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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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LEVERRIER-LAGUERRE ALGORITHM FOR THE MATRIX POLYNOMIAL OF DEGREE TWO
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作者 吴筑筑 郑兵 王国荣 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2002年第2期226-234,共9页
An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis... An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis of Laguerre orthogonal polynomials. This algorithm is a new extension of Leverrier-Fadeev algorithm.. 展开更多
关键词 adjoint determinant inverse matrix ORTHOGONAL polynomial.
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On Humbert Matrix Polynomials of Two Variables
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作者 Ghazi S. Khammash A. Shehata 《Advances in Pure Mathematics》 2012年第6期423-427,共5页
In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansi... In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansions of the Humbert matrix polynomials of two variables in series of Hermite polynomials are given. Results of Gegenbauer ma-trix polynomials of two variables follow as particular cases of Humbert matrix polynomials of two variables. 展开更多
关键词 HUMBERT matrix polynomialS of TWO VARIABLES HYPERGEOMETRIC matrix Function matrix Functional Calculus
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Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators
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作者 XU Xiu-Wei REN Ting-Qi LIU Shu-Yan MA Qiu-Ming LIU Sheng-Dian 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第1期41-44,共4页
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
关键词 Boson exponential quadratic polynomial operator matrix element P representation partition function of Boson quadratic polynomial system
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Reply to Comment on “On Humbert Matrix Polynomials of Two Variables”
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作者 Ghazi S. Khammash Ayman Shehata 《Advances in Pure Mathematics》 2014年第7期324-325,共2页
The formula subject to comment in Reference [1] is correct.
关键词 matrix Functions HUMBERT matrix polynomialS
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A Comment on “On Humbert Matrix Polynomials of Two Variables”
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作者 Vicente Soler Basauri 《Advances in Pure Mathematics》 2013年第5期470-471,共2页
In this comment we will demonstrate that one of the main formulas given in Ref. [1] is incorrect.
关键词 HUMBERT matrix polynomialS
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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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Generalized Form of Hermite Matrix Polynomials via the Hypergeometric Matrix Function
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作者 Raed S. Batahan 《Advances in Linear Algebra & Matrix Theory》 2014年第2期134-141,共8页
The object of this paper is to present a new generalization of the Hermite matrix polynomials by means of the hypergeometric matrix function. An integral representation, differential recurrence relation and some other... The object of this paper is to present a new generalization of the Hermite matrix polynomials by means of the hypergeometric matrix function. An integral representation, differential recurrence relation and some other properties of these generalized forms are established here. Moreover, some new properties of the Hermite and Chebyshev matrix polynomials are obtained. In particular, the two-variable and two-index Chebyshev matrix polynomials of two matrices are presented. 展开更多
关键词 HERMITE and CHEBYSHEV matrix polynomialS Three Terms Recurrence Relation HYPERGEOMETRIC matrix FUNCTION and Gamma matrix FUNCTION
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THE CHARACTERISTIC POLYNOMIAL ANDEIGENVALUES OF FINILE RIODAN MATRIXTHE CHARACTERISTIC POLYNOMIAL ANDEIGENVALUES OF FINILE RIODAN MATRIX
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作者 周持中 《岳阳师范学院学报(自然科学版)》 2000年第3期1-6,共6页
In this paper we deal with the characteristic polynomial of finite Riodan matix. We giveseveral forms of its explicit expressions. Its applications to combinatorial identities, specially to F-Lidentities, are stated.
