Maximizing and minimizing the number of generalized colorings of trees

We classify the trees on $n$ vertices with the maximum and the minimum number of certain generalized colorings, including conflict-free, odd, non-monochromatic, star, and star rainbow vertex colorings. We also extend a result of Cutler and Radcliffe on the maximum and minimum number of existence homomorphisms from a tree to a completely looped graph on $q$ vertices.     

Pluriassociative algebras I: The pluriassociative operad

Diassociative algebras form a category of algebras recently introduced by Loday. A diassociative algebra is a vector space endowed with two associative binary operations satisfying some very natural relations. Any diassociative algebra is an algebra over the diassociative operad, and, among its most notable properties, this operad is the Koszul dual of the dendriform operad. We introduce here, by adopting the point of view and the tools offered by the theory of operads, a generalization on a nonnegative integer parameter γ of diassociative algebras, called γ-pluriassociative algebras, so that 1-pluriassociative algebras are diassociative algebras. Pluriassociative algebras are vector spaces endowed with 2γ associative binary operations satisfying some relations. We provide a complete study of the γ-pluriassociative operads, the underlying operads of the category of γ-pluriassociative algebras. We exhibit a realization of these operads, establish several presentations by generators and relations, compute their Hilbert series, show that they are Koszul, and construct the free objects in the corresponding categories. We also study several notions of units in γ-pluriassociative algebras and propose a general way to construct such algebras. This paper ends with the introduction of an analogous generalization of the triassociative operad of Loday and Ronco.     

一种快速稀疏分解图像去噪新方法*

提出了一种基于分层树型结构正交匹配追踪算法的快速图像去噪方法.通过选择高斯函数和墨西哥草帽小波母函数构建混合冗余字典,采用分层树状结构表示字典,结合构正交匹配追踪算法,实现图像稀疏表示,提高了图像表示的稀疏性,降低了算法的复杂度.依据噪音能量阈值,通过多次迭代达到图像去噪的目的.实验结果表明,在相同的噪音水平下,该迭代去噪算法取得了较高的较好的PSNR,获得更好的视觉效果.     

某新型装备维修策略的研究

本文对如何借助于专家的知识、经验,科学、合理地制定某新型武器装备的维修策略进行了研究、探讨,提出了具有军事意义、又具有经济价值的新方法。为该新型装备的贮存、管理提供了决策依据,同时也为其它新型装备维修策略的制定提供了思路。     

Rational solutions of the graphsack problem

A graphsack problem is a certain binary linear optimization problem with applications in optimal network design. From there a rational graphsack problem is derived by allowing the variables to vary continuously between 0 and 1. In this paper we deal with rational graphsack problems. First we develop the concept of compressed solutions and the concept of augmenting cuts. Making use of these concepts a very simple optimality criterion is derived. Finally an efficient algorithm solving rational graphsack problems is given which is polynomially bounded in time and which is closely related to the simplex algorithm.     

几种常见树种叶片光谱秋季变化特征分析

叶片随着时间生长产生变化,其光谱特征也会发生变化。研究相同树种叶片不同时间条件下的光谱变化规律以及不同树种叶片相同时间条件下的光谱特征,不仅为植被叶片光谱随时间变化的规律研究提供理论基础,也是高光谱遥感精确识别植被信息的关键。选取北京市10种常见树种,利用地物光谱仪观测各树种不同时间叶片光谱,同时将观测的光谱进行一阶微分处理和典型波段分析,对比相同时间不同树种叶片光谱的差异,分析相同树种不同时间的光谱变化规律,探索不同时相条件下高光谱遥感识别树种的有效波段。结果表明：不同树种叶片光谱均随时间的改变而产生显著变化,但差异规律各不相同;不同树种相同时间叶片光谱在部分波段存在显著差异,为高精度树种识别提供了理论依据和叶片基础光谱数据。     

Matching subsequences in trees

Given two rooted, labeled trees P and T the tree path subsequence problem is to determine which paths in P are subsequences of which paths in T. Here a path begins at the root and ends at a leaf. In this paper we propose this problem as a useful query primitive for XML data, and provide new algorithms improving the previously best known time and space bounds.     

On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree

A different approach is given to recent results due mainly to R. C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The techniques developed are based on some results of matching polynomials and used a work by O. L. Heilmann and E. H. Lieb on an apparently unrelated topic.