非线性奇异边值问题的正解

利用锥映射的不动点指数定量，研究了一类非线性奇异边值问题多个正解的存在性问题。在构造的解的存在条件之下，证明了奇异边值问题至少有两个正解的存在性定理。     

一维光学格子孤子的传输特性及控制研究

利用解析和数值方法研究了在具有横向折射率周期性调制的克尔型非线性介质中光学格子孤子的传输，得到了孤子参数的演化方程以及格子孤子的形成和稳定传输的条件.结果表明：当光束的入射角小于某临界角度时，光束可被类似波导形式的路径俘获而稳定传输，该临界角随折射率调制周期、调制深度的增加而增大，且光束越窄临界值越大.此外，线性空间啁啾虽然对光束传输的中心位置没有任何影响，但会导致光束发散从而破坏格子孤子的形成和稳定传输，对此提出了采用特定功率取值来补偿啁啾作用从而形成格子孤子的方案. 关键词： 光孤子 光学格子 光传输 矩方法     

宽带膜厚实时监控过程中膜层折射率的确定方法

为了准确计算出镀膜过程中每层膜的折射率，介绍了实时监控过程中确定膜层折射率的2种方法：一种是由实测的透射比光谱直接反算出膜层的折射率；另一种是用最小二乘法的优化算法实时拟合折射率。试验结果表明：在线反算适合单点监控，所得折射率误差小于2%。然而在实际镀膜过程中,由于宽带内膜层参数误差较大,一般大于25%。为此，采用最小二乘法拟合，即在整个宽光谱范围内采集每个波长点的信息，所得结果误差很小，一般都在2％～5%之间,有时可达到10%,在很大程度上提高了实际镀膜时膜厚监控的精度。     

A Modified Quasi-Newton Method for Structured Optimization with Partial Information on the Hessian

This paper develops a modified quasi-Newton method for structured unconstrained optimization with partial information on the Hessian, based on a better approximation to the Hessian in current search direction. The new approximation is decided by both function values and gradients at the last two iterations unlike the original one which only uses the gradients at the last two iterations. The modified method owns local and superlinear convergence. Numerical experiments show that the proposed method is encouraging comparing with the methods proposed in [4] for structured unconstrained optimization Presented at the 6th International Conference on Optimization: Techniques and Applications, Ballarat, Australia, December 9–11, 2004     

烷基硫酸盐表面张力的量子化学研究

用AMl量子化学计算法优化了十三烷基硫酸根阴离子和——CH3在不同取代位的十二烷基硫酸根阴离子的几何构型，得到最优构型时最高占据分子轨道能级EHOMO、最低空轨道能级ELUMO、电子能量Eele和偶极矩μ等数据．将这些电子结构数据分别与表面张力相拟合，得到很好的相关性。文中讨论了——CH3在不同位置取代对表面张力的影响。     

解奇异非光滑方程组的牛顿法和不精确牛顿法

本文主要解决奇异非光滑方程组的解法。应用一种新的次微分的外逆，我们提出了牛顿法和不精确牛顿法，它们的收敛性同时也得到了证明。这种方法能更容易在一引起实际应用中实现。这种方法可以看作是已存在的解非光滑方程组的方法的延伸。     

Chemical bonding in isolated molecules and crystals of zwitterionic pentacoordinate silicon chelates

The electronic structures of a number of zwitterionic pentacoordinate silicon chelates were investigated using the results of X-ray diffraction studies and quantum-chemical calculatoins by the MPW1PW91/6-311G(d) method. The topological analysis of the electron density distribution function and the study in the framework of the natural bond orbital partitioning scheme showed that the character of chemical bonding in the axial fragments of the molecules under consideration changes from dative to three-center, four-electron as the silicon atom assumes a trigonal-bipyramidal coordination.     

Singularity conjecture and constructions of Jacobi forms

This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-typeL-series.     

Modified Three-Dimensional Formulations of Bending Problems of Homogeneous Plates and Beams under Complex Fixing Conditions

Modified three-dimensional formulations of bending problems of homogeneous elastic plates and beams are considered. Modification of the known three-dimensional formulations reduces to using additional constraints imposed on displacement functions. An advantage of the formulations proposed is that complex fixing conditions of plates and beams can be taken into account.     

On Poisson–Malcev Structures

Malcev–Poisson structure on a manifold is analogous to a Poisson structure with the Lie identity replaced by a slightly more general Malcev identity. Examples of such structures arise naturally. In the second part of the paper we study Malcev bialgebras. A theorem of characterization is proved.