scholarly journals Generalization of the matrix product ansatz for integrable chains

2006 ◽  
Vol 39 (36) ◽  
pp. 11335-11337 ◽  
Author(s):  
F C Alcaraz ◽  
M J Lazo
Keyword(s):  
Matrix Product ◽  
Matrix Product Ansatz ◽  
The Matrix ◽  
Integrable Chains

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

scholarly journals 2D DOA Estimation with a Two-Parallel Array Consisting of Two Uniform Large-Spacing Linear Arrays

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Sheng Liu ◽  
Jing Zhao ◽  
Yu Zhang
Keyword(s):  
Mutual Coupling ◽  
Elevation Angle ◽  
Doa Estimation ◽  
Matrix Product ◽  
Linear Arrays ◽  
Parallel Array ◽  
Propagator Method ◽  
The Matrix ◽  
2D Doa Estimation ◽  
Estimation Precision

In this paper, an improved propagator method (PM) is proposed by using a two-parallel array consisting of two uniform large-spacing linear arrays. Because of the increase of element spacing, the mutual coupling between two sensors can be reduced. Firstly, two matrices containing elevation angle information are obtained by PM. Then, by performing EVD of the product of the two matrices, the elevation angles of incident signals can be estimated without direction ambiguity. At last, the matrix product is used again to obtain the estimations of azimuth angles. Compared with the existed PM algorithms based on conventional uniform two-parallel linear array, the proposed PM algorithm based on the large-spacing linear arrays has higher estimation precision. Many simulation experiments are presented to verify the effect of proposed scheme in reducing the mutual coupling and improving estimation precision.

scholarly journals The matrix product approach to quantum spin ladders

1998 ◽  
Vol 31 (48) ◽  
pp. 9729-9759 ◽  
Author(s):  
J M Román ◽  
G Sierra ◽  
J Dukelsky ◽  
M A Martín-Delgado
Keyword(s):  
Quantum Spin ◽  
Matrix Product ◽  
The Matrix ◽  
Product Approach
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