闭极大线性子空间正交补的判别及应用

继续前面的工作,证得对于赋范线性空间中固定线性子空间成为迫近子空间的充分必要条件.特别的,对于闭极大线性子空间来说,的迫近性等价于的正交可补性.做为其直接推论,给出Banach空间成为自反空间的5个等价条件,其中4个条件为经典结果,一个条件为已有文献中给出的条件,但给出全新的证明.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

正交多相码连续波主动声呐回波检测算法设计

与常规脉冲式主动声呐相比,连续波主动声呐能够提高目标回波的时间处理增益和目标信息更新速率。该文提出一种由正交多相码合成的连续发射波形,分析了发射信号和目标回波模型,设计了多通道匹配滤波器组完成回波检测。为了进一步提高接收机检测性能,提出了多通道非相干积累的处理方法。通过数值仿真,分析提出的连续波形的多普勒分辨性能和目标信息更新率。通过蒙特卡罗法获取接收机工作特性曲线,比较了脉冲式主动声呐和连续波主动声呐在均匀混响背景下对单目标检测性能的差异。仿真结果表明,该文设计的连续波波形具有较好的多普勒分辨性能,在均匀混响背景下,回波检测算法能够明显提高单个目标的探测能力。     

基于量子粒子群优化的正交小波加权多模盲均衡算法

针对常数模盲均衡算法(CMA)均衡高阶正交振幅调制信号(QAM)存在收敛速度慢、稳态误差大的缺点, 提出了基于量子粒子群优化的正交小波加权多模盲均衡算法(QPSO-WTWMMA). 该算法根据高阶QAM信号星座图分布特点, 将量子粒子群优化算法(QPSO) 和正交小波变换融入于加权多模盲均衡算法(WMMA)中. 因而, 利用QPSO对均衡器权向量进行了优化, 利用正交小波变换降低了输入信号的自相关性, 利用WMMA选择了合适的误差模型匹配QAM星座图. 理论分析及水声信道仿真结果表明, QPSO-WTWMMA算法可以获得更快的收敛速度和更低的稳态误差, 在水声通信中具有重要的参考价值.     

两台恒速机上的MapReduce排序算法研究

研究源自于MapReduce系统的一类排序问题。给定两台恒速机和一组按列表到达的工件，每个工件包含两类任务：Map Task和Reduce Task。假设Map任务和Reduce任务都是不可中断的，Map任务可以并行处理，即可以任意分割成若干小的任务并在两台机器上同时处理，而Reduce任务只可以在单台机器上处理。一旦工件到达，必须为其指派机器和开工时间，目标是使得最后完工时间最小。对LSc算法的竞争比进行了分析，得到其一般情形下的竞争比当$s\geq（1+\sqrt{5}）/2$时为$1+1/s$，否则为$1+s/（s+1）$。而当每个工件$J_j$都满足其Map任务总长大于等于Reduce任务总长时，其竞争比当$s\geq（1+\sqrt{3}）/2$时不超过$1+1/（2s）$，否则为不超过$1+s/（2s+1）$。     

Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach.     

Cyclic Designs with Block Size 4 and Related Optimal Optical Orthogonal Codes

We prove the existence of a cyclic (4p, 4, 1)-BIBD—and hence, equivalently, that of a cyclic (4, 1)-GDD of type 4 ^p —for any prime such that (p–1)/6 has a prime factor q not greater than 19. This was known only for q=2, i.e., for . In this case an explicit construction was given for . Here, such an explicit construction is also realized for .We also give a strong indication about the existence of a cyclic (4p 4, 1)-BIBD for any prime , p>7. The existence is guaranteed for p>(2q ³–3q ²+1)²+3q ² where q is the least prime factor of (p–1)/6.Finally, we prove, giving explicit constructions, the existence of a cyclic (4, 1)-GDD of type 6 ^p for any prime p>5 and the existence of a cyclic (4, 1)-GDD of type 8 ^p for any prime . The result on GDD's with group size 6 was already known but our proof is new and very easy.All the above results may be translated in terms of optimal optical orthogonal codes of weight four with =1.     

On the Right-Definite and Left-Definite Spectral Theory of the Legendre Polynomials

In this paper, we further develop the left-definite and right-definite spectral theory associated with the self-adjoint differential operator A in L²(-1,1), generated from the classical second-order Legendre differential equation, having the sequence of Legendre polynomials as eigenfunctions. Specifically, we determine the first three left-definite spaces associated with the pair (L²(-1,1),A). As a consequence of these results, we determine the explicit domain of both the associated left-definite operator A₁, first observed by Everitt, and the self-adjoint operator A^1/2. In addition, we give a new characterization of the domain D(A) of A and, as a corollary, we present a new proof of the Everitt-Mari result which gives optimal global smoothness of functions in D(A).     

Group Representation of Waves in Gyrotropic Crystals

A new group (linear) representation of the propagation of waves in properly and naturally gyrotropic crystals in the general case where the nonreciprocity effect takes place has been developed. Simple expressions of the dependence of ray (group) velocities and polarization vectors of isonormal waves on the complex vector of principal velocities dual to the unitary tensor by which the optical properties of crystals are directly characterized have been obtained. The relationship between gyrotropy and anisotropy and the dipole moment and displacement current induced by the radiation in the crystal has been established. It is shown that the presence of gyrotropy and nonlinear polarization of radiation together with the elimination of conical points entails a phase ambiguity of the ray velocity of the quantummechanical type and a smearing and layering of the wave surface, as well as a discreteness of the spectrum of velocity values of isonormal waves.