A study on the (2 + 1)‐dimensional KdV4 equation derived by using the KdV recursion operator

We derive a new ( 2 + 1)‐dimensional Korteweg–de Vries 4 (KdV4) equation by using the recursion operator of the KdV equation. This study shows that the new KdV4 equation possess multiple soliton solutions the same as the multiple soliton solutions of the KdV hierarchy, but differ only in the dispersion relations. We also derive other traveling wave solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

基于二维压缩感知和分层特征的图像检索算法

为了保留图像分析时的像素点位置关系及降维处理,把一维压缩感知理论推广到二维,建立了二维可稀疏信号的压缩测量模型,研究了一种二维信号的自适应梯度下降重构AGDR(Adaptive Gradient Descent Recursion)算法,由此提出了一种图像分层特征提取与检索方法.首先对图像在RGB颜色空间上进行网格离散划分,通过分层算子对图像进行分层映射,定义一种基于颜色网格空间的扩展灰度共生矩阵,采用二维测量模型获取图像的分层测量特征、纹理特征与分层颜色统计特征,图像分层测量特征综合反映出图像的颜色及像素点位置的关系,扩展灰度共生矩阵反映纹理特征.其次用AGDR算法计算检索图像之间的原始信号差量及其稀疏值.最后结合两类分层特征差量、稀疏值和颜色统计特征,融合计算图像间整体相似度度量指标.仿真实验表明,应用分层二维压缩感知测量与AGDR算法的图像检索方法在检索时间、查全率和查准率等指标上具有优越性能,为图像检索提供了新思路.     

Linear recurrent subsequences of generalized meta-Fibonacci sequences

In a recent paper, Frank Ruskey asked whether every linear recurrent sequence can occur in some solution of a meta-Fibonacci sequence. In this paper, we consider the natural generalization of meta-Fibonacci recurrences to more than two terms. In this context, we show, using an explicit construction, that any sequence satisfying a linear recurrence with positive coefficients occurs as an evenly-spaced subsequence in some generalized meta-Fibonacci sequence.     

The weak density of properly d-r.e. branching degree in the d-r.e. degrees

It is proved that for any r.e. degreesv <u, there exists a properly d-r.e. degreec such thatc is a branching degree andv <c <u. Project supported by the National Natural Science Foundation of China (Grant No. 19771045) and National 863 Hi-Tech R&D Programme.     

24点问题的一种简易算法的设计与实现

实践是敏捷软件开发的核心,对代码要求精益求精,在开发的过程中,简单设计,用测试驱动,通过重构和迭代代码实现设计.24点问题是一类趣味数字游戏问题,开始想用递归思想解决,在编写代码的过程中,写出了递推的过程,程序重复的地方太多,经过重构写出了递归算法,在增量式开发中应用重构技术实现了递归算法并对算法进行了扩展.     

Recursions in Calogero-Sutherland Model Based on Virasoro Singular Vectors

The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function, which is the spectrum generating function for the Calogero-Sutherland (CS) model. To accomplish this work, the hidden Virasoro structure in the CS model is much explored. In particular, we found that the Virasoro singular vectors form a skew hierarchy in the CS model. Literally, skew is analogous to coset, but here specifically refer to the operation on the Young tableaux. In fact, based on the construction of the Virasoro singular vectors, this hierarchical structure can be used to give a complete construction of the CS states, i.e. the Jack symmetric functions, recursively. The construction is given both in operator formalism as well as in integral representation. This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.