GH-CONGRUENCE CANONICAL FORM OF QUATERNION MATRIX AND SIMULTANEOUS DIAGONALIZATION OF MATRICES

In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

New Criteria for Judging Generalized Strictly Diagonally Dominant Matrix

Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.

A New Approximation to the Linear Matrix Equation AX = B by Modification of He’s Homotopy Perturbation Method

It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.

GENERALIZED DIAGONALIZATION OF MATRICES OVER QUATERNION FIELD

A concept of [GRAPHICS] diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a [GRAPHICS] diagonalization one are discussed, and a method of [GRAPHICS] diagonalization of matrices over quaternion field is given.

Criteria Condition for Generalized Diagonally Dominant Matrices

In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.

Electric dipole moments of lithium atoms in Rydberg states

Recently, the diverse properties of Rydberg atoms, which probably arise from its large electric dipole moment （EDM）, have been explored. In this paper, we report electric dipole moments along with Stark energies and charge densities of lithium Rydberg states in the presence of electric fields, calculated by matrix diagonalization. Huge electric dipole moments are discovered. In order to check the validity of the EDMs, we also use these electric dipole moments to calculate the Stark energies by numerical integration. The results agree with those calculated by matrix diagonalization.

Studyon hardware-in-the-loopsimulation of beer fermentation system

Beer fermentation process is a complex biochemical reaction process.It is the most important to control temperature of the wort in fermentation tank in accordance with the beer fermentation temperature curve so as to ensure the completion of fermentation.The controlled object is characterized by large inertia,long time delay and mutual coupling of three temperature areas.Based on this,a temperature control method for beer fermentation system is designed.Using digital incremental proportion integration differentiation （PID） control algorithm,the controlled quantity is transmitted to the controlled object after diagonal matrix decoupling.This simulation system can be completed in laboratory using VB and Kingview software,so it has the features of good security and low cost.It is very suitable for experimental teaching.

Necessary and Sufficient Condition for Generalized Diagonal Dominance Matrices

In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.

Sufficient Conditions of Nonsingular H-matrices

From the concept of α diagonally dominant matrix, two sufficient conditions of nonsingular H-matrices were obtained in this paper. An example was given to show that these results improve the known results.

Comparison of Two Simulation Methods in Electron Crystallography： BW Method and a Modified Direct Product Method of Scattering Matrix

In this paper, a modified direct product method of scattering matrix （DPSM） was presented and the cal- culation formulawas derived as follows： φ（z）=∑n1/n!（Mz）nφ（O）and φ（z＋εj）=∑n1/n!（Mεj）nφ（z）,whereM is the scattering matrix of which the dimension can be reduced by ＇Bethe potential method＇ drastically and therefore the calculation speed can be increased tremendously without losing accuracy very much. The results calculated with the DPSM method are in almost exact agreement with those calculated with BW method. However, the calculation speed for the modified DPSM method is approximately three times faster than that for the BW method. Furthermore, the DPSM is suitable for computing all types of ma- trices without requiring symmetry or conjugate symmetry.

State of Charge Estimation for Lithium-Ion Battery Based on Improved Cubature Kalman Filter Algorithm

An improved cubature Kalman filter(CKF)algorithm for estimating the state of charge of lithium-ion batteries is proposed.This improved algorithm implements the diagonalization decomposition of the covariance matrix and a strong tracking filter.First,a first-order RC equivalent circuit model is first established and verified,whose voltage estimation error is within 1.5%;this confirms that the model can be used to describe the characteristics of a battery.Then the calculation processes of the traditional and proposed CKF algorithms are compared.Subsequently,the improved CKF algorithm is applied to the state of charge estimation under the constant-current discharge and dynamic stress test conditions.The average errors for these two conditions are 0.76%and 1.2%,respectively,and the maximum absolute error is only 3.25%.The results indicate that the proposed method has higher filter stability and estimation accuracy than the extended Kalman filter(EKF),unscented Kalman filter(UKF)and traditional CKF algorithms.Finally,the convergence rates of the above four algorithms are compared,among which the proposed algorithm track the referenced values at the highest speed.

GENERALIZED NEKRASOV MATRICES AND APPLICATIONS

In this paper, the concept of generalized Nekrasov matrices is introduced, some properties of these matrices are discussed, obtained equivalent representation of generalized diagonally dominant matrices.

Optimal Estimation for Power of Variance with Application to Gene-Set Testing

Detecting differential expression of genes in genom research(e.g.,2019-nCoV)is not uncommon,due to the cost only small sample is employed to estimate a large number of variances(or their inverse)of variables simultaneously.However,the commonly used approaches perform unreliable.Borrowing information across different variables or priori information of variables,shrinkage estimation approaches are proposed and some optimal shrinkage estimators are obtained in the sense of asymptotic.In this paper,we focus on the setting of small sample and a likelihood-unbiased estimator for power of variances is given under the assumption that the variances are chi-squared distribution.Simulation reports show that the likelihood-unbiased estimators for variances and their inverse perform very well.In addition,application comparison and real data analysis indicate that the proposed estimator also works well.