Group inverses for some 2 × 2 block matrices over rings

We first consider the group inverses of the block matrices (A0BC) over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices (ACBD) over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B^# and (B^πA) ^# both exist; (ii) B is invertible and m = n; (iii) A^# and (D - CA^#B)^# both exist, C = CAA^# , where A and D are m × m and n × n matrices, respectively.     

New type of exactly solvable potential

It is shown that, starting from an exactly solvable potential and making use of the theory of a system of coupled differential equations, it is possible to construct a new type of second-generation potential which is also exactly solvable.     

Quantum Proxy Multi-Signature Scheme Using Genuinely Entangled Six Qubits State

A quantum proxy multi-signature scheme is presented based on controlled teleportation. Genuinely entangled six qubits quantum state functions as quantum channel. The scheme uses the physical characteristics of quantum mechanics to implement delegation, signature and verification. Quantum key distribution and one-time pad are adopted in our scheme, which could guarantee not only the unconditional security of the scheme but also the anonymity of the messages owner.     

Preparation, thermo-optic property and simulation of optical switch based on azo benzothiazole polymer

An azo chromophore molecule 4-[(benzothiazole-2-yl)diazenyl]phenyl-1,3-diamine (BTPD) was prepared with 2-amino benzothiazole and m-phenylenediamine by diazo-coupling reaction. Then, the chromophore molecule BTPD was polymerized with NJ-210 and isophorone diisocyanate (IPDI) to obtain novel azo benzothiazole polymer (BTPU). The structures of BTPD and BTPU were characterized using the Fourier transform infrared, UV–visible spectroscopy, DSC and TGA. The physical properties of the obtained BTPU were investigated. The refractive index (n) of BTPU was demonstrated at different temperature and wavelength (532, 650 and 850 nm) using attenuated total reflection technique. The transmission loss and dispersion characteristic of BTPU film were investigated using the CCD digital imaging devices and Sellmeyer equation. A Y-branch and 2 × 2 Mach–Zehnder interferometer (MZI) polymeric thermo-optic switches based on the thermo-optic effect of prepared BTPU were proposed and the performance of switches was simulated. The results indicated that the power consumption of the Y-branch thermo-optic switch could be only 0.6 mW. The Y-branch and MZI switching rising and falling times obtained were 8.0 and 1.8 ms.     

Morphology of Polystyrene Core–dPoly(ethylene oxide) Shell Arborescent Copolymer Micelles from Small-Angle Neutron Scattering Analysis

Arborescent (dendrigraft) copolymers with a branched polystyrene (PS) core grafted at the chain termini with deuterated poly(ethylene oxide) segments (PS-dPEO) were characterized in benzene and acetone by small-angle neutron scattering measurements using the contrast matching technique. While copolymers incorporating a G1 (twice-grafted) PS core aggregated to some extent, the portion of the scattering curve corresponding to non-aggregated copolymer molecules could still be analyzed to determine the shape and segment radial density profile for core and shell. These were derived from the pair distance distribution function P(r) and the scattering length density contrast profile Δρ(r) = ρ(r) ? ρ(solvent), obtained by the indirect Fourier transformation and deconvolution methods. The profiles obtained for the G1 copolymer are consistent with a well-defined PS core–dPEO shell morphology, only observed previously for upper generation (G4) polymers with deuterated PS (dPS) chains grafted randomly on arborescent PS substrates. Detailed morphological analysis could not be carried out for an analogous G3 arborescent PS copolymer terminally grafted with dPEO segments due to extensive aggregation in both solvents.     

Ground Penetrating Radar Nondestructive Testing Based on Wavelet Sparse Representation

Now Ground penetrating radar (GPR) nondestructive testing methods have been applied to many fields of physics. But traditional electromagnetic methods (usually based on least square and local iteration) just roughly give the information of location, level and quality. In this paper we consider inverse electromagnetic problem which is concerned with the estimation of electric conductivity of Maxwell’s equations. A wavelet multilevel representation is proposed to inversion of GPR nondestructive testing. Once we decompose the objective functional onto different levels from the smallest to the largest, there are very few local minimum on the largest level component of the problem. Then local convergent Gauss-Newton method could easily find the global minimum on this level which is close to the global optimization solution on the second largest level. So, Gauss-Newton method with initial value which is solved on the largest level has serious possibility to find the global minimum of the second largest level. Repeating this step one could find the global optimization solution of the original inverse problem. On each level, the stable and fast local convergent Gauss-Newton method is carried out. Results exhibits clear advantages over damping Gauss-Newton method and testify that it is an available method, especially on aspects of wide convergence and precision.     

行波前置短磁聚焦飞秒条纹管设计

设计了一款长度为265 mm的飞秒条纹管。采用短磁聚焦透镜和行波偏转板,并将行波偏转板置于磁透镜之前以提高偏转灵敏度。采用蒙特卡罗方法对阴极表面理想点和阴极狭缝发射的光电子初始参量进行了模拟抽样,用CST软件的Particle Tracking模块模拟跟踪了光电子的运行轨迹,统计分析了光电子在最佳像面上的位置分布和渡越时间,给出了光电子在最佳像面上的点扩展函数和调制传递函数。计算结果显示,所设计的条纹管阴极有效尺寸达到6 mm,放大率为2.4~2.5,动态空间分辨力大于55 lp/mm。经保守估算,条纹管的时间分辨力有望达到245 fs。     

双路输出超宽谱高功率微波驱动源Tesla变压器

为实现25 GW级双路输出超宽谱高功率微波驱动源的小型化,选择研制了一种与双筒脉冲形成线(Blumlein线)相配一体化的带有开路磁芯的Tesla变压器,作为初级脉冲功率源。进行了Tesla变压器的理论分析,利用简化的磁路模型研究了Tesla变压器初次级线圈电感等电参数的估算方法,给出了Tesla变压器磁芯截面的估算和磁芯制作方法。该Tesla变压器最大输出电压880 kV,充电时间约20 s,耦合系数约0.95,实验结果与理论设计相符。     

推广的Volterra方程的极限环问题

在生物数学中,基本研究对象之一是系统 其中,b>0,c>0,d>0,a(x)为x的至少二阶可微函数。 系统(1)是描述捕食者——食饵相互作用的一种近似数学模型,是对Lotka—Volterra数学模型的推广。这里,x是指食饵种群的密度,y是指捕食者种群的密度,函数a(x)则描述了食饵种群在脱离捕食者情况下的增殖过程。