The generalized matrix product and its applications

An iterative criterion for the asymptotic steadiness of a linear descriptor system is considered. The criterion is based on an iterative algorithm for computing a generalized matrix sign-function. As an example, the problem of analyzing the asymptotic steadiness of a large descriptor system is given. Keywords linear descriptor system; steadiness criterion; matrix sign-function; search algorithm

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

Fractal and Fractional ◽

10.3390/fractalfract5010008 ◽

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.

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Optimal sampling of dynamical large deviations via matrix product states

Physical Review E ◽

10.1103/physreve.103.062144 ◽

2021 ◽

Vol 103 (6) ◽

Author(s):

Luke Causer ◽

Mari Carmen Bañuls ◽

Juan P. Garrahan

Keyword(s):

Large Deviations ◽

Matrix Product ◽

Optimal Sampling ◽

Matrix Product States

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Research on the Influence of Energy Utilization and Economic Development on Human Well-Being in Qinghai-Tibet Plateau

Sustainability ◽

10.3390/su13010196 ◽

2020 ◽

Vol 13 (1) ◽

pp. 196

Author(s):

Mengmeng Meng ◽

Weiguo Fan ◽

Jianchang Lu ◽

Xiaobin Dong ◽

Hejie Wei

Keyword(s):

Economic Development ◽

Well Being ◽

Resource Acquisition ◽

Energy Utilization ◽

Western China ◽

Tibet Plateau ◽

Four Dimensions ◽

Generalized Matrix ◽

Qinghai Tibet Plateau ◽

Means Of Production

Qinghai-Tibet Plateau is a typical resource-rich but economically backward region in western China, and it is of great urgency to improve human well-being. Combined with previous scholars’ research and the characteristics of Qinghai-Tibet Plateau, this paper constructs an index system of human well-being including four dimensions: income and consumption, means of production, means of subsistence, and resource acquisition ability. Then, it uses generalized matrix method estimations to measure the influence of energy utilization and economic development on human well-being and makes a regression analysis on the influence of energy utilization and economic development on human well-being in various provinces in this region. It is found that per capita GDP and coke utilization promote the well-being of all dimensions, while the urban registered unemployment rate only promotes the well-being of means of subsistence. The utilization of gasoline and natural gas promotes income and consumption and inhibits the means of subsistence and resource acquisition ability, but they have opposite effects on means of production. The impacts of energy utilization and economic development in different provinces on human well-being are different. This study is of great significance to the related research aiming at improving people’s livelihood and promoting regional development.

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