像头实时检测运动人体前景,应用立体视觉方法定位人体空间位置,采用向量进行姿势表示和识别。基于行走隐喻将人体空间位置和姿势作为交互输入信号,借助有限状态机实现交互状态间转换。实现的原型系统表明,该方法可实现自然的虚拟场景漫游交互。

基于有限域上射影空间构造分裂认证码

传统的认证码中,报文由信源和编码规则唯一确定,但现实情况中,信源在同一编码规则作用下能够产生不止一个报文。分裂认证码正是基于这种现状而产生。本研究的目的是构造新的分裂认证码。运用有限域上射影空间的子空间结构和相关计数定理,构造了两个分裂认证码,并计算其参数。当所有规则都按等概率分布选取时,计算了敌方的假冒攻击和替代攻击成功的概率。结果表明,所构造的码能有效地抵抗敌方的假冒和替代攻击。

百色水利枢纽溢流重力坝空间有限元分析研究

百色水利枢纽招标设计阶段 ,通过动态规划法获得的溢流重力坝断面较初步设计阶段的断面有所改变 ,上游面由直立改为 146 0 0 0m高程以下采用 1∶0 2的斜坡 ,下游面坡率改陡为 1∶0 70。对最高溢流坝块的空间有限元分析计算成果表明 ,修改后的坝断面应力应变状况良好。

费马曲线上的有理点

当i∈{1,2,3}时,给出费马曲线uq-1+avq-1+wq-1=0(a∈Fq*)上-iqF有理点[u,v,w]的具体形式及其个数公式N.当a∈Fq2*时,给出P2(Fq2)上该费马曲线有理点个数的简单公式,并得到了这些曲线上的有理点乘积uvw为iqF上立方数的充分条件.

有限域上向量空间性质的研究

通过有限域中的平面以及非零向量空间的集合等定义,运用射影几何与群论的方法推导有限域中向量平面的一系列特性。

t-blocking集合的一个新上界

给出了PG(2,q)上的t-blocking集合的一个一般上界,此上界比以往的上界稍好,同时对知之甚少包含一条线的t-blocking也给出了一个上界.

大跨径人行桥人致振动舒适度分析

人行桥的主要荷载源于行人和非机动车,对于大跨径轻柔桥梁结构,在行人激励之下更容易发生大幅振动,引起舒适度问题。依托国内某大跨径人行提篮拱桥,参考国外人行桥设计指南,通过有限元时程分析方法,计算获得不同荷载激励下结构最大加速度响应时程曲线,进行行人振动舒适度评价。另外,针对不同模态设计相应的TMD减振系统,并进行减振效果分析。

判定二正规卵形线重合所需的最少交点

本文给出特征２有限域Ｆｑ上，２－维射影空间ＰＧ（２，Ｆｑ）中，判定两条正规卵形线重合所需的最少交点数．一般情况下，当３｜（ｑ—１）时，其最少交点数为７；否则为６．若二正规卵形线所含的两条二次曲线有共同的核，其最少交点数是４．

n维有限射影空间上d^e——析取矩阵的新构作

利用n维有限射影空间上的一些性质,构作了组合群验的数学模型de-析取矩阵,并研究了它的参数和Hamming距离.

Robust linear receivers for STBC systems with unknown co-channel interference

Focusing on space-time block code （STBC） systems with unknown co-channel interference, an oblique projection-based robust linear receiver is proposed in this paper.Based on the oblique projection, the desired signal subspace and interference-plus-noise subspace are first identified from the received signal.Then the matched filter receiver is used to decode the STBC encoded signals in the desired signal subspace.Simulation results show that the proposed linear receiver obtains significant performance improvement over conventional Capon-type receivers under finite sample-size situations and in the presence of channel estimation errors.