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双语推荐:双随机矩阵

文章主要研究了奇、偶双随机矩阵及其(奇、偶)积和式的有关问题。一方面,通过分析双随机矩阵的奇偶性,说明了刻画奇双随机矩阵和偶双随机矩阵的等价性;另一方面,参照双随机矩阵其积和式的下确界问题(即著名的Van der Waerden-Egorychev-Falikman定理),对奇、偶双随机矩阵其(奇、偶)积和式的确界问题分别进行了探讨。
This paper mainly studies odd and even doubly-stochastic matrices,and the ( odd and even) per?manents of them, respectively. On one hand, by analyzing the parity of doubly-stochastic matrices, we illustrate the equivalence of characterizing the odd and even doubly-stochastic matrices. On the other hand, with reference to the best lower bound for the permanents of doubly-stochastic matrices ( that is, the famous Van der Waerden-Ego?rychev-Falikman theorem) , we discuss the best bound problems for the ( odd and even) permanents of odd and e?ven doubly-stochastic matrices, respectively.

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对给定的实或复 n-重Λ={λ1,…,λn},决定是否存在以Λ为谱的非负(随机矩阵的问题称为非负(随机矩阵逆特征值问题,这一直是非负矩阵理论中尚未完全解决的一个研究热点。作者曾对 n ∈{2,3,4,5},研究 n 阶双随机矩阵逆特征值问题有解的充分条件并给出相应解的公式。最近,又对任意正整数 n,先给出行和为常数的对称矩阵的逆特征值问题的充要条件和解的公式,后给出对称随机矩阵逆特征值问题有解的两种充分条件和解的公式。论文在提出任意阶对称随机矩阵逆特征值问题通解的概念和3阶对称随机矩阵逆特征值问题完全通解的概念之后,首先给出3阶对称随机矩阵逆特征值问题存在完全通解的充要条件和完全通解的公式;其次给出3阶对称随机矩阵逆特征值问题存在通解的充要条件和通解的公式;最后给出4阶对称随机矩阵逆特征值问题有解的几种充分条件和相应解的公式。
Given an n-tuple Λ of numbers, real or complex, the problem of deciding the existence of a nonnegative (stochastic) matrix with spectrum Λ is called the nonnegative (stochastic) inverse eigenvalue problem. This problem has long time been one of the problems of main interest in the theory of matrices. Other reference gave the sufficient conditions for doubly stochastic inverse eigenvalue problem of order two to five to have a solution and the formulas of the corresponding solution, and firstly gave the sufficient conditions for constant row sums symmetric inverse eigenvalue problem (of any order) to have a solution and the formula of corresponding solution, and then gave the sufficient conditions for the symmetric stochastic inverse eigenvalue problem to have a solution and the corresponding solution. In this paper, after presenting the concept of general solution of an inverse eigenvalue problem ( of any order) and the concept of totally general solution of a 3 ×3 symmetri
双随机矩阵有许多重要的应用,紧图族可以看作是组合矩阵论中关于双随机矩阵的著名的Birkhoff定理的拓广,有重要的研究价值.确定一个图是否紧的是个困难的问题,目前已知的紧图族尚不多,本文介绍从某些已知的紧图出发构造紧图族的加边法,从而构造很多紧图族.
Doubly stochastic matrix has many important applications,the family of compact graph can be seen as the generalization of the famous Birkhoff theorem which is about doubly stochastic matrix, has important research value. Determine whether a graph is a compact graph is an difficult problem, at present there are only few compact graphs known. In this paper, we introduced the method of constructing compact graphs continuously by adding pendant edges to some already known compact graphs. Using this method we can construct a lot of compact graphs.

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介绍了固定点处严格保序的线性映射,利用其严格保等价性,研究一个与此线性映射所对应的线性映射,证明了该线性映射所对应的矩阵双随机矩阵
In this paper , it introduces linear mapping of strictly isotone at a fixed point .Using its strictly preserving equivalent , researches the linear mapping corresponding from a linear mapping , and prooffs the matrix corresponding from the linear mapping is a doubly stochastic matrix .

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根据非奇异M-矩阵的特点和性质,对两个M-矩阵的Hadamard积的最小特征值下界进行新的估计,并给出q(BoA-1)和q(AoA-1)的估计式,同时得到了当A-1是双随机矩阵时,q(BoA-1)的一个新估计式.经算例验证,这些估计式在某些情况下提高了现有估计式的估计精确度.
According to the characteristics and properties of nonsingular M-matrices ,for the Hadamard product of two M-matrices is further estamated ,and some new estimation formulas on lower bounds of q(B° A-1 ) and q(A° A-1 ) are given .When A-1 is a doubly stochastic matrix ,a new inequality q(B°A-1 )of is derived .The given numerical examples show that these inequalities improve several existing results in some cases .

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为了实现单通道彩色图像的同时加密,首先将两幅待加密的彩色图像转换成索引图像的形式,保留索引图像的颜色映射矩阵,然后仅对数据矩阵采用复数合成、分数傅里叶变换、随机调制实现了图像的加密。结果表明,只有在使用完全正确密钥的情况下才能恢复出两幅无失真的图像。该算法具有很高的安全性。
In order to encrypt double color images in a single channel , firstly, two color images to be encrypted were converted to indexed images instead of RGB model and the color mapping matrix of the index images was reserved .Then, after the logarithm operation , fraction Fourier transformation and random modulation of the data matrix , both the images were encrypted .The theoretical analysis and experiment results indicate that two color images can be retrieved without distortion only when correct keys are used .The algorithm has high security .