关键词 riodan matrix CHARACTERISTIC polynomial F-L IDENTITY
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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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A SEMI-CONJUGATE MATRIX BOUNDARY VALUE PROBLEM FOR GENERAL ORTHOGONAL POLYNOMIALS ON AN ARBITRARY SMOOTH JORDAN CURVE 被引量:1
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作者 杜志华 《Acta Mathematica Scientia》 SCIE CSCD 2008年第2期401-407,共7页
In this article, the author characterizes orthogonal polynomials on an arbitrary smooth Jordan curve by a semi-conjugate matrix boundary value problem, which is different from the Riemann-Hilbert problems that appear ... In this article, the author characterizes orthogonal polynomials on an arbitrary smooth Jordan curve by a semi-conjugate matrix boundary value problem, which is different from the Riemann-Hilbert problems that appear in the theory of Riemann -Hilbert approach to asymptotic analysis for orthogonal polynomials on a real interval introduced by Fokas, Its, and Kitaev and on the unit circle introduced by Baik, Deift, and Johansson. The author hopes that their characterization may be applied to asymptotic analysis for general orthogonal polynomials by combining with a new extension of steepest descent method which we are looking for. 展开更多
关键词 Semi-conjugate matrix boundary value problem orthogonal polynomials smooth Jordan curve
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An explicit solution to polynomial matrix right coprime factorization with application in eigenstructure assignment 被引量:2
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作者 Bin ZHOU Guangren DUAN 《控制理论与应用(英文版)》 EI 2006年第2期147-154,共8页
在这篇论文,输入状态转移功能的多项式矩阵权利 coprimefactorization 的一个明确的答案以 Krylov 矩阵和系数矩阵的对的 thePseudo 可控制性索引被获得。建议途径仅仅需要解决一系列线性方程。generalizedSylvester 矩阵方程和由州的... 在这篇论文,输入状态转移功能的多项式矩阵权利 coprimefactorization 的一个明确的答案以 Krylov 矩阵和系数矩阵的对的 thePseudo 可控制性索引被获得。建议途径仅仅需要解决一系列线性方程。generalizedSylvester 矩阵方程和由州的反馈的参量的 eigenstructure 赋值的问题的一种类型的这个答案的应用程序被调查。这些新答案简单,他们拥有更好结构的性质和方便的空想使用。一个例子显示出建议结果的效果。 展开更多
关键词 伪可控性指数 Krylov矩阵 多项式矩阵 因式分解 Sylvester矩阵方程
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Hermite Matrix Polynomial Collocation Method for Linear Complex Differential Equations and Some Comparisons 被引量:1
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作者 Mina Bagherpoorfard Fahime Akhavan Ghassabzade 《Journal of Applied Mathematics and Physics》 2013年第5期58-64,共7页
In this paper, we introduce a Hermite operational matrix collocation method for solving higher-order linear complex differential equations in rectangular or elliptic domains. We show that based on a linear algebra the... In this paper, we introduce a Hermite operational matrix collocation method for solving higher-order linear complex differential equations in rectangular or elliptic domains. We show that based on a linear algebra theorem, the use of different polynomials such as Hermite, Bessel and Taylor in polynomial collocation methods for solving differential equations leads to an equal solution, and the difference in the numerical results arises from the difference in the coefficient matrix of final linear systems of equations. Some numerical examples will also be given. 展开更多
关键词 APPROXIMATE Solution COLLOCATION Methods Complex Differential Equations HERMITE polynomialS Operational matrix
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Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms 被引量:1
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作者 Mamoudou Amadou Bondabou Ousmane Moussa Tessa Amidou Morou 《Advances in Linear Algebra & Matrix Theory》 2021年第1期1-13,共13页
We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>... We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>×<i>n</i> Fiedler companion matrix <i>C</i>, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix <i>L<sub>r</sub></i>, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of <i>L<sub>r</sub></i>, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful. 展开更多
关键词 Fiedler Matrices polynomial’s Roots Bounds for polynomials Companion Matrices Sparse Companion Matrices Hessenberg Matrices Submultiplicative matrix Norm
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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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Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique
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作者 冯毅夫 张庆灵 冯德志 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第10期179-188,共10页
The global stability problem of Takagi-Sugeno(T-S) fuzzy Hopfield neural networks(FHNNs) with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guar... The global stability problem of Takagi-Sugeno(T-S) fuzzy Hopfield neural networks(FHNNs) with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler's lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches. 展开更多
关键词 Hopfield neural networks linear matrix inequality Takagi-Sugeno fuzzy model homogeneous polynomially technique
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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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Pseudo Laguerre Matrix Polynomials, Operational Identities and Quasi-Monomiality
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作者 Maged G. Bin-Saad M. A. Pathan 《Advances in Linear Algebra & Matrix Theory》 2018年第2期87-95,共9页
The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to der... The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to derive a number of properties for pseudo Laguerre matrix polynomials. 展开更多
关键词 PSEUDO LAGUERRE matrix polynomials Lowering OPERATORS Raising OPERATORS Quasi-Monomiality Operational Rules
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