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CONSTRUCTION OF POLYNOMIAL MATRIX USING BLOCK COEFFICIENT MATRIX REPRESENTATION AUTO-REGRESSIVE MOVING AVERAGE MODEL FOR ACTIVELY CONTROLLED STRUCTURES 被引量:1
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作者 李春祥 周岱 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2004年第6期661-667,共7页
The polynomial matrix using the block coefficient matrix representation auto-regressive moving average(referred to as the PM-ARMA)model is constructed in this paper for actively controlled multi-degree-of-freedom(MDOF... The polynomial matrix using the block coefficient matrix representation auto-regressive moving average(referred to as the PM-ARMA)model is constructed in this paper for actively controlled multi-degree-of-freedom(MDOF)structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization.The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average(ARMA)model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators.(The sensors and actuators are required to maintain the identical number.)under any dimensional stationary stochastic excitation. 展开更多
关键词 actively controlled MDOF structures stationary stochastic processes polynomial matrix auto-regressive moving average
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Smith Form of Triangular Multivariate Polynomial Matrix
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作者 LIU Jinwang WU Tao LI Dongmei 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2023年第1期151-164,共14页
The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate main... The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively. 展开更多
关键词 Degree-Lexicographical order equivalence of matrix multidimensional system multivariate polynomial matrix Smith form
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ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO LINEAR MATRIX MOMENT FUNCTION ALS:THEORY AND APPLICATIONS 被引量:5
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作者 L.Jódar E.Defez E.Ponsoda 《Analysis in Theory and Applications》 1996年第1期96-115,共20页
In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Erro... In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given. 展开更多
关键词 ORTHOGONAL matrix polynomialS WITH RESPECT TO LINEAR matrix MOMENT FUNCTION ALS 艺人 APPI
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HERMITE MATRIX POLYNOMIALS AND SECOND ORDER MATRIX DIFFERENTIAL EQUATIONS 被引量:6
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作者 L.Jódar R.Company 《Analysis in Theory and Applications》 1996年第2期20-30,共11页
In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermit... In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given. 展开更多
关键词 exp HERMITE matrix polynomialS AND SECOND ORDER matrix DIFFERENTIAL EQUATIONS
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PSEUDO-DIVISION ALGORITHM FOR MATRIX MULTIVARIABLE POLYNOMIAL AND ITS APPLICATION 被引量:1
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作者 阿拉坦仓 张鸿庆 钟万勰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第7期733-740,共8页
Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equation... Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonianian system and its concrete form are obtained. Then by combining this method with Wu's method, a new method of constructing general solution of a class of mechanical equations is got, which several examples show very effective. 展开更多
关键词 matrix multivariable polynomial infinite dimensional Hamiltonianian system Wu's method general solution
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ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A CONJUGATE BILINEAR MATRIX MOMENT FUNCTIONAL: BASIC THEORY 被引量:1
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作者 Lucas Jodar and Emilio Defez (Polytechnical University of Valencia, Spain) 《Analysis in Theory and Applications》 1997年第1期66-79,共14页
In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a th... In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined. 展开更多
关键词 ORTHOGONAL matrix polynomialS WITH RESPECT TO A CONJUGATE BILINEAR matrix MOMENT FUNCTIONAL
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A NOTE ON SOBOLEV ORTHOGONALITY FOR LAGUERRE MATRIX POLYNOMIALS
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作者 Zhihui Zhu Zhongkai Li 《Analysis in Theory and Applications》 2007年第1期26-34,共9页
Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×... Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) 〉 -1 for every z E or(a). In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln^(A,λ)(x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case. 展开更多
关键词 Laguerre matrix polynomial Sobolev orthogonality matrix moment functional
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Volterra Integral Equation of Hermite Matrix Polynomials
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作者 Raed S. Batahan 《Analysis in Theory and Applications》 2013年第2期97-103,共7页
The primary purpose of this paper is to present the Volterra integral equa- tion of the two-variable Hermite matrix polynomials. Moreover, a new representation of these matrix polynomials are established here.
关键词 Hermite matrix polynomials three terms recurrence relation and Volterra integralequation.
