Meyniel's conjecture holds for random d‐regular graphs

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. The biggest open conjecture in this area is the one of Meyniel, which asserts that for some absolute constant C, the cop number of every connected graph G is at most . In a separate paper, we showed that Meyniel's conjecture holds asymptotically almost surely for the binomial random graph. The result was obtained by showing that the conjecture holds for a general class of graphs with some specific expansion‐type properties. In this paper, this deterministic result is used to show that the conjecture holds asymptotically almost surely for random d‐regular graphs when d = d(n) ≥ 3.     

处理噪声问题的泰勒展开交替最小化算法

为了处理图像、计算机视觉和生物信息等领域中广泛存在的稀疏大噪声和高斯噪声问题,提出了一种利用交替方向最小化思想求解主成分追求松弛模型的泰勒展开交替最小化算法(TEAM).采用推广泰勒展开和收缩算子等技术推导出低秩矩阵和稀疏大噪声矩阵的迭代方向矩阵,加入连续技术提高算法的收敛速率,设计出TEAM算法的求解步骤.实验中,将TEAM算法与该领域的顶级算法作分析对比.结果表明,TEAM算法时间优势明显,误差优势略好.     

A major index for matchings and set partitions

We introduce a statistic pmaj(P) for partitions of [n], and show that it is equidistributed with cr₂, the number of 2-crossings, over all partitions of [n] with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inv and maj.     

投影寻踪模型在国民经济综合评价中的应用

文章针对区域国民经济发展的多属性,采用投影寻踪评价模型,用加速遗传算法寻找最佳投影方向,将多维属性指标转换为一维投影值.在此基础上,通过建立单属性指标的分类等级区间,给出区域国民经济发展水平分类的投影值区间,从而实现对区域国民经济发展水平的分类.应用表明,它是国民经济评价的一种计算过程简单、直观的新方法.     

用于新一代高密度可录光盘的有机材料研究进展

本文在总结近几年来国内外文献和专利报道的最新研究成果基础上,简要阐述了新一代高密度可录光盘的数据存储机理以及激光器工作波长与有机材料薄膜最大吸收波长相匹配的要求,介绍了在蓝(紫)光波段内(350～400nm)具有显著吸收的有机材料研究概况,并讨论了这些有机材料作为新一代高密度可录光盘数据存储介质的可能性。最后,对有机材料用于新一代高密度可录光盘数据存储介质的研究重点以及今后的发展前景进行简要讨论和展望。     

The role of matching thickness on the wideband electromagnetic wave suppresser using single layer doped barium ferrite

The effect of Mg²⁺, Co²⁺and Ti⁴⁺ substitution on microwave absorption has been studied for BaMg_0.5Co_0.5Ti_1.0Fe₁₀O₁₉ ferrite-acrylic resin composite in frequency range from 13 to 20 GHz. X-ray diffraction (XRD), scanning electron microscopy (SEM), vector network analysis and vibrating sample magnetometry (VSM) were employed to analyze structure, electromagnetic and microwave absorption properties of prepared ferrite. The obtained results of reflectivity demonstrate that by varying matching thickness along with weight percentage of ferrite to acrylic resin, the bandwidth coupled with reflection loss values of prepared composites can be easily tuned. Based on microwave measurement on reflectivity, it is found that BaMg_0.5Co_0.5Ti_1.0Fe₁₀O₁₉ is a good candidate for wideband electromagnetic compatibility and other practical applications at high frequency.     

Analysis of orthogonal multi-matching pursuit under restricted isometry property

Orthogonal multi-matching pursuit(OMMP)is a natural extension of orthogonal matching pursuit(OMP)in the sense that N(N≥1)indices are selected per iteration instead of 1.In this paper,the theoretical performance of OMMP under the restricted isometry property(RIP)is presented.We demonstrate that OMMP can exactly recover any K-sparse signal from fewer observations y=φx,provided that the sampling matrixφsatisfiesδKN-N+1+(K/N)~(1/2)θKN-N+1,N1.Moreover,the performance of OMMP for support recovery from noisy observations is also discussed.It is shown that,for l_2 bounded and l_∞bounded noisy cases,OMMP can recover the true support of any K-sparse signal under conditions on the restricted isometry property of the sampling matrixφand the minimum magnitude of the nonzero components of the signal.     

基于组合权重的系统评价模型

提出了基于组合权重的系统评价新模型 ( CWSE) ,即 :直接根据评价指标样本数据集 ,用基于加速遗传算法的投影寻踪方法确定各评价指标的分类权重 ,用基于加速遗传算法的层次分析法确定各评价指标的排序权重 ,用加速遗传算法对各评价指标的分类权重和排序权重进行综合得到组合权重 ,然后以这些组合权重与各评价对象相应评价指标的标准化值进行加权平均 ,得到系统评价的综合指标值 ,据此可对各评价对象进行分类排序 .用 CW SE模型评价中国 30个区域 1995年开发度的结果表明 ,根据开发度的强弱可把这些区域分成 3个强开发区域、6个较强开发区域、10个中等开发区域和 11个弱开发区域 ;CWSE模型简便、通用 ,计算结果较为客观和稳定 ,为系统工程理论和实践提供了新的研究方法 .     

The capture into parametric autoresonance

In this work, we show that the capture into parametric resonance may be explained as pitchfork bifurcation in the primary parametric resonance equation. We prove that the solution close to the moment of the capture is descibed by the Painlevé-2 equation. We obtain connection formulae for the asymptotic solution of the primary parametric resonance equation before and after the capture using the matching of asymptotic expansions.