产生特殊聚焦图形的二元光学元件

通过面积编码将伽博（Gabor)波带片的透过率函数的余弦分布等效为二元分布，研制了能产生各种特殊聚焦图形的二元光学元件。根据透镜聚焦的物理原理制作的二元振幅型波带片可以方便地产生多种聚焦线，给出了相应的实验结果，并讨论了改善聚焦效果的优化条件。     

鞅变换φ-不等式

本文对于可预报鞅证明了鞅变换的均方函数、极大函数的Φ 不等式 ,并讨论了鞅变换的极大函数的αLΦ 范数与鞅的αKΦ 范数的比较关系     

Enhanced pulse compression induced by the interaction between the third—order dispersion and the cross—phase modulation in birefringent fibres

In this paper,we report on the enhanced pulse compression due to the interaction between the positive third-order dispersion (TOD) and the nonlinear effect (cross-phase modulation effect) in birefringent fibres.Polarization soliton compression along the slow axis can be enhanced in a birefringent fibre with positive third-order dispersion,while the polarization soliton compression along the fast axis can be enhanced in the fibre with negative third-order dispersion.Moreover,there is an optimal third-order dispersion parameter for obtaining the optimal pulse compression.Redshifted initial chirp is helpful to the pulse compression,while blueshifted chirp is detrimental to the pulse compression.There is also an optimal chirp parameter to reach maximum pulse compression.The optimal pulse compression for TOD parameters under different N-order solitons is also found.     

Optical responses of dilute anisotropic composites：numerical calculations via Green‘s function formalism

We investigate the linear and nonlinear optical responses of dilute anisotropic networks using Green's function formalism [Gu Y et al 1999 Phys. Rev. B 59 12847]. For different applied fields, numerical calculations indicate that a large third-order nonlinear enhancement and a broad infrared absorption arise from the geometric anisotropy. We also show the overlap and separation between the absorption peak and nonlinear enhancement peak when the applied field is parallel and perpendicular to the anisotropy, respectively. The results can be understood in terms of the inverse participation ratios with q=2 and the spectral distribution of optical responses.     

带有不等式约束的全局最优性条件

本文利用不连续罚函数方法将带有不等式约束的全局优化问题的求解转化为 讨论一非线性方程的求根问题,从而得到若干个全局最优性条件.     

完美非线性映射的一类构造

在分组密码中 ,为了抗差分攻击 ,需要完美非线性映射 .利用有限域 Zp上的广义 Bent函数和不可约多项式 ,给出了完美非线性映射的一类构造 .     

若干中点迭代法的收敛性

The King-Werner iteration xn 1= xn -F‘(1/2(xn yn))^-1 F(xn);yn 1=xn 1-F‘(1/2(xn yn))^-1F(xn 1) which is used for solving the operator eqution in Banach space F(x) = 0 requires the inverse of the opterator‘s derivative.Now in this paper a deformation King-Werner method without use of inverse is presented and the convergence of this method is proved with the skill of the majoring function. In addition, for the existed convergent theorem the convergent condtions are amended. The corresponding convergence theorem holds also with the amended conditions and its error bounds is obtained. At last a midpoint method of order 1 √2 : yn=xn-F‘(xn)^-1F(xn);xn 1=xn-F‘(xn yn/2)^-1F(xn) which is studied by D.Chen and I.K.Argros is convergent withby milder conditions by recurence relations.     

四元数矩阵方程AX-YB=C的最佳逼近解

本利用四元数矩阵的广义Frobenius范数建立一个关于四元数矩阵的实函数，并讨论了它的极值问题．然后在四元数矩阵方程AX-YB=C的解集合中导出了与给定矩阵的最佳逼近解的表达式．     

Nehari函数族的偏差定理与拟共形延拓

本文讨论了Nehari函数族的偏差性质,得到了这类函数及其导数的若干偏差定理,同时研究了这类函数的拟共形延拓,并给出拟共形延拓的精确表达式.     

ON THE BOREL DIRECTION OF K-QUASIMEROMORPHIC MAPPINGS

For the K-quasimeromorphic mappings, a precise fundamental inequality for the angular domain is established. From this, the Borel direction of the K-quasimeromorphic mappings of zero order is derived.