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RELATIVE ASYMPTOTICS FOR ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A PERTURBED MATRIX MEASURE ON THE UNIT CIRCLE
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作者 Hossain O. Yakhlef Francisco Marcellán 《Approximation Theory and Its Applications》 2002年第4期1-19,共19页
Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w... Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I. 展开更多
关键词 RELATIVE ASYMPTOTICS FOR ORTHOGONAL matrix polynomialS WITH RESPECT TO A PERTURBED matrix MEASURE ON THE UNIT CIRCLE
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ON HERMITE MATRIX POLYNOMIALS AND HERMITE MATRIX FUNCTIONS 被引量:1
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作者 LucasJodar EmilloDefez 《Analysis in Theory and Applications》 1998年第1期36-48,共0页
In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix ... In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed. 展开更多
关键词 ON HERMITE matrix polynomialS AND HERMITE matrix FUNCTIONS
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Matrix orthogonal polynomials,non-abelian Toda lattices,and Bäcklund transformations
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作者 Shi-Hao Li 《Science China Mathematics》 SCIE CSCD 2024年第9期2071-2090,共20页
A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper.The normalization factors of matrix orthogonal polynomials expressed using quasideterminants are sho... A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper.The normalization factors of matrix orthogonal polynomials expressed using quasideterminants are shown to be the solutions to the non-abelian Toda lattice in semi-discrete and full-discrete cases.Moreover,with a moment modification method,we demonstrate that the B¨acklund transformation of the non-abelian Toda lattice given by Popowicz(1983)is equivalent to the non-abelian Volterra lattice,whose solutions can be expressed using quasi-determinants as well. 展开更多
关键词 matrix orthogonal polynomial non-abelian Toda lattice Backlund transformation quasideterminant technique
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k-Order Fibonacci Polynomials on AES-Like Cryptology
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作者 Mustafa Asci Suleyman Aydinyuz 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第4期277-293,共17页
The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography... The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography.This encryption method on AES is a method that uses polynomials on Galois fields.In this paper,we generalize the AES-like cryptology on 2×2 matrices.We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm.So,this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix. 展开更多
关键词 Fibonacci numbers Fibonacci polynomials k-order Fibonacci polynomials Fibonacci matrix k-order Fibonacci polynomial matrix Galois field
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THE DISCUSSION ON ALGEBRAIC PROPERTIESOF POLYNOMIAL MATRICES
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作者 梁治安 叶庆凯 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第10期951-956,共6页
By using the results about polynomial matrix in the system and control theory. this paper gives some discussions about the algebraic properties of polynomial,matrices. The obtained main results include that the,ring o... By using the results about polynomial matrix in the system and control theory. this paper gives some discussions about the algebraic properties of polynomial,matrices. The obtained main results include that the,ring of rr x n polynomial matrices is a principal ideal and principal one-sided ideal ring. 展开更多
关键词 polynomial matrix left (right) coprime principal ideal ring
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On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices
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作者 LU Dong WANG Dingkang XIAO Fanghui 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2024年第3期1295-1307,共13页
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented.The key idea is to establish a relationship between ... A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented.The key idea is to establish a relationship between a matrix and any of its full row rank submatrices.Based on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system Maple.Two examples are given to illustrate the effectiveness of the algorithm,and experimental data shows that the algorithm is efficient. 展开更多
关键词 Free modules Grobner bases minor left prime(MLP) multivariate polynomial matrices polynomial matrix factorizations
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New Results on the Equivalence of Bivariate Polynomial Matrices 被引量:1
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作者 ZHENG Xiaopeng LU Dong +1 位作者 WANG Dingkang XIAO Fanghui 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2023年第1期77-95,共19页
This paper investigates the equivalence problem of bivariate polynomial matrices.A necessary and sufficient condition for the equivalence of a square matrix with the determinant being some power of a univariate irredu... This paper investigates the equivalence problem of bivariate polynomial matrices.A necessary and sufficient condition for the equivalence of a square matrix with the determinant being some power of a univariate irreducible polynomial and its Smith form is proposed.Meanwhile,the authors present an algorithm that reduces this class of bivariate polynomial matrices to their Smith forms,and an example is given to illustrate the effectiveness of the algorithm.In addition,the authors generalize the main result to the non-square case. 展开更多
