Finding optimal memoryless policies of POMDPs under the expected average reward criterion

In this paper, partially observable Markov decision processes (POMDPs) with discrete state and action space under the average reward criterion are considered from a recent-developed sensitivity point of view. By analyzing the average-reward performance difference formula, we propose a policy iteration algorithm with step sizes to obtain an optimal or local optimal memoryless policy. This algorithm improves the policy along the same direction as the policy iteration does and suitable step sizes guarantee the convergence of the algorithm. Moreover, the algorithm can be used in Markov decision processes (MDPs) with correlated actions. Two numerical examples are provided to illustrate the applicability of the algorithm.     

均值—动态VaR多阶段投资组合优化研究

将动态风险度量方法运用到多阶段投资组合中,提出了具有交易成本和交易量限制的均值—动态VaR多阶段投资组合模型,并运用自创算法——离散近似迭代法求解.方法的基本思路为:首先,将模型中的连续型状态变量离散化,并将上述模型转化多阶段赋权有向图,然后,运用极大代数求出起点至终点的最长路程,即获得模型的一个可行解;最后,以该可行解为基础,继续迭代直到前后两个可行解非常接近.证明了该方法的收敛性,并以一个具体的算例,验证了该算法可以较快地计算出不同终期财富所对应的最优投资策略.     

鞅差序列滑动和过程的极限结果

该文获得了鞅差序列滑动和过程的完全收敛性, Marcinkiewicz-Zygmund强大数定律, 矩完全收敛性以及讨论了极大值矩的存在性问题, 推广和改进了已有的结果.     

An approximation to the solution of telegraph equation by variational iteration method

The variational iteration method (VIM) has been applied to solve many functional equations. In this article, this method is applied to obtain an approximate solution for the Telegraph equation. Some examples are presented to show the ability of the proposed method. The results of applying VIM are exactly the same as those obtained by Adomian decomposition method. It seems less computation is needed in proposed method.© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Strong convergence theorems by hybrid method for asymptotically -strict pseudo-contractive mapping in Hilbert space

In this paper, we introduce the hybrid method of modified Mann’s iteration for an asymptotically k-strict pseudo-contractive mapping. Then we prove that such a sequence converges strongly to P_F(T)x₀. This main theorem improves the result of Issara Inchan [I. Inchan, Strong convergence theorems of modified Mann iteration methods for asymptotically nonexpansive mappings in Hilbert spaces, Int. J. Math. Anal. 2 (23) (2008) 1135–1145] and concerns the result of Takahashi et al. [W. Takahashi, Y. Takeuchi, R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 341 (2008) 276–286], and many others.     

Sequence-Controlled Catalytic One-Pot Synthesis of Siloxane Oligomers

Silicones are highly valuable poly- and oligomeric materials with a broad range of applications due to their outstanding physicochemical properties. The core framework of silicone materials consists of siloxane (Si−O−Si) bonds, and thus, the development of efficient siloxane-bond-forming reactions has attracted much attention. However, these reactions, especially “catalytic” siloxane-bond-forming reactions that enable the selective formation of unsymmetrical siloxane bonds, remain relatively underdeveloped. On the other hand, controlled iteration has become a powerful tool for the sequence-controlled synthesis of poly- and oligomeric compounds. Recently, control over the siloxane sequence has been achieved by the one-pot iteration of a B(C₆F₅)₃-catalyzed dehydrocarbonative cross-coupling of alkoxysilanes with hydrosilanes and a B(C₆F₅)₃-catalyzed hydrosilylation of carbonyl compounds. Thus, it is now possible to generate linear, branched, and cyclic sequence-specific oligosiloxanes in a highly selective manner under chloride-free conditions.     

Strong Convergence of New Iteration Process for a Strongly Continuous Semigroup of Asymptotically Pseudocontractive Mappings

In this article, we establish strong convergence theorems for fixed points of strongly continuous semigroup of uniformly Lipschitzian asymptotically pseudocontractive mappings, in the framework of real Banach space.     

High precision localization for profiled extended object based on GHT

A high precision localization scheme for profiled extended objects based-on Generalized Hough Transform (GHT) is proposed. The proposed localization scheme utilizes the edge points’ gratitude orientations of profiled extended objects to build an R-table in frame t-1. When frame t is coming, we search the R-table according to the pre-computed edge points’ gratitude orientations of profiled extended objects in current frame, generating an accumulator array. The coordination corresponding to the accumulator's peak value is regarded as coarse localization point in current frame. Then, a relaxation iteration method is proposed to refine the coarse localization point to obtain a sub-pixel localization point. Numerical experiments show that the localization scheme has following characteristics: high-precision and stability. Furthermore, we present the results of our work which involves investigation of the performance evaluation for the proposed localization scheme.     

Split Bregman iteration solution for sparse optimization in image restoration

It is always a challenging task to develop effective and accurate models for robust image restoration. In this paper, the family of sparse and redundant representation frameworks is considered as an alternative for the above problem. The principle of the family is expatiated on the development and research progress. Two well-known denoising methods are presented and analyzed on their properties. The K-SVD algorithm is an effective method for sparse representation. The iteratively approximate algorithms are always used for the solution of sparse coding operations. Here, a convexification of the l₀ norm to the l₁ norm is adopted in the implementation of K-SVD method. Then a split Bregman iteration solution is proposed for l₁ regularization problems in the performance of the sparse representation of the K-SVD algorithm. The split Bregman iterative method is well studied and fused into the famous K-SVD method. The PSNR (Peak Signal to Noise Ratio) and MSSIM (Mean Structural Similarity) are used to evaluate the performance of those methods. Experimental results on different types of images indicate that our proposed method not only achieve comparable results with the state of art methods, but also make the original method more efficient. Besides, it also provides a valuable and promising reference for image restoration techniques.