The Transmission Problem of Viscoelastic Waves

In this paper we consider the transmission problem of viscoelastic waves. That is, we study the wave propagations over materials consisting of elastic and viscoelastic components. We show that for this types of materials the dissipation produced by the viscoelastic part is strong enough to produce exponential decay of the solution, no matter how small is its size. We also show that the linear model is well posed.     

No optimal 1‐planar graph triangulates any nonorientable closed surface

Suzuki [Discrete Math. 310 (2010), 6–11] proved that for any orientable closed surface F² other than the sphere, there exists an optimal 1‐planar graph which can be embedded on F² as a triangulation. However, for nonorientable closed surfaces, the existence of such graphs is unknown. In this article, we prove that no optimal 1‐planar graph triangulates a nonorientable closed surface.     

Estimation of partially specified spatial panel data models with random-effects

In this article, we study estimation of a partially specified spatial panel data linear regression with random-effects. Under the conditions of exogenous spatial weighting matrix and exogenous regressors, we give an instrumental variable estimation. Under certain sufficient assumptions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and asymptotically distributed. Consistent estimators for the asymptotic variance-covariance matrices of both the parametric and unknown components are provided. The Monte Carlo simulation results verify our theory and suggest that the approach has some practical value.     

部分相干光学成像系统的光学传递函数和像质评价准则

根据光学成像理论，建立了部分相干成像光学系统的光学传递函数。该函数与非相干成像光学系统传递函数相同，因而部分相干成像和非相干成像两者的光学系统波面像差公差标准也是相同的。这一点解释了显微镜光学系统的光学设计惯用法则：镜头像差公差标准的选择，并不因为采用成像照明方式的不同而有所差异。     

Partially coherent nonparaxial modified Bessel--Gauss beams

The concept of partially coherent nonparaxial modified Bessel--Gauss (MBG) beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order $m$, \textit{$\xi $} and $f$ parameters, and to compare the difference between the paraxial and nonparaxial results.     

左截断右删失数据光滑分位估计的渐近性质

文中提出了随机左截断右删失数据下的一种光滑分位估计,推导出此光滑估计的相合性和渐近正态性,同时获得了该估计的强弱Bahadur表示定理。     

Quantum circuits for realizing deterministic and exact teleportation via two partially entangled pairs of particles

Deterministic and exact teleportation can be achieved via two partially entangled pairs of particles [Gu Y J 2006 {\em Opt. Comm.} {\bf 259} 385]. The key point of the protocol is a generalized measurement described by a positive operator-valued measure, which can be realized by performing a unitary operation in the extended space and a conventional Von Neumann orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the teleportation. Our method for constructing quantum circuits differs from the usual methods based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.     

用于曲面精密检测的新型光纤三角传感器研究

基于光纤传感技术和三角测量方法，提出了一种用于曲面检测的新型光纤三角传感器。根据所设计的轮辐式接收光纤结构，可以在测量曲面与传感头间位移时，首先获取被测点处微面元的倾斜信息，以便对传感器测量值进行实时误差修正，从而解决了被测表面倾斜对坐标测量带来的影响。该传感器还能有效地消除环境光干扰、光源波动、表面反射率变化等对测量带来的影响。建立了传感器测量的数学模型。理论分析和初步的实验结果证明了系统的有效性和实用性。该传感器系统不稳定性好于0.3%，横向分辨率好于8μm，高度分辨率好于0.1μm。     

部分相干涡旋光束形成的相干涡旋特性研究

推导出部分相干涡旋平顶光束的传输解析公式,并用以研究了聚焦场和自由空间中部分相干涡旋光束形成相干涡旋的特性.结果表明,相干涡旋与光束阶数N,空间相干参数α和参考点位置(x1,y1)有关.依赖于参考点的选择,光谱相干度可能存在零值点,也可能没有零值点.特别是,若选取x1=y1=0,光谱相干度零值点处的位相可以是确定的,因而不存在相干涡旋.     

ON THE PARTIAL EQUIASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS

In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results.