实行(列)对称矩阵的QR分解

提出了行(列)倒置矩阵与行(列)对称矩阵的概念,研究了它们的性质,获得了一些新的结果,给出了实行(列)对称矩阵的QR分解的公式,它们可极大地减少行(列)对称矩阵的QR分解的计算量与存储量,而且不会降低数值精度.     

子矩阵约束下的反对称阵特征值反问题

矩阵的特征值反问题在结构设计、振动系统参数识别和自动控制等领域具有广泛应用。给出了子矩阵约束下反对称矩阵反问题解的一般表达式,并且给出了解的最佳逼近解。     

框架的行置换和列置换——处理复杂系统的新思维系列之四

本系列论文基于《多边矩阵理论》,由东方整体性思维所启迪,试图提供并完善一套从整体到局部处理复杂系统多指标问题、非均匀性问题、非线性问题的强有力的数学工具,并对其进行严格的理论推导和证明。本文利用群论的相关概念和结论,将其和框架的剖分运算相结合,引入了导出框架和对称框架的定义,证明了框架的行置换等价于列置换的结论,从而以后可以统一地处理指标间的置换问题。     

基于模糊神经网络的大场景人群密度估计方法 *

提出了一种估计大场景下密集人群密度的方法。该方法根据人类视觉的模糊性原理,认为用模糊集来划分人群密度范围比用确定的方法更符合人眼视知觉的认知方式,利用统计的方法确定灰度共生矩阵各指标对于各个密度类别的隶属函数;设计基于误差反向传播训练算法（BP）的模糊神经网络,计算样本模式对于各个密度类别的隶属度,并根据人群密度变化的时域连续性原理对人群密度范围进行合理估计。实验表明该方法提高了估计精度。     

关于某些特殊分块矩阵的群逆

分块矩阵的广义逆不仅在数学理论上有广泛研究而且在自动控制、系统理论、概率统计、数学规划等领域有着广泛的实际研究背景.该文对形如[A B/C 0]分块矩阵的群逆的表达式问题进行了研究.设P是复数域上的幂等阵.令矩阵A,B,C取自集合{P,PP*,PP*P },则可以得到27个形如[A B/C 0]的分块矩阵.给出了这27个分块矩阵群逆的存在性与表示形式.     

海洋平台灰预测和支持向量机的逆控制

导管架式海洋平台在随机波浪等外载荷作用下极易产生有害振动,且其动力响应具有极强的非线性和时变性,采用被动控制方法和基于精确数学模型的主动控制方法控制海洋平台的有害振动很难达到理想的控制效果.结合灰预测和支持向量机的优点,提出了基于灰预测和支持向量机的自适应逆控制方法,并将其与动态刚度阵法相结合应用于导管架式海洋平台的振动主动控制中.数值算例分析表明,该控制方法可有效地控制波浪和风载荷作用下引起导管架式平台的有害振动,并能解决由于控制信号传输等原因引起的时滞问题.     

A macro-meso constitutive law for concrete having imperfect interface and nonlinear matrix

The overall behavior of concrete depends on its meso structures such as aggregate shape, interface status, and mortar matrix property. The two key meso structure characters of concrete, bond status of interface and nonlinear property of matrix, are considered in focus. The variational structure principle is adopted to establish the macro-meso constitutive law of concrete. Specially, a linear reference composite material is selected to make its effective behavior approach the nonlinear overall behavior of concrete. And the overall property of linear reference composite can be estimated by classical estimation method such as self-consistent estimates method and Mori-Tanaka method. This variational structure method involves an optimum problem ultimately. Finally, the macro-meso constitutive law of concrete is established by optimizing the shear modulus of matrix of the linear reference composite. By analyzing the constitutive relation of concrete established, we find that the brittleness of concrete stems from the imperfect interface and the shear dilation property of concrete comes from the micro holes contained in concrete. Supported by the National Natural Science Foundation of China (Grant Nos. 50679022, 90510017, 50539090) and National Basic Research Program of China (Grant No. 2007CB714104)     

基于模糊层次分析法综合评判工会竞赛成绩

为综合评判工会组织的各项竞赛活动的成绩,提出了基于模糊层次分析法的综合评判措施,主要包括竞赛项目权重的确定、竞赛成绩的量化和综合评判等过程.实际应用表明,模糊层次分析法可以最大限度减少主观因素对评价结果的影响,合理地确定各项赛事在工会竞赛活动中的权重,结合竞赛成绩的量化矩阵,使得综合评价结果科学、可信.     

Highly ion-conductive solid polymer electrolytes based on polyethylene non-woven matrix

Highly ion-conductive solid polymer electrolyte (SPE) based on polyethylene (PE) non-woven matrix is prepared by filling poly(ethylene glycol) (PEG)-based crosslinked electrolyte inside the pores of the non-woven matrix. The PE non-woven matrix not only shows good mechanical strength for SPE to be a free-standing film, but also has very porous structure for high ion conductivity. The ion conductivity of SPE based on PE non-woven matrix can be enhanced by adding sufficient non-volatile plasticizer such as poly(ethylene glycol) dimethyl ether (PEGDME) into ion conduction phase without sacrificing mechanical strength. SPE with 20 wt.% crosslinking agent and 80 wt.% non-volatile plasticizer shows 3.1 × 10⁻⁴ S cm⁻¹ at room temperature (20 °C), to our knowledge, which is the highest level for SPEs. It is also electrochemically stable up to 5.2 V and has high transference number about 0.52 due to the introduction of anion receptor as an additive. The interfacial resistance between Li electrode and SPE is low enough to perform charge/discharge test of unit cell consisting of LiCoO₂/SPE/Li at room temperature. The discharge capacity of the unit cell shows 87% of theoretical value with 86% Coulombic efficiency.     

决策表中基于对象的μ-约简方法研究

研究了不协调决策表中基于对象的μ-约简问题,给出了μ-约简的一些性质及等价定义,得到了μ-约简的判定定理和相应的可辨识矩阵及辨识公式,从而提供了不协调目标信息系统知识约简的新方法。并通过实例将决策表中基于对象的约简与整体约简进行了对比,结果表明前者可以得到更简洁的知识。该方法也适用于协调目标信息系统。