关于Sperner系矩阵表示的一个注记

令r(n)=max{S((?)):(?)是n-1元集X上的Sperner系},我们证明了:

关于分块极大极小矩阵性质的研究

利用矩阵分解、矩阵的Hadamard积和数学归纳法研究分块极大极小矩阵的性质．将极大和极小矩阵推广为分块极大和分块极小矩阵．在给出矩阵行列式、逆和特征多项式的同时，得到该类矩阵半正定的充要条件，还讨论了矩阵的无限可分性．

Numerical Methods for a Class of Quadratic Matrix Equations

Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.

一种面部图像处理的边缘检测方法

介绍在3×3小矩阵中直接采用中心像素值与周围各像素值分别求差,再分别将各个差值与阈值相比较,最后将各个结果综合起来判断此像素点是否为边缘点的方法。判断过的像素点对当前阈值进行了一定的修改,使之随实际情况上下浮动,更有利于当前像素点的判断。实验证明,该方法检测出的边缘更完整,噪声也能更有效地去除。

物理光学 光的吸收、透射与散射

O436．2 2005053253 计算轴对称粒子光散射问题的简化T矩阵方法=Simpli- fied T-matrix method of calculating light scattering by axi- symmetric particle[刊,中]／苏宁(西安电子科技大学技术 物理学院．陕西,西安(710071)),安毓英…∥激光杂志．- 2005,26(2)．-54-56 首先给出了光散射计算中的T矩阵方法的推导过程, 分析了轴对称粒子T矩阵的特点-方位模m的独立性,并 由此特点对原始的T矩阵进行了简化和变形,去除了其中 的零元素并将其分成关于方位模m的小矩阵。然后运用 基于方位模m的独立方程求得散射场系数。最后以球形 粒子为例得到散射场的仿真结果与用微元法有很好的吻 合。图2参7(杨妹清)

Gravity compression forward modeling and multiscale inversion based on wavelet transform

The main problems in three-dimensional gravity inversion are the non-uniqueness of the solutions and the high computational cost of large data sets. To minimize the high computational cost, we propose a new sorting method to reduce fluctuations and the high frequency of the sensitivity matrix prior to applying the wavelet transform. Consequently, the sparsity and compression ratio of the sensitivity matrix are improved as well as the accuracy of the forward modeling. Furthermore, memory storage requirements are reduced and the forward modeling is accelerated compared with uncompressed forward modeling. The forward modeling results suggest that the compression ratio of the sensitivity matrix can be more than 300. Furthermore, multiscale inversion based on the wavelet transform is applied to gravity inversion. By decomposing the gravity inversion into subproblems of different scales, the non-uniqueness and stability of the gravity inversion are improved as multiscale data are considered. Finally, we applied conventional focusing inversion and multiscale inversion on simulated and measured data to demonstrate the effectiveness of the proposed gravity inversion method.

The Least Square Solutions to the Quaternion Matrix Equation AX=B

A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.

Comparison of Improved Meshless Interpolation Schemes for SPH Method and Accuracy Analysis

In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been used for this purpose.Traditional particle interpolation (TPI) is simple and easy to do, but its low accuracy has become an obstacle to its wider application.This can be seen in the cases of particle disorder arrangements and derivative calculations.There are many different methods to improve accuracy, with the moving least square (MLS) method one of the most important meshless interpolation methods.Unfortunately, it requires complex matrix computing and so is quite time-consuming.The authors developed a simpler scheme, called higher-order particle interpolation (HPI).This scheme can get more accurate derivatives than the MLS method, and its function value and derivatives can be obtained simultaneously.Although this scheme was developed for the SPH method, it has been found useful for other meshless methods.

A Roller Bearing Fault Diagnosis Method Based on Improved LMD and SVM

Aiming at the non-stationary feattwes of the roller bearing fault vibration signal, a roller bearing fault diagnosis methtxt based on improved Local Mean Decomposition （LMD） and Support Vector Machine （SVM） is proposed. In this paper, firstly, the wavelet analysis is introduced to the signal decomposition and reconstruction; secondly, the LMD method is used to decompose the recomtnion signal obtained by the wavelet analysis into a ntmaber of Product Ftmctions （PFs） that include main fault characteristics, thus, the initial feattwe vector matrixes could be formed automatically; Thirdly, by applying the Singular Valueition （SVD） techniques to the initial feature vector matrixes, the singular values of the matrixes can be obtained, which can be used as the fault feature vectors of the roller bearing and serve as the input vectors of the SVM classifier; Finally, the recognition results can be obtained from the SVM output. The results of analysis show that the propsed method can be applied to roller beating fault diagnosis effectively.

Wavelet matrix transform for time-series similarity measurement

A time-series similarity measurement method based on wavelet and matrix transform was proposed,and its anti-noise ability,sensitivity and accuracy were discussed. The time-series sequences were compressed into wavelet subspace,and sample feature vector and orthogonal basics of sample time-series sequences were obtained by K-L transform. Then the inner product transform was carried out to project analyzed time-series sequence into orthogonal basics to gain analyzed feature vectors. The similarity was calculated between sample feature vector and analyzed feature vector by the Euclid distance. Taking fault wave of power electronic devices for example,the experimental results show that the proposed method has low dimension of feature vector,the anti-noise ability of proposed method is 30 times as large as that of plain wavelet method,the sensitivity of proposed method is 1/3 as large as that of plain wavelet method,and the accuracy of proposed method is higher than that of the wavelet singular value decomposition method. The proposed method can be applied in similarity matching and indexing for lager time series databases.