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在深入研究单像素相机原理及结构的基础上,发现单像素相机存在固有的结构缺陷,需要预先测量和补偿操作,导致运算复杂、系统误差增大等问题。针对这些问题,对单像素相机结构进行改进,设计对称信号通路收集数字微镜器(DMD)阵列2个状态的反射光,然后将2路测量结果相减直接得到测量值。该方案简化了单像素相机的测量和计算过程,有效减少了系统误差;更为重要的是,像素相机的测量矩阵相当于三值伪随机测量矩阵,相对于单像素相机的二值伪随机测量,可大大提高信号重建精度。基于像素压缩成像系统方案,采用上海辛同公司开发的数字微镜阵列,搭建了成像系统硬件平台并进行测试,验证了系统的有效性。
In light of the thorough research on its principle and structure,it has been found that the single-pixel cam-era always needs beforehand measurements and compensated operations,leading to complex calculation and larger system error. To resolve the problems above and improve the performance of the single-pixel camera,the symmetri-cal signal pathway were designed to collect the reflecting light from the two states of digital micromirror de-vice(DMD)array. Then one of the two measurement results subtracts the other to gain the final measurement value. The proposed design simplifies the measurement and calculation process of the single-pixel camera and reduces the system error effectively. More importantly,the measurement matrix of the proposed dual-pixel camera is equivalent to the ternary random matrix,which can considerably improve the reconstruction accuracy compared to the binary random matrix of the single-pixel compressed sensing. According to the scheme of the proposed du

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针对率系统,采用基于辅助模型的改进随机牛顿递推算法辨识输出误差模型。若当前参数估计对应的估计系统不稳定,则出现中间不可测时刻输出估计发散,辨识过程停止。增加非线性模型与常规辅助模型一起为下步递推提供信息估计,确保递推进行。为避免出现输入不充分或者广泛时Hessian阵奇异或者接近奇异的情况,在Hessian阵的递推中增加对称正定矩阵。最后给出了所提出辨识算法的一致收敛性证明。
An auxiliary-model-based improved stochastic Newton recursive algorithm is utilized to identify the output-error model for the dual-rate system. The output estimations at the time between two slow-sampled periods will diverge when the unstable estimated system arises and the identification process will cease. Therefore, a nonlinear model is proposed as the sub-auxiliary model. Together with the general auxiliary model, the proposed model provides estimated information for the next recursion. When the input is not general enough, the Hessian matrix will be singular or nearly singular. A positive definite symmetric matrix is added to the recursion for Hessian matrix to ensure it positive definite. Finally, the uniform convergence of the proposed algorithm is proved.

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风能的随机波动性使得风力发电机输出的有功功率随风速变化而波动,影响风力发电机输送到电网的电能质量。在对风电系统传递函数进行推导的基础上,对风电系统的稳定性能进行了分析,并针对现有有功功率平滑控制中存在的风电系统稳定性、功率平滑性和风能利用率之间的矛盾,提出了一种基于模糊指数移动平均(exponential moving average,EMA)算法的有功功率平滑控制策略。该策略同时兼顾了系统稳定性、功率平滑性和风能利用率3个方面的要求,即能够根据风速情况实时对周期数进行调整,使得系统在风速下降时,首先确保风电系统能够安全稳定运行;在风速波动剧烈段,有效抑制风电系统输出有功功率的随机波动;在风速平稳段,提高风能利用率。在Matlab/Simulink仿真平台上搭建了矩阵变换器(two-stage matrix converter,TSMC)风电系统模型,仿真结果验证了该控制策略的可行性和有效性。
Random fluctuation of wind energy makes the output active power of wind power generators fluctuated with variation of wind speed, so the quality of the power transmitted to power grid from wind farm is affected. On the basis of deriving the transfer function of wind power generation system, the stability of wind power generation system is analyzed, and in allusion to the contradictions among system stability, power smoothness and wind energy utilization rate in existing active power smoothing control, a fuzzy exponential moving average (EMA) algorithm based active power smoothing control strategy is proposed. In the proposed strategy the demands on system stability, power smoothness and wind energy utilization rate are simultaneously considered, namely according to the condition of wind speed the real-time adjustment of periodicity is performed, to make the secure and stable operation of wind power system while the wind speed decreases; to effectively suppress random fluctuation during
基于钻削工步质量波动与监测信号特征变化之间的耦合现象,提出一种基于监测信号谱特征的高精度批量钻削工步质量一致性控制检测方法。认为正常钻削过程的声发射和三向加速度振动监测信号可视为随机过程,满足或近似高斯分布,信号偏离高斯分布的程度与各钻孔加工质量波动间存在对应关系;以各钻孔声发射和加速度振动监测信号为研究对象,提取各钻孔监测信号的谱幅值平均值为特征,对不同钻削情况下信号偏离高斯分布的程度进行定量分析;采用基于ReliefF算法的特征加权模糊聚类分析,进行基于监测信号谱幅值均值特征矩阵的钻孔质量分类,并与人工检测的工步质量一致性结果对比分析。计算和分析结果表明,监测信号谱特征与各钻削工步质量之间存在有机联系,对信号谱特征进行融合聚类可分析批量钻削工步质量的一致性。
Based on the coupling phenomena between the batch drilling process quality fluctuation and monitoring signals features changes, a kind of signals feature extraction method based on bi-spectrum feature is proposed to solve the quality consistency control and testing problem of the high-precision batch drilling step. Theoretically, the acoustic emission signal and acceleration vibration signal of a normal drilling process is viewed as a stochastic process to meet with Gaussian distribution, and there could be a corresponding relationship between the deviation degree from Gaussian distribution of signal and the drilling step quality fluctuation. The acoustic emission signals and acceleration vibration signals of batch drilling are taken as research objects, the quantitative analysis of the deviation degree from Gaussian distribution under different conditions could be expressed by the average bi-spectrum amplitude of each signal. The ReliefF algorithm is used to assign the weigh

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