关键词 Bivariate polynomial matrix matrix equivalence smith form
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FREQUENCY DOMAIN CRITERIA FOR ROBUST D-STABILITY OF MIMO SYSTEMS BASED ON LMI METHOD
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作者 李海滨 王志珍 +2 位作者 王龙 李兆平 李尔效 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第2期207-213,共7页
The problem of checking robust D-stability of multi-in and multi-out (MIMO) systems was studied. Three system models were introduced, i.e. multilinear polynomial matrix, polytopic polynomial matrix and feedback syst... The problem of checking robust D-stability of multi-in and multi-out (MIMO) systems was studied. Three system models were introduced, i.e. multilinear polynomial matrix, polytopic polynomial matrix and feedback system model. Furthermore, the convex property of each model with respect to the parametric uncertainties was estabilished respectively. Based on this, sufficient conditions for D-stability were expressed in terms of linear matrix inequalities (LMIs) involving only the convex vertices. Therefore, the robust D-stability was tested by solving an LMI optimal problem. 展开更多
关键词 polynomial matrix robust D-stability Linear matrix inequalities parametric uncertainty
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Transient transport processes in deformable porous media 被引量:1
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作者 Cs.Mészáros A.Bálint 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第11期167-175,共9页
The basic partial differential equations relevant for convection-diffusion and convection-diffusion-wave phenomena arc presented and solved analytically by using the MAPLE symbolic computer algebra system. The possibl... The basic partial differential equations relevant for convection-diffusion and convection-diffusion-wave phenomena arc presented and solved analytically by using the MAPLE symbolic computer algebra system. The possible general nonlinear character of the constitutive equation of the convection-discussion process is replaced by a direct posteriori stochastic refinement of its solution represented for Dirichlet-type boundary conditions. A thermodynamic analysis is performed for connecting the relaxation time constants and Jacobi-determinants of deformations at transient transport processes. Finally, a new procedure for general description of coupled transport processes on the basis of the formalism originally developed for convection-free phenomena is presented by matrix analysis methods in the Fourier space. 展开更多
关键词 CONVECTION binary mixtures relaxation time matrix polynomials
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Linearly McCoy Rings and Their Generalizations 被引量:1
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作者 CUI JIAN CHEN JIAN-LONG 《Communications in Mathematical Research》 CSCD 2010年第2期159-175,共17页
A ring R is called linearly McCoy if whenever linear polynomials f(x), g(x) e R[x]/{0) satisfy f(x)g(x) : O, then there exist nonzero elements r, s ∈ R such that f(x)r : sg(x) =0. For a ring endomorph... A ring R is called linearly McCoy if whenever linear polynomials f(x), g(x) e R[x]/{0) satisfy f(x)g(x) : O, then there exist nonzero elements r, s ∈ R such that f(x)r : sg(x) =0. For a ring endomorphism α, we introduced the notion of α-skew linearly McCoy rings by considering the polynomials in the skew polynomial ring R[x; α] in place of the ring R[x]. A number of properties of this generalization are established and extension properties of α-skew linearly McCoy rings are given. 展开更多
关键词 linearly McCoy ring a-skew linearly McCoy ring polynomial ring matrix ring
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Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix
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作者 Rachid Belgacem Ahmed Bokhari +1 位作者 Salih Djilali Sunil Kumar 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2022年第1期251-264,共14页
We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix.The efficiency of the presented approach is demon... We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix.The efficiency of the presented approach is demonstrated by solving some differential equations.Also,this technique is combined with the standard Laplace Homotopy Per-turbation Method.The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions. 展开更多
关键词 Laplace transform Boubaker polynomials operational matrix homotopy per-turbation method numerical method
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Existence of Multiple Positive Periodic Solutions for Second Order Differential Equations
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作者 Lü Yue Sun Peng +1 位作者 Cai Hua Han Pei-shan 《Communications in Mathematical Research》 CSCD 2016年第3期272-280,共9页
Let α be a nonzero endomorphism of a ring R, n be a positive integer and T_n(R, α) be the skew triangular matrix ring. We show that some properties related to nilpotent elements of R are inherited by T_n(R, α).... Let α be a nonzero endomorphism of a ring R, n be a positive integer and T_n(R, α) be the skew triangular matrix ring. We show that some properties related to nilpotent elements of R are inherited by T_n(R, α). Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring R[x; α]/(x^n), where R[x; α] is the skew polynomial ring. 展开更多
关键词 skew triangular matrix ring skew polynomial ring weak zip property strongly prime radical generalized prime radical
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