Short-time prediction for traffic flow based on wavelet de-noising and LSTM model

Aiming at the problem that some existing traffic flow prediction models are only for a single road segment and the model input data are not pre-processed,a heuristic threshold algorithm is used to de-noise the original traffic flow data after wavelet decomposition.The correlation coefficients of road traffic flow data are calculated and the data compression matrix of road traffic flow is constructed.Data de-noising minimizes the interference of data to the model,while the correlation analysis of road network data realizes the prediction at the road network level.Utilizing the advantages of long short term memory(LSTM)network in time series data processing,the compression matrix is input into the constructed LSTM model for short-term traffic flow prediction.The LSTM-1 and LSTM-2 models were respectively trained by de-noising processed data and original data.Through simulation experiments,different prediction times were set,and the prediction results of the prediction model proposed in this paper were compared with those of other methods.It is found that the accuracy of the LSTM-2 model proposed in this paper increases by 10.278%on average compared with other prediction methods,and the prediction accuracy reaches 95.58%,which proves that the short-term traffic flow prediction method proposed in this paper is efficient.

Matrix Expression of the Orthogonal Wavelet (Packets) Transform

Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provided yet. In this paper, the formulation to generate the re-lated matrix is put forward and the theorem on the orthogonality of this matrix proved. This effort deploys a basis for more deeper and wider applications in chemical processes. *

A Property of MRA of Multiplicity r with an Arbitrary Dilation Matrix

In this paper, we give a property for multivariate multiresolution analysis of multiplicity r with an arbitrary dilatiion matrix.

Practical Method for Determining All the Minimum Solutions of Fuzzy Matrix Equation and Transitive Closure of Fuzzy Relation

In this paper,the new theory frame and practical methhod for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the miero-computer quickly and accurately.

{P,Q,k+1}-reflexive solutions to a system of matrix equations

In this paper,we investigate the{P,Q,k+1}-reflexive and anti-reflexive solutions to the system of matrix equations AX=C,XB=D and AXB=E.We present the necessary and sufficient conditions for the system men-tioned above to have the{P,Q,k+1}-reflexive and anti-reflexive solutions.We also obtain the expressions of such solutions to the system by the singular value decomposition.Moreover,we consider the least squares{P,Q,k+1}-reflexive and anti-reflexive solutions to the system.Finally,we give an algorithm to illustrate the results of this paper.

On the p-norm joint spectral radius

The p-norm joint spectral radius is defined by a bounded collection of square matrices with complex entries and of the same size. In the present paper the author investigates the p-norm joint spectral radius for integers. The method introduced in this paper yields some basic formulas for these spectral radii. The approach used in this paper provides a simple proof of Berger-Wang' s relation concerning the ∞-norm joint spectral radius.

Minimum Cycle of Row Vector of a Generalized Circulant Fuzzy Matrix

In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.

ON ANALYSIS METHOD FOR INFRARED MULTI-SITES SYSTEM PERFORMANCE

The calculation method about infrared multi-sites passive system location is introduced based on the principle of the weighted least square method, and the variance matrix of estimated error is offered. Through deduction, it can be found out that treated appraise precision can be directly analyzed and deduced without carrying out real measure and reaching estimation value. The simulation result shows that the system performance based on the weighted least square method is much better than the traditional passive location method, and it can be also used for reference to the research of the location algorithm of similar system.

Minimum distance constrained nonnegative matrix factorization for hyperspectral data unmixing

This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is proposed, namely minimum distance constrained nonnegative matrix factoriza- tion （MDC-NMF）. In this paper, firstly, a new regularization term, called endmember distance （ED） is considered, which is defined as the sum of the squared Euclidean distances from each end- member to their geometric center. Compared with the simplex volume, ED has better optimization properties and is conceptually intuitive. Secondly, a projected gradient （PG） scheme is adopted, and by the virtue of ED, in this scheme the optimal step size along the feasible descent direction can be calculated easily at each iteration. Thirdly, a finite step （ no more than the number of endmem- bers） terminated algorithm is used to project a point on the canonical simplex, by which the abun- dance nonnegative constraint and abundance sum-to-one constraint can be accurately satisfied in a light amount of computation. The experimental results, based on a set of synthetic data and real da- ta, demonstrate that, in the same running time, MDC-NMF outperforms several other similar meth- ods proposed recently.

A novel stabilization approach for small signal disturbance of power system with time-varying delay

Small signal instability may cause severe accidents for power system if it can not be dear correctly and timely. How to maintain power system stable under small signal disturbance is a big challenge for power system operators and dispatchers. Time delay existing in signal transmission process makes the problem more complex. Conventional eigenvalue analysis method neglects time delay influence and can not precisely describe power system dynamic behaviors. In this work, a modified small signal stability model considering time varying delay influence was constructed and a new time delay controller was proposed to stabilize power system under disturbance. By Lyapunov-Krasovskii function, the control law in the form of nonlinear matrix inequality （NLMI） was derived. Considering synthesis method limitation for time delay controller at present, both parameter adjustment method by using linear matrix inequality （LMI） solver and iteration searching method by solving nonlinear minimization problem were suggested to design the controller. Simulation tests were carried out on synchronous-machine infinite-bus power system. Satisfactory test results verify the correctness of the proposed model and the feasibility of the stabilization approach.