A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a pol...In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.展开更多
The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with ...The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.展开更多
In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method...In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method.Because of the nonlinear relationship between the output signals of capacitance sensors and fluid in pipeline,nonlinear blind source separation is applied.In nonlinear blind source separation,the odd polynomials of higher order are used to fit the nonlinear transformation function,and the mutual information of separation signals is used as the evaluation function.Then the parameters of polynomial and linear separation matrix can be estimated by mutual information of separation signals and particle swarm optimization algorithm,thus the source signals can be separated from the mixed signals.The two-phase flow signals with noise which are obtained from upstream and downstream sensors are respectively processed by nonlinear blind source separation method so that the noise can be effectively removed.Therefore,based on these noise-suppressed signals,the distinct curves of cross correlation function and the transit times are obtained,and then the velocities of two-phase flow can be accurately calculated.Finally,the simulation experimental results are given.The results have proved that this method can meet the measurement requirements of two-phase flow velocity.展开更多
In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a re...In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.展开更多
Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been pr...Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been proposed to address this problem, including computing matrix curves from curves in Euclidean space by registration, representing one-parameter curves on manifold by rational representations, changing subdivisional methods generating curves in Euclidean space to corresponding methods working for matrix curve generation, and variational methods. In this paper, we propose a scheme to generate rational one-parameter matrix curves based on exponential map for interpolation, and demonstrate how to obtain higher smoothness from existing curves. We also give an iterative technique for rapid computing of these curves. We take the computation as solving an ordinary differential equation on manifold numerically by a generalized Euler method. Furthermore, we give this algorithm’s bound of the error and prove that the bound is proportional to the shift length when the shift length is sufficiently small. Compared to direct computation of the matrix functions, our Euler solution is faster.展开更多
Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary m...Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.展开更多
In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod pow...In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod powers on product of two generators. Finally an algorithm was given to obtain these matrices.展开更多
In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by ter...In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by term from lower to higher degree.By using a random vector and randomly shifting,it requires no condition on the input matrix and works with probability one.In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation,by using the modular technique,a parallelized version of the RCH method is also given.Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.展开更多
It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering applications.For a class of systems,whose coefficients matrix is based on time-varying polynomial,a modified hi...It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering applications.For a class of systems,whose coefficients matrix is based on time-varying polynomial,a modified highly precise direct integration(VHPD-T method)was presented.Through introducing new variables and expanding dimensions,the system can be transformed into a timeinvariant system,in which the transfer matrix can be computed for once and used forever with a highly precise direct integration method.The method attains higher precision than the common methods(e.g.RK4 and power series)and high efficiency in computation.Some numerical examples demonstrate the validity and efficiency of the method proposed.展开更多
Let Fq be the finite field of q elements and f be a nonzero polynomial over Fq. For each b ∈ Fq, let Nq（f = b） denote the number of Fq-rational points on the affine hypersurface f = b. We obtain the formula of Nq（...Let Fq be the finite field of q elements and f be a nonzero polynomial over Fq. For each b ∈ Fq, let Nq（f = b） denote the number of Fq-rational points on the affine hypersurface f = b. We obtain the formula of Nq（f= b） for a class of hypersurfaces over Fq by using the greatest invariant factors of degree matrices under certain cases, which generalizes the previously known results. We also give another simple direct proof to the known results.展开更多
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute...Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton＇s interpolation method with error control for solving Vandermonde systems. The authors also present the degree matrix to estimate the degree of variables in a matrix with polynomial entries, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally.展开更多
Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any str...Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in B as their substrings.From the fact that a string in the language is equivalent to a path in the corresponding graph,we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.展开更多
This paper studies the estimation and inference for a class of varying-coefficient regression models with error-prone covariates.The authors focus on the situation where the covariates are unobserved,there are no repe...This paper studies the estimation and inference for a class of varying-coefficient regression models with error-prone covariates.The authors focus on the situation where the covariates are unobserved,there are no repeated measurements,and the covariance matrix of the measurement errors is unknown,but some auxiliary information is available.The authors propose an instrumental variable type local polynomial estimator for the unknown varying-coefficient functions,and show that the estimator achieves the optimal nonparametric convergence rate,is asymptotically normal,and avoids using undersmoothing to allow the bandwidths to be selected using data-driven methods.A simulation is carried out to study the finite sample performance of the proposed estimator,and a real date set is analyzed to illustrate the usefulness of the developed methodology.展开更多
文摘A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
文摘In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.
文摘The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.
