An Analysis of the Key Elements and Barriers of English Listening

While illustrating the process and the essence of listening and analyzing various subjective and objective barriers in listening, the author tries to show that English learners can improve their quality of listening comprehension by transferring the negative elements to the positive ones.

Some Inequalities about the Positive Elements in C~*-Algebra

In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.

A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

In this article, a proper orthogonal decomposition （POD） method is used to study a classical splitting positive definite mixed finite element （SPDMFE） formulation for second- order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.

Generalized Domination in Ordered Banach Algebras

The following problem in an OBA （ordered Banach algebra） has been studied by various authors： If a and b are positiveelements in an OBA such that 0 ≤ α ≤ b and ifb has a certain property, under what conditions does a inherit that property？ This will be referred to as the domination problem. In this paper we will introduce absolute value ｜.｜ in an OBA and obtain results for the domination problem under the more general inequality ｜α｜ ≤｜b｜. We will show that these results are applicable to positive operators on a Banach lattice. Furthermore, it will be demonstrated that some known results for the domination problem in OBAs continue to hold true if 0 ≤ α≤ b is replaced by ｜a｜≤｜b｜.

Superconvergence Analysis of Splitting Positive Definite Nonconforming Mixed Finite Element Method for Pseudo-hyperbolic Equations

In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.

Evaluation of E-sail parameters on central spacecraft attitude stability using a high-fidelity rigid–flexible coupling model

This study examines the impact of electric solar wind sail(E-sail)parameters on the attitude stability of E-sail’s central spacecraft by using a comprehensive rigid–flexible coupling dynamic model.In this model,the nodal position finite element method is used to model the elastic deformation of the tethers through interconnected two-node tensile elements.The attitude dynamics of the central spacecraft is described using a natural coordinate formulation.The rigid–flexible coupling between the central spacecraft and its flexible tethers is established using Lagrange multipliers.Our research reveals the significant influences of parameters such as tether numbers,tether’s electric potential,and solar wind velocity on attitude stability.Specifically,solar wind fluctuations and the distribution of electric potential on the main tethers considerably affect the attitude stability of the spacecraft.For consistent management,the angular velocities of the spacecraft must remain at target values.Moreover,the attitude stability of a spacecraft has a pronounced dependence on the geometrical configuration of the E-sail,with axisymmetric E-sails proving to be more stable.