基于散斑成像技术的扩展目标高分辨率复原

大气湍流对实现扩展目标的高分辨率重建具有重要影响.针对此问题,本文提出了一种改进的散斑成像算法.传统散斑成像算法在相位恢复计算中存在双谱数据量大和计算复杂等问题,改进算法利用图像的厄米特对称性和查找表技术将相位恢复和双谱计算紧密结合,通过计算截止频率内的每个空间频率点邻域双谱和添加双谱坐标约束使得双谱数据量减小.建立傅里叶频域相邻两象限共用的坐标查找表,确定双谱和相位恢复计算顺序,避免了双谱的对称操作从而使得整个计算简单易行.仿真实验结果表明:改进算法相对于双谱截切法使得双谱数据量至少减少了24%并准确恢复出目标相位谱,恢复相位谱经过傅里叶逆变换后清晰地显示了目标的轮廓和结构,再结合Labeyrie-Kroff法得到了目标的高分辨率图像;最后对实际天文图像进行处理,使恢复后图像的分辨率相对于原始图像得到明显提高,并且改进算法以更少的计算时间获得了与双谱截切法几乎同样的恢复效果.     

On computation of real eigenvalues of matrices via the Adomian decomposition

The problem of matrix eigenvalues is encountered in various fields of engineering endeavor. In this paper, a new approach based on the Adomian decomposition method and the Faddeev-Leverrier’s algorithm is presented for finding real eigenvalues of any desired real matrices. The method features accuracy and simplicity. In contrast to many previous techniques which merely afford one specific eigenvalue of a matrix, the method has the potential to provide all real eigenvalues. Also, the method does not require any initial guesses in its starting point unlike most of iterative techniques. For the sake of illustration, several numerical examples are included.     

On a new geometric constant related to the modulus of smoothness of a Banach space

We shall introduce a new geometric constant A(X) of a Banach space X,which is closely related to the modulus of smoothness ρX(τ),and investigate it in relation with the constant A2(X) by Baronti et al.,the von Neumann–Jordan constant CNJ(X) and the James constant J(X).A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved.     

基于Matlab的数学分析极限概念教学实践

极限概念是数学分析理论的基础,贯穿数学分析教学的始终,在数学分析的理论体系中占有十分重要的地位.由于极限概念的严谨性和抽象性,在教学实践当中发现学生对极限概念难以理解.本文借助Matlab软件的图形处理功能,将数列极限,一元函数极限以及多元函数极限的形成过程展示出来,从而强化学生对极限概念的理解.     

锥中调和函数的下界及其应用

本文首先给出锥中一类调和函数的下界,所得结果推广了张艳慧、邓冠铁和高洁欣在半空间中的相关结论;作为应用,接着证明了锥中的Levin型定理;最后,给出了锥中Dirichlet问题解积分表示形式的唯一性定理.     

关于Toeplitz+Hankel线性方程组的迭代解法

本文研究Toeplitz+Hankel线性方程组的预处理迭代解法.我们提出了几个新的预条件子,并分析了预处理矩阵的谱性质,当生成函数在Wiener类中时,预处理矩阵的特征值聚集在1附近.数值实验表明该预处理子比文[5]中的预处理子更有效.     

Integrability and soliton-like solutions for the coupled higher-order nonlinear Schrödinger equations with variable coefficients in inhomogeneous optical fibers

Under investigation in this paper are the coupled higher-order nonlinear Schrödinger equations with variable coefficients, which represent the propagation of femtosecond soliton pulses comprising of two fields with the left and right polarization in the inhomogeneous optical fiber media. Infinitely-many conservation laws are obtained based on the Lax pair. Via the Hirota method and symbolic computation, bilinear forms, bilinear Bäcklund transformations, one- and two-soliton-like solutions are also derived. With different coefficients, bell-shaped, periodic-changing, quadratic-varying, exponential-decreasing and exponential-increasing soliton-like profiles are seen, to describe the propagation and interactions of the femtosecond soliton pulses. Head-on and overtaking elastic interactions are shown, which are decided by the directions of the velocities. We also get the bound states with periodic attraction and repulsion between two solitons.     

FC-空间中新的连续选择定理及其对广义模糊约束多目标对策的应用

建立了非紧FC-空间中新的连续选择定理,作为应用,获得了非紧FC-空间中广义模糊约束多目标对策的弱Pareto平衡存在定理.我们的结论统一、改进和推广了一些近期文献的已知结果.     

Measurement-induced disturbance between two atoms in Tavis-Cummings model with dipole dipole interaction

Quantum correlation, measured by measurement-induced disturbance （MID）, between two two-level atoms is investi- gated in detail in Tavis-Cummings model with dipole--dipole interaction （DDI）. We find that MID can be determined only by the dipole-dipole interaction between the two atoms when the cavity and atoms are at resonance. Moreover, DDI will have different effects on MID for two different kinds of initial states.     

Measurement of the friction coefficient of a fluctuating contact line using an AFM-based dual-mode mechanical resonator

A dual-mode mechanical resonator using an atomic force microscope （AFM） as a force sensor is developed. The resonator consists of a long vertical glass fiber with one end glued onto a rectangular cantilever beam and the other end immersed through a liquid-air interface. By measuring the resonant spectrum of the modified AFM cantilever, one is able to accurately determine the longitudinal friction coefficient ξv along the fiber axis associated with the vertical oscillation of the hanging fiber and the traversal friction coefficient ξh perpendicular to the fiber axis associated with the horizontal swing of the fiber around its joint with the cantilever. The technique is tested by measurement of the friction coefficient of a fluctuating （and slipping） contact line between the glass fiber and the liquid interface. The experiment verifies the theory and demonstrates its applications. The dual-mode mechanical resonator provides a powerful tool for the study of the contact line dynamics and the rheological property of anisotropic fluids.