Combination of non-classical pseudospectral and direct methods for the solution of brachistochrone problem

In this paper, we propose a combination of non-classical pseudospectral and direct methods to find the solution of brachistochrone problem. The method converts the optimal control problem of brachistochrone, into a sequence of quadratic programming problems. To this end, the quasilinearization method is used to replace the nonlinear optimal control problem into a sequence of constrained linear-quadratic optimal control problems; then each of the state variables is approximated by a weighted interpolation function based on the non-classical orthogonal polynomials. The method gives the information of the quadratic programming problems explicitly (the Hessian and the gradient of the cost function). Using this method, the solution of the brachistochrone problem is compared with those in the literature.     

Optimal error estimates of the penalty method for the linearized viscoelastic flows

In this article, optimal error estimates of the penalty method for the linearized viscoelastic flows equations arising in the Oldroyd model are derived. Furthermore, error estimates for the backward Euler time discretization scheme in L ² and H ¹-norms are obtained.     

An iterative algorithm based on the piecewise linear system for solving bilateral obstacle problems

In this paper, we derive the piecewise linear system (PLS) associated with the bilateral obstacle problem and illustrate the equivalence between the linear system and finite-dimensional complementary problem. The existence and the uniqueness of the solution to the PLS are also demonstrated. Based on the PLS, a Picard iterative algorithm is proposed. The convergence analysis is given and examples are presented to verify the effectiveness of the method.     

Decidability and undecidability in cellular automata

We survey results on decidability questions concerning cellular automata. Properties discussed include reversibility and surjectivity and their variants, time-symmetry and conservation laws, nilpotency and other properties of the limit set and the trace, properties chaoticity related such as sensitivity to initial conditions and mixing of the space, and dynamics from finite initial configurations. We also discuss briefly the tiling problem and its variants, and consider the influence of the dimension of the space on the decidability status of the questions.     

基于多子空间线性判别分析的特征提取与分类

为了解决高维小样本数据的分类中Fisherface思想判别分析方法的不足,在最大散度差准则的基础上,提出了利用多线性子空间技术对每类样本进行单独描述的方法,该方法能更准确地反映样本在类内类间的分布关系.在分类中不是以距离作为判别依据,而是按照贝叶斯决策规则得到的隶属置信度作为衡量标准.实验结果表明了该方法的有效性,和同类方法相比,有更高的识别率.     

An improved SVD-based watermarking technique for copyright protection

The drawbacks of SVD-based image watermarking are false positive, robust and transparency. The former can be overcome by embedding the principal components of the watermark into the host image, the latter is dependent on how much the quantity (i.e., scaling factor) of the principal components is embedded. For the existing methods, the scaling factor is a fixed value; actually, it is image-dependent. Different watermarks need the different scaling factors, although they are embedded in the same host image. In this paper, two methods are proposed to improve the reliability and robustness. To improve the reliability, for the first method, the principal components of the watermark are embedded into the host image in discrete cosine transform (DCT); and for the second method, those are embedded into the host image in discrete wavelets transform (DWT). To improve the robustness, the particle swarm optimization (PSO) is used for finding the suitable scaling factors. The experimental results demonstrate that the performance of the proposed methods outperforms than those of the existing methods.     

世界耐除草剂转基因作物的发展及问题

介绍了耐除草剂转基因作物的发展概况及存在问题，以及它们的解决措施。     

基于Matlab的0-1背包问题的动态规划方法求解

背包问题是经典的NP-hard组合优化问题之一,在经济管理、资源分配、投资决策、装载设计等领域有着重要的应用价值。文中用动态规划方法解决0-1背包问题,通过在Matlab6.5环境下对其算法进行测试和与其他方法对比分析,表明应用该方法可节省大量的计算时间,因而具有更高运行效率。     

The generalized Riemann problem method for the shallow water equations with bottom topography

This paper extends the generalized Riemann problem method (GRP) to the system of shallow water equations with bottom topography. The main contribution is that the generalized Riemann problem method (J. Comput. Phys. 1984; 55 (1):1–32) is used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is included in numerical fluxes, and at the same step the source term is discretized with an interface method in which only mid‐point values are plugged in. This scheme is well balanced between the flux gradient and bottom topography when incorporating the surface gradient method (SGM) (J. Comput. Phys. 2001; 168 (1):1–25) into data reconstruction step, and it is also suitable for both steady and unsteady flow simulations. We illustrate the accuracy of this scheme by several 1‐D and 2‐D numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

“两课”改革必须处理好的几个问题

长期以来，两课的教学效果不尽如人意，这既有两课的课程设置和教学内容选择方面的问题，也有教学的方式方法问题。只有正确处理好“做人的学问”和“做事的学问”；马克思主义理论与人文素质教育；国家意志和学生需要；教学与科研等方面的关系，两课教学才能充分发挥其在培养具有中国特色社会主义事业的建设者和接班人中的应有作用。