On the Matrix Equation X^{ - 1} X* = A

Solvability conditions are examined for the matrix equation , which cannot be found in the well-known reference books on matrix theory. Methods for constructing solutions to this equation are indicated.     

Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices

We study the perturbation theory for the eigenvalue problem of a formal matrix product A ₁ ^{s 1} ··· A _p ^{s p}, where all A _k are square and s _k {–1, 1}. We generalize the classical perturbation results for matrices and matrix pencils to perturbation results for generalized deflating subspaces and eigenvalues of such formal matrix products. As an application we then extend the structured perturbation theory for the eigenvalue problem of Hamiltonian matrices to Hamiltonian/skew-Hamiltonian pencils.     

Effect of matrix metallo-proteinase-26 (MMP-26) during embryo implantation in the mouse

Matrix metalloproteinase-26 (MMP-26, endometase and matrilysin-2), a novel member of the MMPs family, is detected not only in the placenta and uterus, but is widely expressed in malignant tumors from different sources as well as in diverse tumor cell lines. However, the function of MMP-26 in the reproductive system has never been reported. Expression of MMP-26 in mouse embryos and the function of the MMP-26 antibody during mouse embryo implantation was examined for the first time by injecting the uterine horn, immunohistochemistry,in situ hybridization, co-culture of mouse blastocysts and uterine monolayer epithelial cells, Western blot, RT-PCR, Northern blot and zymography. Our results show that there is strong expression of MMP-26 mRNA and protein in the mouse embryo. Furthermore, the MMP-26 antibody dramatically inhibited mouse embryo implantation and significantly inhibited adhesion and outgrowth of mouse blastocysts onin vitro uterine monolayer epithelial cells. At the same time, the MMP-26 antibody inhibited the expression of integrin αV mRNA and protein in a dose-dependent manner. These data suggest that MMP-26 may play a role in some of the tissue-remodeling events associated with the invasion of the endometrium by trophoblast cells and facilitate successfully embryo implantation.     

Potassium Sensing by Using a Newly Synthesized Squaraine Dye in Sol-Gel Matrix

Squaraines are a group of fluorescent dyes and pigments derived from squaric acid and dialkylanilines well known in applications such as photoreceptors, organic solar cells, optical recording media, and non-linear optics. Their very promising spectral properties, long wavelength absorption and emission, and high absorptivity and quantum yields have not been exploited so far in relation to optical sensor design. They exhibit excellent solubility in sol-gel matrices, and the ligand is an integral part of the fluorophore system, which makes the molecule a fluoroionophore. In this work, potassium-sensing agent, bis[4-N-(1-aza-4,7,10,13,16-pentaox acyclooctadecyl)-3,5-dihydroxyphenyl] squaraine has been used for potassium sensing in a sol-gel matrix. The spectrofluorimetric response of dye-doped tetraethyl ortosilicate (TEOS) film after exposure to certain concentrations of K⁺ has been investigated, and 62% of relative signal change was achieved. The dynamic working range of the sensor membrane has been found between 10^–9 and 10^–6 M K⁺, in other terms from nanomolar to micromolar levels, which is an advantage over flame emission spectroscopy, in view of detection limit. The sensor is fully reversible within the dynamic range and the response time (₉₀) is found to be 2 min under batch conditions. The cross-sensitivity of the molecule to Na⁺, Ba²⁺, Ca²⁺, and NH⁺ ₄ was also tested in separate solutions.     

基于存储的矩阵乘积优化算法

提出了一种基于存储的矩阵乘积优化算法.该算法转置矩阵,提高cache命中率,从而降低矩阵乘积时间. 实验结果表明此算法是行之有效的.     

Research on the magnetic material of Sm-Fe matrix nitrides

In this paper, the types of Sm-Fe matrix compounds and their correlations are introduced, and progress of research on the magnetic materials of Sm-Fe matrix nitrides is also reviewed. Possible research trends of future permanent magnetic materials of SmFe matrix nitrides are briefly predicted.     

Rough set-based feature selection method

A new feature selection method is proposed based on the discern matrix in rough set in this paper. The main idea of this method is that the most effective feature, if used for classification, can distinguish the most number of samples belonging to different classes. Experiments are performed using this method to select relevant features for artificial datasets and real-world datasets. Results show that the selection method proposed can correctly select all the relevant features of artificial datasets and drastically reduce the number of features at the same time. In addition, when this method is used for the selection of classification features of real-world underwater targets,the number of classification features after selection drops to 20% of the original feature set, and the classification accuracy increases about 6% using dataset after feature selection.     

一类不确定时滞系统的鲁棒绝对稳定性

基于一类不确定时滞系统，给出了使得闭环系统鲁棒绝对稳定的状态反馈控制律的设计方法，通过求解一组时滞依赖型的线性矩阵不等式，给出使得闭环系统鲁棒绝对稳定的无记忆状态反馈控制律，并能够利用Matlab工具箱计算出最大的允许时滞界。     

层次分析法在智能大厦系统建设中的应用

运用层次分析法解决了智能大厦系统建设中的多目标投资决策分析问题.通过对智能大厦建设中结构、系统、服务、运营及其相互联系的全面综合的叙述和分析,对于A、B、C3个设计方案,选取了6个评价准则,并运用层次分析法建立层次指标体系,通过对用户和专家的调查和评分,将分目标在相对总目标的前提下两两比较,得到比较矩阵.通过权重计算得到准则层的权重为(D1,D2,D3,D4,D5,D6)=(0.168,0.189,0.187,0.05,0.15,0.256)T,方案层相对总目标的权重排序为(A,B,C)=(0.381,0.404,0.215)T.由计算结果知,方案B权重最重,其次是方案A,再次是C.所得判断矩阵都满足一致性要求,误差均小于0.1.     

矩阵方程A^HXA=B的反自反解及其最佳逼近

利用广义奇异值分解定理，得到了矩阵方程A^HXA=B的反自反解存在的一个充要条件，并获得了相应的通解表达式和最佳逼近解，最后获得了最小范数解。