基金Supported by the National Natural Science Foundation of China (50736002,61072005)the Youth Backbone Teacher Project of University,Ministry of Education,China+1 种基金the Scientific Research Foundation of the Department of Science and Technology of Liaoning Province (20102082)the Changjiang Scholars and Innovative Team Development Plan (IRT0952)
文摘In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method.Because of the nonlinear relationship between the output signals of capacitance sensors and fluid in pipeline,nonlinear blind source separation is applied.In nonlinear blind source separation,the odd polynomials of higher order are used to fit the nonlinear transformation function,and the mutual information of separation signals is used as the evaluation function.Then the parameters of polynomial and linear separation matrix can be estimated by mutual information of separation signals and particle swarm optimization algorithm,thus the source signals can be separated from the mixed signals.The two-phase flow signals with noise which are obtained from upstream and downstream sensors are respectively processed by nonlinear blind source separation method so that the noise can be effectively removed.Therefore,based on these noise-suppressed signals,the distinct curves of cross correlation function and the transit times are obtained,and then the velocities of two-phase flow can be accurately calculated.Finally,the simulation experimental results are given.The results have proved that this method can meet the measurement requirements of two-phase flow velocity.
文摘In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.
基金Project (No. 200038) partially supported by FANEDD, China
文摘Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been proposed to address this problem, including computing matrix curves from curves in Euclidean space by registration, representing one-parameter curves on manifold by rational representations, changing subdivisional methods generating curves in Euclidean space to corresponding methods working for matrix curve generation, and variational methods. In this paper, we propose a scheme to generate rational one-parameter matrix curves based on exponential map for interpolation, and demonstrate how to obtain higher smoothness from existing curves. We also give an iterative technique for rapid computing of these curves. We take the computation as solving an ordinary differential equation on manifold numerically by a generalized Euler method. Furthermore, we give this algorithm’s bound of the error and prove that the bound is proportional to the shift length when the shift length is sufficiently small. Compared to direct computation of the matrix functions, our Euler solution is faster.
基金The authors would like to thank Prof. Y.D. Zhang for selfless helps and valuable discussions.
文摘Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.
文摘In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod powers on product of two generators. Finally an algorithm was given to obtain these matrices.
基金supported by the National Natural Science Foundation of China under Grant No.11171051the Major Research plan of the National Natural Science Foundation of China under Grant No.91230103the Fundamental Research Funds for the Central Universities under Grant No.DUT14RC(3)023
文摘In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by term from lower to higher degree.By using a random vector and randomly shifting,it requires no condition on the input matrix and works with probability one.In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation,by using the modular technique,a parallelized version of the RCH method is also given.Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.
基金supported by the National Natural Science Foundation of China(Grant No.50876066)
文摘It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering applications.For a class of systems,whose coefficients matrix is based on time-varying polynomial,a modified highly precise direct integration(VHPD-T method)was presented.Through introducing new variables and expanding dimensions,the system can be transformed into a timeinvariant system,in which the transfer matrix can be computed for once and used forever with a highly precise direct integration method.The method attains higher precision than the common methods(e.g.RK4 and power series)and high efficiency in computation.Some numerical examples demonstrate the validity and efficiency of the method proposed.
基金The authors would like to give thanks to the referees for many helpful suggestions. This work was jointly supported by the National Natural Science Foundation of China （11371208）, Zhejiang Provincial Natural Science Foundation of China （LY17A010008） and Ningbo Natural Science Foundation （2017A610134）, and sponsored by the K. C. Wong Magna Fund in Ningbo University.
文摘Let Fq be the finite field of q elements and f be a nonzero polynomial over Fq. For each b ∈ Fq, let Nq（f = b） denote the number of Fq-rational points on the affine hypersurface f = b. We obtain the formula of Nq（f= b） for a class of hypersurfaces over Fq by using the greatest invariant factors of degree matrices under certain cases, which generalizes the previously known results. We also give another simple direct proof to the known results.
基金supported by China 973 Project under Grant No.2011CB302402the National Natural Science Foundation of China under Grant Nos.61402537,11671377,91118001China Postdoctoral Science Foundation funded project under Grant No.2012M521692
文摘Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton＇s interpolation method with error control for solving Vandermonde systems. The authors also present the degree matrix to estimate the degree of variables in a matrix with polynomial entries, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally.
基金This research is supported by the National Natural Science Foundation of China (No. 10271103) Natural Science Foundation of Yunnan Province(No. 2003F0015M).
文摘Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in B as their substrings.From the fact that a string in the language is equivalent to a path in the corresponding graph,we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.
基金supported by the Graduate Student Innovation Foundation of SHUFE(#CXJJ-2011-351)supported by the Natural Sciences and Engineering Research Council of Canada
文摘This paper studies the estimation and inference for a class of varying-coefficient regression models with error-prone covariates.The authors focus on the situation where the covariates are unobserved,there are no repeated measurements,and the covariance matrix of the measurement errors is unknown,but some auxiliary information is available.The authors propose an instrumental variable type local polynomial estimator for the unknown varying-coefficient functions,and show that the estimator achieves the optimal nonparametric convergence rate,is asymptotically normal,and avoids using undersmoothing to allow the bandwidths to be selected using data-driven methods.A simulation is carried out to study the finite sample performance of the proposed estimator,and a real date set is analyzed to illustrate the usefulness of the developed methodology.
